diff --git a/.ai-instructions b/.ai-instructions index 40e0ac6b8..68dc3f486 160000 --- a/.ai-instructions +++ b/.ai-instructions @@ -1 +1 @@ -Subproject commit 40e0ac6b8bb25db29d305cff43c8b027ac7d0f09 +Subproject commit 68dc3f4867cb075b0e0d8eadf383800ea33f5995 diff --git a/.github/workflows/benchmark-main.yml b/.github/workflows/benchmark-main.yml index a010efd8a..bc05aa198 100644 --- a/.github/workflows/benchmark-main.yml +++ b/.github/workflows/benchmark-main.yml @@ -24,7 +24,7 @@ jobs: sleep 60 done echo "GPU is free." - - uses: actions/checkout@v6 + - uses: actions/checkout@v7 with: fetch-depth: 0 - name: Install environment diff --git a/.github/workflows/benchmark-pr.yml b/.github/workflows/benchmark-pr.yml index 43ad13a23..e6455c64a 100644 --- a/.github/workflows/benchmark-pr.yml +++ b/.github/workflows/benchmark-pr.yml @@ -32,7 +32,7 @@ jobs: sleep 60 done echo "GPU is free." - - uses: actions/checkout@v6 + - uses: actions/checkout@v7 with: ref: ${{ github.event.pull_request.head.sha }} fetch-depth: 0 diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml index 16f8e5d78..af7014857 100644 --- a/.github/workflows/main.yml +++ b/.github/workflows/main.yml @@ -29,11 +29,17 @@ jobs: - windows-latest python-version: - '3.14' + # The small macOS runner can't host four parallel JAX AOT compiles of the + # DC-EGM solve/oracle battery (it swap-thrashes for hours). Drop the `slow` + # set there; the platform-independent kernel stays covered on Linux + GPU. + include: + - os: macos-latest + pytest_extra: -m "not slow" steps: - - uses: actions/checkout@v6 - - uses: prefix-dev/setup-pixi@v0.9.6 + - uses: actions/checkout@v7 + - uses: prefix-dev/setup-pixi@v0.10.0 with: - pixi-version: v0.70.1 + pixi-version: v0.72.0 cache: true cache-write: ${{ github.event_name == 'push' && github.ref_name == 'main' }} environments: tests-cpu @@ -41,15 +47,28 @@ jobs: frozen: true - name: Run pytest shell: bash {0} - run: pixi run -e tests-cpu tests + run: pixi run -e tests-cpu tests ${{ matrix.pytest_extra }} if: runner.os != 'Linux' || matrix.python-version != '3.14' - name: Run pytest and collect coverage shell: bash {0} - run: pixi run -e tests-cpu tests-with-cov + # Phased: JAX compile caches make a pytest process's resident memory + # grow with every distinct compiled program it has run, and the DC-EGM + # solve/oracle battery (`slow`) compiles enough programs that one + # full-suite pass exhausts the 16 GB runner (the agent receives a + # shutdown signal mid-suite). Sequential invocations release each + # phase's memory before the next starts; coverage is appended across + # them. + run: | + pixi run -e tests-cpu pytest tests -m "not slow" \ + --cov=./ --cov-report= -n 4 \ + && pixi run -e tests-cpu pytest tests/solution -m slow \ + --cov=./ --cov-append --cov-report= -n 2 \ + && pixi run -e tests-cpu pytest tests --ignore=tests/solution -m slow \ + --cov=./ --cov-append --cov-report=xml -n 2 if: runner.os == 'Linux' && matrix.python-version == '3.14' - name: Upload coverage report if: runner.os == 'Linux' && matrix.python-version == '3.14' - uses: codecov/codecov-action@v6.0.1 + uses: codecov/codecov-action@v7.0.0 with: token: ${{ secrets.CODECOV_TOKEN }} run-ty: @@ -61,17 +80,19 @@ jobs: python-version: - '3.14' steps: - - uses: actions/checkout@v6 - - uses: prefix-dev/setup-pixi@v0.9.6 + - uses: actions/checkout@v7 + - uses: prefix-dev/setup-pixi@v0.10.0 with: - pixi-version: v0.70.1 + pixi-version: v0.72.0 cache: true cache-write: ${{ github.event_name == 'push' && github.ref_name == 'main' }} environments: type-checking frozen: true - name: Run ty shell: bash {0} - run: pixi run ty + # The prek `ty` hook is skipped on pre-commit.ci (no pixi envs there); + # this job runs it against the `type-checking` env instead. + run: pixi run -e type-checking prek run ty --all-files run-tests-gpu: name: Run tests on GPU # Config: @@ -84,17 +105,29 @@ jobs: run: | nvidia-smi nvcc --version || echo "nvcc not found" - - uses: actions/checkout@v6 - - uses: prefix-dev/setup-pixi@v0.9.6 + - uses: actions/checkout@v7 + - uses: prefix-dev/setup-pixi@v0.10.0 with: - pixi-version: v0.70.1 + pixi-version: v0.72.0 cache: true cache-write: ${{ github.event_name == 'push' && github.ref_name == 'main' }} environments: tests-cuda12 frozen: false - name: Run pytest on GPU shell: bash {0} - run: pixi run -e tests-cuda12 tests + # Run serially (-n0 overrides the task's -n 4): the single GPU runner is + # starved of host CPU/memory by parallel JAX AOT compiles. CPU jobs keep -n 4. + # + # The GPU-scale Mahler & Yum module runs first, in its own process: its + # solve kernels only fit the device when XLA fully fuses the + # max-over-actions reduction, and compiling them late in a long-lived + # process that has run the whole DC-EGM battery has produced an + # unfused executable whose scratch arena (half the state-action product) + # exceeds device memory. A fresh process pins the fused compile. + run: | + pixi run -e tests-cuda12 pytest tests/test_mahler_yum_2024.py -n0 \ + && pixi run -e tests-cuda12 pytest tests -n0 \ + --ignore=tests/test_mahler_yum_2024.py run-tests-gpu-32bit: name: Run tests on GPU (32-bit precision) runs-on: ubuntu-latest-gpu @@ -103,25 +136,27 @@ jobs: run: | nvidia-smi nvcc --version || echo "nvcc not found" - - uses: actions/checkout@v6 - - uses: prefix-dev/setup-pixi@v0.9.6 + - uses: actions/checkout@v7 + - uses: prefix-dev/setup-pixi@v0.10.0 with: - pixi-version: v0.70.1 + pixi-version: v0.72.0 cache: true cache-write: ${{ github.event_name == 'push' && github.ref_name == 'main' }} environments: tests-cuda12 frozen: false - name: Run pytest on GPU with 32-bit precision shell: bash {0} - run: pixi run -e tests-cuda12 tests-32bit + # Run serially (-n0 overrides the task's -n 4): the single GPU runner is + # starved of host CPU/memory by parallel JAX AOT compiles. CPU jobs keep -n 4. + run: pixi run -e tests-cuda12 tests-32bit -n0 run-explanation-notebooks: name: Run explanation notebooks on Python 3.14 runs-on: ubuntu-latest steps: - - uses: actions/checkout@v6 - - uses: prefix-dev/setup-pixi@v0.9.6 + - uses: actions/checkout@v7 + - uses: prefix-dev/setup-pixi@v0.10.0 with: - pixi-version: v0.70.1 + pixi-version: v0.72.0 cache: true cache-write: ${{ github.event_name == 'push' && github.ref_name == 'main' }} environments: docs diff --git a/.github/workflows/publish-to-pypi.yml b/.github/workflows/publish-to-pypi.yml index 4feea0af7..6f5045720 100644 --- a/.github/workflows/publish-to-pypi.yml +++ b/.github/workflows/publish-to-pypi.yml @@ -6,7 +6,7 @@ jobs: name: Build and publish Python 🐍 distributions πŸ“¦ to PyPI runs-on: ubuntu-latest steps: - - uses: actions/checkout@v6 + - uses: actions/checkout@v7 - name: Set up Python 3.13 uses: actions/setup-python@v6 with: diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml index 0193aa6df..b5785c651 100644 --- a/.pre-commit-config.yaml +++ b/.pre-commit-config.yaml @@ -5,7 +5,7 @@ repos: - id: check-hooks-apply - id: check-useless-excludes - repo: https://github.com/tox-dev/pyproject-fmt - rev: v2.23.0 + rev: v2.25.1 hooks: - id: pyproject-fmt - repo: https://github.com/lyz-code/yamlfix @@ -39,7 +39,7 @@ repos: - id: name-tests-test args: - --pytest-test-first - exclude: tests/mock_regime.py|^tests/test_models/|^tests/data/ + exclude: tests/mock_regime.py|^tests/test_models/|^tests/data/|tests/solution/_envelope_oracle.py|tests/solution/_rfc_2d_host.py|tests/solution/_branch_aware_vfi_oracle.py|tests/solution/_ds2024_housing_vfi_oracle.py - id: no-commit-to-branch args: - --branch @@ -50,11 +50,11 @@ repos: hooks: - id: yamllint - repo: https://github.com/python-jsonschema/check-jsonschema - rev: 0.37.2 + rev: 0.37.4 hooks: - id: check-github-workflows - repo: https://github.com/astral-sh/ruff-pre-commit - rev: v0.15.16 + rev: v0.15.20 hooks: - id: ruff-check args: @@ -68,6 +68,15 @@ repos: - jupyter - pyi - python + - repo: https://github.com/astral-sh/ty-pre-commit + rev: v0.0.56 + hooks: + - id: ty + # `--no-project` keeps uv from creating a `.venv`/`uv.lock` in this + # pixi-managed repo; ty resolves third-party imports from the env named + # in `[tool.ty] environment.python` (run `pixi install` once). + args: + - --no-project - repo: https://github.com/kynan/nbstripout rev: 0.9.1 hooks: @@ -99,3 +108,7 @@ repos: exclude: docs/index\.md ci: autoupdate_schedule: monthly + # pre-commit.ci has no pixi environments and blocks network at hook runtime; + # the GitHub Actions run-ty job covers type checking. + skip: + - ty diff --git a/.roborev.toml b/.roborev.toml new file mode 100644 index 000000000..db4ff0886 --- /dev/null +++ b/.roborev.toml @@ -0,0 +1,49 @@ +# roborev local repo config. +# review_guidelines is injected into every review prompt for this repo as a +# "## Project Guidelines" section. Agent/model/reasoning come from the global +# ~/.roborev/config.toml (review_agent = codex, reasoning = thorough). + +display_name = "dev-pylcm" + +review_guidelines = ''' +Run this review as a sequence of GATES. Treat the diff as work that must earn a +PASS at each gate before you sign off. Default to FAIL under uncertainty β€” +absence of evidence is not evidence of correctness. + +At each gate, evaluate the change from TWO adversarial stances, then reconcile +them into a single PASS/FAIL verdict for that gate: + + PROSECUTOR β€” "This change is broken. Find the failure." + Assume a defect exists. Hunt for: incorrect logic, off-by-one and boundary + errors, unhandled None/empty/NaN/error cases, broken invariants, mutable + default or aliasing bugs, race conditions, resource leaks, data loss, + regressions in callers, and silent behavior changes. Construct the concrete + input or call sequence that breaks it. If you cannot construct one after a + genuine attempt, say so explicitly. + + DEFENDER β€” "This change is correct and complete. Justify it." + Point to the evidence: tests covering the new/changed paths, invariants + preserved, edge cases handled, types/docs updated. Where the defense relies + on an assumption not visible in the diff, name the assumption. + + VERDICT: PASS only if the defense withstands the prosecution with evidence in + the diff. Otherwise FAIL, and report the prosecutor's strongest concrete + finding. + +GATES (apply each; a gate that does not apply to this diff is PASS β€” state why): + 1. Correctness & logic β€” does it do what the commit intends, for all inputs? + 2. Edge cases & error handling β€” empty, None, zero, large, concurrent, + failure paths; numerical stability where relevant. + 3. Tests β€” are the changed paths actually exercised? New behavior without a + test is a finding unless tests are clearly out of scope for this commit. + 4. Interfaces & callers β€” are all call sites updated; any breaking + signature/behavior change? + 5. Safety β€” data loss/corruption, unsafe deserialization, injection, secrets, + path traversal. + 6. Clarity & maintainability β€” naming, dead code, needless complexity + (report as low severity only). + +Report only findings that survive the adversarial pass. For each: file:line, +the gate it failed, severity, and the concrete failure scenario or the minimal +fix. Do not pad the review with style nits dressed up as defects. +''' diff --git a/AGENTS.md b/AGENTS.md index 1ad46ec96..0c5651e55 100644 --- a/AGENTS.md +++ b/AGENTS.md @@ -19,8 +19,10 @@ automation. Python 3.14+ is required. - `pixi run tests-with-cov` - Run tests with coverage reporting - `pytest tests/test_specific_module.py` - Run specific test file - `pytest tests/test_specific_module.py::test_function_name` - Run specific test -- `pixi run ty` - Type checking with ty -- `prek run --all-files` - Run all pre-commit hooks +- `prek run ty --all-files` - Type checking with ty (a pre-commit hook; resolves + third-party imports from the pixi env named in `[tool.ty] environment.python`, so run + `pixi install` once) +- `prek run --all-files` - Run all pre-commit hooks (includes the `ty` hook) - `pixi run -e docs build-docs` - Build documentation - `pixi run -e docs view-docs` - Live preview documentation - `pixi install` - Install dependencies @@ -572,7 +574,7 @@ prose hides cases. - Extensive use of typing with custom types: user-facing aliases in `src/lcm/typing.py`, engine-side aliases and protocols in `src/_lcm/typing.py` -- Type checking with ty (pixi run ty) +- Type checking with ty (`prek run ty --all-files`) - Use `# ty: ignore[error-code]` for type suppression, never `# type: ignore` - JAX typing integration via jaxtyping diff --git a/CHANGES.md b/CHANGES.md index 7950286c3..b068c0bff 100644 --- a/CHANGES.md +++ b/CHANGES.md @@ -7,55 +7,26 @@ chronological order. We follow [semantic versioning](https://semver.org/). ## Unreleased -### Phase grammar, cross-regime transitions, and model-level regime slots - -- `Phased(solve=..., simulate=...)` gives any regime-slot value a per-phase - variant; a bare value broadcasts to both phases. Carried states β€” - `Phased(solve=callable, simulate=Grid)` in `states` β€” are derived functions - during backward induction and genuine seeded-and-evolved states in - simulation. See the [phase grammar](docs/explanations/phase_grammar.ipynb) - explanation. - -- `fixed_transition(state_name)` marks a fixed state (identity law) in - `state_transitions`. The `None` spelling for fixed states is removed; a - regime-level `None` now masks a model-level entry instead. - -- Regime transitions take a third form: a per-target dict - `{target_regime: MarkovTransition(prob_func)}` whose key set declares the regime's - reachable targets β€” omitted regimes are structurally unreachable. Per-target - dicts in `state_transitions` hand state values across regime boundaries, - including into states the source regime does not carry and across grids that - differ between regimes. - -- Model-level regime slots: `Model(functions=..., constraints=..., states=..., - state_transitions=..., actions=...)` declares shared structure once and - merges it into every regime under the exactly-one-level rule. Broadcast - states and actions are pruned per regime by DAG reachability; - `model.pruned_variables` records the result. - -- `model.user_regimes` holds plain `lcm.regime.Regime` instances, finalized at - model build (model-level slots merged, default `H` injected, completeness - validated). - -### Per-target parameters - -- Per-target transition parameters nest under the target regime's name in the - params template β€” `template[regime][target][func][param]` β€” replacing the - `to__…` spelling. Param qnames parallel engine function qnames. - -- Parameters resolve at four levels, most to least specific: target / function - (one value broadcasts over the law's targets) / regime / model. Exactly one - level per parameter; multi-level specifications are ambiguity errors. - -- Canonical flat params always key transition-law params per target, every - target of a broadcast value sharing one leaf object. A coarse regime - transition is evaluated once and shared, so it takes no per-target - parameters. - -- Model-level `derived_categoricals` follow the exactly-one-level rule of the - other model-level slots: a name declared at model level and regime level is - an ambiguity error, also when the grids match. - +- Adds the DC-EGM solver (Iskhakov, JΓΈrgensen, Rust & Schjerning 2017) as a + per-regime alternative to grid search: `Regime(solver=lcm.DCEGM(...))`. + Euler-equation inversion on an exogenous savings grid with a fast + upper-envelope scan (Dobrescu & Shanker 2022) β€” no consumption grid enters + the solve, and the credit-constrained segment is exact. Requires declared + `resources`, post-decision, and `inverse_marginal_utility` regime functions; + the model contract is validated at `Model` construction. Supports discrete + states and actions, EV1 taste shocks, stochastic processes, and passive + continuous states. Forward simulation works with grid-restricted consumption + (the intrinsic budget constraint is applied as a feasibility mask). + +- Adds regime-level EV1 taste shocks as a model property: + `Regime(taste_shocks=lcm.ExtremeValueTasteShocks())` with the scale as the + runtime param `{"taste_shocks": {"scale": ...}}`. The solve aggregates + discrete actions by the smoothed expected maximum and simulation draws the + discrete action by Gumbel-max β€” identical solutions under either solver. + +- Promotes the Iskhakov et al. (2017) retirement model to + `lcm_examples.iskhakov_et_al_2017` (brute-force and DC-EGM variants) with an + explanation notebook comparing the two solvers. ## 0.0.1 diff --git a/NOTICE b/NOTICE new file mode 100644 index 000000000..92f66fb37 --- /dev/null +++ b/NOTICE @@ -0,0 +1,18 @@ +PyLCM +Copyright (c) 2023- The PyLCM Authors + +This product includes software adapted from third-party open-source projects. +Their copyright notices and license terms are reproduced in the `licenses/` +directory. + +-------------------------------------------------------------------------------- +OpenSourceEconomics/upper-envelope +https://github.com/OpenSourceEconomics/upper-envelope + +Copyright (c) 2023-2025 The Upper-Envelope Authors +Licensed under the Apache License, Version 2.0 +(full text in `licenses/upper-envelope-LICENSE`). + +The Fast Upper-Envelope Scan in `src/_lcm/egm/upper_envelope/fues.py` was adapted +from this package and has since been substantially modified. +-------------------------------------------------------------------------------- diff --git a/README.md b/README.md index 904bf896c..6bccc5cdf 100644 --- a/README.md +++ b/README.md @@ -46,14 +46,14 @@ This will install the development environment and run the tests. You can run [ty](https://docs.astral.sh/ty) using ```console -$ pixi run ty +$ prek run ty --all-files ``` Before committing, install the pre-commit hooks using ```console -$ pixi global install pre-commit -$ pre-commit install +$ pixi global install prek +$ prek install ``` ## Questions @@ -61,6 +61,15 @@ $ pre-commit install If you have any questions, feel free to ask them on the PyLCM [Zulip chat](https://ose.zulipchat.com/#narrow/channel/491562-PyLCM). +## Acknowledgments + +PyLCM builds on the endogenous grid method (Carroll, 2006), its discrete-continuous +extension (Iskhakov, JΓΈrgensen, Rust & Schjerning, 2017), the Fast Upper-Envelope Scan +(Dobrescu & Shanker, 2022), and the broader open-source ecosystem for dynamic +programming β€” including OpenSourceEconomics, NumEconCopenhagen, and QuantEcon. See the +[Credits & Acknowledgments](docs/credits.md) page for the full list of methods, +replicated models, and software we are grateful to. + ## License This project is licensed under the Apache License, Version 2.0. See the diff --git a/asv.conf.json b/asv.conf.json index 45130adce..7218ad89c 100644 --- a/asv.conf.json +++ b/asv.conf.json @@ -4,7 +4,7 @@ "project_url": "https://github.com/OpenSourceEconomics/pylcm", "repo": ".", "environment_type": "existing:python", - "benchmark_dir": "benchmarks", + "benchmark_dir": "benchmarks/asv", "results_dir": ".asv/results", "html_dir": ".asv/html", "branches": ["main"] diff --git a/benchmarks/asv/__init__.py b/benchmarks/asv/__init__.py new file mode 100644 index 000000000..d8653399e --- /dev/null +++ b/benchmarks/asv/__init__.py @@ -0,0 +1 @@ +"""Airspeed-velocity benchmark suite (the only asv-discovered package).""" diff --git a/benchmarks/_gpu_mem.py b/benchmarks/asv/_gpu_mem.py similarity index 93% rename from benchmarks/_gpu_mem.py rename to benchmarks/asv/_gpu_mem.py index 3b93763f1..72f9213a5 100644 --- a/benchmarks/_gpu_mem.py +++ b/benchmarks/asv/_gpu_mem.py @@ -33,8 +33,10 @@ class MahlerYumGpuPeakMem(GpuPeakMem): from collections.abc import Mapping from pathlib import Path -# Project root: the directory containing the benchmarks/ package. -_PROJECT_ROOT = Path(__file__).resolve().parent.parent +# Project root: the directory containing the benchmarks/ package. This file lives +# at benchmarks/asv/_gpu_mem.py, so the repo root is three parents up β€” the cwd the +# `python -m benchmarks.asv._gpu_mem` subprocess needs for `benchmarks` to import. +_PROJECT_ROOT = Path(__file__).resolve().parent.parent.parent # Marks the peak-memory line on the subprocess's stdout. The subprocess imports # lcm, whose beartype claw can emit diagnostics to stdout, so the parent locates @@ -72,7 +74,7 @@ def measure_gpu_peak(bench_module: str, bench_class: str) -> int: """ result = subprocess.run( - [sys.executable, "-m", "benchmarks._gpu_mem", bench_module, bench_class], + [sys.executable, "-m", "benchmarks.asv._gpu_mem", bench_module, bench_class], capture_output=True, text=True, check=False, diff --git a/benchmarks/bench_aca_baseline.py b/benchmarks/asv/bench_aca_baseline.py similarity index 98% rename from benchmarks/bench_aca_baseline.py rename to benchmarks/asv/bench_aca_baseline.py index 23395338a..75b597561 100644 --- a/benchmarks/bench_aca_baseline.py +++ b/benchmarks/asv/bench_aca_baseline.py @@ -56,7 +56,7 @@ import cloudpickle -from benchmarks import _gpu_mem +from . import _gpu_mem _N_SUBJECTS = 1000 @@ -193,12 +193,12 @@ def teardown(self, cache: bytes | None = None) -> None: class AcaBaselineGpuPeakMem(_gpu_mem.GpuPeakMem): - bench_module = "benchmarks.bench_aca_baseline" + bench_module = "benchmarks.asv.bench_aca_baseline" bench_class = "AcaBaseline" timeout = 3600 class AcaBaselineDebugLogGpuPeakMem(_gpu_mem.GpuPeakMem): - bench_module = "benchmarks.bench_aca_baseline" + bench_module = "benchmarks.asv.bench_aca_baseline" bench_class = "AcaBaselineDebugLog" timeout = 3600 diff --git a/benchmarks/bench_iskhakov_et_al_2017.py b/benchmarks/asv/bench_iskhakov_et_al_2017.py similarity index 52% rename from benchmarks/bench_iskhakov_et_al_2017.py rename to benchmarks/asv/bench_iskhakov_et_al_2017.py index 5edf39859..df20e8a0d 100644 --- a/benchmarks/bench_iskhakov_et_al_2017.py +++ b/benchmarks/asv/bench_iskhakov_et_al_2017.py @@ -17,7 +17,7 @@ import gc import time -from benchmarks import _gpu_mem +from . import _gpu_mem _N_PERIODS = 10 _TASTE_SHOCK_SCALE = 0.1 @@ -25,14 +25,35 @@ _SOLVE_WEALTH_N_POINTS = 1_000 _SOLVE_CONSUMPTION_N_POINTS = 5_000 +# 200 cubically clustered savings nodes resolve the DC-EGM solve, clustering +# toward the borrowing limit where the value function curves hardest. At +# matched value-function accuracy the brute consumption grid this model needs +# still runs faster than the DC-EGM envelope: the sequential upper-envelope +# `lax.scan` carries a fixed per-solve cost that brute's single parallel +# reduction does not, so brute is the faster solver here on both CPU and β€” more +# so β€” the GPU benchmark runner. A genuine DC-EGM speed win waits on the +# envelope GPU-performance work; the value of this pair is the head-to-head +# itself, not a DC-EGM win. +_SOLVE_SAVINGS_N_POINTS = 200 _SIMULATE_WEALTH_N_POINTS = 500 _SIMULATE_CONSUMPTION_N_POINTS = 500 -def _make_model_and_params(*, wealth_n_points: int, consumption_n_points: int): +def _make_model_and_params( + *, + wealth_n_points: int, + consumption_n_points: int, + solver: str = "brute_force", +): """Build the taste-shock retirement model and its parameters. + The `"dcegm"` solver variant is the same economic model in the DC-EGM + contract: the wealth transition consumes the post-decision savings, the + borrowing constraint is dropped (the savings grid's lower bound enforces + it), and `resources`/`savings`/`inverse_marginal_utility` are declared as + regime functions. The consumption grid plays no role in the DC-EGM solve. + lcm and jax imports are deferred to the function body so ASV's forkserver never loads the XLA backend before forking workers (see `bench_aca_baseline._build` for the failure mode). @@ -43,12 +64,20 @@ def _make_model_and_params(*, wealth_n_points: int, consumption_n_points: int): AgeGrid, DiscreteGrid, ExtremeValueTasteShocks, + IrregSpacedGrid, LinSpacedGrid, Model, Regime, categorical, ) - from lcm.typing import DiscreteAction, ScalarInt + from lcm.solvers import DCEGM + from lcm.typing import ( + ContinuousAction, + ContinuousState, + DiscreteAction, + FloatND, + ScalarInt, + ) from lcm_examples.mortality import ( LaborSupply, borrowing_constraint, @@ -83,6 +112,20 @@ def next_regime_from_working( def next_regime_from_retirement(age: float, final_age_alive: float) -> ScalarInt: return jnp.where(age >= final_age_alive, RegimeId.dead, RegimeId.retirement) + def resources(wealth: ContinuousState) -> FloatND: + return wealth + + def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + def next_wealth_from_savings( + savings: FloatND, labor_income: FloatND, interest_rate: float + ) -> ContinuousState: + return (1 + interest_rate) * savings + labor_income + + def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + ages = AgeGrid(start=40, stop=40 + _N_PERIODS - 1, step="Y") last_age = ages.exact_values[-1] @@ -117,6 +160,41 @@ def next_regime_from_retirement(age: float, final_age_alive: float) -> ScalarInt active=lambda age: age < last_age, ) + if solver == "dcegm": + dcegm_solver = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + # Cubically clustered toward the borrowing limit: the value + # function curves hardest where the constraint starts to bind, + # and a uniform grid under-resolves the lowest wealth nodes by + # orders of magnitude. + savings_grid=IrregSpacedGrid( + points=tuple( + 400.0 * (i / (_SOLVE_SAVINGS_N_POINTS - 1)) ** 3 + for i in range(_SOLVE_SAVINGS_N_POINTS) + ) + ), + ) + dcegm_functions = { + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + } + working_life = working_life.replace( + state_transitions={"wealth": next_wealth_from_savings}, + constraints={}, + functions={**dict(working_life.functions), **dcegm_functions}, + solver=dcegm_solver, + ) + retirement = retirement.replace( + state_transitions={"wealth": next_wealth_from_savings}, + constraints={}, + functions={**dict(retirement.functions), **dcegm_functions}, + solver=dcegm_solver, + ) + dead = Regime( transition=None, functions={"utility": lambda: 0.0}, @@ -207,10 +285,61 @@ def track_compilation_time(self) -> float: class IskhakovEtAl2017SolveGpuPeakMem(_gpu_mem.GpuPeakMem): - bench_module = "benchmarks.bench_iskhakov_et_al_2017" + bench_module = "benchmarks.asv.bench_iskhakov_et_al_2017" bench_class = "IskhakovEtAl2017Solve" +class IskhakovEtAl2017DCEGMSolve: + """DC-EGM solve of the same model: Euler inversion replaces the grid search. + + Reading the head-to-head: the upper-envelope refinement is a sequential + `lax.scan` over the savings nodes with a fixed per-solve cost, whereas brute + force is one vectorized parallel reduction. At matched value-function + accuracy brute is therefore the faster solver on both CPU and the GPU + benchmark runner β€” the GPU's parallelism widens the gap. DC-EGM's advantage + here is memory and asymptotic scaling, not wall clock at these grid sizes; a + speed win waits on the envelope GPU-performance work. + """ + + version = "2" + timeout = 600 + + def _build(self) -> None: + self.model, self.model_params = _make_model_and_params( + wealth_n_points=_SOLVE_WEALTH_N_POINTS, + consumption_n_points=_SOLVE_CONSUMPTION_N_POINTS, + solver="dcegm", + ) + + def setup(self) -> None: + self._build() + start = time.perf_counter() + self.model.solve(params=self.model_params, log_level="off") + self._compile_time = time.perf_counter() - start + + def setup_for_gpu_measurement(self) -> None: + self._build() + + def time_execution(self) -> None: + self.model.solve(params=self.model_params, log_level="off") + + def peakmem_execution(self) -> None: + self.model.solve(params=self.model_params, log_level="off") + + def teardown(self) -> None: + _clear_gpu_memory() + + def track_compilation_time(self) -> float: + return self._compile_time + + track_compilation_time.unit = "seconds" + + +class IskhakovEtAl2017DCEGMSolveGpuPeakMem(_gpu_mem.GpuPeakMem): + bench_module = "benchmarks.asv.bench_iskhakov_et_al_2017" + bench_class = "IskhakovEtAl2017DCEGMSolve" + + class IskhakovEtAl2017Simulate: """Simulate with Gumbel-max discrete choices from a pre-solved model.""" @@ -267,5 +396,72 @@ def track_compilation_time(self) -> float: class IskhakovEtAl2017SimulateGpuPeakMem(_gpu_mem.GpuPeakMem): - bench_module = "benchmarks.bench_iskhakov_et_al_2017" + bench_module = "benchmarks.asv.bench_iskhakov_et_al_2017" bench_class = "IskhakovEtAl2017Simulate" + + +class IskhakovEtAl2017DCEGMSimulate: + """Simulate the DC-EGM variant from a pre-solved model. + + The simulate path is the standard per-subject grid argmax in both solver + variants; the DC-EGM variant additionally synthesizes the intrinsic + budget mask, so this benchmark measures the simulate-side overhead of a + DC-EGM regime against `IskhakovEtAl2017Simulate`. + """ + + version = "1" + timeout = 600 + + def _build(self) -> None: + self.model, self.model_params = _make_model_and_params( + wealth_n_points=_SIMULATE_WEALTH_N_POINTS, + consumption_n_points=_SIMULATE_CONSUMPTION_N_POINTS, + solver="dcegm", + ) + self.period_to_regime_to_V_arr = self.model.solve( + params=self.model_params, log_level="off" + ) + self.initial_conditions = _make_initial_conditions(_N_SUBJECTS) + + def setup(self) -> None: + self._build() + start = time.perf_counter() + self.model.simulate( + params=self.model_params, + initial_conditions=self.initial_conditions, + period_to_regime_to_V_arr=self.period_to_regime_to_V_arr, + log_level="off", + ) + self._compile_time = time.perf_counter() - start + + def setup_for_gpu_measurement(self) -> None: + self._build() + + def time_execution(self) -> None: + self.model.simulate( + params=self.model_params, + initial_conditions=self.initial_conditions, + period_to_regime_to_V_arr=self.period_to_regime_to_V_arr, + log_level="off", + ) + + def peakmem_execution(self) -> None: + self.model.simulate( + params=self.model_params, + initial_conditions=self.initial_conditions, + period_to_regime_to_V_arr=self.period_to_regime_to_V_arr, + log_level="off", + ) + + def teardown(self) -> None: + _clear_gpu_memory() + + def track_compilation_time(self) -> float: + return self._compile_time + + track_compilation_time.unit = "seconds" + + +class IskhakovEtAl2017DCEGMSimulateGpuPeakMem(_gpu_mem.GpuPeakMem): + bench_module = "benchmarks.asv.bench_iskhakov_et_al_2017" + bench_class = "IskhakovEtAl2017DCEGMSimulate" diff --git a/benchmarks/bench_mahler_yum.py b/benchmarks/asv/bench_mahler_yum.py similarity index 95% rename from benchmarks/bench_mahler_yum.py rename to benchmarks/asv/bench_mahler_yum.py index aa254723f..c14848a7c 100644 --- a/benchmarks/bench_mahler_yum.py +++ b/benchmarks/asv/bench_mahler_yum.py @@ -3,7 +3,7 @@ import gc import time -from benchmarks import _gpu_mem +from . import _gpu_mem _N_SUBJECTS = 100 @@ -72,5 +72,5 @@ def track_compilation_time(self): class MahlerYumGpuPeakMem(_gpu_mem.GpuPeakMem): - bench_module = "benchmarks.bench_mahler_yum" + bench_module = "benchmarks.asv.bench_mahler_yum" bench_class = "MahlerYum" diff --git a/benchmarks/bench_precautionary_savings.py b/benchmarks/asv/bench_precautionary_savings.py similarity index 96% rename from benchmarks/bench_precautionary_savings.py rename to benchmarks/asv/bench_precautionary_savings.py index 9a44f9828..28c06119a 100644 --- a/benchmarks/bench_precautionary_savings.py +++ b/benchmarks/asv/bench_precautionary_savings.py @@ -3,7 +3,7 @@ import gc import time -from benchmarks import _gpu_mem +from . import _gpu_mem _N_SUBJECTS = 1_000 @@ -81,7 +81,7 @@ def track_compilation_time(self): class PrecautionarySavingsSolveGpuPeakMem(_gpu_mem.GpuPeakMem): - bench_module = "benchmarks.bench_precautionary_savings" + bench_module = "benchmarks.asv.bench_precautionary_savings" bench_class = "PrecautionarySavingsSolve" @@ -136,7 +136,7 @@ def track_compilation_time(self): class PrecautionarySavingsSimulateGpuPeakMem(_gpu_mem.GpuPeakMem): - bench_module = "benchmarks.bench_precautionary_savings" + bench_module = "benchmarks.asv.bench_precautionary_savings" bench_class = "PrecautionarySavingsSimulate" @@ -191,7 +191,7 @@ def track_compilation_time(self): class PrecautionarySavingsSimulateWithSolveGpuPeakMem(_gpu_mem.GpuPeakMem): - bench_module = "benchmarks.bench_precautionary_savings" + bench_module = "benchmarks.asv.bench_precautionary_savings" bench_class = "PrecautionarySavingsSimulateWithSolve" @@ -247,5 +247,5 @@ def track_compilation_time(self): class PrecautionarySavingsSimulateWithSolveIrregGpuPeakMem(_gpu_mem.GpuPeakMem): - bench_module = "benchmarks.bench_precautionary_savings" + bench_module = "benchmarks.asv.bench_precautionary_savings" bench_class = "PrecautionarySavingsSimulateWithSolveIrreg" diff --git a/benchmarks/ds_replication/__init__.py b/benchmarks/ds_replication/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/benchmarks/ds_replication/app1_retirement_accuracy.py b/benchmarks/ds_replication/app1_retirement_accuracy.py new file mode 100644 index 000000000..14f799a2f --- /dev/null +++ b/benchmarks/ds_replication/app1_retirement_accuracy.py @@ -0,0 +1,554 @@ +"""Euler-error accuracy harness for Dobrescu & Shanker (2026) Application 1. + +Application 1 of the FUES paper is the deterministic discrete-retirement model +"Γ  la Iskhakov et al. (2017)": a worker chooses consumption and whether to keep +working or retire (retirement absorbing), with log utility, a per-period work +disutility `tau`, deterministic wage income while working, and a constant gross +return. This module recalibrates pylcm's Iskhakov-et-al.-2017 building blocks to +the paper's Table 2 parameters (`r = 0.02`, `beta = 0.96`, `T = 50`, `y = 20`, +`A_max = 500`) and reproduces the paper's FUES accuracy column. + +FUES is pylcm's default DC-EGM upper envelope, so the accuracy column needs no +new solver: build the model, solve with DC-EGM, simulate a sample path, and +score the consumption Euler equation along it. + +The Euler-error metric (Judd 1992) is the mean over a simulated sample path of +`log10` of the relative deviation between chosen consumption and the consumption +implied by the Euler equation. For log utility `u'(c) = 1/c` and the +deterministic baseline the conditional expectation collapses to the realized +next-period consumption, so + + c_euler_t = c_{t+1} / (beta * (1 + r)), deviation_t = |c_euler_t / c_t - 1|, + +and the metric is `mean(log10(deviation_t))` over the valid points. A point is +valid only where the agent works this period and next (the continuous Euler +equation governs the working regime; the retirement-switch period and the +retiree problem are excluded) and where consumption is interior and +unconstrained (the constraint margin holds with a multiplier, not the plain +Euler equation). + +Use `app1_euler_error` for a single `(tau, n_grid)` cell and `app1_accuracy_table` +for the paper's `tau`-by-grid sweep. The full grids `{1000, 2000, 3000, 6000, +10000}` are GPU/CI-scale; pass smaller grids for a local run. +""" + +import functools +import logging +import time +from collections.abc import Sequence +from typing import Literal + +import jax +import jax.numpy as jnp +import numpy as np +import pandas as pd + +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + Model, +) +from lcm.regime import Regime +from lcm.solvers import DCEGM +from lcm.taste_shocks import ExtremeValueTasteShocks +from lcm_examples.iskhakov_et_al_2017 import ( + LaborSupply, + RegimeId, + dead, + inverse_marginal_utility, + is_working, + labor_income, + next_regime_from_retirement, + next_regime_from_working, + next_wealth_from_savings, + resources, + savings, + utility_retirement, + utility_working, +) + +_logger = logging.getLogger("lcm") + +# Paper Table 2 calibration (deterministic baseline, no taste shock). +ASSET_MAX = 500.0 +INTEREST_RATE = 0.02 +DISCOUNT_FACTOR = 0.96 +WAGE = 20.0 +N_PERIODS = 50 + +# The paper's reported FUES grids for Application 1. +PAPER_GRIDS = (1000, 2000, 3000, 6000, 10000) +PAPER_TAUS = (0.25, 0.50, 1.00, 2.00) + + +@functools.cache +def build_app1_model( + *, + n_grid: int, + n_periods: int = N_PERIODS, + asset_max: float = ASSET_MAX, + upper_envelope: Literal["fues", "rfc", "ltm", "mss"] = "fues", + taste_shock_scale: float = 0.0, +) -> Model: + """Build the DS-2026 Application 1 model solved by DC-EGM/FUES. + + Args: + n_grid: Number of financial-asset (wealth) grid points; also the + number of clustered exogenous savings nodes the DC-EGM solver scans. + n_periods: Number of model periods. The final period is the terminal + `dead` regime, so the number of decision periods is `n_periods - 1`. + asset_max: Upper bound of the asset grid `a in [0, asset_max]`. + + Returns: + A configured `Model` with a worker, an absorbing retiree, and a terminal + dead regime, all DC-EGM regimes scanning the same savings grid. + + """ + wealth_grid = LinSpacedGrid(start=1.0, stop=asset_max, n_points=n_grid) + # Consumption never enters the DC-EGM solve (Euler inversion replaces the + # grid search); the action grid only bounds the simulated consumption draw, + # so it tracks the wealth resolution. + consumption_grid = LinSpacedGrid(start=1.0, stop=asset_max, n_points=n_grid) + # Cubically clustered savings nodes toward the borrowing limit: the value + # function curves hardest where the constraint starts to bind, and a + # uniform grid under-resolves the lowest wealth nodes by orders of + # magnitude. The lower bound (savings >= 0) encodes `consumption <= wealth`. + savings_grid = IrregSpacedGrid( + points=tuple(asset_max * (i / (n_grid - 1)) ** 3 for i in range(n_grid)) + ) + solver = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=savings_grid, + upper_envelope=upper_envelope, + # The final decision period consumes everything, so its carry in the + # queried resources range is constrained-segment points only; a small + # count keeps the geometric spacing ratio and the carry interpolation + # error small. + n_constrained_points=64, + ) + + ages = AgeGrid(start=0, stop=n_periods - 1, step="Y") + last_age = ages.exact_values[-1] + + taste_shock_kwargs = ( + {"taste_shocks": ExtremeValueTasteShocks()} if taste_shock_scale > 0.0 else {} + ) + working_life = Regime( + transition=next_regime_from_working, + actions={ + "labor_supply": DiscreteGrid(LaborSupply), + "consumption": consumption_grid, + }, + states={"wealth": wealth_grid}, + state_transitions={"wealth": next_wealth_from_savings}, + functions={ + "utility": utility_working, + "labor_income": labor_income, + "is_working": is_working, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=solver, + active=lambda age, la=last_age: age < la, + **taste_shock_kwargs, + ) + retirement = Regime( + transition=next_regime_from_retirement, + actions={"consumption": consumption_grid}, + states={"wealth": wealth_grid}, + state_transitions={"wealth": next_wealth_from_savings}, + functions={ + "utility": utility_retirement, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=solver, + active=lambda age, la=last_age: age < la, + ) + + return Model( + regimes={ + "working_life": working_life, + "retirement": retirement, + "dead": dead, + }, + ages=ages, + regime_id_class=RegimeId, + ) + + +def build_app1_params( + *, + tau: float, + n_periods: int = N_PERIODS, + interest_rate: float = INTEREST_RATE, + discount_factor: float = DISCOUNT_FACTOR, + wage: float = WAGE, + taste_shock_scale: float = 0.0, +) -> dict: + """Build the parameter dict for the Application 1 model. + + Args: + tau: Per-period utility cost of working (`u(c) = log(c) - tau`). + n_periods: Number of model periods (must match `build_app1_model`). + interest_rate: Net asset return `r`. + discount_factor: Discount factor `beta`. + wage: Deterministic per-period wage while working. + + Returns: + Parameter dict ready for `model.solve()` / `model.simulate()`. + + """ + # All but the final period is a decision period; death arrives at the last + # decision age, so `final_age_alive` is the second-to-last age. + final_age_alive = n_periods - 2 + working_life_params: dict = { + "utility": {"disutility_of_work": tau}, + "labor_income": {"wage": wage}, + } + if taste_shock_scale > 0.0: + working_life_params["taste_shocks"] = {"scale": taste_shock_scale} + return { + "discount_factor": discount_factor, + "interest_rate": interest_rate, + "final_age_alive": final_age_alive, + "working_life": working_life_params, + "retirement": { + "next_wealth": {"labor_income": 0.0}, + }, + } + + +def _initial_conditions(*, n_subjects: int, asset_max: float): + """Spread initial wealth so the sample path spans early and late retirement.""" + return { + "wealth": jnp.linspace(1.0, asset_max / 5.0, n_subjects), + "age": jnp.zeros(n_subjects), + "regime_id": jnp.full(n_subjects, RegimeId.working_life, dtype=jnp.int32), + } + + +def sample_path_euler_error( + *, + panel: pd.DataFrame, + interest_rate: float = INTEREST_RATE, + discount_factor: float = DISCOUNT_FACTOR, +) -> float: + """Mean log10 consumption Euler error along a simulated working-regime path. + + For log utility the Euler equation `u'(c_t) = beta*(1+r)*u'(c_{t+1})` implies + `c_euler_t = c_{t+1} / (beta*(1+r))`, and the metric is the mean over valid + points of `log10(|c_euler_t / c_t - 1|)`. A point is valid only where the + subject works this period and the next (the working-regime continuous Euler + equation; the retirement switch and the retiree problem are excluded) and + where consumption is interior and unconstrained. The borrowing-constrained + points β€” where consumption exhausts the period's resources β€” are dropped + because the Euler equation there holds with a constraint multiplier. + + Args: + panel: Long-format simulation panel with columns `subject_id`, `period`, + `regime_name`, `labor_supply`, `consumption`, and `wealth`. + interest_rate: Net asset return `r`. + discount_factor: Discount factor `beta`. + + Returns: + The mean base-10 log relative consumption Euler error over the valid + working-regime sample-path points. + + """ + working = panel.query("regime_name == 'working_life'").copy() + working = working.sort_values(["subject_id", "period"]) + + consumption = working["consumption"].to_numpy() + wealth = working["wealth"].to_numpy() + labor = working["labor_supply"].to_numpy() + subject = working["subject_id"].to_numpy() + period = working["period"].to_numpy() + + next_consumption = np.full_like(consumption, np.nan) + same_subject = subject[:-1] == subject[1:] + consecutive = period[1:] == period[:-1] + 1 + has_next = np.zeros(consumption.shape, dtype=bool) + has_next[:-1] = same_subject & consecutive + next_consumption[:-1] = np.where(has_next[:-1], consumption[1:], np.nan) + + works_this = labor == "work" + works_next = np.zeros(consumption.shape, dtype=bool) + works_next[:-1] = has_next[:-1] & (labor[1:] == "work") + + # Unconstrained interior: consumption leaves strictly positive savings, so + # the borrowing constraint does not bind. A tiny absolute floor guards the + # finite-grid edge where chosen consumption equals available resources. + unconstrained = consumption < wealth - 1e-6 + + valid = works_this & works_next & has_next & unconstrained + if not valid.any(): + msg = "No valid interior working-regime points to score the Euler error." + raise ValueError(msg) + + consumption_valid = consumption[valid] + next_consumption_valid = next_consumption[valid] + consumption_euler = next_consumption_valid / ( + discount_factor * (1.0 + interest_rate) + ) + relative_error = np.abs(consumption_euler / consumption_valid - 1.0) + log10_error = np.log10(relative_error) + finite = np.isfinite(log10_error) + return float(np.mean(log10_error[finite])) + + +def app1_euler_error( + *, + tau: float, + n_grid: int, + n_periods: int = N_PERIODS, + n_subjects: int = 1000, + seed: int = 0, + asset_max: float = ASSET_MAX, + interest_rate: float = INTEREST_RATE, + discount_factor: float = DISCOUNT_FACTOR, + wage: float = WAGE, + upper_envelope: Literal["fues", "rfc", "ltm", "mss"] = "fues", + taste_shock_scale: float = 0.0, +) -> float: + """Solve, simulate, and score the FUES Euler error for one `(tau, n_grid)`. + + Args: + tau: Per-period utility cost of working. + n_grid: Number of financial-asset grid points. + n_periods: Number of model periods. + n_subjects: Number of simulated sample paths. + seed: Simulation seed. + asset_max: Upper bound of the asset grid. + interest_rate: Net asset return `r`. + discount_factor: Discount factor `beta`. + wage: Deterministic per-period wage while working. + + Returns: + The mean log10 consumption Euler error along the simulated sample path. + + """ + model = build_app1_model( + n_grid=n_grid, + n_periods=n_periods, + asset_max=asset_max, + upper_envelope=upper_envelope, + taste_shock_scale=taste_shock_scale, + ) + params = build_app1_params( + tau=tau, + n_periods=n_periods, + interest_rate=interest_rate, + discount_factor=discount_factor, + wage=wage, + taste_shock_scale=taste_shock_scale, + ) + result = model.simulate( + params=params, + initial_conditions=_initial_conditions( + n_subjects=n_subjects, asset_max=asset_max + ), + period_to_regime_to_V_arr=None, + log_level="off", + seed=seed, + ) + panel = result.to_dataframe() + euler_error = sample_path_euler_error( + panel=panel, + interest_rate=interest_rate, + discount_factor=discount_factor, + ) + _logger.info( + "DS App.1 %s Euler error: tau=%.2f n_grid=%d -> %.3f", + upper_envelope.upper(), + tau, + n_grid, + euler_error, + ) + return euler_error + + +def app1_accuracy_table( + *, + taus: Sequence[float] = PAPER_TAUS, + n_grids: Sequence[int] = PAPER_GRIDS, + n_periods: int = N_PERIODS, + n_subjects: int = 1000, + seed: int = 0, + upper_envelope: Literal["fues", "rfc", "ltm", "mss"] = "fues", +) -> pd.DataFrame: + """Run the `tau`-by-grid Euler-error sweep, reproducing the FUES column. + + One solve+simulate per `(tau, n_grid)` cell. The full paper grids are + GPU/CI-scale; pass smaller `n_grids` for a local run. + + Args: + taus: Work-cost values to sweep. + n_grids: Asset-grid sizes to sweep. + n_periods: Number of model periods. + n_subjects: Number of simulated sample paths per cell. + seed: Simulation seed. + + Returns: + Long-format DataFrame with columns `tau`, `n_grid`, and + `fues_euler_error`. + + """ + rows = [ + { + "tau": tau, + "n_grid": n_grid, + f"{upper_envelope}_euler_error": app1_euler_error( + tau=tau, + n_grid=n_grid, + n_periods=n_periods, + n_subjects=n_subjects, + seed=seed, + upper_envelope=upper_envelope, + ), + } + for tau in taus + for n_grid in n_grids + ] + return pd.DataFrame(rows) + + +def app1_timing( + *, + tau: float, + n_grid: int, + upper_envelope: Literal["fues", "rfc", "ltm", "mss"] = "fues", + n_periods: int = N_PERIODS, + n_runs: int = 3, + asset_max: float = ASSET_MAX, + interest_rate: float = INTEREST_RATE, + discount_factor: float = DISCOUNT_FACTOR, + wage: float = WAGE, + taste_shock_scale: float = 0.0, +) -> dict[str, float]: + """Measure compile and steady-state run time of one DC-EGM solve. + + JAX JIT-compiles on the first solve and reuses the cached executable on later + solves of the same model, so the first call times compile-plus-run and the + later calls time pure execution; the compile cost is the difference. Every + solve is forced to completion with `block_until_ready` before the clock is + read, since JAX dispatch is asynchronous. + + Args: + tau: Per-period utility cost of working. + n_grid: Number of financial-asset grid points. + upper_envelope: DC-EGM upper-envelope backend to time. + n_periods: Number of model periods. + n_runs: Number of post-compile solves; the fastest is the runtime estimate. + asset_max: Upper bound of the asset grid. + interest_rate: Net asset return. + discount_factor: Discount factor. + wage: Deterministic per-period wage while working. + + Returns: + Mapping with `compile_time` and `runtime` in seconds. + + """ + model = build_app1_model( + n_grid=n_grid, + n_periods=n_periods, + asset_max=asset_max, + upper_envelope=upper_envelope, + taste_shock_scale=taste_shock_scale, + ) + params = build_app1_params( + tau=tau, + n_periods=n_periods, + interest_rate=interest_rate, + discount_factor=discount_factor, + wage=wage, + taste_shock_scale=taste_shock_scale, + ) + + # Clear the JAX compilation cache so the first solve genuinely compiles even + # if a solve of this (method, shape) ran earlier in the process; otherwise the + # cached executable turns the first call into pure runtime and the compile + # estimate collapses to measurement noise. + jax.clear_caches() + start = time.perf_counter() + jax.block_until_ready(model.solve(params=params, log_level="off")) + compile_plus_run = time.perf_counter() - start + + runtimes = [] + for _ in range(n_runs): + start = time.perf_counter() + jax.block_until_ready(model.solve(params=params, log_level="off")) + runtimes.append(time.perf_counter() - start) + runtime = min(runtimes) + + result = {"compile_time": compile_plus_run - runtime, "runtime": runtime} + _logger.info( + "DS App.1 %s timing: tau=%.2f n_grid=%d -> compile=%.3fs run=%.3fs", + upper_envelope.upper(), + tau, + n_grid, + result["compile_time"], + result["runtime"], + ) + return result + + +def app1_timing_table( + *, + upper_envelopes: Sequence[Literal["fues", "rfc", "ltm", "mss"]] = ( + "fues", + "rfc", + "ltm", + "mss", + ), + taus: Sequence[float] = (1.0,), + n_grids: Sequence[int] = PAPER_GRIDS, + n_periods: int = N_PERIODS, + n_runs: int = 3, +) -> pd.DataFrame: + """Sweep compile and run time across methods and grids (the Table 1 shape). + + One model solve per `(method, tau, n_grid)` cell, with compile and runtime as + separate columns. The full paper grids are GPU/CI-scale; pass smaller + `n_grids` for a local run. + + Args: + upper_envelopes: DC-EGM upper-envelope backends to compare. + taus: Work-cost values to sweep. + n_grids: Asset-grid sizes to sweep. + n_periods: Number of model periods. + n_runs: Number of post-compile solves per cell. + + Returns: + Long-format DataFrame with columns `method`, `tau`, `n_grid`, + `compile_time`, and `runtime`. + + """ + rows = [] + for upper_envelope in upper_envelopes: + for tau in taus: + for n_grid in n_grids: + timing = app1_timing( + tau=tau, + n_grid=n_grid, + upper_envelope=upper_envelope, + n_periods=n_periods, + n_runs=n_runs, + ) + rows.append( + { + "method": upper_envelope, + "tau": tau, + "n_grid": n_grid, + "compile_time": timing["compile_time"], + "runtime": timing["runtime"], + } + ) + return pd.DataFrame(rows) diff --git a/benchmarks/ds_replication/app2_fues_accuracy.py b/benchmarks/ds_replication/app2_fues_accuracy.py new file mode 100644 index 000000000..d5362e660 --- /dev/null +++ b/benchmarks/ds_replication/app2_fues_accuracy.py @@ -0,0 +1,532 @@ +"""Euler-error + timing harness for the DS-2026 App.2 EGM-FUES column. + +Application 2's Table 3 compares EGM-FUES and NEGM on the continuous-housing +model. This module scores the **EGM-FUES** column, which pylcm builds as a +discrete-choice DC-EGM over the housing grid (`ds_app2_housing_fues.py`): it +solves the model, simulates a sample path plus a per-period on-grid policy +panel, and scores the consumption Euler equation along the path with the Judd +(1992) metric, plus a compile-vs-runtime timing split. The companion NEGM column +lives in `app2_housing_accuracy.py`. + +## The stochastic Euler equation + +Utility is the App.2 separable CES, so the consumption marginal utility is +`u'(c) = alpha*c^{-gamma_C}` and the housing-service term drops. The wage is a +Markov (Tauchen AR1) process, so the conditional expectation is a +transition-probability-weighted sum over next-period wage nodes, + + E_t[u'(c_{t+1})] + = sum_j P[wage_t, j] * alpha*c_{t+1}(a', H', wage_j)^{-gamma_C}, + +evaluated at the chosen post-decision liquid assets `a'` and next housing level +`H'` held fixed, with `c_{t+1}(., H', wage_j)` the period-(t+1) consumption +policy of the `(H', wage_j)` cell interpolated in liquid assets. The implied +consumption is `c_euler_t = (beta*(1+r)*E_t[u'(c_{t+1})] / alpha)^{-1/gamma_C}` +and the metric is `mean(log10(|c_euler_t / c_t - 1|))`. + +## Valid points + +A path point is scored only where the continuous consumption Euler equation +governs the optimum: + +- the subject is in the working regime this period and the next; +- next-period liquid assets are strictly positive (the no-borrowing constraint + is slack); +- the discrete housing level is not adjusted this period and not adjusted next + period (`housing == housing_choice` at both `t` and `t+1`) β€” the housing + switch is a value-function kink the smooth consumption Euler equation skips. + +pylcm's simulate is grid-restricted for all solvers, so the magnitude at coarse +grids is coarse-grid, not a methodological ceiling; the paper grids (NG in +{250...1000}) exceed local memory and require a GPU sweep. +""" + +import functools +import logging +import time +from collections.abc import Sequence + +import jax +import jax.numpy as jnp +import numpy as np +import pandas as pd + +from lcm import TauchenAR1Process +from tests.test_models import ds_app2_housing_fues as fues +from tests.test_models.ds_app2_housing_fues import HousingFuesRegimeId + +_logger = logging.getLogger("lcm") + +# Paper Table 3 calibration (default no-tax column). +INTEREST_RATE = 0.04 +DISCOUNT_FACTOR = 0.94 +ALPHA = 0.70 +GAMMA_C = 3.5 +RHO_W = 0.82 +SIGMA_W = 0.11 +MU_W = 0.0 +N_PERIODS = 8 + + +def _wage_nodes_and_transition( + *, + rho: float = RHO_W, + sigma: float = SIGMA_W, + mu: float = MU_W, +) -> tuple[np.ndarray, np.ndarray]: + """Return the Markov wage node values and the transition-probability matrix. + + Constructed from the same `TauchenAR1Process` the model's working regime + uses; the Tauchen build-time grid is a NaN placeholder resolved from the + runtime `(rho, sigma, mu)` parameters. + """ + process = TauchenAR1Process(n_points=fues.N_WAGE_NODES, gauss_hermite=True) + nodes = np.asarray( + process.compute_gridpoints( + rho=jnp.asarray(rho), sigma=jnp.asarray(sigma), mu=jnp.asarray(mu) + ) + ) + transition = np.asarray( + process.compute_transition_probs( + rho=jnp.asarray(rho), sigma=jnp.asarray(sigma), mu=jnp.asarray(mu) + ) + ) + return nodes, transition + + +def _nearest_wage_index(wage_values: np.ndarray, nodes: np.ndarray) -> np.ndarray: + """Map each (possibly rounded) path wage value to its wage-node index.""" + return np.abs(wage_values[:, None] - nodes[None, :]).argmin(axis=1) + + +# Cap on the liquid-seed resolution of the policy reconstruction; bounds the +# panel size so the Euler scales to paper-scale NG (see `_policy_lookup`). +_MAX_POLICY_SEED_LIQUID = 24 + + +def _subsample(grid: np.ndarray, max_points: int) -> np.ndarray: + """Return at most `max_points` evenly-spaced nodes of `grid`, ends included.""" + if len(grid) <= max_points: + return grid + index = np.unique(np.linspace(0, len(grid) - 1, max_points).round().astype(int)) + return grid[index] + + +@functools.cache +def _build_solved( + *, + n_grid: int, + n_housing: int, + n_periods: int, + n_consumption: int, + tau: float, + liquid_batch_size: int = 0, +): + """Build and solve the EGM-FUES App.2 model, caching the solution.""" + model = fues.build_model( + variant="dcegm", + n_grid=n_grid, + n_housing=n_housing, + n_periods=n_periods, + n_consumption=n_consumption, + liquid_batch_size=liquid_batch_size, + ) + params = fues.build_params(variant="dcegm", tau=tau) + solution = model.solve(params=params, log_level="off") + return model, params, solution + + +def _liquid_grid(model) -> np.ndarray: + """Return the working regime's liquid-asset grid node array.""" + return np.asarray(model.user_regimes["working"].states["liquid"].to_jax()) + + +def _full_grid_initial_conditions( + *, + liquid_grid: np.ndarray, + n_housing: int, + wage_nodes: np.ndarray, + age: float, +) -> dict: + """Seed one subject at every `(liquid, housing, wage)` product-grid cell.""" + housing_codes = np.arange(n_housing) + liquid = np.repeat(liquid_grid, len(housing_codes) * len(wage_nodes)) + housing = np.tile(np.repeat(housing_codes, len(wage_nodes)), len(liquid_grid)) + wage = np.tile(wage_nodes, len(liquid_grid) * len(housing_codes)) + n_subjects = liquid.size + return { + "liquid": jnp.asarray(liquid), + "housing": jnp.asarray(housing, dtype=jnp.int32), + "wage": jnp.asarray(wage), + "age": jnp.full(n_subjects, age), + "regime_id": jnp.full(n_subjects, HousingFuesRegimeId.working, dtype=jnp.int32), + } + + +def _policy_lookup( + *, + model, + params, + solution, + liquid_grid: np.ndarray, + n_housing: int, + wage_nodes: np.ndarray, + n_periods: int, + seed: int, +) -> dict[tuple[int, int, int], tuple[np.ndarray, np.ndarray]]: + """Per-`(period, housing, wage)` sorted `(liquid, consumption)` policy. + + The period-`p` policy is read off a fresh simulation seeded over the full + `(liquid, housing, wage)` product grid at period `p`'s age, so the first + simulated period lands on the regular grid; each `(housing, wage)` cell maps + to the sorted liquid samples and the chosen consumption, ready for linear + interpolation in liquid at an arbitrary `a'`. + """ + # Subsample the liquid seed so the panel (liquid x n_housing x wage subjects, + # each argmaxing over consumption x housing_choice) stays within device + # memory at paper-scale NG; consumption is smooth in liquid, so a coarser + # interpolation grid is adequate. + liquid_grid = _subsample(liquid_grid, _MAX_POLICY_SEED_LIQUID) + ages = model.ages.exact_values + lookup: dict[tuple[int, int, int], tuple[np.ndarray, np.ndarray]] = {} + for period in range(n_periods): + initial_conditions = _full_grid_initial_conditions( + liquid_grid=liquid_grid, + n_housing=n_housing, + wage_nodes=wage_nodes, + age=float(ages[period]), + ) + panel = ( + model.simulate( + params=params, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=solution, + log_level="off", + seed=seed, + ) + .to_dataframe() + .query(f"period == {period} and regime_name == 'working'") + ) + if panel.empty: + continue + panel = panel.copy() + panel["wage_index"] = _nearest_wage_index(panel["wage"].to_numpy(), wage_nodes) + panel["housing_code"] = panel["housing"].map(_housing_code).to_numpy() + grouped = panel.groupby(["housing_code", "wage_index"], observed=True) + for (housing_code, wage_index), cell in grouped: + order = np.argsort(cell["liquid"].to_numpy()) + liquid = cell["liquid"].to_numpy()[order] + consumption = cell["consumption"].to_numpy()[order] + lookup[(int(period), int(housing_code), int(wage_index))] = ( + liquid, + consumption, + ) + return lookup + + +def _housing_code(label) -> int: + """Map a housing level label `h` to its integer code `i`.""" + return int(str(label).removeprefix("h")) + + +def _interp_policy( + *, + lookup: dict[tuple[int, int, int], tuple[np.ndarray, np.ndarray]], + period: int, + housing_code: int, + wage_index: int, + liquid: float, +) -> float: + """Linearly interpolate the consumption policy of a cell at `liquid`. + + Returns NaN when the cell has no policy samples, so the point is dropped + rather than scored against a fabricated value. + """ + key = (period, housing_code, wage_index) + if key not in lookup: + return float("nan") + liquid_samples, consumption_samples = lookup[key] + if liquid_samples.size == 0: + return float("nan") + return float(np.interp(liquid, liquid_samples, consumption_samples)) + + +def _expected_next_marginal_utility( + *, + lookup: dict[tuple[int, int, int], tuple[np.ndarray, np.ndarray]], + wage_transition: np.ndarray, + source_wage_index: int, + next_period: int, + next_housing_code: int, + next_liquid: float, + n_wage_nodes: int, + alpha: float, + gamma_c: float, +) -> float: + """Transition-weighted expected next-period consumption marginal utility.""" + expected_marginal = 0.0 + for next_wage_index in range(n_wage_nodes): + probability = wage_transition[source_wage_index, next_wage_index] + if probability <= 0.0: + continue + next_consumption = _interp_policy( + lookup=lookup, + period=next_period, + housing_code=next_housing_code, + wage_index=next_wage_index, + liquid=next_liquid, + ) + if not np.isfinite(next_consumption) or next_consumption <= 0.0: + return float("nan") + expected_marginal += probability * (alpha * next_consumption ** (-gamma_c)) + return expected_marginal + + +def sample_path_euler_error( + *, + sample_panel: pd.DataFrame, + lookup: dict[tuple[int, int, int], tuple[np.ndarray, np.ndarray]], + wage_nodes: np.ndarray, + wage_transition: np.ndarray, + interest_rate: float = INTEREST_RATE, + discount_factor: float = DISCOUNT_FACTOR, + alpha: float = ALPHA, + gamma_c: float = GAMMA_C, +) -> float: + """Mean log10 stochastic consumption Euler error along a simulated path.""" + working = sample_panel.query("regime_name == 'working'").copy() + working = working.sort_values(["subject_id", "period"]).reset_index(drop=True) + + subject = working["subject_id"].to_numpy() + period = working["period"].to_numpy() + consumption = working["consumption"].to_numpy() + liquid = working["liquid"].to_numpy() + housing_code = working["housing"].map(_housing_code).to_numpy() + choice_code = working["housing_choice"].map(_housing_code).to_numpy() + wage_value = working["wage"].to_numpy() + wage_index = _nearest_wage_index(wage_value, wage_nodes) + + same_subject = subject[:-1] == subject[1:] + consecutive = period[1:] == period[:-1] + 1 + has_next = np.zeros(consumption.shape, dtype=bool) + has_next[:-1] = same_subject & consecutive + + errors: list[float] = [] + for t in range(len(working) - 1): + if not has_next[t]: + continue + if working["regime_name"].iloc[t + 1] != "working": + continue + next_liquid = liquid[t + 1] + if next_liquid <= 1e-4 or consumption[t] <= 0.0: + continue + # No housing switch this period or next: the discrete housing-adjustment + # margin is a value-function kink the smooth Euler equation skips. + if housing_code[t] != choice_code[t]: + continue + if housing_code[t + 1] != choice_code[t + 1]: + continue + + expected_marginal = _expected_next_marginal_utility( + lookup=lookup, + wage_transition=wage_transition, + source_wage_index=int(wage_index[t]), + next_period=int(period[t + 1]), + next_housing_code=int(choice_code[t]), + next_liquid=float(next_liquid), + n_wage_nodes=wage_nodes.size, + alpha=alpha, + gamma_c=gamma_c, + ) + if not np.isfinite(expected_marginal) or expected_marginal <= 0.0: + continue + + consumption_euler = ( + discount_factor * (1.0 + interest_rate) * expected_marginal / alpha + ) ** (-1.0 / gamma_c) + relative_error = abs(consumption_euler / consumption[t] - 1.0) + if relative_error > 0.0: + errors.append(np.log10(relative_error)) + + if not errors: + msg = "No valid interior working-regime points to score the Euler error." + raise ValueError(msg) + return float(np.mean(errors)) + + +def app2_fues_euler_error( + *, + n_grid: int, + n_housing: int = 5, + n_periods: int = N_PERIODS, + n_consumption: int = 400, + n_subjects: int = 400, + tau: float = 0.07, + seed: int = 0, + interest_rate: float = INTEREST_RATE, + discount_factor: float = DISCOUNT_FACTOR, + alpha: float = ALPHA, + gamma_c: float = GAMMA_C, + liquid_batch_size: int = 0, +) -> float: + """Solve the EGM-FUES App.2 model and score the consumption Euler error.""" + model, params, solution = _build_solved( + n_grid=n_grid, + n_housing=n_housing, + n_periods=n_periods, + n_consumption=n_consumption, + tau=tau, + liquid_batch_size=liquid_batch_size, + ) + wage_nodes, wage_transition = _wage_nodes_and_transition() + liquid_grid = _liquid_grid(model) + + sample_panel = _simulate_sample_path( + model=model, + params=params, + solution=solution, + n_subjects=n_subjects, + liquid_grid=liquid_grid, + n_housing=n_housing, + wage_nodes=wage_nodes, + seed=seed, + ) + lookup = _policy_lookup( + model=model, + params=params, + solution=solution, + liquid_grid=liquid_grid, + n_housing=n_housing, + wage_nodes=wage_nodes, + n_periods=n_periods, + seed=seed, + ) + error = sample_path_euler_error( + sample_panel=sample_panel, + lookup=lookup, + wage_nodes=wage_nodes, + wage_transition=wage_transition, + interest_rate=interest_rate, + discount_factor=discount_factor, + alpha=alpha, + gamma_c=gamma_c, + ) + _logger.info("DS App.2 EGM-FUES Euler error: n_grid=%d -> %.3f", n_grid, error) + return error + + +def _simulate_sample_path( + *, + model, + params, + solution, + n_subjects: int, + liquid_grid: np.ndarray, + n_housing: int, + wage_nodes: np.ndarray, + seed: int, +) -> pd.DataFrame: + """Simulate a spread of working subjects at the median wage node.""" + rng = np.random.default_rng(seed) + median_wage = float(wage_nodes[len(wage_nodes) // 2]) + initial_conditions = { + "liquid": jnp.asarray( + rng.uniform(2.0, float(liquid_grid[-1]) * 0.6, n_subjects) + ), + "housing": jnp.asarray(rng.integers(1, n_housing, n_subjects), dtype=jnp.int32), + "wage": jnp.full(n_subjects, median_wage), + "age": jnp.full(n_subjects, float(model.ages.exact_values[0])), + "regime_id": jnp.full(n_subjects, HousingFuesRegimeId.working, dtype=jnp.int32), + } + result = model.simulate( + params=params, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=solution, + log_level="off", + seed=seed, + ) + return result.to_dataframe() + + +def app2_fues_timing( + *, + n_grid: int, + n_housing: int = 5, + n_periods: int = N_PERIODS, + n_consumption: int = 400, + tau: float = 0.07, + n_runs: int = 3, + liquid_batch_size: int = 0, +) -> dict[str, float]: + """Measure compile and steady-state run time of one EGM-FUES solve. + + The first solve times compile-plus-run; later solves of the same model reuse + the cached executable and time pure execution, so the compile cost is the + difference. Every solve is forced to completion with `block_until_ready`. + + `liquid_batch_size > 0` chunks the liquid Euler grid to bound peak device + memory at large `n_grid`; it leaves the solved value function unchanged. + """ + model = fues.build_model( + variant="dcegm", + n_grid=n_grid, + n_housing=n_housing, + n_periods=n_periods, + n_consumption=n_consumption, + liquid_batch_size=liquid_batch_size, + ) + params = fues.build_params(variant="dcegm", tau=tau) + + jax.clear_caches() + start = time.perf_counter() + jax.block_until_ready(model.solve(params=params, log_level="off")) + compile_plus_run = time.perf_counter() - start + + runtimes = [] + for _ in range(n_runs): + start = time.perf_counter() + jax.block_until_ready(model.solve(params=params, log_level="off")) + runtimes.append(time.perf_counter() - start) + runtime = min(runtimes) + + result = {"compile_time": compile_plus_run - runtime, "runtime": runtime} + _logger.info( + "DS App.2 EGM-FUES timing: n_grid=%d -> compile=%.3fs run=%.3fs", + n_grid, + result["compile_time"], + result["runtime"], + ) + return result + + +def app2_fues_accuracy_table( + *, + n_grids: Sequence[int] = (12, 18), + n_housing: int = 5, + n_periods: int = N_PERIODS, + n_consumption: int = 400, + n_subjects: int = 400, + tau: float = 0.07, + seed: int = 0, +) -> pd.DataFrame: + """Run the EGM-FUES Euler-error sweep across liquid-grid sizes. + + One solve+simulate per grid size. The paper grids (NG in {250...1000}) exceed + local memory and require a GPU sweep; pass smaller `n_grids` for a local run. + """ + rows = [ + { + "n_grid": n_grid, + "fues_euler_error": app2_fues_euler_error( + n_grid=n_grid, + n_housing=n_housing, + n_periods=n_periods, + n_consumption=n_consumption, + n_subjects=n_subjects, + tau=tau, + seed=seed, + ), + } + for n_grid in n_grids + ] + return pd.DataFrame(rows) diff --git a/benchmarks/ds_replication/app2_housing_accuracy.py b/benchmarks/ds_replication/app2_housing_accuracy.py new file mode 100644 index 000000000..d69eb5cc2 --- /dev/null +++ b/benchmarks/ds_replication/app2_housing_accuracy.py @@ -0,0 +1,598 @@ +"""Euler-error accuracy harness for Dobrescu & Shanker (2026) Application 2. + +Application 2 of the FUES paper is the continuous-housing model of DS Section 2.2: +a finite-horizon problem with a liquid financial asset, an illiquid housing stock +carrying a proportional transaction cost, a **stochastic (Markov) wage**, and a +discrete adjust/keep choice. It maps onto pylcm's nested-EGM (NEGM) solver β€” an +inner DC-EGM on the liquid consumption-savings margin nested over an outer grid +search on the next housing stock. This module scores the **NEGM** consumption +Euler equation along a simulated sample path, the same Judd (1992) metric the +Application 1 and Application 3 harnesses use. + +## The stochastic Euler equation + +Utility is additively separable CES over consumption and the serviced house, +`u(c, H') = alpha*(c^{1-gamma_C} - 1)/(1 - gamma_C) ++ (1-alpha)*kappa*(H'^{1-gamma_H} - 1)/(1 - gamma_H)`, so the consumption +marginal utility is `u'(c) = alpha*c^{-gamma_C}` and the housing service term +drops from the consumption Euler equation. The wage is Markov, so the +conditional expectation is a transition-probability-weighted sum over +next-period wage nodes, + + E_t[u'(c_{t+1})] + = sum_j P[wage_t, j] * alpha*c_{t+1}(a', H', wage_j)^{-gamma_C}, + +evaluated at the chosen post-decision liquid assets `a'` and next housing `H'` +held fixed, with `c_{t+1}(., ., wage_j)` the period-(t+1) consumption policy +linearly interpolated in `(liquid, housing)` for that wage node. The implied +consumption is + + c_euler_t = ( beta*(1+r)*E_t[u'(c_{t+1})] / alpha )^{-1/gamma_C}, + +and the metric is `mean(log10(|c_euler_t / c_t - 1|))` over the valid points. + +## Valid points + +A path point is scored only where the continuous consumption Euler equation +governs the optimum: + +- the subject is in the working regime this period and the next (the retirement + switch and the terminal bequest regime are excluded); +- next-period liquid assets are strictly positive, so chosen consumption did not + exhaust resources and the no-borrowing constraint is slack (the constrained + margin holds with a multiplier, not the plain Euler equation). + +The housing margin is not a kink to exclude here: the housing service flow is +additively separable, so the consumption Euler equation holds at every interior +unconstrained point regardless of whether the house is adjusted. + +## The on-grid consumption policy + +`E_t[u'(c_{t+1})]` needs the period-(t+1) consumption policy at the +*counterfactual* wage nodes the agent did not realise, so the realised sample +path alone is not enough. The policy is reconstructed from a second simulation +seeded over the full `(liquid, housing, wage)` product grid: each subject's +period-`p` row records its chosen consumption, giving per-`(period, wage)` +samples that are linearly interpolated in `(liquid, housing)` to evaluate +`c_{t+1}(a', H', wage_j)`. + +pylcm's simulate is grid-restricted for **all** solvers (so is the App.1 FUES +column), so the magnitude at coarse grids is *coarse-grid*, not a methodological +ceiling β€” it falls monotonically as the grid refines. The full paper grids (NG in +{250...1000}, many wage nodes) exceed local memory and require a GPU/CI sweep, +exactly like App.1's `{1000...10000}`; the small grids here (n_grid <= ~20, <= 5 +wage nodes) run locally because the lifecycle is short. +""" + +import functools +import logging +import time +from collections.abc import Sequence + +import jax +import jax.numpy as jnp +import numpy as np +import pandas as pd +from scipy.interpolate import RegularGridInterpolator + +from lcm import TauchenAR1Process +from tests.test_models import ds_app2_housing as app2 +from tests.test_models.ds_app2_housing import HousingRegimeId + +_logger = logging.getLogger("lcm") + +# Paper Table 3 calibration (default no-tax column). +INTEREST_RATE = 0.04 +DISCOUNT_FACTOR = 0.94 +ALPHA = 0.70 +GAMMA_C = 3.5 +RHO_W = 0.82 +SIGMA_W = 0.11 +MU_W = 0.0 +N_PERIODS = 8 + + +def _wage_nodes_and_transition( + *, + rho: float = RHO_W, + sigma: float = SIGMA_W, + mu: float = MU_W, +) -> tuple[np.ndarray, np.ndarray]: + """Return the Markov wage node values and the transition-probability matrix. + + Constructed from the same `TauchenAR1Process` the model's working regime + uses (`app2.N_WAGE_NODES` Gauss-Hermite nodes), so the harness and the solve + discretise the AR1 wage identically. The Tauchen build-time grid is a NaN + placeholder resolved from the runtime `(rho, sigma, mu)` parameters. + """ + process = TauchenAR1Process(n_points=app2.N_WAGE_NODES, gauss_hermite=True) + nodes = np.asarray( + process.compute_gridpoints( + rho=jnp.asarray(rho), sigma=jnp.asarray(sigma), mu=jnp.asarray(mu) + ) + ) + transition = np.asarray( + process.compute_transition_probs( + rho=jnp.asarray(rho), sigma=jnp.asarray(sigma), mu=jnp.asarray(mu) + ) + ) + return nodes, transition + + +def _nearest_wage_index(wage_values: np.ndarray, nodes: np.ndarray) -> np.ndarray: + """Map each (possibly rounded) path wage value to its wage-node index.""" + return np.abs(wage_values[:, None] - nodes[None, :]).argmin(axis=1) + + +@functools.cache +def _build_solved( + *, + n_grid: int, + n_periods: int, + n_consumption: int, + tau: float, + liquid_batch_size: int = 0, + outer_batch_size: int = 0, +): + """Build and solve the App.2 NEGM housing model, caching the solution.""" + model = app2.build_model( + n_grid=n_grid, + n_periods=n_periods, + n_consumption=n_consumption, + liquid_batch_size=liquid_batch_size, + outer_batch_size=outer_batch_size, + ) + params = app2.build_params(tau=tau) + solution = model.solve(params=params, log_level="off") + return model, params, solution + + +def app2_negm_timing( + *, + n_grid: int, + n_periods: int = N_PERIODS, + n_consumption: int = 400, + tau: float = 0.07, + n_runs: int = 3, + liquid_batch_size: int = 0, + outer_batch_size: int = 0, +) -> dict[str, float]: + """Measure compile and steady-state run time of one NEGM solve. + + The first solve times compile-plus-run; later solves of the same model reuse + the cached executable and time pure execution, so the compile cost is the + difference. Every solve is forced to completion with `block_until_ready`. + + `liquid_batch_size`/`outer_batch_size > 0` chunk the liquid Euler grid and the + NEGM outer durable search to bound peak device memory at large `n_grid`; both + leave the solved value function unchanged. + """ + model = app2.build_model( + n_grid=n_grid, + n_periods=n_periods, + n_consumption=n_consumption, + liquid_batch_size=liquid_batch_size, + outer_batch_size=outer_batch_size, + ) + params = app2.build_params(tau=tau) + + jax.clear_caches() + start = time.perf_counter() + jax.block_until_ready(model.solve(params=params, log_level="off")) + compile_plus_run = time.perf_counter() - start + + runtimes = [] + for _ in range(n_runs): + start = time.perf_counter() + jax.block_until_ready(model.solve(params=params, log_level="off")) + runtimes.append(time.perf_counter() - start) + runtime = min(runtimes) + + result = {"compile_time": compile_plus_run - runtime, "runtime": runtime} + _logger.info( + "DS App.2 NEGM timing: n_grid=%d -> compile=%.3fs run=%.3fs", + n_grid, + result["compile_time"], + result["runtime"], + ) + return result + + +def _liquid_housing_grids(model) -> tuple[np.ndarray, np.ndarray]: + """Return the working regime's liquid and housing grid node arrays.""" + working = model.user_regimes["working"] + liquid = np.asarray(working.states["liquid"].to_jax()) + housing = np.asarray(working.states["housing"].to_jax()) + return liquid, housing + + +# Cap on the per-axis resolution of the policy-reconstruction seed grid. The +# panel simulate argmaxes over (consumption x housing_investment) per seeded +# subject, so a full liquid x housing seed at paper NG (NG^2 subjects) blows up +# device memory; a capped seed grid keeps the panel small while still resolving +# the consumption policy for linear interpolation. +_MAX_POLICY_SEED_POINTS = 16 + +# Chunk the forward-simulation subject axis so the grid-restricted argmax over the +# `(consumption x housing_investment)` action space β€” `n_consumption x NG` combos +# per subject β€” stays within device memory at paper-scale NG. Subject batching is +# value-invariant (the per-subject RNG is independent of the chunk shape), so the +# scored Euler error is unchanged; it only bounds the simulate's peak memory. +_SIMULATE_SUBJECT_BATCH_SIZE = 256 + + +def _subsample(grid: np.ndarray, max_points: int) -> np.ndarray: + """Return at most `max_points` evenly-spaced nodes of `grid`, ends included.""" + if len(grid) <= max_points: + return grid + index = np.unique(np.linspace(0, len(grid) - 1, max_points).round().astype(int)) + return grid[index] + + +def _policy_interpolators( + *, + model, + params, + solution, + liquid_grid: np.ndarray, + housing_grid: np.ndarray, + wage_nodes: np.ndarray, + n_periods: int, + seed: int, +) -> dict[tuple[int, int], RegularGridInterpolator]: + """Build a per-`(period, wage)` consumption interpolator over `(liquid, housing)`. + + The period-`p` consumption policy is read off a fresh simulation seeded over a + `(liquid, housing, wage)` *regular* grid at period `p`'s age: the first + simulated period then lands exactly on that regular grid, so its chosen + consumption reshapes into a `RegularGridInterpolator` on `(liquid, housing)` + per wage node. Seeding once at age 0 and reading later periods would not work + β€” the agent evolves off the regular grid after period 0. The seed grid is + subsampled to `_MAX_POLICY_SEED_POINTS` per axis so the panel stays within + device memory at paper-scale NG; the policy is smooth enough that the coarser + interpolation grid is adequate. + """ + liquid_grid = _subsample(liquid_grid, _MAX_POLICY_SEED_POINTS) + housing_grid = _subsample(housing_grid, _MAX_POLICY_SEED_POINTS) + liquid = np.repeat(liquid_grid, len(housing_grid) * len(wage_nodes)) + housing = np.tile(np.repeat(housing_grid, len(wage_nodes)), len(liquid_grid)) + wage = np.tile(wage_nodes, len(liquid_grid) * len(housing_grid)) + n_subjects = liquid.size + expected = len(liquid_grid) * len(housing_grid) + ages = model.ages.exact_values + + interpolators: dict[tuple[int, int], RegularGridInterpolator] = {} + for period in range(n_periods): + initial_conditions = { + "liquid": jnp.asarray(liquid), + "housing": jnp.asarray(housing), + "wage": jnp.asarray(wage), + "age": jnp.full(n_subjects, float(ages[period])), + "regime_id": jnp.full(n_subjects, HousingRegimeId.working, dtype=jnp.int32), + } + panel = ( + model.simulate( + params=params, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=solution, + log_level="off", + seed=seed, + subject_batch_size=_SIMULATE_SUBJECT_BATCH_SIZE, + ) + .to_dataframe() + .query(f"period == {period} and regime_name == 'working'") + ) + if panel.empty: + continue + panel = panel.copy() + panel["wage_index"] = _nearest_wage_index(panel["wage"].to_numpy(), wage_nodes) + for wage_index, cell in panel.groupby("wage_index", observed=True): + if len(cell) != expected: + continue + grid = ( + cell.sort_values(["liquid", "housing"])["consumption"] + .to_numpy() + .reshape(len(liquid_grid), len(housing_grid)) + ) + interpolators[(int(period), int(wage_index))] = RegularGridInterpolator( + (liquid_grid, housing_grid), + grid, + bounds_error=False, + fill_value=None, + ) + return interpolators + + +def _expected_next_marginal_utility( + *, + interpolators: dict[tuple[int, int], RegularGridInterpolator], + wage_transition: np.ndarray, + source_wage_index: int, + next_period: int, + next_liquid: float, + next_housing: float, + n_wage_nodes: int, + alpha: float, + gamma_c: float, +) -> float: + """Transition-weighted expected next-period consumption marginal utility. + + Sums `P[source_wage, j] * alpha*c_{next}(a', H', j)^{-gamma_C}` over the next-period + wage nodes `j`. Returns NaN when any positive-probability next-wage cell has + no interpolator (so the path point is dropped, not scored against a + fabricated value). + """ + expected_marginal = 0.0 + for next_wage_index in range(n_wage_nodes): + probability = wage_transition[source_wage_index, next_wage_index] + if probability <= 0.0: + continue + interpolator = interpolators.get((next_period, next_wage_index)) + if interpolator is None: + return float("nan") + next_consumption = float(interpolator([[next_liquid, next_housing]])[0]) + if not np.isfinite(next_consumption) or next_consumption <= 0.0: + return float("nan") + expected_marginal += probability * (alpha * next_consumption ** (-gamma_c)) + return expected_marginal + + +def sample_path_euler_error( + *, + sample_panel: pd.DataFrame, + interpolators: dict[tuple[int, int], RegularGridInterpolator], + wage_nodes: np.ndarray, + wage_transition: np.ndarray, + interest_rate: float = INTEREST_RATE, + discount_factor: float = DISCOUNT_FACTOR, + alpha: float = ALPHA, + gamma_c: float = GAMMA_C, +) -> float: + """Mean log10 stochastic consumption Euler error along a simulated path. + + For each interior, unconstrained working-to-working transition the conditional + expectation of next-period marginal utility is summed over the next-period + wage nodes weighted by the wage transition probabilities, + + E_t[u'(c_{t+1})] + = sum_j P[wage_t, j] * alpha*c_{t+1}(a', H', wage_j)^{-gamma_C}, + + with `c_{t+1}` the period-(t+1) consumption policy interpolated in + `(liquid, housing)`. The implied consumption is + `c_euler_t = (beta*(1+r)*E_t[u'(c_{t+1})] / alpha)^{-1/gamma_C}` and the metric is + `mean(log10(|c_euler_t / c_t - 1|))`. + + Args: + sample_panel: Long-format simulation panel of the scored sample path, with + columns `subject_id`, `period`, `regime_name`, `liquid`, `housing`, + `wage`, and `consumption`. + interpolators: Mapping of `(period, wage_index)` to the period's + consumption-policy `RegularGridInterpolator` over `(liquid, housing)`, + from `_policy_interpolators`. + wage_nodes: Array of discretised log-wage node values. + wage_transition: Wage transition-probability matrix `P[i, j]`. + interest_rate: Net liquid return `r`. + discount_factor: Discount factor `beta`. + alpha: Consumption weight in the separable CES utility. + gamma_c: Consumption CRRA curvature `gamma_C` (so `u'(c) = alpha*c^{-gamma_C}`). + + Returns: + The mean base-10 log relative consumption Euler error over the valid + working-regime sample-path points. + """ + working = sample_panel.query("regime_name == 'working'").copy() + working = working.sort_values(["subject_id", "period"]).reset_index(drop=True) + + subject = working["subject_id"].to_numpy() + period = working["period"].to_numpy() + consumption = working["consumption"].to_numpy() + liquid = working["liquid"].to_numpy() + housing = working["housing"].to_numpy() + wage_value = working["wage"].to_numpy() + wage_index = _nearest_wage_index(wage_value, wage_nodes) + + same_subject = subject[:-1] == subject[1:] + consecutive = period[1:] == period[:-1] + 1 + has_next = np.zeros(consumption.shape, dtype=bool) + has_next[:-1] = same_subject & consecutive + + errors: list[float] = [] + for t in range(len(working) - 1): + if not has_next[t]: + continue + if working["regime_name"].iloc[t + 1] != "working": + continue + next_liquid = liquid[t + 1] + next_housing = housing[t + 1] + if next_liquid <= 1e-4 or consumption[t] <= 0.0: + continue + + expected_marginal = _expected_next_marginal_utility( + interpolators=interpolators, + wage_transition=wage_transition, + source_wage_index=int(wage_index[t]), + next_period=int(period[t + 1]), + next_liquid=float(next_liquid), + next_housing=float(next_housing), + n_wage_nodes=wage_nodes.size, + alpha=alpha, + gamma_c=gamma_c, + ) + if not np.isfinite(expected_marginal) or expected_marginal <= 0.0: + continue + + consumption_euler = ( + discount_factor * (1.0 + interest_rate) * expected_marginal / alpha + ) ** (-1.0 / gamma_c) + relative_error = abs(consumption_euler / consumption[t] - 1.0) + if relative_error > 0.0: + errors.append(np.log10(relative_error)) + + if not errors: + msg = "No valid interior working-regime points to score the Euler error." + raise ValueError(msg) + return float(np.mean(errors)) + + +def app2_negm_euler_error( + *, + n_grid: int, + n_periods: int = N_PERIODS, + n_consumption: int = 400, + n_subjects: int = 400, + tau: float = 0.07, + seed: int = 0, + interest_rate: float = INTEREST_RATE, + discount_factor: float = DISCOUNT_FACTOR, + alpha: float = ALPHA, + gamma_c: float = GAMMA_C, + liquid_batch_size: int = 0, + outer_batch_size: int = 0, +) -> float: + """Solve the App.2 NEGM housing model and score the consumption Euler error. + + Solves the continuous-housing model with the nested-EGM solver, simulates a + sample path and a full-grid policy panel, and returns the mean log10 + stochastic consumption Euler error along the sample path. The wage being + Markov, the Euler expectation is a transition-probability-weighted sum over + next-period wage nodes (see `sample_path_euler_error`). + + Args: + n_grid: Number of liquid/housing/outer grid points per axis. + n_periods: Number of model periods. + n_consumption: Number of inner consumption-grid points. + n_subjects: Number of simulated sample paths. + tau: Proportional housing-transaction cost. + seed: Simulation seed. + interest_rate: Net liquid return `r`. + discount_factor: Discount factor `beta`. + alpha: Consumption weight in the separable CES utility. + gamma_c: Consumption CRRA curvature `gamma_C`. + + Returns: + The mean log10 consumption Euler error along the simulated sample path. + """ + model, params, solution = _build_solved( + n_grid=n_grid, + n_periods=n_periods, + n_consumption=n_consumption, + tau=tau, + liquid_batch_size=liquid_batch_size, + outer_batch_size=outer_batch_size, + ) + wage_nodes, wage_transition = _wage_nodes_and_transition() + liquid_grid, housing_grid = _liquid_housing_grids(model) + + sample_panel = _simulate_sample_path( + model=model, + params=params, + solution=solution, + n_subjects=n_subjects, + liquid_grid=liquid_grid, + housing_grid=housing_grid, + wage_nodes=wage_nodes, + seed=seed, + ) + interpolators = _policy_interpolators( + model=model, + params=params, + solution=solution, + liquid_grid=liquid_grid, + housing_grid=housing_grid, + wage_nodes=wage_nodes, + n_periods=n_periods, + seed=seed, + ) + + error = sample_path_euler_error( + sample_panel=sample_panel, + interpolators=interpolators, + wage_nodes=wage_nodes, + wage_transition=wage_transition, + interest_rate=interest_rate, + discount_factor=discount_factor, + alpha=alpha, + gamma_c=gamma_c, + ) + _logger.info( + "DS App.2 NEGM Euler error: n_grid=%d -> %.3f", + n_grid, + error, + ) + return error + + +def _simulate_sample_path( + *, + model, + params, + solution, + n_subjects: int, + liquid_grid: np.ndarray, + housing_grid: np.ndarray, + wage_nodes: np.ndarray, + seed: int, +) -> pd.DataFrame: + """Simulate a spread of working subjects at the median wage node.""" + rng = np.random.default_rng(seed) + median_wage = float(wage_nodes[len(wage_nodes) // 2]) + initial_conditions = { + "liquid": jnp.asarray( + rng.uniform(2.0, float(liquid_grid[-1]) * 0.6, n_subjects) + ), + "housing": jnp.asarray(rng.choice(housing_grid[1:], n_subjects)), + "wage": jnp.full(n_subjects, median_wage), + "age": jnp.full(n_subjects, float(model.ages.exact_values[0])), + "regime_id": jnp.full(n_subjects, HousingRegimeId.working, dtype=jnp.int32), + } + result = model.simulate( + params=params, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=solution, + log_level="off", + seed=seed, + subject_batch_size=_SIMULATE_SUBJECT_BATCH_SIZE, + ) + return result.to_dataframe() + + +def app2_negm_accuracy_table( + *, + n_grids: Sequence[int] = (12, 18), + n_periods: int = N_PERIODS, + n_consumption: int = 400, + n_subjects: int = 400, + tau: float = 0.07, + seed: int = 0, +) -> pd.DataFrame: + """Run the NEGM Euler-error sweep across per-axis grid sizes. + + One solve+simulate per grid size. The paper grids (NG in {250...1000}) exceed + local memory and require a GPU sweep; pass smaller `n_grids` for a local run. + + Args: + n_grids: Per-axis grid sizes to sweep. + n_periods: Number of model periods. + n_consumption: Number of inner consumption-grid points. + n_subjects: Number of simulated sample paths per cell. + tau: Proportional housing-transaction cost. + seed: Simulation seed. + + Returns: + Long-format DataFrame with columns `n_grid` and `negm_euler_error`. + """ + rows = [ + { + "n_grid": n_grid, + "negm_euler_error": app2_negm_euler_error( + n_grid=n_grid, + n_periods=n_periods, + n_consumption=n_consumption, + n_subjects=n_subjects, + tau=tau, + seed=seed, + ), + } + for n_grid in n_grids + ] + return pd.DataFrame(rows) diff --git a/benchmarks/ds_replication/app3_discrete_housing_accuracy.py b/benchmarks/ds_replication/app3_discrete_housing_accuracy.py new file mode 100644 index 000000000..8c0aab7fe --- /dev/null +++ b/benchmarks/ds_replication/app3_discrete_housing_accuracy.py @@ -0,0 +1,690 @@ +"""Euler-error accuracy harness for Dobrescu & Shanker (2026) Application 3. + +Application 3 of the FUES paper is the discrete-housing model of DS Section 2.3 +(an extended Fella 2014): a finite-horizon consumption-savings problem with a +*discrete* housing stock, an own-vs-rent choice, a proportional +housing-adjustment cost, and a **stochastic (Markov) wage**. This module scores +the **VFI / grid-search (GridSearch)** column of the paper's no-tax accuracy +tables (Table 4 / Table 7): it builds the brute variant of +`tests.test_models.ds_app3_discrete_housing`, solves it by backward induction, +simulates a sample path, and scores the consumption Euler equation along it. + +## The stochastic Euler equation + +The interior, unconstrained consumption Euler equation is + + u'(c_t) = beta * (1 + r) * E_t[u'(c_{t+1})], + +with `u(c, h) = alpha * log(c) + (1 - alpha) * log(kappa * (h + iota))`, so the +consumption marginal utility is `u'(c) = alpha / c` and the housing-service term +drops out. The **key difference from Application 1** is the wage: it is a Markov +process, so the conditional expectation `E_t[u'(c_{t+1})]` is *not* the realized +next-period marginal utility β€” it is a sum over next-period wage nodes weighted +by the wage transition probabilities, + + E_t[u'(c_{t+1})] = sum_j P[wage_node_t, j] * u'( c_{t+1}(a', H', wage_j) ), + +evaluated at the chosen post-decision financial assets `a'` and next-period +housing `H' = housing_choice` held fixed, with `c_{t+1}(., H', wage_j)` the +period-(t+1) consumption policy on the asset grid for that `(housing, wage)` +cell. The implied consumption is then + + c_euler_t = alpha / ( beta * (1 + r) * E_t[u'(c_{t+1})] ), + +and the metric is `mean(log10(|c_euler_t / c_t - 1|))` over the valid points +(Judd 1992). + +## Valid points + +Mirroring Application 1, a path point is scored only where the continuous +consumption Euler equation governs the optimum: + +- the subject is in the working regime this period and the next (the terminal + bequest regime is excluded); +- consumption is interior and unconstrained β€” chosen consumption leaves strictly + positive financial savings, so the no-borrowing constraint does not bind; +- housing is *not* adjusted this period and is *not* adjusted next period + (`housing == housing_choice` at both `t` and `t+1`) β€” the discrete + housing-switch margin is a kink in the value function, exactly like + Application 1 excludes the work/retire switch. + +## The on-grid consumption policy + +`E_t[u'(c_{t+1})]` needs the period-(t+1) consumption policy evaluated at the +*counterfactual* wage nodes the agent did not realise, so the realized sample +path alone is not enough. The policy is reconstructed from a second simulation +seeded at the full `(assets, housing, wage)` product grid: each subject's +period-`p` row records `c_p` at its period-`p` state, giving per-period +`(housing, wage) -> [(assets, consumption)]` samples that are linearly +interpolated in assets to evaluate `c_{t+1}(a', H', wage_j)`. + +The full paper grids ({2000, 4000, ...} asset points, 7 wage nodes, T=20) are a +GPU/CI sweep; the small grids here (asset points <= ~80, wage nodes <= 5) are +local-safe because T=20 is short. The FUES/MSS/LTM columns of Table 4 are +kernel-gated on `feat/dcegm` and are *not* produced here β€” this module produces +the VFI column only. +""" + +import functools +import logging +import time +from collections.abc import Sequence + +import jax +import jax.numpy as jnp +import numpy as np +import pandas as pd + +from lcm import RouwenhorstAR1Process +from tests.test_models import ds_app3_discrete_housing as app3 +from tests.test_models.ds_app3_discrete_housing import ( + DiscreteHousingRegimeId, + Housing, +) + +_logger = logging.getLogger("lcm") + +# Paper Table 4/7 calibration (no tax). +INTEREST_RATE = 0.06 +DISCOUNT_FACTOR = 0.93 +ALPHA = 0.77 +RHO_W = 0.977 +SIGMA_W = 0.063 +MU_W = 0.0 +ASSET_MAX = 40.0 +N_PERIODS = 20 + + +def _wage_nodes_and_transition( + *, + n_wage_nodes: int, + rho: float = RHO_W, + sigma: float = SIGMA_W, + mu: float = MU_W, +) -> tuple[np.ndarray, np.ndarray]: + """Return the Markov wage node values and the transition-probability matrix. + + The node values are the discretised log-wage grid and the matrix `P[i, j]` + is the probability of moving from wage node `i` to node `j`, both from the + same Rouwenhorst discretisation the model's wage process uses. + """ + process = RouwenhorstAR1Process(n_points=n_wage_nodes, rho=rho, sigma=sigma, mu=mu) + nodes = np.asarray( + process.compute_gridpoints( + rho=jnp.asarray(rho), sigma=jnp.asarray(sigma), mu=jnp.asarray(mu) + ) + ) + transition = np.asarray( + process.compute_transition_probs( + rho=jnp.asarray(rho), sigma=jnp.asarray(sigma), mu=jnp.asarray(mu) + ) + ) + return nodes, transition + + +def _nearest_wage_index(wage_values: np.ndarray, nodes: np.ndarray) -> np.ndarray: + """Map each (possibly rounded) path wage value to its wage-node index.""" + return np.abs(wage_values[:, None] - nodes[None, :]).argmin(axis=1) + + +def _full_grid_initial_conditions( + *, + n_assets: int, + asset_max: float, + wage_nodes: np.ndarray, +) -> dict: + """Seed one subject at every `(assets, housing, wage)` product-grid cell. + + Simulating from this seeding records, at each period, the consumption policy + at every discrete `(housing, wage)` cell over a spread of asset values β€” the + on-grid policy lookup the stochastic Euler expectation interpolates. + """ + asset_nodes = np.linspace(0.0, asset_max, n_assets) + housing_codes = np.arange(len(Housing.__annotations__)) + assets = np.repeat(asset_nodes, len(housing_codes) * len(wage_nodes)) + housing = np.tile(np.repeat(housing_codes, len(wage_nodes)), len(asset_nodes)) + wage = np.tile(wage_nodes, len(asset_nodes) * len(housing_codes)) + n_subjects = assets.size + return { + "assets": jnp.asarray(assets), + "housing": jnp.asarray(housing, dtype=jnp.int32), + "wage": jnp.asarray(wage), + "age": jnp.zeros(n_subjects), + "regime_id": jnp.full( + n_subjects, DiscreteHousingRegimeId.working, dtype=jnp.int32 + ), + } + + +def _policy_lookup( + *, + policy_panel: pd.DataFrame, + wage_nodes: np.ndarray, +) -> dict[tuple[int, int, int], tuple[np.ndarray, np.ndarray]]: + """Build a per-`(period, housing, wage)` sorted `(assets, consumption)` policy. + + Each cell maps to the sorted financial-asset samples and the consumption the + policy chose there, ready for linear interpolation at an arbitrary `a'`. + """ + working = policy_panel.query("regime_name == 'working'").copy() + housing_codes = {name: idx for idx, name in enumerate(Housing.__annotations__)} + working["housing_code"] = working["housing"].map(housing_codes).to_numpy() + working["wage_index"] = _nearest_wage_index(working["wage"].to_numpy(), wage_nodes) + + lookup: dict[tuple[int, int, int], tuple[np.ndarray, np.ndarray]] = {} + grouped = working.groupby(["period", "housing_code", "wage_index"], observed=True) + for (period, housing_code, wage_index), cell in grouped: + order = np.argsort(cell["assets"].to_numpy()) + assets = cell["assets"].to_numpy()[order] + consumption = cell["consumption"].to_numpy()[order] + lookup[(int(period), int(housing_code), int(wage_index))] = ( + assets, + consumption, + ) + return lookup + + +def _interp_policy( + *, + lookup: dict[tuple[int, int, int], tuple[np.ndarray, np.ndarray]], + period: int, + housing_code: int, + wage_index: int, + assets: float, +) -> float: + """Linearly interpolate the consumption policy of a cell at `assets`. + + Returns NaN when the cell has no policy samples (the agent never visits that + `(period, housing, wage)` cell in the full-grid simulation), so the point is + dropped from the Euler score rather than scored against a fabricated value. + """ + key = (period, housing_code, wage_index) + if key not in lookup: + return float("nan") + asset_samples, consumption_samples = lookup[key] + if asset_samples.size == 0: + return float("nan") + return float(np.interp(assets, asset_samples, consumption_samples)) + + +def _expected_next_marginal_utility( + *, + lookup: dict[tuple[int, int, int], tuple[np.ndarray, np.ndarray]], + wage_transition: np.ndarray, + source_wage_index: int, + next_period: int, + next_housing_code: int, + next_assets: float, + n_wage_nodes: int, + alpha: float, +) -> float: + """Transition-weighted expected next-period consumption marginal utility. + + Sums `P[source_wage, j] * alpha / c_{next}(next_assets, next_housing, j)` + over the next-period wage nodes `j`. Returns NaN when any positive-probability + next-wage cell has no policy sample (so the path point is dropped rather than + scored against a fabricated value). + """ + expected_marginal = 0.0 + for next_wage_index in range(n_wage_nodes): + probability = wage_transition[source_wage_index, next_wage_index] + if probability <= 0.0: + continue + next_consumption = _interp_policy( + lookup=lookup, + period=next_period, + housing_code=next_housing_code, + wage_index=next_wage_index, + assets=next_assets, + ) + if not np.isfinite(next_consumption) or next_consumption <= 0.0: + return float("nan") + expected_marginal += probability * (alpha / next_consumption) + return expected_marginal + + +def _euler_marginal_return( + *, next_assets: float, interest_rate: float, use_taxes: bool +) -> float: + """Marginal return on a unit of saving, `1 + r - T'(a')`. + + Without taxes the gross return `1 + r`. With the piecewise-linear capital-income + tax `T`, a unit of saving nets the realized bracket marginal rate + `tau_k = T'(a')`, so the interior consumption Euler equation discounts by + `1 + r - tau_k`. The bracket of `a'` is selected left-closed, matching + `piecewise_capital_income_tax`. + """ + if not use_taxes: + return 1.0 + interest_rate + bracket = min( + max( + int(np.searchsorted(app3.TAX_BRACKET_LOWER, next_assets, side="right")) - 1, + 0, + ), + len(app3.TAX_BRACKET_LOWER) - 1, + ) + return 1.0 + interest_rate - app3.TAX_BRACKET_RATE[bracket] + + +def _is_near_tax_notch(*, next_assets: float, tol: float) -> bool: + """Whether `next_assets` sits within `tol` of a tax-bracket boundary. + + At a bracket boundary the capital-income tax's level jump makes `T'` ill-defined + (a one-sided derivative against a discontinuity), so the smooth Euler equality + does not apply and the point is excluded from the with-tax score. + """ + return any(abs(next_assets - lower) <= tol for lower in app3.TAX_BRACKET_LOWER[1:]) + + +def sample_path_euler_error( # noqa: C901 + *, + sample_panel: pd.DataFrame, + policy_panel: pd.DataFrame, + wage_nodes: np.ndarray, + wage_transition: np.ndarray, + interest_rate: float = INTEREST_RATE, + discount_factor: float = DISCOUNT_FACTOR, + alpha: float = ALPHA, + use_taxes: bool = False, + tax_notch_tol: float = 1e-3, +) -> float: + """Mean log10 stochastic consumption Euler error along a simulated path. + + For each interior, unconstrained, non-housing-switch working-to-working + transition the conditional expectation of next-period marginal utility is + summed over the next-period wage nodes weighted by the wage transition + probabilities, + + E_t[u'(c_{t+1})] = sum_j P[wage_t, j] * alpha / c_{t+1}(a', H', wage_j), + + with `c_{t+1}(., H', wage_j)` the period-(t+1) consumption policy of the + `(H', wage_j)` cell interpolated at the chosen post-decision financial + assets `a' = assets_t - consumption_t + (1 + r) * (...)` read off the path as + the next period's `assets`. The implied consumption is + `c_euler_t = alpha / (beta * (1 + r - T'(a')) * E_t[u'(c_{t+1})])` and the metric + is `mean(log10(|c_euler_t / c_t - 1|))`. Without taxes `T' = 0` and the return is + the gross `1 + r`; with taxes the realized bracket marginal rate enters and points + whose `a'` sits on a bracket boundary are excluded. + + Args: + sample_panel: Long-format simulation panel of the scored sample path, + with columns `subject_id`, `period`, `regime_name`, `assets`, + `housing`, `wage`, `consumption`, and `housing_choice`. + policy_panel: Long-format simulation panel seeded over the full + `(assets, housing, wage)` grid, used to reconstruct the per-period + on-grid consumption policy. + wage_nodes: Array of discretised log-wage node values. + wage_transition: Wage transition-probability matrix `P[i, j]`. + interest_rate: Net financial return `r`. + discount_factor: Discount factor `beta`. + alpha: Consumption weight in the Cobb-Douglas log utility (so + `u'(c) = alpha / c`). + use_taxes: Whether the model carries the piecewise capital-income tax. When + `True`, the Euler return is `1 + r - T'(a')` (the realized bracket + marginal rate) and points whose `a'` lands on a bracket boundary are + dropped; when `False`, the gross return `1 + r` is used (Table 4/7 path). + tax_notch_tol: Half-width of the excluded neighborhood around each tax-bracket + boundary, in asset units. Only consulted when `use_taxes` is `True`. + + Returns: + The mean base-10 log relative consumption Euler error over the valid + working-regime sample-path points. + """ + lookup = _policy_lookup(policy_panel=policy_panel, wage_nodes=wage_nodes) + housing_codes = {name: idx for idx, name in enumerate(Housing.__annotations__)} + + working = sample_panel.query("regime_name == 'working'").copy() + working = working.sort_values(["subject_id", "period"]).reset_index(drop=True) + + subject = working["subject_id"].to_numpy() + period = working["period"].to_numpy() + consumption = working["consumption"].to_numpy() + assets = working["assets"].to_numpy() + wage_value = working["wage"].to_numpy() + housing = working["housing"].to_numpy() + housing_choice = working["housing_choice"].to_numpy() + wage_index = _nearest_wage_index(wage_value, wage_nodes) + + # The next row is the same subject's next period when it is consecutive and + # the same subject. + same_subject = subject[:-1] == subject[1:] + consecutive = period[1:] == period[:-1] + 1 + has_next = np.zeros(consumption.shape, dtype=bool) + has_next[:-1] = same_subject & consecutive + + errors: list[float] = [] + for t in range(len(working) - 1): + if not has_next[t]: + continue + if working["regime_name"].iloc[t + 1] != "working": + continue + # Interior, unconstrained: the post-decision financial savings carried + # forward as next period's assets are strictly positive, so chosen + # consumption did not exhaust resources and the no-borrowing constraint + # is slack. The constrained margin holds with a multiplier, not the plain + # Euler equation, so it is dropped. + next_assets = assets[t + 1] + if next_assets <= 1e-6: + continue + # At a tax-bracket boundary `T'` is ill-defined (one-sided against the level + # jump), so the smooth Euler equality does not apply there. + if use_taxes and _is_near_tax_notch( + next_assets=float(next_assets), tol=tax_notch_tol + ): + continue + # No housing switch this period and next: the discrete housing-adjustment + # margin is a value-function kink the smooth Euler equation skips. + if housing[t] != housing_choice[t]: + continue + if housing[t + 1] != housing_choice[t + 1]: + continue + + expected_marginal = _expected_next_marginal_utility( + lookup=lookup, + wage_transition=wage_transition, + source_wage_index=int(wage_index[t]), + next_period=int(period[t + 1]), + next_housing_code=housing_codes[housing_choice[t]], + next_assets=float(next_assets), + n_wage_nodes=wage_nodes.size, + alpha=alpha, + ) + if not np.isfinite(expected_marginal) or expected_marginal <= 0.0: + continue + + marginal_return = _euler_marginal_return( + next_assets=float(next_assets), + interest_rate=interest_rate, + use_taxes=use_taxes, + ) + consumption_euler = alpha / ( + discount_factor * marginal_return * expected_marginal + ) + relative_error = abs(consumption_euler / consumption[t] - 1.0) + if relative_error > 0.0: + errors.append(np.log10(relative_error)) + + if not errors: + msg = "No valid interior working-regime points to score the Euler error." + raise ValueError(msg) + return float(np.mean(errors)) + + +@functools.cache +def _build_solved( + *, + n_assets: int, + n_wage_nodes: int, + n_periods: int, + n_consumption: int, + asset_max: float, + tau: float, + variant: str = "brute", + upper_envelope: str = "fues", + use_taxes: bool = False, +): + """Build and solve the App.3 model (brute or DC-EGM), caching the solution.""" + model = app3.build_model( + variant=variant, + n_assets=n_assets, + n_wage_nodes=n_wage_nodes, + n_periods=n_periods, + n_consumption=n_consumption, + asset_max=asset_max, + upper_envelope=upper_envelope, + use_taxes=use_taxes, + ) + params = app3.build_params( + variant=variant, n_periods=n_periods, tau=tau, use_taxes=use_taxes + ) + solution = model.solve(params=params, log_level="off") + return model, params, solution + + +def app3_timing( + *, + n_assets: int, + n_wage_nodes: int = 5, + n_periods: int = N_PERIODS, + n_consumption: int = 60, + asset_max: float = ASSET_MAX, + tau: float = 0.07, + variant: str = "dcegm", + upper_envelope: str = "fues", + use_taxes: bool = False, + n_runs: int = 3, +) -> dict[str, float]: + """Measure compile and steady-state run time of one App.3 solve. + + The first solve times compile-plus-run; later solves of the same model reuse + the cached executable and time pure execution, so the compile cost is the + difference. Every solve is forced to completion with `block_until_ready`. + """ + model = app3.build_model( + variant=variant, + n_assets=n_assets, + n_wage_nodes=n_wage_nodes, + n_periods=n_periods, + n_consumption=n_consumption, + asset_max=asset_max, + upper_envelope=upper_envelope, + use_taxes=use_taxes, + ) + params = app3.build_params( + variant=variant, n_periods=n_periods, tau=tau, use_taxes=use_taxes + ) + + jax.clear_caches() + start = time.perf_counter() + jax.block_until_ready(model.solve(params=params, log_level="off")) + compile_plus_run = time.perf_counter() - start + + runtimes = [] + for _ in range(n_runs): + start = time.perf_counter() + jax.block_until_ready(model.solve(params=params, log_level="off")) + runtimes.append(time.perf_counter() - start) + runtime = min(runtimes) + + result = {"compile_time": compile_plus_run - runtime, "runtime": runtime} + _logger.info( + "DS App.3 %s timing (use_taxes=%s): n_assets=%d -> compile=%.3fs run=%.3fs", + upper_envelope.upper() if variant == "dcegm" else "VFI", + use_taxes, + n_assets, + result["compile_time"], + result["runtime"], + ) + return result + + +def app3_vfi_euler_error( + *, + n_assets: int, + n_wage_nodes: int = 5, + n_periods: int = N_PERIODS, + n_consumption: int = 60, + n_subjects: int = 400, + asset_max: float = ASSET_MAX, + tau: float = 0.07, + seed: int = 0, + interest_rate: float = INTEREST_RATE, + discount_factor: float = DISCOUNT_FACTOR, + alpha: float = ALPHA, + variant: str = "brute", + upper_envelope: str = "fues", + use_taxes: bool = False, +) -> float: + """Solve the App.3 model (brute or DC-EGM) and score the consumption Euler error. + + Solves the discrete-housing model by grid search (VFI), simulates a sample + path and a full-grid policy panel, and returns the mean log10 stochastic + consumption Euler error along the sample path. The wage being Markov, the + Euler expectation is a transition-probability-weighted sum over next-period + wage nodes (see `sample_path_euler_error`). + + Args: + n_assets: Number of financial-asset grid points. + n_wage_nodes: Number of Markov wage discretisation nodes. + n_periods: Number of model periods (the paper uses `T = 20`). + n_consumption: Number of consumption-grid points the grid search scans. + n_subjects: Number of simulated sample paths. + asset_max: Upper bound of the financial-asset grid. + tau: Proportional housing-adjustment cost. + seed: Simulation seed. + interest_rate: Net financial return `r`. + discount_factor: Discount factor `beta`. + alpha: Consumption weight in the Cobb-Douglas log utility. + + Returns: + The mean log10 consumption Euler error along the simulated sample path. + """ + model, params, solution = _build_solved( + n_assets=n_assets, + n_wage_nodes=n_wage_nodes, + n_periods=n_periods, + n_consumption=n_consumption, + asset_max=asset_max, + tau=tau, + variant=variant, + upper_envelope=upper_envelope, + use_taxes=use_taxes, + ) + wage_nodes, wage_transition = _wage_nodes_and_transition(n_wage_nodes=n_wage_nodes) + + sample_panel = _simulate_sample_path( + model=model, + params=params, + solution=solution, + n_subjects=n_subjects, + asset_max=asset_max, + wage_nodes=wage_nodes, + seed=seed, + ) + policy_panel = _simulate_policy_panel( + model=model, + params=params, + solution=solution, + n_assets=n_assets, + asset_max=asset_max, + wage_nodes=wage_nodes, + seed=seed, + ) + + error = sample_path_euler_error( + sample_panel=sample_panel, + policy_panel=policy_panel, + wage_nodes=wage_nodes, + wage_transition=wage_transition, + interest_rate=interest_rate, + discount_factor=discount_factor, + alpha=alpha, + use_taxes=use_taxes, + ) + _logger.info( + "DS App.3 VFI Euler error: n_assets=%d n_wage=%d -> %.3f", + n_assets, + n_wage_nodes, + error, + ) + return error + + +def _simulate_sample_path( + *, + model, + params, + solution, + n_subjects: int, + asset_max: float, + wage_nodes: np.ndarray, + seed: int, +) -> pd.DataFrame: + """Simulate a spread of subjects starting as renters at the median wage.""" + median_wage = float(wage_nodes[len(wage_nodes) // 2]) + initial_conditions = { + "assets": jnp.linspace(0.5, asset_max / 4.0, n_subjects), + "housing": jnp.full(n_subjects, Housing.rent, dtype=jnp.int32), + "wage": jnp.full(n_subjects, median_wage), + "age": jnp.zeros(n_subjects), + "regime_id": jnp.full( + n_subjects, DiscreteHousingRegimeId.working, dtype=jnp.int32 + ), + } + result = model.simulate( + params=params, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=solution, + log_level="off", + seed=seed, + ) + return result.to_dataframe() + + +def _simulate_policy_panel( + *, + model, + params, + solution, + n_assets: int, + asset_max: float, + wage_nodes: np.ndarray, + seed: int, +) -> pd.DataFrame: + """Simulate from the full product grid to reconstruct the on-grid policy.""" + initial_conditions = _full_grid_initial_conditions( + n_assets=n_assets, asset_max=asset_max, wage_nodes=wage_nodes + ) + result = model.simulate( + params=params, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=solution, + log_level="off", + seed=seed, + ) + return result.to_dataframe() + + +def app3_vfi_accuracy_table( + *, + n_assets_grid: Sequence[int] = (40, 60, 80), + n_wage_nodes: int = 5, + n_periods: int = N_PERIODS, + n_consumption: int = 60, + n_subjects: int = 400, + seed: int = 0, +) -> pd.DataFrame: + """Run the VFI Euler-error sweep across financial-asset grid sizes. + + One solve+simulate per asset-grid size. The columns mirror the paper's + accuracy tables but report the VFI column only β€” the FUES/MSS/LTM columns are + kernel-gated on `feat/dcegm`. + + Args: + n_assets_grid: Financial-asset grid sizes to sweep. + n_wage_nodes: Number of Markov wage discretisation nodes. + n_periods: Number of model periods. + n_consumption: Number of consumption-grid points the grid search scans. + n_subjects: Number of simulated sample paths per cell. + seed: Simulation seed. + + Returns: + Long-format DataFrame with columns `n_assets`, `n_wage_nodes`, and + `vfi_euler_error`. + """ + rows = [ + { + "n_assets": n_assets, + "n_wage_nodes": n_wage_nodes, + "vfi_euler_error": app3_vfi_euler_error( + n_assets=n_assets, + n_wage_nodes=n_wage_nodes, + n_periods=n_periods, + n_consumption=n_consumption, + n_subjects=n_subjects, + seed=seed, + ), + } + for n_assets in n_assets_grid + ] + return pd.DataFrame(rows) diff --git a/benchmarks/ds_replication/ds2024_housing_comparison.py b/benchmarks/ds_replication/ds2024_housing_comparison.py new file mode 100644 index 000000000..c3ccf1b00 --- /dev/null +++ b/benchmarks/ds_replication/ds2024_housing_comparison.py @@ -0,0 +1,187 @@ +"""DS-2024 housing RFC-vs-NEGM method comparison (timing + accuracy). + +Reproduces the Dobrescu-Shanker (2024) housing-model method comparison β€” the +paper reports RFC at 19.03 s/iter against NEGM at 28.12 s/iter (RFC faster). Here +pylcm solves its *own* RFC-vs-NEGM comparison on the same housing model and +reports absolute per-method timings (compilation split from runtime, since pylcm +JIT-compiles the solve) plus a value-function accuracy check against the +grid-search (VFI) oracle: + +- the **NEGM** column is the nested-EGM solver (`ds2024_housing.py`): outer + housing search, inner liquid DC-EGM; +- the **RFC** / **FUES** columns are the discrete-housing DC-EGM + (`ds2024_housing_fues.py`) with the 1-D rooftop-cut / fast-upper-envelope-scan + backend nested over the housing grid β€” the source's per-housing-column + refinement. + +Both solve the same DS-2024 housing economics (faithful at `delta = 0`). The +comparison is timing (does RFC beat NEGM?) and accuracy (each method against the +VFI oracle), not a reproduction of the paper's absolute seconds. +""" + +import time +from dataclasses import dataclass + +import jax +import numpy as np + +from tests.test_models import ds2024_housing, ds2024_housing_fues + + +@dataclass(frozen=True) +class HousingMethodBenchmark: + """One method's compile/runtime split and accuracy at one grid resolution.""" + + method: str + """Solution-method name (`"NEGM"`, `"RFC"`, `"FUES"`).""" + n_grid: int + """Liquid / housing grid points.""" + compile_seconds: float + """Wall-clock of the first (compiling) solve minus the warm runtime.""" + runtime_seconds: float + """Wall-clock of a warm (compiled) solve to device-ready.""" + accuracy_mean_abs: float + """Mean absolute interior value-function difference from the VFI oracle.""" + + +def _time_solve(solve, n_warm: int = 2) -> tuple[float, float, dict]: + """Return `(compile_seconds, runtime_seconds, solution)` for a solve closure. + + The first call compiles and runs; the warm calls run the compiled program. + Compile time is the cold call minus the fastest warm runtime. + """ + start = time.perf_counter() + solution = solve() + jax.block_until_ready([v for regime in solution.values() for v in regime.values()]) + cold = time.perf_counter() - start + + warm_times = [] + for _ in range(n_warm): + start = time.perf_counter() + warm = solve() + jax.block_until_ready([v for regime in warm.values() for v in regime.values()]) + warm_times.append(time.perf_counter() - start) + runtime = min(warm_times) + return max(cold - runtime, 0.0), runtime, solution + + +def _interior_mean_abs(solution: dict, oracle: dict, n_grid: int) -> float: + """Mean absolute alive-regime value difference from the oracle on the interior.""" + interior = (Ellipsis, slice(3, n_grid - 2)) + differences = [] + for period in sorted(solution): + if "alive" not in solution[period]: + continue + solved = np.asarray(solution[period]["alive"])[interior] + reference = np.asarray(oracle[period]["alive"])[interior] + finite = np.isfinite(solved) & np.isfinite(reference) + differences.append(np.abs(solved - reference)[finite]) + return float(np.concatenate(differences).mean()) + + +def benchmark_ds2024_housing( + *, + n_grid: int = 12, + n_housing: int = 6, + n_consumption: int = 300, + n_periods: int = 5, +) -> list[HousingMethodBenchmark]: + """Benchmark NEGM, RFC, and FUES on the DS-2024 housing model. + + Args: + n_grid: Liquid / housing grid points. + n_housing: Discrete housing levels for the DC-EGM column. + n_consumption: Consumption-grid points for the grid-search oracle. + n_periods: Lifecycle periods. + + Returns: + List of `HousingMethodBenchmark` rows, one per method. + """ + brute_fues = ds2024_housing_fues.build_model( + variant="brute", + n_grid=n_grid, + n_housing=n_housing, + n_consumption=n_consumption, + n_periods=n_periods, + upper_envelope="rfc", + ).solve( + params=ds2024_housing_fues.build_params(variant="brute", delta=0.0), + log_level="off", + ) + + rows: list[HousingMethodBenchmark] = [] + + def negm_solve() -> dict: + model = ds2024_housing.build_model( + variant="negm", n_grid=n_grid, n_periods=n_periods + ) + return model.solve( + params=ds2024_housing.build_params(variant="negm", delta=0.0), + log_level="off", + ) + + compile_s, runtime_s, negm_solution = _time_solve(negm_solve) + # The NEGM model carries housing as a continuous state, so its oracle is its own + # grid-search twin (same continuous-housing economics). + negm_oracle = ds2024_housing.build_model( + variant="brute", n_grid=n_grid, n_periods=n_periods + ).solve( + params=ds2024_housing.build_params(variant="brute", delta=0.0), log_level="off" + ) + rows.append( + HousingMethodBenchmark( + method="NEGM", + n_grid=n_grid, + compile_seconds=compile_s, + runtime_seconds=runtime_s, + accuracy_mean_abs=_interior_mean_abs(negm_solution, negm_oracle, n_grid), + ) + ) + + for method, backend in (("RFC", "rfc"), ("FUES", "fues")): + + def dcegm_solve(backend: str = backend) -> dict: + model = ds2024_housing_fues.build_model( + variant="dcegm", + n_grid=n_grid, + n_housing=n_housing, + n_periods=n_periods, + upper_envelope=backend, + ) + return model.solve( + params=ds2024_housing_fues.build_params(variant="dcegm", delta=0.0), + log_level="off", + ) + + compile_s, runtime_s, solution = _time_solve(dcegm_solve) + rows.append( + HousingMethodBenchmark( + method=method, + n_grid=n_grid, + compile_seconds=compile_s, + runtime_seconds=runtime_s, + accuracy_mean_abs=_interior_mean_abs(solution, brute_fues, n_grid), + ) + ) + + return rows + + +def format_comparison_table(rows: list[HousingMethodBenchmark]) -> str: + """Render the housing method-comparison rows as a fixed-width table.""" + header = ( + f"{'method':<8} {'n_grid':>6} {'compile_s':>10} " + f"{'runtime_s':>10} {'accuracy':>10}" + ) + separator = "-" * len(header) + body = [ + f"{row.method:<8} {row.n_grid:>6} {row.compile_seconds:>10.3f} " + f"{row.runtime_seconds:>10.4f} {row.accuracy_mean_abs:>10.4f}" + for row in rows + ] + return "\n".join([header, separator, *body]) + + +if __name__ == "__main__": + benchmark_rows = benchmark_ds2024_housing() + print(format_comparison_table(benchmark_rows)) diff --git a/benchmarks/ds_replication/run_app2_incremental.py b/benchmarks/ds_replication/run_app2_incremental.py new file mode 100644 index 000000000..34d7b51b1 --- /dev/null +++ b/benchmarks/ds_replication/run_app2_incremental.py @@ -0,0 +1,124 @@ +"""Run the App.2 housing Table 3 sweep incrementally, one (tau, NG) row at a time. + +Each row is appended to the output markdown the instant it finishes, so a wall-clock +timeout on a short partition leaves every completed row on disk. Designed for the +A100 sgpu_devel partition where the full 2-D NEGM solve fits but the 1-hour limit may +not cover the whole 3-tau x 4-NG matrix in a single job. + +Usage (CUDA env), e.g. + + XLA_PYTHON_CLIENT_PREALLOCATE=false python -m \ + benchmarks.ds_replication.run_app2_incremental \ + --out ds_paper_tables --ngs 250 500 750 1000 --taus 0.05 0.07 0.12 + +`--liquid-batch-size > 0` chunks the liquid Euler grid to bound peak device memory. +""" + +import argparse +import logging +import time +from pathlib import Path + +from benchmarks.ds_replication.app2_fues_accuracy import ( + app2_fues_euler_error, + app2_fues_timing, +) +from benchmarks.ds_replication.app2_housing_accuracy import ( + app2_negm_euler_error, + app2_negm_timing, +) + +_logger = logging.getLogger("lcm") + +_HEADER = ( + "| NG | tau | FUES_eerr | NEGM_eerr | FUES_compile | FUES_run " + "| NEGM_compile | NEGM_run |\n" + "|---:|----:|----------:|----------:|-------------:|---------:" + "|-------------:|--------:|\n" +) + + +def _safe(label, func, **kwargs): + """Run one accuracy/timing measurement, returning None on a runtime failure. + + The FUES and NEGM columns are scored independently so a memory failure in one + method (the dense NEGM outer argmax can exceed a single GPU at large `n_grid`) + leaves the other method's number on the row instead of voiding the whole cell. + """ + try: + return func(**kwargs) + except Exception: + _logger.exception("%s failed", label) + return None + + +def _fmt(value, spec): + return format(value, spec) if value is not None else "OOM" + + +def _row(*, ng: int, tau: float, liquid_batch_size: int, outer_batch_size: int) -> str: + fues_kw = {"n_grid": ng, "tau": tau, "liquid_batch_size": liquid_batch_size} + negm_kw = {**fues_kw, "outer_batch_size": outer_batch_size} + fues_t = _safe("FUES timing", app2_fues_timing, **fues_kw) + negm_t = _safe("NEGM timing", app2_negm_timing, **negm_kw) + fues_e = _safe("FUES euler", app2_fues_euler_error, **fues_kw) + negm_e = _safe("NEGM euler", app2_negm_euler_error, **negm_kw) + fc = fues_t["compile_time"] if fues_t else None + fr = fues_t["runtime"] if fues_t else None + nc = negm_t["compile_time"] if negm_t else None + nr = negm_t["runtime"] if negm_t else None + return ( + f"| {ng} | {tau} | {_fmt(fues_e, '.4f')} | {_fmt(negm_e, '.4f')} " + f"| {_fmt(fc, '.3f')} | {_fmt(fr, '.4f')} " + f"| {_fmt(nc, '.3f')} | {_fmt(nr, '.4f')} |\n" + ) + + +def main() -> None: + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--out", type=Path, default=Path("ds_paper_tables")) + parser.add_argument("--ngs", type=int, nargs="+", default=[250, 500, 750, 1000]) + parser.add_argument("--taus", type=float, nargs="+", default=[0.05, 0.07, 0.12]) + parser.add_argument( + "--liquid-batch-size", + type=int, + default=0, + help="Chunk the liquid Euler grid to bound peak memory (0 = no chunking).", + ) + parser.add_argument( + "--outer-batch-size", + type=int, + default=0, + help="Chunk the NEGM outer durable search (0 = solve all nodes at once).", + ) + args = parser.parse_args() + logging.basicConfig(level=logging.INFO) + + args.out.mkdir(parents=True, exist_ok=True) + path = args.out / "table3_app2_housing.md" + if not path.exists(): + path.write_text("# App.2 housing β€” Table 3 (EGM-FUES vs NEGM)\n\n" + _HEADER) + + for tau in args.taus: + for ng in args.ngs: + start = time.perf_counter() + _logger.info("=== App.2 NG=%d tau=%s ===", ng, tau) + try: + row = _row( + ng=ng, + tau=tau, + liquid_batch_size=args.liquid_batch_size, + outer_batch_size=args.outer_batch_size, + ) + except Exception as exc: + row = f"| {ng} | {tau} | FAILED: {type(exc).__name__} | | | | | |\n" + _logger.exception("NG=%d tau=%s FAILED", ng, tau) + with path.open("a") as handle: + handle.write(row) + elapsed = time.perf_counter() - start + _logger.info("NG=%d tau=%s done in %.1fs -> %s", ng, tau, elapsed, path) + _logger.info("all rows done -> %s", path) + + +if __name__ == "__main__": + main() diff --git a/benchmarks/ds_replication/run_ds2024_pension.py b/benchmarks/ds_replication/run_ds2024_pension.py new file mode 100644 index 000000000..ea71e0b76 --- /dev/null +++ b/benchmarks/ds_replication/run_ds2024_pension.py @@ -0,0 +1,58 @@ +"""Reproduce the DS-2024 multidimensional pension comparison: G2EGM vs RFC. + +Dobrescu & Shanker (2024) compare solution methods for the two-asset +(liquid + pension) discrete-continuous lifecycle model on solve time and the +distribution of consumption Euler errors. The pylcm P6/P7 stack provides both a +G2EGM (four-segment KKT envelope) and an RFC (combined-cloud rooftop cut) solver +on the shared multidimensional EGM foundation; this driver sweeps the liquid grid +resolution, benchmarks both methods at each, and writes the comparison table. + +Run (CUDA env), e.g. + + XLA_PYTHON_CLIENT_PREALLOCATE=false python -m \ + benchmarks.ds_replication.run_ds2024_pension --out ds_paper_tables \ + --n-liquid 20 40 80 +""" + +import argparse +import logging +from pathlib import Path + +from _lcm.egm.ds_pension_benchmark import ( + benchmark_ds_pension_methods, + format_comparison_table, +) + +_logger = logging.getLogger("lcm") + + +def main() -> None: + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--out", type=Path, default=Path("ds_paper_tables")) + parser.add_argument("--n-liquid", type=int, nargs="+", default=[20, 40, 80]) + args = parser.parse_args() + logging.basicConfig(level=logging.INFO) + + args.out.mkdir(parents=True, exist_ok=True) + path = args.out / "ds2024_pension_g2egm_vs_rfc.md" + + rows = [] + for n_liquid in args.n_liquid: + _logger.info("=== DS-2024 pension n_liquid=%d ===", n_liquid) + rows.extend(benchmark_ds_pension_methods(n_liquid=n_liquid)) + + table = format_comparison_table(rows) + text = ( + "# DS-2024 multidimensional pension β€” G2EGM vs RFC\n\n" + "Solve time and consumption Euler-error accuracy per method, over the\n" + "liquid-grid resolution. EE = log10 relative consumption Euler error on the\n" + "unconstrained interior (more negative = more accurate).\n\n" + "```\n" + table + "\n```\n" + ) + path.write_text(text) + _logger.info("wrote %s", path) + print(text) + + +if __name__ == "__main__": + main() diff --git a/benchmarks/ds_replication/run_paper_scale.py b/benchmarks/ds_replication/run_paper_scale.py new file mode 100644 index 000000000..92a4cb1ff --- /dev/null +++ b/benchmarks/ds_replication/run_paper_scale.py @@ -0,0 +1,199 @@ +"""Produce the paper-scale DS-2026 comparison tables in one run. + +Every model, method, oracle, and harness for Dobrescu & Shanker (2026) is built +and CPU-validated at small grids. The *paper-scale* table numbers (App.1 grids up +to 10000, App.2 NG up to 1000, App.3 W up to 4000) exceed local memory, so this +script runs the full sweeps on a CUDA-capable GPU. + +Run with the CUDA env, e.g. + + XLA_PYTHON_CLIENT_PREALLOCATE=false \\ + pixi run --environment tests-cuda12 \\ + python -m benchmarks.ds_replication.run_paper_scale --out /tmp/ds_tables + +`--smoke` swaps the paper grids for tiny ones so the whole pipeline can be +validated end-to-end on CPU in a couple of minutes before the real run. `--tables` +selects a subset. Each table is written to its own markdown file under `--out` as +soon as it finishes, so a long run leaves partial results on interruption. + +Timing is always compile-vs-runtime separated (the timing helpers clear the JAX +cache before the compile measurement). +""" + +import argparse +import logging +from pathlib import Path + +import pandas as pd + +from benchmarks.ds_replication.app1_retirement_accuracy import ( + PAPER_GRIDS, + PAPER_TAUS, + app1_accuracy_table, + app1_timing_table, +) +from benchmarks.ds_replication.app2_fues_accuracy import ( + app2_fues_euler_error, + app2_fues_timing, +) +from benchmarks.ds_replication.app2_housing_accuracy import ( + app2_negm_euler_error, + app2_negm_timing, +) +from benchmarks.ds_replication.app3_discrete_housing_accuracy import ( + app3_timing, + app3_vfi_euler_error, +) + +_logger = logging.getLogger("lcm") + +# Paper grids per application (exceed local memory; require a CUDA-capable GPU). +APP2_NG = (250, 500, 750, 1000) +APP2_TAUS = (0.05, 0.07, 0.12) +APP3_W = (1000, 2000, 4000) +APP3_H = (3, 5, 7) + +# Tiny stand-ins for `--smoke` end-to-end validation on CPU. +SMOKE = { + "app1_grids": (200, 400), + "app1_taus": (1.0,), + "app2_ng": (10, 14), + "app2_taus": (0.07,), + "app3_w": (30, 40), + "app3_h": (3,), +} + + +def _write(out: Path, name: str, text: str) -> None: + out.mkdir(parents=True, exist_ok=True) + path = out / f"{name}.md" + path.write_text(text) + _logger.info("wrote %s", path) + + +def table12_app1(*, out: Path, smoke: bool) -> None: + """App.1 retirement Tables 1 (timing) + 2 (accuracy): FUES/RFC/LTM/MSS.""" + grids = SMOKE["app1_grids"] if smoke else PAPER_GRIDS + taus = SMOKE["app1_taus"] if smoke else PAPER_TAUS + methods = ("fues", "rfc", "ltm", "mss") + accuracy = pd.concat( + app1_accuracy_table(upper_envelope=ue, taus=taus, n_grids=grids) + .rename(columns={f"{ue}_euler_error": "euler_error"}) + .assign(method=ue) + for ue in methods + ) + timing = app1_timing_table(upper_envelopes=methods, taus=(taus[0],), n_grids=grids) + _write( + out, + "table1_2_app1_retirement", + "# App.1 retirement β€” Table 2 (accuracy) + Table 1 (timing)\n\n" + "## Table 2 β€” mean log10 Euler error\n\n" + + accuracy.to_markdown(index=False) + + "\n\n## Table 1 β€” compile vs runtime (s)\n\n" + + timing.to_markdown(index=False) + + "\n", + ) + + +def table3_app2(*, out: Path, smoke: bool) -> None: + """App.2 housing Table 3: EGM-FUES vs NEGM, Euler + timing, over NG x tau.""" + ngs = SMOKE["app2_ng"] if smoke else APP2_NG + taus = SMOKE["app2_taus"] if smoke else APP2_TAUS + rows = [] + for tau in taus: + for ng in ngs: + fues_t = app2_fues_timing(n_grid=ng, tau=tau) + negm_t = app2_negm_timing(n_grid=ng, tau=tau) + rows.append( + { + "NG": ng, + "tau": tau, + "FUES_eerr": app2_fues_euler_error(n_grid=ng, tau=tau), + "NEGM_eerr": app2_negm_euler_error(n_grid=ng, tau=tau), + "FUES_compile": fues_t["compile_time"], + "FUES_run": fues_t["runtime"], + "NEGM_compile": negm_t["compile_time"], + "NEGM_run": negm_t["runtime"], + } + ) + _write( + out, + "table3_app2_housing", + "# App.2 housing β€” Table 3 (EGM-FUES vs NEGM)\n\n" + + pd.DataFrame(rows).to_markdown(index=False) + + "\n", + ) + + +def table5_app3_taxed(*, out: Path, smoke: bool) -> None: + """App.3 discrete housing with taxes Table 5: FUES vs VFI, Euler + timing.""" + ws = SMOKE["app3_w"] if smoke else APP3_W + hs = SMOKE["app3_h"] if smoke else APP3_H + n_periods = 6 if smoke else 20 + rows = [] + for h in hs: + for w in ws: + common = { + "n_assets": w, + "n_wage_nodes": h, + "n_periods": n_periods, + "use_taxes": True, + } + fues_t = app3_timing(variant="dcegm", upper_envelope="fues", **common) + vfi_t = app3_timing(variant="brute", **common) + rows.append( + { + "W": w, + "H": h, + "FUES_eerr": app3_vfi_euler_error( + variant="dcegm", upper_envelope="fues", **common + ), + "VFI_eerr": app3_vfi_euler_error(variant="brute", **common), + "FUES_compile": fues_t["compile_time"], + "FUES_run": fues_t["runtime"], + "VFI_compile": vfi_t["compile_time"], + "VFI_run": vfi_t["runtime"], + } + ) + _write( + out, + "table5_app3_taxed", + "# App.3 discrete housing with taxes β€” Table 5 (FUES vs VFI)\n\n" + + pd.DataFrame(rows).to_markdown(index=False) + + "\n", + ) + + +TABLES = { + "table12": table12_app1, + "table3": table3_app2, + "table5": table5_app3_taxed, +} + + +def main() -> None: + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--out", type=Path, default=Path("ds_paper_tables")) + parser.add_argument( + "--tables", + nargs="+", + choices=sorted(TABLES), + default=sorted(TABLES), + help="Which tables to produce (default: all).", + ) + parser.add_argument( + "--smoke", + action="store_true", + help="Tiny grids to validate the pipeline end-to-end on CPU.", + ) + args = parser.parse_args() + logging.basicConfig(level=logging.INFO) + + for name in args.tables: + _logger.info("=== producing %s ===", name) + TABLES[name](out=args.out, smoke=args.smoke) + _logger.info("done -> %s", args.out) + + +if __name__ == "__main__": + main() diff --git a/benchmarks/publish.py b/benchmarks/publish.py index 30dab9e17..9faf3011b 100644 --- a/benchmarks/publish.py +++ b/benchmarks/publish.py @@ -41,6 +41,7 @@ def publish() -> None: subprocess.run(["asv", "publish"], check=True) _patch_html_title(html_dir / "index.html") + _default_x_axis_to_date(html_dir / "graphdisplay.js") _pad_sparse_graphs(html_dir / "graphs") _generate_comparison(results_dir) @@ -210,6 +211,35 @@ def _pad_sparse_graphs(graphs_dir: Path) -> None: print(f"Padded sparse benchmark graphs with {total} null entries.") +def _default_x_axis_to_date(graphdisplay_js: Path) -> None: + """Default the per-benchmark graph x-axis to the date scale. + + asv's detail-view defaults the x-axis to the revision index and switches to a + real date axis only when the `x-axis-scale=date` URL param is present. Add an + `else` branch to the param parser so the date scale is the default when no + param is given. Best-effort β€” a parser change upstream just leaves the asv + default in place. + """ + if not graphdisplay_js.is_file(): + logger.warning("graphdisplay.js not found β€” skipping date-axis default") + return + anchor = " delete params['x-axis-scale'];\n }\n" + replacement = ( + " delete params['x-axis-scale'];\n" + " } else {\n" + " $('#date-scale').addClass('active');\n" + " date_scale = true;\n" + " }\n" + ) + text = graphdisplay_js.read_text(encoding="utf-8") + if anchor not in text: + logger.warning( + "x-axis-scale parser not found in graphdisplay.js β€” skipping date default" + ) + return + graphdisplay_js.write_text(text.replace(anchor, replacement, 1), encoding="utf-8") + + def _patch_html_title(index_html: Path) -> None: """Replace ASV's default page title with a project-specific one.""" text = index_html.read_text(encoding="utf-8") diff --git a/benchmarks/test_gpu_mem.py b/benchmarks/test_gpu_mem.py index b76786431..c7451cb32 100644 --- a/benchmarks/test_gpu_mem.py +++ b/benchmarks/test_gpu_mem.py @@ -1,6 +1,6 @@ """Tests for the GPU peak-memory measurement harness.""" -from benchmarks._gpu_mem import _subprocess_env +from benchmarks.asv._gpu_mem import _subprocess_env def test_subprocess_env_disables_autotuning(): diff --git a/docs/credits.md b/docs/credits.md new file mode 100644 index 000000000..e3d54da08 --- /dev/null +++ b/docs/credits.md @@ -0,0 +1,118 @@ +# Credits & Acknowledgments + +pylcm stands on a large body of methodological and applied research, and on a vibrant +open-source ecosystem for solving discrete-continuous dynamic models. This page credits +the methods, models, and software pylcm draws on. We are grateful to all of these +authors and maintainers. + +## Authors & maintainers + +pylcm is developed under the +[OpenSourceEconomics](https://github.com/OpenSourceEconomics) organization by Tim +Mensinger, Maximilian Jahn, Janos Gabler, and Hans-Martin von Gaudecker. + +## Numerical methods + +### The endogenous grid method (EGM) + +The endogenous grid method β€” inverting the Euler equation on an exogenous end-of-period +grid instead of root-finding on a dense grid β€” originates with Carroll (2006), "The +Method of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems," +*Economics Letters* 91(3), 312–320, +[doi:10.1016/j.econlet.2005.09.013](https://doi.org/10.1016/j.econlet.2005.09.013). + +### Discrete-continuous EGM (DC-EGM) + +pylcm's `DCEGM` solver implements the discrete-continuous endogenous grid method of +Iskhakov, JΓΈrgensen, Rust & Schjerning (2017), "The endogenous grid method for +discrete-continuous dynamic choice models with (or without) taste shocks," *Quantitative +Economics* 8(2), 317–365, [doi:10.3982/QE643](https://doi.org/10.3982/QE643). The +deterministic retirement model from that paper is shipped as a closed-form test oracle +(see below). + +- Original MATLAB implementation: + [fediskhakov/dcegm](https://github.com/fediskhakov/dcegm). +- A fully JAX-compatible Python implementation in the same organization, whose design + pylcm draws on: + [OpenSourceEconomics/dcegm](https://github.com/OpenSourceEconomics/dcegm). + +### Upper-envelope refinement + +pylcm refines the (non-monotone) EGM candidate correspondence into the upper envelope +with the Fast Upper-Envelope Scan (FUES) of Dobrescu & Shanker (2022), "Fast +Upper-Envelope Scan for Discrete-Continuous Dynamic Programming," SSRN working paper +[4181302](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4181302). The treatment of +non-smooth, non-concave value functions traces to Fella (2014), "A Generalized +Endogenous Grid Method for Non-Smooth and Non-Concave Problems," *Review of Economic +Dynamics* 17(2), 329–344, +[doi:10.1016/j.red.2013.07.001](https://doi.org/10.1016/j.red.2013.07.001). + +pylcm's FUES backend is **adapted from** +[OpenSourceEconomics/upper-envelope](https://github.com/OpenSourceEconomics/upper-envelope) +(Apache-2.0, Β© The Upper-Envelope Authors), then substantially modified for the JAX +kernel. The reference implementation by the method's authors is +[akshayshanker/FUES](https://github.com/akshayshanker/FUES). + +### Multidimensional & nested EGM (reserved / planned backends) + +pylcm reserves an upper-envelope backend slot for multidimensional envelopes and is +designed to grow toward solving models with more than one continuous (Euler) state. That +roadmap builds on: + +- Druedahl (2021), "A Guide on Solving Non-convex Consumption-Saving Models," + *Computational Economics* 58(3), 747–775, + [doi:10.1007/s10614-020-10045-x](https://doi.org/10.1007/s10614-020-10045-x) β€” nested + EGM (NEGM). Code: + [NumEconCopenhagen/ConsumptionSaving](https://github.com/NumEconCopenhagen/ConsumptionSaving). +- Druedahl & JΓΈrgensen (2017), "A General Endogenous Grid Method for Multi-Dimensional + Models with Non-Convexities and Constraints," *Journal of Economic Dynamics and + Control* 74, 87–107, + [doi:10.1016/j.jedc.2016.11.005](https://doi.org/10.1016/j.jedc.2016.11.005) β€” G2EGM. + Code: [JeppeDruedahl/G2EGM](https://github.com/JeppeDruedahl/G2EGM). +- Dobrescu & Shanker (2024), "Using Inverse Euler Equations to Solve Multidimensional + Discrete-Continuous Dynamic Models: A General Method," SSRN working paper + [4850746](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4850746) β€” the + inverse-Euler / Rooftop-Cut (RFC) multidimensional envelope. Code: + [akshayshanker/InverseDCDP](https://github.com/akshayshanker/InverseDCDP). + +## Stochastic-process discretization + +pylcm's AR(1) / Markov discretization follows Tauchen (1986), Rouwenhorst (1995), and +Kopecky & Suen (2010), with the Tauchen implementation following +[QuantEcon](https://quanteconpy.readthedocs.io/). The choice of Rouwenhorst as the +default for non-stationary lifecycle processes follows Fella, Gallipoli & Pan (2019), +"Markov-Chain Approximations for Life-Cycle Models," *Review of Economic Dynamics* 34, +183–201, [doi:10.1016/j.red.2019.03.013](https://doi.org/10.1016/j.red.2019.03.013), +against whose results pylcm's discretization accuracy is validated. Code & data: +[RePEc red/ccodes/17-149](https://ideas.repec.org/c/red/ccodes/17-149.html). + +## Replicated example models + +Models shipped with pylcm (`src/lcm_examples/`) that replicate published work: + +- **Iskhakov, JΓΈrgensen, Rust & Schjerning (2017)** β€” the deterministic retirement model + (`lcm_examples.iskhakov_et_al_2017`), used as a closed-form test oracle. +- **Mahler & Yum (2024)**, "Lifestyle Behaviors and Wealth-Health Gaps in Germany," + *Econometrica* 92(5), 1697–1733, + [doi:10.3982/ECTA20603](https://doi.org/10.3982/ECTA20603) β€” a finite-horizon + discrete-continuous lifecycle model (`lcm_examples.mahler_yum_2024`). The replication + package is available via the Econometrica supplemental materials. + +## Pedagogy + +pylcm's design and documentation are informed by Sargent & Stachurski's +[*Dynamic Programming*](https://dp.quantecon.org/) (QuantEcon, 2024). + +## The open-source ecosystem + +pylcm interoperates with, learns from, and is grateful to the broader ecosystem for +solving discrete-continuous dynamic models: + +- [OpenSourceEconomics](https://github.com/OpenSourceEconomics) β€” `dcegm`, + `upper-envelope`. +- [NumEconCopenhagen](https://github.com/NumEconCopenhagen) β€” `ConsumptionSaving` + (ConSav), `EconModel`. +- [akshayshanker](https://github.com/akshayshanker) β€” `FUES`, `InverseDCDP`. +- [JeppeDruedahl](https://github.com/JeppeDruedahl) β€” `G2EGM`. +- [fediskhakov](https://github.com/fediskhakov) β€” `dcegm` (original DC-EGM). +- [QuantEcon](https://quantecon.org/) β€” dynamic-programming pedagogy and reference code. diff --git a/docs/development/setup.md b/docs/development/setup.md index f2e129a4e..e0c494d03 100644 --- a/docs/development/setup.md +++ b/docs/development/setup.md @@ -44,10 +44,11 @@ pixi run pytest tests/test_specific_module.py::test_function_name ## Code Quality ```bash -# Type checking (ty, not mypy) -pixi run ty +# Type checking (ty, not mypy; a pre-commit hook that resolves third-party +# imports from the pixi env named in `[tool.ty] environment.python`) +prek run ty --all-files -# Run all pre-commit hooks +# Run all pre-commit hooks (includes the ty hook) prek run --all-files ``` diff --git a/docs/examples/iskhakov_et_al_2017.md b/docs/examples/iskhakov_et_al_2017.md index c07265ea3..a35323756 100644 --- a/docs/examples/iskhakov_et_al_2017.md +++ b/docs/examples/iskhakov_et_al_2017.md @@ -14,7 +14,7 @@ analytical oracle (`tests/data/analytical_solution/`). The discrete retirement c makes the value function non-concave and produces the paper's signature saw-tooth consumption function β€” see the [discrete-continuous choice explanation](../explanations/iskhakov_et_al_2017.ipynb) for -figures and the upcoming brute-force vs DC-EGM comparison. +figures and the brute-force vs DC-EGM comparison. [View source on GitHub](https://github.com/OpenSourceEconomics/pylcm/blob/main/src/lcm_examples/iskhakov_et_al_2017.py) @@ -22,7 +22,7 @@ figures and the upcoming brute-force vs DC-EGM comparison. ```python import jax.numpy as jnp -from lcm_examples.iskhakov_et_al_2017 import get_model, get_params +from lcm_examples.iskhakov_et_al_2017 import get_dcegm_model, get_model, get_params model = get_model(n_periods=6) params = get_params( diff --git a/docs/explanations/index.md b/docs/explanations/index.md index 18cc5f50f..ce90e8d68 100644 --- a/docs/explanations/index.md +++ b/docs/explanations/index.md @@ -25,6 +25,6 @@ hood. system to model consumers with this particular form of time-inconsistent preferences. - [Discrete-Continuous Choice: Iskhakov et al. (2017)](iskhakov_et_al_2017.ipynb) β€” Why discrete choices produce saw-tooth consumption functions, illustrated on the paper's - retirement model; will grow into a brute-force vs DC-EGM comparison. + retirement model, with a brute-force vs DC-EGM accuracy comparison. - [Internal Architecture](architecture.md) β€” Map of the source tree, the user/engine boundary, and the role each package plays. diff --git a/docs/explanations/iskhakov_et_al_2017.ipynb b/docs/explanations/iskhakov_et_al_2017.ipynb index 7d6a89ad8..cddbe6367 100644 --- a/docs/explanations/iskhakov_et_al_2017.ipynb +++ b/docs/explanations/iskhakov_et_al_2017.ipynb @@ -18,8 +18,8 @@ "A worker chooses consumption and whether to keep working or to retire; retirement is\n", "absorbing. The discrete retirement choice destroys the concavity of the value function\n", "and produces the paper's signature **saw-tooth consumption function**, which we plot\n", - "below. The notebook currently solves the model by brute-force grid search; it will\n", - "grow into a side-by-side comparison with the DC-EGM solver." + "below β€” first by brute-force grid search, then side by side with the DC-EGM\n", + "solver, which needs no consumption grid at all." ] }, { @@ -304,10 +304,106 @@ "solve scales with their size.\n", "\n", "This is exactly the situation the DC-EGM algorithm of Iskhakov et al. (2017) is built\n", - "for: it inverts the Euler equation (no consumption grid at all), locates the kinks\n", - "exactly via an upper-envelope step, and handles the borrowing constraint in closed\n", - "form. Once pylcm's DC-EGM solver lands, this section will compare the two solvers'\n", - "accuracy and runtime on this model side by side." + "for. Instead of searching a consumption grid, it inverts the Euler equation on an\n", + "exogenous end-of-period *savings* grid, locates the kinks with an upper-envelope scan,\n", + "and handles the borrowing constraint in closed form. Selecting it is a per-regime\n", + "`solver=DCEGM(...)` declaration plus three regime functions (`resources`, `savings`,\n", + "and `inverse_marginal_utility`) and a wealth transition written in terms of savings;\n", + "the borrowing constraint is dropped because DC-EGM enforces the budget identity and\n", + "the savings-grid lower bound intrinsically. `get_dcegm_model` builds exactly this\n", + "variant of the model above β€” `get_params` works unchanged.\n", + "\n", + "To compare accuracy, we treat the fine-grid brute-force solution (500 Γ— 2500) as the\n", + "reference and look at the period-0 value function of the working regime on the default\n", + "100-point wealth grid." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "11", + "metadata": {}, + "outputs": [], + "source": [ + "import time\n", + "\n", + "from lcm_examples.iskhakov_et_al_2017 import get_dcegm_model\n", + "\n", + "PARAMS_6 = get_params(6, **PAPER_PARAMS)\n", + "WEALTH_NODES = jnp.linspace(1, 400, 100) # the default wealth grid\n", + "\n", + "V_default = get_model(6).solve(params=PARAMS_6, log_level=\"warning\")\n", + "V_dcegm = get_dcegm_model(6).solve(params=PARAMS_6, log_level=\"warning\")\n", + "V_fine = build_model(6).solve(params=PARAMS_6, log_level=\"warning\")\n", + "\n", + "reference = jnp.interp(\n", + " WEALTH_NODES, jnp.linspace(1, 400, 500), V_fine[0][\"working_life\"]\n", + ")\n", + "err_default = jnp.abs(V_default[0][\"working_life\"] - reference)\n", + "err_dcegm = jnp.abs(V_dcegm[0][\"working_life\"] - reference)\n", + "\n", + "for label, model in [\n", + " (\"brute force, default grids (100 Γ— 500)\", get_model(6)),\n", + " (\"DC-EGM, no consumption grid\", get_dcegm_model(6)),\n", + "]:\n", + " start = time.perf_counter()\n", + " model.solve(params=PARAMS_6, log_level=\"off\") # warm: compilation cached above\n", + " print(f\"{label}: {time.perf_counter() - start:.3f}s per solve\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "12", + "metadata": {}, + "outputs": [], + "source": [ + "fig = go.Figure()\n", + "fig.add_trace(\n", + " go.Scatter(\n", + " x=WEALTH_NODES,\n", + " y=err_default,\n", + " mode=\"lines\",\n", + " line={\"color\": \"#bbbbbb\"},\n", + " name=\"brute force, default grids (100 Γ— 500)\",\n", + " )\n", + ")\n", + "fig.add_trace(\n", + " go.Scatter(\n", + " x=WEALTH_NODES,\n", + " y=err_dcegm,\n", + " mode=\"lines\",\n", + " line={\"color\": \"steelblue\"},\n", + " name=\"DC-EGM, no consumption grid\",\n", + " )\n", + ")\n", + "fig.update_layout(\n", + " title=\"Distance to the fine-grid solution (500 Γ— 2500), period 0, working life\",\n", + " xaxis_title=\"wealth\",\n", + " yaxis_title=\"|V βˆ’ V_fine|\",\n", + " yaxis_type=\"log\",\n", + " template=\"simple_white\",\n", + ")\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "id": "13", + "metadata": {}, + "source": [ + "DC-EGM tracks the fine-grid reference much more closely than the equally-sized\n", + "brute-force solve β€” without any consumption grid β€” and the contrast is sharpest at low\n", + "wealth, where the borrowing constraint binds: DC-EGM computes the constrained segment\n", + "in closed form, while grid search has to approximate it from feasible grid points. At\n", + "this resolution the comparison is limited by the reference's own grid error, so the\n", + "DC-EGM curve is best read as an upper bound on its distance to the exact solution.\n", + "\n", + "Two practical notes. The value functions DC-EGM returns live on the same wealth grid\n", + "as the brute-force ones, so everything downstream of `solve()` is unchanged, and the\n", + "two solvers can be mixed freely across regimes. Forward simulation works; simulated\n", + "consumption is chosen from the consumption grid (so the policy figures above look the\n", + "same under either solver), while the solve itself needs no consumption grid at all." ] } ], diff --git a/docs/myst.yml b/docs/myst.yml index d868adc71..de45b305f 100644 --- a/docs/myst.yml +++ b/docs/myst.yml @@ -77,6 +77,8 @@ project: - file: development/setup.md - file: development/conventions.md - file: development/benchmarking.md + - file: credits.md + title: Credits & Acknowledgments error_rules: - rule: link-resolves severity: ignore diff --git a/docs/references.bib b/docs/references.bib index 6d39f912f..88211006e 100644 --- a/docs/references.bib +++ b/docs/references.bib @@ -47,7 +47,7 @@ @article{mahler2024 journal = {Econometrica}, volume = {92}, number = {5}, - pages = {1307--1343}, + pages = {1697--1733}, year = {2024}, doi = {10.3982/ECTA20603}, } @@ -70,3 +70,62 @@ @article{iskhakov2017 year = {2017}, doi = {10.3982/QE643}, } + +@article{carroll2006, + title = {The Method of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems}, + author = {Carroll, Christopher D.}, + journal = {Economics Letters}, + volume = {91}, + number = {3}, + pages = {312--320}, + year = {2006}, + doi = {10.1016/j.econlet.2005.09.013}, +} + +@article{fella2014, + title = {A Generalized Endogenous Grid Method for Non-Smooth and Non-Concave Problems}, + author = {Fella, Giulio}, + journal = {Review of Economic Dynamics}, + volume = {17}, + number = {2}, + pages = {329--344}, + year = {2014}, + doi = {10.1016/j.red.2013.07.001}, +} + +@article{dobrescu2022, + title = {Fast Upper-Envelope Scan for Discrete-Continuous Dynamic Programming}, + author = {Dobrescu, Loretti I. and Shanker, Akshay}, + year = {2022}, + note = {SSRN working paper 4181302}, + doi = {10.2139/ssrn.4181302}, +} + +@article{druedahl2021, + title = {A Guide on Solving Non-convex Consumption-Saving Models}, + author = {Druedahl, Jeppe}, + journal = {Computational Economics}, + volume = {58}, + number = {3}, + pages = {747--775}, + year = {2021}, + doi = {10.1007/s10614-020-10045-x}, +} + +@article{druedahl2017, + title = {A General Endogenous Grid Method for Multi-Dimensional Models with Non-Convexities and Constraints}, + author = {Druedahl, Jeppe and J{\o}rgensen, Thomas H.}, + journal = {Journal of Economic Dynamics and Control}, + volume = {74}, + pages = {87--107}, + year = {2017}, + doi = {10.1016/j.jedc.2016.11.005}, +} + +@article{dobrescu2024, + title = {Using Inverse {Euler} Equations to Solve Multidimensional Discrete-Continuous Dynamic Models: A General Method}, + author = {Dobrescu, Loretti I. and Shanker, Akshay}, + year = {2024}, + note = {SSRN working paper 4850746}, + doi = {10.2139/ssrn.4850746}, +} diff --git a/licenses/upper-envelope-LICENSE b/licenses/upper-envelope-LICENSE new file mode 100644 index 000000000..3d1fe8d30 --- /dev/null +++ b/licenses/upper-envelope-LICENSE @@ -0,0 +1,203 @@ +Copyright (c) 2023-2025 The Upper-Envelope Authors + + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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The brute search axis is the full product + + periods x income_nodes x N_X x N_Z x N_C x N_Iz + +which is exactly the curse the NEGM/multidim build targets. + +Usage: python brute_feasibility_probe.py N_X N_Z N_C N_Iz N_INCOME N_PERIODS + +Run on gpu-01 (V100 16 GB) with `XLA_PYTHON_CLIENT_PREALLOCATE=false` so the +reported peak is the true high-water mark, not the preallocated pool. +""" + +# ruff: noqa: T201, INP001, PLR2004 (throwaway Phase-0 probe: prints results) + +import os +import sys +import time + +os.environ.setdefault("JAX_ENABLE_X64", "1") + +import jax +import jax.numpy as jnp + +from lcm import ( + AgeGrid, + LinSpacedGrid, + Model, + Regime, + RouwenhorstAR1Process, + categorical, +) +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + FloatND, + ScalarInt, +) + +N_X = int(sys.argv[1]) +N_Z = int(sys.argv[2]) +N_C = int(sys.argv[3]) +N_IZ = int(sys.argv[4]) +N_INCOME = int(sys.argv[5]) +N_PERIODS = int(sys.argv[6]) + +ILLIQUID_FLOW = 0.05 # iota: utility flow from the illiquid stock +WITHDRAWAL_PENALTY = 0.10 # kappa on illiquid withdrawals (Iz < 0) +RISK_AVERSION = 2.0 + + +@categorical(ordered=False) +class RegimeId: + alive: ScalarInt + dead: ScalarInt + + +def liquid_savings( + wealth: ContinuousState, + consumption: ContinuousAction, + illiquid_investment: ContinuousAction, + income: ContinuousState, +) -> FloatND: + """End-of-period liquid balance after consumption and the illiquid transfer. + + A withdrawal (`illiquid_investment < 0`) is penalised: only a fraction + `1 - kappa` of withdrawn funds reaches the liquid account. + """ + credited = jnp.where( + illiquid_investment < 0.0, + (1.0 - WITHDRAWAL_PENALTY) * illiquid_investment, + illiquid_investment, + ) + return wealth + jnp.exp(income) - consumption - credited + + +def next_wealth(liquid_savings: FloatND, interest_rate: float) -> ContinuousState: + return (1.0 + interest_rate) * liquid_savings + + +def next_illiquid( + illiquid: ContinuousState, illiquid_investment: ContinuousAction +) -> ContinuousState: + return illiquid + illiquid_investment + + +def utility(consumption: ContinuousAction, illiquid: ContinuousState) -> FloatND: + flow = consumption + ILLIQUID_FLOW * illiquid + return flow ** (1.0 - RISK_AVERSION) / (1.0 - RISK_AVERSION) + + +def liquid_floor(liquid_savings: FloatND) -> BoolND: + return liquid_savings >= 0.0 + + +def illiquid_floor( + illiquid: ContinuousState, illiquid_investment: ContinuousAction +) -> BoolND: + return illiquid + illiquid_investment >= 0.0 + + +def positive_consumption(consumption: ContinuousAction) -> BoolND: + return consumption > 0.05 + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where(age >= final_age_alive, RegimeId.dead, RegimeId.alive) + + +def build_model() -> Model: + final_age_alive = 20 + (N_PERIODS - 2) * 5 + alive = Regime( + active=lambda age, n=final_age_alive: age <= n, + states={ + "wealth": LinSpacedGrid(start=0.0, stop=40.0, n_points=N_X), + "illiquid": LinSpacedGrid(start=0.0, stop=40.0, n_points=N_Z), + "income": RouwenhorstAR1Process(n_points=N_INCOME), + }, + state_transitions={ + "wealth": next_wealth, + "illiquid": next_illiquid, + }, + actions={ + "consumption": LinSpacedGrid(start=0.1, stop=30.0, n_points=N_C), + "illiquid_investment": LinSpacedGrid(start=-10.0, stop=10.0, n_points=N_IZ), + }, + transition=next_regime, + constraints={ + "liquid_floor": liquid_floor, + "illiquid_floor": illiquid_floor, + "positive_consumption": positive_consumption, + }, + functions={ + "utility": utility, + "liquid_savings": liquid_savings, + }, + ) + dead = Regime( + transition=None, + active=lambda age, n=final_age_alive: age > n, + functions={"utility": lambda: 0.0}, + ) + return Model( + regimes={"alive": alive, "dead": dead}, + regime_id_class=RegimeId, + ages=AgeGrid(start=20, stop=20 + (N_PERIODS - 1) * 5, step="5Y"), + fixed_params={"final_age_alive": final_age_alive}, + ) + + +params = { + "discount_factor": 0.95, + "alive": { + "income": {"mu": 0.0, "sigma": 0.2, "rho": 0.9}, + "next_wealth": {"interest_rate": 0.03}, + }, +} + +search_width = N_INCOME * N_X * N_Z * N_C * N_IZ +print( + f"grids: N_X={N_X} N_Z={N_Z} N_C={N_C} N_Iz={N_IZ} N_income={N_INCOME} " + f"T={N_PERIODS} | per-period brute width = {search_width:,}", + flush=True, +) + +t0 = time.perf_counter() +model = build_model() +t_build = time.perf_counter() - t0 + +t0 = time.perf_counter() +solution = model.solve(params=params, log_level="off") +jax.block_until_ready(solution) +t_solve = time.perf_counter() - t0 + +stats = jax.devices()[0].memory_stats() or {} +peak = stats.get("peak_bytes_in_use", 0) +print( + f"OK build={t_build:.2f}s solve={t_solve:.2f}s " + f"gpu_peak={peak / 1e6:.1f} MB periods_solved={len(solution)}", + flush=True, +) +print(f" mem_stats_keys={sorted(stats)}", flush=True) diff --git a/negm_phase0/kinked_toy_oracle.py b/negm_phase0/kinked_toy_oracle.py new file mode 100644 index 000000000..31def85ff --- /dev/null +++ b/negm_phase0/kinked_toy_oracle.py @@ -0,0 +1,326 @@ +"""Phase-0 kinked 2-asset toy + brute oracle (the NEGM parity target). + +The smallest model carrying the Laibson frictions a NEGM prototype must +reproduce: liquid `X` + illiquid `Z`, a credit-card borrowing-rate kink at the +liquid post-state `a^X = 0`, an illiquid withdrawal penalty (kink at `Iz = 0`), +the hard `Z >= 0` floor, and the direct illiquid utility flow `u(C + iota*Z)`. + +Solved with the `BruteForce` solver as the oracle. The liquid `wealth` grid +covers the reachable negative-wealth range: the liquid floor `a^X >= -5` and the +borrow rate `0.12` put the minimum reachable `next_wealth` at `1.12 * -5 = -5.6`, +so a grid starting at `0` would force the brute V-interpolation to extrapolate +below its own support at every low-wealth cell and inflate the value there. The +grid starts at `-6` so every reachable `next_wealth` lands inside the support. + +Prints `V` at a few fixed grid coordinates so the NEGM solve can be checked for +V-parity by concrete value, plus a provenance block (lcm build, git SHA, x64 +flag, grid shapes and checksums, the corner cell's independently recomputed +maximizing `(c, Iz, a^X, next_wealth, next_illiquid)`, and the interpolation +mode) so a future reader can reproduce the pinned numbers exactly. + +Run: python kinked_toy_oracle.py +""" + +# ruff: noqa: T201, INP001, PLR2004, S607 (Phase-0 probe: prints, calls git) + +import os +import subprocess +from pathlib import Path + +os.environ.setdefault("JAX_ENABLE_X64", "1") + +import jax +import jax.numpy as jnp + +import lcm +from lcm import ( + AgeGrid, + LinSpacedGrid, + Model, + Regime, + categorical, +) +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + FloatND, + ScalarInt, +) + +N_X = 12 +N_Z = 12 +N_C = 25 +N_IZ = 25 +N_PERIODS = 4 + +WEALTH_MIN = -6.0 # covers the reachable next_wealth floor 1.12 * -5 = -5.6 +WEALTH_MAX = 30.0 +ILLIQUID_MAX = 30.0 +LABOUR_INCOME = 5.0 +LIQUID_CREDIT_LIMIT = -5.0 # a^X >= -5 + +ILLIQUID_FLOW = 0.05 # iota +WITHDRAWAL_PENALTY = 0.10 # kappa on Iz < 0 +BORROW_RATE = 0.12 # credit-card rate on a^X < 0 +SAVE_RATE = 0.03 # rate on a^X >= 0 +RISK_AVERSION = 2.0 + + +@categorical(ordered=False) +class RegimeId: + alive: ScalarInt + dead: ScalarInt + + +def liquid_savings( + wealth: ContinuousState, + consumption: ContinuousAction, + illiquid_investment: ContinuousAction, +) -> FloatND: + """Liquid post-decision balance `a^X`, with the withdrawal penalty wedge.""" + credited = jnp.where( + illiquid_investment < 0.0, + (1.0 - WITHDRAWAL_PENALTY) * illiquid_investment, + illiquid_investment, + ) + return wealth + LABOUR_INCOME - consumption - credited + + +def next_wealth(liquid_savings: FloatND) -> ContinuousState: + """Liquid law with the credit-card rate kink at `a^X = 0`.""" + rate = jnp.where(liquid_savings < 0.0, BORROW_RATE, SAVE_RATE) + return (1.0 + rate) * liquid_savings + + +def next_illiquid( + illiquid: ContinuousState, illiquid_investment: ContinuousAction +) -> ContinuousState: + return illiquid + illiquid_investment + + +def utility(consumption: ContinuousAction, illiquid: ContinuousState) -> FloatND: + flow = consumption + ILLIQUID_FLOW * illiquid + return flow ** (1.0 - RISK_AVERSION) / (1.0 - RISK_AVERSION) + + +def liquid_floor(liquid_savings: FloatND) -> BoolND: + return liquid_savings >= LIQUID_CREDIT_LIMIT + + +def illiquid_floor( + illiquid: ContinuousState, illiquid_investment: ContinuousAction +) -> BoolND: + return illiquid + illiquid_investment >= 0.0 + + +def positive_consumption(consumption: ContinuousAction) -> BoolND: + return consumption > 0.05 + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where(age >= final_age_alive, RegimeId.dead, RegimeId.alive) + + +WEALTH_GRID = LinSpacedGrid(start=WEALTH_MIN, stop=WEALTH_MAX, n_points=N_X) +ILLIQUID_GRID = LinSpacedGrid(start=0.0, stop=ILLIQUID_MAX, n_points=N_Z) +CONSUMPTION_GRID = LinSpacedGrid(start=0.1, stop=20.0, n_points=N_C) +ILLIQUID_INVESTMENT_GRID = LinSpacedGrid(start=-8.0, stop=8.0, n_points=N_IZ) + + +def build_model() -> Model: + final_age_alive = 20 + (N_PERIODS - 2) * 5 + alive = Regime( + active=lambda age, n=final_age_alive: age <= n, + states={"wealth": WEALTH_GRID, "illiquid": ILLIQUID_GRID}, + state_transitions={"wealth": next_wealth, "illiquid": next_illiquid}, + actions={ + "consumption": CONSUMPTION_GRID, + "illiquid_investment": ILLIQUID_INVESTMENT_GRID, + }, + transition=next_regime, + constraints={ + "liquid_floor": liquid_floor, + "illiquid_floor": illiquid_floor, + "positive_consumption": positive_consumption, + }, + functions={"utility": utility, "liquid_savings": liquid_savings}, + ) + dead = Regime( + transition=None, + active=lambda age, n=final_age_alive: age > n, + functions={"utility": lambda: 0.0}, + ) + return Model( + regimes={"alive": alive, "dead": dead}, + regime_id_class=RegimeId, + ages=AgeGrid(start=20, stop=20 + (N_PERIODS - 1) * 5, step="5Y"), + fixed_params={"final_age_alive": final_age_alive}, + ) + + +PARAMS = {"discount_factor": 0.95, "alive": {}} +DISCOUNT_FACTOR = 0.95 + +_CORNER = (0, 0) +_REPORT_COORDS = [ + (0, 0), + (0, N_Z // 2), + (N_X // 2, 0), + (N_X // 2, N_Z // 2), + (N_X - 1, N_Z - 1), +] + + +def _checksum(values: FloatND) -> float: + """Order-stable scalar fingerprint of a 1-D grid.""" + return float(jnp.sum(jnp.asarray(values) * jnp.arange(1, values.shape[0] + 1))) + + +def _git_sha() -> str: + """Short git SHA of the working tree, or `unknown` outside a checkout.""" + try: + return subprocess.run( + ["git", "rev-parse", "--short", "HEAD"], + cwd=Path(__file__).resolve().parent, + capture_output=True, + text=True, + check=True, + ).stdout.strip() + except subprocess.CalledProcessError, FileNotFoundError: + return "unknown" + + +def _interp_next_v( + v_next: FloatND, wealth_query: FloatND, illiquid_query: FloatND +) -> FloatND: + """Bilinear interpolation of the next-period `alive` V at a query point. + + Mirrors the brute solver's `map_coordinates` (order-1, edge-clamped) + V-interpolation: fractional coordinates on each state grid, clamped to the + grid range, then a bilinear blend. Used to recompute the corner cell's + Bellman maximizer independently of the solver's own search. + """ + + def _coord(query: FloatND, lo: float, hi: float, n: int) -> FloatND: + frac = (query - lo) / (hi - lo) * (n - 1) + return jnp.clip(frac, 0.0, n - 1.0) + + cw = _coord(wealth_query, WEALTH_MIN, WEALTH_MAX, N_X) + ci = _coord(illiquid_query, 0.0, ILLIQUID_MAX, N_Z) + w0 = jnp.floor(cw).astype(jnp.int32) + i0 = jnp.floor(ci).astype(jnp.int32) + w1 = jnp.clip(w0 + 1, 0, N_X - 1) + i1 = jnp.clip(i0 + 1, 0, N_Z - 1) + fw = cw - w0 + fi = ci - i0 + return ( + v_next[w0, i0] * (1 - fw) * (1 - fi) + + v_next[w1, i0] * fw * (1 - fi) + + v_next[w0, i1] * (1 - fw) * fi + + v_next[w1, i1] * fw * fi + ) + + +def _recompute_corner_maximizer(v_next_alive: FloatND) -> dict[str, float]: + """Brute-search the period-0 corner-cell Bellman against the solved V[period 1]. + + Recomputes `V[corner]` and its maximizing action by an explicit grid search + over `(consumption, illiquid_investment)` β€” interpolating the next-period + `alive` value with the brute solver's order-1 edge-clamped scheme β€” so the + pinned corner value carries an independent argmax record, not just the + solver's scalar. + """ + ix, iz = _CORNER + wealth = WEALTH_MIN + (WEALTH_MAX - WEALTH_MIN) * ix / (N_X - 1) + illiquid = ILLIQUID_MAX * iz / (N_Z - 1) + consumption = jnp.asarray(CONSUMPTION_GRID.to_jax()) + investment = jnp.asarray(ILLIQUID_INVESTMENT_GRID.to_jax()) + c_mesh, iz_mesh = jnp.meshgrid(consumption, investment, indexing="ij") + credited = jnp.where(iz_mesh < 0.0, (1.0 - WITHDRAWAL_PENALTY) * iz_mesh, iz_mesh) + savings = wealth + LABOUR_INCOME - c_mesh - credited + next_w = jnp.where(savings < 0.0, 1.0 + BORROW_RATE, 1.0 + SAVE_RATE) * savings + next_z = illiquid + iz_mesh + flow = c_mesh + ILLIQUID_FLOW * illiquid + flow_utility = flow ** (1.0 - RISK_AVERSION) / (1.0 - RISK_AVERSION) + continuation = _interp_next_v(v_next_alive, next_w, next_z) + feasible = (savings >= LIQUID_CREDIT_LIMIT) & (next_z >= 0.0) & (c_mesh > 0.05) + objective = jnp.where( + feasible, flow_utility + DISCOUNT_FACTOR * continuation, -jnp.inf + ) + flat = int(jnp.argmax(objective)) + best_c_idx, best_iz_idx = divmod(flat, investment.shape[0]) + return { + "V": float(objective.reshape(-1)[flat]), + "consumption": float(consumption[best_c_idx]), + "illiquid_investment": float(investment[best_iz_idx]), + "liquid_savings": float(savings[best_c_idx, best_iz_idx]), + "next_wealth": float(next_w[best_c_idx, best_iz_idx]), + "next_illiquid": float(next_z[best_c_idx, best_iz_idx]), + } + + +def main() -> None: + """Solve the oracle, print its pinned values and the provenance block.""" + solution = build_model().solve(params=PARAMS, log_level="off") + v0 = solution[0]["alive"] + v1 = solution[1]["alive"] + + print(f"lcm.__file__ = {lcm.__file__}", flush=True) + print(f"git SHA = {_git_sha()}", flush=True) + print(f"jax_enable_x64 = {jax.config.jax_enable_x64}", flush=True) + print("interpolation = order-1 (linear) edge-clamped map_coordinates", flush=True) + wealth_grid = jnp.asarray(WEALTH_GRID.to_jax()) + illiquid_grid = jnp.asarray(ILLIQUID_GRID.to_jax()) + print( + f"wealth grid: shape={wealth_grid.shape} " + f"[{float(wealth_grid[0])}, {float(wealth_grid[-1])}] " + f"checksum={_checksum(wealth_grid):.6f}", + flush=True, + ) + print( + f"illiquid grid: shape={illiquid_grid.shape} " + f"[{float(illiquid_grid[0])}, {float(illiquid_grid[-1])}] " + f"checksum={_checksum(illiquid_grid):.6f}", + flush=True, + ) + print( + f"consumption grid: shape=({N_C},) checksum=" + f"{_checksum(jnp.asarray(CONSUMPTION_GRID.to_jax())):.6f}", + flush=True, + ) + print( + f"illiquid_investment grid: shape=({N_IZ},) checksum=" + f"{_checksum(jnp.asarray(ILLIQUID_INVESTMENT_GRID.to_jax())):.6f}", + flush=True, + ) + + print(f"V[period 0, alive] shape = {v0.shape}", flush=True) + for ix, iz in _REPORT_COORDS: + print( + f" V[wealth_idx={ix}, illiquid_idx={iz}] = {float(v0[ix, iz]):.10f}", + flush=True, + ) + print( + f"PARITY-TARGET period0_alive sum={float(jnp.sum(v0)):.8f} " + f"min={float(jnp.min(v0)):.8f} max={float(jnp.max(v0)):.8f}", + flush=True, + ) + + maximizer = _recompute_corner_maximizer(v1) + print(f"corner cell {_CORNER} independent Bellman recomputation:", flush=True) + print(f" solver V = {float(v0[_CORNER]):.10f}", flush=True) + print(f" recomputed V = {maximizer['V']:.10f}", flush=True) + print( + " argmax (c, Iz, a^X, next_wealth, next_illiquid) = " + f"({maximizer['consumption']:.4f}, " + f"{maximizer['illiquid_investment']:.4f}, " + f"{maximizer['liquid_savings']:.4f}, " + f"{maximizer['next_wealth']:.4f}, " + f"{maximizer['next_illiquid']:.4f})", + flush=True, + ) + + +if __name__ == "__main__": + main() diff --git a/negm_phase0/negm-phase0-findings.md b/negm_phase0/negm-phase0-findings.md new file mode 100644 index 000000000..73955b3c7 --- /dev/null +++ b/negm_phase0/negm-phase0-findings.md @@ -0,0 +1,172 @@ +# NEGM / multidim DC-EGM β€” Phase-0 risk-gate findings + +Date: 2026-06-17. Branch: `feat/dcegm-negm` (off `feat/dcegm` @ `5f67a5de`). +All solves on gpu-01 (V100 16 GB, env `tests-cuda12`, `XLA_PYTHON_CLIENT_PREALLOCATE=false`). + +## Gate recommendation: **BUILD for the general capability β€” but the necessity premise is refuted; reframe the justification** + +The single sharpest Phase-0 finding **contradicts the plan's premise**: brute force is +*not* the bottleneck. A two-continuous-state (liquid + illiquid) + two-continuous-action +(C, IαΆ») + income-shock lifecycle solves on a single V100 in **~4–9 s using < 600 MB even at +2.5 billion state-action combinations per period**, and the authors' own paper solves by +**numerical backward induction** (not EGM). So: + +- **Brute replicates the paper's model class** (it *is* the authors' method) and is + single-solve-feasible at fine grids in pylcm today. The Laibson replication does **not + require** NEGM/EGM for feasibility. +- **The real case for NEGM is accuracy + estimation throughput + generality**, not + single-solve feasibility: brute restricts the continuous policy to the action grid, + biasing exactly the consumption/savings Euler moments the paper identifies discount + parameters from; MSM estimation re-solves under numerical gradients (the paper calls each + moment computation "numerically costly"), so per-solve cost and smooth/unbiased moments + compound. + +Recommendation: **`build_but_resequence`, leaning toward the general-capability rationale** +the user already chose β€” but **drop "brute is infeasible at Laibson scale" from the +plan's motivation** (it is false on a V100) and replace it with the accuracy/throughput/ +generality argument. NEGM is justified as a *general pylcm 2-asset capability* and an +*accuracy* upgrade, not a feasibility rescue. The NEGM nesting holds analytically (below). + +## 1. Brute-feasibility probe β€” results + +Model: states `wealth X`, `illiquid Z` (LinSpaced) + `income` (Rouwenhorst AR(1)); actions +`consumption C`, `illiquid_investment IαΆ»` (LinSpaced); withdrawal penalty on `IαΆ»<0`; +liquid/illiquid floors; `u(C + ΞΉZ)`. `BruteForce` solver. Script: +`negm_phase0/brute_feasibility_probe.py`. + +| N_X | N_Z | N_C | N_IαΆ» | N_inc | T | per-period width | solve | GPU peak | +|----:|----:|----:|----:|----:|--:|---:|---:|---:| +| 20 | 20 | 20 | 20 | 5 | 10 | 0.8 M | 3.49 s | 1.0 MB | +| 30 | 30 | 30 | 30 | 5 | 10 | 4.05 M | 3.51 s | 4.5 MB | +| 40 | 40 | 40 | 40 | 5 | 10 | 12.8 M | 3.51 s | 17.4 MB | +| 50 | 50 | 50 | 50 | 5 | 10 | 31.25 M | 3.48 s | 34.5 MB | +| 60 | 60 | 60 | 60 | 5 | 16 | 64.8 M | 4.13 s | 69.2 MB | +| 80 | 80 | 80 | 80 | 5 | 16 | 204.8 M | 4.09 s | 138.1 MB | +| 100 | 100 | 100 | 100 | 5 | 16 | 500 M | 3.87 s | 274.5 MB | +| 120 | 120 | 120 | 120 | 5 | 16 | 1.04 B | 9.06 s | 312.0 MB | +| 150 | 150 | 150 | 150 | 5 | 16 | 2.53 B | 4.86 s | 550.7 MB | +| 60 | 60 | **150** | **150** | 7 | **60** | 567 M | 8.04 s | 280.4 MB | + +Reading: solve time is essentially **flat (~3.5–9 s)** and GPU memory **tiny (≀ 0.55 GB)** +across a >3000Γ— range of search width. The V100 is far from saturated β€” the solve is +latency/overhead-bound, not compute- or memory-bound, because pylcm's brute solver +vectorizes the search and the retained `V` arrays are small (`N_XΒ·N_ZΒ·N_inc` per period). +A full annual-frequency lifecycle (T=60) with fine action grids (150Γ—150) solves in **8 s**. +No OOM was reached on a 16 GB card up to 2.5 B/period; the memory wall would sit around +`Nβ‰ˆ200` per dimension (absurdly fine), and `savings_grid.batch_size` would push it further. + +**Implication for estimation:** at ~8 s/solve, an MSM loop of even a few thousand solves +(parameter search + numerical-gradient SEs + multistart) is hours, not days β€” feasible. +So brute is a viable interim replication backend. EGM/NEGM's win is **accuracy** (no +action-grid restriction on the policy β†’ unbiased Euler moments at coarse grids) and +**per-solve speed** (compounds over the estimation loop), plus **generality**. + +## 2. Kinked toy + brute oracle (the NEGM parity target) + +Script: `negm_phase0/kinked_toy_oracle.py`. Smallest model with all Laibson frictions: +credit-card rate kink at `a^X=0` (12% borrow / 3% save), withdrawal penalty (ΞΊ=0.10) at +`IαΆ»=0`, `Zβ‰₯0` floor, `u(C+ΞΉZ)`, ΞΉ=0.05, CRRA(2), T=4, grids 12Γ—12 states / 25Γ—25 actions. +Brute-solved on gpu-01. **Parity target** (period 0, regime `alive`, shape (12,12)): + +``` +V[wealth=0, illiquid=0 ] = -0.4002052501 +V[wealth=0, illiquid=6 ] = -0.2250119814 +V[wealth=6, illiquid=0 ] = -0.2334363467 +V[wealth=6, illiquid=6 ] = -0.1619449719 +V[wealth=11, illiquid=11] = -0.1331192126 +sum = -26.82990570 min = -0.40020525 max = -0.13311921 +``` + +V is correctly monotone-increasing in both assets. A future NEGM prototype (outer search +over `a^Z` + inner 1-D EGM on `X`) must reproduce these to ~1e-4 (brute carries action-grid +discretization, so exact parity is not expected β€” assert the brute value is a *lower bound* +the off-grid NEGM weakly improves on, and match dense-brute as `N_C, N_IαΆ» β†’ ∞`). + +## 3. NEGM nesting derivation for the toy (the make-or-break analytical check) + +**It nests.** Period-`t` problem, state `(X, Z, ΞΆ)`: + +``` +V_t(X,Z,ΞΆ) = max_{C, IαΆ»} u(C + ΞΉZ) + Ξ²Β·E[ V_{t+1}(X', Z', ΞΆ') | ΞΆ ] + a^X = X + Y(ΞΆ) βˆ’ C βˆ’ credited(IαΆ»), credited(IαΆ») = IαΆ» if IαΆ»β‰₯0 else (1βˆ’ΞΊ)Β·IαΆ» + X' = R^X(a^X)Β·a^X (R^X kinked at a^X=0: borrow vs save rate) + Z' = Z + IαΆ» β‰₯ 0 (so IαΆ» β‰₯ βˆ’Z) + a^X β‰₯ βˆ’limit, C > 0 +``` + +Reparametrize the illiquid margin by the **outer post-state** `a^Z ≑ Z' = Z + IαΆ»`. Fix +`a^Z`; then `IαΆ» = a^Z βˆ’ Z` is fixed, so `credited(Β·)` is a constant and `ΞΉZ` (current `Z`) +is a constant. The **inner** problem is a standard 1-D DC-EGM consumption problem on the +liquid margin: + +``` +W_t(X,Z,ΞΆ; a^Z) = max_C u(C + ΞΉZ) + Ξ²Β·E[ V_{t+1}(R^X(a^X)Β·a^X, a^Z, ΞΆ') ] + R_inner = X + Y(ΞΆ) βˆ’ credited(a^Z βˆ’ Z) (resources, fixed given a^Z, Z) + C = R_inner βˆ’ a^X (consumption recovery) +V_t(X,Z,ΞΆ) = max_{a^Z β‰₯ 0} W_t(X,Z,ΞΆ; a^Z) (OUTER deterministic max) +``` + +Why the inner solve is the *existing* kernel, with three small modifications: +- **Euler state = X, action = C, post-decision = a^X, resources = R_inner.** Endogenous + grid lives in `R_inner`-space exactly as 1-D DC-EGM. +- **Inverse marginal utility carries a constant shift.** `u'(C+ΞΉZ)=m β‡’ C=(u')⁻¹(m)βˆ’ΞΉZ`. + The scalar inversion is unchanged; the `βˆ’ΞΉZ` is a constant offset. **Feasibility guard + (P1): C>0 ⟺ (u')⁻¹(m) > ΞΉZ.** +- **The credit-card rate kink lives in the inner continuation** (`R^X(a^X)` kinked at + `a^X=0`). **Split the liquid/savings grid at `a^X=0` (P1)** so the post-decision return + is piecewise-smooth and the envelope sees the kink. + +**The outer problem is a deterministic max over `a^Z`, not an Euler inversion (B2).** +`W_t(Β·; a^Z)` is generally **non-concave in `a^Z`** (withdrawal-penalty kink at `a^Z=Z`, +the `Z'β‰₯0` floor, the rate kink), which is *why* the outer margin is a grid+candidate max, +not a second inverse-Euler. **Mandatory outer candidates (P1):** +- `a^Z = Z` (i.e. `IαΆ»=0`, no adjustment) β€” the withdrawal-penalty kink; **current-state- + specific**, so a fixed exogenous `a^Z` grid misses it unless inserted per node. +- `a^Z = 0` (full withdrawal, `Z'=0` floor corner). +- segment the outer grid into `[0, Z]` (withdrawal, penalized slope) and `[Z, Z_max]` + (deposit, unpenalized slope); the kink at `a^Z=Z` separates the segments. + +**P2 timing (no taste shock in the toy, but the contract):** with a genuine taste-shocked +discrete choice `d` (work/retire), the order is **`max` over `a^Z` (and `C`) inside each +`d`, then `logsumexp` over `d`** β€” deterministic search nested inside the random-utility +aggregation. `max_{a^Z} logsumexp_d β‰  logsumexp_d max_{a^Z}`; the toy omits taste shocks so +it is a pure nested max. + +**Residual risk (NEGMβ†’RFC slide):** the outer max over a finite `a^Z` grid + candidates +carries discretization error in the illiquid policy. If the optimal `a^Z` is sharply +sensitive near the withdrawal kink, a coarse outer grid mislocates it. The P6 convergence +study (NEGM vs dense brute over a grid sequence: policies, Euler residuals, moments) is the +gate. With the mandatory candidates capturing the kinks, NEGM should hold β€” consistent with +the ~60–70 % prior. If outer refinement is prohibitively dense, slide to RFC (2-D envelope). + +## 4. Build-vs-buy + +| Tool | Solves Laibson? | Verified how | Adopt vs reimplement | +|---|---|---|---| +| **Authors' replication code** | yes (it *is* the paper) | Paper Β§"Code Availability" (`laibson-paper.md:1045`): "replication code is available in the Harvard Dataverse." Method = **numerical backward induction**, annual frequency, nonuniform grid (`:463`, `:1474`, `:1518`). Did not inspect the archive. | Best for *pure paper reproduction*; their own (non-pylcm, likely MATLAB/Fortran) code. Use as an **oracle**. | +| **pylcm BruteForce (today)** | yes, with action-grid bias | This probe: T=60 fine-grid 2-asset solve in 8 s / 280 MB on a V100. | Viable **interim replication backend** inside pylcm β€” matches the authors' method class. EGM upgrades accuracy, not feasibility. | +| Druedahl **G2EGM** (`github.com/JeppeDruedahl/G2EGM`) | with work | Pro-cited; the closest published 2-asset (liquid+illiquid) EGM analog. Not re-verified here. | Strong **oracle** for the C2-RFC fallback; MATLAB/C++ research code, not a pylcm backend. | +| NumEconCopenhagen **ConSav** / Dobrescu–Shanker **InverseDCDP** | with work | Pro-cited algorithm references (NEGM/durables; RFC/inverse-Euler). Not re-verified here. | Algorithm/oracle references; not drop-in pylcm backends. | + +Net: **brute (pylcm) or the authors' code reproduces the paper; build NEGM for the general +capability + accuracy + estimation throughput.** Use brute as the immediate oracle (already +working β€” Β§2) and G2EGM as the fallback-route oracle. + +## 5. What this changes in the plan + +- **Remove the false necessity premise.** Phase-0 #1 ("does brute clear the accuracy / + where does it break") is answered: brute is single-solve-feasible at fine grids; it + breaks (memory) only at `N≳200`/dim. The plan's "likely past brute comfort" is wrong for + a single solve β€” correct it to "brute is feasible but action-grid-biased; NEGM is an + accuracy/throughput/generality play." +- **NEGM nesting confirmed** analytically for the toy (Β§3) with the exact P1 kink-candidate + handling. The make-or-break check passes on paper; the empirical V-parity gate is the + next step (prototype outer-search vs the Β§2 oracle). +- **The kinked-toy oracle exists and is committed** as the parity target. +- Brute stays the **oracle of record** for C2 (cheap, already working) and a credible + interim replication backend. + +Concrete next step (C2 prototype): implement the outer `a^Z` search (deterministic axis, +B2) + inner 1-D EGM on `X` against a B1-tabulated continuation, with the mandatory +candidates `a^Z∈{0, Z}` and the liquid grid split at `a^X=0`, and assert convergence to the +Β§2 dense-brute oracle. diff --git a/pixi.lock b/pixi.lock index 4d698ca2a..a971b4c55 100644 --- a/pixi.lock +++ b/pixi.lock @@ -1,8 +1,36 @@ version: 7 platforms: - name: linux-64 + virtual-packages: + - __unix=0=0 + - __linux=4.18 + - __glibc=2.28 + - __archspec=0=x86_64 - name: osx-arm64 + virtual-packages: + - __unix=0=0 + - __osx=13.0 + - __archspec=0=m1 +- name: p1 + subdir: linux-64 + virtual-packages: + - __cuda=12 + - __unix=0=0 + - __linux=4.18 + - __glibc=2.28 + - __archspec=0=x86_64 +- name: p2 + subdir: linux-64 + virtual-packages: + - __cuda=13 + - __unix=0=0 + - __linux=4.18 + - __glibc=2.28 + - __archspec=0=x86_64 - name: win-64 + virtual-packages: + - __win=10.0 + - __archspec=0=x86_64 environments: benchmarks-cuda12: channels: @@ -10,7 +38,7 @@ environments: indexes: - https://pypi.org/simple packages: - linux-64: + p1: - conda: https://conda.anaconda.org/conda-forge/linux-64/_openmp_mutex-4.5-20_gnu.conda - conda: https://conda.anaconda.org/conda-forge/linux-64/argon2-cffi-bindings-25.1.0-py314h5bd0f2a_2.conda - conda: https://conda.anaconda.org/conda-forge/linux-64/asv-0.6.5-py314ha160325_3.conda @@ -337,7 +365,7 @@ environments: indexes: - https://pypi.org/simple packages: - linux-64: + p1: - conda: https://conda.anaconda.org/conda-forge/linux-64/_openmp_mutex-4.5-20_gnu.conda - conda: 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benchmarks-cuda12 = { features = [ "benchmarks", "cuda12" ], solve-group = "cuda cuda12 = { features = [ "cuda12" ], solve-group = "cuda12" } cuda13 = { features = [ "cuda13" ], solve-group = "cuda13" } docs = { features = [ "docs" ], solve-group = "default" } -metal = { features = [ "metal" ], solve-group = "metal" } tests-cpu = { features = [ "tests" ], solve-group = "default" } tests-cuda12 = { features = [ "tests", "cuda12" ], solve-group = "cuda12" } tests-cuda13 = { features = [ "tests", "cuda13" ], solve-group = "cuda13" } -tests-metal = { features = [ "tests", "metal" ], solve-group = "metal" } type-checking = { features = [ "type-checking", "tests" ], solve-group = "default" } [tool.pixi.feature.benchmarks.pypi-dependencies] # Pinned to the aca-model version this solver-seam work is developed against @@ -108,15 +105,13 @@ type-checking = { features = [ "type-checking", "tests" ], solve-group = "defaul # eligibility); flip back to branch = "main" once both sides have merged. aca-model = { git = "https://github.com/OpenSourceEconomics/aca-model.git", rev = "54fb8df1f83865eee421a4b656676ce4e6787928" } [tool.pixi.feature.cuda12] -platforms = [ "linux-64" ] -system-requirements = { cuda = "12" } +platforms = [ "linux-64-cuda12" ] [tool.pixi.feature.cuda12.target.linux-64.dependencies] cuda-nvcc = "~=12.0" [tool.pixi.feature.cuda12.target.linux-64.pypi-dependencies] jax = { version = ">=0.9", extras = [ "cuda12" ] } [tool.pixi.feature.cuda13] -platforms = [ "linux-64" ] -system-requirements = { cuda = "13" } +platforms = [ "linux-64-cuda13" ] [tool.pixi.feature.cuda13.target.linux-64.dependencies] cuda-nvcc = "~=13.0" [tool.pixi.feature.cuda13.target.linux-64.pypi-dependencies] @@ -130,11 +125,6 @@ quantecon = "*" build-docs = { cmd = "jupyter book build --html --execute", cwd = "docs", env = { JAX_PLATFORMS = "cpu" } } explanation-notebooks = "jupyter execute docs/explanations/*.ipynb" view-docs = { cmd = "jupyter book start --execute", cwd = "docs", env = { JAX_PLATFORMS = "cpu" } } -[tool.pixi.feature.metal] -platforms = [ "osx-arm64" ] -[tool.pixi.feature.metal.target.osx-arm64.pypi-dependencies] -jax = ">=0.9" -jax-metal = ">=0.1.1" [tool.pixi.feature.tests.dependencies] pytest = "*" pytest-cov = "*" @@ -142,16 +132,20 @@ pytest-xdist = "*" [tool.pixi.feature.tests.pypi-dependencies] quantecon = "*" [tool.pixi.feature.tests.tasks] -tests = "pytest tests" -tests-32bit = "pytest tests --precision=32" -tests-with-cov = "pytest tests --cov-report=xml --cov=./" +# Run the suite across 4 xdist workers (`--dist loadfile` in addopts keeps each +# file on one worker). `XLA_PYTHON_CLIENT_PREALLOCATE=false` is a no-op on CPU but +# required on GPU: it stops each of the 4 worker processes from preallocating ~75% +# of the device and OOMing β€” they grow to their actual (small) per-test need +# instead, and `loadfile` keeps the one heavy file (Mahler-Yum) on a single worker. +tests = { cmd = "pytest tests -n 4", env = { XLA_PYTHON_CLIENT_PREALLOCATE = "false" } } +tests-32bit = { cmd = "pytest tests --precision=32 -n 4", env = { XLA_PYTHON_CLIENT_PREALLOCATE = "false" } } +tests-with-cov = { cmd = "pytest tests --cov-report=xml --cov=./ -n 4", env = { XLA_PYTHON_CLIENT_PREALLOCATE = "false" } } [tool.pixi.feature.type-checking.dependencies] +# The env ty analyzes against (`[tool.ty] environment.python`); the ty binary +# itself is managed by the `ty` pre-commit hook (`prek run ty --all-files`). matplotlib = "*" pandas-stubs = "*" scipy-stubs = "*" -ty = "*" -[tool.pixi.feature.type-checking.tasks] -ty = "ty check" [tool.pixi.pypi-dependencies] jax = ">=0.9" pdbp = "*" @@ -169,7 +163,13 @@ asv-run-and-pr-comment = { depends-on = [ "asv-run", "asv-pr-comment" ] } asv-run-and-publish-main = { depends-on = [ "asv-run", "asv-publish" ] } [tool.pixi.workspace] channels = [ "conda-forge" ] -platforms = [ "linux-64", "osx-arm64", "win-64" ] +platforms = [ + "linux-64", + "osx-arm64", + "win-64", + { name = "linux-64-cuda12", platform = "linux-64", cuda = "12" }, + { name = "linux-64-cuda13", platform = "linux-64", cuda = "13" }, +] [tool.ruff] target-version = "py314" @@ -295,7 +295,6 @@ expand_tables = [ "tool.pixi.feature.tests.pypi-dependencies", "tool.pixi.feature.tests.tasks", "tool.pixi.feature.type-checking.dependencies", - "tool.pixi.feature.type-checking.tasks", "tool.pixi.pypi-dependencies", "tool.pixi.tasks", "tool.pixi.workspace", @@ -304,6 +303,10 @@ expand_tables = [ [tool.ty] src.exclude = [ "docs/**/*.ipynb" ] src.include = [ "src/", "tests/" ] +# ty resolves third-party imports from this pixi env (the ty-pre-commit hook runs +# `uv check --no-project`, so uv neither creates a `.venv` nor resolves deps). Run +# `pixi install` once. +environment.python = ".pixi/envs/type-checking" rules.ambiguous-protocol-member = "error" rules.deprecated = "error" rules.division-by-zero = "error" @@ -326,6 +329,7 @@ ini_options.addopts = [ ini_options.markers = [ "gpu: Tests that require a GPU (skipped on CPU-only machines)", "illustrative: Tests are designed for illustrative purposes", + "slow: heavy DC-EGM solve/oracle tests (deselected on small runners)", ] ini_options.filterwarnings = [ # JAX emits this UserWarning when user code asks for a dtype wider diff --git a/src/_lcm/egm/__init__.py b/src/_lcm/egm/__init__.py new file mode 100644 index 000000000..8cfcb1036 --- /dev/null +++ b/src/_lcm/egm/__init__.py @@ -0,0 +1,25 @@ +"""Endogenous Grid Method (EGM) building blocks. + +Submodules: + +- `_lcm.egm.validation`: DC-EGM model-contract validation. +- `_lcm.egm.regime_introspection`: pure spec-introspection of regimes and carry + targets, shared by the kernel build, continuation, and scope checks. +- `_lcm.egm.kernel_scope`: build-time checks naming features outside the kernel's + current scope (the source of the raising-step message). +- `_lcm.egm.continuation`: the expected next-period value and marginal over the + regime's targets (multi-target carry, passive blend, taste shocks, stochastic + nodes) that the EGM step consumes per savings node. +- `_lcm.egm.step_core`: the textbook single-post-state DC-EGM solve (Euler + inversion β†’ constrained candidates β†’ upper envelope β†’ publish V + carry). +- `_lcm.egm.asset_row`: the per-Euler-node solve for Euler-state-dependent + savings stages (maps `step_core` over the asset grid; the ACA path). +- `_lcm.egm.budget`: resources and post-decision (budget) evaluation. +- `_lcm.egm.euler`: Euler-equation inversion to candidate consumption. +- `_lcm.egm.carry`: the per-period marginal-utility carry passed between periods. +- `_lcm.egm.step`: the backward-induction EGM step tying the pieces together. +- `_lcm.egm.terminal`: the terminal-period carry producer. +- `_lcm.egm.upper_envelope`: upper-envelope refinement of EGM candidates. +- `_lcm.egm.interp`: interpolation on the NaN-padded grids the refinement produces. +- `_lcm.egm.published_policy`: the simulation-facing policy emitted by the solve. +""" diff --git a/src/_lcm/egm/asset_row.py b/src/_lcm/egm/asset_row.py new file mode 100644 index 000000000..186ef915f --- /dev/null +++ b/src/_lcm/egm/asset_row.py @@ -0,0 +1,520 @@ +"""Asset-row DC-EGM: the per-Euler-node solve for Euler-state-dependent stages. + +When any savings-stage function reads the current Euler state β€” the state's own +law, the regime-transition probabilities, a transition weight, or a passive +state's law β€” the kernel solves once per exogenous asset node instead of once +per combo. Conditional on a node, every such read is a per-combo constant, so +`step_core`'s single-post-state pipeline is exact within the node's row, and the +row publishes only its own node (brute-force-equivalent by construction). This +module maps that core pipeline over the Euler grid, differentiates the +continuation in the Euler slot for the per-node marginal $dV/dR$, and publishes +each node's scalar value and optimal action at its single resources query. The +per-combo carry holds the per-node published points, not the envelope workspace. +""" + +from collections.abc import Callable, Mapping +from types import MappingProxyType +from typing import Any + +import jax +import jax.numpy as jnp + +from _lcm.egm.carry import EGMCarry +from _lcm.egm.continuation import ( + bind_continuation, +) +from _lcm.egm.interp import ( + _interp_between_nodes, + interp_on_padded_grid, +) +from _lcm.egm.step_core import ( + _candidate_supgradient, + _compute_constrained_candidates, + _compute_nodes_over_savings, + _EgmKernelPieces, + _get_compute_node, +) +from _lcm.egm.upper_envelope.fues import ( + QueryBracket, +) +from _lcm.typing import ( + RegimeName, + StateName, +) +from lcm.typing import ( + Float1D, + FloatND, + ScalarFloat, + ScalarInt, +) + + +def _get_solve_one_combo_asset_rows( + *, + pieces: _EgmKernelPieces, + pool: dict[str, Any], + state_grid: Float1D, + next_regime_to_egm_carry: MappingProxyType[RegimeName, EGMCarry], + euler_batch_size: int, + savings_batch_size: int, + resolved_process_grids: Mapping[StateName, FloatND] = MappingProxyType({}), +) -> Callable[ + [tuple[ScalarInt | ScalarFloat, ...]], + tuple[Float1D, Float1D, Float1D, Float1D, Float1D], +]: + """Build the per-combo EGM computation solving per exogenous asset node. + + Used when any savings-stage function (the Euler state's law, the + regime-transition probabilities, a stochastic transition weight, a + passive state's law) reads the current Euler state: conditional on one + node of the Euler grid every such read is a per-combo constant, so the + single-post-state pipeline (Euler inversion over the savings nodes, + constrained candidates, upper-envelope refinement) is exact within the + node's row, and each row publishes only its own node β€” exactly where + the brute-force oracle evaluates the same decision-time functions. The + per-combo carry row holds the per-node published points: abscissa the + node resources (strictly increasing by the resources monotonicity check), + value the published V, and marginal the corrected + $dV/dR = u'(c^*) + \\beta\\, (\\partial W/\\partial a)|_{A^*} / R'(a)$, + NaN-padded to the carry length. The Euler-state gradient + $\\partial W/\\partial a$ rebuilds the full continuation closure from + the traced node value, so it carries every direct channel: the law's + residual, $\\sum \\partial P/\\partial a \\cdot EV$ from the + probabilities, the weights' and passive laws' derivatives. + """ + dtype = state_grid.dtype + n_state = int(state_grid.shape[0]) + + def solve_one_combo( + combo_values: tuple[ScalarInt | ScalarFloat, ...], + ) -> tuple[Float1D, Float1D, Float1D, Float1D, Float1D]: + """Run the per-asset-node EGM step for one (discrete x passive) combo. + + Takes the combo's values (discrete codes and passive node values) + positionally so `jax.vmap` can batch over flattened combo arrays. + + Returns: + Tuple of the combo's value row on the exogenous state grid and + its per-node endogenous grid, the published consumption policy on + that grid, and the value and marginal-utility carry + rows. + + """ + combo_pool = { + **pool, + **dict(zip(pieces.combo_names, combo_values, strict=True)), + } + # Validation pins the default Bellman aggregator, whose single + # non-(utility, E_next_V) parameter is the discount factor. + (discount_factor,) = tuple(pieces.build_H_kwargs(combo_pool).values()) + + def own_resources_of_state(state_value: ScalarFloat) -> ScalarFloat: + return pieces.own_resources_func( + **{pieces.euler_state_name: state_value}, **combo_pool + ) + + def continuation_of_euler_state( + state_value: ScalarFloat, savings_value: ScalarFloat + ) -> ScalarFloat: + """Expected continuation with the Euler slot as the grad argument. + + Rebuilds the per-combo continuation closure with the Euler slot + of the combo pool bound to `state_value` (positional, so + `jax.grad` differentiates the law's direct Euler-state channel) + and evaluates it at fixed savings. + """ + node_pool = {**combo_pool, pieces.euler_state_name: state_value} + expected_continuation = _get_expected_continuation_value( + pieces=pieces, + combo_pool=node_pool, + next_regime_to_egm_carry=next_regime_to_egm_carry, + dtype=dtype, + resolved_process_grids=resolved_process_grids, + ) + return expected_continuation(savings_value) + + def solve_one_node( + node_value: ScalarFloat, + ) -> tuple[ScalarFloat, ScalarFloat, ScalarFloat]: + """Run the single-post-state pipeline conditional on one node.""" + node_pool = {**combo_pool, pieces.euler_state_name: node_value} + + def utility_of_action(action_value: ScalarFloat) -> ScalarFloat: + return pieces.utility_func( + **{pieces.action_name: action_value}, **node_pool + ) + + compute_node = _get_compute_node( + pieces=pieces, + combo_pool=node_pool, + discount_factor=discount_factor, + utility_of_action=utility_of_action, + next_regime_to_egm_carry=next_regime_to_egm_carry, + dtype=dtype, + resolved_process_grids=resolved_process_grids, + ) + actions, endog_grid, values, expected_values = _compute_nodes_over_savings( + compute_node=compute_node, + savings_nodes=pieces.savings_nodes, + savings_batch_size=savings_batch_size, + ) + + resources_at_node, resources_gradient = jax.value_and_grad( + own_resources_of_state + )(node_value) + + constrained_actions, constrained_values = _compute_constrained_candidates( + first_endogenous_point=endog_grid[0], + publish_resources=resources_at_node, + borrowing_limit=pieces.borrowing_limit, + n_constrained=pieces.n_constrained, + constrained_ratio=pieces.constrained_ratio, + utility_of_action=utility_of_action, + discounted_expected_value_at_limit=discount_factor * expected_values[0], + ) + + candidate_grid = jnp.concatenate( + [pieces.borrowing_limit + constrained_actions, endog_grid] + ) + candidate_policy = jnp.concatenate([constrained_actions, actions]) + candidate_value = jnp.concatenate([constrained_values, values]) + # Same `-inf` masking as the default per-combo computation: dead + # candidates become the envelope scan's absent form (NaN). + candidate_dead = jnp.isneginf(candidate_value) + candidate_marginal = _candidate_supgradient( + policy=candidate_policy, + dead=candidate_dead, + utility_of_action=utility_of_action, + ) + # The node reads its refined envelope at one query + # (`resources_at_node`): FUES streams the bracketing pair (the + # `n_pad` envelope never materializes), while RFC has no streamed + # finder and materializes the full envelope before locating the same + # bracket β€” the published `(V, policy)` is identical, but RFC's + # asset-row path does not yet get the streaming `n_pad` memory win. + bracket = pieces.refine_to_bracket( + endog_grid=jnp.where(candidate_dead, jnp.nan, candidate_grid), + policy=jnp.where(candidate_dead, jnp.nan, candidate_policy), + value=jnp.where(candidate_dead, jnp.nan, candidate_value), + marginal_utility=candidate_marginal, + x_query=resources_at_node, + ) + + V_node, policy_node = publish_node_from_bracket( + bracket=bracket, + n_pad=pieces.n_pad, + resources_at_node=resources_at_node, + borrowing_limit=pieces.borrowing_limit, + utility_of_action=utility_of_action, + discounted_expected_value_at_limit=discount_factor * expected_values[0], + ) + + # The carry marginal at this node: + # dV/dR = u'(c*) + discount_factor * (dW/da at fixed A*) / R'(a), + # with A* = R(a) - c*(a). The envelope term u'(c*) covers the + # savings channel; the second term is the law's direct + # Euler-state channel through the continuation, mapped into + # resources space by the resources slope. + marginal_utility_node = jax.grad(utility_of_action)( + jnp.where(jnp.isnan(policy_node), 1.0, policy_node) + ) + savings_at_optimum = resources_at_node - policy_node + continuation_gradient = jax.grad(continuation_of_euler_state)( + node_value, savings_at_optimum + ) + mu_node = ( + marginal_utility_node + + discount_factor * continuation_gradient / resources_gradient + ) + mu_node = jnp.where(jnp.isnan(policy_node), jnp.nan, mu_node) + + # A node with no live candidate (its entire continuation is + # `-inf`) is worth `-inf`, like an infeasible combo; its + # marginal is exactly zero so probability-weighted sums stay + # finite. + no_live_candidate = jnp.all(candidate_dead) + V_node = jnp.where(no_live_candidate, -jnp.inf, V_node) + mu_node = jnp.where(jnp.isneginf(V_node) | no_live_candidate, 0.0, mu_node) + + return V_node, policy_node, mu_node + + # Splay the per-asset-node solve into `lax.map` blocks of + # `euler_batch_size` to shed peak working-set memory; `0` (or a size + # covering the whole grid) keeps the fused vmap. The two are + # numerically identical β€” only the schedule differs. + if 0 < euler_batch_size < n_state: + V_vec, policy_vec, mu_vec = jax.lax.map( + solve_one_node, state_grid, batch_size=euler_batch_size + ) + else: + V_vec, policy_vec, mu_vec = jax.vmap(solve_one_node)(state_grid) + publish_resources = jax.vmap(own_resources_of_state)(state_grid) + + pad = jnp.full((pieces.n_carry_rows - n_state,), jnp.nan, dtype=dtype) + grid_row = jnp.concatenate([publish_resources.astype(dtype), pad]) + policy_row = jnp.concatenate([policy_vec.astype(dtype), pad]) + value_row = jnp.concatenate([V_vec.astype(dtype), pad]) + marginal_row = jnp.concatenate([mu_vec.astype(dtype), pad]) + + if pieces.feasibility_func is not None: + # Infeasible discrete combos: -inf value rows so they win no + # maximum and carry zero choice probability; exactly-zero + # marginal utility so probability-weighted sums stay finite. + feasible = pieces.feasibility_func(**combo_pool) + V_vec = jnp.where(feasible, V_vec, -jnp.inf) + value_row = jnp.where(feasible, value_row, -jnp.inf) + marginal_row = jnp.where(feasible, marginal_row, 0.0) + + return ( + V_vec.astype(dtype), + grid_row, + policy_row, + value_row, + marginal_row, + ) + + return solve_one_combo + + +def _get_expected_continuation_value( + *, + pieces: _EgmKernelPieces, + combo_pool: dict[str, Any], + next_regime_to_egm_carry: MappingProxyType[RegimeName, EGMCarry], + dtype: Any, # noqa: ANN401 + resolved_process_grids: Mapping[StateName, FloatND] = MappingProxyType({}), +) -> Callable[[ScalarFloat], ScalarFloat]: + """Build the expected-continuation map $W(A)$ for one combo pool. + + Mirrors the expected-value aggregation of the per-savings-node Euler + inversion: per-target smoothed carry reads, regime-transition-probability + weighted, plus the scalar targets' constant values. The asset-row mode + differentiates this map in the Euler slot of the combo pool to obtain + the direct Euler-state channel $\\partial W/\\partial a$. The + probabilities, transition weights, and child next-state reads are all + evaluated from the combo pool *inside* this builder, so when the pool's + Euler slot is a traced value the gradient carries their first-order + terms (e.g. $\\sum \\partial P/\\partial a \\cdot EV$) β€” precomputing + them outside the differentiated closure would silently drop those + terms (Danskin does not cancel them: the probabilities are not the + softmax of the values they weight). + """ + continuation = bind_continuation( + plan=pieces.continuation_plan, + combo_pool=combo_pool, + next_regime_to_egm_carry=next_regime_to_egm_carry, + dtype=dtype, + resolved_process_grids=resolved_process_grids, + ) + + def expected_continuation(savings_value: ScalarFloat) -> ScalarFloat: + expected_value, _ = continuation(savings_value) + return expected_value + + return expected_continuation + + +def _publish_node_V_and_policy( + *, + refined_grid: Float1D, + refined_policy: Float1D, + refined_value: Float1D, + n_kept: ScalarInt, + n_pad: int, + resources_at_node: ScalarFloat, + borrowing_limit: ScalarFloat, + utility_of_action: Callable[[ScalarFloat], ScalarFloat], + discounted_expected_value_at_limit: ScalarFloat, +) -> tuple[ScalarFloat, ScalarFloat]: + """Publish one asset node's value and optimal action at its single query. + + The scalar-query counterpart of `_publish_V_and_carry_rows`: below the + lowest refined envelope point the closed-form constrained value is + published outright; everywhere else the Hermite read of the refined + envelope is floored at the constrained value, which remains a + feasible-policy lower bound. The published action follows the winning + branch β€” the closed-form action `R - borrowing_limit` where the + constrained value wins, the interpolated refined policy otherwise. + Envelope overflow NaN-poisons both outputs so the solve loop's NaN + diagnostics surface the offending (regime, period). + + Args: + refined_grid: Refined endogenous grid row from the envelope backend. + refined_policy: Refined policy row. + refined_value: Refined value row. + n_kept: Number of envelope points the backend kept. + n_pad: Static length of the refined rows. + resources_at_node: Resources at this exogenous Euler node (the row's + single publish query). + borrowing_limit: Lower bound of the savings grid. + utility_of_action: Utility with everything but the continuous action + bound. + discounted_expected_value_at_limit: Discounted expected continuation + value at the lowest savings node. + + Returns: + Tuple of the node's published value and published optimal action. + + """ + dtype = resources_at_node.dtype + overflowed = n_kept > n_pad + + marginal_utility = jax.vmap(jax.grad(utility_of_action))( + jnp.where(jnp.isnan(refined_policy), 1.0, refined_policy) + ) + marginal_utility = jnp.where(jnp.isnan(refined_policy), jnp.nan, marginal_utility) + marginal_utility = jnp.where(jnp.isneginf(refined_value), 0.0, marginal_utility) + + value_interpolated = interp_on_padded_grid( + x_query=resources_at_node, + xp=refined_grid, + fp=refined_value, + fp_slopes=marginal_utility, + ) + policy_interpolated = interp_on_padded_grid( + x_query=resources_at_node, + xp=refined_grid, + fp=refined_policy, + ) + closed_form_action = resources_at_node - borrowing_limit + value_constrained = jnp.where( + closed_form_action > 0.0, + utility_of_action(jnp.maximum(closed_form_action, jnp.finfo(dtype).tiny)) + + discounted_expected_value_at_limit, + -jnp.inf, + ) + below_refined = (closed_form_action > 0.0) & (resources_at_node <= refined_grid[0]) + constrained_wins = below_refined | (value_constrained >= value_interpolated) + V_node = jnp.where( + below_refined, + value_constrained, + jnp.maximum(value_interpolated, value_constrained), + ) + policy_node = jnp.where(constrained_wins, closed_form_action, policy_interpolated) + V_node = jnp.where(overflowed, jnp.nan, V_node).astype(dtype) + policy_node = jnp.where(overflowed, jnp.nan, policy_node).astype(dtype) + return V_node, policy_node + + +def publish_node_from_bracket( + *, + bracket: QueryBracket, + n_pad: int, + resources_at_node: ScalarFloat, + borrowing_limit: ScalarFloat, + utility_of_action: Callable[[ScalarFloat], ScalarFloat], + discounted_expected_value_at_limit: ScalarFloat, +) -> tuple[ScalarFloat, ScalarFloat]: + """Publish one asset node's value and optimal action from its query bracket. + + The streamed counterpart of `_publish_node_V_and_policy`: it consumes the + two envelope nodes that `refine_to_bracket` captured around + `resources_at_node` instead of the full NaN-padded refined row, so the + `n_pad` envelope is never materialized. The published economics are + identical: + + - The value is the cubic-Hermite read of the envelope between the two + bracket nodes (the value slope at each node is `grad(utility_of_action)` + at that node's policy, the envelope-theorem marginal), floored at the + closed-form constrained value, which is a feasible-policy lower bound. + - Below the lowest envelope node the closed-form constrained value is + published outright; the winning branch sets the action (the closed-form + `R - borrowing_limit` where constrained wins, the interpolated policy + otherwise). + - Envelope overflow (`n_kept > n_pad`) NaN-poisons both outputs, identical + to the row path, so the solve loop's NaN diagnostics surface the offending + (regime, period). + + Because the value and policy arithmetic is the shared `_interp_between_nodes` + primitive β€” the same one the row path reaches through + `interp_on_padded_grid` β€” the streamed publish cannot diverge from + row-then-interpolate: only the bracket-finding differs. + + Args: + bracket: The query bracket from `refine_to_bracket`. + n_pad: Static length of the envelope-refinement workspace (the overflow + threshold). + resources_at_node: Resources at this exogenous Euler node (the row's + single publish query). + borrowing_limit: Lower bound of the savings grid. + utility_of_action: Utility with everything but the continuous action + bound. + discounted_expected_value_at_limit: Discounted expected continuation + value at the lowest savings node. + + Returns: + Tuple of the node's published value and published optimal action. + + """ + dtype = resources_at_node.dtype + overflowed = bracket.n_kept > n_pad + + # The value Hermite slope is the envelope-theorem marginal `u'(c*)`, masked + # exactly as the row path: NaN where the node's policy is NaN (a padded + # slot), 0.0 where the node's value is `-inf` (an infeasible endpoint), so + # `_interp_between_nodes` falls back to the linear rule on those brackets. + slope_lower = _node_value_slope( + policy=bracket.lower_policy, + value=bracket.lower_value, + utility_of_action=utility_of_action, + ) + slope_upper = _node_value_slope( + policy=bracket.upper_policy, + value=bracket.upper_value, + utility_of_action=utility_of_action, + ) + + value_interpolated = _interp_between_nodes( + x_query=resources_at_node, + xp_lower=bracket.lower_grid, + xp_upper=bracket.upper_grid, + fp_lower=bracket.lower_value, + fp_upper=bracket.upper_value, + slope_lower=slope_lower, + slope_upper=slope_upper, + ) + policy_interpolated = _interp_between_nodes( + x_query=resources_at_node, + xp_lower=bracket.lower_grid, + xp_upper=bracket.upper_grid, + fp_lower=bracket.lower_policy, + fp_upper=bracket.upper_policy, + ) + + closed_form_action = resources_at_node - borrowing_limit + value_constrained = jnp.where( + closed_form_action > 0.0, + utility_of_action(jnp.maximum(closed_form_action, jnp.finfo(dtype).tiny)) + + discounted_expected_value_at_limit, + -jnp.inf, + ) + below_refined = (closed_form_action > 0.0) & ( + resources_at_node <= bracket.first_grid + ) + constrained_wins = below_refined | (value_constrained >= value_interpolated) + V_node = jnp.where( + below_refined, + value_constrained, + jnp.maximum(value_interpolated, value_constrained), + ) + policy_node = jnp.where(constrained_wins, closed_form_action, policy_interpolated) + V_node = jnp.where(overflowed, jnp.nan, V_node).astype(dtype) + policy_node = jnp.where(overflowed, jnp.nan, policy_node).astype(dtype) + return V_node, policy_node + + +def _node_value_slope( + *, + policy: ScalarFloat, + value: ScalarFloat, + utility_of_action: Callable[[ScalarFloat], ScalarFloat], +) -> ScalarFloat: + """Envelope-theorem value slope at one bracket node, masked like the row. + + The slope is `grad(utility_of_action)` at the node's policy β€” NaN where the + policy is a padded NaN slot, 0.0 where the node value is `-inf` β€” matching + the per-node masking the row path applies before interpolating. + """ + slope = jax.grad(utility_of_action)(jnp.where(jnp.isnan(policy), 1.0, policy)) + slope = jnp.where(jnp.isnan(policy), jnp.nan, slope) + return jnp.where(jnp.isneginf(value), 0.0, slope) diff --git a/src/_lcm/egm/budget.py b/src/_lcm/egm/budget.py new file mode 100644 index 000000000..765bf4b52 --- /dev/null +++ b/src/_lcm/egm/budget.py @@ -0,0 +1,104 @@ +"""Intrinsic budget constraint of a DC-EGM regime, for the simulate phase. + +A DC-EGM regime's spec carries no borrowing constraint β€” the EGM solve +enforces `continuous_action <= resources - savings_grid lower bound` +intrinsically by inverting the Euler equation on the exogenous savings grid. +The forward simulation, however, recomputes the argmax over the gridded +action space, so the constraint must be made explicit there: without a mask, +consumption points above resources imply below-limit savings whose +continuation is edge-clamped to the lowest wealth node and can win the +argmax. The builder here synthesizes that mask as an ordinary constraint +function; the simulation-phase builder injects it into the regime's +constraint set, where it enters the feasibility array `F` exactly like a +user-declared constraint. +""" + +from dags import get_annotations, with_signature +from dags.annotations import ensure_annotations_are_strings + +from _lcm.typing import ( + ConstraintFunction, + EconFunctionsMapping, + FunctionName, + StateOrActionName, +) +from lcm.solvers import DCEGM, NEGM +from lcm.typing import BoolND, FloatND + +DCEGM_BUDGET_CONSTRAINT_NAME: FunctionName = "dcegm_budget_constraint" + + +def get_intrinsic_budget_constraint( + *, + solver: DCEGM | NEGM, + functions: EconFunctionsMapping, +) -> ConstraintFunction: + """Build the budget-feasibility mask the EGM solve enforces intrinsically. + + The returned function reads the regime's continuous action and resources + function from the DAG and marks an action feasible iff + `continuous_action <= resources - borrowing_limit`, where the borrowing + limit is the savings grid's lowest node. + + A `NEGM` regime nests the same 1-D consumption-savings solve, so its mask + is built from the inner `DCEGM` config (`solver.inner`): the bound governs + the inner liquid margin, with the outer durable margin already folded into + the inner resources. + + Args: + solver: The regime's DC-EGM solver configuration, or the NEGM solver + whose inner DC-EGM config supplies the liquid margin. + functions: The regime's processed functions, used to stamp argument + annotations consistent with the rest of the DAG (the resources + function's return annotation, and the continuous action's + annotation as the other functions declare it). + + Returns: + Constraint function over the continuous action and the resources + function. + + """ + inner = solver.inner if isinstance(solver, NEGM) else solver + borrowing_limit = float(inner.savings_grid.to_jax()[0]) + action_name = inner.continuous_action + resources_name = inner.resources + + @with_signature( + args={ + action_name: _find_annotation_of_arg( + functions=functions, arg_name=action_name + ), + resources_name: ensure_annotations_are_strings( + get_annotations(functions[resources_name]) + )["return"], + }, + return_annotation="BoolND", + enforce=False, + ) + def budget_constraint(**action_and_resources: FloatND) -> BoolND: + return ( + action_and_resources[action_name] + <= action_and_resources[resources_name] - borrowing_limit + ) + + return budget_constraint # ty: ignore[invalid-return-type] + + +def _find_annotation_of_arg( + *, + functions: EconFunctionsMapping, + arg_name: StateOrActionName, +) -> str: + """Return the annotation the regime's functions use for one argument. + + The DAG's annotation-consistency check requires every consumer of a leaf + to agree on its annotation, so the synthesized constraint copies it from + the first regime function that declares the argument. Falls back to + `"FloatND"` when no function annotates it. + """ + for func in functions.values(): + annotations = ensure_annotations_are_strings(get_annotations(func)) + annotation = annotations.get(arg_name, "no_annotation_found") + if annotation != "no_annotation_found": + return annotation + return "FloatND" diff --git a/src/_lcm/egm/carry.py b/src/_lcm/egm/carry.py new file mode 100644 index 000000000..f4957ceac --- /dev/null +++ b/src/_lcm/egm/carry.py @@ -0,0 +1,116 @@ +"""Cross-period data channel of the DC-EGM solver. + +Backward induction with DC-EGM threads more than the value-function array +between adjacent periods: the parent's Euler inversion needs the child's +value and marginal utility on the child's endogenous (resources-space) grid. +`EGMCarry` bundles these rows; the solve loop rolls a +`next_regime_to_egm_carry` mapping alongside `next_regime_to_V_arr`, with one +entry per carry-producing regime (DC-EGM regimes and terminal regimes a +DC-EGM regime can target). +""" + +from collections.abc import Sequence +from dataclasses import dataclass +from typing import Any + +import jax +import jax.numpy as jnp + +from _lcm.dtypes import canonical_float_dtype +from lcm.typing import FloatND, ScalarFloat + + +@dataclass(frozen=True, kw_only=True) +class EGMCarry: + """Per-regime EGM solution rows threaded between adjacent periods. + + All rows share the trailing grid axis of static, per-regime length so the + carry has a period-invariant pytree shape (periods sharing a compiled + program never trigger retracing). Regimes with combo dimensions carry one + row per combo: leading axes are the regime's discrete states (in V state + order; process states are node-valued discrete dimensions), then its + passive continuous states (in V continuous-state order, one node per + combo), then its discrete actions. Every array is pinned to the canonical + float dtype. + """ + + endog_grid: FloatND + """Endogenous grid in resources space, NaN-padded in the tail. + + Weakly ascending per row: envelope kink abscissae appear twice, carrying + the left- and right-extrapolated policy values. + """ + + value: FloatND + """Choice-specific value at `endog_grid`; `-inf` marks infeasible rows.""" + + marginal_utility: FloatND + """Marginal value of resources $\\partial v / \\partial R$ at `endog_grid`. + + Exactly `0.0` (never NaN) wherever `value` is `-inf`: infeasible rows get + zero choice probability, and `0 \\cdot \\mu` must stay finite in the + parent's probability-weighted expectation. + """ + + taste_shock_scale: ScalarFloat + """EV1 taste-shock scale of the regime as a 0-d array; `0.0` = hard max.""" + + +# Pytree registration with an `__init__`-bypassing unflatten: JAX's transform +# and AOT-lowering machinery reconstructs pytrees with non-array leaves +# (`ArgInfo`, tracers, `None`), which the runtime-checked constructor would +# reject. Flatten order matches field declaration order. +_EGM_CARRY_FIELDS = ( + "endog_grid", + "value", + "marginal_utility", + "taste_shock_scale", +) + + +def _flatten_egm_carry(carry: EGMCarry) -> tuple[tuple[Any, ...], None]: + return tuple(getattr(carry, name) for name in _EGM_CARRY_FIELDS), None + + +def _unflatten_egm_carry(_aux: None, children: Sequence[Any]) -> EGMCarry: + carry = object.__new__(EGMCarry) + for name, child in zip(_EGM_CARRY_FIELDS, children, strict=True): + object.__setattr__(carry, name, child) + return carry + + +jax.tree_util.register_pytree_node(EGMCarry, _flatten_egm_carry, _unflatten_egm_carry) + + +def build_template_egm_carry( + *, + n_rows: int, + leading_shape: tuple[int, ...] = (), +) -> EGMCarry: + """Build a benign all-finite carry template with `n_rows` grid slots. + + Used to initialize the rolling `next_regime_to_egm_carry` mapping before + a regime has been solved, and as the lowering argument when AOT-compiling + EGM kernels. The endogenous grid is strictly ascending and every row is + finite, so a parent kernel evaluated against the template produces finite + (probability-zeroed) contributions rather than NaN. + + Args: + n_rows: Static length of the carry rows. + leading_shape: Sizes of the regime's combo dimensions (discrete + states, then passive states, then discrete actions); empty for + regimes without combo dimensions. + + Returns: + Carry with an ascending unit-interval grid and all-zero value and + marginal-utility rows, broadcast over `leading_shape`. + + """ + dtype = canonical_float_dtype() + shape = (*leading_shape, n_rows) + return EGMCarry( + endog_grid=jnp.broadcast_to(jnp.linspace(0.0, 1.0, n_rows, dtype=dtype), shape), + value=jnp.zeros(shape, dtype=dtype), + marginal_utility=jnp.zeros(shape, dtype=dtype), + taste_shock_scale=jnp.asarray(0.0, dtype=dtype), + ) diff --git a/src/_lcm/egm/cell_locator.py b/src/_lcm/egm/cell_locator.py new file mode 100644 index 000000000..733522cc1 --- /dev/null +++ b/src/_lcm/egm/cell_locator.py @@ -0,0 +1,490 @@ +"""Point-in-quad location on a curvilinear image mesh, with bilinear reads. + +The two-continuous-state EGM step maps a regular post-decision grid in $(a, b)$ +onto an irregular quadrilateral mesh in endogenous current-state space $(m, n)$: +each source cell of the product grid becomes one quad in the image, with fixed +product topology (source cell $(i, j)$ has image corners at nodes $(i, j)$, +$(i{+}1, j)$, $(i, j{+}1)$, $(i{+}1, j{+}1)$). To read a continuation on a +regular target $(m, n)$ grid, every target point must be located in the quad +that contains it together with its bilinear coordinates inside that quad. + +Two shortcuts are wrong and this module avoids them: + +- **Independent marginal search.** Two separate 1-D `searchsorted`s on the + marginal image coordinates do not locate the cell in a *coupled* monotone + image β€” a shear `F(a,b)=(a+0.4b, b+0.4a)` is strictly increasing in each + coordinate yet the marginal search lands in the wrong source cell. The locator + instead inverts the full bilinear cell map and tests $(\\xi, \\eta) \\in [0,1]^2$. +- **Constant-sign-Jacobian acceptance.** A positive Jacobian everywhere gives + only *local* invertibility. A polar map `F(a,b)=(e^a\\cos b, e^a\\sin b)` has a + positive Jacobian throughout yet folds over itself. `validate_quad_mesh` + detects folded / self-intersecting / inconsistently oriented cells and raises. + +The locator computes, for each query and *every* source cell, the analytic +inverse-bilinear coordinates, marks the cell that brackets the query, and +selects it β€” a static-shape, `vmap`-friendly scan with no data-dependent control +flow. `read_bilinear` then reads a value and a gradient at the located +coordinates. The bilinear value and the gradient are two distinct approximants: +the value is the bilinear interpolant of the node values, the gradient is that +interpolant's spatial derivative through the cell's geometric Jacobian. +""" + +from dataclasses import dataclass + +import jax +import jax.numpy as jnp + +from lcm.exceptions import PyLCMError +from lcm.typing import ( + BoolND, + Float1D, + Float2D, + FloatND, + Int1D, + ScalarFloat, + ScalarInt, +) + +# Slack on the [0, 1] membership test, to keep shared edges/corners owned. +_INSIDE_TOL = 1e-7 +# Below this absolute signed area a cell counts as degenerate (non-invertible). +_DEGENERATE_AREA_TOL = 1e-12 +# Slack on the boundary-turn sign used to detect a self-intersecting quad. +_TURN_SIGN_TOL = 1e-12 +# Below this the bilinear cross-term degenerates and the cell map is affine. +_AFFINE_CELL_TOL = 1e-12 + + +@dataclass(frozen=True) +class LocatedQueries: + """Per-query location of a batch of points in a quadrilateral image mesh. + + Carries the located cell's geometric Jacobian at the query coordinates so a + bilinear read can map $(\\xi, \\eta)$-partials to $(m, n)$-partials without + re-touching the image mesh. + """ + + cell_i: Int1D + """Source-cell row index $i$ (the $a$-axis cell) containing each query.""" + cell_j: Int1D + """Source-cell column index $j$ (the $b$-axis cell) containing each query.""" + xi: Float1D + """Bilinear coordinate $\\xi \\in [0, 1]$ along the cell's $a$-edge.""" + eta: Float1D + """Bilinear coordinate $\\eta \\in [0, 1]$ along the cell's $b$-edge.""" + geom_dm_dxi: Float1D + """$\\partial m / \\partial \\xi$ of the cell's geometric map at the query.""" + geom_dm_deta: Float1D + """$\\partial m / \\partial \\eta$ of the cell's geometric map at the query.""" + geom_dn_dxi: Float1D + """$\\partial n / \\partial \\xi$ of the cell's geometric map at the query.""" + geom_dn_deta: Float1D + """$\\partial n / \\partial \\eta$ of the cell's geometric map at the query.""" + + +@dataclass(frozen=True) +class BilinearRead: + """Bilinear value and spatial gradient at located query coordinates.""" + + value: Float1D + """Bilinear interpolant of the node values at each query.""" + grad_m: Float1D + """Partial derivative of the value w.r.t. $m$ (the first image coordinate).""" + grad_n: Float1D + """Partial derivative of the value w.r.t. $n$ (the second image coordinate).""" + + +def locate_in_quad_mesh( + *, + m_image: Float2D, + n_image: Float2D, + queries: Float2D, +) -> LocatedQueries: + """Locate each query in the source quad that contains it. + + For every query and every source cell the analytic inverse-bilinear map + yields candidate coordinates $(\\xi, \\eta)$; a query lies in a cell when those + fall in $[0, 1]^2$. The first such cell in row-major order is selected (shared + edges and corners are owned by the lowest-index neighbour). A query outside + the whole image falls back to the nearest boundary cell with clamped + coordinates, so the read stays defined. + + Args: + m_image: First image coordinate of every source node, shape `(n_a, n_b)`. + n_image: Second image coordinate of every source node, shape `(n_a, n_b)`. + queries: Query points, shape `(n_queries, 2)` as `(m, n)` pairs. + + Returns: + Located cell indices and bilinear coordinates, one entry per query. + + """ + corners = _cell_corners(m_image=m_image, n_image=n_image) + flat_corners = tuple(corner.reshape(-1, 2) for corner in corners) + n_j = m_image.shape[1] - 1 + + def locate_one( + query: Float1D, + ) -> tuple[ + ScalarInt, + ScalarInt, + ScalarFloat, + ScalarFloat, + ScalarFloat, + ScalarFloat, + ScalarFloat, + ScalarFloat, + ]: + xi, eta = _inverse_bilinear_all_cells(corners=corners, query=query) + inside = _is_inside(xi, eta) + # Distance-to-cell-centre penalty breaks ties / drives the no-hit + # fallback to the nearest boundary cell. + center_penalty = (xi - 0.5) ** 2 + (eta - 0.5) ** 2 + score = jnp.where(inside, -1.0, center_penalty) + flat = jnp.argmin(score).astype(jnp.int32) + i = flat // n_j + j = flat % n_j + xi_sel = jnp.clip(xi[flat], 0.0, 1.0) + eta_sel = jnp.clip(eta[flat], 0.0, 1.0) + jac = _geometric_jacobian( + flat_corners=flat_corners, flat=flat, xi=xi_sel, eta=eta_sel + ) + return i.astype(jnp.int32), j.astype(jnp.int32), xi_sel, eta_sel, *jac + + cell_i, cell_j, xi, eta, dm_dxi, dm_deta, dn_dxi, dn_deta = jax.vmap(locate_one)( + queries + ) + return LocatedQueries( + cell_i=cell_i, + cell_j=cell_j, + xi=xi, + eta=eta, + geom_dm_dxi=dm_dxi, + geom_dm_deta=dm_deta, + geom_dn_dxi=dn_dxi, + geom_dn_deta=dn_deta, + ) + + +def read_bilinear( + *, + node_values: Float2D, + located: LocatedQueries, +) -> BilinearRead: + """Read a bilinear value and spatial gradient at located coordinates. + + The value is the bilinear interpolant of the four cell-corner node values at + $(\\xi, \\eta)$. The gradient is that interpolant's derivative w.r.t. $(m, n)$, + obtained by pushing the $(\\xi, \\eta)$ partials through the inverse of the + cell's geometric Jacobian $\\partial(m, n)/\\partial(\\xi, \\eta)$. Value and + gradient are therefore separate approximants of the underlying field. + + Args: + node_values: Scalar field sampled on every source node, shape + `(n_a, n_b)` β€” aligned with the image-coordinate arrays. + located: Located cells and coordinates from `locate_in_quad_mesh`. + + Returns: + Bilinear value and gradient components per query. + + """ + i = located.cell_i + j = located.cell_j + v00 = node_values[i, j] + v10 = node_values[i + 1, j] + v01 = node_values[i, j + 1] + v11 = node_values[i + 1, j + 1] + xi = located.xi + eta = located.eta + + value = ( + (1 - xi) * (1 - eta) * v00 + + xi * (1 - eta) * v10 + + (1 - xi) * eta * v01 + + xi * eta * v11 + ) + dv_dxi = (1 - eta) * (v10 - v00) + eta * (v11 - v01) + dv_deta = (1 - xi) * (v01 - v00) + xi * (v11 - v10) + grad_m, grad_n = _push_gradient_through_geometry( + located=located, dv_dxi=dv_dxi, dv_deta=dv_deta + ) + return BilinearRead(value=value, grad_m=grad_m, grad_n=grad_n) + + +def validate_quad_mesh(*, m_image: Float2D, n_image: Float2D) -> None: + """Reject a folded, self-intersecting, or inconsistently oriented image mesh. + + Every source cell maps to a quad. A valid mesh β€” locally invertible *and* + globally one-to-one over the domain β€” must pass three checks: + + - **Orientation.** Each quad's signed area (shoelace over its corners in + boundary order) must be nonzero and share one sign across all cells. A + zero area is a degenerate (non-invertible) cell; a flipped sign is a cell + folded relative to its neighbours. + - **Convexity.** No quad may self-intersect (a bow-tie), detected by a turn + sign-flip while walking the cell boundary. + - **No global overlap.** No cell's centroid may fall inside any *other* + cell. A consistent local orientation does not rule out the image folding + back over itself far away in index space β€” the polar map + `F(a,b)=(e^a\\cos b, e^a\\sin b)` keeps every cell positively oriented yet + wraps so distant cells cover the same region. The overlap check catches + that global fold a per-cell test cannot. + + A positive geometric Jacobian everywhere does not imply any of these. + + Args: + m_image: First image coordinate of every source node, shape `(n_a, n_b)`. + n_image: Second image coordinate of every source node, shape `(n_a, n_b)`. + + Raises: + PyLCMError: If any cell is degenerate, self-intersecting, oriented + against the others, or overlaps another cell (a fold or overlap). + + """ + corners = _cell_corners(m_image=m_image, n_image=n_image) + p00, p10, p11, p01 = corners[0], corners[1], corners[3], corners[2] + + signed_area = 0.5 * (_cross(p10 - p00, p01 - p00) + _cross(p11 - p10, p01 - p11)) + areas = jnp.asarray(signed_area).ravel() + + if bool(jnp.any(jnp.abs(areas) < _DEGENERATE_AREA_TOL)): + msg = ( + "Degenerate image cell: a source cell maps to a zero-area quad, so " + "the mesh is not locally invertible. The mesh must have strictly " + "oriented cells (no fold / overlap)." + ) + raise PyLCMError(msg) + + positive = bool(jnp.all(areas > 0)) + negative = bool(jnp.all(areas < 0)) + if not (positive or negative): + msg = ( + "Inconsistently oriented image cells: the signed areas of the source " + "cells do not all share one sign, so the image folds over itself " + "(overlapping cells). The mesh is not globally one-to-one." + ) + raise PyLCMError(msg) + + if _has_self_intersecting_cell(corners=corners): + msg = ( + "Self-intersecting image cell: a source cell maps to a bow-tie quad " + "whose edges cross, so the cell folds on itself. The mesh must have " + "convex, consistently oriented cells (no fold / overlap)." + ) + raise PyLCMError(msg) + + if _has_overlapping_cells(corners=corners): + msg = ( + "Overlapping image cells: a source cell's centroid falls inside " + "another cell, so the image folds back over itself and is not " + "globally one-to-one (a fold / overlap)." + ) + raise PyLCMError(msg) + + +def _cell_corners(*, m_image: Float2D, n_image: Float2D) -> FloatND: + """Stack the four corner image-points of every cell. + + Returns an array of shape `(4, n_a-1, n_b-1, 2)` whose leading axis runs over + the corners $(i, j)$, $(i{+}1, j)$, $(i, j{+}1)$, $(i{+}1, j{+}1)$ as + `(m, n)` pairs. + """ + points = jnp.stack([m_image, n_image], axis=-1) + p00 = points[:-1, :-1] + p10 = points[1:, :-1] + p01 = points[:-1, 1:] + p11 = points[1:, 1:] + return jnp.stack([p00, p10, p01, p11], axis=0) + + +def _inverse_bilinear_all_cells( + *, corners: FloatND, query: Float1D +) -> tuple[FloatND, FloatND]: + """Solve the inverse-bilinear cell map for one query against every cell. + + Returns flattened $(\\xi, \\eta)$ over all cells (row-major), each of shape + `(n_cells,)`. For each cell the bilinear map + $Q - A = B\\,\\xi + C\\,\\eta + D\\,\\xi\\eta$ is inverted by solving a quadratic + in $\\eta$ (linear when the bilinear cross-term degenerates to affine) and + back-substituting $\\xi$; the root yielding coordinates closest to the unit + square is kept. + """ + p00 = corners[0].reshape(-1, 2) + p10 = corners[1].reshape(-1, 2) + p01 = corners[2].reshape(-1, 2) + p11 = corners[3].reshape(-1, 2) + + coeff_a = p00 + coeff_b = p10 - p00 + coeff_c = p01 - p00 + coeff_d = p00 - p10 - p01 + p11 + q_minus_a = query[None, :] - coeff_a + + quad_a = _cross(-coeff_c, coeff_d) + quad_b = _cross(q_minus_a, coeff_d) + _cross(-coeff_c, coeff_b) + quad_c = _cross(q_minus_a, coeff_b) + + eta_linear = -quad_c / _nonzero(quad_b) + disc = jnp.maximum(quad_b**2 - 4 * quad_a * quad_c, 0.0) + sqrt_disc = jnp.sqrt(disc) + eta_root1 = (-quad_b + sqrt_disc) / _nonzero(2 * quad_a) + eta_root2 = (-quad_b - sqrt_disc) / _nonzero(2 * quad_a) + + is_affine = jnp.abs(quad_a) < _AFFINE_CELL_TOL + xi1, eta1 = _xi_from_eta(coeff_b, coeff_c, coeff_d, q_minus_a, eta_root1) + xi2, eta2 = _xi_from_eta(coeff_b, coeff_c, coeff_d, q_minus_a, eta_root2) + xi_lin, eta_lin = _xi_from_eta(coeff_b, coeff_c, coeff_d, q_minus_a, eta_linear) + + # Prefer the root that lands inside the unit square; fall back to the one + # closest to the cell centre. + pick_root1 = _prefer(xi1, eta1, xi2, eta2) + xi_quad = jnp.where(pick_root1, xi1, xi2) + eta_quad = jnp.where(pick_root1, eta1, eta2) + + xi = jnp.where(is_affine, xi_lin, xi_quad) + eta = jnp.where(is_affine, eta_lin, eta_quad) + return xi, eta + + +def _geometric_jacobian( + *, + flat_corners: tuple[FloatND, FloatND, FloatND, FloatND], + flat: ScalarInt, + xi: ScalarFloat, + eta: ScalarFloat, +) -> tuple[ScalarFloat, ScalarFloat, ScalarFloat, ScalarFloat]: + """Bilinear geometric Jacobian of the selected cell at $(\\xi, \\eta)$. + + Returns $(\\partial m/\\partial\\xi, \\partial m/\\partial\\eta, + \\partial n/\\partial\\xi, \\partial n/\\partial\\eta)$ for the cell indexed by + `flat` in the flattened (row-major) cell ordering. + """ + p00 = flat_corners[0][flat] + p10 = flat_corners[1][flat] + p01 = flat_corners[2][flat] + p11 = flat_corners[3][flat] + d_dxi = (1 - eta) * (p10 - p00) + eta * (p11 - p01) + d_deta = (1 - xi) * (p01 - p00) + xi * (p11 - p10) + return d_dxi[0], d_deta[0], d_dxi[1], d_deta[1] + + +def _xi_from_eta( + coeff_b: FloatND, + coeff_c: FloatND, + coeff_d: FloatND, + q_minus_a: FloatND, + eta: FloatND, +) -> tuple[FloatND, FloatND]: + """Back-substitute $\\xi$ from a chosen $\\eta$ via the better-conditioned row. + + From $\\xi\\,(B + D\\eta) = (Q - A) - C\\eta$, divide by whichever component of + $B + D\\eta$ has larger magnitude to avoid cancellation. + """ + denom = coeff_b + coeff_d * eta[:, None] + rhs = q_minus_a - coeff_c * eta[:, None] + use_first = jnp.abs(denom[:, 0]) >= jnp.abs(denom[:, 1]) + xi = jnp.where( + use_first, + rhs[:, 0] / _nonzero(denom[:, 0]), + rhs[:, 1] / _nonzero(denom[:, 1]), + ) + return xi, eta + + +def _prefer(xi1: FloatND, eta1: FloatND, xi2: FloatND, eta2: FloatND) -> BoolND: + """Boolean mask selecting root 1 over root 2 per cell.""" + inside1 = _is_inside(xi1, eta1) + inside2 = _is_inside(xi2, eta2) + dist1 = (xi1 - 0.5) ** 2 + (eta1 - 0.5) ** 2 + dist2 = (xi2 - 0.5) ** 2 + (eta2 - 0.5) ** 2 + return inside1 | (~inside2 & (dist1 <= dist2)) + + +def _is_inside(xi: FloatND, eta: FloatND) -> BoolND: + """Boolean mask: coordinates within the unit square up to a small slack.""" + return ( + (xi >= -_INSIDE_TOL) + & (xi <= 1 + _INSIDE_TOL) + & (eta >= -_INSIDE_TOL) + & (eta <= 1 + _INSIDE_TOL) + ) + + +def _push_gradient_through_geometry( + *, located: LocatedQueries, dv_dxi: Float1D, dv_deta: Float1D +) -> tuple[Float1D, Float1D]: + """Map $(\\xi, \\eta)$-partials to $(m, n)$-partials via the inverse Jacobian. + + The value's spatial gradient is + $\\nabla_{m,n} V = J^{-1\\top} \\, (\\partial V/\\partial\\xi, + \\partial V/\\partial\\eta)$, with $J = \\partial(m, n)/\\partial(\\xi, \\eta)$ + the cell's geometric Jacobian evaluated at the located coordinates. The + gradient is read from the same located cell as the value but is its own + bilinear approximant. + """ + j_m_xi = located.geom_dm_dxi + j_m_eta = located.geom_dm_deta + j_n_xi = located.geom_dn_dxi + j_n_eta = located.geom_dn_deta + det = j_m_xi * j_n_eta - j_m_eta * j_n_xi + # Floor the magnitude (keeping the sign) so a degenerate cell never divides + # by zero; a valid mesh has det well away from zero here. + safe_sign = jnp.where(det < 0, -1.0, 1.0) + det = safe_sign * jnp.maximum(jnp.abs(det), 1e-12) + # Inverse-transpose times the (xi, eta) gradient. + grad_m = (j_n_eta * dv_dxi - j_n_xi * dv_deta) / det + grad_n = (-j_m_eta * dv_dxi + j_m_xi * dv_deta) / det + return grad_m, grad_n + + +def _has_self_intersecting_cell(*, corners: FloatND) -> bool: + """Detect a bow-tie quad via a sign flip across a splitting diagonal.""" + p00 = corners[0] + p10 = corners[1] + p01 = corners[2] + p11 = corners[3] + # Walk the boundary p00 -> p10 -> p11 -> p01; a convex (non-self-crossing) + # quad keeps the same turn sign at every vertex. + turn0 = _cross(p10 - p00, p11 - p10) + turn1 = _cross(p11 - p10, p01 - p11) + turn2 = _cross(p01 - p11, p00 - p01) + turn3 = _cross(p00 - p01, p10 - p00) + turns = jnp.stack( + [turn0.ravel(), turn1.ravel(), turn2.ravel(), turn3.ravel()], axis=0 + ) + all_nonneg = jnp.all(turns >= -_TURN_SIGN_TOL, axis=0) + all_nonpos = jnp.all(turns <= _TURN_SIGN_TOL, axis=0) + convex = all_nonneg | all_nonpos + return bool(jnp.any(~convex)) + + +def _has_overlapping_cells(*, corners: FloatND) -> bool: + """Detect a global fold: any cell centroid landing inside a different cell. + + For every cell centroid the inverse-bilinear map is solved against all cells; + a valid mesh contains each centroid in exactly one cell (its own). A centroid + contained by any other cell means two source cells cover the same image + region β€” a fold the per-cell orientation check misses. + """ + p00 = corners[0].reshape(-1, 2) + p10 = corners[1].reshape(-1, 2) + p01 = corners[2].reshape(-1, 2) + p11 = corners[3].reshape(-1, 2) + centroids = (p00 + p10 + p01 + p11) / 4.0 + + def count_containers(centroid: Float1D) -> ScalarInt: + xi, eta = _inverse_bilinear_all_cells(corners=corners, query=centroid) + return jnp.sum(_is_inside(xi, eta).astype(jnp.int32)).astype(jnp.int32) + + container_counts = jax.vmap(count_containers)(centroids) + # Each centroid is inside its own cell; >1 means an overlap with another. + return bool(jnp.any(container_counts > 1)) + + +def _cross(u: FloatND, v: FloatND) -> FloatND: + """2-D scalar cross product $u_x v_y - u_y v_x$ over the last axis.""" + return u[..., 0] * v[..., 1] - u[..., 1] * v[..., 0] + + +def _nonzero(x: FloatND) -> FloatND: + """Replace exact zeros with a tiny signed value to keep divisions finite.""" + return jnp.where(x == 0, 1e-30, x) diff --git a/src/_lcm/egm/continuation.py b/src/_lcm/egm/continuation.py new file mode 100644 index 000000000..266d4b332 --- /dev/null +++ b/src/_lcm/egm/continuation.py @@ -0,0 +1,1096 @@ +"""The DC-EGM continuation: expected next-period value and marginal over targets. + +Both the per-savings-node Euler inversion and the asset-row Euler-state gradient +need one quantity β€” the expected continuation as a function of end-of-period +savings, aggregated over the regime's reachable next-period targets. This module +builds that aggregation from the period's carry: it selects each target's carry +rows by the child's discrete state, maps the child state into the child's +resources space, interpolates each row at its own next-period resources, blends +over passive states, smooths the child's discrete choices (hard max or EV1 +logsum), and weights stochastic-process nodes by their intrinsic transition. The +core EGM step and the asset-row step consume the per-target reader it produces; +everything multi-target, passive-state, taste-shock, and stochastic-node lives +behind that boundary. +""" + +from collections.abc import Callable, Mapping +from dataclasses import dataclass +from types import MappingProxyType +from typing import Any, cast + +import jax +import jax.numpy as jnp +from dags import concatenate_functions + +from _lcm.dtypes import canonical_float_dtype +from _lcm.egm.carry import EGMCarry +from _lcm.egm.interp import ( + interp_on_prepared_grid, + locate_on_grid, + prepare_padded_grid, +) +from _lcm.egm.regime_introspection import ( + _get_child_discrete_actions, + _get_child_resources_arg_names, + _get_child_resources_function, + _get_child_state_name, + _get_discrete_state_names, + _get_passive_state_names, +) +from _lcm.grids import Grid +from _lcm.logsum import logsum_and_softmax +from _lcm.processes import _ContinuousStochasticProcess +from _lcm.regime_building.next_state import get_next_state_function_for_solution +from _lcm.regime_building.Q_and_F import get_period_targets +from _lcm.regime_building.V import VInterpolationInfo +from _lcm.typing import ( + ActionName, + EconFunctionsMapping, + FunctionName, + RegimeName, + RegimeTransitionFunction, + StateName, + TransitionFunctionName, + TransitionFunctionsMapping, +) +from lcm.regime import Regime as UserRegime +from lcm.typing import ( + Float1D, + FloatND, + IntND, + ScalarFloat, + ScalarInt, +) + + +def _is_runtime_process(grid: Grid) -> bool: + """Whether the grid is a process whose nodes resolve only at solve time.""" + return ( + isinstance(grid, _ContinuousStochasticProcess) and not grid.is_fully_specified + ) + + +def get_egm_continuation_targets( + *, + period: int, + transitions: TransitionFunctionsMapping, + reachable_targets: frozenset[RegimeName], + regimes_to_active_periods: MappingProxyType[RegimeName, tuple[int, ...]], + regime_to_v_interpolation_info: MappingProxyType[RegimeName, VInterpolationInfo], +) -> tuple[tuple[RegimeName, ...], tuple[RegimeName, ...]]: + """Split next-period-active targets into carry-interpolated and scalar ones. + + This adapter is the single place where the EGM step derives "which target + regimes / which transition functions" from the engine regime's + transitions; changes to the transition representation swap this body + without touching the kernel. + + - *Carry targets* have state-transition entries; their continuation is + interpolated from their `EGMCarry` rows. + - *Scalar targets* are stateless (no transition entries, no states; e.g. + a `dead` regime); their continuation is the constant value of their + carry rows and their marginal continuation is zero. Only declared- + reachable regimes qualify: a stateless regime the model contains for + other regimes' sake has no transition-probability cell here, and the + regime transition is the single source of truth for reachability. + + Args: + period: The period the kernel solves. + transitions: Immutable mapping of target regime names to their state + transition functions. + reachable_targets: The regime's declared-reachable target names. + regimes_to_active_periods: Immutable mapping of regime names to their + active period tuples. + regime_to_v_interpolation_info: Mapping of regime names to + V-interpolation info. + + Returns: + Tuple of carry-target names and scalar-target names. + + """ + carry_targets = get_period_targets( + period=period, + transitions=transitions, + regimes_to_active_periods=regimes_to_active_periods, + ) + scalar_targets = tuple( + name + for name in regime_to_v_interpolation_info + if name in reachable_targets + and period + 1 in regimes_to_active_periods.get(name, ()) + and not regime_to_v_interpolation_info[name].state_names + and name not in carry_targets + ) + return carry_targets, scalar_targets + + +@dataclass(frozen=True, kw_only=True) +class _ChildRead: + """Build-time statics for reading one carry target's rows. + + The row block of a child carry β€” after the deterministic discrete-state + and stochastic-node indices are applied β€” has the child's passive nodes as + leading axes and its discrete-action combos as trailing axes; the + per-row binding values and the block shape are precomputed here so the + kernel's per-savings-node read is pure array work. + """ + + next_state_func: Callable[..., Any] + """The target's next-state function (post-decision function removed).""" + + next_state_key: TransitionFunctionName + """`next_` key of the child's continuous (Euler) state.""" + + euler_state_name: StateName + """Name of the child's continuous (Euler) state.""" + + has_taste_shocks: bool + """Whether the target regime declares EV1 taste shocks. + + Selects the child's discrete-action aggregation: the `scale > 0` logsum + when set, the hard maximum (one-hot argmax) when not. + """ + + resources_func: Callable[..., ScalarFloat] + """The child's concatenated resources function (kwargs-based).""" + + resources_arg_names: frozenset[str] + """Leaf argument names of the child's resources function.""" + + resources_param_names: frozenset[str] + """Qualified param leaves of the child's resources function. + + Bound per node from the combo pool (the regime's flat params, plus `age` + / `period`). Constant in the savings node, so they ride through the + composed resources gradients without contributing a savings derivative. + """ + + resources_is_simple: bool + """Whether the resources function reads only the child's Euler state. + + The simple case computes one query and one composed gradient per savings + node and broadcasts them across the carry rows; the general case + evaluates both per row. Params and `age` / `period` are constants, so a + resources function reading only the Euler state and params still counts + as simple. + """ + + discrete_state_names: tuple[StateName, ...] + """Child discrete-state names (stochastic states included) in carry-axis order.""" + + stochastic_flags: tuple[bool, ...] + """Per discrete-state dimension: whether it is a stochastic node axis. + + A dimension is stochastic when its next-period node is distributed by a + transition law: a continuous AR(1) process state, or a Markov-discrete + state whose `next_` is a stochastic transition into the target. Both + are integrated over the child's node axis with the intrinsic weights. + """ + + stochastic_state_names: tuple[StateName, ...] + """Child stochastic node-axis names (process or Markov) in carry-axis order.""" + + stochastic_node_values: tuple[FloatND | IntND, ...] + """Per stochastic dimension: the node values fed into the resources query. + + Process dimensions carry the continuous AR(1) grid points (NaN when + supplied at runtime β€” `process_grid_names` then names the runtime grid + that overrides the placeholder); Markov-discrete dimensions carry the + integer category codes (which equal the carry's leading-axis indices). + """ + + process_grid_names: tuple[StateName | None, ...] + """Per stochastic dimension: the process state's name, or `None`. + + A continuous AR(1) process state with runtime-supplied distribution params + has its grid points resolved only at solve time; this names the state whose + resolved grid the kernel substitutes for the build-time placeholder in + `stochastic_node_values`. `None` for Markov-discrete dimensions and for + fully-specified processes (whose build-time grid is already final).""" + + weight_keys: tuple[str, ...] + """`weight___next_` keys aligned with the stochastic dims.""" + + weights_func: Callable[..., Any] | None + """Concatenated intrinsic-weights function, or `None` without stochastic dims.""" + + passive_state_names: tuple[StateName, ...] + """Child passive-state names in carry-axis order.""" + + passive_grids: tuple[Float1D, ...] + """Child passive grids, aligned with `passive_state_names`.""" + + row_arg_names: tuple[StateName | ActionName, ...] + """Names bound per carry row: passive states, then discrete actions.""" + + row_values: tuple[FloatND | IntND, ...] + """Flattened row-binding value meshes, aligned with `row_arg_names`. + + Passive entries are float node values; discrete-action entries are + integer codes. + """ + + row_block_shape: tuple[int, ...] + """Shape of the carry's row block: passive sizes, then action sizes.""" + + +@dataclass(frozen=True, kw_only=True) +class ContinuationPlan: + """Build-time statics for the per-savings-node continuation aggregation. + + Binding a plan to one combo pool and the next period's carries (via + `bind_continuation`) yields the regime's expected continuation value and + marginal continuation as a function of end-of-period savings, aggregated + over all reachable targets. The EGM step and the asset-row step read only + that bound callable, never these statics directly. + """ + + carry_targets: tuple[RegimeName, ...] + """Targets whose continuation is interpolated from their carry rows.""" + + scalar_targets: tuple[RegimeName, ...] + """Stateless targets contributing a constant continuation value.""" + + child_reads: Mapping[RegimeName, _ChildRead] + """Per-carry-target statics of the child carry read.""" + + compute_regime_transition_probs: RegimeTransitionFunction + """Regime transition probability function for solve.""" + + post_decision_name: FunctionName + """Name of the post-decision function (the savings node's input slot).""" + + stochastic_node_batch_size: int + """Block size for splaying the child stochastic-node expectation (0 = fused).""" + + +def bind_continuation( + *, + plan: ContinuationPlan, + combo_pool: dict[str, Any], + next_regime_to_egm_carry: MappingProxyType[RegimeName, EGMCarry], + dtype: Any, # noqa: ANN401 + resolved_process_grids: Mapping[StateName, FloatND] = MappingProxyType({}), +) -> Callable[[ScalarFloat], tuple[ScalarFloat, ScalarFloat]]: + """Bind a continuation plan to one combo pool and the next period's carries. + + Returns a map from an end-of-period savings node to the regime's expected + continuation value and expected marginal continuation (both in savings + space): per-carry-target smoothed carry reads weighted by the + regime-transition probabilities, plus the scalar targets' constant values. + The probabilities, transition weights, and child next-state reads are all + evaluated from `combo_pool` *inside* this builder, so when the pool's Euler + slot is a traced value (asset-row mode) the value's gradient carries their + first-order terms (e.g. $\\sum \\partial P/\\partial a \\cdot EV$) β€” + precomputing them outside the differentiated closure would silently drop + those terms (Danskin does not cancel them: the probabilities are not the + softmax of the values they weight). + + `resolved_process_grids` maps each runtime-resolved process state name to + its solve-time grid (the node values its distribution params imply). A + child read whose stochastic dimension is such a process substitutes that + grid for the build-time NaN placeholder, so a resources function reading + the process node integrates over the resolved nodes. + """ + regime_transition_probs = plan.compute_regime_transition_probs(**combo_pool) + # Carry rows are indexed here along their whole leading discrete axes (the + # carry-producing target's combo axes). A target state sharded across devices + # (`distributed=True`) would split those axes per device, so this index could + # not cross shards β€” and unlike the continuation V-array (co-mapped device-local + # via `co_mapped_in_axes` in `max_Q_over_a`), the carry channel has no such + # co-map, so a sharded carry into a DCEGM parent is unsupported. It is currently + # unreachable, not merely unhandled: a distributed state cannot reach a DCEGM + # regime or its carry-producing targets β€” regime-level `distributed` is rejected + # (must be model-level), a model-level sharded state pruned from a non-terminal + # regime is rejected, and a sharded discrete state surviving on a DCEGM regime is + # rejected by grid hygiene. Lifting the restriction is not infeasible: extend the + # continuation-V co-map to `next_regime_to_egm_carry` (map each carry's leading + # discrete axis device-local, as for the V-array); or gather carry rows + # shard-aware before indexing (an all-gather on just the carry's leading axis); + # or carve out sharded axes that appear in no carry via a validation check. + child_readers = { + target: _get_child_carry_reader( + read=plan.child_reads[target], + carry=next_regime_to_egm_carry[target], + combo_pool=combo_pool, + post_decision_name=plan.post_decision_name, + stochastic_node_batch_size=plan.stochastic_node_batch_size, + resolved_process_grids=resolved_process_grids, + ) + for target in plan.carry_targets + } + + def continuation( + savings_value: ScalarFloat, + ) -> tuple[ScalarFloat, ScalarFloat]: + """Expected continuation value and marginal at one savings node.""" + expected_marginal = jnp.asarray(0.0, dtype=dtype) + expected_value = jnp.asarray(0.0, dtype=dtype) + for target in plan.carry_targets: + # The smoothed marginal is already in savings space: the composed + # gradient factor is applied per carry row inside the read. + smoothed_value, smoothed_marginal = child_readers[target](savings_value) + prob = regime_transition_probs[target] + # Zero unreachable-target contributions on the results, never by + # multiplying into a possibly non-finite value. The else branch is + # `prob * 0.0` (not `0.0`) so a NaN probability poisons the sum + # instead of vanishing. + expected_marginal = expected_marginal + jnp.where( + prob > 0.0, prob * smoothed_marginal, prob * 0.0 + ) + expected_value = expected_value + jnp.where( + prob > 0.0, prob * smoothed_value, prob * 0.0 + ) + for target in plan.scalar_targets: + prob = regime_transition_probs[target] + constant_value = next_regime_to_egm_carry[target].value[0] + expected_value = expected_value + jnp.where( + prob > 0.0, prob * constant_value, prob * 0.0 + ) + return expected_value, expected_marginal + + return continuation + + +def _get_child_carry_reader( + *, + read: _ChildRead, + carry: EGMCarry, + combo_pool: dict[str, Any], + post_decision_name: FunctionName, + stochastic_node_batch_size: int, + resolved_process_grids: Mapping[StateName, FloatND] = MappingProxyType({}), +) -> Callable[[ScalarFloat], tuple[ScalarFloat, ScalarFloat]]: + """Build the per-savings-node carry read of one target for one combo. + + The returned callable maps a savings node to the target's smoothed + continuation value and smoothed marginal continuation in savings space + (the composed gradient $\\partial R'/\\partial A$ is applied per carry + row inside the read). With child stochastic states (a continuous AR(1) + process state or a Markov-discrete state), the read runs per child node + combo and the per-node results are summed with the intrinsic transition + weights $w(\\text{node}' \\mid \\text{node})$ β€” *outside* the + discrete-action aggregation, matching the brute-force expectation over + the already action-aggregated next-period V. The weights are evaluated + once per combo (they depend on the current node values, params, and β€” in + asset-row mode β€” the combo pool's Euler value, never on the savings + node β€” validated). + + A runtime-resolved process dimension reads its node values from + `resolved_process_grids` (keyed by the process state name) rather than the + build-time NaN placeholder in `read.stochastic_node_values`, so a resources + function reading the process node integrates over the resolved nodes. + """ + stochastic_node_values = tuple( + resolved_process_grids[name] + if name is not None and name in resolved_process_grids + else values + for name, values in zip( + read.process_grid_names, read.stochastic_node_values, strict=True + ) + ) + weight_vecs: tuple[Float1D, ...] = () + if read.weights_func is not None: + weights = read.weights_func(**combo_pool) + weight_vecs = tuple(weights[key] for key in read.weight_keys) + resources_reads_stochastic = bool( + set(read.stochastic_state_names) & read.resources_arg_names + ) + + # The child's carry rows are fixed for the period; prepare each row's `+inf` + # search key and valid prefix length once here β€” above the per-savings-node + # and per-stochastic-node reads β€” so the per-query interpolation never + # recomputes the row's NaN mask. That mask, recomputed and held for every + # query lane, is the grid-length working buffer that dominates `egm_step` at + # scale; preparing it once collapses it to a carry-sized array. + n_carry_rows = carry.endog_grid.shape[-1] + flat_search, flat_valid = jax.vmap(prepare_padded_grid)( + carry.endog_grid.reshape(-1, n_carry_rows) + ) + prepared_search_grid = flat_search.reshape(carry.endog_grid.shape) + prepared_valid_length = flat_valid.reshape(carry.endog_grid.shape[:-1]) + + def read_child(savings_value: ScalarFloat) -> tuple[ScalarFloat, ScalarFloat]: + """Read the child's carry at one savings node.""" + # The solution-phase next-state function returns a flat mapping of + # `next_` names to scalars; the shared protocol's nested + # return type is the simulation form. Everything but the child's + # Euler state is savings-independent (validated), so these values + # ride as constants through the composed gradients below. + next_states = read.next_state_func( + **combo_pool, **{post_decision_name: savings_value} + ) + deterministic_index = tuple( + cast("ScalarInt", next_states[f"next_{name}"]) + for name, is_stochastic in zip( + read.discrete_state_names, read.stochastic_flags, strict=True + ) + if not is_stochastic + ) + # A passive next-state is normally produced by `next_state_func`. Under + # NEGM the outer post-decision's transition is stripped (it is bound per + # outer-grid node, not recomputed), so that margin's next value is read + # from the combo pool instead. + child_passive_values = tuple( + cast( + "ScalarFloat", + next_states[f"next_{name}"] + if f"next_{name}" in next_states + else combo_pool[f"next_{name}"], + ) + for name in read.passive_state_names + ) + deterministic_resources_kwargs = { + name: next_states[f"next_{name}"] + for name, is_stochastic in zip( + read.discrete_state_names, read.stochastic_flags, strict=True + ) + if not is_stochastic and name in read.resources_arg_names + } + # The child resources function may read the regime's flat params and + # `age` / `period` (e.g. a capital-income return rate); bind them from + # the combo pool once. They are constant in the savings node, so they + # ride through the composed gradients as constants. + resources_param_kwargs = { + name: combo_pool[name] for name in read.resources_param_names + } + + def child_euler_state(savings: ScalarFloat) -> ScalarFloat: + inner = read.next_state_func(**combo_pool, **{post_decision_name: savings}) + return cast("ScalarFloat", inner[read.next_state_key]) + + def queries_and_gradients( + stochastic_values: tuple[ScalarFloat | ScalarInt, ...], + ) -> tuple[FloatND, FloatND]: + return _compute_row_queries_and_gradients( + read=read, + child_euler_state=child_euler_state, + deterministic_resources_kwargs=deterministic_resources_kwargs, + resources_param_kwargs=resources_param_kwargs, + savings_value=savings_value, + stochastic_values=stochastic_values, + ) + + if not read.stochastic_state_names: + queries, gradients = queries_and_gradients(()) + return _aggregate_child_choices( + carry=carry, + prepared_search_grid=prepared_search_grid, + prepared_valid_length=prepared_valid_length, + has_taste_shocks=read.has_taste_shocks, + child_index=deterministic_index, + child_passive_values=child_passive_values, + child_passive_grids=read.passive_grids, + row_queries=queries, + row_gradients=gradients, + ) + + return _expect_over_stochastic_nodes( + read=read, + carry=carry, + prepared_search_grid=prepared_search_grid, + prepared_valid_length=prepared_valid_length, + stochastic_node_values=stochastic_node_values, + weight_vecs=weight_vecs, + deterministic_index=deterministic_index, + child_passive_values=child_passive_values, + queries_and_gradients=queries_and_gradients, + resources_reads_stochastic=resources_reads_stochastic, + stochastic_node_batch_size=stochastic_node_batch_size, + ) + + return read_child + + +def _compute_row_queries_and_gradients( + *, + read: _ChildRead, + child_euler_state: Callable[[ScalarFloat], ScalarFloat], + deterministic_resources_kwargs: dict[str, Any], + resources_param_kwargs: dict[str, Any], + savings_value: ScalarFloat, + stochastic_values: tuple[ScalarFloat | ScalarInt, ...], +) -> tuple[FloatND, FloatND]: + """Per-row $R'$ queries and composed gradients for one node combo. + + The composed map differentiated per row is + $A \\mapsto R'(\\mathcal{T}(A), z', d', p'; \\theta)$ β€” only the child's + Euler state depends on the savings node; the discrete-state codes, + stochastic node values, passive node values, action codes, and model + params $\\theta$ ride as constants. With a simple resources function + (Euler state and params only), one query and gradient is computed and + broadcast across the row block. + """ + if read.resources_is_simple: + + def composed(savings: ScalarFloat) -> ScalarFloat: + return read.resources_func( + **{read.euler_state_name: child_euler_state(savings)}, + **resources_param_kwargs, + ) + + query, gradient = jax.value_and_grad(composed)(savings_value) + return ( + jnp.broadcast_to(query, read.row_block_shape), + jnp.broadcast_to(gradient, read.row_block_shape), + ) + + # Empty when the resources function reads no stochastic state: the shared + # (node-independent) computation passes no node values. + stochastic_kwargs = ( + dict(zip(read.stochastic_state_names, stochastic_values, strict=True)) + if stochastic_values + else {} + ) + + def composed_row( + savings: ScalarFloat, row_values: tuple[ScalarFloat | ScalarInt, ...] + ) -> ScalarFloat: + bound = { + read.euler_state_name: child_euler_state(savings), + **deterministic_resources_kwargs, + **stochastic_kwargs, + **dict(zip(read.row_arg_names, row_values, strict=True)), + } + return read.resources_func( + **{k: v for k, v in bound.items() if k in read.resources_arg_names}, + **resources_param_kwargs, + ) + + if read.row_values: + queries, gradients = jax.vmap( + jax.value_and_grad(composed_row), in_axes=(None, 0) + )(savings_value, read.row_values) + return ( + queries.reshape(read.row_block_shape), + gradients.reshape(read.row_block_shape), + ) + query, gradient = jax.value_and_grad(composed_row)(savings_value, ()) + return ( + jnp.broadcast_to(query, read.row_block_shape), + jnp.broadcast_to(gradient, read.row_block_shape), + ) + + +def _expect_over_stochastic_nodes( + *, + read: _ChildRead, + carry: EGMCarry, + prepared_search_grid: FloatND, + prepared_valid_length: IntND, + stochastic_node_values: tuple[FloatND | IntND, ...], + weight_vecs: tuple[Float1D, ...], + deterministic_index: tuple[ScalarInt, ...], + child_passive_values: tuple[ScalarFloat, ...], + queries_and_gradients: Callable[ + [tuple[ScalarFloat | ScalarInt, ...]], tuple[FloatND, FloatND] + ], + resources_reads_stochastic: bool, + stochastic_node_batch_size: int, +) -> tuple[ScalarFloat, ScalarFloat]: + """Weight the carry read over the child's stochastic-node combos. + + Runs the full read (per-row queries, mixed passive interpolation, choice + aggregation) at every child node combo and sums the per-node smoothed + values and marginals with the joint intrinsic weights β€” the stochastic + expectation sits *outside* the discrete-action aggregation, matching the + brute-force solver's weighted average of the already action-aggregated + next-period V. The node axes are the child's continuous AR(1) process + states and Markov-discrete states alike; a Markov node feeds its integer + code into the resources query (when read) and selects the carry's leading + discrete axis by that code. + """ + # The queries depend on the node combo only when the resources function + # reads a stochastic state; otherwise compute them once and share. + if not resources_reads_stochastic: + shared_queries, shared_gradients = queries_and_gradients(()) + + def read_at_nodes( + node_indices: tuple[ScalarInt, ...], + ) -> tuple[ScalarFloat, ScalarFloat]: + """Run the full carry read at one child stochastic-node combo.""" + if resources_reads_stochastic: + stochastic_values = tuple( + values[index] + for values, index in zip( + stochastic_node_values, node_indices, strict=True + ) + ) + queries, gradients = queries_and_gradients(stochastic_values) + else: + queries, gradients = shared_queries, shared_gradients + return _aggregate_child_choices( + carry=carry, + prepared_search_grid=prepared_search_grid, + prepared_valid_length=prepared_valid_length, + has_taste_shocks=read.has_taste_shocks, + child_index=_interleave_child_index( + deterministic_index=deterministic_index, + node_indices=node_indices, + stochastic_flags=read.stochastic_flags, + ), + child_passive_values=child_passive_values, + child_passive_grids=read.passive_grids, + row_queries=queries, + row_gradients=gradients, + ) + + node_index_mesh = jnp.meshgrid( + *( + jnp.arange(values.shape[0], dtype=jnp.int32) + for values in stochastic_node_values + ), + indexing="ij", + ) + flat_node_indices = tuple(mesh.ravel() for mesh in node_index_mesh) + joint_weights = weight_vecs[0][flat_node_indices[0]] + for vec, indices in zip(weight_vecs[1:], flat_node_indices[1:], strict=True): + joint_weights = joint_weights * vec[indices] + + def _weighted_node_sum(values: FloatND, weights: FloatND) -> ScalarFloat: + # A zero-weight node contributes exactly 0.0 even when its smoothed + # value is -inf (never 0 * inf = NaN). The else branch is `weights * + # 0.0` (not a bare `0.0`) so a NaN weight poisons the sum instead of + # vanishing. + return jnp.sum(jnp.where(weights > 0.0, weights * values, weights * 0.0)) + + # The expectation mesh (the product of the child's stochastic-node counts) + # is the dominant `egm_step` working buffer's child-node axis. A positive + # `stochastic_node_batch_size` below the mesh length accumulates the + # weighted expectation in `lax.scan` blocks: each block reads only its + # `batch_size` nodes (shedding the per-node gather working-set) AND folds + # the weighted sum into the scan carry, so the full node-stacked + # `(..., n_nodes)` result is never materialised β€” the savings the single + # fused vmap below cannot reach, because there the reduction is downstream + # of the materialised stack. `0` (or a size covering the whole mesh) keeps + # that fused vmap + reduction. The weighted sum is associative, so the + # value function matches the fused solve to numerical tolerance (the block + # reduction reorders the floating-point adds). + n_nodes = flat_node_indices[0].shape[0] + if 0 < stochastic_node_batch_size < n_nodes: + n_blocks = -(-n_nodes // stochastic_node_batch_size) + pad = n_blocks * stochastic_node_batch_size - n_nodes + blocked_indices = tuple( + jnp.concatenate([indices, jnp.zeros(pad, dtype=indices.dtype)]).reshape( + n_blocks, stochastic_node_batch_size + ) + for indices in flat_node_indices + ) + # Pad weights with 0.0, not the pad slots' real weights: the pad slots + # reuse node index 0, so their values are read but zero-weighted, and + # contribute exactly 0.0 to every block sum. + blocked_weights = jnp.concatenate( + [joint_weights, jnp.zeros(pad, dtype=joint_weights.dtype)] + ).reshape(n_blocks, stochastic_node_batch_size) + + def accumulate( + carry: tuple[ScalarFloat, ScalarFloat], + block: tuple[tuple[IntND, ...], FloatND], + ) -> tuple[tuple[ScalarFloat, ScalarFloat], None]: + block_indices, block_weights = block + block_values, block_marginals = jax.vmap(read_at_nodes)(block_indices) + acc_value, acc_marginal = carry + return ( + acc_value + _weighted_node_sum(block_values, block_weights), + acc_marginal + _weighted_node_sum(block_marginals, block_weights), + ), None + + zero = jnp.zeros((), dtype=joint_weights.dtype) + (smoothed_value, smoothed_marginal), _ = jax.lax.scan( + accumulate, (zero, zero), (blocked_indices, blocked_weights) + ) + return smoothed_value, smoothed_marginal + + node_values, node_marginals = jax.vmap(read_at_nodes)(flat_node_indices) + smoothed_value = _weighted_node_sum(node_values, joint_weights) + smoothed_marginal = _weighted_node_sum(node_marginals, joint_weights) + return smoothed_value, smoothed_marginal + + +def _interleave_child_index( + *, + deterministic_index: tuple[ScalarInt, ...], + node_indices: tuple[ScalarInt, ...], + stochastic_flags: tuple[bool, ...], +) -> tuple[ScalarInt, ...]: + """Merge deterministic codes and stochastic node indices in carry-axis order.""" + deterministic_iter = iter(deterministic_index) + node_iter = iter(node_indices) + return tuple( + next(node_iter) if is_stochastic else next(deterministic_iter) + for is_stochastic in stochastic_flags + ) + + +def _hard_max_and_one_hot( + *, values: FloatND, axes: tuple[int, ...] +) -> tuple[FloatND, FloatND]: + """Hard maximum over `axes` and a one-hot indicator of the (first) argmax. + + The no-taste-shocks aggregation: the smoothed maximum a regime without + declared EV1 taste shocks uses in place of the `scale > 0` logsum. Ties + break toward the first flat index. A slice that is `-inf` everywhere yields + a `-inf` maximum and a one-hot at index 0, so the marginal it weights (zero + on infeasible rows) stays consistent. + + Args: + values: Choice-specific values; infeasible entries are `-inf`. + axes: Axes to aggregate over (the discrete-choice axes). + + Returns: + Tuple of the hard maximum (shape of `values` with `axes` removed) and + the one-hot argmax indicator (shape of `values`). + + """ + hard_max = jnp.max(values, axis=axes) + moved = jnp.moveaxis(values, axes, tuple(range(len(axes)))) + lead_shape = moved.shape[: len(axes)] + flat = moved.reshape((-1, *moved.shape[len(axes) :])) + one_hot = ( + jnp.arange(flat.shape[0]).reshape((-1,) + (1,) * (flat.ndim - 1)) + == jnp.argmax(flat, axis=0) + ).astype(values.dtype) + one_hot = jnp.moveaxis( + one_hot.reshape(lead_shape + moved.shape[len(axes) :]), + tuple(range(len(axes))), + axes, + ) + return hard_max, one_hot + + +def _aggregate_child_choices( + *, + carry: EGMCarry, + prepared_search_grid: FloatND, + prepared_valid_length: IntND, + has_taste_shocks: bool, + child_index: tuple[ScalarInt, ...], + child_passive_values: tuple[ScalarFloat, ...], + child_passive_grids: tuple[Float1D, ...], + row_queries: FloatND, + row_gradients: FloatND, +) -> tuple[ScalarFloat, ScalarFloat]: + """Read one child's carry with mixed interpolation and aggregate its choices. + + The carry rows matching the child's discrete-state values are selected + by integer indexing on the leading state axes (discrete codes equal grid + positions, stochastic dims indexed at one node); the remaining leading axes + are the child's passive nodes, then its discrete-action combos. Every + row is interpolated 1-D at its own resources query and its marginal is + multiplied by its own composed gradient $(\\partial R'/\\partial A)$ β€” + per row, because each row's envelope lives in its own resources space. + The passive axes are then blended away with edge-clamped linear weights + on the two neighboring nodes of each passive grid β€” *before* the choice + aggregation, so the logsum sees blended choice-specific values. Finally + the discrete-action rows are aggregated with the child's taste-shock + scale: the smoothed value is the logsum and the smoothed marginal is + $\\sum_{d'} P_{d'} \\mu_{d'} (\\partial R'/\\partial A)_{d'}$ β€” exact + for EV1 by Danskin's theorem, no $\\partial P/\\partial R$ terms. Scale + zero yields the hard max / one-hot argmax through the same code path. + Rows that are $-\\infty$ everywhere (infeasible child combos) get zero + probability and contribute exactly zero marginal utility; a zero-weight + passive neighbor contributes exactly zero even when its row is + $-\\infty$ (`jnp.where` on results, never `0 \\cdot \\infty`). + + Args: + carry: The child's EGM carry. + prepared_search_grid: The whole carry's `+inf`-padded search key + (`carry.endog_grid`'s shape), prepared once above the read fan-out. + prepared_valid_length: The whole carry's per-row valid prefix lengths + (`carry.endog_grid`'s shape without the row axis). + child_index: The child's discrete-state values at this savings node + (stochastic dims: the node index of this read). + child_passive_values: The child's passive values at this savings + node, aligned with `child_passive_grids`. + child_passive_grids: The child's passive grids in carry-axis order. + row_queries: Per-row resources queries with the row block's shape + (passive dims, then action dims). + row_gradients: Per-row composed gradients $\\partial R'/\\partial A$ + with the row block's shape. + + Returns: + Tuple of the smoothed continuation value and the smoothed marginal + continuation $\\partial W/\\partial A$. + + """ + n_pad = carry.value.shape[-1] + grid_block = carry.endog_grid[child_index] + value_block = carry.value[child_index] + marginal_block = carry.marginal_utility[child_index] + # The prepared search key and valid length are indexed by the same + # `child_index` as the carry rows, so each row reads its own precomputed + # pair instead of recomputing the NaN mask per query. + search_block = prepared_search_grid[child_index] + valid_block = prepared_valid_length[child_index] + # Leading axes of the blocks: the child's passive nodes, then its + # discrete-action combos. + block_shape = value_block.shape[:-1] + grid_rows = grid_block.reshape(-1, n_pad) + value_rows = value_block.reshape(-1, n_pad) + marginal_rows = marginal_block.reshape(-1, n_pad) + search_rows = search_block.reshape(-1, n_pad) + valid_rows = valid_block.reshape(-1) + queries_flat = row_queries.reshape(-1) + gradients_flat = row_gradients.reshape(-1) + + # The marginal-utility row is the value row's exact slope (envelope + # theorem), upgrading the value read to cubic Hermite; the mu read itself + # stays linear (a policy-grade quantity, and its interpolation error + # enters the value only at second order through the Euler inversion). + def interp_value_row( + search_grid: Float1D, + valid_length: ScalarInt, + xp: Float1D, + fp: Float1D, + fp_slopes: Float1D, + x_query: ScalarFloat, + ) -> ScalarFloat: + """Interpolate one carry value row at its query; positional per `jax.vmap`.""" + return interp_on_prepared_grid( + x_query=x_query, + search_grid=search_grid, + valid_length=valid_length, + xp=xp, + fp=fp, + fp_slopes=fp_slopes, + ) + + def interp_row( + search_grid: Float1D, + valid_length: ScalarInt, + xp: Float1D, + fp: Float1D, + x_query: ScalarFloat, + ) -> ScalarFloat: + """Interpolate one carry row at its own query; positional per `jax.vmap`.""" + return interp_on_prepared_grid( + x_query=x_query, + search_grid=search_grid, + valid_length=valid_length, + xp=xp, + fp=fp, + ) + + value_at_child = jax.vmap(interp_value_row)( + search_rows, valid_rows, grid_rows, value_rows, marginal_rows, queries_flat + ) + marginal_at_child = jax.vmap(interp_row)( + search_rows, valid_rows, grid_rows, marginal_rows, queries_flat + ) + # `-inf` entries interpolate pointwise to `-inf` (never NaN) and carry + # exactly-zero marginal utility, so an infeasible-everywhere row reads as + # the `-inf` / zero pair while a row with isolated `-inf` nodes (e.g. a + # bequest at zero wealth) keeps its finite region intact. A `-inf` value + # read pins the marginal read to zero so the pair stays consistent at + # queries clamped onto a `-inf` node. + marginal_at_child = jnp.where( + jnp.isneginf(value_at_child), 0.0, marginal_at_child * gradients_flat + ) + value_at_child = value_at_child.reshape(block_shape) + marginal_at_child = marginal_at_child.reshape(block_shape) + + for passive_value, passive_grid in zip( + child_passive_values, child_passive_grids, strict=True + ): + lower, upper, weight_upper = locate_on_grid( + x_query=passive_value, grid=passive_grid + ) + weight_lower = 1.0 - weight_upper + # Blend on results: a zero-weight neighbor contributes exactly 0.0, + # so an on-node read reproduces the node rows and a -inf neighbor + # never turns into 0 * inf = NaN; a positive-weight -inf neighbor + # correctly forces the blend to -inf. + value_at_child = jnp.where( + weight_lower > 0.0, weight_lower * value_at_child[lower], 0.0 + ) + jnp.where(weight_upper > 0.0, weight_upper * value_at_child[upper], 0.0) + # Marginal rows are finite everywhere (exactly 0.0 on infeasible + # rows), so a plain blend is safe. + marginal_at_child = ( + weight_lower * marginal_at_child[lower] + + weight_upper * marginal_at_child[upper] + ) + + value_at_child = value_at_child.reshape(-1) + marginal_at_child = marginal_at_child.reshape(-1) + if has_taste_shocks: + smoothed_value, choice_probs = logsum_and_softmax( + values=value_at_child, scale=carry.taste_shock_scale, axes=(0,) + ) + else: + smoothed_value, choice_probs = _hard_max_and_one_hot( + values=value_at_child, axes=(0,) + ) + smoothed_marginal = jnp.sum(choice_probs * marginal_at_child) + return smoothed_value, smoothed_marginal + + +def _build_child_reads( + *, + user_regimes: Mapping[RegimeName, UserRegime], + functions: EconFunctionsMapping, + transitions: TransitionFunctionsMapping, + stochastic_transition_names: frozenset[TransitionFunctionName], + carry_targets: tuple[RegimeName, ...], + post_decision_name: FunctionName, + regime_to_v_interpolation_info: MappingProxyType[RegimeName, VInterpolationInfo], +) -> MappingProxyType[RegimeName, _ChildRead]: + """Build the per-carry-target statics of the EGM kernel's child reads. + + The post-decision function is removed from the DAG, so its output (the + savings node) becomes an external input of the next-state functions. + Passing the full `functions` mapping would let the DAG compute savings + internally from the (unknown) state and action leaves β€” it runs, but is + silently wrong. + + Returns: + Immutable mapping of carry-target names to their read statics. + + """ + functions_without_post = MappingProxyType( + {name: func for name, func in functions.items() if name != post_decision_name} + ) + reads: dict[RegimeName, _ChildRead] = {} + for target in carry_targets: + target_info = regime_to_v_interpolation_info[target] + target_regime = user_regimes[target] + euler_state_name = _get_child_state_name(user_regime=target_regime) + discrete_state_names = _get_discrete_state_names( + v_interpolation_info=target_info + ) + # A discrete dimension is a stochastic node axis when its next-period + # node is distributed by a transition law: a continuous AR(1) process + # state, or a Markov-discrete state whose `next_` is a stochastic + # transition into this target. Both are integrated over the child's + # node axis with the intrinsic weights `weight___next_`. + target_transition_names = frozenset(transitions[target]) + + def _is_stochastic( + name: StateName, + target_info: VInterpolationInfo = target_info, + target_transition_names: frozenset[ + TransitionFunctionName + ] = target_transition_names, + ) -> bool: + if isinstance( + target_info.discrete_states[name], _ContinuousStochasticProcess + ): + return True + transition_name = f"next_{name}" + return ( + transition_name in target_transition_names + and transition_name in stochastic_transition_names + ) + + stochastic_flags = tuple(_is_stochastic(name) for name in discrete_state_names) + stochastic_state_names = tuple( + name + for name, is_stochastic in zip( + discrete_state_names, stochastic_flags, strict=True + ) + if is_stochastic + ) + # Process axes feed the continuous AR(1) grid points into the resources + # query; Markov axes feed their integer category codes (`to_jax()` + # returns `[0, 1, ...]`, which also equal the carry's leading-axis + # indices). Both serve as the node-axis range of the integration mesh. + stochastic_node_values = tuple( + ( + jnp.asarray( + target_info.discrete_states[name].to_jax(), + dtype=canonical_float_dtype(), + ) + if isinstance( + target_info.discrete_states[name], _ContinuousStochasticProcess + ) + else jnp.asarray(target_info.discrete_states[name].to_jax()) + ) + for name in stochastic_state_names + ) + # A process state whose distribution params arrive at runtime has its + # `to_jax()` grid as a NaN placeholder above; name it so the kernel + # substitutes the resolved grid (the same node values the regime's own + # combo axes iterate, shared with the source regime) at solve time. A + # fully-specified process keeps its final build-time grid (`None`). + process_grid_names = tuple( + name if _is_runtime_process(target_info.discrete_states[name]) else None + for name in stochastic_state_names + ) + weight_keys = tuple( + f"weight_{target}__next_{name}" for name in stochastic_state_names + ) + weights_func = None + if weight_keys: + weights_func = concatenate_functions( + functions={ + name: func + for name, func in functions_without_post.items() + if name != "H" + }, + targets=list(weight_keys), + return_type="dict", + enforce_signature=False, + set_annotations=True, + ) + passive_state_names = _get_passive_state_names( + v_interpolation_info=target_info, + euler_state_name=euler_state_name, + ) + passive_grids = tuple( + jnp.asarray( + target_info.continuous_states[name].to_jax(), + dtype=canonical_float_dtype(), + ) + for name in passive_state_names + ) + action_names, action_values = _get_child_discrete_actions( + user_regime=target_regime + ) + resources_func = _get_child_resources_function(user_regime=target_regime) + resources_arg_names = frozenset( + _get_child_resources_arg_names(user_regime=target_regime) + ) + # Everything the resources function reads beyond the child's own + # states and discrete actions is a (qualified) param or `age` / + # `period`: a per-node constant bound from the combo pool. + child_binding_names = ( + {euler_state_name} + | set(discrete_state_names) + | set(passive_state_names) + | set(action_names) + ) + resources_param_names = resources_arg_names - child_binding_names + row_grids = passive_grids + action_values + if row_grids: + row_mesh = jnp.meshgrid(*row_grids, indexing="ij") + row_values = tuple(mesh.ravel() for mesh in row_mesh) + row_block_shape = tuple(int(grid.shape[0]) for grid in row_grids) + else: + row_values = () + row_block_shape = () + reads[target] = _ChildRead( + next_state_func=get_next_state_function_for_solution( + transitions=transitions[target], + functions=functions_without_post, + ), + next_state_key=f"next_{euler_state_name}", + euler_state_name=euler_state_name, + has_taste_shocks=target_regime.taste_shocks is not None, + resources_func=resources_func, + resources_arg_names=resources_arg_names, + resources_param_names=resources_param_names, + resources_is_simple=(resources_arg_names - resources_param_names) + <= {euler_state_name}, + discrete_state_names=discrete_state_names, + stochastic_flags=stochastic_flags, + stochastic_state_names=stochastic_state_names, + stochastic_node_values=stochastic_node_values, + process_grid_names=process_grid_names, + weight_keys=weight_keys, + weights_func=weights_func, + passive_state_names=passive_state_names, + passive_grids=passive_grids, + row_arg_names=passive_state_names + action_names, + row_values=row_values, + row_block_shape=row_block_shape, + ) + return MappingProxyType(reads) diff --git a/src/_lcm/egm/ds_pension_benchmark.py b/src/_lcm/egm/ds_pension_benchmark.py new file mode 100644 index 000000000..efacf1212 --- /dev/null +++ b/src/_lcm/egm/ds_pension_benchmark.py @@ -0,0 +1,298 @@ +"""The DS pension comparison harness β€” solve time and Euler-error accuracy per method. + +Reproduces the structure of the Dobrescu--Shanker pension comparison table: for each +solution method and grid resolution, the total solve time and the distribution of +unit-free consumption Euler errors. This module populates the **G2EGM** and **RFC** +rows by solving the DS pension model with the corresponding interior two-asset step, +timing the solve, and pooling the working consumption Euler errors across the +working->working periods. `benchmark_ds_pension_methods` runs both at one grid +resolution and `format_comparison_table` renders the rows β€” the DS-2024 multidimensional +pension comparison this harness reproduces. + +The Euler error is reported on the unconstrained, grid-resolved interior β€” the +low-liquid borrowing-constrained band and the off-grid top-pension boundary layer are +excluded, as they reflect grid extent rather than method accuracy. +""" + +import time +from dataclasses import dataclass +from typing import Literal + +import jax +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.euler_errors import working_consumption_euler_error_log10 +from _lcm.egm.one_asset_egm_step import egm_one_asset_step +from _lcm.egm.rfc_two_asset_step import rfc_two_asset_step +from _lcm.egm.two_asset_g2egm_step import ( + G2EGMResult, + g2egm_retiring_step, + g2egm_step, +) +from lcm.typing import Float1D + +StepKind = Literal["g2egm", "rfc"] +_METHOD_NAMES: dict[StepKind, str] = {"g2egm": "G2EGM", "rfc": "RFC"} + + +@dataclass(frozen=True) +class MethodBenchmark: + """One method's solve time and Euler-error accuracy at one grid resolution.""" + + method: str + """Solution method name (e.g. `"G2EGM"`).""" + n_liquid: int + """Number of liquid grid points.""" + n_pension: int + """Number of pension grid points.""" + solve_seconds: float + """Wall-clock time for the backward-induction solve.""" + euler_error_median_log10: float + """Median interior consumption Euler error, base-10 log relative.""" + euler_error_p90_log10: float + """90th-percentile interior consumption Euler error, base-10 log relative.""" + + +def _benchmark_ds_pension( + *, + step_kind: StepKind, + n_periods: int = 5, + retirement_period: int = 3, + n_liquid: int = 12, + n_pension: int = 10, + liquid_max: float = 20.0, + pension_max: float = 15.0, + discount_factor: float = 0.98, + crra: float = 2.0, + work_disutility: float = 0.25, + match_rate: float = 0.10, + return_liquid: float = 0.02, + return_pension: float = 0.04, + wage: float = 1.0, + retirement_income: float = 0.50, + pension_payout_return: float = 1.04, + post_decision_factor: float = 2.0, + low_liquid_skip: int = 3, + pension_interior: int = 6, +) -> MethodBenchmark: + """Solve the DS pension model by G2EGM and measure its time and Euler errors. + + Args: + n_periods: Number of lifecycle periods. + retirement_period: First retired period. + n_liquid: Liquid grid points. + n_pension: Pension grid points. + liquid_max: Liquid grid upper bound. + pension_max: Pension grid upper bound. + discount_factor: Discount factor `beta`. + crra: Coefficient of relative risk aversion. + work_disutility: Additive disutility of work. + match_rate: Pension employer-match coefficient. + return_liquid: Liquid net return. + return_pension: Pension net return. + wage: Working labor income. + retirement_income: Retirement income. + pension_payout_return: Factor the pension is paid out at on retirement. + post_decision_factor: Post-decision grid points per state grid point. Druedahl + & Jorgensen (2017) recommend roughly 4x (the post-decision grid drives + accuracy); the default 2x keeps the benchmark fast. + low_liquid_skip: Liquid rows excluded as the borrowing-constrained band. + pension_interior: Pension columns retained (excludes the off-grid edge layer). + + Returns: + The G2EGM method's benchmark row. + + """ + liquid_grid = jnp.linspace(0.1, liquid_max, n_liquid) + pension_grid = jnp.linspace(0.0, pension_max, n_pension) + # The post-decision (endogenous) grids drive accuracy, so they scale with the state + # resolution rather than staying fixed; under-refining them caps the Euler error. + n_a = max(18, int(post_decision_factor * n_liquid)) + n_b = max(18, int(post_decision_factor * n_pension)) + a_grid = jnp.linspace(0.0, liquid_max, n_a) + b_grid = jnp.linspace(0.0, 2.0 * pension_max, n_b) + consumption_grid = jnp.linspace(0.1, liquid_max, n_a) + savings_grid = jnp.linspace(0.0, liquid_max, 4 * n_liquid) + + def solve() -> dict[int, G2EGMResult]: + return _solve_pension_policies( + step_kind=step_kind, + n_periods=n_periods, + retirement_period=retirement_period, + liquid_grid=liquid_grid, + pension_grid=pension_grid, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + savings_grid=savings_grid, + discount_factor=discount_factor, + crra=crra, + work_disutility=work_disutility, + match_rate=match_rate, + return_liquid=return_liquid, + return_pension=return_pension, + wage=wage, + retirement_income=retirement_income, + pension_payout_return=pension_payout_return, + ) + + # Warm up the compile, then time a fresh solve to device-ready. + solve() + start = time.perf_counter() + working_policies = solve() + jax.block_until_ready([p.value for p in working_policies.values()]) + solve_seconds = time.perf_counter() - start + + interior = np.s_[low_liquid_skip:, :pension_interior] + + # Working->working periods (continuation is a working period): pool their interior + # Euler errors. The boundary period's transition is the lump-sum payout, not a + # working transition, so it is not part of this pool. + def period_errors(period: int) -> np.ndarray: + errors = np.asarray( + working_consumption_euler_error_log10( + m_grid=liquid_grid, + n_grid=pension_grid, + consumption=working_policies[period].consumption, + deposit=working_policies[period].deposit, + next_consumption=working_policies[period + 1].consumption, + discount_factor=discount_factor, + crra=crra, + return_liquid=return_liquid, + return_pension=return_pension, + match_rate=match_rate, + wage=wage, + ) + )[interior] + return errors[np.isfinite(errors)] + + all_errors = np.concatenate( + [period_errors(period) for period in range(retirement_period - 1)] + ) + return MethodBenchmark( + method=_METHOD_NAMES[step_kind], + n_liquid=n_liquid, + n_pension=n_pension, + solve_seconds=solve_seconds, + euler_error_median_log10=float(np.median(all_errors)), + euler_error_p90_log10=float(np.percentile(all_errors, 90)), + ) + + +def benchmark_g2egm_ds_pension(**kwargs: object) -> MethodBenchmark: + """Benchmark the DS pension model solved by the four-segment G2EGM envelope.""" + return _benchmark_ds_pension(step_kind="g2egm", **kwargs) # ty: ignore[invalid-argument-type] + + +def benchmark_rfc_ds_pension(**kwargs: object) -> MethodBenchmark: + """Benchmark the DS pension model solved by the combined-cloud RFC envelope.""" + return _benchmark_ds_pension(step_kind="rfc", **kwargs) # ty: ignore[invalid-argument-type] + + +def benchmark_ds_pension_methods(**kwargs: object) -> list[MethodBenchmark]: + """Benchmark the DS pension model by G2EGM and RFC at the same grid resolution. + + Returns the two method rows (G2EGM then RFC) for one grid resolution, ready for + `format_comparison_table` β€” the DS-2024 pension comparison the harness reproduces. + """ + return [ + benchmark_g2egm_ds_pension(**kwargs), + benchmark_rfc_ds_pension(**kwargs), + ] + + +def format_comparison_table(rows: list[MethodBenchmark]) -> str: + """Render benchmark rows as a fixed-width DS-style comparison table.""" + header = ( + f"{'method':<8} {'n_liq':>6} {'n_pen':>6} {'time (s)':>10} " + f"{'EE median':>11} {'EE p90':>9}" + ) + body = [ + f"{r.method:<8} {r.n_liquid:>6} {r.n_pension:>6} " + f"{r.solve_seconds:>10.3f} {r.euler_error_median_log10:>11.2f} " + f"{r.euler_error_p90_log10:>9.2f}" + for r in rows + ] + return "\n".join([header, "-" * len(header), *body]) + + +def _solve_pension_policies( + *, + step_kind: StepKind, + n_periods: int, + retirement_period: int, + liquid_grid: Float1D, + pension_grid: Float1D, + a_grid: Float1D, + b_grid: Float1D, + consumption_grid: Float1D, + savings_grid: Float1D, + discount_factor: float, + crra: float, + work_disutility: float, + match_rate: float, + return_liquid: float, + return_pension: float, + wage: float, + retirement_income: float, + pension_payout_return: float, +) -> dict[int, G2EGMResult]: + """Backward-induct the working phase, returning each period's G2EGM result.""" + bequest_value = liquid_grid ** (1.0 - crra) / (1.0 - crra) + next_retired_value = bequest_value + retired_marginal = liquid_grid ** (-crra) + for _ in range(n_periods - 2, retirement_period - 1, -1): + retired = egm_one_asset_step( + next_value=next_retired_value, + next_marginal=retired_marginal, + liquid_grid=liquid_grid, + savings_grid=savings_grid, + discount_factor=discount_factor, + crra=crra, + return_liquid=return_liquid, + income=retirement_income, + ) + next_retired_value = retired.value + retired_marginal = retired.marginal + + working_policies = {} + boundary = g2egm_retiring_step( + next_value_retired=next_retired_value, + next_marginal_retired=retired_marginal, + liquid_grid=liquid_grid, + m_grid=liquid_grid, + n_grid=pension_grid, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + return_liquid=return_liquid, + pension_payout_return=pension_payout_return, + retirement_income=retirement_income, + ) + working_policies[retirement_period - 1] = boundary + next_working_value = boundary.value - work_disutility + # The boundary (retiring) period always uses the G2EGM retiring step; the interior + # working->working steps use the selected envelope. RFC has no retiring variant. + interior_step = rfc_two_asset_step if step_kind == "rfc" else g2egm_step + for period in range(retirement_period - 2, -1, -1): + step = interior_step( + next_value=next_working_value, + m_grid=liquid_grid, + n_grid=pension_grid, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + return_liquid=return_liquid, + return_pension=return_pension, + wage=wage, + ) + working_policies[period] = step + next_working_value = step.value - work_disutility + return working_policies diff --git a/src/_lcm/egm/ds_pension_driver.py b/src/_lcm/egm/ds_pension_driver.py new file mode 100644 index 000000000..409b45a07 --- /dev/null +++ b/src/_lcm/egm/ds_pension_driver.py @@ -0,0 +1,156 @@ +"""Backward-induction driver solving the DS pension model by the G2EGM method. + +Assembles the endogenous-grid steps into a full lifecycle solve of the DS pension model: + +- the terminal period is the CRRA bequest on the liquid grid; +- retired periods are the 1-D consumption--saving EGM step (`egm_one_asset_step`), + carrying the marginal value of liquid backward; +- the single working->retired boundary period is the four-segment G2EGM step reading the + 1-D retired continuation through the lump-sum payout (`g2egm_retiring_step`); +- earlier working periods are the four-segment G2EGM step reading the 2-D working + continuation (`g2egm_step`). + +The working utility carries an additive work disutility the generic envelope objective +omits; it is an additive constant (it shifts the value level without changing the +policy), so the driver subtracts it from each working period's value. + +This standalone driver is the numerical core validated against the brute solve before it +is wrapped as a prime-time `Solver`. It threads raw grids and scalar parameters rather +than the engine's regime machinery. +""" + +import jax.numpy as jnp + +from _lcm.egm.one_asset_egm_step import egm_one_asset_step +from _lcm.egm.two_asset_g2egm_step import g2egm_retiring_step, g2egm_step +from lcm.typing import Float1D, FloatND, RegimeName + + +def solve_ds_pension_g2egm( + *, + n_periods: int, + retirement_period: int, + liquid_grid: Float1D, + pension_grid: Float1D, + a_grid: Float1D, + b_grid: Float1D, + consumption_grid: Float1D, + savings_grid: Float1D, + discount_factor: float, + crra: float, + work_disutility: float, + match_rate: float, + return_liquid: float, + return_pension: float, + wage: float, + retirement_income: float, + pension_payout_return: float, + threshold: float = 0.25, +) -> dict[int, dict[RegimeName, FloatND]]: + """Solve the DS pension model by backward induction with the G2EGM steps. + + Args: + n_periods: Number of lifecycle periods (the last is the terminal dead period). + retirement_period: First retired period; working spans `0..retirement_period-1`. + liquid_grid: Regular liquid-state grid, shared by working and retired (the + working `m` grid and the retired state grid). + pension_grid: Regular working pension-state grid (the working `n` grid). + a_grid: Liquid post-decision grid for the working `ucon`/`dcon` segments. + b_grid: Pension post-decision grid for the working segments. + consumption_grid: Consumption sweep for the working `acon`/`con` segments. + savings_grid: Post-decision savings grid for the retired EGM step. + discount_factor: Discount factor `beta`. + crra: Coefficient of relative risk aversion `rho`. + work_disutility: Additive disutility of work, subtracted from working values. + match_rate: Pension employer-match coefficient `chi`. + return_liquid: Liquid net return `r^a`. + return_pension: Pension net return `r^b`. + wage: Deterministic labor income while working. + retirement_income: Retirement income added to the retired liquid state. + pension_payout_return: Factor the pension is paid out at on retirement. + threshold: Barycentric extrapolation tolerance for the working envelope. + + Returns: + Mapping of period to a mapping of regime name to this model's value array: + `working` (2-D on `(liquid, pension)`) for `0..retirement_period-1`, `retired` + (1-D on `liquid`) for `retirement_period..n_periods-2`, and `dead` (the terminal + bequest) for `n_periods-1`. + + """ + bequest_value = _crra_utility(liquid_grid, crra) + bequest_marginal = liquid_grid ** (-crra) + + solution: dict[int, dict[RegimeName, FloatND]] = { + n_periods - 1: {"dead": bequest_value} + } + + # Retired periods, backward to the first retired period. The continuation is the + # terminal bequest at the last retired period, else next period's retired value. + retired_marginal = bequest_marginal + next_retired_value = bequest_value + for period in range(n_periods - 2, retirement_period - 1, -1): + step = egm_one_asset_step( + next_value=next_retired_value, + next_marginal=retired_marginal, + liquid_grid=liquid_grid, + savings_grid=savings_grid, + discount_factor=discount_factor, + crra=crra, + return_liquid=return_liquid, + income=retirement_income, + ) + retired_marginal = step.marginal + solution[period] = {"retired": step.value} + next_retired_value = step.value + + # Working->retired boundary period: read the 1-D retired continuation through the + # lump-sum payout. + boundary_value = g2egm_retiring_step( + next_value_retired=next_retired_value, + next_marginal_retired=retired_marginal, + liquid_grid=liquid_grid, + m_grid=liquid_grid, + n_grid=pension_grid, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + return_liquid=return_liquid, + pension_payout_return=pension_payout_return, + retirement_income=retirement_income, + threshold=threshold, + ) + next_working_value = boundary_value.value - work_disutility + solution[retirement_period - 1] = {"working": next_working_value} + + # Earlier working periods: read the 2-D working continuation. + for period in range(retirement_period - 2, -1, -1): + step = g2egm_step( + next_value=next_working_value, + m_grid=liquid_grid, + n_grid=pension_grid, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + return_liquid=return_liquid, + return_pension=return_pension, + wage=wage, + threshold=threshold, + ) + next_working_value = step.value - work_disutility + solution[period] = {"working": next_working_value} + + return solution + + +def _crra_utility(consumption: Float1D, crra: float) -> Float1D: + return jnp.where( + crra == 1.0, + jnp.log(consumption), + consumption ** (1.0 - crra) / (1.0 - crra), + ) diff --git a/src/_lcm/egm/euler.py b/src/_lcm/egm/euler.py new file mode 100644 index 000000000..c987ba5ca --- /dev/null +++ b/src/_lcm/egm/euler.py @@ -0,0 +1,63 @@ +"""Euler inversion on the exogenous savings grid. + +The first-order condition at an interior optimum equates the marginal utility +of the continuous action with the discounted expected marginal continuation +value: $u'(c_j) = \\beta \\, \\mathbb{E}[\\partial V' / \\partial R' \\cdot +\\partial R' / \\partial A]$ at each savings node $A_j$. Inverting via the +regime's `inverse_marginal_utility` function yields the optimal action and +the endogenous resources point $R_j = A_j + c_j$ without any root finding. +""" + +from collections.abc import Callable + +import jax.numpy as jnp + +from lcm.typing import ScalarFloat + + +def invert_euler( + *, + expected_marginal_continuation: ScalarFloat, + discount_factor: ScalarFloat, + inverse_marginal_utility: Callable[..., ScalarFloat], +) -> ScalarFloat: + """Invert the Euler equation at one savings node. + + The discounted expected marginal continuation is clamped at a small + positive epsilon *before* inversion (the degenerate-inversion guard): an + exactly zero discounted marginal continuation β€” e.g. every reachable + child is a stateless terminal regime, or the discount factor is zero β€” + means saving has no marginal value, so the consume-everything corner is + optimal. Without the clamp, $(u')^{-1}(0) = +\\infty$ would inject an + infinite endogenous grid point that poisons the candidate sort and the + envelope scan; with it, the inversion returns a very large but finite + action and the closed-form credit-constrained segment represents the + corner. The clamp acts on the discounted product, so a zero discount + factor cannot reintroduce the degenerate inversion. + + The clamp is a numerical guard, not an economic identity: a discounted + marginal continuation that is *positive but below the dtype's machine + epsilon* is also clamped, so the returned action is $(u')^{-1}(eps)$ rather + than the mathematical inverse at that tiny value. Such a candidate lies far + to the right (a near-zero marginal implies near-total consumption) and is + normally dominated or outside the queried resources range β€” but it is a + numerical artifact the upper envelope discards, not a genuine interior + optimum. + + Args: + expected_marginal_continuation: Probability- and shock-weighted + expected marginal continuation value + $\\mathbb{E}[\\partial V'/\\partial R' \\cdot \\partial R'/\\partial A]$ + at the savings node. + discount_factor: Discount factor $\\beta$ of the Bellman aggregator. + inverse_marginal_utility: The regime's inverse-marginal-utility + function with every parameter except `marginal_continuation` + already bound. + + Returns: + The optimal continuous action at the savings node. + + """ + discounted = discount_factor * expected_marginal_continuation + eps = jnp.finfo(discounted.dtype).eps + return inverse_marginal_utility(marginal_continuation=jnp.maximum(discounted, eps)) diff --git a/src/_lcm/egm/euler_errors.py b/src/_lcm/egm/euler_errors.py new file mode 100644 index 000000000..2b7846298 --- /dev/null +++ b/src/_lcm/egm/euler_errors.py @@ -0,0 +1,118 @@ +"""Unit-free consumption Euler errors β€” a brute-free solution-accuracy metric. + +The accuracy column of the DS comparison tables is the Euler error: at an interior +(unconstrained) consumption--saving optimum the Euler equation +`u'(c) = beta*(1+r)*u'(c_next)` holds exactly, so the relative gap between the chosen +consumption and the consumption the equation implies measures how well a method nulls +the first-order condition β€” independent of any reference solve. It is reported as the +base-10 logarithm of the relative consumption error, so `-3` reads as a 0.1% error. + +The metric is meaningful only on the unconstrained interior: where the borrowing +constraint binds the Euler equation holds with a positive multiplier, and the residual +there reflects the constraint, not solution error. +""" + +import jax.numpy as jnp +from jax.scipy.ndimage import map_coordinates + +from lcm.typing import Float1D, Float2D + + +def consumption_euler_error_log10( + *, + liquid_grid: Float1D, + consumption: Float1D, + next_consumption: Float1D, + discount_factor: float, + crra: float, + return_liquid: float, + income: float, +) -> Float1D: + """Compute the log10 unit-free consumption Euler error at each liquid grid point. + + For chosen consumption `c` the next-period liquid state is + `(1 + r)*(liquid - c) + income`, and the Euler equation implies + `c_euler = (beta*(1+r)*u'(c_next))**(-1/crra)`, with `c_next` the next-period + consumption policy interpolated at the next-period liquid state. The error is + `log10(|c_euler / c - 1|)`. + + Args: + liquid_grid: Regular liquid-state grid (ascending) the policy is defined on. + consumption: Chosen consumption policy on `liquid_grid`. + next_consumption: Next period's consumption policy on `liquid_grid`. Pass the + identity `liquid_grid` for a terminal bequest (all wealth consumed). + discount_factor: Discount factor `beta`. + crra: Coefficient of relative risk aversion `rho`. + return_liquid: Liquid net return `r`. + income: Deterministic income added to next-period liquid. + + Returns: + The base-10 log relative consumption error at each liquid grid point, shape + `(len(liquid_grid),)`. + + """ + next_liquid = (1.0 + return_liquid) * (liquid_grid - consumption) + income + consumption_next = jnp.interp(next_liquid, liquid_grid, next_consumption) + marginal_next = consumption_next ** (-crra) + consumption_euler = (discount_factor * (1.0 + return_liquid) * marginal_next) ** ( + -1.0 / crra + ) + relative_error = jnp.abs(consumption_euler / consumption - 1.0) + return jnp.log10(relative_error) + + +def working_consumption_euler_error_log10( + *, + m_grid: Float1D, + n_grid: Float1D, + consumption: Float2D, + deposit: Float2D, + next_consumption: Float2D, + discount_factor: float, + crra: float, + return_liquid: float, + return_pension: float, + match_rate: float, + wage: float, +) -> Float2D: + """Compute the log10 consumption Euler error at each working `(m, n)` grid point. + + The liquid-margin intertemporal first-order condition for the two-asset working + problem is `u'(c_t) = beta*(1+r^a)*u'(c_{t+1})`, with the next working state + `m' = (1+r^a)*(m - c - d) + wage`, `n' = (1+r^b)*(n + d + chi*log(1+d))` reached + under the chosen policy and `c_{t+1}` the next period's working consumption policy + bilinearly interpolated there. The error is `log10(|c_euler / c - 1|)`. + + Args: + m_grid: Regular working liquid-state grid (ascending, evenly spaced). + n_grid: Regular working pension-state grid (ascending, evenly spaced). + consumption: This period's consumption policy on the `(m, n)` grid. + deposit: This period's deposit policy on the `(m, n)` grid. + next_consumption: Next period's working consumption policy on the `(m, n)` grid. + discount_factor: Discount factor `beta`. + crra: Coefficient of relative risk aversion `rho`. + return_liquid: Liquid net return `r^a`. + return_pension: Pension net return `r^b`. + match_rate: Pension employer-match coefficient `chi`. + wage: Deterministic labor income. + + Returns: + The base-10 log relative consumption error per `(m, n)` grid point. + + """ + m_mesh, n_mesh = jnp.meshgrid(m_grid, n_grid, indexing="ij") + liquid_next = (1.0 + return_liquid) * (m_mesh - consumption - deposit) + wage + pension_next = (1.0 + return_pension) * ( + n_mesh + deposit + match_rate * jnp.log1p(deposit) + ) + m_index = (liquid_next - m_grid[0]) / (m_grid[1] - m_grid[0]) + n_index = (pension_next - n_grid[0]) / (n_grid[1] - n_grid[0]) + consumption_next = map_coordinates( + next_consumption, [m_index, n_index], order=1, mode="nearest" + ) + marginal_next = consumption_next ** (-crra) + consumption_euler = (discount_factor * (1.0 + return_liquid) * marginal_next) ** ( + -1.0 / crra + ) + relative_error = jnp.abs(consumption_euler / consumption - 1.0) + return jnp.log10(relative_error) diff --git a/src/_lcm/egm/interp.py b/src/_lcm/egm/interp.py new file mode 100644 index 000000000..3a482a4f1 --- /dev/null +++ b/src/_lcm/egm/interp.py @@ -0,0 +1,330 @@ +"""Interpolation on NaN-padded, weakly ascending EGM grids. + +The upper-envelope refinement emits grid rows of static length whose unused +tail slots hold NaN and whose kink abscissae appear twice (left- and +right-extrapolated function values). `interp_on_padded_grid` interpolates on +such rows without ever dividing by a zero-width bracket; passing the row's +exact slopes upgrades the linear interpolant to a monotone cubic Hermite one. +`locate_on_grid` produces edge-clamped bracket indices and weights on +ordinary (unpadded) grids, e.g. the passive-state grids of the mixed carry +read. +""" + +import jax.numpy as jnp + +from lcm.typing import Float1D, FloatND, ScalarFloat, ScalarInt + + +def interp_on_padded_grid( + *, + x_query: FloatND, + xp: Float1D, + fp: Float1D, + fp_slopes: Float1D | None = None, +) -> FloatND: + """Interpolate on a NaN-padded, weakly ascending grid row. + + The NaN padding must form a contiguous tail of `xp` (matched by NaNs in + `fp`); it is treated as $+\\infty$ when locating brackets, so padding never + influences the result. Behavior at the boundaries and at duplicated + abscissae: + + - Queries outside the non-NaN range are clamped to the boundary values. + - At a duplicated abscissa (an envelope kink carrying left and right + values), queries strictly below the duplicate interpolate toward the + left value; queries at or above it use the right value. The zero-width + bracket between the duplicates is never used as a divisor. + - A `-inf` endpoint (an infeasible value) forces the bracket's interior + to `-inf` instead of NaN; a query exactly on a finite neighbor returns + that neighbor's value. + + Without `fp_slopes` the interpolant is piecewise linear. With `fp_slopes` + β€” the derivatives $f'(x)$ at the `xp` nodes, *exact at the nodes* (for an + EGM value row, the marginal-utility row via the envelope theorem) β€” each + bracket gets a cubic Hermite correction instead, with Fritsch-Carlson slope + limiting so the interpolant stays monotone on monotone data. The slopes are + exact node derivatives, but the cubic value interpolant and a *separate* + linear interpolant of the marginal row (read for the Euler step) are two + distinct approximants: between nodes the value's derivative and the + interpolated marginal need not coincide. The discrepancy is $O(h^2)$ and + enters the value only at second order through the Euler inversion. Linear + interpolation of a concave value row is biased downward by $O(h^2)$ per read + and the bias compounds across backward induction; exact slopes remove it at + no extra data cost. Brackets with a non-finite endpoint or slope fall back + to the linear rule, so the NaN-padding, kink, and `-inf` contracts above are + unchanged. + + Args: + x_query: Points at which to evaluate the interpolant; any shape. + xp: Weakly ascending grid row with NaNs only in the tail. + fp: Function values on `xp`, NaN-padded in lockstep with `xp`. + fp_slopes: Derivatives of `fp` with respect to `xp` at the `xp` + nodes, NaN-padded in lockstep; `None` selects linear + interpolation. + + Returns: + Interpolated values with the shape of `x_query`. + + """ + search_grid, valid_length = prepare_padded_grid(xp) + return interp_on_prepared_grid( + x_query=x_query, + search_grid=search_grid, + valid_length=valid_length, + xp=xp, + fp=fp, + fp_slopes=fp_slopes, + ) + + +def prepare_padded_grid(xp: Float1D) -> tuple[Float1D, ScalarInt]: + """Build a NaN-padded grid row's search key and valid prefix length. + + Both outputs depend only on the row, never on a query, so a caller that + reads one row at many queries prepares them once and passes them to + `interp_on_prepared_grid`. The per-query path then does only a + scalar-carry `searchsorted` plus gathers β€” it never recomputes the NaN + mask or the `+inf`-filled grid, the grid-length intermediates that an + in-line preamble would materialize and hold for every query lane. + + Args: + xp: Weakly ascending grid row with NaNs only in the tail. + + Returns: + Tuple of the search key β€” `xp` with its NaN tail replaced by `+inf`, + so padding sorts above every query β€” and the valid prefix length (the + count of non-NaN nodes). + + """ + search_grid = jnp.where(jnp.isnan(xp), jnp.inf, xp) + valid_length = jnp.sum(~jnp.isnan(xp)).astype(jnp.int32) + return search_grid, valid_length + + +def interp_on_prepared_grid( + *, + x_query: FloatND, + search_grid: Float1D, + valid_length: ScalarInt, + xp: Float1D, + fp: Float1D, + fp_slopes: Float1D | None = None, +) -> FloatND: + """Interpolate on a row whose search key and valid length are prepared. + + The interpolation contract is identical to `interp_on_padded_grid` (linear + or Hermite, edge-clamped, tie-safe at kinks, `-inf`-propagating); this form + only takes the row's `search_grid` and `valid_length` precomputed (via + `prepare_padded_grid`) instead of deriving them from `xp` per call. + `search_grid` is used solely to locate brackets; the abscissae, values, and + slopes are gathered from the original NaN-padded `xp` / `fp` / `fp_slopes`, + so the result matches the NaN-padded path exactly, including on degenerate + rows whose valid prefix is one node or empty. + + Args: + x_query: Points at which to evaluate the interpolant; any shape. + search_grid: The row's `+inf`-padded search key from + `prepare_padded_grid`. + valid_length: The row's non-NaN prefix length from + `prepare_padded_grid`. + xp: The original NaN-padded grid row (the abscissa gather source). + fp: Function values on `xp`, NaN-padded in lockstep. + fp_slopes: Node derivatives, NaN-padded in lockstep; `None` selects + linear interpolation. + + Returns: + Interpolated values with the shape of `x_query`. + + """ + # An empty valid prefix (`valid_length == 0`) can only arise from an + # already-poisoned carry; the index clamp below keeps the gather in bounds, + # and the result stays NaN so the runtime NaN diagnostics surface the + # poisoned carry rather than masking it with an edge-clamped constant. + # The bracket indices span the full query mesh (the dominant egm_step + # working buffer at scale), and never exceed the grid length (a few + # hundred), so int32 holds them with vast headroom. Under x64 `searchsorted` + # would default to int64 and double these gather-index buffers; the cast + # halves them with no effect on the gathered values. + upper = jnp.clip( + jnp.searchsorted(search_grid, x_query, side="right"), + 1, + jnp.maximum(valid_length - 1, 1), + ).astype(jnp.int32) + lower = upper - 1 + return _interp_between_nodes( + x_query=x_query, + xp_lower=xp[lower], + xp_upper=xp[upper], + fp_lower=fp[lower], + fp_upper=fp[upper], + slope_lower=None if fp_slopes is None else fp_slopes[lower], + slope_upper=None if fp_slopes is None else fp_slopes[upper], + ) + + +def _interp_between_nodes( + *, + x_query: FloatND, + xp_lower: FloatND, + xp_upper: FloatND, + fp_lower: FloatND, + fp_upper: FloatND, + slope_lower: FloatND | None = None, + slope_upper: FloatND | None = None, +) -> FloatND: + """Interpolate a query between its two bracketing grid nodes. + + The pure two-node arithmetic of the padded-grid interpolant, shared by + `interp_on_prepared_grid` (which gathers the bracket from a full row) and + the streamed asset-row publish (which captures the bracket directly during + the upper-envelope scan). Having both paths reduce to this one function + guarantees the streamed value cannot diverge from the row-then-interpolate + value: only *which two nodes* differs, not the arithmetic on them. + + The bracket must already be edge-clamped to a real pair of nodes (queries + below the first node bracket the first pair, queries at or above the last + bracket the last pair). The interpolant is then edge-safe by construction: + + - At a zero-width bracket (a duplicated kink abscissa) the relative position + is forced to `1.0`, so the right node's value applies and the zero width + is never used as a divisor. + - A `-inf` endpoint yields `-inf` wherever it carries positive weight + (instead of the NaN of `fp_lower + rel * (fp_upper - fp_lower)`) and + contributes exactly nothing at weight zero. + + Args: + x_query: Point(s) at which to evaluate the interpolant. + xp_lower: Lower bracket node abscissa. + xp_upper: Upper bracket node abscissa. + fp_lower: Function value at the lower node. + fp_upper: Function value at the upper node. + slope_lower: Node derivative at the lower node; `None` selects linear + interpolation. + slope_upper: Node derivative at the upper node; `None` selects linear + interpolation. + + Returns: + Interpolated value(s) with the shape of `x_query`. + + """ + bracket_width = xp_upper - xp_lower + safe_width = jnp.where(bracket_width == 0.0, 1.0, bracket_width) + # Zero-width brackets arise only when a duplicated abscissa sits at the end + # of the non-NaN prefix; queries there are at or above the duplicate, so + # the right value applies. + relative_position = jnp.where( + bracket_width == 0.0, + 1.0, + jnp.clip((x_query - xp_lower) / safe_width, 0.0, 1.0), + ) + weight_lower = 1.0 - relative_position + # Blend on results with zero-weight short-circuits: a `-inf` endpoint + # yields `-inf` wherever it carries positive weight (instead of the NaN + # of `fp_lower + rel * (fp_upper - fp_lower)`), and contributes exactly + # nothing at weight zero. + linear = jnp.where(weight_lower > 0.0, weight_lower * fp_lower, 0.0) + jnp.where( + relative_position > 0.0, relative_position * fp_upper, 0.0 + ) + if slope_lower is None or slope_upper is None: + return linear + return linear + _hermite_correction( + relative_position=relative_position, + bracket_width=bracket_width, + safe_width=safe_width, + fp_lower=fp_lower, + fp_upper=fp_upper, + slope_lower=slope_lower, + slope_upper=slope_upper, + ) + + +def locate_on_grid( + *, + x_query: ScalarFloat, + grid: Float1D, +) -> tuple[ScalarInt, ScalarInt, ScalarFloat]: + """Locate the bracketing nodes and upper weight of a query on a sorted grid. + + The bracket is edge-clamped: queries below the first node get upper + weight `0.0` on the first bracket, queries above the last node get upper + weight `1.0` on the last bracket, so the linear blend + `(1 - weight) * f[lower] + weight * f[upper]` never extrapolates. A query + exactly on a node yields a weight of exactly `0.0` or `1.0`, so on-node + reads reproduce the node values without interpolation error. + + Args: + x_query: The query point. + grid: Strictly ascending grid nodes (at least two). + + Returns: + Tuple of the lower node index, the upper node index, and the weight + of the upper node. + + """ + n_nodes = grid.shape[0] + # int32 bracket indices: the grid has at most a few hundred nodes, so the + # x64-default int64 only doubles the index buffers for nothing. + upper = jnp.clip( + jnp.searchsorted(grid, x_query, side="right"), + 1, + n_nodes - 1, + ).astype(jnp.int32) + lower = upper - 1 + bracket_width = grid[upper] - grid[lower] + safe_width = jnp.where(bracket_width == 0.0, 1.0, bracket_width) + weight_upper = jnp.where( + bracket_width == 0.0, + 1.0, + jnp.clip((x_query - grid[lower]) / safe_width, 0.0, 1.0), + ) + return lower, upper, weight_upper + + +def _hermite_correction( + *, + relative_position: FloatND, + bracket_width: FloatND, + safe_width: FloatND, + fp_lower: FloatND, + fp_upper: FloatND, + slope_lower: FloatND, + slope_upper: FloatND, +) -> FloatND: + """Cubic Hermite correction on top of the linear blend, per bracket. + + With $t$ the relative position, $h$ the bracket width, $\\Delta f$ the + value difference, and limited node slopes $m_0, m_1$, the cubic Hermite + interpolant is the linear blend plus + $t (1-t) \\left[ (1-t)(h m_0 - \\Delta f) + t (\\Delta f - h m_1) \\right]$, + which vanishes at both endpoints β€” boundary clamps and zero-width-bracket + reads are untouched. The slopes are Fritsch-Carlson limited (same sign as + the secant, magnitude at most three times it), a sufficient condition for + the interpolant to be monotone on each monotone bracket. The correction + is applied only on positive-width brackets whose endpoint values and + slopes are all finite; everywhere else it is zero and the linear rule + (with its `-inf` and NaN-padding contracts) stands. + """ + df = fp_upper - fp_lower + safe_df = jnp.where(jnp.isfinite(df), df, 0.0) + secant = safe_df / safe_width + + def limit(slope: FloatND) -> FloatND: + same_sign = slope * secant > 0.0 + limited = jnp.sign(secant) * jnp.minimum(jnp.abs(slope), 3.0 * jnp.abs(secant)) + return jnp.where(same_sign, limited, 0.0) + + coeff_lower = safe_width * limit(slope_lower) - safe_df + coeff_upper = safe_df - safe_width * limit(slope_upper) + correction = ( + relative_position + * (1.0 - relative_position) + * ((1.0 - relative_position) * coeff_lower + relative_position * coeff_upper) + ) + applicable = ( + (bracket_width > 0.0) + & jnp.isfinite(fp_lower) + & jnp.isfinite(fp_upper) + & jnp.isfinite(slope_lower) + & jnp.isfinite(slope_upper) + ) + return jnp.where(applicable, correction, 0.0) diff --git a/src/_lcm/egm/kernel_scope.py b/src/_lcm/egm/kernel_scope.py new file mode 100644 index 000000000..273294497 --- /dev/null +++ b/src/_lcm/egm/kernel_scope.py @@ -0,0 +1,374 @@ +"""Build-time scope checks for the DC-EGM kernel. + +A validated DC-EGM regime always builds a `Model` successfully; features the +kernel does not cover yet are reported here, per period and target, so the +kernel build can install a step that raises `NotImplementedError` at solve +time with a precise message. These checks read the processed kernel-build +context (period carry targets, qualified flat params, the regime's +`VInterpolationInfo`, the processed transition functions), which the +model-time `validation` module does not have β€” so they live alongside the +kernel build rather than with the model-construction validators. +""" + +from collections.abc import Mapping +from types import MappingProxyType + +from _lcm.egm.regime_introspection import ( + _concatenate_regime_function, + _get_child_discrete_actions, + _get_child_resources_arg_names, + _get_child_state_name, + _get_process_state_names, +) +from _lcm.processes import _ContinuousStochasticProcess +from _lcm.regime_building.V import VInterpolationInfo +from _lcm.typing import ( + ActionName, + ConstraintFunctionsMapping, + EconFunctionsMapping, + RegimeName, + RegimeTransitionFunction, + StateName, + TransitionFunctionName, + TransitionFunctionsMapping, +) +from _lcm.utils.functools import get_union_of_args +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM + + +def _find_unsupported_feature( + *, + solver: DCEGM, + regime_name: RegimeName, + user_regimes: Mapping[RegimeName, UserRegime], + functions: EconFunctionsMapping, + constraints: ConstraintFunctionsMapping, + carry_targets: tuple[RegimeName, ...], + transitions: TransitionFunctionsMapping, + stochastic_transition_names: frozenset[TransitionFunctionName], + compute_regime_transition_probs: RegimeTransitionFunction, + regime_to_v_interpolation_info: MappingProxyType[RegimeName, VInterpolationInfo], + flat_param_names: frozenset[str], + regime_to_flat_param_names: MappingProxyType[RegimeName, frozenset[str]], + own_discrete_state_names: tuple[StateName, ...], + own_passive_state_names: tuple[StateName, ...], + own_discrete_action_names: tuple[ActionName, ...], + asset_row_mode: bool, +) -> str | None: + """Return a message naming the first feature outside the kernel's scope. + + Returns `None` when the configuration is fully supported. + """ + message: str | None = None + for target in carry_targets: + message = _find_unsupported_target_feature( + target=target, + user_regimes=user_regimes, + functions=functions, + transitions=transitions, + stochastic_transition_names=stochastic_transition_names, + regime_to_v_interpolation_info=regime_to_v_interpolation_info, + own_discrete_state_names=own_discrete_state_names, + euler_state_name=solver.continuous_state, + own_passive_state_names=own_passive_state_names, + allowed_param_names=flat_param_names | regime_to_flat_param_names[target], + ) + if message is not None: + break + + if message is None: + message = _find_unsupported_function_args( + solver=solver, + functions=functions, + constraints=constraints, + carry_targets=carry_targets, + compute_regime_transition_probs=compute_regime_transition_probs, + regime_to_v_interpolation_info=regime_to_v_interpolation_info, + flat_param_names=flat_param_names, + own_discrete_state_names=own_discrete_state_names, + own_passive_state_names=own_passive_state_names, + own_discrete_action_names=own_discrete_action_names, + asset_row_mode=asset_row_mode, + ) + + if message is None: + return None + return ( + f"The DC-EGM solver cannot solve regime '{regime_name}' yet: {message} " + "This configuration is outside the DC-EGM kernel's current scope." + ) + + +def _find_unsupported_target_feature( + *, + target: RegimeName, + user_regimes: Mapping[RegimeName, UserRegime], + functions: EconFunctionsMapping, + transitions: TransitionFunctionsMapping, + stochastic_transition_names: frozenset[TransitionFunctionName], + regime_to_v_interpolation_info: MappingProxyType[RegimeName, VInterpolationInfo], + own_discrete_state_names: tuple[StateName, ...], + euler_state_name: StateName, + own_passive_state_names: tuple[StateName, ...], + allowed_param_names: frozenset[str], +) -> str | None: + """Return a message naming the first unsupported feature of one target. + + `allowed_param_names` is the union of the source regime's flat params and + the target regime's flat params: a cross-regime carry evaluates the + target's resources / transition functions, which read the *target's* + params (e.g. a pension factor the source never reads), so admitting the + target's params mirrors the kernel's runtime reach. + """ + target_info = regime_to_v_interpolation_info[target] + target_process_states = _get_process_state_names(v_interpolation_info=target_info) + if user_regimes[target].terminal: + terminal_message = _find_unsupported_terminal_target_feature( + target=target, + user_regime=user_regimes[target], + target_info=target_info, + stochastic_transition_names=stochastic_transition_names, + own_discrete_state_names=own_discrete_state_names, + euler_state_name=euler_state_name, + own_passive_state_names=own_passive_state_names, + ) + if terminal_message is not None: + return terminal_message + for process_name in target_process_states: + # The child's node distribution comes from the intrinsic transition + # of the shared process state; without it (the source regime does + # not carry the process) there is nothing to weight the child's + # node axis with. + has_transition = f"next_{process_name}" in transitions[target] + has_weights = f"weight_{target}__next_{process_name}" in functions + if not (has_transition and has_weights): + return ( + f"the process state '{process_name}' of target regime " + f"'{target}' has no intrinsic transition from this regime " + "(both regimes must carry the same process state)." + ) + child_state_name = _get_child_state_name(user_regime=user_regimes[target]) + resources_arg_names = _get_child_resources_arg_names( + user_regime=user_regimes[target] + ) + child_action_names, _ = _get_child_discrete_actions( + user_regime=user_regimes[target] + ) + # Mirror the function-args allowance (`_find_unsupported_function_args`): + # beyond the child's states and discrete actions, the resources function + # may read the regime's flat params and the lifecycle `age` / `period`. + # Solve-phase imputed intermediates (a carried state's solve law) are + # baked into the resources DAG, so their leaf inputs (the passive states + # and params they read) are what surfaces here β€” the imputed output is + # computed, never demanded as a leaf. + allowed_resources_args = ( + {child_state_name} + | set(target_info.state_names) + | set(child_action_names) + | set(allowed_param_names) + | {"age", "period"} + ) + extra_resources_args = sorted(resources_arg_names - allowed_resources_args) + if extra_resources_args: + return ( + f"the resources function of target regime '{target}' depends on " + f"{extra_resources_args}; beyond the Euler state it may read " + "only the child's states and discrete actions, the regime's " + "params, and age/period." + ) + return None + + +def _find_unsupported_terminal_target_feature( + *, + target: RegimeName, + user_regime: UserRegime, + target_info: VInterpolationInfo, + stochastic_transition_names: frozenset[TransitionFunctionName], + own_discrete_state_names: tuple[StateName, ...], + euler_state_name: StateName, + own_passive_state_names: tuple[StateName, ...], +) -> str | None: + """Return a message naming the first unsupported feature of a terminal target. + + A terminal carry covers the parent's Euler continuous state and no actions. + It may additionally carry: + - discrete states reached by a *deterministic* transition into a + parent-carried discrete combo axis (the carry holds one row per target + discrete combo; the parent gathers the row at the next-state code), and + - passive continuous states the parent itself carries (the durable / outer + margin of a NEGM parent): the carry holds those as leading axes the parent + interpolates, the same alignment the non-terminal child read uses (the + Dobrescu-Shanker housing-bequest shape, `bequest(liquid, housing)`). + + A *stochastic* transition into a discrete state would need an expectation + over its node distribution rather than a single-index gather, which is a + separate, unsupported gap. + """ + own_discrete = set(own_discrete_state_names) + for name, grid in target_info.discrete_states.items(): + if isinstance(grid, _ContinuousStochasticProcess): + return ( + f"its terminal target regime '{target}' has the process state " + f"'{name}'; terminal carries cover deterministically-reached " + "discrete states only." + ) + if name not in own_discrete: + return ( + f"its terminal target regime '{target}' has the discrete state " + f"'{name}', which the parent does not carry; a terminal carry's " + "discrete states must be shared with the parent's own discrete " + "combo axes." + ) + if f"next_{name}" in stochastic_transition_names: + return ( + f"its terminal target regime '{target}' is reached by a " + f"stochastic transition into the discrete state '{name}'; a " + "terminal carry's discrete states must be reached " + "deterministically (the carry is gathered at a single " + "next-state code, not integrated over a node distribution)." + ) + continuous_message = _find_unsupported_terminal_continuous_state( + target=target, + user_regime=user_regime, + target_info=target_info, + euler_state_name=euler_state_name, + own_passive_state_names=own_passive_state_names, + ) + if continuous_message is not None: + return continuous_message + if user_regime.actions: + return ( + f"its terminal target regime '{target}' has actions " + f"{list(user_regime.actions)}, so its carry is not " + "its utility on the state grid." + ) + return None + + +def _find_unsupported_terminal_continuous_state( + *, + target: RegimeName, + user_regime: UserRegime, + target_info: VInterpolationInfo, + euler_state_name: StateName, + own_passive_state_names: tuple[StateName, ...], +) -> str | None: + """Return a message if the terminal's continuous states are out of scope. + + The terminal carry's endogenous grid is the parent's Euler-state grid, so + the terminal must declare that state first (the parent's child read takes + the first state as the Euler axis); any further continuous states must be + passive states the parent itself carries (the durable / outer margin). + """ + continuous_state_names = list(target_info.continuous_states) + if euler_state_name not in continuous_state_names: + return ( + f"its terminal target regime '{target}' has continuous states " + f"{continuous_state_names}, none of which is the parent's Euler " + f"state '{euler_state_name}'; the terminal carry's endogenous grid " + "is the parent's Euler-state grid." + ) + if next(iter(user_regime.states), None) != euler_state_name: + return ( + f"its terminal target regime '{target}' must declare the parent's " + f"Euler state '{euler_state_name}' as its first state; the parent's " + "child read takes the terminal's first state as the Euler axis." + ) + unsupported_extra = [ + name + for name in continuous_state_names + if name != euler_state_name and name not in set(own_passive_state_names) + ] + if unsupported_extra: + return ( + f"its terminal target regime '{target}' has continuous states " + f"{unsupported_extra} the parent does not carry as passive states; " + "a terminal carry's extra continuous states must be passive states " + "shared with the parent (the durable / outer margin)." + ) + return None + + +def _find_unsupported_function_args( + *, + solver: DCEGM, + functions: EconFunctionsMapping, + constraints: ConstraintFunctionsMapping, + carry_targets: tuple[RegimeName, ...], + compute_regime_transition_probs: RegimeTransitionFunction, + regime_to_v_interpolation_info: MappingProxyType[RegimeName, VInterpolationInfo], + flat_param_names: frozenset[str], + own_discrete_state_names: tuple[StateName, ...], + own_passive_state_names: tuple[StateName, ...], + own_discrete_action_names: tuple[ActionName, ...], + asset_row_mode: bool, +) -> str | None: + """Return a message naming the first function with out-of-scope arguments.""" + # Combo inputs are bound per (discrete state, passive node, discrete + # action) combination, so any of them may feed these functions. + allowed_combo_inputs = ( + set(own_discrete_state_names) + | set(own_passive_state_names) + | set(own_discrete_action_names) + ) + # In asset-row mode the combo pool carries the Euler node's value, so + # savings-stage functions (regime transition probabilities, transition + # weights) may read the Euler state; the single-post-state kernel has no + # Euler value in the pool. + allowed_savings_stage_inputs = allowed_combo_inputs | ( + {solver.continuous_state} if asset_row_mode else set() + ) + allowed_params = flat_param_names | {"age", "period"} + utility_func = _concatenate_regime_function(functions=functions, target="utility") + arg_requirements: list[tuple[str, frozenset[str], set[str]]] = [ + ( + "the utility function", + frozenset(get_union_of_args([utility_func])), + {solver.continuous_action} | allowed_combo_inputs | allowed_params, + ), + ( + "the regime transition probability function", + frozenset(get_union_of_args([compute_regime_transition_probs])), + allowed_savings_stage_inputs | allowed_params, + ), + ] + # Intrinsic process-weight functions are evaluated per combo at the + # savings-node stage, mirroring the savings-stage independence the + # validation requires of every other stochastic weight function. + for target in carry_targets: + target_process_states = _get_process_state_names( + v_interpolation_info=regime_to_v_interpolation_info[target] + ) + for process_name in target_process_states: + weight_key = f"weight_{target}__next_{process_name}" + if weight_key not in functions: + continue + weight_func = _concatenate_regime_function( + functions=functions, target=weight_key + ) + arg_requirements.append( + ( + f"the transition-weight function '{weight_key}'", + frozenset(get_union_of_args([weight_func])), + allowed_savings_stage_inputs | allowed_params, + ) + ) + for constraint_name in constraints: + constraint_func = _concatenate_regime_function( + functions=MappingProxyType({**dict(functions), **dict(constraints)}), + target=constraint_name, + ) + arg_requirements.append( + ( + f"the constraint '{constraint_name}'", + frozenset(get_union_of_args([constraint_func])), + allowed_combo_inputs | allowed_params, + ) + ) + for label, needed, allowed in arg_requirements: + extra = sorted(needed - allowed) + if extra: + return f"{label} depends on {extra}." + return None diff --git a/src/_lcm/egm/mesh_envelope.py b/src/_lcm/egm/mesh_envelope.py new file mode 100644 index 000000000..c9a3f9894 --- /dev/null +++ b/src/_lcm/egm/mesh_envelope.py @@ -0,0 +1,164 @@ +"""The 2-D G2EGM upper envelope over triangular segment meshes. + +Each constraint segment's endogenous candidate cloud is imaged into the current-state +$(m, n)$ plane and triangulated (`mesh_geometry`). The upper envelope selects, at every +common-grid target, the best feasible policy across all segments: + +1. **First (within-segment) envelope.** For one segment and one target, consider every + triangle the target is *admissible* to (barycentric weights above a negative + threshold β€” covering and mildly extrapolated triangles alike), interpolate the + segment's policy there, recompute the Bellman objective, drop infeasible candidates, + and take the maximum. Admissible-not-only-covering matters: an extrapolated triangle + can hold the true maximizer even when another triangle covers the target. +2. **Second (across-segment) envelope.** Take the per-target maximum over the segments' + first-envelope values, gathering the winning segment's policy. + +The objective is supplied as a callable `(state, policy) -> (value, feasible)` so the +envelope is independent of any one model: it recomputes the Bellman value from the +interpolated policy (never transports an interpolated value) and masks economically +infeasible candidates to minus infinity before either maximum. +""" + +from collections.abc import Callable +from typing import NamedTuple + +import jax +import jax.numpy as jnp + +from _lcm.egm.mesh_geometry import ( + barycentric_weights, + interpolate_on_triangle, + is_admissible, +) +from lcm.typing import BoolND, Float1D, Float2D, FloatND, Int2D, IntND + +# Maps `(state, policy)` to `(value, feasible)`; infeasible candidates are masked. +ObjectiveEvaluator = Callable[[Float1D, Float1D], tuple[FloatND, BoolND]] + + +class SegmentMesh(NamedTuple): + """One constraint segment's triangulated candidate cloud in the state plane. + + Each node is a candidate: the endogenous current state it is optimal at and the + policy chosen there. The triangles connect the nodes; a node flagged invalid (e.g. + an off-grid NaN-inverse) drops every triangle that touches it. + """ + + region_label: int + """Which KKT segment (`ucon`/`dcon`/`acon`/`con`) produced the mesh.""" + node_state: Float2D + """Endogenous current state `(m, n)` per node, shape `(n_node, 2)`.""" + node_policy: Float2D + """Policy `(c, d)` per node, shape `(n_node, n_policy)`.""" + simplices: Int2D + """Triangle node-index triples, shape `(n_simplex, 3)`.""" + valid_node: BoolND + """Per-node validity mask, shape `(n_node,)`.""" + + +class EnvelopeResult(NamedTuple): + """The published upper-envelope value and policy on the common target grid.""" + + value: FloatND + """Envelope value per target, shape `(n_target,)` (`-inf` where no candidate).""" + policy: Float2D + """Winning policy per target, shape `(n_target, n_policy)`.""" + segment: IntND + """Stack index of the winning segment per target, shape `(n_target,)`.""" + region_label: IntND + """KKT region label of the winning segment per target, shape `(n_target,)`. + + The winning segment's own `SegmentMesh.region_label`, not its position in the + stack β€” meaningful only where `has_candidate` is `True` (otherwise the value is + `-inf` and the argmax falls back to stack index 0). + """ + has_candidate: BoolND + """Whether any segment supplied a finite candidate, shape `(n_target,)`.""" + + +def first_envelope( + *, + mesh: SegmentMesh, + targets: Float2D, + objective: ObjectiveEvaluator, + threshold: float, +) -> tuple[FloatND, Float2D]: + """Maximize the recomputed objective over admissible triangles, per target. + + For each target, every triangle is scored: its barycentric weights locate the + target, the segment policy is interpolated, the objective and feasibility are + recomputed, and the candidate is kept only if the triangle is admissible (all + weights above `-threshold`, all three nodes valid) and the policy feasible. + + Args: + mesh: The segment's triangulated candidate cloud. + targets: Common-grid query states, shape `(n_target, 2)`. + objective: Recomputes `(value, feasible)` from `(state, policy)`. + threshold: Non-negative barycentric extrapolation tolerance. + + Returns: + Tuple of the segment's per-target value (`-inf` where no admissible feasible + candidate exists), shape `(n_target,)`, and its winning policy, shape + `(n_target, n_policy)`. + + """ + triangle_states = mesh.node_state[mesh.simplices] + triangle_policies = mesh.node_policy[mesh.simplices] + triangle_valid = jnp.all(mesh.valid_node[mesh.simplices], axis=1) + + def at_target(target: Float1D) -> tuple[FloatND, Float1D]: + def per_triangle( + triangle: Float2D, node_policy: Float2D, valid: BoolND + ) -> tuple[FloatND, Float1D]: + weights = barycentric_weights(triangle=triangle, query=target) + policy = interpolate_on_triangle(node_values=node_policy, weights=weights) + value, feasible = objective(target, policy) + admissible = is_admissible(weights=weights, threshold=threshold) & valid + # Mask non-finite value/policy to -inf so a NaN candidate (from a + # degenerate triangle or clamped continuation) cannot be selected by argmax. + finite = jnp.isfinite(value) & jnp.all(jnp.isfinite(policy)) + candidate = jnp.where(admissible & feasible & finite, value, -jnp.inf) + return candidate, policy + + candidates, policies = jax.vmap(per_triangle)( + triangle_states, triangle_policies, triangle_valid + ) + best = jnp.argmax(candidates) + return candidates[best], policies[best] + + return jax.vmap(at_target)(targets) + + +def second_envelope( + *, + segment_values: Float2D, + segment_policies: FloatND, + region_labels: IntND, +) -> EnvelopeResult: + """Take the per-target maximum across segments and gather the winning policy. + + Args: + segment_values: First-envelope values, shape `(n_segment, n_target)`. + segment_policies: First-envelope policies, shape + `(n_segment, n_target, n_policy)`. + region_labels: KKT region label of each stacked segment, shape `(n_segment,)`, + in the same stack order as `segment_values`. + + Returns: + The envelope value, winning policy, winning segment stack index, the winner's + KKT region label, and a per-target flag for whether any candidate was finite. + + """ + winning_segment = jnp.argmax(segment_values, axis=0).astype(jnp.int32) + value = jnp.max(segment_values, axis=0) + target_index = jnp.arange(segment_values.shape[1]) + policy = segment_policies[winning_segment, target_index] + region_label = region_labels[winning_segment] + has_candidate = jnp.isfinite(value) + return EnvelopeResult( + value=value, + policy=policy, + segment=winning_segment, + region_label=region_label, + has_candidate=has_candidate, + ) diff --git a/src/_lcm/egm/mesh_geometry.py b/src/_lcm/egm/mesh_geometry.py new file mode 100644 index 000000000..0bc656e12 --- /dev/null +++ b/src/_lcm/egm/mesh_geometry.py @@ -0,0 +1,122 @@ +"""Triangular-mesh barycentric geometry for the 2-D G2EGM upper envelope. + +The G2EGM upper envelope maps each constraint segment's endogenous candidate cloud +(a regular source grid imaged into the current-state $(m, n)$ plane) onto a common +state grid by interpolating policies and recomputing the Bellman objective. The +geometry is **triangular**: each regular source cell is split into two triangles, and +a target state is located in a triangle by its barycentric weights. Triangles, unlike +mapped quadrilaterals, are convex simplices with a unique affine inverse β€” a mapped +quad can fold (a sign-changing bilinear Jacobian) and have no unique inverse, so the +reference method triangulates. + +A target is an **admissible** candidate of a triangle when every barycentric weight +exceeds a (negative) extrapolation threshold: a mildly extrapolated triangle stays a +candidate (the within-segment envelope decides), rather than being dropped unless no +triangle strictly covers the target. +""" + +import jax.numpy as jnp + +from lcm.typing import BoolND, Float1D, Float2D, FloatND, Int2D + +# A grid needs at least this many rows and columns to contain one cell (two triangles). +_MIN_GRID_SIDE = 2 + + +def triangulate_regular_grid(*, n_rows: int, n_cols: int) -> Int2D: + """Split each cell of an `n_rows` by `n_cols` regular grid into two triangles. + + Node $(i, j)$ has the row-major flat index `i * n_cols + j`. Each cell + $(i, j)$ contributes the two triangles `(n00, n10, n01)` and `(n10, n11, n01)` + β€” the diagonal split that keeps both halves non-degenerate even when the cell's + image folds. + + Args: + n_rows: Number of source-grid rows. + n_cols: Number of source-grid columns. + + Returns: + Integer array of shape `(2 * (n_rows - 1) * (n_cols - 1), 3)`; each row is the + three flat node indices of one triangle. + + """ + if n_rows < _MIN_GRID_SIDE or n_cols < _MIN_GRID_SIDE: + msg = ( + "triangulate_regular_grid needs at least 2 rows and 2 columns to form a " + f"cell, got n_rows={n_rows}, n_cols={n_cols}." + ) + raise ValueError(msg) + rows = jnp.arange(n_rows - 1)[:, None] + cols = jnp.arange(n_cols - 1)[None, :] + n00 = (rows * n_cols + cols).reshape(-1) + n01 = n00 + 1 + n10 = n00 + n_cols + n11 = n10 + 1 + lower = jnp.stack([n00, n10, n01], axis=1) + upper = jnp.stack([n10, n11, n01], axis=1) + return jnp.concatenate([lower, upper], axis=0).astype(jnp.int32) + + +def barycentric_weights(*, triangle: Float2D, query: Float1D) -> Float1D: + """Compute the barycentric weights of `query` with respect to `triangle`. + + The weights $(w_0, w_1, w_2)$ satisfy $\\sum_k w_k = 1$ and + $\\sum_k w_k\\,p_k = q$ for triangle vertices $p_k$ and query $q$. A query inside + the triangle has all weights in $[0, 1]$; a negative weight marks extrapolation + beyond the opposite edge. The weights are exact for an affine (triangular) map. + + Args: + triangle: Vertex coordinates, shape `(3, 2)`. + query: Query point, shape `(2,)`. + + Returns: + Barycentric weights, shape `(3,)`. + + """ + p0, p1, p2 = triangle[0], triangle[1], triangle[2] + # Solve [p1 - p0, p2 - p0] @ (w1, w2) = q - p0 by Cramer's rule; w0 = 1 - w1 - w2. + e1 = p1 - p0 + e2 = p2 - p0 + rhs = query - p0 + det = e1[0] * e2[1] - e1[1] * e2[0] + w1 = (rhs[0] * e2[1] - rhs[1] * e2[0]) / det + w2 = (e1[0] * rhs[1] - e1[1] * rhs[0]) / det + w0 = 1.0 - w1 - w2 + return jnp.stack([w0, w1, w2]) + + +def is_admissible(*, weights: Float1D, threshold: float) -> BoolND: + """Whether a triangle is an admissible candidate for its query. + + A triangle is admissible when every barycentric weight is at least `-threshold` + (`threshold >= 0`) and finite: strictly covering triangles (weights non-negative) + qualify, and so do mildly extrapolated ones within the band. Equality at the + boundary `-threshold` is admissible, matching the reference rejection rule (a weight + is rejected only when strictly below `-threshold`). A degenerate (collinear-image) + triangle yields non-finite weights and is inadmissible. The within-segment envelope + then maximizes over all admissible triangles rather than only the covering one. + + Args: + weights: Barycentric weights, shape `(3,)`. + threshold: Non-negative extrapolation tolerance on each weight. + + Returns: + Boolean scalar: `True` if every weight is finite and at least `-threshold`. + + """ + return jnp.all((weights >= -threshold) & jnp.isfinite(weights)) + + +def interpolate_on_triangle(*, node_values: Float2D, weights: Float1D) -> FloatND: + """Barycentrically interpolate node values at the query. + + Args: + node_values: Per-vertex values, shape `(3, n_fields)` (e.g. the policy + `(c, d)` at the triangle's three vertices). + weights: Barycentric weights, shape `(3,)`. + + Returns: + Interpolated values, shape `(n_fields,)`. + + """ + return weights @ node_values diff --git a/src/_lcm/egm/mesh_gradient.py b/src/_lcm/egm/mesh_gradient.py new file mode 100644 index 000000000..30e35087a --- /dev/null +++ b/src/_lcm/egm/mesh_gradient.py @@ -0,0 +1,86 @@ +"""Region-aware envelope gradient and the cross-segment switch mask. + +The upper envelope publishes the marginal value of wealth at the selected policy. For +the two-asset model the envelope theorem gives, at the optimum, + +$$V_m = u'(c), \\qquad V_n = \\beta\\, W_b,$$ + +with $u'(c) = c^{-\\rho}$. This holds in **every** KKT region: where the borrowing +constraint binds ($a = 0$) the consumption FOC is $u'(c) = \\beta w_a + \\mu_a$ with a +non-negative multiplier $\\mu_a$, so $V_m = u'(c)$ but $V_m \\ne \\beta w_a$. Publishing +$\\beta w_a$ there understates the marginal value. Using $u'(c)$ directly is correct in +all regions and matches the region inverses' `value_grad_m`. + +At a **cross-segment switch** the pointwise maximum of the segment value functions is +generally not differentiable, so no unique gradient exists. The switch mask flags every +target whose winning segment differs from a grid neighbour's; the published gradient +there is the winning branch's one-sided derivative, explicitly marked. +""" + +from typing import NamedTuple + +import jax.numpy as jnp + +from lcm.typing import BoolND, FloatND, IntND + + +class RegionGradient(NamedTuple): + """The region-aware marginal value of liquid and pension wealth.""" + + value_grad_m: FloatND + """`V_m = u'(c) = c**(-crra)`, valid in every KKT region.""" + value_grad_n: FloatND + """`V_n = discount_factor * W_b`.""" + + +def region_aware_gradient( + *, + consumption: FloatND, + post_decision_grad_b: FloatND, + discount_factor: float, + crra: float, +) -> RegionGradient: + """Compute the envelope marginal values from the selected policy. + + Args: + consumption: Selected consumption `c` per target. + post_decision_grad_b: Post-decision value gradient `W_b` at the selected policy. + discount_factor: Discount factor `beta`. + crra: Coefficient of relative risk aversion `rho`. + + Returns: + The marginal value of liquid wealth `u'(c)` and of pension wealth + `discount_factor * W_b`, region-independent. + + """ + return RegionGradient( + value_grad_m=consumption ** (-crra), + value_grad_n=discount_factor * post_decision_grad_b, + ) + + +def switch_mask(*, segment: IntND, grid_shape: tuple[int, int]) -> BoolND: + """Flag targets at a cross-segment switch (the envelope is non-differentiable). + + A target is flagged when its winning segment differs from any of its four grid + neighbours: the pointwise-max envelope has a kink across that boundary, so the + published gradient is one-sided there. + + Args: + segment: Winning segment index per target, shape `(n_m * n_n,)`, row-major over + the `(m, n)` grid. + grid_shape: The `(n_m, n_n)` shape the targets were flattened from. + + Returns: + Boolean mask per target, shape `(n_m * n_n,)`, `True` at a switch. + + """ + seg = segment.reshape(grid_shape) + mask = jnp.zeros(grid_shape, dtype=bool) + row_diff = seg[1:, :] != seg[:-1, :] + mask = mask.at[1:, :].set(mask[1:, :] | row_diff) + mask = mask.at[:-1, :].set(mask[:-1, :] | row_diff) + col_diff = seg[:, 1:] != seg[:, :-1] + mask = mask.at[:, 1:].set(mask[:, 1:] | col_diff) + mask = mask.at[:, :-1].set(mask[:, :-1] | col_diff) + return mask.reshape(-1) diff --git a/src/_lcm/egm/negm_validation.py b/src/_lcm/egm/negm_validation.py new file mode 100644 index 000000000..c4c095a4d --- /dev/null +++ b/src/_lcm/egm/negm_validation.py @@ -0,0 +1,321 @@ +"""Build-time validation of the NEGM model contract. + +A regime configured with `solver=NEGM(inner=DCEGM(...), ...)` must satisfy the +nested-EGM contract on top of the inner DC-EGM contract. NEGM is a +**1-D-inner + outer-search** algorithm: the inner consumption-savings problem is +solved by DC-EGM conditional on a fixed outer (durable/illiquid) margin, and the +outer margin is a deterministic grid search. Every violation raises +`ModelInitializationError` at `Model` construction, naming the offending feature +**and** the correct alternative solver, so no rejection path silently degrades to +a different algorithm. The inner 1-D DC-EGM contract is validated separately, +against the outer-margin-bound inner view the kernel builds; this module checks +only the *outer*/nesting contract. The rules, in the order they are checked: + +- the outer margin exists: `outer_action` is a continuous action of the regime + and `outer_post_decision` is a function the regime declares β€” a regime with + no outer margin is a pure 1-D consumption-savings problem and must use + `DCEGM`, +- the two margins are distinct: the outer action is not the inner continuous + action and the outer post-decision is not the inner post-decision (also + guarded at `NEGM` construction; re-checked here for a single fail-loud point), +- no coupled-2-Euler structure: the outer post-decision enters the inner + resources and/or an additively-separable utility term and the child-state + index ONLY. If it enters the inner Euler-state transition or any other + savings-stage function (the differentiated continuation pool), the `c` and the + outer FOCs invert on the same continuation β€” the DS pension shape β€” and NEGM's + deterministic outer max is invalid; the model needs the 2-D EGM foundation + (G2EGM / multidim-RFC), +- discrete-aggregation ordering: a taste-shocked discrete choice must be the + outermost aggregation, with the outer search living inside each discrete + branch. The single-inner-`DCEGM` composition wraps the outer max *around* the + inner solve (which already performs the discrete `logsumexp`), so the outer + max sits outside the discrete aggregation β€” the wrong order + (`max_{s'} logsumexp_d β‰  logsumexp_d max_{s'}`). A taste-shocked NEGM regime is + therefore rejected. + +The coupled-2-Euler detector is structural and deliberately over-rejects: +catching the DS pension coupling (the outer post-decision feeding the inner +Euler law) and accepting the kinked-toy / housing-adjuster shape (the outer +post-decision read only by inner resources/utility and indexing the child +durable state) is the boundary it provably distinguishes. A model that couples +the two margins through a channel other than the inner Euler law and the +savings-stage functions β€” e.g. a non-additively-separable utility cross-term in +`(c, s')` β€” is rejected by the additive-separability check on utility. +""" + +import inspect +from collections.abc import Mapping +from typing import cast + +from _lcm.egm.validation import ( + _continuous_non_process_names, + _dag_ancestors, + _resolve_solve_functions, + _savings_stage_candidates, + _solve_grids, + _without, +) +from _lcm.typing import FunctionName, RegimeName +from lcm.exceptions import ModelInitializationError +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM, NEGM +from lcm.typing import UserFunction + + +def validate_negm_regimes( + *, + user_regimes: Mapping[RegimeName, UserRegime], +) -> None: + """Validate the NEGM contract for every regime with an `NEGM` solver. + + Args: + user_regimes: Mapping of regime names to user-provided `Regime` + instances. + + Raises: + ModelInitializationError: If any regime with `solver=NEGM(...)` violates + the NEGM model contract. + + """ + for regime_name, user_regime in user_regimes.items(): + if isinstance(user_regime.solver, NEGM): + _validate_negm_regime( + regime_name=regime_name, + user_regime=user_regime, + ) + + +def _validate_negm_regime( + *, + regime_name: RegimeName, + user_regime: UserRegime, +) -> None: + """Run all NEGM contract checks for a single regime, in order.""" + solver = cast("NEGM", user_regime.solver) + inner = solver.inner + + functions = _resolve_solve_functions(user_regime=user_regime) + + _fail_if_outer_margin_absent( + regime_name=regime_name, + user_regime=user_regime, + functions=functions, + solver=solver, + ) + _fail_if_margins_not_distinct(regime_name=regime_name, solver=solver, inner=inner) + _fail_if_outer_margin_euler_coupled( + regime_name=regime_name, + user_regime=user_regime, + functions=functions, + solver=solver, + ) + _fail_if_taste_shock_ordering_violated( + regime_name=regime_name, user_regime=user_regime + ) + + +def _fail_if_outer_margin_absent( + *, + regime_name: RegimeName, + user_regime: UserRegime, + functions: dict[FunctionName, UserFunction], + solver: NEGM, +) -> None: + """The outer durable margin must be a real action and post-decision function. + + A regime that declares no outer continuous margin (the outer action is not + among its continuous actions, or the outer post-decision is not a declared + function) is a pure 1-D consumption-savings problem; NEGM would silently run + as plain DC-EGM, so it is rejected with the `DCEGM` pointer. + """ + continuous_actions = _continuous_non_process_names( + grids=_solve_grids(slot=user_regime.actions) + ) + if solver.outer_action not in continuous_actions: + msg = ( + f"NEGM.outer_action '{solver.outer_action}' is not a continuous " + f"action of regime '{regime_name}'. NEGM nests an outer continuous " + f"margin; this regime declares none (continuous actions: " + f"{continuous_actions}) β€” use `DCEGM` for a pure 1-D " + "consumption-savings regime." + ) + raise ModelInitializationError(msg) + # The outer post-decision `s'` is either a declared regime function or the + # auto-generated transition `next_` of the durable state (its law of + # motion produces the next durable stock). + transition_names = {f"next_{name}" for name in user_regime.states} + if ( + solver.outer_post_decision not in functions + and solver.outer_post_decision not in transition_names + ): + msg = ( + f"NEGM.outer_post_decision '{solver.outer_post_decision}' is neither " + f"a declared function of regime '{regime_name}' nor the transition " + "of one of its states. The outer post-decision (the next-period " + "durable stock) must be a regime function or the durable state's " + f"`next_` law that the inner resources and the child-state " + "index read; declare it, or use `DCEGM` for a pure 1-D " + "consumption-savings regime." + ) + raise ModelInitializationError(msg) + + +def _fail_if_margins_not_distinct( + *, + regime_name: RegimeName, + solver: NEGM, + inner: DCEGM, +) -> None: + """The outer and inner margins must be distinct actions and post-decisions. + + Re-checks the construction-time guards at model build so every NEGM + rejection surfaces from one validation entry point. + """ + if solver.outer_action == inner.continuous_action: + msg = ( + f"NEGM.outer_action '{solver.outer_action}' of regime " + f"'{regime_name}' coincides with the inner DC-EGM continuous action " + f"'{inner.continuous_action}'. The outer durable/illiquid margin and " + "the inner consumption margin must be distinct actions." + ) + raise ModelInitializationError(msg) + if solver.outer_post_decision == inner.post_decision_function: + msg = ( + f"NEGM.outer_post_decision '{solver.outer_post_decision}' of regime " + f"'{regime_name}' coincides with the inner DC-EGM post-decision " + f"function '{inner.post_decision_function}'. The outer post-decision " + "(the next-period durable stock) and the inner post-decision (the " + "liquid savings) must be distinct functions." + ) + raise ModelInitializationError(msg) + + +def _fail_if_outer_margin_euler_coupled( + *, + regime_name: RegimeName, + user_regime: UserRegime, + functions: dict[FunctionName, UserFunction], + solver: NEGM, +) -> None: + """The outer margin must not enter the inner differentiated-Euler pool. + + NEGM's deterministic outer max is valid only when the inner 1-D Euler + inversion is independent of the outer choice: the outer post-decision may be + read by the inner resources and an additively-separable utility term, and it + indexes the child durable state β€” but it must NOT enter the inner + Euler-state transition or any other savings-stage function (the regime + transition, stochastic weights, non-Euler state laws). Those functions feed + the differentiated continuation the inner Euler equation inverts on, so the + `c` and outer FOCs would invert on the same continuation β€” the DS pension + coupling β€” which a single inverse-Euler cannot represent. + + The post-decision and resources functions are removed from the DAG (they + become leaves), so an ancestor hit on the outer post-decision is a genuine + decision-time coupling, not the legitimate resources read. + """ + inner = solver.inner + opaque_functions = _without( + functions=functions, + names={inner.post_decision_function, inner.resources}, + ) + coupling_msg = ( + f"the outer margin '{solver.outer_post_decision}' is Euler-coupled to " + f"the inner state '{inner.continuous_state}' of regime '{regime_name}' " + "through the shared continuation" + ) + for _role, label, func in _savings_stage_candidates( + user_regime=user_regime, solver=inner + ): + ancestors = _dag_ancestors(functions=opaque_functions, target_func=func) + if solver.outer_post_decision in ancestors: + msg = ( + f"In regime '{regime_name}', the {label} reads the outer " + f"post-decision '{solver.outer_post_decision}', so {coupling_msg}: " + "the inner Euler inversion is no longer independent of the outer " + "choice. NEGM's deterministic outer max is invalid here β€” use the " + "2-D EGM foundation (G2EGM / multidim-RFC), not NEGM." + ) + raise ModelInitializationError(msg) + + # Utility may carry the outer margin only additively-separably from the + # inner action: a cross-term in (consumption, outer post-decision) makes the + # inner marginal utility depend on the outer choice, so the inner Euler + # inversion couples to it. + _fail_if_utility_couples_action_and_outer_margin( + regime_name=regime_name, + functions=functions, + solver=solver, + ) + + +def _fail_if_utility_couples_action_and_outer_margin( + *, + regime_name: RegimeName, + functions: dict[FunctionName, UserFunction], + solver: NEGM, +) -> None: + """Utility must read the outer margin additively-separably from consumption. + + The inner Euler inversion treats the outer margin's utility term as a + constant (`u(c, s') = Ε©(c) + g(s')`). If `utility` reaches both the inner + continuous action and the outer post-decision through a single function that + multiplies/composes them (a cross-term), the inner marginal utility depends + on the outer choice and the deterministic outer max over a frozen inner + inversion is invalid. The structural proxy: no individual utility-DAG + function may take both the inner action and the outer post-decision (or the + outer action) as direct arguments. + """ + inner = solver.inner + outer_names = {solver.outer_action, solver.outer_post_decision} + utility_dag_names = _dag_ancestors( + functions=functions, + target_func=functions["utility"], + ) | {"utility"} + for func_name in utility_dag_names: + func = functions.get(func_name) + if func is None: + continue + arg_names = set(inspect.signature(func).parameters) + if inner.continuous_action in arg_names and arg_names & outer_names: + crossed = sorted(arg_names & outer_names) + msg = ( + f"In regime '{regime_name}', the utility-DAG function " + f"'{func_name}' takes both the inner consumption action " + f"'{inner.continuous_action}' and the outer margin {crossed} as " + "arguments, so utility couples the two margins (it is not " + "additively separable in them). The inner marginal utility then " + "depends on the outer choice, so NEGM's deterministic outer max " + "over a frozen inner Euler inversion is invalid β€” use the 2-D EGM " + "foundation (G2EGM / multidim-RFC), not NEGM." + ) + raise ModelInitializationError(msg) + + +def _fail_if_taste_shock_ordering_violated( + *, + regime_name: RegimeName, + user_regime: UserRegime, +) -> None: + """A taste-shocked discrete choice must be the outermost aggregation. + + The single-inner-`DCEGM` composition wraps the outer search around the whole + inner solve, which already performs the discrete `logsumexp` aggregation. + The outer max therefore sits *outside* the discrete aggregation, computing + `max_{s'} logsumexp_d` β€” but with EV taste shocks the correct order is + `logsumexp_d max_{s'}`, the search nested inside each discrete branch + (`max_{s'} logsumexp_d β‰  logsumexp_d max_{s'}`). A taste-shocked NEGM regime + is rejected until the outer search can be pushed inside each discrete branch. + """ + if user_regime.taste_shocks is not None: + msg = ( + f"Regime '{regime_name}' declares EV1 taste shocks and uses the NEGM " + "solver. NEGM wraps its outer durable-margin search around the inner " + "DC-EGM solve, which performs the discrete-choice aggregation β€” so " + "the outer max sits outside the taste-shock aggregation. With taste " + "shocks the discrete choice must be the outermost aggregation, with " + "the outer search nested inside each discrete branch " + "(max over the durable margin of logsumexp over the discrete choice " + "is not logsumexp of the max). Remove the taste shocks or use the " + "grid-search solver for this regime." + ) + raise ModelInitializationError(msg) diff --git a/src/_lcm/egm/numeric_inverse.py b/src/_lcm/egm/numeric_inverse.py new file mode 100644 index 000000000..babbc49e2 --- /dev/null +++ b/src/_lcm/egm/numeric_inverse.py @@ -0,0 +1,156 @@ +"""Numerical inverse of marginal utility for the iEGM path. + +EGM needs $(u')^{-1}$ to recover the optimal action from the Euler equation. When +the model supplies no closed-form `inverse_marginal_utility`, this module inverts +`u'` numerically by a bracketed bisection on the action, so EGM solves any model +whose marginal utility is continuous and strictly decreasing (the concavity the +Euler step already assumes). + +The forward solve is a fixed-count safeguarded Newton iteration in +log-consumption β€” a Newton step from the live bracket when it stays inside it, a +bisection step otherwise β€” bounded, jittable, and vmap-safe. In `log c` the CRRA +family is exactly linear (`log u' = -crra log c`), so Newton converges in a single +step and stays well-conditioned for any power-law-like $u'$ whose steep-near-zero, +flat-at-large-$c$ curvature would make a plain-$c$ Newton overshoot; the bisection +fallback keeps a step that leaves the bracket from diverging. Its branch +comparisons are not differentiated: the root is detached and the gradient is +supplied analytically by the implicit-function theorem through a single corrector +step. At the converged +root $c^*$ the correction $(u'(c^*) - m)/u''(c^*)$ is numerically zero, so the +value is the iterated root, while its derivative is the exact implicit derivative + +$$\\frac{\\partial c^*}{\\partial m} = \\frac{1}{u''(c^*)}, \\qquad +\\frac{\\partial c^*}{\\partial \\theta} = +-\\frac{\\partial_\\theta u'(c^*)}{u''(c^*)},$$ + +independent of the iteration count. Differentiating through the iteration +branches instead would yield a wrong or iteration-dependent gradient, which is a +bug in a JAX solver β€” hence the detached forward solve plus analytic corrector. + +The inverse is defined for an *interior* root: the target must be bracketed by +`[c_lower, c_upper]`. The borrowing-constrained corner is represented separately +(the closed-form constrained candidate), and the Euler step's epsilon clamp keeps +a near-zero marginal continuation from forcing the root to the upper bound. +""" + +from collections.abc import Callable + +import jax +import jax.numpy as jnp + +from lcm.typing import ScalarFloat + +_NEWTON_ITERATIONS = 30 + + +def numeric_inverse_marginal_utility( + *, + marginal_continuation: ScalarFloat, + marginal_utility: Callable[[ScalarFloat], ScalarFloat], + c_lower: ScalarFloat, + c_upper: ScalarFloat, + n_iter: int = _NEWTON_ITERATIONS, +) -> ScalarFloat: + """Solve `marginal_utility(c) = marginal_continuation` for the action `c`. + + `marginal_utility` must be continuous and strictly decreasing on + `[c_lower, c_upper]` (the marginal utility of a concave utility), so the root + is unique where it is bracketed. The forward solve is a detached fixed-count + safeguarded Newton iteration; the returned value carries the exact + implicit-function-theorem derivative through a single analytic corrector step, + not autodiff through the iteration branches. + + Args: + marginal_continuation: The Euler target $m$ β€” the discounted expected + marginal continuation value the action's marginal utility must equal. + marginal_utility: The marginal utility $u'$ as a callable of the action, + with every utility parameter already bound. Strictly decreasing. + c_lower: Lower bracket on the action (a small positive floor). + c_upper: Upper bracket on the action (from the resources upper bound). + n_iter: Fixed safeguarded-Newton iteration count; quadratic convergence + reaches a smooth root well below machine epsilon in a handful of + steps, and the bisection fallback guarantees progress otherwise. + + Returns: + The action `c` at which `marginal_utility(c) == marginal_continuation`. + + """ + m = marginal_continuation + marginal_curvature = jax.grad(marginal_utility) + + # The iteration runs in log-consumption space: in `log_c`, the residual + # `r(log_c) = log u'(e^{log_c}) - log m` is exactly linear for the CRRA family + # (`log u' = -crra log_c`), so Newton converges in a single step there and + # stays well-conditioned for any power-law-like `u'` β€” the steep-near-zero, + # flat-at-large-`c` curvature that makes a plain-`c` Newton overshoot. The log + # is defined only where `u' > 0` and `m > 0` (marginal utility of an increasing + # utility, a discounted positive continuation) β€” the iEGM precondition. A + # utility violating it (a bliss point, a marginal touching zero inside the + # bracket, a non-finite inactive `where` branch) would make `log u'`/`log m` + # non-finite; the `log_well_defined` gate below fails such a call *loud* (NaN), + # so the solve's NaN diagnostics name the offending (regime, period) rather + # than the log path silently returning a clamped bound. + mu_lower = marginal_utility(c_lower) + mu_upper = marginal_utility(c_upper) + log_m = jnp.log(m) + # A bracket marginal that overflows to `+inf` (a power-law `u'` at a + # near-zero `c_lower`) is `> 0.0` but not finite: `log(+inf)` is `+inf`, not + # NaN, so the positivity checks alone would let the log path proceed on a + # non-finite endpoint. Require finiteness explicitly so the gate fails loud. + log_well_defined = ( + (m > 0.0) + & (mu_lower > 0.0) + & (mu_upper > 0.0) + & jnp.isfinite(mu_lower) + & jnp.isfinite(mu_upper) + & jnp.isfinite(log_m) + ) + + def log_marginal_utility(log_c: ScalarFloat) -> ScalarFloat: + return jnp.log(marginal_utility(jnp.exp(log_c))) + + log_marginal_slope = jax.grad(log_marginal_utility) + + # Static-count safeguarded Newton, unrolled at trace time (`n_iter` is a + # Python int). `r` is decreasing in `log_c`: `r > 0` means `c` is below the + # root (raise the lower bound), `r < 0` means it is above (lower the upper + # bound). After that bracket update the root lies in `[log_low, log_high]`; + # the Newton step is taken only when it lands strictly inside that live + # bracket (and the slope is non-zero), else the iterate bisects. Branches are + # `jnp.where`, so the loop is jittable and vmap-safe, and the detached root + # below keeps autodiff out of it. + log_low, log_high = jnp.log(c_lower), jnp.log(c_upper) + log_c = 0.5 * (log_low + log_high) + for _ in range(n_iter): + residual = log_marginal_utility(log_c) - log_m + below_root = residual > 0.0 + log_low = jnp.where(below_root, log_c, log_low) + log_high = jnp.where(below_root, log_high, log_c) + slope = log_marginal_slope(log_c) + safe_slope = jnp.where(slope == 0.0, -1.0, slope) + log_c_newton = log_c - residual / safe_slope + take_newton = ( + (log_c_newton > log_low) & (log_c_newton < log_high) & (slope != 0.0) + ) + log_c = jnp.where(take_newton, log_c_newton, 0.5 * (log_low + log_high)) + c_star = jax.lax.stop_gradient(jnp.exp(log_c)) + + # The implicit-derivative corrector below is valid only at an *interior, + # bracketed* root. `u'` is decreasing, so the target is bracketed iff + # `u'(c_upper) <= m <= u'(c_lower)`; outside that the iteration clamps to a + # bound and the interior `1/u''` Jacobian would silently extrapolate a wrong + # gradient. At a binding bound the active-set derivative is zero, so the + # unbracketed branch returns the clamped root detached (value at the bound, + # `dc/dm = 0`) rather than the bogus interior slope. + bracketed = (mu_upper <= m) & (mu_lower >= m) + + # Implicit-derivative corrector: detached root + one Newton-style step whose + # value is ~`c_star` (residual β‰ˆ 0 at convergence) but whose gradient is the + # exact implicit derivative. `u''` is detached so it enters only as the + # constant `1/u''` Jacobian, never differentiated itself. + second_derivative = jax.lax.stop_gradient(marginal_curvature(c_star)) + interior = c_star - (marginal_utility(c_star) - m) / second_derivative + root = jnp.where(bracketed, interior, c_star) + # Fail loud where the log-space preconditions do not hold: NaN surfaces in the + # kernel's NaN diagnostics instead of a silently-wrong clamped bound. + return jnp.where(log_well_defined, root, jnp.nan) diff --git a/src/_lcm/egm/one_asset_egm_step.py b/src/_lcm/egm/one_asset_egm_step.py new file mode 100644 index 000000000..c1ca189dd --- /dev/null +++ b/src/_lcm/egm/one_asset_egm_step.py @@ -0,0 +1,106 @@ +"""One backward EGM step for a 1-D consumption--saving problem. + +The retired phase of the DS pension model is a plain consumption--saving problem: a +single continuous state `liquid`, a single continuous action `consumption`, and no +discrete choice. With one continuous state the endogenous grid method needs no upper +envelope β€” invert the consumption Euler equation + +$$u'(c) = \\beta (1+r) V'_{\\text{next}}\\big((1+r)(\\text{liquid}-c)+y\\big)$$ + +on a post-decision savings grid $s = \\text{liquid} - c \\ge 0$, read the next-period +value and its marginal off the prior arrays, and map the resulting endogenous liquid +back onto the regular liquid grid. Below the natural borrowing limit the constraint +binds and the agent consumes all liquid. + +The step carries the **marginal value of liquid** $V'(\\text{liquid})$ between periods +rather than finite-differencing the value array: by the envelope theorem +$V'(\\text{liquid}) = u'(c^*)$, which is exact, whereas a finite difference of the value +array is badly inaccurate where the value is steep (low liquid). Each step therefore +both consumes `next_marginal` and publishes this period's marginal. +""" + +from typing import NamedTuple + +import jax.numpy as jnp + +from lcm.typing import Float1D, ScalarFloat + + +class RetiredEGMResult(NamedTuple): + """A retired EGM step's value, marginal value of liquid, and consumption policy.""" + + value: Float1D + """This period's value on `liquid_grid`.""" + marginal: Float1D + """This period's marginal value of liquid `V' = u'(c*)` on `liquid_grid`.""" + consumption: Float1D + """This period's optimal consumption on `liquid_grid`.""" + + +def egm_one_asset_step( + *, + next_value: Float1D, + next_marginal: Float1D, + liquid_grid: Float1D, + savings_grid: Float1D, + discount_factor: ScalarFloat | float, + crra: ScalarFloat | float, + return_liquid: ScalarFloat | float, + income: ScalarFloat | float, +) -> RetiredEGMResult: + """Solve one period of the 1-D consumption--saving problem by EGM. + + Args: + next_value: Next period's value on `liquid_grid`, shape `(n_liquid,)`. + next_marginal: Next period's marginal value of liquid `V'` on `liquid_grid`, + shape `(n_liquid,)`. For a terminal bequest `u(liquid)` this is + `liquid ** (-crra)`. + liquid_grid: Regular liquid-state grid (ascending). + savings_grid: Post-decision savings grid `s = liquid - consumption` (ascending, + starting at 0), shape `(n_savings,)`. + discount_factor: Discount factor `beta`. + crra: Coefficient of relative risk aversion `rho`. + return_liquid: Liquid net return `r`. + income: Deterministic income added to next-period liquid. + + Returns: + This period's value, marginal value of liquid, and consumption policy on + `liquid_grid`. + + """ + gross_return = 1.0 + return_liquid + next_liquid = gross_return * savings_grid + income + value_next = jnp.interp(next_liquid, liquid_grid, next_value) + marginal_next = jnp.interp(next_liquid, liquid_grid, next_marginal) + + consumption = (discount_factor * gross_return * marginal_next) ** (-1.0 / crra) + liquid_endog = consumption + savings_grid + value_endog = _crra_utility(consumption, crra) + discount_factor * value_next + + # Interior: interpolate the endogenous value and consumption onto the regular grid. + interior_value = jnp.interp(liquid_grid, liquid_endog, value_endog) + interior_consumption = jnp.interp(liquid_grid, liquid_endog, consumption) + + # Constrained: below the smallest endogenous liquid the borrowing constraint binds, + # so the agent consumes all liquid and saves nothing (`next_liquid = income`). + constrained = liquid_grid < liquid_endog[0] + value_at_zero_savings = jnp.interp(income, liquid_grid, next_value) + constrained_value = ( + _crra_utility(liquid_grid, crra) + discount_factor * value_at_zero_savings + ) + consumption_on_grid = jnp.where(constrained, liquid_grid, interior_consumption) + value = jnp.where(constrained, constrained_value, interior_value) + # Envelope theorem: the marginal value of liquid is the marginal utility of the + # optimal consumption. + marginal = consumption_on_grid ** (-crra) + return RetiredEGMResult( + value=value, marginal=marginal, consumption=consumption_on_grid + ) + + +def _crra_utility(consumption: Float1D, crra: ScalarFloat | float) -> Float1D: + return jnp.where( + crra == 1.0, + jnp.log(consumption), + consumption ** (1.0 - crra) / (1.0 - crra), + ) diff --git a/src/_lcm/egm/outer_envelope.py b/src/_lcm/egm/outer_envelope.py new file mode 100644 index 000000000..d4a161b73 --- /dev/null +++ b/src/_lcm/egm/outer_envelope.py @@ -0,0 +1,333 @@ +"""The NEGM cash-on-hand outer-max carry envelope. + +The NEGM kernel collapses the outer durable choice by `V = max_j W_j` on the +exogenous state grid, but the continuation it threads to the parent period is a +carry β€” value and marginal-utility rows on an endogenous (resources) grid. The +keeper and every adjuster outer-grid node produce one such candidate row per +durable state, each in its *own* resources space: the adjuster `j` pays a +credited durable cost, so its resources are the keeper's cash-on-hand shifted +down by `credited(z, z'_j)`. + +The envelope lifts every candidate into a common cash-on-hand (coh) axis by adding +back its credited cost (`βˆ‚coh/βˆ‚R = 1`, so the value and the resource-marginal +carry over unchanged), interpolates each candidate's value and marginal onto a +shared coh grid per durable state, and takes the pointwise maximum β€” the genuine +upper envelope in coh space. An adjuster that wins strictly between two keeper +nodes therefore survives, because each candidate is read at the shared coh nodes +by interpolation, not only at its own abscissae. The published marginal is the +*winning* candidate's resource slope at each coh node, never an average across a +branch crossing. The parent's keeper-identity continuation read then interpolates +the published carry exactly as before; the carry it reads is the outer-max +envelope rather than the keeper alone. + +The envelope is built by *folding* candidates one at a time into a running +maximum (`init_outer_envelope` β†’ `fold_outer_envelope` per candidate β†’ +`finalize_outer_envelope`), so the caller never materialises all outer-grid +candidates at once. Folding is value-identical to a single stacked maximum: +`max` is associative, the shared coh grid is fixed at the keeper's grid for every +fold, and the strict `>` update keeps the earliest candidate on ties β€” matching a +stacked `argmax` that returns the first maximiser. `build_outer_envelope_carry` +wraps the fold over a candidate tuple for callers (and tests) that hold them all. +""" + +from typing import NamedTuple + +import jax +import jax.numpy as jnp + +from _lcm.egm.carry import EGMCarry +from _lcm.egm.interp import interp_on_padded_grid +from lcm.typing import Float1D, FloatND, ScalarFloat + +# Smallest sub-grid island win, as a fraction of the row's value scale. The +# shared-grid read is a cubic-Hermite interpolant, so a smooth branch's apparent +# excess over the running envelope is O(h^2) representation noise. A genuine +# (S, s) island beats the envelope by an economically meaningful margin far above +# that floor, so this threshold separates the two without depending on the +# absolute value scale (which grows through backward induction). +_ISLAND_RELATIVE_FLOOR = 1e-2 + + +class OuterEnvelopeState(NamedTuple): + """Running coh-space upper envelope over the outer durable candidates. + + The rows are flattened over the carry's leading cells `(discrete..., durable)` + so a single candidate folds in with one batched interpolation; `finalize` + restores the leading shape. + """ + + shared_coh: FloatND + """The fixed shared coh grid (the keeper's), `(n_leading_cells, n_pad)`.""" + value: FloatND + """Running envelope value at `shared_coh`, `(n_leading_cells, n_pad)`.""" + marginal: FloatND + """Running winner's marginal at `shared_coh`, `(n_leading_cells, n_pad)`.""" + extra_coh: FloatND + """Coh of each adjuster's island peak, `(n_leading_cells, n_adjusters)`. + + The shared-grid maximum samples each adjuster only at the keeper's nodes, so + an adjuster that wins only on a coh sub-interval narrower than the grid + spacing is lost. Each fold records that adjuster's best win β€” its largest + value over the running envelope, read at the adjuster's own nodes β€” in its + own pre-allocated column, so the bound is the adjuster count (additive), not + the grid product. A fold with no interior win records `NaN` (dropped on + merge). `finalize` merges these peaks into the published row. + """ + extra_value: FloatND + """Value at each adjuster's island peak, `(n_leading_cells, n_adjusters)`.""" + extra_marginal: FloatND + """Marginal at each adjuster's island peak, `(n_leading_cells, n_adjusters)`.""" + leading_shape: tuple[int, ...] + """The carry's leading shape `(discrete..., durable)` for `finalize`.""" + n_durable: int + """Number of durable-margin states β€” the last leading axis.""" + taste_shock_scale: ScalarFloat + """The keeper carry's taste-shock scale, carried through to the result.""" + + +def init_outer_envelope(keeper_carry: EGMCarry, n_adjusters: int) -> OuterEnvelopeState: + """Start the running envelope from the keeper's own coh grid. + + The keeper is already in coh space (`credited(z, z) = 0`), so its endogenous + grid is the shared coh grid every candidate is read onto. The running value + and marginal are the keeper read through the same identity interpolate-and-mask + path every adjuster uses (its own grid, zero shift), so the keeper is the + baseline an adjuster must strictly beat β€” matching a stacked `argmax` that + returns the first maximiser (the keeper) on a tie. + + `n_adjusters` pre-allocates one island-peak slot per adjuster so the fold + writes a fixed-shape (jit-safe) column rather than growing the carry. + """ + n_pad = keeper_carry.endog_grid.shape[-1] + leading_shape = keeper_carry.endog_grid.shape[:-1] + n_durable = leading_shape[-1] + shared_coh = keeper_carry.endog_grid.reshape(-1, n_pad) + keeper_value = keeper_carry.value.reshape(-1, n_pad) + keeper_marginal = keeper_carry.marginal_utility.reshape(-1, n_pad) + value, marginal = jax.vmap(_read_candidate_row)( + shared_coh, shared_coh, keeper_value, keeper_marginal + ) + n_cells = shared_coh.shape[0] + extra = jnp.full((n_cells, n_adjusters), jnp.nan, dtype=shared_coh.dtype) + return OuterEnvelopeState( + shared_coh=shared_coh, + value=value, + marginal=marginal, + extra_coh=extra, + extra_value=extra, + extra_marginal=extra, + leading_shape=leading_shape, + n_durable=n_durable, + taste_shock_scale=keeper_carry.taste_shock_scale, + ) + + +def fold_outer_envelope( + state: OuterEnvelopeState, + candidate_carry: EGMCarry, + coh_shift: Float1D, + adjuster_index: int, +) -> OuterEnvelopeState: + """Fold one outer candidate into the running coh-space maximum. + + The candidate's endogenous grid is shifted into coh space by `coh_shift` (per + durable state), its value and marginal are interpolated onto the shared coh + grid, queries below its own first finite coh node are masked to `-inf`, and a + strict `value > running` update keeps the candidate where it wins (so the + earliest candidate survives a tie, matching a stacked `argmax`). + + The shared-grid maximum samples the candidate only at the keeper's nodes, so an + adjuster that wins only on a coh sub-interval narrower than the grid spacing is + invisible to it. To recover that sub-grid island, the candidate is *also* read + at its own coh nodes against the running envelope; its single best win (largest + value over the envelope) is recorded in the adjuster's own pre-allocated column, + so the carry grows by a bounded `n_adjusters`, never the grid product. `finalize` + merges these island peaks into the published row. + + Args: + state: The running envelope. + candidate_carry: The candidate's carry β€” one row per leading cell, in its + own resources space. + coh_shift: The credited cost `credited(z, z'_j)` added to the candidate's + endogenous grid per durable state, shape `(n_durable,)`. Zero for the + keeper. + adjuster_index: This candidate's static column in the island-peak slots. + + Returns: + The updated running envelope. + + """ + n_pad = state.shared_coh.shape[-1] + n_cells = state.shared_coh.shape[0] + # The durable margin is the last leading axis, so a row-major flatten makes it + # the fastest-varying index: leading cell `i` sits at durable `i % n_durable`. + durable_of_cell = jnp.arange(n_cells) % state.n_durable + shift_per_cell = coh_shift[durable_of_cell][:, None] + + cand_endog = candidate_carry.endog_grid.reshape(-1, n_pad) + shift_per_cell + cand_value = candidate_carry.value.reshape(-1, n_pad) + cand_marginal = candidate_carry.marginal_utility.reshape(-1, n_pad) + + value_on, marginal_on = jax.vmap(_read_candidate_row)( + state.shared_coh, cand_endog, cand_value, cand_marginal + ) + takes = value_on > state.value + + # Sub-grid island: read the running envelope at the candidate's own coh nodes + # and keep the candidate's single largest win there. A node where the candidate + # does not strictly beat the envelope (or is dead/padding) contributes nothing. + # The win must lie strictly inside the shared grid's finite support: below its + # first node the envelope read is masked to `-inf` (an artificial `+inf` + # excess), and beyond its last node any candidate that wins also wins at the + # top shared node, so the shared-grid maximum already captures it β€” only an + # interior peak between two shared nodes can be missed. + env_at_cand, _ = jax.vmap(_read_candidate_row)( + cand_endog, state.shared_coh, state.value, state.marginal + ) + finite_shared = jnp.isfinite(state.shared_coh) + shared_lower = jnp.min( + jnp.where(finite_shared, state.shared_coh, jnp.inf), axis=1, keepdims=True + ) + shared_upper = jnp.max( + jnp.where(finite_shared, state.shared_coh, -jnp.inf), axis=1, keepdims=True + ) + interior = ( + jnp.isfinite(cand_endog) + & jnp.isfinite(env_at_cand) + & (cand_endog >= shared_lower) + & (cand_endog <= shared_upper) + ) + excess = jnp.where(interior, cand_value - env_at_cand, -jnp.inf) + peak = jnp.argmax(jnp.where(jnp.isnan(excess), -jnp.inf, excess), axis=1) + # A genuine sub-grid island clears the carry's interpolation-residual floor: + # the shared-grid read is a slope-aware (cubic-Hermite) interpolant, so on a + # smooth branch the adjuster's node sits within `O(h^2)` of the running + # envelope and the apparent excess is representation noise, not a real win. A + # true (S, s) island beats the envelope by an economically meaningful margin β€” + # orders of magnitude above that noise β€” so only an excess exceeding a small + # fraction of the row's value scale is spliced. + value_scale = jnp.max( + jnp.where(jnp.isfinite(state.value), jnp.abs(state.value), 0.0), + axis=1, + keepdims=True, + ) + peak_excess = jnp.take_along_axis(excess, peak[:, None], axis=1) + has_win = (peak_excess > _ISLAND_RELATIVE_FLOOR * value_scale)[:, 0] + pick = lambda src: jnp.where( # noqa: E731 + has_win, jnp.take_along_axis(src, peak[:, None], axis=1)[:, 0], jnp.nan + ) + peak_coh = pick(cand_endog) + peak_value = pick(cand_value) + peak_marginal = pick(cand_marginal) + + return state._replace( + value=jnp.where(takes, value_on, state.value), + marginal=jnp.where(takes, marginal_on, state.marginal), + extra_coh=state.extra_coh.at[:, adjuster_index].set(peak_coh), + extra_value=state.extra_value.at[:, adjuster_index].set(peak_value), + extra_marginal=state.extra_marginal.at[:, adjuster_index].set(peak_marginal), + ) + + +def finalize_outer_envelope(state: OuterEnvelopeState) -> EGMCarry: + """Restore the leading shape and emit the published continuation carry. + + The published row is the shared-grid envelope with each adjuster's recorded + island peak spliced in, sorted into ascending coh order. The slots that no + adjuster filled carry `NaN` coh; sorting them to the high end keeps them as + trailing padding the interpolator's first-finite-node search ignores. The + published width is `n_pad + n_adjusters`, fixed at build time. + """ + merged_coh = jnp.concatenate([state.shared_coh, state.extra_coh], axis=1) + merged_value = jnp.concatenate([state.value, state.extra_value], axis=1) + merged_marginal = jnp.concatenate([state.marginal, state.extra_marginal], axis=1) + + # NaN coh sorts to the high end so empty island slots become trailing padding. + sort_key = jnp.where(jnp.isnan(merged_coh), jnp.inf, merged_coh) + order = jnp.argsort(sort_key, axis=1) + sorted_coh = jnp.take_along_axis(merged_coh, order, axis=1) + sorted_value = jnp.take_along_axis(merged_value, order, axis=1) + sorted_marginal = jnp.take_along_axis(merged_marginal, order, axis=1) + + n_pad_out = merged_coh.shape[-1] + shape = (*state.leading_shape, n_pad_out) + return EGMCarry( + endog_grid=sorted_coh.reshape(shape), + value=sorted_value.reshape(shape), + marginal_utility=sorted_marginal.reshape(shape), + taste_shock_scale=state.taste_shock_scale, + ) + + +def build_outer_envelope_carry( + *, + keeper_carry: EGMCarry, + adjuster_carries: tuple[EGMCarry, ...], + coh_shifts: FloatND, +) -> EGMCarry: + """Build the outer-max continuation carry as a coh-space upper envelope. + + Folds the keeper and every adjuster candidate into a running coh-space + maximum (see the module docstring). The published value row is that maximum; + the published marginal row is the winning candidate's marginal at each coh + node, so the marginal stays winner-consistent rather than averaged across a + crossing. A candidate whose borrowing-constrained support starts above the + shared grid's lower end is masked to `-inf` there and cannot win in that + region. + + The carry's leading axes are the inner DC-EGM's outer states β€” any + discrete/process states first, then the single passive durable margin β€” so the + durable is the *last* leading axis. The credited shift depends only on the + durable margin and the adjuster node, so it is applied per durable state; the + upper envelope is taken independently per leading cell `(discrete..., durable)`. + + Args: + keeper_carry: The keeper's continuation carry β€” one row per leading cell + `(discrete..., durable)`, already in coh space (`credited(z, z) = 0`). + adjuster_carries: One carry per outer-grid node, each in its own resources + space; aligned with the columns of `coh_shifts`. + coh_shifts: Per durable state (rows) and adjuster node (columns), the + constant `credited(z, z'_j)` added to that adjuster's endogenous grid + to map it into coh space. Shape `(n_durable, n_adjusters)`. + + Returns: + The published continuation carry β€” the coh-space upper envelope of the + keeper and all adjuster candidates, one row per leading cell. + + """ + state = init_outer_envelope(keeper_carry, len(adjuster_carries)) + for adjuster_index, adjuster_carry in enumerate(adjuster_carries): + state = fold_outer_envelope( + state, adjuster_carry, coh_shifts[:, adjuster_index], adjuster_index + ) + return finalize_outer_envelope(state) + + +def _read_candidate_row( + shared_coh: Float1D, + cand_endog: Float1D, + cand_value: Float1D, + cand_marginal: Float1D, +) -> tuple[Float1D, Float1D]: + """Interpolate one candidate's value and marginal onto the shared coh grid. + + Below the candidate's own first finite coh node the value is masked to `-inf` + (its borrowing-constrained support has not started), so the candidate cannot + win there. The marginal is interpolated independently and carried only where + the candidate wins. + """ + cand_lower = jnp.min(jnp.where(jnp.isfinite(cand_endog), cand_endog, jnp.inf)) + value_on_shared = interp_on_padded_grid( + x_query=shared_coh, + xp=cand_endog, + fp=cand_value, + fp_slopes=cand_marginal, + ) + marginal_on_shared = interp_on_padded_grid( + x_query=shared_coh, + xp=cand_endog, + fp=cand_marginal, + ) + below_support = shared_coh < cand_lower + value_on_shared = jnp.where(below_support, -jnp.inf, value_on_shared) + return value_on_shared, marginal_on_shared diff --git a/src/_lcm/egm/published_policy.py b/src/_lcm/egm/published_policy.py new file mode 100644 index 000000000..8464b2bcb --- /dev/null +++ b/src/_lcm/egm/published_policy.py @@ -0,0 +1,78 @@ +"""Published continuous-action policy for off-grid DC-EGM forward simulation. + +The DC-EGM solve recovers an exact, off-grid consumption function: Euler +inversion plus the upper envelope give the optimal continuous action on the +endogenous (resources-space) grid. `EGMSimPolicy` is the per-period snapshot of +that function β€” the off-grid policy a simulated subject's continuous action +*could* be interpolated from at its resources, rather than an argmax snapped to +the action grid. + +It is produced and carried for *every* solved period alongside the +value-function arrays, but it is **not consumed by `simulate` today**: forward +simulation re-optimizes the gridded continuous action via +`argmax_and_max_Q_over_a` (the grid-restricted path documented on `DCEGM`), so +simulated actions live on the action grid. `EGMSimPolicy` is built ahead of an +off-grid simulation path that is not yet wired in. + +Invariant for whoever wires it in: the stored policy is the **solve-phase** +optimum. It may be used at simulate time only when the solve-phase and +simulate-phase aggregators `H` coincide. With a phase-variant `H` (e.g. naive +present bias β€” solve under the exponential `Ξ΄`, simulate under `Ξ²ΜƒΞ²`) the stored +policy encodes the wrong continuous-action FOC; such models must keep the +re-optimization path, which re-applies the simulate-phase decision. A regression +should assert that DC-EGM simulation of a present-bias model differs from the +exponential one in the expected direction before any off-grid lookup replaces +the re-optimization. + +Unlike the rolling `EGMCarry` (the cross-period continuation channel, overwritten +each period), this is saved for every solved period and travels to `simulate` +alongside the value-function arrays. Its `endog_grid` rows are shared with the +period's carry; only the `policy` row is additional state. +""" + +from collections.abc import Sequence +from dataclasses import dataclass +from typing import Any + +import jax + +from lcm.typing import FloatND + + +@dataclass(frozen=True, kw_only=True) +class EGMSimPolicy: + """Per-regime refined continuous-action policy on the resources grid. + + Leading axes match the regime's combo layout (discrete states, then passive + states, then discrete actions, as in `EGMCarry`); the trailing axis is the + static refined-grid length. Both rows are NaN-padded in lockstep in the tail. + """ + + endog_grid: FloatND + """Endogenous grid in resources space, NaN-padded in the tail. + + Shared with the period's `EGMCarry.endog_grid`; weakly ascending per row, + with envelope-kink abscissae duplicated. + """ + + policy: FloatND + """Optimal continuous action at `endog_grid` (NaN on padding slots).""" + + +_EGM_SIM_POLICY_FIELDS = ("endog_grid", "policy") + + +def _flatten_egm_sim_policy(policy: EGMSimPolicy) -> tuple[tuple[Any, ...], None]: + return tuple(getattr(policy, name) for name in _EGM_SIM_POLICY_FIELDS), None + + +def _unflatten_egm_sim_policy(_aux: None, children: Sequence[Any]) -> EGMSimPolicy: + policy = object.__new__(EGMSimPolicy) + for name, child in zip(_EGM_SIM_POLICY_FIELDS, children, strict=True): + object.__setattr__(policy, name, child) + return policy + + +jax.tree_util.register_pytree_node( + EGMSimPolicy, _flatten_egm_sim_policy, _unflatten_egm_sim_policy +) diff --git a/src/_lcm/egm/regime_introspection.py b/src/_lcm/egm/regime_introspection.py new file mode 100644 index 000000000..7c9be7004 --- /dev/null +++ b/src/_lcm/egm/regime_introspection.py @@ -0,0 +1,249 @@ +"""Pure spec-introspection helpers for DC-EGM regimes and their carry targets. + +These read a regime's (or a carry target's) static specification β€” its +`VInterpolationInfo`, its `UserRegime`, its function set β€” and return the +names, grids, and composed functions the kernel build, the continuation +subsystem, and the kernel-scope checks all need. They hold no kernel state and +perform no numerics, so they form the dependency leaf the other `egm` step +modules import from. +""" + +from collections.abc import Callable +from typing import Any, cast + +from dags import concatenate_functions, get_annotations, with_signature +from dags.annotations import ensure_annotations_are_strings + +from _lcm.params.regime_template import create_regime_params_template +from _lcm.processes import _ContinuousStochasticProcess +from _lcm.regime_building.V import VInterpolationInfo +from _lcm.typing import ActionName, EconFunctionsMapping, FunctionName, StateName +from _lcm.utils.functools import get_union_of_args +from _lcm.variables import from_regime, get_grids +from lcm.phased import Phased +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM, NEGM +from lcm.typing import ScalarFloat, UserFunction + + +def _as_dcegm(user_regime: UserRegime) -> DCEGM | None: + """Return the DC-EGM config a carry target solves its inner Euler with. + + A `DCEGM` regime solves directly; a `NEGM` regime nests the same 1-D + DC-EGM consumption-savings solve, so its child read uses `solver.inner`. Any + other solver (e.g. a terminal grid-search regime) returns `None` β€” the + target's carry lives in M-space and is read with the identity map. + """ + solver = user_regime.solver + if isinstance(solver, DCEGM): + return solver + if isinstance(solver, NEGM): + return solver.inner + return None + + +def _get_discrete_state_names( + *, + v_interpolation_info: VInterpolationInfo, +) -> tuple[StateName, ...]: + """Discrete-state names of a regime in carry-axis (V state) order.""" + return tuple( + name + for name in v_interpolation_info.state_names + if name in v_interpolation_info.discrete_states + ) + + +def _get_passive_state_names( + *, + v_interpolation_info: VInterpolationInfo, + euler_state_name: StateName, +) -> tuple[StateName, ...]: + """Passive-state names of a regime in carry-axis (V continuous-state) order. + + Every continuous state other than the Euler state is passive β€” DC-EGM + validation enforces this for DC-EGM regimes, and terminal carry targets + are restricted to a single continuous state. + """ + return tuple( + name + for name in v_interpolation_info.continuous_states + if name != euler_state_name + ) + + +def _get_process_state_names( + *, + v_interpolation_info: VInterpolationInfo, +) -> tuple[StateName, ...]: + """Names of a regime's process states (node-valued discrete dimensions).""" + return tuple( + name + for name, grid in v_interpolation_info.discrete_states.items() + if isinstance(grid, _ContinuousStochasticProcess) + ) + + +def _get_child_state_name(*, user_regime: UserRegime) -> StateName: + """Name of a carry target's continuous (Euler) state. + + For a DC-EGM or NEGM target this is its configured (inner) Euler state; for a + terminal target it is its only state (uniqueness is checked by + `_find_unsupported_feature`). + """ + dcegm = _as_dcegm(user_regime) + if dcegm is not None: + return dcegm.continuous_state + return next(iter(user_regime.states)) + + +def _get_child_discrete_actions( + *, user_regime: UserRegime +) -> tuple[tuple[ActionName, ...], tuple[Any, ...]]: + """Discrete-action names and grid values of a carry target, in combo order. + + The order matches the target's own kernel combos (its state-action + space's discrete actions), so per-row bindings line up with the carry's + action axes. Terminal targets have no actions (guarded). + """ + variables = from_regime(user_regime) + grids = get_grids(user_regime) + names = tuple(variables.discrete_action_names) + return names, tuple(grids[name].to_jax() for name in names) + + +def _concatenate_regime_function( + *, + functions: EconFunctionsMapping, + target: FunctionName, +) -> UserFunction: + """Concatenate one regime-function target from the H-free DAG.""" + return concatenate_functions( + functions={name: func for name, func in functions.items() if name != "H"}, + targets=target, + enforce_signature=False, + set_annotations=True, + ) + + +def _get_child_resources_function( + *, user_regime: UserRegime +) -> Callable[..., ScalarFloat]: + """Build the closed-over resources map of one carry target. + + For a DC-EGM or NEGM target the map is its (inner) resources function + (resolved to the solve-phase variant); for a terminal target the carry lives + in M-space and the map is the identity. The returned callable takes the + child's state, passive, and discrete-action values as keyword arguments + (child names) so the kernel can compose it with the state transition and + differentiate the composition per carry row. + """ + if _as_dcegm(user_regime) is not None: + return _concatenate_child_resources(user_regime=user_regime) + + state_name = next(iter(user_regime.states)) + + def identity_resources(**kwargs: ScalarFloat) -> ScalarFloat: + return kwargs[state_name] + + return identity_resources + + +def _get_child_resources_arg_names(*, user_regime: UserRegime) -> set[str]: + """Argument names of a carry target's resources map.""" + if _as_dcegm(user_regime) is not None: + return set( + get_union_of_args([_concatenate_child_resources(user_regime=user_regime)]) + ) + return {next(iter(user_regime.states))} + + +def _concatenate_child_resources(*, user_regime: UserRegime) -> UserFunction: + """Concatenate a DC-EGM / NEGM target's resources function from its user DAG. + + Each user function's params are renamed to their qualified names + (`__`) before concatenation, matching the engine's binding + vocabulary so the kernel feeds them straight from the combo pool (which + carries the regime's flat params). Solve-phase imputed intermediates (a + `Phased` function or a carried state's solve law) are resolved to their + solve variant and baked into the DAG, so their outputs are computed from + leaf states and params rather than demanded as leaves. + + For a NEGM target the published continuation is the keeper's (the durable + stays put), so the inner resources' outer post-decision is replaced by the + durable identity `next_ = `. The child resources then read + `` (a bound passive state) rather than demanding the outer + post-decision as an unbound leaf. + """ + # Imported lazily: `regime_building.processing` imports the solver + # registry, which imports this module, so a top-level import would cycle. + from _lcm.regime_building import processing as _proc # noqa: PLC0415 + + dcegm = cast("DCEGM", _as_dcegm(user_regime)) + regime_params_template = create_regime_params_template(user_regime) + resolved: dict[str, UserFunction] = {} + for name, func in user_regime.functions.items(): + if isinstance(func, Phased): + resolved[name] = cast("UserFunction", func.solve) + elif func is not None: + resolved[name] = func + # A carried state contributes a solve-phase imputation function under its + # own name; include it so resources may read the imputed value. + for name, value in user_regime.states.items(): + if isinstance(value, Phased) and name not in resolved: + resolved[name] = cast("UserFunction", value.solve) + if isinstance(user_regime.solver, NEGM): + resolved[user_regime.solver.outer_post_decision] = _keeper_identity_function( + outer_post_decision=user_regime.solver.outer_post_decision, + functions=resolved, + ) + qnamed = { + name: _proc._rename_params_to_qnames( # noqa: SLF001 + func=func, + regime_params_template=regime_params_template, + param_key=name, + ) + for name, func in resolved.items() + } + return concatenate_functions( + functions=qnamed, + targets=dcegm.resources, + enforce_signature=False, + set_annotations=True, + ) + + +def _keeper_identity_function( + *, outer_post_decision: FunctionName, functions: dict[str, UserFunction] +) -> UserFunction: + """Build the keeper identity `next_(durable) = durable`. + + The injected function declares the durable state as its single argument and + copies its annotation off the first regime function that declares it, so the + DAG's annotation-consistency check (which requires every consumer of a leaf + to agree) stays satisfied. + """ + durable_state = outer_post_decision.removeprefix("next_") + annotation = _annotation_of_arg(functions=functions, arg_name=durable_state) + + @with_signature(args={durable_state: annotation}, return_annotation=annotation) + def keep_outer_post_decision(**kwargs: ScalarFloat) -> ScalarFloat: + return kwargs[durable_state] + + keep_outer_post_decision.__name__ = outer_post_decision + return cast("UserFunction", keep_outer_post_decision) + + +def _annotation_of_arg( + *, functions: dict[str, UserFunction], arg_name: StateName +) -> str: + """Return the annotation the regime's functions use for one argument. + + Falls back to `"FloatND"` when no function annotates it. + """ + for func in functions.values(): + annotations = ensure_annotations_are_strings(get_annotations(func)) + annotation = annotations.get(arg_name, "no_annotation_found") + if annotation != "no_annotation_found": + return annotation + return "FloatND" diff --git a/src/_lcm/egm/rfc_two_asset_step.py b/src/_lcm/egm/rfc_two_asset_step.py new file mode 100644 index 000000000..07813f4eb --- /dev/null +++ b/src/_lcm/egm/rfc_two_asset_step.py @@ -0,0 +1,260 @@ +"""One two-asset backward step that selects the upper envelope by the 2-D RFC. + +The Roof-top Cut alternative to the G2EGM mesh envelope (`two_asset_g2egm_step`). It +builds the same four KKT candidate clouds (`ucon`, `dcon`, `acon`, `con`) by the +closed-form inverse Euler step, then β€” instead of triangulating each segment and taking +within- and across-segment maxima β€” merges all four clouds into one and applies the +global rooftop-cut delete (`rfc_delete_mask_2d`) followed by a single local-simplex +barycentric publish (`rfc_publish_2d`) at the regular `(m, n)` targets. This is the +Dobrescu-Shanker 2024 multidimensional method (their Box 1): a combined-cloud +delete-then-interpolate-once, with no per-segment republication. + +Infeasible cloud points (NaN/inf value, state, or supgradient at a KKT corner that does +not bind) are marked invalid: their states are pushed to a far sentinel and value to +`-inf` so they neither dominate nor are published, and the validity mask is passed to +both the cut and the publisher. +""" + +import jax.numpy as jnp + +from _lcm.egm.two_asset_g2egm_step import G2EGMResult +from _lcm.egm.two_asset_inverse import ( + RegionCloud, + invert_acon_cloud, + invert_con_cloud, + invert_dcon_cloud, + invert_ucon_cloud, +) +from _lcm.egm.two_asset_post_decision import post_decision_value_and_grad +from _lcm.egm.upper_envelope.rfc_2d import ( + J_BAR_DEFAULT, + K_PUBLISH_DEFAULT, + RADIUS_DEFAULT, + rfc_delete_mask_2d, + rfc_publish_2d, +) +from lcm.typing import Float1D, FloatND, ScalarFloat + +_FAR_SENTINEL = 1e9 + + +def rfc_two_asset_step( + *, + next_value: FloatND, + m_grid: Float1D, + n_grid: Float1D, + a_grid: Float1D, + b_grid: Float1D, + consumption_grid: Float1D, + discount_factor: ScalarFloat | float, + crra: ScalarFloat | float, + match_rate: ScalarFloat | float, + return_liquid: ScalarFloat | float, + return_pension: ScalarFloat | float, + wage: ScalarFloat | float, + j_bar: float = J_BAR_DEFAULT, + radius: float = RADIUS_DEFAULT, + k_cut: int = 5, + k_publish: int = K_PUBLISH_DEFAULT, +) -> G2EGMResult: + """Solve one two-asset period by the combined-cloud 2-D RFC upper envelope. + + Args: + next_value: Next period's value on the regular `(m, n)` grid. + m_grid: Regular liquid-state grid (ascending, evenly spaced). + n_grid: Regular pension-state grid (ascending, evenly spaced). + a_grid: Liquid post-decision grid for `ucon`/`dcon` (should include 0). + b_grid: Pension post-decision grid (shared by all segments). + consumption_grid: Consumption sweep for `acon`/`con` at `a = 0`. + discount_factor: Discount factor `beta`. + crra: Coefficient of relative risk aversion `rho`. + match_rate: Pension employer-match coefficient `chi`. + return_liquid: Liquid net return `r^a`. + return_pension: Pension net return `r^b`. + wage: Deterministic labor income. + j_bar: RFC policy-jump threshold. + radius: RFC neighbour distance threshold. + k_cut: RFC neighbours (including self) the delete inspects. + k_publish: Nearest survivors forming the publish local-simplex set. + + Returns: + This period's upper-envelope value and policy on the regular `(m, n)` grid. + """ + clouds = _build_region_clouds( + next_value=next_value, + m_grid=m_grid, + n_grid=n_grid, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + return_liquid=return_liquid, + return_pension=return_pension, + wage=wage, + ) + + states = jnp.concatenate( + [ + jnp.stack([c.m_endog.reshape(-1), c.n_endog.reshape(-1)], axis=1) + for c in clouds + ] + ) + values = jnp.concatenate([c.value.reshape(-1) for c in clouds]) + supgradients = jnp.concatenate( + [ + jnp.stack([c.value_grad_m.reshape(-1), c.value_grad_n.reshape(-1)], axis=1) + for c in clouds + ] + ) + policies = jnp.concatenate( + [ + jnp.stack([c.consumption.reshape(-1), c.deposit.reshape(-1)], axis=1) + for c in clouds + ] + ) + + # Each region cloud carries a `valid_region` KKT mask: the complementary- + # slackness test its inverse assumes, false at finite-but-KKT-inconsistent + # candidates (a region's FOCs solved where its inequalities do not hold). These + # are dropped here so only genuine KKT candidates enter the cut and publish. + # Dropping them thins the valid survivors at coarse grids, so the publisher + # selects the *smallest* containing simplex (`rfc_publish_2d`) to keep the + # affine fit local across the holes the mask opens. + region_valid = jnp.concatenate([c.valid_region.reshape(-1) for c in clouds]) + valid = ( + jnp.isfinite(values) + & jnp.all(jnp.isfinite(states), axis=1) + & jnp.all(jnp.isfinite(supgradients), axis=1) + & jnp.all(jnp.isfinite(policies), axis=1) + & region_valid + ) + # Sanitize invalid candidates so they neither dominate (value -inf, gradient 0) nor + # sit near any target (state at a far sentinel); the validity mask keeps them out of + # both the cut and the publish. + safe_states = jnp.where(valid[:, None], states, _FAR_SENTINEL) + safe_values = jnp.where(valid, values, -jnp.inf) + safe_supgradients = jnp.where(valid[:, None], supgradients, 0.0) + safe_policies = jnp.where(valid[:, None], policies, 0.0) + + # The reference cut constants (radius, J_bar) assume O(1) state and policy scales, + # so normalize the cut to unit grid ranges: states by the state range, supgradients + # by the state range (chain rule, which leaves the below-tangent test scale- + # invariant), and the consumption selector by its range, so radius and the jump + # ratio are meaningful on the pension state space. The publish stays in original + # units (its barycentric local-simplex is affine-invariant). + state_scale = jnp.array([m_grid[-1] - m_grid[0], n_grid[-1] - n_grid[0]]) + policy_scale = jnp.array([consumption_grid[-1] - consumption_grid[0], 1.0]) + keep = rfc_delete_mask_2d( + states=safe_states / state_scale, + supgradients=safe_supgradients * state_scale, + values=safe_values, + policies=safe_policies / policy_scale, + j_bar=j_bar, + radius=radius, + k=k_cut, + ) + survives = keep & valid + + m_mesh, n_mesh = jnp.meshgrid(m_grid, n_grid, indexing="ij") + targets = jnp.stack([m_mesh.reshape(-1), n_mesh.reshape(-1)], axis=1) + published_value, published_policy = rfc_publish_2d( + survivor_states=safe_states, + survivor_values=safe_values, + survivor_policies=safe_policies, + target_states=targets, + valid=survives, + k=k_publish, + ) + + return G2EGMResult( + value=published_value.reshape(m_mesh.shape), + consumption=published_policy[:, 0].reshape(m_mesh.shape), + deposit=published_policy[:, 1].reshape(m_mesh.shape), + ) + + +def _build_region_clouds( + *, + next_value: FloatND, + m_grid: Float1D, + n_grid: Float1D, + a_grid: Float1D, + b_grid: Float1D, + consumption_grid: Float1D, + discount_factor: ScalarFloat | float, + crra: ScalarFloat | float, + match_rate: ScalarFloat | float, + return_liquid: ScalarFloat | float, + return_pension: ScalarFloat | float, + wage: ScalarFloat | float, +) -> tuple[RegionCloud, RegionCloud, RegionCloud, RegionCloud]: + """Build the four KKT candidate clouds, identical to the G2EGM step's clouds.""" + a_mesh, b_mesh = jnp.meshgrid(a_grid, b_grid, indexing="ij") + post = post_decision_value_and_grad( + next_value=next_value, + m_grid=m_grid, + n_grid=n_grid, + a=a_mesh, + b=b_mesh, + return_liquid=return_liquid, + return_pension=return_pension, + wage=wage, + ) + ucon = invert_ucon_cloud( + a=a_mesh, + b=b_mesh, + w_a=post.grad_a, + w_b=post.grad_b, + post_decision_value=post.value, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + ) + dcon = invert_dcon_cloud( + a=a_mesh, + b=b_mesh, + w_a=post.grad_a, + w_b=post.grad_b, + post_decision_value=post.value, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + ) + a_zero = jnp.zeros_like(b_grid) + post_zero = post_decision_value_and_grad( + next_value=next_value, + m_grid=m_grid, + n_grid=n_grid, + a=a_zero, + b=b_grid, + return_liquid=return_liquid, + return_pension=return_pension, + wage=wage, + ) + c_mesh, cb_mesh = jnp.meshgrid(consumption_grid, b_grid, indexing="ij") + value_at_zero = jnp.broadcast_to(post_zero.value[None, :], c_mesh.shape) + grad_b_at_zero = jnp.broadcast_to(post_zero.grad_b[None, :], c_mesh.shape) + grad_a_at_zero = jnp.broadcast_to(post_zero.grad_a[None, :], c_mesh.shape) + acon = invert_acon_cloud( + consumption=c_mesh, + b=cb_mesh, + post_decision_value_at_zero_a=value_at_zero, + w_b_at_zero_a=grad_b_at_zero, + w_a_at_zero_a=grad_a_at_zero, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + ) + con = invert_con_cloud( + consumption=c_mesh, + b=cb_mesh, + post_decision_value_at_zero_a=value_at_zero, + w_b_at_zero_a=grad_b_at_zero, + w_a_at_zero_a=grad_a_at_zero, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + ) + return ucon, dcon, acon, con diff --git a/src/_lcm/egm/step.py b/src/_lcm/egm/step.py new file mode 100644 index 000000000..b3a27bf3d --- /dev/null +++ b/src/_lcm/egm/step.py @@ -0,0 +1,838 @@ +"""The per-(period, regime) DC-EGM solve kernel. + +`build_egm_step_functions` turns a regime's processed functions, transitions, +and `DCEGM` solver configuration into per-period kernels that replace the +brute-force `max_Q_over_a` during backward induction. Each kernel runs the +DC-EGM step per combination of the regime's discrete states, passive +continuous states (deterministic non-process states whose transitions are +independent of the decision, e.g. an AIME-like skill level β€” one node per +combo), and discrete actions, with the exogenous savings grid as the inner +axis: + +1. compute child states at every savings node (the post-decision function is + removed from the DAG so the savings node enters as an external input), +2. map the child state into the child's resources space, select the carry + rows matching the child's discrete-state values, and interpolate the + child's value and marginal utility there per child discrete-action combo. + The child's resources space is *per combo*: when the child's resources + function reads its discrete states, passive states, or discrete actions, + each carry row is queried at its own $R'$ and carries its own composed + gradient $\\partial R'/\\partial A$ of the map + $A \\mapsto R'(\\mathcal{T}(A), z', d', p')$ β€” the non-Euler inputs are + savings-independent (validated) and ride as constants through the + gradient. When the resources function reads only the child's Euler state, + a single query and gradient is computed and broadcast across the rows. + The child's passive values land off-grid, so the read is *mixed*: linear + weights on the two neighboring nodes of the child's passive grid + (edge-clamped), each neighbor's row interpolated 1-D in its own node's + resources space, then blended per discrete-action row β€” before the choice + aggregation, so the logsum sees blended choice-specific values, +3. aggregate over the child's discrete-action rows with the child's EV1 + taste-shock scale: the smoothed value is the logsum and the smoothed + marginal is the choice-probability-weighted marginal + $\\sum_{d'} P_{d'} \\mu_{d'} (\\partial R'/\\partial A)_{d'}$ β€” the + composed factor sits inside the aggregation because each choice's + envelope lives in its own resources space (exact for EV1 by Danskin's + theorem; scale zero degrades to the hard max / one-hot argmax), +4. take the stochastic-node and regime-transition expectations: a child + stochastic state's node β€” a continuous AR(1) process state or a + Markov-discrete state β€” is distributed per its intrinsic transition weights + $w(\\text{node}' \\mid \\text{node}, \\text{params})$, so steps 2-3 run + per child node combo and the results are weight-summed β€” the stochastic + expectation sits *outside* the action aggregation (the shock realizes + before the next period's choice), matching the brute-force solver's + weighted average of the already action-aggregated next-period V β€” and the + per-target results are regime-transition-probability weighted, +5. invert the Euler equation per savings node (with the degenerate-inversion + guard) to obtain the optimal action and the endogenous resources grid, +6. add the closed-form credit-constrained segment as additional candidates, +7. refine the candidate correspondence through the configured upper-envelope + backend (one envelope per discrete combo), +8. publish the value function on the regime's exogenous state grid β€” + discrete-state and passive-state combos remain axes of the value-function + array (the Euler axis is moved to its canonical position among the + continuous states), the regime's own discrete-action combos are + aggregated with the regime's own taste-shock scale β€” and assemble the + per-combo carry rows for the regime's parents. The publish step never + evaluates anything at off-grid passive values: each combo's rows are + interpolated in resources only, on the regime's own grid axes. + +When any savings-stage function reads the current Euler state β€” the Euler +state's own law (an additive residual like a means-tested capital-income +supplement), the regime-transition probabilities, a stochastic transition +weight, or a passive state's law β€” the kernel solves *per exogenous asset +node* instead: conditional on one node of the Euler grid every such read is +a per-combo constant, so the single-post-state pipeline above is exact +within the node's row, and the row publishes only its own node. This is +brute-force-equivalent by construction β€” the brute solver evaluates the +same decision-time functions at the same exogenous nodes. The per-combo +carry then holds the per-node published points (one row per combo, no asset +axis): abscissa the node resources, policy the published optimal action, +value the published V, and marginal +$dV/dR = u'(c^*) + \\beta\\, (\\partial W/\\partial a)\\big|_{A^*} / R'(a)$ +β€” the envelope term $u'(c^*)$ plus the savings-stage functions' direct +Euler-state channels through the continuation $W$, divided by the resources +slope. The Euler-state channel is differentiated through the *whole* +continuation closure: regime-transition probabilities and transition +weights are evaluated inside it, so first-order terms like +$\\sum_{targets} \\partial P/\\partial a \\cdot EV_{target}$ survive β€” the +probabilities are not the softmax of the values they weight, so Danskin +does not cancel them, and hoisting them out of the differentiated closure +would silently drop them. The mode requires every savings-stage Euler-state +read to be *continuous* in the Euler state at the resolution of the Euler +grid (kinks are fine): a residual that jumps makes the child's value +function discontinuous, the true policy bunches next-period wealth exactly +at the discontinuity β€” an Euler-equation-free corner outside EGM's +candidate families (interior Euler inversions plus the closed-form +credit-constrained segment) β€” and a jump in the probabilities or weights +breaks the smoothness-at-node-resolution assumption the per-node solve +relies on, so such functions are rejected at build time rather than solved +approximately. The switch is a build-time Python branch; the default path +is untouched and costs nothing when the mode is unused. + +The canonical combo-axis order β€” single-sourced through +`_EgmKernelPieces.combo_names` and the carry template's leading shape β€” is +discrete states (V state order, process states included as node-valued +discrete dimensions), then passive states (V continuous-state order), then +discrete actions (action-grid order), then the carry's grid axis. Discrete +states lead so the child carry can be selected by integer indexing; passive +axes follow so the mixed read blends them away next, leaving exactly the +discrete-action rows the choice aggregation consumes. + +Discrete-only constraints mask infeasible discrete combos: their value rows +are $-\\infty$ and their marginal-utility rows are exactly zero, so they +carry zero choice probability and stay finite inside the parent's +probability-weighted expectation. + +A terminal carry target may carry discrete states, but only those shared +with the parent's own discrete combo axes and reached by the identity +(fixed) transition β€” at a parent combo with the state at value $k$ the +terminal carry row is its utility evaluated at $k$, selected by the parent's +own integer combo index, exactly as the non-terminal child read selects its +combo. A fixed `pref_type` whose terminal bequest differs by type is the +motivating case. + +A child Markov-discrete state β€” one whose `next_` is a stochastic +transition into the target β€” is integrated exactly like a process state: its +node axis is the *child's* discrete grid (codes $0, 1, \\dots$, which also +index the carry's leading axis), distributed per the intrinsic weights +$w(\\text{node}' \\mid \\text{node}, \\text{params})$, summed outside the +action aggregation. The child grid need not match the source's: a 3-state +health remapped onto a 2-state target carries a length-2 weight vector, and +the integration ranges over the child axis. + +Out of scope: +terminal carry targets with actions, with a discrete state the parent does +not carry, or with a non-identity transition into a shared discrete state, +child resources functions reading anything beyond the child's states and +discrete actions (e.g. free child params), and child process states whose +grid points are supplied at runtime while feeding the child's resources +function. Such configurations build kernels that raise `NotImplementedError` +at solve time, so `Model` construction always succeeds for a validated +DC-EGM regime. +""" + +import math +from collections.abc import Callable, Mapping +from types import MappingProxyType +from typing import Any, cast + +import jax +import jax.numpy as jnp +from dags import concatenate_functions, with_signature + +from _lcm.dtypes import canonical_float_dtype +from _lcm.egm.asset_row import _get_solve_one_combo_asset_rows +from _lcm.egm.carry import EGMCarry, build_template_egm_carry +from _lcm.egm.continuation import ( + ContinuationPlan, + _build_child_reads, + _is_runtime_process, + get_egm_continuation_targets, +) +from _lcm.egm.kernel_scope import _find_unsupported_feature +from _lcm.egm.published_policy import EGMSimPolicy +from _lcm.egm.regime_introspection import ( + _concatenate_regime_function, + _get_discrete_state_names, + _get_passive_state_names, + _get_process_state_names, +) +from _lcm.egm.step_core import ( + CONSTRAINED_OFFSET_FRACTION, + _EgmKernelPieces, + _get_solve_one_combo, +) +from _lcm.egm.upper_envelope import get_bracket_finder, get_upper_envelope +from _lcm.egm.validation import _reachable_target_names, savings_stage_reads_euler_state +from _lcm.engine import StateActionSpace +from _lcm.grids import ContinuousGrid, Grid +from _lcm.logsum import logsum_and_softmax +from _lcm.regime_building.h_dag import _get_build_H_kwargs +from _lcm.regime_building.max_Q_over_a import TASTE_SHOCK_SCALE_PARAM +from _lcm.regime_building.V import VInterpolationInfo +from _lcm.typing import ( + ActionName, + ConstraintFunctionsMapping, + EconFunctionsMapping, + EGMStepFunction, + RegimeName, + RegimeTransitionFunction, + StateName, + StateOrActionName, + TransitionFunctionName, + TransitionFunctionsMapping, +) +from _lcm.utils.dispatchers import productmap +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.typing import ( + Float1D, + FloatND, + IntND, + ScalarBool, + ScalarFloat, + ScalarInt, +) + + +def build_egm_step_functions( + *, + solver: DCEGM, + regime_name: RegimeName, + user_regimes: Mapping[RegimeName, UserRegime], + functions: EconFunctionsMapping, + constraints: ConstraintFunctionsMapping, + transitions: TransitionFunctionsMapping, + stochastic_transition_names: frozenset[TransitionFunctionName], + compute_regime_transition_probs: RegimeTransitionFunction, + regime_to_v_interpolation_info: MappingProxyType[RegimeName, VInterpolationInfo], + regimes_to_active_periods: MappingProxyType[RegimeName, tuple[int, ...]], + flat_param_names: frozenset[str], + regime_to_flat_param_names: MappingProxyType[RegimeName, frozenset[str]], + state_action_space: StateActionSpace, + has_taste_shocks: bool, +) -> tuple[MappingProxyType[int, EGMStepFunction], EGMCarry, frozenset[RegimeName]]: + """Build per-period DC-EGM kernels and the regime's carry template. + + Periods sharing the same continuation-target configuration share one + kernel (and hence one compiled program), mirroring the per-period + grouping of the Q-and-F builders. + + Args: + solver: The regime's DC-EGM solver configuration. + regime_name: Name of the regime the kernels solve. + user_regimes: Mapping of regime names to user-provided `Regime` + instances (the carry targets' resources functions are read from + here). + functions: The regime's processed functions (params renamed to + qualified names). + constraints: Immutable mapping of the regime's constraint names to + constraint functions (discrete-only after DC-EGM validation). + transitions: Immutable mapping of target regime names to their state + transition functions. + stochastic_transition_names: Frozenset of stochastic transition + function names. + compute_regime_transition_probs: Regime transition probability + function for solve. + regime_to_v_interpolation_info: Mapping of regime names to + V-interpolation info. + regimes_to_active_periods: Immutable mapping of regime names to their + active period tuples. + flat_param_names: Frozenset of flat parameter names for the regime. + regime_to_flat_param_names: Immutable mapping of every regime name to + its flat parameter names. A carry target's resources / transition + functions read the target regime's params, so the validator admits + and the kernel binds the union of the source and its reachable + carry targets' params. + state_action_space: The regime's state-action space (source of the + discrete-action grids and their canonical order). + has_taste_shocks: Whether the regime declares EV1 taste shocks on its + discrete actions. + + Returns: + Tuple of the per-period kernel mapping, the regime's all-finite carry + template (leading axes: discrete states, then passive states, then + discrete actions), and the regime's reachable-target names β€” the only + carry keys any of its kernels read, used to filter the rolling carry + mapping the solve loop hands each kernel. + + """ + n_pad = compute_egm_carry_length(solver=solver) + # `batch_size` on the Euler-state grid splays the per-asset-node solve into + # blocks (`lax.map`) to shed peak working-set memory; 0 keeps the fused + # vmap. Only the asset-row kernel has a per-node axis to splay. + euler_grid = cast( + "ContinuousGrid", user_regimes[regime_name].states[solver.continuous_state] + ) + euler_batch_size = euler_grid.batch_size + # `batch_size` on the exogenous savings grid splays the inner per-savings-node + # continuation computation into `lax.map` blocks, shedding the dominant + # egm_step working buffer (savings x child-stochastic mesh x combos); 0 keeps + # the fused vmap. The upper envelope still runs on the gathered full grid. + savings_batch_size = solver.savings_grid.batch_size + own_v_info = regime_to_v_interpolation_info[regime_name] + # Any savings-stage Euler-state read (the Euler law's residual, regime + # transition probabilities, stochastic transition weights, non-Euler + # laws) switches the kernel to the per-exogenous-asset-node solve; the + # single-post-state kernel has no defined Euler value at the savings + # stage, so dispatching it would be silently wrong. + asset_row_mode = savings_stage_reads_euler_state( + user_regime=user_regimes[regime_name], solver=solver + ) + # The persisted carry length is split from the envelope-workspace length + # `n_pad`: in asset-row mode the stored row holds one published point per + # exogenous Euler node and the dense workspace is transient (FUES/RFC runs + # per node and publishes a single point), so the carry needs only + # `n_euler_nodes` rows. The padding to `n_pad` it would otherwise carry is + # pure dead storage (`interp_on_padded_grid` masks the NaN tail). In the + # single-post-state kernel the carry *is* the refined envelope, so its + # length stays `n_pad`. + n_carry_rows = n_pad + if asset_row_mode: + n_euler_nodes = int( + own_v_info.continuous_states[solver.continuous_state].to_jax().shape[0] + ) + n_pad = max(n_pad, n_euler_nodes) + n_carry_rows = n_euler_nodes + own_discrete_state_names = _get_discrete_state_names( + v_interpolation_info=own_v_info + ) + own_passive_state_names = _get_passive_state_names( + v_interpolation_info=own_v_info, + euler_state_name=solver.continuous_state, + ) + own_discrete_action_values = MappingProxyType( + dict(state_action_space.discrete_actions) + ) + # Process states whose distribution params arrive at runtime have their + # grids resolved per solve; thread those resolved grids into the + # continuation so a process-reading resources function integrates over the + # solve-time nodes rather than the build-time NaN placeholder. + own_runtime_process_names = tuple( + name + for name in _get_process_state_names(v_interpolation_info=own_v_info) + if _is_runtime_process(own_v_info.discrete_states[name]) + ) + # `batch_size` on a discrete-state, process, or passive-state grid splays + # that combo axis (per-axis `productmap` blocks) to shed memory; 0 keeps + # the fused vmap. Discrete-action axes are never split (the discrete-action + # logsum needs every action value at once), so they map to 0. + combo_state_batch_sizes = MappingProxyType( + { + name: cast("Grid", user_regimes[regime_name].states[name]).batch_size + for name in own_discrete_state_names + own_passive_state_names + } + ) + # Canonical position of the Euler axis in the published V array: after + # the discrete-state axes, at its slot within the continuous-state order. + euler_axis_in_V = len(own_discrete_state_names) + tuple( + own_v_info.continuous_states + ).index(solver.continuous_state) + leading_shape = ( + tuple( + int(own_v_info.discrete_states[name].to_jax().shape[0]) + for name in own_discrete_state_names + ) + + tuple( + int(own_v_info.continuous_states[name].to_jax().shape[0]) + for name in own_passive_state_names + ) + + tuple(int(v.shape[0]) for v in own_discrete_action_values.values()) + ) + carry_template = build_template_egm_carry( + n_rows=n_carry_rows, leading_shape=leading_shape + ) + + reachable_targets = frozenset( + _reachable_target_names( + user_regime=user_regimes[regime_name], user_regimes=user_regimes + ) + ) + configs: dict[tuple[tuple[RegimeName, ...], tuple[RegimeName, ...]], list[int]] = {} + for period in regimes_to_active_periods[regime_name]: + target_split = get_egm_continuation_targets( + period=period, + transitions=transitions, + reachable_targets=reachable_targets, + regimes_to_active_periods=regimes_to_active_periods, + regime_to_v_interpolation_info=regime_to_v_interpolation_info, + ) + configs.setdefault(target_split, []).append(period) + + built: dict[ + tuple[tuple[RegimeName, ...], tuple[RegimeName, ...]], EGMStepFunction + ] = {} + for carry_targets, scalar_targets in configs: + unsupported = _find_unsupported_feature( + solver=solver, + regime_name=regime_name, + user_regimes=user_regimes, + functions=functions, + constraints=constraints, + carry_targets=carry_targets, + transitions=transitions, + stochastic_transition_names=stochastic_transition_names, + compute_regime_transition_probs=compute_regime_transition_probs, + regime_to_v_interpolation_info=regime_to_v_interpolation_info, + flat_param_names=flat_param_names, + regime_to_flat_param_names=regime_to_flat_param_names, + own_discrete_state_names=own_discrete_state_names, + own_passive_state_names=own_passive_state_names, + own_discrete_action_names=tuple(own_discrete_action_values), + asset_row_mode=asset_row_mode, + ) + if unsupported is not None: + kernel = _get_raising_egm_step(reason=unsupported) + else: + kernel = _get_egm_step( + solver=solver, + user_regimes=user_regimes, + functions=functions, + constraints=constraints, + transitions=transitions, + stochastic_transition_names=stochastic_transition_names, + compute_regime_transition_probs=compute_regime_transition_probs, + carry_targets=carry_targets, + scalar_targets=scalar_targets, + n_pad=n_pad, + n_carry_rows=n_carry_rows, + own_discrete_state_names=own_discrete_state_names, + own_passive_state_names=own_passive_state_names, + own_discrete_action_values=own_discrete_action_values, + own_runtime_process_names=own_runtime_process_names, + euler_axis_in_V=euler_axis_in_V, + has_taste_shocks=has_taste_shocks, + regime_to_v_interpolation_info=regime_to_v_interpolation_info, + asset_row_mode=asset_row_mode, + euler_batch_size=euler_batch_size, + savings_batch_size=savings_batch_size, + combo_state_batch_sizes=combo_state_batch_sizes, + ) + built[(carry_targets, scalar_targets)] = kernel + + result: dict[int, EGMStepFunction] = {} + for target_split, periods in configs.items(): + for period in periods: + result[period] = built[target_split] + + return ( + MappingProxyType(dict(sorted(result.items()))), + carry_template, + reachable_targets, + ) + + +def compute_egm_carry_length(*, solver: DCEGM) -> int: + """Static carry-row length for a DC-EGM regime. + + Covers the Euler candidates (one per savings node), the closed-form + constrained candidates, and the headroom factor for envelope-kink + insertions (each costs two slots). + + Args: + solver: The regime's DC-EGM solver configuration. + + Returns: + Number of slots in the regime's carry rows. + + """ + n_savings = int(solver.savings_grid.to_jax().shape[0]) + n_candidates = n_savings + solver.n_constrained_points + return math.ceil(solver.refined_grid_factor * n_candidates) + + +def _get_egm_step( + *, + solver: DCEGM, + user_regimes: Mapping[RegimeName, UserRegime], + functions: EconFunctionsMapping, + constraints: ConstraintFunctionsMapping, + transitions: TransitionFunctionsMapping, + stochastic_transition_names: frozenset[TransitionFunctionName], + compute_regime_transition_probs: RegimeTransitionFunction, + carry_targets: tuple[RegimeName, ...], + scalar_targets: tuple[RegimeName, ...], + n_pad: int, + n_carry_rows: int, + own_discrete_state_names: tuple[StateName, ...], + own_passive_state_names: tuple[StateName, ...], + own_discrete_action_values: MappingProxyType[ActionName, Any], + own_runtime_process_names: tuple[StateName, ...], + euler_axis_in_V: int, + has_taste_shocks: bool, + regime_to_v_interpolation_info: MappingProxyType[RegimeName, VInterpolationInfo], + asset_row_mode: bool, + euler_batch_size: int, + savings_batch_size: int, + combo_state_batch_sizes: MappingProxyType[StateName, int], +) -> EGMStepFunction: + """Build the EGM kernel for one continuation-target configuration. + + `asset_row_mode` selects the per-combo computation at build time: the + per-exogenous-asset-node solve when any savings-stage function reads the + current Euler state, the single-post-state default otherwise. + + `euler_batch_size` (the Euler grid's `batch_size`) splays the asset-row + per-node solve into `lax.map` blocks to shed peak memory; it has no effect + in the single-post-state (non-asset-row) kernel, which has no per-node axis. + """ + get_solve_one_combo = ( + _get_solve_one_combo_asset_rows if asset_row_mode else _get_solve_one_combo + ) + pieces = _build_kernel_pieces( + solver=solver, + user_regimes=user_regimes, + functions=functions, + constraints=constraints, + transitions=transitions, + stochastic_transition_names=stochastic_transition_names, + compute_regime_transition_probs=compute_regime_transition_probs, + carry_targets=carry_targets, + scalar_targets=scalar_targets, + n_pad=n_pad, + n_carry_rows=n_carry_rows, + own_discrete_state_names=own_discrete_state_names, + own_passive_state_names=own_passive_state_names, + own_discrete_action_values=own_discrete_action_values, + euler_axis_in_V=euler_axis_in_V, + regime_to_v_interpolation_info=regime_to_v_interpolation_info, + ) + + def egm_step( + next_regime_to_V_arr: MappingProxyType[RegimeName, FloatND], # noqa: ARG001 + next_regime_to_egm_carry: MappingProxyType[RegimeName, EGMCarry], + **kwargs: Any, # noqa: ANN401 + ) -> tuple[FloatND, EGMCarry, EGMSimPolicy]: + """Run the DC-EGM step and publish V on the exogenous grid. + + Args: + next_regime_to_V_arr: The next period's value-function arrays; + accepted so solve treats all kernels uniformly (continuation + values come from the carries). + next_regime_to_egm_carry: The next period's EGM carries. + **kwargs: The regime's state grids, flat params, `period`, and + `age`. + + Returns: + Tuple of the value-function array on the exogenous state grid + (discrete-state axes leading, continuous states in canonical + order) and the regime's carry (one row per discrete-state x + passive-node x discrete-action combo). + + """ + dtype = canonical_float_dtype() + own_state_names = { + pieces.euler_state_name, + *own_discrete_state_names, + *own_passive_state_names, + } + pool = {k: v for k, v in kwargs.items() if k not in own_state_names} + state_grid = jnp.asarray(kwargs[pieces.euler_state_name], dtype=dtype) + own_taste_shock_scale = ( + jnp.asarray(kwargs[TASTE_SHOCK_SCALE_PARAM], dtype=dtype) + if has_taste_shocks + else jnp.asarray(0.0, dtype=dtype) + ) + resolved_process_grids = MappingProxyType( + { + name: jnp.asarray(kwargs[name], dtype=dtype) + for name in own_runtime_process_names + } + ) + solve_one_combo = get_solve_one_combo( + pieces=pieces, + pool=pool, + state_grid=state_grid, + next_regime_to_egm_carry=next_regime_to_egm_carry, + euler_batch_size=euler_batch_size, + savings_batch_size=savings_batch_size, + resolved_process_grids=resolved_process_grids, + ) + + if pieces.combo_names: + combo_var_names = ( + own_discrete_state_names + + own_passive_state_names + + tuple(own_discrete_action_values) + ) + + @with_signature(args=list(combo_var_names)) + def solve_one_combo_over_axes( + **combo_values: ScalarFloat | ScalarInt, + ) -> tuple[Float1D, Float1D, Float1D, Float1D, Float1D]: + return solve_one_combo( + tuple(combo_values[name] for name in combo_var_names) + ) + + # Map the per-combo solve over the Cartesian product of the combo + # axes: a discrete state / process / passive grid's `batch_size` + # splays its axis (shedding memory), actions stay fused (the + # discrete-action logsum needs every value at once). Splayed axes + # share one `lax.map` (one scan carry) rather than nesting one per + # axis. Outputs come back with the combo axes in `combo_var_names` + # order, preserving whole discrete axes for the carry. + combo_axis_values = { + **{ + name: jnp.asarray(kwargs[name]) + for name in own_discrete_state_names + own_passive_state_names + }, + **{ + name: jnp.asarray(values) + for name, values in own_discrete_action_values.items() + }, + } + V_stack, grid_stack, policy_stack, value_stack, marginal_stack = ( + _map_combo_product( + func=solve_one_combo_over_axes, + combo_var_names=combo_var_names, + combo_axis_values=combo_axis_values, + batch_sizes={ + **dict(combo_state_batch_sizes), + **dict.fromkeys(own_discrete_action_values, 0), + }, + ) + ) + n_state_axes = len(own_discrete_state_names) + len(own_passive_state_names) + action_axes = tuple(range(n_state_axes, len(combo_var_names))) + if action_axes and has_taste_shocks: + V_arr, _ = logsum_and_softmax( + values=V_stack, scale=own_taste_shock_scale, axes=action_axes + ) + elif action_axes: + # Without taste shocks the smoothed maximum is the hard maximum + # over the discrete-action axes (the logsum is for `scale > 0`). + V_arr = jnp.max(V_stack, axis=action_axes) + else: + V_arr = V_stack + # The combo layout puts the Euler axis last; the canonical V + # layout interleaves it with the passive axes in V state order. + V_arr = jnp.moveaxis(V_arr, -1, pieces.euler_axis_in_V) + carry = EGMCarry( + endog_grid=grid_stack, + value=value_stack, + marginal_utility=marginal_stack, + taste_shock_scale=own_taste_shock_scale, + ) + sim_policy = EGMSimPolicy(endog_grid=grid_stack, policy=policy_stack) + else: + V_arr, grid_row, policy_row, value_row, marginal_row = solve_one_combo(()) + carry = EGMCarry( + endog_grid=grid_row, + value=value_row, + marginal_utility=marginal_row, + taste_shock_scale=own_taste_shock_scale, + ) + sim_policy = EGMSimPolicy(endog_grid=grid_row, policy=policy_row) + return V_arr, carry, sim_policy + + return egm_step + + +def _map_combo_product( + *, + func: Callable[..., tuple[Float1D, ...]], + combo_var_names: tuple[StateOrActionName, ...], + combo_axis_values: dict[StateOrActionName, FloatND | IntND], + batch_sizes: dict[StateOrActionName, int], +) -> tuple[FloatND, ...]: + """Map the per-combo solve over the Cartesian product of the combo axes. + + `func` has a `combo_var_names` keyword signature and returns one tuple of + 1-D arrays per combo. Each combo axis with `batch_size == 0` is vmapped; + axes with `batch_size > 0` are splayed (run in `lax.map` blocks) to shed + peak memory. Returns the stacked outputs with the combo axes as leading + dims in `combo_var_names` order (the canonical carry layout). + + With ≀1 splayed axis this is plain `productmap` (one `lax.map`, no + nesting). With β‰₯2 splayed axes, `productmap` would nest one `lax.map` + per axis and stack a scan carry per level; instead the splayed axes are + flattened into a *single* `lax.map` (one carry) with the unsplayed axes + vmapped within each step, then the result is transposed back into + `combo_var_names` order. Numerically identical to the nested form β€” only + the schedule (and its peak resident) differs. + """ + splayed = tuple(name for name in combo_var_names if batch_sizes[name] > 0) + vmapped = tuple(name for name in combo_var_names if batch_sizes[name] == 0) + + if len(splayed) <= 1: + mapped = productmap( + func=func, # ty: ignore[invalid-argument-type] + variables=combo_var_names, + batch_sizes=batch_sizes, + ) + return mapped(**combo_axis_values) + + # One `lax.map` over the flattened splayed product, unsplayed axes vmapped + # within each step (all-`batch_size=0` `productmap` lowers to nested vmaps, + # no scan carry). + inner = productmap( + func=func, # ty: ignore[invalid-argument-type] + variables=vmapped, + batch_sizes=dict.fromkeys(vmapped, 0), + ) + vmapped_values = {name: combo_axis_values[name] for name in vmapped} + splayed_dims = tuple(int(combo_axis_values[name].shape[0]) for name in splayed) + mesh = jnp.meshgrid(*(combo_axis_values[name] for name in splayed), indexing="ij") + flat_splayed = tuple(grid.ravel() for grid in mesh) + block = 1 + for name in splayed: + block *= batch_sizes[name] + + def at_one_splayed_combo( + splayed_values: tuple[ScalarFloat | ScalarInt, ...], + ) -> tuple[FloatND, ...]: + return inner( + **dict(zip(splayed, splayed_values, strict=True)), **vmapped_values + ) + + stacked = jax.lax.map(at_one_splayed_combo, flat_splayed, batch_size=block) + + # Restore `combo_var_names` order: `stacked` axes are + # (flattened splayed, *vmapped, *per-element); reshape the flat axis back + # to the splayed dims, then transpose the combo axes into canonical order. + current_order = splayed + vmapped + perm = tuple(current_order.index(name) for name in combo_var_names) + n_combo = len(combo_var_names) + + def _reorder(arr: FloatND) -> FloatND: + arr = arr.reshape(*splayed_dims, *arr.shape[1:]) + trailing = tuple(range(n_combo, arr.ndim)) + return jnp.transpose(arr, (*perm, *trailing)) + + return tuple(_reorder(arr) for arr in stacked) + + +def _build_kernel_pieces( + *, + solver: DCEGM, + user_regimes: Mapping[RegimeName, UserRegime], + functions: EconFunctionsMapping, + constraints: ConstraintFunctionsMapping, + transitions: TransitionFunctionsMapping, + stochastic_transition_names: frozenset[TransitionFunctionName], + compute_regime_transition_probs: RegimeTransitionFunction, + carry_targets: tuple[RegimeName, ...], + scalar_targets: tuple[RegimeName, ...], + n_pad: int, + n_carry_rows: int, + own_discrete_state_names: tuple[StateName, ...], + own_passive_state_names: tuple[StateName, ...], + own_discrete_action_values: MappingProxyType[ActionName, Any], + euler_axis_in_V: int, + regime_to_v_interpolation_info: MappingProxyType[RegimeName, VInterpolationInfo], +) -> _EgmKernelPieces: + """Assemble the build-time statics of the EGM kernel.""" + savings_nodes = jnp.asarray( + solver.savings_grid.to_jax(), dtype=canonical_float_dtype() + ) + n_constrained = solver.n_constrained_points + child_reads = _build_child_reads( + user_regimes=user_regimes, + functions=functions, + transitions=transitions, + stochastic_transition_names=stochastic_transition_names, + carry_targets=carry_targets, + post_decision_name=solver.post_decision_function, + regime_to_v_interpolation_info=regime_to_v_interpolation_info, + ) + continuation_plan = ContinuationPlan( + carry_targets=carry_targets, + scalar_targets=scalar_targets, + child_reads=child_reads, + compute_regime_transition_probs=compute_regime_transition_probs, + post_decision_name=solver.post_decision_function, + stochastic_node_batch_size=solver.stochastic_node_batch_size, + ) + return _EgmKernelPieces( + euler_state_name=solver.continuous_state, + action_name=solver.continuous_action, + savings_nodes=savings_nodes, + borrowing_limit=savings_nodes[0], + n_constrained=n_constrained, + # Static geometric ratio: the constrained actions run from + # `span * CONSTRAINED_OFFSET_FRACTION` up to `span`, so the ratio + # depends only on the offset fraction and the point count. + constrained_ratio=(1.0 / CONSTRAINED_OFFSET_FRACTION) + ** (1.0 / max(n_constrained - 1, 1)), + n_pad=n_pad, + n_carry_rows=n_carry_rows, + combo_names=own_discrete_state_names + + own_passive_state_names + + tuple(own_discrete_action_values), + euler_axis_in_V=euler_axis_in_V, + utility_func=_concatenate_regime_function( + functions=functions, target="utility" + ), + inverse_marginal_utility_func=( + _concatenate_regime_function( + functions=functions, target="inverse_marginal_utility" + ) + if "inverse_marginal_utility" in functions + else None + ), + own_resources_func=_concatenate_regime_function( + functions=functions, target=solver.resources + ), + feasibility_func=_build_feasibility_function( + functions=functions, constraints=constraints + ), + build_H_kwargs=_get_build_H_kwargs(functions), + refine=get_upper_envelope(solver=solver, n_refined=n_pad), + refine_to_bracket=get_bracket_finder(solver=solver, n_refined=n_pad), + continuation_plan=continuation_plan, + ) + + +def _build_feasibility_function( + *, + functions: EconFunctionsMapping, + constraints: ConstraintFunctionsMapping, +) -> Callable[..., ScalarBool] | None: + """Build the discrete-feasibility predicate of a combo, or `None`. + + DC-EGM validation guarantees that no constraint reaches the continuous + state or action, so every constraint is evaluable per discrete combo. + + Returns: + Callable mapping a combo's pool (discrete values plus flat params) + to a scalar feasibility indicator, or `None` without constraints. + + """ + if not constraints: + return None + constraints_func = concatenate_functions( + functions={ + **{name: func for name, func in functions.items() if name != "H"}, + **dict(constraints), + }, + targets=list(constraints), + return_type="dict", + enforce_signature=False, + set_annotations=True, + ) + + def feasibility(**combo_pool: Any) -> ScalarBool: # noqa: ANN401 + """Evaluate all constraints for one combo and combine them.""" + outputs = constraints_func(**combo_pool) + return jnp.all(jnp.stack([jnp.asarray(out) for out in outputs.values()])) + + return feasibility + + +def _get_raising_egm_step(*, reason: str) -> EGMStepFunction: + """Build a kernel that raises at solve time for unsupported configurations. + + `Model` construction with a validated DC-EGM regime always succeeds; + features the kernel does not cover yet surface as `NotImplementedError` + when the model is solved. + """ + + def raising_egm_step( + next_regime_to_V_arr: MappingProxyType[RegimeName, FloatND], + next_regime_to_egm_carry: MappingProxyType[RegimeName, EGMCarry], + **kwargs: Any, # noqa: ANN401 + ) -> tuple[FloatND, EGMCarry, EGMSimPolicy]: + raise NotImplementedError(reason) + + return raising_egm_step diff --git a/src/_lcm/egm/step_core.py b/src/_lcm/egm/step_core.py new file mode 100644 index 000000000..ef7abf9fa --- /dev/null +++ b/src/_lcm/egm/step_core.py @@ -0,0 +1,543 @@ +"""The textbook DC-EGM step: Euler inversion to the upper-envelope value row. + +The single-post-state algorithm a reviewer can read top to bottom. For one +discrete-choice combo it Euler-inverts the continuation over the savings grid, +appends the closed-form credit-constrained candidates, refines the candidate +value correspondence to its upper envelope, and publishes the value function and +the next period's carry rows on the regime's exogenous state grid. It reads the +expected continuation through `continuation`'s per-target carry reader and knows +nothing about asset-row mode, the multi-target machinery itself, or the kernel +orchestration that maps it over the discrete-combo product. +""" + +from collections.abc import Callable, Mapping +from dataclasses import dataclass +from types import MappingProxyType +from typing import Any + +import jax +import jax.numpy as jnp + +from _lcm.egm.carry import EGMCarry +from _lcm.egm.continuation import ( + ContinuationPlan, + bind_continuation, +) +from _lcm.egm.euler import invert_euler +from _lcm.egm.interp import ( + interp_on_padded_grid, +) +from _lcm.egm.numeric_inverse import numeric_inverse_marginal_utility +from _lcm.egm.upper_envelope.fues import QueryBracket +from _lcm.typing import ( + ActionName, + RegimeName, + StateName, +) +from lcm.typing import ( + BoolND, + Float1D, + FloatND, + ScalarBool, + ScalarFloat, + ScalarInt, + UserFunction, +) + +# Smallest constrained-segment action as a fraction of the segment's span. +# The constrained candidates are geometrically spaced from this offset toward +# the borrowing limit (additive, so a non-positive limit stays well-defined). +CONSTRAINED_OFFSET_FRACTION = 1e-4 + + +@dataclass(frozen=True, kw_only=True) +class _EgmKernelPieces: + """Build-time statics shared by every per-combo EGM computation.""" + + euler_state_name: StateName + """Name of the regime's continuous (Euler) state.""" + + action_name: ActionName + """Name of the regime's continuous action.""" + + savings_nodes: Float1D + """The exogenous end-of-period savings grid.""" + + borrowing_limit: ScalarFloat + """Lower bound of the savings grid.""" + + n_constrained: int + """Number of closed-form credit-constrained candidate points.""" + + constrained_ratio: float + """Static geometric spacing ratio of the constrained candidates.""" + + n_pad: int + """Static length of the envelope-refinement workspace (FUES/RFC, overflow).""" + + n_carry_rows: int + """Static length of the persisted carry rows. + + Equals `n_pad` in the single-post-state kernel (the carry is the refined + envelope) and `n_euler_nodes` in asset-row mode (the carry is one published + point per exogenous Euler node, with no envelope-workspace padding).""" + + combo_names: tuple[StateName | ActionName, ...] + """Discrete-state, passive-state, then discrete-action names (carry-axis order).""" + + euler_axis_in_V: int + """Canonical axis of the Euler state in the published value-function array.""" + + utility_func: UserFunction + """The regime's concatenated utility function.""" + + inverse_marginal_utility_func: UserFunction | None + """The regime's concatenated inverse-marginal-utility function. + + `None` when the regime supplies no analytic inverse: EGM then inverts `u'` + numerically (the iEGM path), deriving the marginal utility from `utility_func` + at the call site. + """ + + own_resources_func: UserFunction + """The regime's concatenated resources function.""" + + feasibility_func: Callable[..., ScalarBool] | None + """Discrete-feasibility predicate of a combo, or `None`.""" + + build_H_kwargs: Callable[[Mapping[str, Any]], dict[str, Any]] + """Closure assembling the Bellman aggregator's keyword arguments.""" + + refine: Callable[..., tuple[Float1D, Float1D, Float1D, ScalarInt]] + """The configured upper-envelope backend (single-post-state carry).""" + + refine_to_bracket: Callable[..., QueryBracket] + """The streaming single-query bracket finder (asset-row publish).""" + + continuation_plan: ContinuationPlan + """Build-time statics of the per-savings-node continuation aggregation.""" + + +def _get_solve_one_combo( + *, + pieces: _EgmKernelPieces, + pool: dict[str, Any], + state_grid: Float1D, + next_regime_to_egm_carry: MappingProxyType[RegimeName, EGMCarry], + euler_batch_size: int, + savings_batch_size: int, + resolved_process_grids: Mapping[StateName, FloatND] = MappingProxyType({}), +) -> Callable[ + [tuple[ScalarInt | ScalarFloat, ...]], + tuple[Float1D, Float1D, Float1D, Float1D, Float1D], +]: + """Build the per-combo EGM computation for one kernel invocation. + + `euler_batch_size` is accepted for a uniform builder signature but unused: + the single-post-state kernel solves once per combo, with no per-asset-node + axis to splay (only the asset-row kernel honors it). + + `resolved_process_grids` maps each runtime-resolved process state to its + solve-time grid, threaded into the continuation so a resources function + reading a process node integrates over the resolved nodes. + """ + del euler_batch_size + dtype = state_grid.dtype + + def solve_one_combo( + combo_values: tuple[ScalarInt | ScalarFloat, ...], + ) -> tuple[Float1D, Float1D, Float1D, Float1D, Float1D]: + """Run the EGM step for one (discrete x passive-node) combo. + + Takes the combo's values (discrete codes and passive node values) + positionally so `jax.vmap` can batch over flattened combo arrays. + + Returns: + Tuple of the combo's value row on the exogenous state grid and + its refined endogenous grid, the published consumption policy on + that grid, and the value and marginal-utility carry rows. + + """ + combo_pool = { + **pool, + **dict(zip(pieces.combo_names, combo_values, strict=True)), + } + # Validation pins the default Bellman aggregator, whose single + # non-(utility, E_next_V) parameter is the discount factor. + (discount_factor,) = tuple(pieces.build_H_kwargs(combo_pool).values()) + + def utility_of_action(action_value: ScalarFloat) -> ScalarFloat: + return pieces.utility_func( + **{pieces.action_name: action_value}, **combo_pool + ) + + compute_node = _get_compute_node( + pieces=pieces, + combo_pool=combo_pool, + discount_factor=discount_factor, + utility_of_action=utility_of_action, + next_regime_to_egm_carry=next_regime_to_egm_carry, + dtype=dtype, + resolved_process_grids=resolved_process_grids, + ) + actions, endog_grid, values, expected_values = _compute_nodes_over_savings( + compute_node=compute_node, + savings_nodes=pieces.savings_nodes, + savings_batch_size=savings_batch_size, + ) + + def own_resources_of_state(state_value: ScalarFloat) -> ScalarFloat: + return pieces.own_resources_func( + **{pieces.euler_state_name: state_value}, **combo_pool + ) + + publish_resources = jax.vmap(own_resources_of_state)(state_grid) + + constrained_actions, constrained_values = _compute_constrained_candidates( + first_endogenous_point=endog_grid[0], + publish_resources=publish_resources, + borrowing_limit=pieces.borrowing_limit, + n_constrained=pieces.n_constrained, + constrained_ratio=pieces.constrained_ratio, + utility_of_action=utility_of_action, + discounted_expected_value_at_limit=discount_factor * expected_values[0], + ) + + candidate_grid = jnp.concatenate( + [pieces.borrowing_limit + constrained_actions, endog_grid] + ) + candidate_policy = jnp.concatenate([constrained_actions, actions]) + candidate_value = jnp.concatenate([constrained_values, values]) + # A `-inf`-valued candidate (e.g. a corner whose continuation is + # `-inf`) is dominated by every finite candidate and would inject + # `-inf - (-inf) = NaN` into the envelope scan's gradient arithmetic. + # Mask the triple to NaN β€” the scan's absent form. NaN-valued + # candidates stay as they are: genuine poison must keep propagating. + candidate_dead = jnp.isneginf(candidate_value) + candidate_marginal = _candidate_supgradient( + policy=candidate_policy, + dead=candidate_dead, + utility_of_action=utility_of_action, + ) + # No explicit `segment_id` is passed: the candidate chain is a single + # connected branch (the constrained segment joins the unconstrained Euler + # branch continuously at the borrowing limit). Within-period discrete + # choices are maximized across combos in the V array, not stacked here, so + # `refine` never sees two unrelated branches that could be bridged. A + # future-kink-induced fold is data-emergent (the inverted endogenous grid + # decreases) rather than known a priori, so it is the backend's geometry β€” + # not an explicit label β€” that resolves it. Explicit topology is the + # oracle/test path (LTM/MSS/query accept `segment_id`); production has none + # to emit. + refined_grid, refined_policy, refined_value, n_kept = pieces.refine( + endog_grid=jnp.where(candidate_dead, jnp.nan, candidate_grid), + policy=jnp.where(candidate_dead, jnp.nan, candidate_policy), + value=jnp.where(candidate_dead, jnp.nan, candidate_value), + marginal_utility=candidate_marginal, + ) + + V_row, value_row, marginal_utility_row = _publish_V_and_carry_rows( + refined_grid=refined_grid, + refined_policy=refined_policy, + refined_value=refined_value, + n_kept=n_kept, + n_pad=pieces.n_pad, + publish_resources=publish_resources, + borrowing_limit=pieces.borrowing_limit, + utility_of_action=utility_of_action, + discounted_expected_value_at_limit=discount_factor * expected_values[0], + ) + + # A combo with no live candidate (its entire continuation is `-inf`) + # is worth `-inf` everywhere, like an infeasible combo. + no_live_candidate = jnp.all(candidate_dead) + V_row = jnp.where(no_live_candidate, -jnp.inf, V_row) + value_row = jnp.where(no_live_candidate, -jnp.inf, value_row) + marginal_utility_row = jnp.where(no_live_candidate, 0.0, marginal_utility_row) + + if pieces.feasibility_func is not None: + # Infeasible discrete combos: -inf value rows so they win no + # maximum and carry zero choice probability; exactly-zero + # marginal utility so probability-weighted sums stay finite. + feasible = pieces.feasibility_func(**combo_pool) + V_row = jnp.where(feasible, V_row, -jnp.inf) + value_row = jnp.where(feasible, value_row, -jnp.inf) + marginal_utility_row = jnp.where(feasible, marginal_utility_row, 0.0) + + return ( + V_row, + refined_grid.astype(dtype), + refined_policy.astype(dtype), + value_row, + marginal_utility_row, + ) + + return solve_one_combo + + +def _compute_nodes_over_savings( + *, + compute_node: Callable, + savings_nodes: Float1D, + savings_batch_size: int, +) -> tuple[FloatND, FloatND, FloatND, FloatND]: + """Run `compute_node` over every savings node, optionally splayed. + + A positive `savings_batch_size` below the grid length splays the + per-savings-node continuation computation β€” the dominant egm_step working + buffer (savings nodes by the child stochastic mesh by the combo block) β€” into + `lax.map` blocks, shedding peak memory; 0 (or a size covering the whole + grid) keeps the fused vmap. The output is identical either way: the per-node + `(action, endogenous resources, value, expected continuation)` candidates + stacked along the savings axis, which the constrained-region assembly and + the upper envelope then consume on the full grid. + """ + n_savings = savings_nodes.shape[0] + if 0 < savings_batch_size < n_savings: + return jax.lax.map(compute_node, savings_nodes, batch_size=savings_batch_size) + return jax.vmap(compute_node)(savings_nodes) + + +def _get_compute_node( + *, + pieces: _EgmKernelPieces, + combo_pool: dict[str, Any], + discount_factor: ScalarFloat, + utility_of_action: Callable[[ScalarFloat], ScalarFloat], + next_regime_to_egm_carry: MappingProxyType[RegimeName, EGMCarry], + dtype: Any, # noqa: ANN401 + resolved_process_grids: Mapping[StateName, FloatND] = MappingProxyType({}), +) -> Callable[[ScalarFloat], tuple[ScalarFloat, ScalarFloat, ScalarFloat, ScalarFloat]]: + """Build the per-savings-node Euler inversion for one discrete combo.""" + continuation = bind_continuation( + plan=pieces.continuation_plan, + combo_pool=combo_pool, + next_regime_to_egm_carry=next_regime_to_egm_carry, + dtype=dtype, + resolved_process_grids=resolved_process_grids, + ) + + analytic_inverse = pieces.inverse_marginal_utility_func + if analytic_inverse is not None: + + def inverse_marginal_utility( + marginal_continuation: ScalarFloat, + ) -> ScalarFloat: + return analytic_inverse( + marginal_continuation=marginal_continuation, **combo_pool + ) + else: + # iEGM: no analytic inverse supplied, so invert `u'` numerically. The + # marginal utility is the action-derivative of the combo-bound utility; + # the bracket spans a small floor to a generous multiple of the savings + # grid's top node (interior optima lie within resources, the savings + # scale; a clamped near-zero-marginal corner whose root exceeds the + # bracket lands far to the right and is discarded by the envelope, exactly + # as the analytic path's large value is). + marginal_utility_of_action = jax.grad(utility_of_action) + action_upper = pieces.savings_nodes[-1] * 1000.0 + 1000.0 + action_lower = jnp.asarray(1e-8, dtype=action_upper.dtype) + + def inverse_marginal_utility( + marginal_continuation: ScalarFloat, + ) -> ScalarFloat: + return numeric_inverse_marginal_utility( + marginal_continuation=marginal_continuation, + marginal_utility=marginal_utility_of_action, + c_lower=action_lower, + c_upper=action_upper, + ) + + def compute_node( + savings_value: ScalarFloat, + ) -> tuple[ScalarFloat, ScalarFloat, ScalarFloat, ScalarFloat]: + """Euler-invert one savings node against the continuation.""" + expected_value, expected_marginal = continuation(savings_value) + action = invert_euler( + expected_marginal_continuation=expected_marginal, + discount_factor=discount_factor, + inverse_marginal_utility=inverse_marginal_utility, + ) + endog_point = savings_value + action + value = utility_of_action(action) + discount_factor * expected_value + return action, endog_point, value, expected_value + + return compute_node + + +def _candidate_supgradient( + *, + policy: Float1D, + dead: BoolND, + utility_of_action: Callable[[ScalarFloat], ScalarFloat], +) -> Float1D: + """Compute the candidate value-row supgradient $\\mu = \\partial v / \\partial R$. + + By the envelope theorem the value row's slope in resources is the marginal + utility of consumption $u'(c)$ at the candidate's optimal action β€” the + same exact slope the published carry row carries. The upper-envelope + backend reads it as the tangent gradient at each candidate; FUES ignores + it. Dead candidates get $0$ (they are dropped before the dominance test). + + Args: + policy: Candidate policy (consumption) values. + dead: Indicator of dead candidates (their continuation is `-inf`). + utility_of_action: Utility with everything but the continuous action + bound. + + Returns: + Supgradient per candidate. + + """ + safe_policy = jnp.where(dead, 1.0, policy) + marginal = jax.vmap(jax.grad(utility_of_action))(safe_policy) + return jnp.where(dead, 0.0, marginal) + + +def _compute_constrained_candidates( + *, + first_endogenous_point: ScalarFloat, + publish_resources: FloatND, + borrowing_limit: ScalarFloat, + n_constrained: int, + constrained_ratio: float, + utility_of_action: Callable[[ScalarFloat], ScalarFloat], + discounted_expected_value_at_limit: ScalarFloat, +) -> tuple[FloatND, FloatND]: + """Compute the closed-form credit-constrained candidate points. + + Below the first endogenous point the borrowing limit binds: the action is + `R - borrowing_limit` and the continuation is the limit-node expectation. + The candidate actions are geometrically spaced toward the limit; the span + is capped at the publish range so a degenerate (huge) first endogenous + point cannot stretch the sample beyond where queries land. + + Args: + first_endogenous_point: The endogenous resources point of the lowest + savings node. + publish_resources: Resources at the regime's exogenous state grid. + borrowing_limit: Lower bound of the savings grid. + n_constrained: Number of constrained candidate points. + constrained_ratio: Static geometric spacing ratio of the candidates. + utility_of_action: Utility with everything but the continuous action + bound. + discounted_expected_value_at_limit: Discounted expected continuation + value at the lowest savings node. + + Returns: + Tuple of constrained candidate actions and values. + + """ + dtype = publish_resources.dtype + span = jnp.maximum( + jnp.minimum(first_endogenous_point, jnp.max(publish_resources)) + - borrowing_limit, + jnp.finfo(dtype).tiny, + ) + constrained_actions = ( + span + * CONSTRAINED_OFFSET_FRACTION + * constrained_ratio ** jnp.arange(n_constrained, dtype=dtype) + ) + constrained_values = ( + jax.vmap(utility_of_action)(constrained_actions) + + discounted_expected_value_at_limit + ) + return constrained_actions, constrained_values + + +def _publish_V_and_carry_rows( + *, + refined_grid: Float1D, + refined_policy: Float1D, + refined_value: Float1D, + n_kept: ScalarInt, + n_pad: int, + publish_resources: FloatND, + borrowing_limit: ScalarFloat, + utility_of_action: Callable[[ScalarFloat], ScalarFloat], + discounted_expected_value_at_limit: ScalarFloat, +) -> tuple[FloatND, Float1D, Float1D]: + """Interpolate V onto the exogenous grid and finish the carry value rows. + + Below the lowest refined envelope point the interpolant edge-clamps, so + the published value there is the closed-form constrained value β€” the + exact value of saving exactly the borrowing limit. Above it, the refined + envelope is read with the cubic Hermite interpolant (the marginal-utility + row is the value row's exact slope by the envelope theorem), floored at + the constrained value, which remains a feasible-policy lower bound + everywhere. + + Envelope overflow is not silent: the outputs are NaN-poisoned so the + solve loop's NaN diagnostics surface the offending (regime, period). + + Args: + refined_grid: Refined endogenous grid row from the envelope backend. + refined_policy: Refined policy row. + refined_value: Refined value row. + n_kept: Number of envelope points the backend kept. + n_pad: Static length of the refined rows. + publish_resources: Resources at the regime's exogenous state grid. + borrowing_limit: Lower bound of the savings grid. + utility_of_action: Utility with everything but the continuous action + bound. + discounted_expected_value_at_limit: Discounted expected continuation + value at the lowest savings node. + + Returns: + Tuple of the value row on the exogenous state grid, the carry value + row, and the carry marginal-utility row. + + """ + dtype = publish_resources.dtype + overflowed = n_kept > n_pad + + marginal_utility = jax.vmap(jax.grad(utility_of_action))( + jnp.where(jnp.isnan(refined_policy), 1.0, refined_policy) + ) + marginal_utility = jnp.where(jnp.isnan(refined_policy), jnp.nan, marginal_utility) + marginal_utility = jnp.where(jnp.isneginf(refined_value), 0.0, marginal_utility) + + value_interpolated = interp_on_padded_grid( + x_query=publish_resources, + xp=refined_grid, + fp=refined_value, + fp_slopes=marginal_utility, + ) + closed_form_actions = publish_resources - borrowing_limit + value_constrained = jnp.where( + closed_form_actions > 0.0, + jax.vmap(utility_of_action)( + jnp.maximum(closed_form_actions, jnp.finfo(dtype).tiny) + ) + + discounted_expected_value_at_limit, + -jnp.inf, + ) + # Below the lowest refined point the interpolant edge-clamps, so the + # closed-form constrained value (the exact value of saving exactly the + # borrowing limit) is published outright there. Everywhere else it is a + # feasible-policy floor under the Hermite read of the refined envelope: + # forcing it further up β€” e.g. to the first Euler point β€” would discard + # envelope information wherever degenerate inversions push that point + # right (a zero-ish marginal continuation makes it ~1/eps), and the + # constrained candidates inside the envelope already carry exact slopes. + refined_grid_start = refined_grid[0] + V_row = jnp.where( + (closed_form_actions > 0.0) & (publish_resources <= refined_grid_start), + value_constrained, + jnp.maximum(value_interpolated, value_constrained), + ) + V_row = jnp.where(overflowed, jnp.nan, V_row).astype(dtype) + + # The carry value row is the refined upper envelope itself β€” the correct + # object for a parent to interpolate. The constrained floor applies only to + # the published `V_row` on the exogenous grid; flooring the carry would lift + # finite envelope nodes above the true envelope wherever the closed-form + # constrained value exceeds them, overstating the parent's continuation. + value_row = jnp.where(overflowed, jnp.nan, refined_value).astype(dtype) + # The carry marginal-utility row is the parent's Hermite slope. On overflow + # the backend still returns a finite truncated prefix, so β€” like the value + # rows β€” it must be NaN-poisoned too, or an overflowed period would feed the + # parent a wrong-but-finite slope past the NaN diagnostics. + marginal_row = jnp.where(overflowed, jnp.nan, marginal_utility).astype(dtype) + return V_row, value_row, marginal_row diff --git a/src/_lcm/egm/terminal.py b/src/_lcm/egm/terminal.py new file mode 100644 index 000000000..6f26582ef --- /dev/null +++ b/src/_lcm/egm/terminal.py @@ -0,0 +1,244 @@ +"""Carry producers for terminal regimes targeted by DC-EGM regimes. + +A terminal regime's value is its utility, so its carry rows are closed-form +rather than the output of an EGM step. Two cases: + +- *Terminal with a wealth state* (e.g. a bequest motive): the carry holds the + terminal utility and its `jax.grad` with respect to the wealth state on the + regime's own wealth grid. The grid lives in M-space with $R \\equiv M$; the + parent's composed-gradient factor $\\partial R'/\\partial A$ handles the + space uniformly. The terminal may additionally carry discrete states shared + with the parent (e.g. a fixed `pref_type` whose bequest weight differs by + type): the carry then has those discrete axes leading (in V state order, + matching the value-function array's layout), one wealth row per discrete + combo, and the parent selects its own combo by integer indexing the leading + axes β€” the same alignment the non-terminal child read uses. +- *Stateless terminal* (e.g. `dead` with `utility=lambda: 0.0`): there is no + wealth grid and the marginal value of resources is identically zero. The + carry holds constant-value, zero-marginal-utility broadcast rows; a parent + whose entire continuation is such a regime hits the degenerate-inversion + guard and correctly produces the consume-everything policy. +""" + +from collections.abc import Callable +from typing import cast + +import jax +import jax.numpy as jnp +from dags import concatenate_functions + +from _lcm.dtypes import canonical_float_dtype +from _lcm.egm.carry import EGMCarry +from _lcm.typing import EconFunctionsMapping, EGMCarryProducer, StateName +from _lcm.utils.functools import get_union_of_args +from lcm.typing import FloatND, IntND, ScalarFloat + +# Static row count of a stateless terminal carry: two grid slots suffice to +# represent a constant function under linear interpolation. +N_STATELESS_CARRY_ROWS = 2 + + +def get_stateless_terminal_carry_producer() -> EGMCarryProducer: + """Build the carry producer for a terminal regime without states. + + Returns: + Producer mapping the regime's scalar value-function array to + constant-value, zero-marginal-utility carry rows. + + """ + + def produce_stateless_carry( + *, + V_arr: FloatND, + **kwargs: FloatND | IntND, # noqa: ARG001 + ) -> EGMCarry: + """Broadcast the scalar terminal value into constant carry rows.""" + dtype = canonical_float_dtype() + zeros = jnp.zeros(N_STATELESS_CARRY_ROWS, dtype=dtype) + return EGMCarry( + endog_grid=jnp.linspace(0.0, 1.0, N_STATELESS_CARRY_ROWS, dtype=dtype), + value=jnp.broadcast_to( + jnp.asarray(V_arr, dtype=dtype), (N_STATELESS_CARRY_ROWS,) + ), + marginal_utility=zeros, + taste_shock_scale=jnp.asarray(0.0, dtype=dtype), + ) + + return produce_stateless_carry + + +def get_terminal_wealth_carry_producer( + *, + functions: EconFunctionsMapping, + state_name: StateName, + discrete_state_names: tuple[StateName, ...] = (), + passive_state_names: tuple[StateName, ...] = (), + continuous_state_order: tuple[StateName, ...] = (), +) -> EGMCarryProducer: + """Build the carry producer for a terminal regime with one Euler state. + + The carry's value rows are the regime's value-function array (terminal + value equals utility on the state grid) and its marginal-utility rows + are `jax.grad` of the utility DAG with respect to the Euler state. The + rows live in M-space ($R \\equiv M$), so the endogenous grid is the + Euler-state grid itself. + + The carry's leading axes are the shared discrete states, then the passive + continuous states (the durable / outer margin of a NEGM parent), both in + value-function-array order; the Euler state is the trailing (row) axis. Each + leading combo holds the terminal utility and its Euler-state gradient + evaluated at that combo's discrete codes and passive node values. The parent + integer-indexes the discrete axes and interpolates the passive axes β€” the + same alignment the non-terminal child read uses. + + Args: + functions: The terminal regime's processed functions (params renamed + to qualified names). + state_name: Name of the regime's Euler state (the parent's continuous + state, gradient and endogenous-grid axis). + discrete_state_names: Shared discrete-state names in value-function + (carry leading-axis) order; empty for a single-Euler-state carry. + passive_state_names: Passive continuous-state names in value-function + order β€” carried as interpolated leading axes; empty for a single + continuous state. + continuous_state_order: The value-function array's continuous-axis + order, used to transpose `V_arr` into `(discrete…, passive…, + Euler)`; empty defaults to `(state_name,)`. + + Returns: + Producer mapping the state grids, the regime's flat params, and its + value-function array to the terminal carry. + + """ + utility_func = concatenate_functions( + functions={name: func for name, func in functions.items() if name != "H"}, + targets="utility", + enforce_signature=False, + set_annotations=True, + ) + utility_extra_arg_names = tuple( + get_union_of_args([utility_func]) + - {state_name} + - set(discrete_state_names) + - set(passive_state_names), + ) + cont_order = continuous_state_order or (state_name,) + + def produce_terminal_wealth_carry( + *, V_arr: FloatND, **kwargs: FloatND | IntND + ) -> EGMCarry: + """Evaluate the terminal value and its Euler-state gradient on the grid.""" + dtype = canonical_float_dtype() + euler_grid = jnp.asarray(kwargs[state_name], dtype=dtype) + passive_grids = tuple( + jnp.asarray(kwargs[name], dtype=dtype) for name in passive_state_names + ) + extra = {name: kwargs[name] for name in utility_extra_arg_names} + discrete_grids = tuple(kwargs[name] for name in discrete_state_names) + + def euler_gradient_at_combo( + discrete_codes: tuple[IntND, ...], + ) -> FloatND: + """Euler-state gradient block for one shared discrete combo. + + Returns a `(passive…, Euler)` block β€” the gradient evaluated over + the mesh of passive node values (leading) and the Euler grid + (trailing). + """ + discrete_kwargs = dict( + zip(discrete_state_names, discrete_codes, strict=True) + ) + + def utility_at_point( + euler_value: ScalarFloat, passive_values: tuple[ScalarFloat, ...] + ) -> ScalarFloat: + passive_kwargs = dict( + zip(passive_state_names, passive_values, strict=True) + ) + return utility_func( + **{state_name: euler_value}, + **discrete_kwargs, + **passive_kwargs, + **extra, + ) + + grad_euler = jax.grad(utility_at_point, argnums=0) + mesh = jnp.meshgrid(*passive_grids, euler_grid, indexing="ij") + flat = jnp.stack([axis.ravel() for axis in mesh], axis=-1) + grad_flat = jax.vmap(lambda row: grad_euler(row[-1], tuple(row[:-1])))(flat) + return grad_flat.reshape(mesh[0].shape) + + value = _reorder_terminal_value( + V_arr=jnp.asarray(V_arr, dtype=dtype), + n_discrete=len(discrete_state_names), + continuous_state_order=cont_order, + passive_state_names=passive_state_names, + euler_state_name=state_name, + ) + marginal_utility = _grad_over_discrete_combos( + wealth_gradient_at_combo=euler_gradient_at_combo, + discrete_grids=discrete_grids, + ) + leading_shape = value.shape[:-1] + endog_grid = jnp.broadcast_to(euler_grid, (*leading_shape, euler_grid.shape[0])) + return EGMCarry( + endog_grid=endog_grid, + value=value, + marginal_utility=jnp.where( + jnp.isneginf(value), 0.0, marginal_utility + ).astype(dtype), + taste_shock_scale=jnp.asarray(0.0, dtype=dtype), + ) + + return produce_terminal_wealth_carry + + +def _reorder_terminal_value( + *, + V_arr: FloatND, + n_discrete: int, + continuous_state_order: tuple[StateName, ...], + passive_state_names: tuple[StateName, ...], + euler_state_name: StateName, +) -> FloatND: + """Transpose `V_arr` into carry layout `(discrete…, passive…, Euler)`. + + `V_arr` has its discrete axes leading, then its continuous axes in + `continuous_state_order`. The carry wants the passive continuous states + (in value-function order) before the Euler state, which trails as the row + axis; the discrete axes keep their leading positions. + """ + target_continuous = (*passive_state_names, euler_state_name) + continuous_perm = [ + n_discrete + continuous_state_order.index(name) for name in target_continuous + ] + axes = list(range(n_discrete)) + continuous_perm + return jnp.transpose(V_arr, axes) + + +def _grad_over_discrete_combos( + *, + wealth_gradient_at_combo: object, + discrete_grids: tuple[FloatND | IntND, ...], +) -> FloatND: + """Stack the per-combo wealth gradients into the carry's leading-axis shape. + + Iterates the shared discrete grids in Python (their sizes are static), so + each combo's gradient is a plain `jax.vmap` over the wealth grid. The + result has the discrete axes leading (in the given order) and the wealth + axis trailing, matching the value-function array's layout. + """ + grad_at_combo = cast( + "Callable[[tuple[IntND, ...]], FloatND]", wealth_gradient_at_combo + ) + + def build_axis( + prefix: tuple[IntND, ...], remaining: tuple[FloatND | IntND, ...] + ) -> FloatND: + if not remaining: + return grad_at_combo(prefix) + head, *tail = remaining + rows = [build_axis((*prefix, code), tuple(tail)) for code in jnp.asarray(head)] + return jnp.stack(rows, axis=0) + + return build_axis((), discrete_grids) diff --git a/src/_lcm/egm/two_asset_g2egm_step.py b/src/_lcm/egm/two_asset_g2egm_step.py new file mode 100644 index 000000000..6a9a0010a --- /dev/null +++ b/src/_lcm/egm/two_asset_g2egm_step.py @@ -0,0 +1,357 @@ +"""One multi-segment 2-D G2EGM upper-envelope step for the two-asset model. + +Assembles the four KKT constraint segments (`ucon`, `dcon`, `acon`, `con`) into a +single backward step. From next period's value on the regular $(m, n)$ grid it builds +each segment's candidate cloud by that segment's closed-form inverse Euler step, +triangulates the clouds into meshes in the current-state plane, and selects β€” at every +common $(m, n)$ target β€” the best feasible policy across all segments by recomputing +the Bellman objective: the first (within-segment) upper envelope over each segment's +admissible triangles, then the second (across-segment) maximum. + +Unlike the `ucon`-only step (`two_asset_step.egm_step`), the constrained corners β€” low +liquid wealth (borrowing binds, `acon`/`con`) and low pension (deposit binds, `dcon`) β€” +are covered by their own segments rather than left to the unconstrained cloud's +poisoning extrapolation. `ucon`/`dcon` are built on the post-decision $(a, b)$ grid; +`acon`/`con` are built on the $(consumption, b)$ grid at $a = 0$. +""" + +from collections.abc import Callable +from typing import NamedTuple + +import jax +import jax.numpy as jnp + +from _lcm.egm.mesh_envelope import ObjectiveEvaluator, first_envelope, second_envelope +from _lcm.egm.two_asset_inverse import ( + invert_acon_cloud, + invert_con_cloud, + invert_dcon_cloud, + invert_ucon_cloud, +) +from _lcm.egm.two_asset_objective import build_two_asset_objective +from _lcm.egm.two_asset_post_decision import ( + PostDecision, + post_decision_value_and_grad, + post_decision_value_and_grad_retiring, +) +from _lcm.egm.two_asset_segment_mesh import build_segment_mesh +from lcm.typing import Float1D, Float2D, FloatND, ScalarFloat + +# Maps a post-decision `(a, b)` mesh to its value and gradients. The working step reads +# next period's working value on the `(m, n)` grid; the retirement-boundary step reads +# the 1-D retired value through the lump-sum payout. The envelope core is identical +# either way β€” only this reader differs. +PostDecisionReader = Callable[[FloatND, FloatND], PostDecision] + + +class G2EGMResult(NamedTuple): + """One G2EGM step's value and policy on the regular working `(m, n)` grid.""" + + value: FloatND + """This period's upper-envelope value, shape `(len(m_grid), len(n_grid))`.""" + consumption: FloatND + """Optimal consumption per `(m, n)` target (invalid at uncovered holes).""" + deposit: FloatND + """Optimal pension deposit per `(m, n)` target (invalid at uncovered holes).""" + + +def g2egm_step( + *, + next_value: FloatND, + m_grid: Float1D, + n_grid: Float1D, + a_grid: Float1D, + b_grid: Float1D, + consumption_grid: Float1D, + discount_factor: ScalarFloat | float, + crra: ScalarFloat | float, + match_rate: ScalarFloat | float, + return_liquid: ScalarFloat | float, + return_pension: ScalarFloat | float, + wage: ScalarFloat | float, + threshold: float = 0.25, +) -> G2EGMResult: + """Solve one period of the two-asset model by the four-segment G2EGM envelope. + + Args: + next_value: Next period's value on the regular `(m, n)` grid. + m_grid: Regular liquid-state grid (ascending, evenly spaced). + n_grid: Regular pension-state grid (ascending, evenly spaced). + a_grid: Liquid post-decision grid for `ucon`/`dcon` (should include 0 so the + objective reads `W(0, b)` accurately at the borrowing-constrained corner). + b_grid: Pension post-decision grid (shared by all segments). + consumption_grid: Consumption sweep for `acon`/`con` at `a = 0`. + discount_factor: Discount factor `beta`. + crra: Coefficient of relative risk aversion `rho`. + match_rate: Pension employer-match coefficient `chi`. + return_liquid: Liquid net return `r^a`. + return_pension: Pension net return `r^b`. + wage: Deterministic labor income. + threshold: Barycentric extrapolation tolerance for triangle admissibility. + + Returns: + This period's upper-envelope value and policy on the regular `(m, n)` grid. + + """ + + def post_reader(a: FloatND, b: FloatND) -> PostDecision: + return post_decision_value_and_grad( + next_value=next_value, + m_grid=m_grid, + n_grid=n_grid, + a=a, + b=b, + return_liquid=return_liquid, + return_pension=return_pension, + wage=wage, + ) + + return _g2egm_envelope_step( + post_reader=post_reader, + m_grid=m_grid, + n_grid=n_grid, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + threshold=threshold, + ) + + +def g2egm_retiring_step( + *, + next_value_retired: Float1D, + next_marginal_retired: Float1D, + liquid_grid: Float1D, + m_grid: Float1D, + n_grid: Float1D, + a_grid: Float1D, + b_grid: Float1D, + consumption_grid: Float1D, + discount_factor: ScalarFloat | float, + crra: ScalarFloat | float, + match_rate: ScalarFloat | float, + return_liquid: ScalarFloat | float, + pension_payout_return: ScalarFloat | float, + retirement_income: ScalarFloat | float, + threshold: float = 0.25, +) -> G2EGMResult: + """Solve the working->retired boundary period by the four-segment G2EGM envelope. + + Identical to `g2egm_step` except the post-decision continuation is the 1-D retired + value read through the lump-sum payout (`post_decision_value_and_grad_retiring`): + on retirement the pension is paid out into liquid, so both post-decision balances + feed a single retired liquid state. The endogenous-grid machinery, segments, and + envelope are unchanged. + + Args: + next_value_retired: Next period's retired value on `liquid_grid`. + next_marginal_retired: Next period's retired marginal value of liquid on + `liquid_grid`. + liquid_grid: Regular retired liquid-state grid (ascending, evenly spaced). + m_grid: Regular working liquid-state grid (ascending, evenly spaced). + n_grid: Regular working pension-state grid (ascending, evenly spaced). + a_grid: Liquid post-decision grid for `ucon`/`dcon`. + b_grid: Pension post-decision grid (shared by all segments). + consumption_grid: Consumption sweep for `acon`/`con` at `a = 0`. + discount_factor: Discount factor `beta`. + crra: Coefficient of relative risk aversion `rho`. + match_rate: Pension employer-match coefficient `chi`. + return_liquid: Liquid net return `r^a`. + pension_payout_return: Factor the pension balance is paid out at on retirement. + retirement_income: First retirement income added to the retired liquid state. + threshold: Barycentric extrapolation tolerance for triangle admissibility. + + Returns: + This period's upper-envelope value and policy on the working `(m, n)` grid. + + """ + + def post_reader(a: FloatND, b: FloatND) -> PostDecision: + return post_decision_value_and_grad_retiring( + next_value_retired=next_value_retired, + next_marginal_retired=next_marginal_retired, + liquid_grid=liquid_grid, + a=a, + b=b, + return_liquid=return_liquid, + pension_payout_return=pension_payout_return, + retirement_income=retirement_income, + ) + + return _g2egm_envelope_step( + post_reader=post_reader, + m_grid=m_grid, + n_grid=n_grid, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + threshold=threshold, + ) + + +def _g2egm_envelope_step( + *, + post_reader: PostDecisionReader, + m_grid: Float1D, + n_grid: Float1D, + a_grid: Float1D, + b_grid: Float1D, + consumption_grid: Float1D, + discount_factor: ScalarFloat | float, + crra: ScalarFloat | float, + match_rate: ScalarFloat | float, + threshold: float, +) -> G2EGMResult: + """Run the four-segment G2EGM envelope given a post-decision reader. + + The reader supplies the post-decision value and gradients on the `(a, b)` mesh; the + rest β€” the four KKT-segment inverses, triangulated meshes, within- and + across-segment envelopes, and the direct-Bellman hole-fill β€” is independent of + whether the continuation is the working or the retired value. + """ + # ucon / dcon: candidate clouds on the (a, b) post-decision grid. + a_mesh, b_mesh = jnp.meshgrid(a_grid, b_grid, indexing="ij") + post = post_reader(a_mesh, b_mesh) + ucon = invert_ucon_cloud( + a=a_mesh, + b=b_mesh, + w_a=post.grad_a, + w_b=post.grad_b, + post_decision_value=post.value, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + ) + dcon = invert_dcon_cloud( + a=a_mesh, + b=b_mesh, + w_a=post.grad_a, + w_b=post.grad_b, + post_decision_value=post.value, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + ) + + # acon / con: candidate clouds on the (consumption, b) grid at a = 0. + a_zero = jnp.zeros_like(b_grid) + post_zero = post_reader(a_zero, b_grid) + c_mesh, cb_mesh = jnp.meshgrid(consumption_grid, b_grid, indexing="ij") + value_at_zero = jnp.broadcast_to(post_zero.value[None, :], c_mesh.shape) + grad_b_at_zero = jnp.broadcast_to(post_zero.grad_b[None, :], c_mesh.shape) + grad_a_at_zero = jnp.broadcast_to(post_zero.grad_a[None, :], c_mesh.shape) + acon = invert_acon_cloud( + consumption=c_mesh, + b=cb_mesh, + post_decision_value_at_zero_a=value_at_zero, + w_b_at_zero_a=grad_b_at_zero, + w_a_at_zero_a=grad_a_at_zero, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + ) + con = invert_con_cloud( + consumption=c_mesh, + b=cb_mesh, + post_decision_value_at_zero_a=value_at_zero, + w_b_at_zero_a=grad_b_at_zero, + w_a_at_zero_a=grad_a_at_zero, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + ) + + meshes = [ + build_segment_mesh(cloud=ucon, region_label=0), + build_segment_mesh(cloud=dcon, region_label=1), + build_segment_mesh(cloud=acon, region_label=2), + build_segment_mesh(cloud=con, region_label=3), + ] + + objective = build_two_asset_objective( + post_decision_value=post.value, + a_grid=a_grid, + b_grid=b_grid, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + ) + + m_mesh, n_mesh = jnp.meshgrid(m_grid, n_grid, indexing="ij") + targets = jnp.stack([m_mesh.reshape(-1), n_mesh.reshape(-1)], axis=1) + + segment_values = [] + segment_policies = [] + for mesh in meshes: + values, policies = first_envelope( + mesh=mesh, targets=targets, objective=objective, threshold=threshold + ) + segment_values.append(values) + segment_policies.append(policies) + result = second_envelope( + segment_values=jnp.stack(segment_values, axis=0), + segment_policies=jnp.stack(segment_policies, axis=0), + region_labels=jnp.array([m.region_label for m in meshes], dtype=jnp.int32), + ) + + # Targets no admissible segment candidate reaches (envelope value `-inf`) are filled + # by a direct-Bellman search over a coarse policy grid β€” the v3 hole-fill. A target + # whose optimal post-state leaves the post-decision grid stays a hole (no in-domain + # candidate exists), which is a grid-coverage limit, not an algorithm gap. + deposit_grid = jnp.linspace(0.0, b_grid[-1] - b_grid[0], consumption_grid.shape[0]) + hole_value, hole_policy = _direct_bellman_fill( + targets=targets, + objective=objective, + consumption_grid=consumption_grid, + deposit_grid=deposit_grid, + ) + # A target the segment envelope misses takes the hole-fill's value *and* its policy, + # so the published consumption and deposit stay consistent with the published value + # rather than the stale failed-envelope policy. + is_hole = ~jnp.isfinite(result.value) + filled_value = jnp.where(is_hole, hole_value, result.value) + filled_policy = jnp.where(is_hole[:, None], hole_policy, result.policy) + return G2EGMResult( + value=filled_value.reshape(m_mesh.shape), + consumption=filled_policy[:, 0].reshape(m_mesh.shape), + deposit=filled_policy[:, 1].reshape(m_mesh.shape), + ) + + +def _direct_bellman_fill( + *, + targets: FloatND, + objective: ObjectiveEvaluator, + consumption_grid: Float1D, + deposit_grid: Float1D, +) -> tuple[FloatND, Float2D]: + """Maximize the recomputed objective over a coarse policy grid, per target. + + The fallback for common-grid targets no segment mesh covers: a direct-Bellman search + over the `(consumption, deposit)` product grid, masking infeasible candidates. + + Returns the per-target maximizing value and the `(consumption, deposit)` candidate + that attains it, so a hole cell's published policy matches its published value. The + value is `-inf` only where every coarse candidate is infeasible (the optimal + post-state leaves the post-decision grid); the returned policy there is the first + candidate and is meaningless, flagged by the `-inf` value. + """ + c_mesh, d_mesh = jnp.meshgrid(consumption_grid, deposit_grid, indexing="ij") + candidates = jnp.stack([c_mesh.reshape(-1), d_mesh.reshape(-1)], axis=1) + + def at_target(target: FloatND) -> tuple[FloatND, Float1D]: + def per_candidate(policy: FloatND) -> FloatND: + value, feasible = objective(target, policy) + return jnp.where(feasible & jnp.isfinite(value), value, -jnp.inf) + + masked = jax.vmap(per_candidate)(candidates) + winner = jnp.argmax(masked) + return masked[winner], candidates[winner] + + return jax.vmap(at_target)(targets) diff --git a/src/_lcm/egm/two_asset_inverse.py b/src/_lcm/egm/two_asset_inverse.py new file mode 100644 index 000000000..05620ef4e --- /dev/null +++ b/src/_lcm/egm/two_asset_inverse.py @@ -0,0 +1,294 @@ +"""Closed-form inverse-Euler step for the two-asset model (unconstrained interior). + +The first kernel piece of the two-continuous-state EGM foundation, for the +unconstrained (`ucon`) region where both the liquid borrowing constraint and the +deposit lower bound are slack. Given a post-decision grid $(a, b)$ (liquid and +pension post-decision balances) and the post-decision value gradients +$w_a = \\partial_a w$, $w_b = \\partial_b w$, the two intratemporal first-order +conditions invert in closed form to the optimal consumption and deposit, and the +budget identities map each post-decision node back to the endogenous current state +$(m, n)$ (cash-on-hand and pension balance) it is optimal at. This is the +single-segment case β€” no upper envelope is involved. + +The inverse is the verified core: $u'(c) = \\beta w_a$ gives $c$, and equating the +marginal value of a liquid dollar to that of a deposited dollar, +$w_a = w_b\\,(1 + \\chi/(1 + d))$, gives $d$. +""" + +from typing import NamedTuple + +import jax.numpy as jnp + +from lcm.typing import BoolND, FloatND, ScalarFloat + + +class RegionCloud(NamedTuple): + """Endogenous cloud produced by a region's inverse-Euler step. + + Each field is shaped like the post-decision $(a, b)$ grid; entry $(i, j)$ is the + current state and policy at which post-decision node $(a_i, b_j)$ is optimal, + conditional on the constraint region (`ucon`, `dcon`, ...) the cloud was built for. + """ + + m_endog: FloatND + """Endogenous cash-on-hand `liquid` at which the node is optimal.""" + n_endog: FloatND + """Endogenous pension balance at which the node is optimal.""" + consumption: FloatND + """Optimal consumption `c`.""" + deposit: FloatND + """Optimal pension deposit `d`.""" + value: FloatND + """Value `u(c) + discount_factor * w` at the endogenous state.""" + value_grad_m: FloatND + """Marginal value of liquid wealth `dV/dm`, equal to `u'(c)` at the optimum. + + By the envelope theorem this is `discount_factor * w_a` where the liquid Euler + equation holds (`ucon`/`dcon`), and `u'(c)` directly at the borrowing-constrained + corner (`acon`/`con`), where all extra liquid is consumed β€” the two coincide at the + optimal policy. + """ + value_grad_n: FloatND + """Marginal value of pension wealth `dV/dn`, equal to `discount_factor * w_b`.""" + valid_region: BoolND + """Whether the node satisfies this region's complementary-slackness conditions. + + Each region inverts its first-order conditions *assuming* its own constraints + bind; the solution is a genuine KKT candidate only where the region's + inequalities also hold. A node failing them is a finite but spurious point + that must be excluded before the upper-envelope selection, not merely a + non-finite one. + """ + + +def invert_ucon_cloud( + *, + a: FloatND, + b: FloatND, + w_a: FloatND, + w_b: FloatND, + post_decision_value: FloatND, + discount_factor: ScalarFloat | float, + crra: ScalarFloat | float, + match_rate: ScalarFloat | float, +) -> RegionCloud: + """Invert the two intratemporal FOCs on the unconstrained region. + + Args: + a: Liquid post-decision balance at each grid node. + b: Pension post-decision balance at each grid node. + w_a: Post-decision value gradient with respect to `a`. + w_b: Post-decision value gradient with respect to `b`. + post_decision_value: Post-decision value `w(a, b)` at each node. + discount_factor: Discount factor `beta`. + crra: Coefficient of relative risk aversion `rho`. + match_rate: Pension employer-match coefficient `chi` (match `chi*log(1+d)`). + + Returns: + The endogenous cloud: current state, policy, value, and value gradient per node. + + """ + consumption = (discount_factor * w_a) ** (-1.0 / crra) + deposit = match_rate * w_b / (w_a - w_b) - 1.0 + # Budget identities, inverted: a = m - c - d, b = n + d + chi*log(1 + d). + m_endog = a + consumption + deposit + n_endog = b - deposit - match_rate * jnp.log1p(deposit) + value = _crra_utility(consumption, crra) + discount_factor * post_decision_value + # KKT: liquid slack (a > 0, so the consumption Euler holds) and an interior + # deposit (d > 0). `deposit > 0` already implies `w_a > w_b`, since a + # non-positive denominator drives the deposit below zero. + valid_region = (a > 0.0) & (deposit > 0.0) & (w_a > w_b) + return RegionCloud( + m_endog=m_endog, + n_endog=n_endog, + consumption=consumption, + deposit=deposit, + value=value, + value_grad_m=discount_factor * w_a, + value_grad_n=discount_factor * w_b, + valid_region=valid_region, + ) + + +def invert_dcon_cloud( + *, + a: FloatND, + b: FloatND, + w_a: FloatND, + w_b: FloatND, + post_decision_value: FloatND, + discount_factor: ScalarFloat | float, + crra: ScalarFloat | float, + match_rate: ScalarFloat | float, +) -> RegionCloud: + """Invert the consumption FOC on the deposit-constrained region (`dcon`, `d = 0`). + + Where the pension is unattractive enough that the optimal deposit hits its lower + bound, the deposit is pinned to zero and only the consumption FOC `u'(c) = beta*w_a` + is inverted. With `d = 0` the pension is unchanged (`n = b`) and the liquid budget + identity is `a = m - c`. + + Args: + a: Liquid post-decision balance at each node. + b: Pension post-decision balance at each node. + w_a: Post-decision value gradient with respect to `a`. + w_b: Post-decision value gradient with respect to `b`. + post_decision_value: Post-decision value `w(a, b)` at each node. + discount_factor: Discount factor. + crra: Coefficient of relative risk aversion. + match_rate: Pension employer-match coefficient `chi`; enters only the + complementary-slackness test for `d = 0` being optimal. + + Returns: + The deposit-constrained endogenous cloud. + + """ + consumption = (discount_factor * w_a) ** (-1.0 / crra) + value = _crra_utility(consumption, crra) + discount_factor * post_decision_value + # KKT: liquid slack (a > 0) and `d = 0` optimal β€” the marginal gain from the + # first deposited dollar, `beta*w_b*(1 + chi)`, must not exceed the marginal + # value of the liquid dollar it costs, `u'(c) = beta*w_a`. + valid_region = (a > 0.0) & (w_b * (1.0 + match_rate) <= w_a) + return RegionCloud( + m_endog=a + consumption, + n_endog=b, + consumption=consumption, + deposit=jnp.zeros_like(consumption), + value=value, + value_grad_m=discount_factor * w_a, + value_grad_n=discount_factor * w_b, + valid_region=valid_region, + ) + + +def invert_acon_cloud( + *, + consumption: FloatND, + b: FloatND, + post_decision_value_at_zero_a: FloatND, + w_b_at_zero_a: FloatND, + w_a_at_zero_a: FloatND, + discount_factor: ScalarFloat | float, + crra: ScalarFloat | float, + match_rate: ScalarFloat | float, +) -> RegionCloud: + """Invert the deposit FOC on the borrowing-constrained region (`acon`, `a = 0`). + + Where the liquid borrowing constraint binds the liquid post-decision balance is + pinned at `a = 0`, so the liquid Euler holds only with a non-negative multiplier and + cannot be inverted for consumption. Instead the region is parameterized by a + consumption sweep against the pension post-decision balance `b` at `a = 0`: + consumption is exogenous, and the still-interior deposit is recovered from its FOC + `u'(c) = beta * w_b * (1 + chi / (1 + d))`. The liquid budget at the corner is + `m = c + d` (no liquid savings), and the pension budget inverts to + `n = b - d - chi*log(1 + d)`. + + Args: + consumption: Exogenous consumption sweep at each node (`a = 0` corner). + b: Pension post-decision balance at each node (evaluated at `a = 0`). + post_decision_value_at_zero_a: Post-decision value `w(0, b)` at each node. + w_b_at_zero_a: Post-decision value gradient w.r.t. `b`, at `a = 0`. + w_a_at_zero_a: Post-decision value gradient w.r.t. `a`, at `a = 0`; enters + only the complementary-slackness test for the binding borrowing limit. + discount_factor: Discount factor. + crra: Coefficient of relative risk aversion. + match_rate: Pension employer-match coefficient `chi`. + + Returns: + The borrowing-constrained endogenous cloud. + + """ + marginal_utility = consumption ** (-crra) + # Deposit FOC at the corner: u'(c) = beta*w_b*(1 + chi/(1 + d)); solve for d. + deposit_ratio = marginal_utility / (discount_factor * w_b_at_zero_a) + deposit = match_rate / (deposit_ratio - 1.0) - 1.0 + value = ( + _crra_utility(consumption, crra) + + discount_factor * post_decision_value_at_zero_a + ) + # KKT: the borrowing limit binds with a non-negative multiplier, i.e. the agent + # would consume more liquid if it could (`u'(c) >= beta*w_a` at a = 0), and the + # deposit stays interior (`d > 0`). + valid_region = (marginal_utility >= discount_factor * w_a_at_zero_a) & ( + deposit > 0.0 + ) + return RegionCloud( + # a = 0 -> m = c + d; pension budget inverts as in the unconstrained region. + m_endog=consumption + deposit, + n_endog=b - deposit - match_rate * jnp.log1p(deposit), + consumption=consumption, + deposit=deposit, + value=value, + # At the binding budget the marginal value of liquid wealth is the common + # marginal value u'(c) (equal to the deposit FOC's right-hand side). + value_grad_m=marginal_utility, + value_grad_n=discount_factor * w_b_at_zero_a, + valid_region=valid_region, + ) + + +def invert_con_cloud( + *, + consumption: FloatND, + b: FloatND, + post_decision_value_at_zero_a: FloatND, + w_b_at_zero_a: FloatND, + w_a_at_zero_a: FloatND, + discount_factor: ScalarFloat | float, + crra: ScalarFloat | float, + match_rate: ScalarFloat | float, +) -> RegionCloud: + """Build the fully-constrained corner cloud (`con`, `a = 0` and `d = 0`). + + Where both the borrowing constraint and the deposit lower bound bind, neither FOC + holds with equality and there is nothing to invert: the agent consumes its entire + liquid budget (`m = c`, since `a = 0` and `d = 0`) and the pension is unchanged + (`n = b`). The region is the deep-constrained corner of the state space, + parameterized by a consumption sweep against the pension balance at `a = 0`. + + Args: + consumption: Exogenous consumption sweep at each node (`m = c` at the corner). + b: Pension post-decision balance at each node (`n = b`, no deposit). + post_decision_value_at_zero_a: Post-decision value `w(0, b)` at each node. + w_b_at_zero_a: Post-decision value gradient w.r.t. `b`, at `a = 0`. + w_a_at_zero_a: Post-decision value gradient w.r.t. `a`, at `a = 0`; enters + only the complementary-slackness test for the binding borrowing limit. + discount_factor: Discount factor. + crra: Coefficient of relative risk aversion. + match_rate: Pension employer-match coefficient `chi`; enters only the + complementary-slackness test for `d = 0` being optimal. + + Returns: + The fully-constrained endogenous cloud. + + """ + marginal_utility = consumption ** (-crra) + value = ( + _crra_utility(consumption, crra) + + discount_factor * post_decision_value_at_zero_a + ) + # KKT: both corners bind with non-negative multipliers β€” the borrowing limit + # (`u'(c) >= beta*w_a` at a = 0) and the deposit lower bound (`d = 0` optimal, + # `u'(c) >= beta*w_b*(1 + chi)` at a = 0). + valid_region = (marginal_utility >= discount_factor * w_a_at_zero_a) & ( + marginal_utility >= discount_factor * w_b_at_zero_a * (1.0 + match_rate) + ) + return RegionCloud( + m_endog=consumption, + n_endog=b, + consumption=consumption, + deposit=jnp.zeros_like(consumption), + value=value, + # All extra liquid is consumed at the corner, so dV/dm = u'(c). + value_grad_m=marginal_utility, + value_grad_n=discount_factor * w_b_at_zero_a, + valid_region=valid_region, + ) + + +def _crra_utility(consumption: FloatND, crra: ScalarFloat | float) -> FloatND: + return jnp.where( + crra == 1.0, + jnp.log(consumption), + consumption ** (1.0 - crra) / (1.0 - crra), + ) diff --git a/src/_lcm/egm/two_asset_objective.py b/src/_lcm/egm/two_asset_objective.py new file mode 100644 index 000000000..d83a032b9 --- /dev/null +++ b/src/_lcm/egm/two_asset_objective.py @@ -0,0 +1,96 @@ +"""The Bellman-objective evaluator for the two-asset G2EGM upper envelope. + +The upper envelope ranks interpolated candidate policies by **recomputing** the Bellman +objective, never by transporting an interpolated value. For the two-asset model the +objective of a policy $(c, d)$ at a current state $(m, n)$ is + +$$Q(m, n; c, d) = u(c) + \\beta\\, W(a, b),$$ + +with the post-decision balances reconstructed from the budget identities +$a = m - c - d$ and $b = n + d + \\chi\\log(1 + d)$, and $W$ read by bilinear +interpolation off the regular post-decision $(a, b)$ value grid. A candidate is +feasible only when $c > 0$, $d \\ge 0$, $a \\ge 0$, and $b \\ge 0$ β€” a policy +interpolated (or extrapolated) outside its segment can violate these, so the evaluator +returns the feasibility flag the envelope masks on before either maximum. +""" + +from collections.abc import Callable + +import jax.numpy as jnp +from jax.scipy.ndimage import map_coordinates + +from lcm.typing import BoolND, Float1D, Float2D, FloatND, ScalarFloat + + +def build_two_asset_objective( + *, + post_decision_value: Float2D, + a_grid: Float1D, + b_grid: Float1D, + discount_factor: ScalarFloat | float, + crra: ScalarFloat | float, + match_rate: ScalarFloat | float, +) -> Callable[[Float1D, Float1D], tuple[FloatND, BoolND]]: + """Build the `(state, policy) -> (value, feasible)` objective evaluator. + + Args: + post_decision_value: Post-decision value `W(a, b)` on the regular post-decision + grid, shape `(len(a_grid), len(b_grid))`. + a_grid: Regular liquid post-decision grid (ascending, evenly spaced). + b_grid: Regular pension post-decision grid (ascending, evenly spaced). + discount_factor: Discount factor `beta`. + crra: Coefficient of relative risk aversion `rho`. + match_rate: Pension employer-match coefficient `chi`. + + Returns: + A callable mapping a state `(m, n)` and policy `(c, d)` to the recomputed + Bellman value and a feasibility flag. The value is finite even for an + infeasible candidate (consumption is clamped before the utility), so the + envelope can mask on the flag without NaN poisoning. + + """ + a_origin = a_grid[0] + a_step = a_grid[1] - a_grid[0] + b_origin = b_grid[0] + b_step = b_grid[1] - b_grid[0] + + def objective(state: Float1D, policy: Float1D) -> tuple[FloatND, BoolND]: + consumption, deposit = policy[0], policy[1] + liquid_post = state[0] - consumption - deposit + pension_post = state[1] + deposit + match_rate * jnp.log1p(deposit) + a_index = (liquid_post - a_origin) / a_step + b_index = (pension_post - b_origin) / b_step + post_value = map_coordinates( + post_decision_value, + [jnp.atleast_1d(a_index), jnp.atleast_1d(b_index)], + order=1, + mode="nearest", + )[0] + # Clamp consumption before the utility so an infeasible candidate's value is + # finite (it is masked out by `feasible`), never NaN. + safe_consumption = jnp.where(consumption > 0.0, consumption, 1.0) + value = _crra_utility(safe_consumption, crra) + discount_factor * post_value + # The continuation reader clamps post-states to the grid boundary, so a + # candidate whose reconstructed `(a, b)` leaves the post-decision grid gets a + # fabricated continuation. Require the post-state inside the grid (subsuming the + # economic `a >= 0`, `b >= 0` floors when the grid starts there), so only + # candidates with a genuine continuation value are eligible for the envelope. + feasible = ( + (consumption > 0.0) + & (deposit >= 0.0) + & (liquid_post >= a_grid[0]) + & (liquid_post <= a_grid[-1]) + & (pension_post >= b_grid[0]) + & (pension_post <= b_grid[-1]) + ) + return value, feasible + + return objective + + +def _crra_utility(consumption: FloatND, crra: ScalarFloat | float) -> FloatND: + return jnp.where( + crra == 1.0, + jnp.log(consumption), + consumption ** (1.0 - crra) / (1.0 - crra), + ) diff --git a/src/_lcm/egm/two_asset_post_decision.py b/src/_lcm/egm/two_asset_post_decision.py new file mode 100644 index 000000000..4b4066a4f --- /dev/null +++ b/src/_lcm/egm/two_asset_post_decision.py @@ -0,0 +1,136 @@ +"""Post-decision value and gradients for the deterministic two-asset model. + +The inverse-Euler step consumes the post-decision value $w(a, b)$ and its gradients +$w_a, w_b$. For the deterministic two-asset model the post-decision value is next +period's value read at the transformed states $m' = (1 + r^a)\\,a + \\text{wage}$ and +$n' = (1 + r^b)\\,b$ (liquid and pension carry forward at their gross returns), and +the gradients follow by the chain rule: $w_a = \\partial_m V'\\,(1 + r^a)$, +$w_b = \\partial_n V'\\,(1 + r^b)$. + +Value and gradient come from the same bilinear interpolant of $V'$ on the regular +$(m, n)$ state grid, so they are mutually consistent (the gradient is the derivative +of the value read). The interpolation is exact for an affine $V'$. +""" + +from typing import NamedTuple + +import jax +import jax.numpy as jnp +from jax.scipy.ndimage import map_coordinates + +from lcm.typing import Float1D, FloatND, ScalarFloat + + +class PostDecision(NamedTuple): + """Post-decision value and gradients on a post-decision $(a, b)$ grid.""" + + value: FloatND + """Post-decision value `w(a, b) = V'(m'(a), n'(b))`.""" + grad_a: FloatND + """`w_a = d/da V'(m'(a), n'(b))`.""" + grad_b: FloatND + """`w_b = d/db V'(m'(a), n'(b))`.""" + + +def post_decision_value_and_grad( + *, + next_value: FloatND, + m_grid: Float1D, + n_grid: Float1D, + a: FloatND, + b: FloatND, + return_liquid: ScalarFloat | float, + return_pension: ScalarFloat | float, + wage: ScalarFloat | float, +) -> PostDecision: + """Evaluate the post-decision value and its gradients on the `(a, b)` grid. + + Args: + next_value: Next period's value on the regular `(m, n)` grid, shape + `(len(m_grid), len(n_grid))`. + m_grid: Regular liquid-state grid (ascending, evenly spaced). + n_grid: Regular pension-state grid (ascending, evenly spaced). + a: Liquid post-decision balance at each node. + b: Pension post-decision balance at each node. + return_liquid: Liquid gross return minus one, `r^a`. + return_pension: Pension gross return minus one, `r^b`. + wage: Deterministic labor income added to next-period liquid wealth. + + Returns: + Post-decision value and gradients, one entry per `(a, b)` node. + + """ + + def value_at(a_node: FloatND, b_node: FloatND) -> FloatND: + m_next = (1.0 + return_liquid) * a_node + wage + n_next = (1.0 + return_pension) * b_node + m_index = (m_next - m_grid[0]) / (m_grid[1] - m_grid[0]) + n_index = (n_next - n_grid[0]) / (n_grid[1] - n_grid[0]) + return map_coordinates(next_value, [m_index, n_index], order=1, mode="nearest") + + flat_a = a.reshape(-1) + flat_b = b.reshape(-1) + value = jax.vmap(value_at)(flat_a, flat_b) + grad_a, grad_b = jax.vmap(jax.grad(value_at, argnums=(0, 1)))(flat_a, flat_b) + return PostDecision( + value=value.reshape(a.shape), + grad_a=grad_a.reshape(a.shape), + grad_b=grad_b.reshape(a.shape), + ) + + +def post_decision_value_and_grad_retiring( + *, + next_value_retired: Float1D, + next_marginal_retired: Float1D, + liquid_grid: Float1D, + a: FloatND, + b: FloatND, + return_liquid: ScalarFloat | float, + pension_payout_return: ScalarFloat | float, + retirement_income: ScalarFloat | float, +) -> PostDecision: + """Post-decision value and gradients at the working->retired boundary. + + On the working->retired transition the pension is paid out as a lump sum, so both + post-decision balances feed a single retired liquid state + $\\ell' = (1 + r^a)\\,a + \\pi\\,b + y_{\\text{ret}}$ ($\\pi$ the pension payout + return, $y_{\\text{ret}}$ the first retirement income). The post-decision value is + the 1-D retired value read there, $w(a, b) = V_{\\text{ret}}(\\ell')$, and the + gradients follow by the chain rule with the **carried** retired marginal + $V'_{\\text{ret}}$ (exact, not a finite difference of the value array): + $w_a = (1 + r^a)\\,V'_{\\text{ret}}$ and $w_b = \\pi\\,V'_{\\text{ret}}$. + + Args: + next_value_retired: Next period's retired value on `liquid_grid`, shape + `(len(liquid_grid),)`. + next_marginal_retired: Next period's retired marginal value of liquid on + `liquid_grid`, shape `(len(liquid_grid),)`. + liquid_grid: Regular retired liquid-state grid (ascending, evenly spaced). + a: Liquid post-decision balance at each node. + b: Pension post-decision balance at each node. + return_liquid: Liquid gross return minus one, `r^a`. + pension_payout_return: Factor the pension balance is paid out at on retirement. + retirement_income: First retirement income added to the retired liquid state. + + Returns: + Post-decision value and gradients, one entry per `(a, b)` node. + + """ + gross_return = 1.0 + return_liquid + origin = liquid_grid[0] + step = liquid_grid[1] - liquid_grid[0] + + def read_at(liquid_next: FloatND, values: Float1D) -> FloatND: + index = (liquid_next - origin) / step + return map_coordinates(values, [jnp.atleast_1d(index)], order=1, mode="nearest") + + liquid_next = gross_return * a + pension_payout_return * b + retirement_income + flat_liquid = liquid_next.reshape(-1) + value = read_at(flat_liquid, next_value_retired) + marginal = read_at(flat_liquid, next_marginal_retired) + return PostDecision( + value=value.reshape(a.shape), + grad_a=(gross_return * marginal).reshape(a.shape), + grad_b=(pension_payout_return * marginal).reshape(a.shape), + ) diff --git a/src/_lcm/egm/two_asset_segment_mesh.py b/src/_lcm/egm/two_asset_segment_mesh.py new file mode 100644 index 000000000..983ee68eb --- /dev/null +++ b/src/_lcm/egm/two_asset_segment_mesh.py @@ -0,0 +1,53 @@ +"""Build a triangulated `SegmentMesh` from a constraint segment's candidate cloud. + +A region inverse (`two_asset_inverse`) returns a `RegionCloud` whose fields are shaped +like the segment's own regular source grid β€” the post-decision $(a, b)$ grid for +`ucon`/`dcon`, or the $(c, b)$ grid at $a = 0$ for `acon`/`con`. The upper envelope +needs that cloud as a triangulated mesh in the current-state $(m, n)$ plane: the nodes +are the cloud's endogenous states and policies, the triangles are the diagonal split of +the source cells, and a node is invalid when its endogenous state is non-finite or its +consumption is non-positive (an off-grid or NaN-inverse node). + +The builder is identical for every segment β€” only the cloud's 2-D source shape is read, +not its coordinates β€” so the heterogeneous parameterization of the regions is preserved +while the geometric output is uniform. +""" + +import jax.numpy as jnp + +from _lcm.egm.mesh_envelope import SegmentMesh +from _lcm.egm.mesh_geometry import triangulate_regular_grid +from _lcm.egm.two_asset_inverse import RegionCloud + + +def build_segment_mesh(*, cloud: RegionCloud, region_label: int) -> SegmentMesh: + """Triangulate a region's candidate cloud into a `SegmentMesh`. + + Args: + cloud: The region inverse's endogenous cloud, fields shaped like the segment's + 2-D source grid `(n_rows, n_cols)`. + region_label: Which KKT segment produced the cloud. + + Returns: + The segment's triangulated mesh: endogenous `(m, n)` node states, `(c, d)` node + policies, the source grid's triangle connectivity, and a per-node validity mask + (finite endogenous state and positive consumption). + + """ + n_rows, n_cols = cloud.m_endog.shape + m_endog = cloud.m_endog.reshape(-1) + n_endog = cloud.n_endog.reshape(-1) + consumption = cloud.consumption.reshape(-1) + valid_node = ( + jnp.isfinite(m_endog) + & jnp.isfinite(n_endog) + & (consumption > 0.0) + & cloud.valid_region.reshape(-1) + ) + return SegmentMesh( + region_label=region_label, + node_state=jnp.stack([m_endog, n_endog], axis=1), + node_policy=jnp.stack([consumption, cloud.deposit.reshape(-1)], axis=1), + simplices=triangulate_regular_grid(n_rows=n_rows, n_cols=n_cols), + valid_node=valid_node, + ) diff --git a/src/_lcm/egm/two_asset_step.py b/src/_lcm/egm/two_asset_step.py new file mode 100644 index 000000000..9bdfd1490 --- /dev/null +++ b/src/_lcm/egm/two_asset_step.py @@ -0,0 +1,84 @@ +"""One backward 2-D EGM step for the two-asset model (unconstrained interior). + +Assembles the verified pieces into a single period of the multidimensional EGM +solve: from next period's value on the regular `(m, n)` grid, compute the +post-decision value and gradients, invert the Euler equations to the endogenous +cloud, and rasterize that cloud back onto the regular `(m, n)` grid with the +inverse-bilinear locator. This is the `ucon` (single-segment) case β€” no envelope. + +Where the regular target is outside the endogenous cloud (the corner where the +borrowing or deposit constraint binds), the locator falls back to the nearest +boundary cell, so the published value there is an extrapolation rather than the +constrained solution; the value matches a dense grid-search solve only on the +unconstrained interior the cloud covers. +""" + +import jax.numpy as jnp + +from _lcm.egm.cell_locator import locate_in_quad_mesh, read_bilinear +from _lcm.egm.two_asset_inverse import invert_ucon_cloud +from _lcm.egm.two_asset_post_decision import post_decision_value_and_grad +from lcm.typing import Float1D, FloatND + + +def egm_step( + *, + next_value: FloatND, + m_grid: Float1D, + n_grid: Float1D, + a_grid: Float1D, + b_grid: Float1D, + discount_factor: float, + crra: float, + match_rate: float, + return_liquid: float, + return_pension: float, + wage: float, +) -> FloatND: + """Solve one period of the two-asset model by 2-D EGM on the unconstrained region. + + Args: + next_value: Next period's value on the regular `(m, n)` grid. + m_grid: Regular liquid-state grid. + n_grid: Regular pension-state grid. + a_grid: Liquid post-decision grid. + b_grid: Pension post-decision grid. + discount_factor: Discount factor. + crra: Coefficient of relative risk aversion. + match_rate: Pension employer-match coefficient. + return_liquid: Liquid net return `r^a`. + return_pension: Pension net return `r^b`. + wage: Deterministic labor income. + + Returns: + This period's value on the regular `(m, n)` grid. + + """ + a_mesh, b_mesh = jnp.meshgrid(a_grid, b_grid, indexing="ij") + post = post_decision_value_and_grad( + next_value=next_value, + m_grid=m_grid, + n_grid=n_grid, + a=a_mesh, + b=b_mesh, + return_liquid=return_liquid, + return_pension=return_pension, + wage=wage, + ) + cloud = invert_ucon_cloud( + a=a_mesh, + b=b_mesh, + w_a=post.grad_a, + w_b=post.grad_b, + post_decision_value=post.value, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + ) + m_mesh, n_mesh = jnp.meshgrid(m_grid, n_grid, indexing="ij") + queries = jnp.stack([m_mesh.reshape(-1), n_mesh.reshape(-1)], axis=1) + located = locate_in_quad_mesh( + m_image=cloud.m_endog, n_image=cloud.n_endog, queries=queries + ) + read = read_bilinear(node_values=cloud.value, located=located) + return read.value.reshape(m_mesh.shape) diff --git a/src/_lcm/egm/upper_envelope/__init__.py b/src/_lcm/egm/upper_envelope/__init__.py new file mode 100644 index 000000000..b9ba5c29a --- /dev/null +++ b/src/_lcm/egm/upper_envelope/__init__.py @@ -0,0 +1,412 @@ +"""Upper-envelope refinement of EGM candidate solutions. + +Discrete choices make the EGM candidate value correspondence multi-valued in +non-concave regions; the algorithms here select the upper envelope and drop +dominated candidates. The EGM step obtains its backend through +`get_upper_envelope`, so additional algorithms slot in without touching the +step itself. Currently implemented: + +- the Fast Upper-Envelope Scan (`_lcm.egm.upper_envelope.fues`), a sequential + scan that inserts exact segment-crossing points, +- the Rooftop-Cut algorithm (`_lcm.egm.upper_envelope.rfc`), a parallel + dominance test that only deletes points (no crossing insertion) and + generalizes to multidimensional endogenous grids, and +- the local-upper-bound brute method (`_lcm.egm.upper_envelope.ltm`), an + $O(K^2)$ dense segment scan that evaluates the envelope at every candidate + abscissa (the quadratic baseline of Dobrescu & Shanker 2026), and +- HARK's EGM upper envelope (`_lcm.egm.upper_envelope.mss`), a left-to-right + sweep that keeps the max-value branch at every abscissa *and* inserts the + exact segment-crossing point (the `MSS` method of Dobrescu & Shanker 2026). + +All backends share one signature: they consume the candidate +`(endog_grid, policy, value)` rows plus the candidate supgradient +`marginal_utility` ($\\mu = \\partial v / \\partial R$, exact by the envelope +theorem) and return a NaN-padded weakly-ascending refined `(grid, policy, +value)` triple plus the kept-point count. FUES, LTM, and MSS ignore the +supgradient (they recover slopes from the segments); RFC uses it to build each +point's tangent. +""" + +from collections.abc import Callable +from typing import Protocol, runtime_checkable + +import jax.numpy as jnp + +from _lcm.egm.interp import prepare_padded_grid +from _lcm.egm.upper_envelope.fues import ( + QueryBracket, + refine_to_bracket, +) +from _lcm.egm.upper_envelope.fues import ( + refine_envelope as refine_envelope_fues, +) +from _lcm.egm.upper_envelope.ltm import refine_envelope as refine_envelope_ltm +from _lcm.egm.upper_envelope.mss import refine_envelope as refine_envelope_mss +from _lcm.egm.upper_envelope.rfc import refine_envelope as refine_envelope_rfc +from lcm.solvers import DCEGM +from lcm.typing import Float1D, ScalarFloat, ScalarInt + + +@runtime_checkable +class UpperEnvelopeBackend(Protocol): + """Refine one row of EGM candidates to its upper envelope.""" + + def __call__( + self, + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, + ) -> tuple[Float1D, Float1D, Float1D, ScalarInt]: + """Return refined (grid, policy, value) rows and the kept-point count. + + The supgradient `marginal_utility` carries $\\mu = \\partial v / + \\partial R$ per candidate β€” the exact value-row slope by the envelope + theorem. The refined rows are NaN-padded to a static length; a + kept-point count exceeding that length signals overflow (the rows then + hold a truncated prefix of the envelope). + """ + ... + + +def get_upper_envelope(*, solver: DCEGM, n_refined: int) -> UpperEnvelopeBackend: + """Build the upper-envelope backend selected by the solver configuration. + + Args: + solver: The regime's DC-EGM solver configuration; `upper_envelope` + selects the backend and the `fues_*` / `rfc_*` fields parametrize + it. + n_refined: Static length of the refined output rows. + + Returns: + The configured backend. + + """ + if solver.upper_envelope == "fues": + + def fues_backend( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, + ) -> tuple[Float1D, Float1D, Float1D, ScalarInt]: + """Run the FUES scan with the solver's thresholds. + + FUES recovers segment slopes from its own forward scan, so the + candidate supgradient is not consumed. + """ + del marginal_utility + return refine_envelope_fues( + endog_grid=endog_grid, + policy=policy, + value=value, + n_refined=n_refined, + jump_thresh=solver.fues_jump_thresh, + n_points_to_scan=solver.fues_n_points_to_scan, + scan_unroll=solver.fues_scan_unroll, + ) + + return fues_backend + + if solver.upper_envelope == "rfc": + + def rfc_backend( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, + ) -> tuple[Float1D, Float1D, Float1D, ScalarInt]: + """Run the rooftop cut with the solver's thresholds.""" + return refine_envelope_rfc( + endog_grid=endog_grid, + policy=policy, + value=value, + marginal_utility=marginal_utility, + n_refined=n_refined, + search_radius=solver.rfc_search_radius, + jump_thresh=solver.rfc_jump_thresh, + ) + + return rfc_backend + + if solver.upper_envelope == "ltm": + + def ltm_backend( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, + ) -> tuple[Float1D, Float1D, Float1D, ScalarInt]: + """Run the brute local-upper-bound scan. + + LTM recovers segment slopes from the candidate chain, so the + candidate supgradient is not consumed. + """ + del marginal_utility + return refine_envelope_ltm( + endog_grid=endog_grid, + policy=policy, + value=value, + n_refined=n_refined, + ) + + return ltm_backend + + if solver.upper_envelope == "mss": + + def mss_backend( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, + ) -> tuple[Float1D, Float1D, Float1D, ScalarInt]: + """Run HARK's EGM upper-envelope sweep with crossing insertion. + + MSS recovers segment slopes from the candidate chain, so the + candidate supgradient is not consumed. + """ + del marginal_utility + return refine_envelope_mss( + endog_grid=endog_grid, + policy=policy, + value=value, + n_refined=n_refined, + ) + + return mss_backend + + msg = f"Unknown upper-envelope backend: {solver.upper_envelope!r}." + raise ValueError(msg) + + +def get_bracket_finder(*, solver: DCEGM, n_refined: int) -> Callable[..., QueryBracket]: + """Build the single-query bracket finder for the asset-row solve. + + The geometry-only counterpart of `get_upper_envelope` for asset-row mode, + where the refined envelope is read at exactly one query per node: it returns + the two bracketing envelope nodes (plus the first node and the kept count). + It is deliberately not on the `UpperEnvelopeBackend` Protocol β€” the backend + returns envelope geometry; the asset-row module owns the EGM economics + (utility gradients, the borrowing limit, the constrained floor). + + The backends differ in how they reach that bracket: + + - `"fues"` streams it: `refine_to_bracket` runs the FUES scan and folds each + step's emissions into an O(1) bracket-capture carry, so the NaN-padded + `n_pad` envelope never materializes. + - `"rfc"`, `"ltm"`, and `"mss"` do *not* stream: their dense scans have no + sequential carry to fold a bracket out of, so the finder materializes the + full refined envelope and locates the same + `searchsorted(side="right")`-clamped bracket the row path would read. The + published `(value, policy)` is therefore identical to a + full-envelope-then-interpolate, but these asset-row paths do *not* yet get + refine-to-query's `n_pad` memory win β€” a streamed dense bracket finder is + future work. + + Args: + solver: The regime's DC-EGM solver configuration; the `fues_*` / `rfc_*` + fields parametrize the scan. + n_refined: Static length of the refined envelope row the dense finder + materializes before locating the bracket (unused by FUES, which + streams). This is the `n_pad` overflow threshold the asset-row + publish compares `n_kept` against. + + Returns: + The configured bracket finder. + + """ + if solver.upper_envelope == "fues": + + def fues_bracket_finder( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, + x_query: ScalarFloat, + ) -> QueryBracket: + """Run the streaming FUES scan with the solver's thresholds. + + FUES recovers segment slopes from its own forward scan, so the + candidate supgradient is not consumed. + """ + del marginal_utility + return refine_to_bracket( + endog_grid=endog_grid, + policy=policy, + value=value, + x_query=x_query, + jump_thresh=solver.fues_jump_thresh, + n_points_to_scan=solver.fues_n_points_to_scan, + scan_unroll=solver.fues_scan_unroll, + ) + + return fues_bracket_finder + + if solver.upper_envelope == "rfc": + + def rfc_bracket_finder( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, + x_query: ScalarFloat, + ) -> QueryBracket: + """Locate the query bracket from RFC's full refined envelope. + + Runs the rooftop cut to a full NaN-padded envelope row, then reads + the bracket the row path would: the `searchsorted(side="right")` + pair clamped to `[1, max(n_kept - 1, 1)]` (the + `interp_on_prepared_grid` rule), so the published value cannot + diverge from full-envelope-then-interpolate. + """ + refined_grid, refined_policy, refined_value, n_kept = refine_envelope_rfc( + endog_grid=endog_grid, + policy=policy, + value=value, + marginal_utility=marginal_utility, + n_refined=n_refined, + search_radius=solver.rfc_search_radius, + jump_thresh=solver.rfc_jump_thresh, + ) + return _bracket_from_refined_row( + refined_grid=refined_grid, + refined_policy=refined_policy, + refined_value=refined_value, + n_kept=n_kept, + x_query=x_query, + ) + + return rfc_bracket_finder + + if solver.upper_envelope == "ltm": + + def ltm_bracket_finder( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, + x_query: ScalarFloat, + ) -> QueryBracket: + """Locate the query bracket from LTM's full refined envelope. + + Runs the brute scan to a full NaN-padded envelope row, then reads + the bracket the row path would: the `searchsorted(side="right")` + pair clamped to `[1, max(n_kept - 1, 1)]` (the + `interp_on_prepared_grid` rule), so the published value cannot + diverge from full-envelope-then-interpolate. Like RFC, LTM has no + sequential carry to stream a bracket from, so it does not get + refine-to-query's `n_pad` memory win. + """ + del marginal_utility + refined_grid, refined_policy, refined_value, n_kept = refine_envelope_ltm( + endog_grid=endog_grid, + policy=policy, + value=value, + n_refined=n_refined, + ) + return _bracket_from_refined_row( + refined_grid=refined_grid, + refined_policy=refined_policy, + refined_value=refined_value, + n_kept=n_kept, + x_query=x_query, + ) + + return ltm_bracket_finder + + if solver.upper_envelope == "mss": + + def mss_bracket_finder( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, + x_query: ScalarFloat, + ) -> QueryBracket: + """Locate the query bracket from MSS's full refined envelope. + + Runs the HARK sweep to a full NaN-padded envelope row, then reads the + bracket the row path would: the `searchsorted(side="right")` pair + clamped to `[1, max(n_kept - 1, 1)]` (the `interp_on_prepared_grid` + rule), so the published value cannot diverge from + full-envelope-then-interpolate. Like RFC and LTM, MSS has no + sequential carry to stream a bracket from, so it does not get + refine-to-query's `n_pad` memory win. + """ + del marginal_utility + refined_grid, refined_policy, refined_value, n_kept = refine_envelope_mss( + endog_grid=endog_grid, + policy=policy, + value=value, + n_refined=n_refined, + ) + return _bracket_from_refined_row( + refined_grid=refined_grid, + refined_policy=refined_policy, + refined_value=refined_value, + n_kept=n_kept, + x_query=x_query, + ) + + return mss_bracket_finder + + msg = f"Unknown upper-envelope backend: {solver.upper_envelope!r}." + raise ValueError(msg) + + +def _bracket_from_refined_row( + *, + refined_grid: Float1D, + refined_policy: Float1D, + refined_value: Float1D, + n_kept: ScalarInt, + x_query: ScalarFloat, +) -> QueryBracket: + """Read the query bracket off a full NaN-padded refined envelope row. + + Reproduces the asset-row publish's bracket location node-for-node by reusing + the `interp_on_prepared_grid` rule: `searchsorted(search_grid, x_query, + side="right")` clamped to `[1, max(valid_length - 1, 1)]`, with the NaN tail + treated as $+\\infty$. The gathered `(lower, upper)` pair, `first_grid`, and + `n_kept` are exactly what `publish_node_from_bracket` consumes, so a + full-envelope-then-interpolate and this bracket read publish identical + `(value, policy)`. + + Args: + refined_grid: Refined endogenous grid row (NaN-padded tail). + refined_policy: Refined policy row, NaN-padded in lockstep. + refined_value: Refined value row, NaN-padded in lockstep. + n_kept: Number of envelope points kept; `> n_pad` signals overflow. + x_query: The single point at which the envelope is read. + + Returns: + The query bracket. + + """ + search_grid, valid_length = prepare_padded_grid(refined_grid) + upper = jnp.clip( + jnp.searchsorted(search_grid, x_query, side="right"), + 1, + jnp.maximum(valid_length - 1, 1), + ).astype(jnp.int32) + lower = upper - 1 + dtype = refined_grid.dtype + return QueryBracket( + lower_grid=refined_grid[lower].astype(dtype), + upper_grid=refined_grid[upper].astype(dtype), + lower_policy=refined_policy[lower].astype(dtype), + upper_policy=refined_policy[upper].astype(dtype), + lower_value=refined_value[lower].astype(dtype), + upper_value=refined_value[upper].astype(dtype), + first_grid=refined_grid[0].astype(dtype), + n_kept=n_kept, + ) diff --git a/src/_lcm/egm/upper_envelope/fues.py b/src/_lcm/egm/upper_envelope/fues.py new file mode 100644 index 000000000..78a7cee80 --- /dev/null +++ b/src/_lcm/egm/upper_envelope/fues.py @@ -0,0 +1,1099 @@ +"""Fast Upper-Envelope Scan (FUES) over EGM candidate solutions. + +Implements the upper-envelope refinement of Dobrescu, L. I., & Shanker, A. +(2022). Fast Upper-Envelope Scan for Discrete-Continuous Dynamic Programming. +SSRN 4181302. + +Adapted from the `OpenSourceEconomics/upper-envelope` package (Apache-2.0, +Β© The Upper-Envelope Authors) and substantially modified for pylcm's JAX kernel. + +Inverting the Euler equation in models with discrete choices yields a value +*correspondence*: in non-concave regions, several candidate points share a +neighborhood of the endogenous grid, each lying on a different choice-specific +value segment. `refine_envelope` scans the candidates once, in ascending grid +order, and keeps only the points on the upper envelope: + +- Candidates on a different segment than the last kept point are detected via + the implied savings $A = R - c$: the segments differ iff + $|\\Delta A / \\Delta R|$ exceeds `jump_thresh`. +- Dominated candidates are dropped (value decreases, savings non-monotone with + a falling value gradient, or the candidate lies below the continuation of + the current segment found by a bounded forward scan). +- Where two kept segments cross, the linear intersection of the segments is + inserted twice β€” once with the left- and once with the right-extrapolated + policy β€” so the refined arrays remain weakly ascending and policy + discontinuities at kinks are preserved exactly. + +All shapes are static, so the kernel can be `jax.jit`-compiled and `jax.vmap`- +batched over a leading dimension of the candidate arrays. +""" + +from typing import NamedTuple + +import jax +import jax.numpy as jnp + +from lcm.typing import BoolND, Float1D, FloatND, ScalarBool, ScalarFloat, ScalarInt + + +class QueryBracket(NamedTuple): + """The two envelope nodes bracketing one query, plus the publish statics. + + The streamed counterpart of a full refined envelope row read at a single + query: instead of materializing the NaN-padded `n_pad` rows and locating + the bracket with `searchsorted(side="right")`, `refine_to_bracket` captures + only the bracketing pair directly during the scan. The arithmetic on the + pair is then identical to the row-then-interpolate path, so the published + value cannot diverge β€” only the bracket-finding differs. + + All fields are arrays so the struct threads through `jax.vmap`/`jax.lax.map`. + The `lower_*`/`upper_*` pair is already edge-clamped to a real node pair + (matching the reference's `clip(searchsorted, 1, max(n_kept - 1, 1))`): a + query below the first node brackets the first pair (weight 0 β‡’ lower value), + a query at or above the last node brackets the last pair (weight 1 β‡’ upper + value), and a query exactly on a duplicated kink abscissa brackets the right + copy as its lower node (the `side="right"` tie-break). + """ + + lower_grid: ScalarFloat + """Abscissa of the bracket's lower node.""" + upper_grid: ScalarFloat + """Abscissa of the bracket's upper node.""" + lower_policy: ScalarFloat + """Policy at the bracket's lower node.""" + upper_policy: ScalarFloat + """Policy at the bracket's upper node.""" + lower_value: ScalarFloat + """Value at the bracket's lower node.""" + upper_value: ScalarFloat + """Value at the bracket's upper node.""" + first_grid: ScalarFloat + """Abscissa of the lowest envelope node (the constrained-floor edge test).""" + n_kept: ScalarInt + """Number of envelope points kept; `> n_pad` signals overflow.""" + + +def _resolve_n_points_to_scan(n_points_to_scan: int | None, *, n_input: int) -> int: + """Resolve the exhaustive-scan sentinel to a concrete window width. + + `None` requests an exhaustive scan β€” every other candidate. That is the only + width proven correct when more than the window's worth of off-segment + candidates interleave between two points of one segment: a bounded window + then never reaches the segment's continuation and silently accepts the + interlopers. A finite value keeps the cheaper $O(\\text{width})$ scan at the + cost of that guarantee. `n_input` is a static shape, so the result stays a + Python int and the downstream `jnp.arange(n_points_to_scan)` stays + static-shape. + """ + if n_points_to_scan is None: + return max(n_input - 1, 1) + return n_points_to_scan + + +def refine_envelope( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + n_refined: int, + jump_thresh: float = 2.0, + n_points_to_scan: int | None = None, + segment_id: Float1D | None = None, + scan_unroll: int = 1, +) -> tuple[Float1D, Float1D, Float1D, ScalarInt]: + """Refine a candidate value correspondence to its upper envelope. + + The candidates may arrive in any order; they are sorted (NaN-stable) + ascending in `endog_grid` first. The refined arrays have static length + `n_refined`, hold the envelope points in weakly ascending grid order, and + are NaN-padded in the tail. Segment crossings contribute their linear + intersection point twice β€” same abscissa, left- and right-extrapolated + policy values. + + Args: + endog_grid: Candidate endogenous grid points (resources), any order. + policy: Candidate policy values at `endog_grid`. + value: Candidate value-correspondence points at `endog_grid`. + n_refined: Static length of the refined output arrays. + jump_thresh: Threshold on $|\\Delta A / \\Delta R|$ of the implied + savings $A = R - c$ above which two points are treated as lying on + different value-function segments. This is a heuristic, *not* a + theorem-level segment detector: a sound value must exceed the + within-segment savings-slope (Lipschitz) bound and lie below the + separated jump signal on the chosen grid, so it is model- and + grid-dependent. The default `2.0` suits the smooth-policy, + discrete-choice-kink models pylcm targets; a model with steep + continuous policies or genuine notches should set it deliberately + (or pass `segment_id`). + n_points_to_scan: Number of subsequent (or preceding) candidates the + bounded scans inspect when searching for the next point on a given + segment. `None` (the default) scans exhaustively β€” every other + candidate β€” which is the only width proven correct when more than + the window's worth of off-segment candidates interleave between two + points of one segment (a bounded window silently accepts the + interlopers). A finite value keeps the cheaper $O(\\text{width})$ + scan at the cost of that guarantee. + segment_id: Optional per-candidate segment/bracket label, aligned with + `endog_grid`. When supplied, two points lie on different segments + iff their policy jumps (above) *or* their labels differ β€” the + label-driven switch the FUES bracket indicator uses for genuine + discontinuities (tax notches) whose policy is locally flat. `None` + (the default) uses the policy-jump test alone. No pylcm model wires + a label yet: the constrained/interior join is a *continuous* concave + kink, not a value-segment switch, so labelling it would insert a + spurious crossing; this parameter is the hook for a future + notch/bracket model. + scan_unroll: Loop-unroll factor for the sequential `jax.lax.scan` over + candidates. Unrolling trades compile time for fewer loop-carry round + trips on accelerators; the refined output is identical across values. + + Returns: + Tuple of refined endogenous grid, refined policy, refined value (each + of length `n_refined`, NaN-padded), and the number of envelope points + `n_kept`. `n_kept > n_refined` signals overflow; the arrays then hold + a valid truncated prefix of the envelope. Callers must check the + counter rather than publish the truncated arrays silently β€” the EGM + step NaN-poisons its published rows on overflow so the solve loop's + NaN diagnostics name the offending (regime, period). + + """ + # Sort ascending in the endogenous grid, breaking ties by descending value + # so the maximal-value candidate leads each run of coincident abscissae; + # NaN grid points sort to the tail. Coincident abscissae with *unequal* + # values are not envelope kinks (those are inserted later, with equal + # value): the lower copies are dominated and collapsed away here β€” NaN-ed + # in place β€” before the scan, so a dominated duplicate can never reach the + # output and corrupt the index-keyed interpolation of a kink. + grid_key = jnp.where(jnp.isnan(endog_grid), jnp.inf, endog_grid) + value_key = jnp.where(jnp.isnan(value), -jnp.inf, value) + order = jnp.lexsort(jnp.stack([-value_key, grid_key])) + grid_sorted = endog_grid[order] + policy_sorted = policy[order] + value_sorted = value[order] + n_input = grid_sorted.shape[0] + n_points_to_scan = _resolve_n_points_to_scan(n_points_to_scan, n_input=n_input) + + # All-zero labels reduce the segment test to a no-op (`seg != seg` is always + # false, `seg == seg` always true), so the `segment_id is None` path is + # bit-identical to the policy-jump-only scan. + segment_sorted = ( + jnp.zeros_like(grid_sorted) + if segment_id is None + else segment_id[order].astype(grid_sorted.dtype) + ) + + # Pre-dedup copies: the dedup below collapses a coincident crossing to one + # branch, so the post-pass recovers the dropped branch's policy/slope here to + # re-insert the on-node dual-policy kink. + presort_grid = grid_sorted + presort_policy = policy_sorted + presort_value = value_sorted + + duplicate = jnp.concatenate( + [ + jnp.zeros((1,), dtype=bool), + (grid_sorted[1:] == grid_sorted[:-1]) & ~jnp.isnan(grid_sorted[1:]), + ] + ) + grid_sorted = jnp.where(duplicate, jnp.nan, grid_sorted) + policy_sorted = jnp.where(duplicate, jnp.nan, policy_sorted) + value_sorted = jnp.where(duplicate, jnp.nan, value_sorted) + + first_point = jnp.stack([grid_sorted[0], policy_sorted[0], value_sorted[0]]) + first_segment = segment_sorted[0] + # Carry layout: the two most recent envelope points, k then j, each as + # (grid, policy, value), then their segment labels (seg_k, seg_j). Initially + # both points are the first sorted candidate. + carry_init = jnp.concatenate( + [first_point, first_point, jnp.stack([first_segment, first_segment])] + ) + + def step( + carry: Float1D, idx: ScalarInt + ) -> tuple[Float1D, tuple[Float1D, Float1D, Float1D, ScalarInt]]: + """Delegate to `_inspect_candidate`; positional per `jax.lax.scan`.""" + return _inspect_candidate( + carry=carry, + idx=idx, + grid_sorted=grid_sorted, + policy_sorted=policy_sorted, + value_sorted=value_sorted, + segment_sorted=segment_sorted, + jump_thresh=jump_thresh, + n_points_to_scan=n_points_to_scan, + ) + + indices = jnp.arange(1, n_input, dtype=jnp.int32) + carry_final, (block_grid, block_policy, block_value, block_count) = jax.lax.scan( + step, carry_init, indices, unroll=scan_unroll + ) + + # Compact the per-step blocks: route each valid block row to its position + # in the refined arrays, NaN rows and overflow positions are dropped. + offsets = jnp.cumsum(block_count) - block_count + total = jnp.sum(block_count, dtype=jnp.int32) + slot = jnp.arange(3, dtype=jnp.int32) + positions = jnp.where( + slot[None, :] < block_count[:, None], + offsets[:, None] + slot[None, :], + n_refined, + ).ravel() + + refined_grid = jnp.full(n_refined, jnp.nan, dtype=grid_sorted.dtype) + refined_policy = jnp.full(n_refined, jnp.nan, dtype=policy_sorted.dtype) + refined_value = jnp.full(n_refined, jnp.nan, dtype=value_sorted.dtype) + refined_grid = refined_grid.at[positions].set(block_grid.ravel(), mode="drop") + refined_policy = refined_policy.at[positions].set(block_policy.ravel(), mode="drop") + refined_value = refined_value.at[positions].set(block_value.ravel(), mode="drop") + + # The last accepted point is still pending in the carry; emit it. + final_grid, final_policy, final_value = ( + carry_final[3], + carry_final[4], + carry_final[5], + ) + final_valid = ~jnp.isnan(final_grid) & ~jnp.isnan(final_value) + final_pos = jnp.where(final_valid, total, n_refined) + refined_grid = refined_grid.at[final_pos].set(final_grid, mode="drop") + refined_policy = refined_policy.at[final_pos].set(final_policy, mode="drop") + refined_value = refined_value.at[final_pos].set(final_value, mode="drop") + + n_kept = (total + final_valid).astype(jnp.int32) + + # The dedup keeps one branch per coincident node, so the scan's value row is + # exact but a node-aligned crossing carries only one branch's policy. Re-insert + # the dropped branch as the on-node dual-policy kink (left then right) so an + # off-node read recovers the right branch rather than interpolating across the + # policy discontinuity. + return _insert_node_crossings( + refined_grid=refined_grid, + refined_policy=refined_policy, + refined_value=refined_value, + n_kept=n_kept, + presort_grid=presort_grid, + presort_policy=presort_policy, + presort_value=presort_value, + segment_sorted=segment_sorted, + n_refined=n_refined, + n_points_to_scan=n_points_to_scan, + jump_thresh=jump_thresh, + ) + + +def _branch_value_slopes( + *, + grid: Float1D, + value: Float1D, + segment: Float1D, + n_points_to_scan: int, +) -> Float1D: + """Value slope of each candidate's branch from its nearest same-segment node. + + Inspects up to `n_points_to_scan` candidates either side (nearest first) and + takes the first finite, same-segment, non-coincident neighbour. A branch is + linear, so any such neighbour gives the exact segment slope; candidates with + no neighbour report `NaN`. + """ + n = grid.shape[0] + mags = 1 + jnp.arange(n_points_to_scan, dtype=jnp.int32) + offsets = jnp.stack([mags, -mags], axis=1).reshape(-1) + nbr_idx = jnp.arange(n, dtype=jnp.int32)[:, None] + offsets[None, :] + in_bounds = (nbr_idx >= 0) & (nbr_idx < n) + clipped = jnp.clip(nbr_idx, 0, n - 1) + nbr_grid = grid[clipped] + nbr_value = value[clipped] + nbr_segment = segment[clipped] + same = ( + in_bounds + & ~jnp.isnan(nbr_grid) + & (nbr_segment == segment[:, None]) + & (nbr_grid != grid[:, None]) + ) + found = jnp.any(same, axis=1) + first = jnp.argmax(same, axis=1) + neighbour_grid = jnp.take_along_axis(nbr_grid, first[:, None], axis=1)[:, 0] + neighbour_value = jnp.take_along_axis(nbr_value, first[:, None], axis=1)[:, 0] + delta = neighbour_grid - grid + safe_delta = jnp.where(delta == 0.0, 1.0, delta) + return jnp.where( + found & (delta != 0.0), (neighbour_value - value) / safe_delta, jnp.nan + ) + + +def _insert_node_crossings( + *, + refined_grid: Float1D, + refined_policy: Float1D, + refined_value: Float1D, + n_kept: ScalarInt, + presort_grid: Float1D, + presort_policy: Float1D, + presort_value: Float1D, + segment_sorted: Float1D, + n_refined: int, + n_points_to_scan: int, + jump_thresh: float, +) -> tuple[Float1D, Float1D, Float1D, ScalarInt]: + """Re-insert on-node crossing kinks dropped by the coincident-node dedup. + + A coincident pair of candidates with equal value but a branch switch is a + node-aligned crossing the dedup collapses to one branch. Recover both branch + policies (left then right, ordered by branch slope: the steeper branch wins + to the right), set the kept node to the left policy, and insert the right + copy at the same abscissa so the refined row carries the kink. + """ + slope = _branch_value_slopes( + grid=presort_grid, + value=presort_value, + segment=segment_sorted, + n_points_to_scan=n_points_to_scan, + ) + grid_left, grid_right = presort_grid[:-1], presort_grid[1:] + value_left, value_right = presort_value[:-1], presort_value[1:] + policy_left, policy_right = presort_policy[:-1], presort_policy[1:] + segment_left, segment_right = segment_sorted[:-1], segment_sorted[1:] + slope_left, slope_right = slope[:-1], slope[1:] + + coincident = (grid_left == grid_right) & ~jnp.isnan(grid_left) + value_equal = jnp.isclose(value_left, value_right, atol=1e-9, rtol=1e-7) + switches = (segment_left != segment_right) | _has_policy_jump( + grid_a=grid_left, + policy_a=policy_left, + grid_b=grid_right, + policy_b=policy_right, + jump_thresh=jump_thresh, + ) + is_crossing = coincident & value_equal & switches + + # Steeper branch wins to the right; the other is the left copy. + right_is_upper = slope_right >= slope_left + left_policy = jnp.where(right_is_upper, policy_left, policy_right) + right_policy = jnp.where(right_is_upper, policy_right, policy_left) + crossing_grid = jnp.where(is_crossing, grid_left, jnp.nan) + + # Set each kept crossing node's policy to the left branch's policy. + match = (refined_grid[:, None] == crossing_grid[None, :]) & is_crossing[None, :] + matched = jnp.any(match, axis=1) + matched_left_policy = jnp.sum(jnp.where(match, left_policy[None, :], 0.0), axis=1) + refined_policy = jnp.where(matched, matched_left_policy, refined_policy) + + # Append the right copies and stable-sort so each lands just after its node. + insert_grid = jnp.where(is_crossing, grid_left, jnp.nan) + insert_policy = jnp.where(is_crossing, right_policy, jnp.nan) + insert_value = jnp.where(is_crossing, value_left, jnp.nan) + all_grid = jnp.concatenate([refined_grid, insert_grid]) + all_policy = jnp.concatenate([refined_policy, insert_policy]) + all_value = jnp.concatenate([refined_value, insert_value]) + copy_order = jnp.concatenate( + [ + jnp.zeros(n_refined, dtype=jnp.int32), + jnp.ones_like(insert_grid, dtype=jnp.int32), + ] + ) + grid_key = jnp.where(jnp.isnan(all_grid), jnp.inf, all_grid) + order = jnp.lexsort(jnp.stack([copy_order, grid_key])) + out_grid = all_grid[order][:n_refined] + out_policy = all_policy[order][:n_refined] + out_value = all_value[order][:n_refined] + new_n_kept = (n_kept + jnp.sum(is_crossing, dtype=jnp.int32)).astype(jnp.int32) + return out_grid, out_policy, out_value, new_n_kept + + +def refine_to_bracket( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + x_query: ScalarFloat, + jump_thresh: float = 2.0, + n_points_to_scan: int | None = None, + segment_id: Float1D | None = None, + scan_unroll: int = 1, +) -> QueryBracket: + """Refine to the two envelope nodes bracketing a single query, streaming. + + Geometry-only counterpart of `refine_envelope` for the asset-row publish, + where the refined envelope is intra-node scratch read at exactly one query + (`resources_at_node`). Runs the same FUES scan (reusing `_inspect_candidate` + verbatim β€” identical drop/dominance/kink decisions), but folds each step's + up-to-three emitted points into an O(1) bracket-capture carry instead of + scattering them into NaN-padded `n_pad` rows. The `[n_input, 3]` per-step + stack and the `[n_pad]` envelope never materialize, so the per-(combo, node) + envelope working set is O(1) rather than O(n_pad). + + The captured bracket reproduces `searchsorted(search_grid, x_query, + side="right")` clamped to `[1, max(n_kept - 1, 1)]` on the full refined + row, node-for-node: + + - The bracket's lower node is the latest emitted point with grid + $\\le$ `x_query`; the upper node is the first emitted point with grid + $>$ `x_query`. At a duplicated kink abscissa (left then right copy, same + abscissa) both copies have grid $\\le$ `x_query` when the query sits on + the kink, so the later-emitted right copy wins the lower slot β€” the + `side="right"` tie-break. + - A query below the first node brackets the first pair (first, second); + below-first weight 0 then publishes the first node's value. + - A query at or above the last node brackets the last pair (second-last, + last); above-last weight 1 then publishes the last node's value. + + This computes envelope geometry only β€” no utility, borrowing limit, or + constrained floor; `publish_node_from_bracket` owns that EGM economics. + + Args: + endog_grid: Candidate endogenous grid points (resources), any order. + policy: Candidate policy values at `endog_grid`. + value: Candidate value-correspondence points at `endog_grid`. + x_query: The single point at which the envelope is read. + jump_thresh: Threshold on $|\\Delta A / \\Delta R|$ above which two + points lie on different value-function segments (see + `refine_envelope`). + n_points_to_scan: Number of candidates the bounded scans inspect; `None` + (the default) scans exhaustively (see `refine_envelope`). + segment_id: Optional per-candidate segment labels (see + `refine_envelope`). + scan_unroll: Loop-unroll factor for the sequential `jax.lax.scan` over + candidates (see `refine_envelope`); the captured bracket is identical + across values. + + Returns: + The query bracket and the kept-point count. + + """ + grid_key = jnp.where(jnp.isnan(endog_grid), jnp.inf, endog_grid) + value_key = jnp.where(jnp.isnan(value), -jnp.inf, value) + order = jnp.lexsort(jnp.stack([-value_key, grid_key])) + grid_sorted = endog_grid[order] + policy_sorted = policy[order] + value_sorted = value[order] + n_input = grid_sorted.shape[0] + n_points_to_scan = _resolve_n_points_to_scan(n_points_to_scan, n_input=n_input) + + duplicate = jnp.concatenate( + [ + jnp.zeros((1,), dtype=bool), + (grid_sorted[1:] == grid_sorted[:-1]) & ~jnp.isnan(grid_sorted[1:]), + ] + ) + grid_sorted = jnp.where(duplicate, jnp.nan, grid_sorted) + policy_sorted = jnp.where(duplicate, jnp.nan, policy_sorted) + value_sorted = jnp.where(duplicate, jnp.nan, value_sorted) + + segment_sorted = ( + jnp.zeros_like(grid_sorted) + if segment_id is None + else segment_id[order].astype(grid_sorted.dtype) + ) + + first_point = jnp.stack([grid_sorted[0], policy_sorted[0], value_sorted[0]]) + first_segment = segment_sorted[0] + fues_carry_init = jnp.concatenate( + [first_point, first_point, jnp.stack([first_segment, first_segment])] + ) + bracket_carry_init = _empty_bracket_carry(dtype=grid_sorted.dtype) + + def step( + carry: tuple[Float1D, Float1D], idx: ScalarInt + ) -> tuple[tuple[Float1D, Float1D], None]: + """Inspect candidate `idx`, then fold its emissions into the bracket.""" + fues_carry, bracket_carry = carry + fues_carry_new, (row_grid, row_policy, row_value, count) = _inspect_candidate( + carry=fues_carry, + idx=idx, + grid_sorted=grid_sorted, + policy_sorted=policy_sorted, + value_sorted=value_sorted, + segment_sorted=segment_sorted, + jump_thresh=jump_thresh, + n_points_to_scan=n_points_to_scan, + ) + bracket_carry_new = _fold_emissions_into_bracket( + bracket_carry=bracket_carry, + row_grid=row_grid, + row_policy=row_policy, + row_value=row_value, + count=count, + x_query=x_query, + ) + return (fues_carry_new, bracket_carry_new), None + + indices = jnp.arange(1, n_input, dtype=jnp.int32) + (fues_carry_final, bracket_carry), _ = jax.lax.scan( + step, (fues_carry_init, bracket_carry_init), indices, unroll=scan_unroll + ) + + # The last accepted point is still pending in the FUES carry; fold it as the + # scan's final single emission (mirrors `refine_envelope`'s post-scan emit). + final_grid, final_policy, final_value = ( + fues_carry_final[3], + fues_carry_final[4], + fues_carry_final[5], + ) + final_valid = ~jnp.isnan(final_grid) & ~jnp.isnan(final_value) + nan_scalar = jnp.full((), jnp.nan, dtype=grid_sorted.dtype) + bracket_carry = _fold_emissions_into_bracket( + bracket_carry=bracket_carry, + row_grid=jnp.stack([final_grid, nan_scalar, nan_scalar]), + row_policy=jnp.stack([final_policy, nan_scalar, nan_scalar]), + row_value=jnp.stack([final_value, nan_scalar, nan_scalar]), + count=final_valid.astype(jnp.int32), + x_query=x_query, + ) + + return _assemble_bracket(bracket_carry=bracket_carry, dtype=grid_sorted.dtype) + + +# Bracket-capture carry layout (flat Float1D so it threads through `lax.scan`): +# six (grid, policy, value) triples, then three counters. +# first (0:3) β€” lowest emitted node (constrained-floor edge test, below clamp) +# second (3:6) β€” second emitted node (below-first clamp upper) +# prev (6:9) β€” second-most-recent emitted node (above-last clamp lower) +# last (9:12) β€” most-recent emitted node (above-last clamp upper) +# lo (12:15) β€” latest emitted node with grid <= x_query (interior lower) +# hi (15:18) β€” first emitted node with grid > x_query (interior upper) +# seen (18) β€” running count of emitted nodes (for first/second/n_kept) +# below (19) β€” running count of emitted nodes with grid <= x_query (`s`) +# hi_set (20) β€” 1.0 once `hi` has been frozen, else 0.0 +_BRACKET_CARRY_LEN = 21 + + +def _empty_bracket_carry(*, dtype: jnp.dtype) -> Float1D: + """Initialize the bracket-capture carry to all-NaN nodes and zero counters.""" + carry = jnp.full((_BRACKET_CARRY_LEN,), jnp.nan, dtype=dtype) + return carry.at[18:21].set(jnp.zeros((3,), dtype=dtype)) + + +def _fold_emissions_into_bracket( + *, + bracket_carry: Float1D, + row_grid: Float1D, + row_policy: Float1D, + row_value: Float1D, + count: ScalarInt, + x_query: ScalarFloat, +) -> Float1D: + """Fold a step's up-to-three emitted nodes into the bracket-capture carry. + + Emissions arrive in ascending grid order; only the first `count` of the + three slots are valid. Each valid node updates, in order: + + - `seen` and the `first`/`second` registers (the first two ever emitted), + - the rolling `prev`/`last` pair (the two most recent), + - on grid $\\le$ `x_query`: the `below` count and the `lo` register + (latest-wins, so a duplicated kink's right copy wins), + - on grid $>$ `x_query`: the `hi` register, frozen on first occurrence. + """ + for slot in range(3): + valid = slot < count + bracket_carry = _fold_one_node( + bracket_carry=bracket_carry, + grid=row_grid[slot], + policy=row_policy[slot], + value=row_value[slot], + valid=valid, + x_query=x_query, + ) + return bracket_carry + + +def _fold_one_node( + *, + bracket_carry: Float1D, + grid: ScalarFloat, + policy: ScalarFloat, + value: ScalarFloat, + valid: ScalarBool, + x_query: ScalarFloat, +) -> Float1D: + """Update the bracket-capture carry with one emitted node when `valid`.""" + node = jnp.stack([grid, policy, value]) + seen = bracket_carry[18] + below = bracket_carry[19] + hi_set = bracket_carry[20] + + is_first = valid & (seen == 0.0) + is_second = valid & (seen == 1.0) + at_or_below = valid & (grid <= x_query) + above = valid & (grid > x_query) + freezes_hi = above & (hi_set == 0.0) + + new = bracket_carry + new = new.at[0:3].set(jnp.where(is_first, node, bracket_carry[0:3])) + new = new.at[3:6].set(jnp.where(is_second, node, bracket_carry[3:6])) + # Roll the most-recent pair: `prev` takes the old `last`, `last` takes the + # node β€” only on a valid emission, so dropped/NaN slots leave them intact. + new = new.at[6:9].set(jnp.where(valid, bracket_carry[9:12], bracket_carry[6:9])) + new = new.at[9:12].set(jnp.where(valid, node, bracket_carry[9:12])) + new = new.at[12:15].set(jnp.where(at_or_below, node, bracket_carry[12:15])) + new = new.at[15:18].set(jnp.where(freezes_hi, node, bracket_carry[15:18])) + new = new.at[18].set(seen + jnp.where(valid, 1.0, 0.0)) + new = new.at[19].set(below + jnp.where(at_or_below, 1.0, 0.0)) + return new.at[20].set(jnp.where(freezes_hi, 1.0, hi_set)) + + +def _assemble_bracket(*, bracket_carry: Float1D, dtype: jnp.dtype) -> QueryBracket: + """Assemble the edge-clamped query bracket from the capture carry. + + Reproduces `clip(searchsorted(side="right"), 1, max(n_kept - 1, 1))` on the + full refined row by selecting among the captured registers on `s` (count of + emitted nodes with grid $\\le$ `x_query`) and `n_kept`: + + - `s == 0` (query below the first node): bracket (first, second). + - `s == n_kept` (query at or above the last node): bracket (prev, last) when + `n_kept >= 2`; with a single live node the reference clamps the upper + index to the NaN-padded slot, so the bracket is (first, second=NaN) there. + - otherwise: bracket (lo, hi) β€” the searchsorted pair node-for-node. + """ + first = bracket_carry[0:3] + second = bracket_carry[3:6] + prev = bracket_carry[6:9] + last = bracket_carry[9:12] + lo = bracket_carry[12:15] + hi = bracket_carry[15:18] + n_kept = bracket_carry[18].astype(jnp.int32) + below = bracket_carry[19].astype(jnp.int32) + + below_first = below == 0 + at_or_above_last = below == n_kept + # The reference clamps the upper index to `max(n_kept - 1, 1)`, so the + # above-last bracket is (second-last, last) once there are at least two + # nodes (`max(n_kept - 1, 1) == n_kept - 1`); with a single node the upper + # index stays at the NaN-padded slot, so the bracket is the (first, + # NaN-padded-second) pair that `first`/`second` already hold (`second` + # stayed NaN, never emitted). + above_clamp_is_last = (n_kept - 1) >= jnp.maximum(n_kept - 1, 1) + above_lower = jnp.where(above_clamp_is_last, prev, first) + above_upper = jnp.where(above_clamp_is_last, last, second) + + lower = jnp.where(below_first, first, jnp.where(at_or_above_last, above_lower, lo)) + upper = jnp.where(below_first, second, jnp.where(at_or_above_last, above_upper, hi)) + return QueryBracket( + lower_grid=lower[0].astype(dtype), + upper_grid=upper[0].astype(dtype), + lower_policy=lower[1].astype(dtype), + upper_policy=upper[1].astype(dtype), + lower_value=lower[2].astype(dtype), + upper_value=upper[2].astype(dtype), + first_grid=first[0].astype(dtype), + n_kept=n_kept, + ) + + +def _inspect_candidate( + *, + carry: Float1D, + idx: ScalarInt, + grid_sorted: Float1D, + policy_sorted: Float1D, + value_sorted: Float1D, + segment_sorted: Float1D, + jump_thresh: float, + n_points_to_scan: int, +) -> tuple[Float1D, tuple[Float1D, Float1D, Float1D, ScalarInt]]: + """Inspect candidate `idx` and emit the envelope points it finalizes. + + The last accepted point `j` stays in the carry until its successor is + decided, so a point revealed as dominated by a later candidate is never + emitted. Each step emits up to three points (in ascending grid order): the + finalized `j`, and the duplicated intersection of two crossing segments. + + Args: + carry: The two most recent envelope points, `k` then `j`, each as + (grid, policy, value). + idx: Index of the candidate to inspect. + grid_sorted: Sorted candidate endogenous grid points. + policy_sorted: Candidate policy values at `grid_sorted`. + value_sorted: Candidate value-correspondence points at `grid_sorted`. + jump_thresh: Threshold on $|\\Delta A / \\Delta R|$ above which two + points lie on different segments. + n_points_to_scan: Number of candidates the bounded scans inspect. + + Returns: + Tuple of the updated carry and the per-step output block: three + emission rows for grid, policy, and value, plus the number of valid + rows. + + """ + grid_k, policy_k, value_k, grid_j, policy_j, value_j, seg_k, seg_j = carry + grid_i = grid_sorted[idx] + policy_i = policy_sorted[idx] + value_i = value_sorted[idx] + seg_i = segment_sorted[idx] + + candidate_valid = ~jnp.isnan(grid_i) & ~jnp.isnan(value_i) + # Two points lie on different segments if the implied-savings policy jumps + # or β€” when labels are supplied β€” their segment labels differ. + switches = _has_policy_jump( + grid_a=grid_j, + policy_a=policy_j, + grid_b=grid_i, + policy_b=policy_i, + jump_thresh=jump_thresh, + ) | (seg_j != seg_i) + secant = _slope(x_a=grid_j, y_a=value_j, x_b=grid_i, y_b=value_i) + grad_before = _slope(x_a=grid_k, y_a=value_k, x_b=grid_j, y_b=value_j) + + # Next candidate on j's segment after i: defines the continuation of the + # current segment for both the suboptimality test and the lower line of a + # crossing between j and i. + j_seg_found, j_seg_grid, j_seg_policy, j_seg_value = _find_same_segment_point( + grid=grid_sorted, + policy=policy_sorted, + value=value_sorted, + segment=segment_sorted, + anchor_grid=grid_j, + anchor_policy=policy_j, + anchor_segment=seg_j, + idx=idx, + direction=1, + n_points_to_scan=n_points_to_scan, + jump_thresh=jump_thresh, + ) + secant_i_to_j_seg = _slope(x_a=grid_i, y_a=value_i, x_b=j_seg_grid, y_b=j_seg_value) + below_j_segment = switches & j_seg_found & (secant < secant_i_to_j_seg) + + # A value drop marks a dominated candidate only *within* a segment, where the + # envelope value is monotone in the grid. Across a segment switch the value may + # legitimately fall (the winning segment changes at a crossing), so a switch is + # judged geometrically by `below_j_segment`, not by the raw value comparison β€” + # otherwise the genuine crossing point of two branches is dropped as dominated. + dropped = ( + ~candidate_valid + | ((value_i < value_j) & ~switches) + | (((grid_i - policy_i) < (grid_j - policy_j)) & (secant < grad_before)) + | below_j_segment + ) + + # A same-segment partner of i defines i's segment line (forward preferred: + # after a crossing, i's segment continues to the right). + fwd_found, fwd_grid, fwd_policy, fwd_value = _find_same_segment_point( + grid=grid_sorted, + policy=policy_sorted, + value=value_sorted, + segment=segment_sorted, + anchor_grid=grid_i, + anchor_policy=policy_i, + anchor_segment=seg_i, + idx=idx, + direction=1, + n_points_to_scan=n_points_to_scan, + jump_thresh=jump_thresh, + ) + bwd_found, bwd_grid, bwd_policy, bwd_value = _find_same_segment_point( + grid=grid_sorted, + policy=policy_sorted, + value=value_sorted, + segment=segment_sorted, + anchor_grid=grid_i, + anchor_policy=policy_i, + anchor_segment=seg_i, + idx=idx, + direction=-1, + n_points_to_scan=n_points_to_scan, + jump_thresh=jump_thresh, + ) + partner_found = fwd_found | bwd_found + partner_grid = jnp.where(fwd_found, fwd_grid, bwd_grid) + partner_policy = jnp.where(fwd_found, fwd_policy, bwd_policy) + partner_value = jnp.where(fwd_found, fwd_value, bwd_value) + i_seg_slope = _slope(x_a=grid_i, y_a=value_i, x_b=partner_grid, y_b=partner_value) + i_seg_policy_slope = _slope( + x_a=grid_i, y_a=policy_i, x_b=partner_grid, y_b=partner_policy + ) + + # j below i's segment line means the crossing happened before j: j is + # dominated and is replaced by the intersection of the line through (k, j) + # with i's segment line. + j_dominated = ~dropped & switches & partner_found & (secant > i_seg_slope) + policy_slope_kj = _slope(x_a=grid_k, y_a=policy_k, x_b=grid_j, y_b=policy_j) + kink_grid_6, kink_value_6 = _intersect_lines( + x_a=grid_j, + y_a=value_j, + slope_a=grad_before, + x_b=grid_i, + y_b=value_i, + slope_b=i_seg_slope, + ) + kink_policy_left_6 = policy_j + policy_slope_kj * (kink_grid_6 - grid_j) + kink_policy_right_6 = policy_i + i_seg_policy_slope * (kink_grid_6 - grid_i) + # The j-dominated crossing happened before j, so the inserted kink lies in + # `(grid_k, grid_j)`. The `< grid_j` bound is implied by the `secant > + # i_seg_slope` precondition in exact arithmetic; it is kept explicit so a + # near-parallel-slope rounding error cannot place the kink past j. + kink_6 = ( + j_dominated + & (kink_grid_6 > grid_k) + & (kink_grid_6 < grid_j) + & (kink_grid_6 < grid_i) + ) + + # Crossing strictly between j and i: both stay on the envelope and the + # intersection of their segment lines is inserted between them. + j_seg_slope = jnp.where( + j_seg_found, + _slope(x_a=grid_j, y_a=value_j, x_b=j_seg_grid, y_b=j_seg_value), + grad_before, + ) + j_seg_policy_slope = jnp.where( + j_seg_found, + _slope(x_a=grid_j, y_a=policy_j, x_b=j_seg_grid, y_b=j_seg_policy), + policy_slope_kj, + ) + kink_grid_5, kink_value_5 = _intersect_lines( + x_a=grid_j, + y_a=value_j, + slope_a=j_seg_slope, + x_b=grid_i, + y_b=value_i, + slope_b=i_seg_slope, + ) + kink_policy_left_5 = policy_j + j_seg_policy_slope * (kink_grid_5 - grid_j) + kink_policy_right_5 = policy_i + i_seg_policy_slope * (kink_grid_5 - grid_i) + kink_5 = ( + ~dropped + & ~j_dominated + & switches + & partner_found + & (kink_grid_5 > grid_j) + & (kink_grid_5 < grid_i) + ) + + plain = ~dropped & ~j_dominated & ~kink_5 + nan_scalar = jnp.full((), jnp.nan, dtype=grid_sorted.dtype) + + emits_j = plain | kink_5 + row_grid = jnp.stack( + [ + jnp.where(kink_6, kink_grid_6, jnp.where(emits_j, grid_j, nan_scalar)), + jnp.where(kink_6, kink_grid_6, jnp.where(kink_5, kink_grid_5, nan_scalar)), + jnp.where(kink_5, kink_grid_5, nan_scalar), + ] + ) + row_policy = jnp.stack( + [ + jnp.where( + kink_6, + kink_policy_left_6, + jnp.where(emits_j, policy_j, nan_scalar), + ), + jnp.where( + kink_6, + kink_policy_right_6, + jnp.where(kink_5, kink_policy_left_5, nan_scalar), + ), + jnp.where(kink_5, kink_policy_right_5, nan_scalar), + ] + ) + row_value = jnp.stack( + [ + jnp.where(kink_6, kink_value_6, jnp.where(emits_j, value_j, nan_scalar)), + jnp.where( + kink_6, kink_value_6, jnp.where(kink_5, kink_value_5, nan_scalar) + ), + jnp.where(kink_5, kink_value_5, nan_scalar), + ] + ) + count = jnp.where(kink_5, 3, jnp.where(kink_6, 2, jnp.where(plain, 1, 0))).astype( + jnp.int32 + ) + + # New k is the point emitted last this step: the right-policy copy of an + # inserted kink, the finalized j on a plain accept, or unchanged when + # nothing was emitted (drop, or j dominated without a valid kink). New j + # is the accepted candidate i. + keeps_k = dropped | (j_dominated & ~kink_6) + new_k_grid = jnp.where( + keeps_k, + grid_k, + jnp.where(kink_5, kink_grid_5, jnp.where(kink_6, kink_grid_6, grid_j)), + ) + new_k_policy = jnp.where( + keeps_k, + policy_k, + jnp.where( + kink_5, + kink_policy_right_5, + jnp.where(kink_6, kink_policy_right_6, policy_j), + ), + ) + new_k_value = jnp.where( + keeps_k, + value_k, + jnp.where(kink_5, kink_value_5, jnp.where(kink_6, kink_value_6, value_j)), + ) + # New k inherits the segment of the point it represents: an inserted kink + # carries `i`'s segment (the crossing continues to the right on i's + # segment), a plain accept carries the finalized `j`'s segment, and a + # retained k keeps its own. New j is the accepted candidate `i`. + new_k_seg = jnp.where(keeps_k, seg_k, jnp.where(kink_5 | kink_6, seg_i, seg_j)) + carry_accepted = jnp.stack( + [ + new_k_grid, + new_k_policy, + new_k_value, + grid_i, + policy_i, + value_i, + new_k_seg, + seg_i, + ] + ) + carry_new = jnp.where(dropped, carry, carry_accepted) + + return carry_new, (row_grid, row_policy, row_value, count) + + +def _find_same_segment_point( + *, + grid: Float1D, + policy: Float1D, + value: Float1D, + segment: Float1D, + anchor_grid: ScalarFloat, + anchor_policy: ScalarFloat, + anchor_segment: ScalarFloat, + idx: ScalarInt, + direction: int, + n_points_to_scan: int, + jump_thresh: float, +) -> tuple[ScalarBool, ScalarFloat, ScalarFloat, ScalarFloat]: + """Find the candidate nearest to `idx` on the anchor's value segment. + + Inspects up to `n_points_to_scan` candidates after (`direction=1`) or + before (`direction=-1`) index `idx` and returns the first whose implied + savings, relative to the anchor point, do not jump and whose segment label + matches the anchor's. + + Args: + grid: Sorted candidate endogenous grid points. + policy: Candidate policy values at `grid`. + value: Candidate value-correspondence points at `grid`. + segment: Candidate segment labels at `grid` (all-zero when unused). + anchor_grid: Endogenous grid point of the anchor. + anchor_policy: Policy value of the anchor. + anchor_segment: Segment label of the anchor. + idx: Index the scan starts from (exclusive). + direction: Scan direction, `1` (forward) or `-1` (backward). + n_points_to_scan: Number of candidates to inspect. + jump_thresh: Threshold on $|\\Delta A / \\Delta R|$ above which two + points lie on different segments. + + Returns: + Tuple of a found-indicator and the grid, policy, and value of the + first same-segment candidate (arbitrary when not found). + + """ + n_input = grid.shape[0] + window = idx + direction * (1 + jnp.arange(n_points_to_scan, dtype=jnp.int32)) + in_bounds = (window >= 0) & (window < n_input) + clipped = jnp.clip(window, 0, n_input - 1) + window_grid = grid[clipped] + window_policy = policy[clipped] + window_value = value[clipped] + window_segment = segment[clipped] + same_segment = ( + in_bounds + & ~jnp.isnan(window_grid) + & ~jnp.isnan(window_value) + & (window_segment == anchor_segment) + & ~_has_policy_jump( + grid_a=anchor_grid, + policy_a=anchor_policy, + grid_b=window_grid, + policy_b=window_policy, + jump_thresh=jump_thresh, + ) + ) + found = jnp.any(same_segment) + pos = jnp.argmax(same_segment) + return found, window_grid[pos], window_policy[pos], window_value[pos] + + +def _has_policy_jump( + *, + grid_a: FloatND, + policy_a: FloatND, + grid_b: FloatND, + policy_b: FloatND, + jump_thresh: float, +) -> BoolND: + """Indicate whether two points lie on different value-function segments. + + Points lie on different segments iff the gradient of the implied savings + $A = R - c$ between them exceeds `jump_thresh` in absolute value. + + Args: + grid_a: Endogenous grid point(s) of the first point. + policy_a: Policy value(s) of the first point. + grid_b: Endogenous grid point(s) of the second point. + policy_b: Policy value(s) of the second point. + jump_thresh: Threshold on $|\\Delta A / \\Delta R|$. + + Returns: + Boolean indicator(s), broadcast over the inputs. + + """ + savings_slope = _slope( + x_a=grid_a, + y_a=grid_a - policy_a, + x_b=grid_b, + y_b=grid_b - policy_b, + ) + return jnp.abs(savings_slope) > jump_thresh + + +def _slope(*, x_a: FloatND, y_a: FloatND, x_b: FloatND, y_b: FloatND) -> FloatND: + """Compute the slope between two points, with `0.0` for coincident abscissae. + + Args: + x_a: Abscissa(e) of the first point. + y_a: Ordinate(s) of the first point. + x_b: Abscissa(e) of the second point. + y_b: Ordinate(s) of the second point. + + Returns: + Slope(s) $\\Delta y / \\Delta x$, broadcast over the inputs. + + """ + delta_x = x_b - x_a + return jnp.where( + delta_x == 0.0, 0.0, (y_b - y_a) / jnp.where(delta_x == 0.0, 1.0, delta_x) + ) + + +def _intersect_lines( + *, + x_a: ScalarFloat, + y_a: ScalarFloat, + slope_a: ScalarFloat, + x_b: ScalarFloat, + y_b: ScalarFloat, + slope_b: ScalarFloat, +) -> tuple[ScalarFloat, ScalarFloat]: + """Intersect two lines given in point-slope form. + + Args: + x_a: Abscissa of a point on the first line. + y_a: Ordinate of a point on the first line. + slope_a: Slope of the first line. + x_b: Abscissa of a point on the second line. + y_b: Ordinate of a point on the second line. + slope_b: Slope of the second line. + + Returns: + Tuple of the intersection's abscissa and ordinate; NaN for parallel + lines. + + """ + denominator = slope_a - slope_b + safe_denominator = jnp.where(denominator == 0.0, 1.0, denominator) + x = jnp.where( + denominator == 0.0, + jnp.nan, + (y_b - y_a + slope_a * x_a - slope_b * x_b) / safe_denominator, + ) + # Evaluate the ordinate from a finite abscissa so the parallel-lines branch + # carries a finite (dead) value: NaN here would poison reverse-mode gradients + # through the `jnp.where` even though the forward result discards it. + safe_x = jnp.where(denominator == 0.0, x_a, x) + y = y_a + slope_a * (safe_x - x_a) + return x, y diff --git a/src/_lcm/egm/upper_envelope/ltm.py b/src/_lcm/egm/upper_envelope/ltm.py new file mode 100644 index 000000000..61811834e --- /dev/null +++ b/src/_lcm/egm/upper_envelope/ltm.py @@ -0,0 +1,190 @@ +"""Local-upper-bound (LTM) upper-envelope refinement of EGM candidates. + +Implements the brute upper-envelope method of Druedahl's `consav` package (the +`upperenvelope` routine), referenced in Dobrescu & Shanker (2026) as the +quadratic baseline (`LTM`). Inverting the Euler equation in models with discrete +choices yields a value *correspondence*: the candidates form a chain of linear +segments between consecutive nodes that, in non-concave regions, overlap in the +endogenous grid. LTM selects the upper envelope by a dense scan: at every output +abscissa it inspects every segment, keeps those that bracket the abscissa, +linearly interpolates the value (and policy) along each, and reports the +highest-value interpolant. + +The cost is `O(N_query x N_segments) = O(K^2)` by construction β€” the +`(N_query, N_segments)` bracket-and-interpolate matrix is materialized in full. +This is deliberate: the method is the paper's quadratic reference, so the kernel +is not folded into a sequential scan. All shapes are static, so the kernel can +be `jax.jit`-compiled and `jax.vmap`-batched over a leading dimension of the +candidate arrays. + +Unlike FUES, LTM inserts no exact segment-crossing abscissa: it evaluates the +envelope at the candidate abscissae, so a kink lands between two output nodes +and the downstream interpolation read recovers it to within the local grid +spacing. Unlike RFC, it consumes no supgradient β€” the segments carry their own +slopes. +""" + +import jax.numpy as jnp + +from lcm.typing import BoolND, Float1D, ScalarInt + + +def refine_envelope( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + n_refined: int, + segment_id: Float1D | None = None, +) -> tuple[Float1D, Float1D, Float1D, ScalarInt]: + """Refine a candidate value correspondence to its upper envelope. + + The candidates arrive as a chain of consecutive linear segments (one segment + per consecutive input pair), as the Euler inversion produces them: the + constrained run followed by the interior run, each ascending along its own + margin but jointly non-monotone in the endogenous grid. The envelope is + evaluated at the candidate abscissae, sorted ascending; the refined arrays + have static length `n_refined`, hold the envelope points in weakly ascending + grid order, and are NaN-padded in the tail. No crossing point is inserted β€” + a kink lands between two output nodes, recovered by the downstream read. + + Args: + endog_grid: Candidate endogenous grid points (resources). Consecutive + entries form the linear segments scanned for the envelope. + policy: Candidate policy values at `endog_grid`. + value: Candidate value-correspondence points at `endog_grid`. + n_refined: Static length of the refined output arrays. + segment_id: Optional per-candidate branch label, aligned with + `endog_grid`. When supplied, a consecutive-pair segment is real iff + both endpoints carry the same label, so unrelated branches are never + bridged. `None` (the default) links every consecutive pair. + + Returns: + Tuple of refined endogenous grid, refined policy, refined value (each + of length `n_refined`, NaN-padded), and the number of envelope points + `n_kept`. `n_kept > n_refined` signals overflow; the arrays then hold a + valid truncated prefix of the envelope. Callers must check the counter + rather than publish the truncated arrays silently β€” the EGM step + NaN-poisons its published rows on overflow so the solve loop's NaN + diagnostics name the offending (regime, period). + + """ + # A dead candidate arrives NaN-filled (the EGM step poisons `-inf`-valued + # corners to NaN before refinement). A segment touching a dead endpoint is + # excluded from the scan, and a dead abscissa sorts to the NaN tail, so it + # is neither queried nor evaluated. + dead = jnp.isnan(endog_grid) | jnp.isnan(value) + + # Sort the candidate abscissae ascending so the output row is weakly + # ascending and the NaN tail is contiguous; dead nodes sort last. + grid_key = jnp.where(dead, jnp.inf, endog_grid) + order = jnp.argsort(grid_key) + query_grid = jnp.where(dead, jnp.nan, endog_grid)[order] + query_dead = dead[order] + + envelope_value, envelope_policy = _evaluate_envelope( + query_grid=query_grid, + endog_grid=endog_grid, + policy=policy, + value=value, + dead=dead, + segment_id=segment_id, + ) + + # A query point no segment brackets (e.g. the lone dead-padded tail) yields + # no envelope value: poison the whole triple to NaN so it joins the tail. + no_segment = jnp.isneginf(envelope_value) + drop = query_dead | no_segment + refined_grid = jnp.where(drop, jnp.nan, query_grid) + refined_policy = jnp.where(drop, jnp.nan, envelope_policy) + refined_value = jnp.where(drop, jnp.nan, envelope_value) + + # Compact the live nodes into the NaN-padded prefix, preserving sorted + # order; the live query points are already a contiguous ascending prefix, so + # the scatter only trims the dropped tail. + survives = ~drop + position = jnp.cumsum(survives.astype(jnp.int32)) - 1 + slot = jnp.where(survives, position, n_refined) + out_grid = jnp.full(n_refined, jnp.nan, dtype=endog_grid.dtype) + out_policy = jnp.full(n_refined, jnp.nan, dtype=policy.dtype) + out_value = jnp.full(n_refined, jnp.nan, dtype=value.dtype) + out_grid = out_grid.at[slot].set(refined_grid, mode="drop") + out_policy = out_policy.at[slot].set(refined_policy, mode="drop") + out_value = out_value.at[slot].set(refined_value, mode="drop") + + n_kept = jnp.sum(survives, dtype=jnp.int32) + return out_grid, out_policy, out_value, n_kept + + +def _evaluate_envelope( + *, + query_grid: Float1D, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + dead: BoolND, + segment_id: Float1D | None = None, +) -> tuple[Float1D, Float1D]: + """Evaluate the upper envelope at every query abscissa over all segments. + + Builds the dense `(N_query, N_segments)` bracket-and-interpolate matrix: each + query `m_j` is tested against every segment `(k, k+1)` of consecutive input + candidates. A segment brackets the query iff `m_j` lies in its abscissa + range; the value and policy are then linearly interpolated along the + segment. The envelope value is the maximum over bracketing segments, and the + policy is the one carried by the winning segment. A query no segment + brackets reports `-inf` value (the absent-envelope sentinel). + + Args: + query_grid: Abscissae at which to evaluate the envelope; NaN tail. + endog_grid: Candidate endogenous grid points (segment endpoints). + policy: Candidate policy values at `endog_grid`. + value: Candidate value-correspondence points at `endog_grid`. + dead: Per-candidate dead indicator; a segment with a dead endpoint is + excluded from the scan. + + Returns: + Tuple of the envelope value and the envelope policy at each query + abscissa. + + """ + # Segment endpoints: candidate `k` to candidate `k+1`, consecutive in input + # order (the EGM cloud's natural segment chain). + left_grid = endog_grid[:-1] + right_grid = endog_grid[1:] + left_policy = policy[:-1] + right_policy = policy[1:] + left_value = value[:-1] + right_value = value[1:] + segment_live = ~dead[:-1] & ~dead[1:] + # With explicit topology, a consecutive-pair link is a real segment only + # within one branch: drop links whose endpoints carry different labels so + # unrelated branches are never bridged. + if segment_id is not None: + segment_live = segment_live & (segment_id[:-1] == segment_id[1:]) + + query = query_grid[:, None] + lower = jnp.minimum(left_grid, right_grid)[None, :] + upper = jnp.maximum(left_grid, right_grid)[None, :] + brackets = segment_live[None, :] & (query >= lower) & (query <= upper) + + # Linear position of the query along each segment; a zero-width segment + # (coincident abscissae) takes weight 0, so its left endpoint applies. + width = (right_grid - left_grid)[None, :] + safe_width = jnp.where(width == 0.0, 1.0, width) + relative = jnp.where(width == 0.0, 0.0, (query - left_grid[None, :]) / safe_width) + + value_interp = left_value[None, :] + relative * (right_value - left_value)[None, :] + policy_interp = ( + left_policy[None, :] + relative * (right_policy - left_policy)[None, :] + ) + + # Keep only bracketing segments; non-bracketing ones get `-inf` value so the + # row maximum ignores them and reports `-inf` when no segment brackets. + masked_value = jnp.where(brackets, value_interp, -jnp.inf) + best_segment = jnp.argmax(masked_value, axis=1) + envelope_value = jnp.max(masked_value, axis=1) + envelope_policy = jnp.take_along_axis(policy_interp, best_segment[:, None], axis=1)[ + :, 0 + ] + return envelope_value, envelope_policy diff --git a/src/_lcm/egm/upper_envelope/mss.py b/src/_lcm/egm/upper_envelope/mss.py new file mode 100644 index 000000000..322d5f270 --- /dev/null +++ b/src/_lcm/egm/upper_envelope/mss.py @@ -0,0 +1,541 @@ +r"""MSS upper-envelope refinement of EGM candidates (HARK's EGM upper envelope). + +Implements the upper-envelope method of HARK (Carroll et al. 2018), referenced +in Dobrescu & Shanker (2026) as the `MSS` method column. Inverting the Euler +equation in models with discrete choices yields a value *correspondence*: the +candidates form a chain of linear segments between consecutive nodes that, in +non-concave regions, overlap in the endogenous grid. MSS sweeps the common grid +left-to-right and, at each output abscissa, evaluates every currently +overlapping segment, keeps the max-value branch, and β€” where the winning branch +switches between two adjacent abscissae β€” inserts the exact segment-crossing +point (the kink). + +Inserting the crossing is what separates MSS from LTM: both evaluate the +envelope at the candidate abscissae, but MSS adds the intersection abscissa as +its own node, so the kink is placed exactly rather than smeared across the local +grid spacing. The refined arrays therefore track the FUES envelope tightly. The +sweep is a single left-to-right scan over the sorted abscissae β€” `O(N)` emitting +steps, each evaluating the segment set β€” in contrast to RFC's per-pair dominance +test, and unlike FUES it consumes no `jump_thresh` heuristic: the winner switch +is read directly off the evaluated values. + +A crossing abscissa is inserted twice β€” same abscissa, left- and +right-extrapolated policy β€” so the refined arrays stay weakly ascending and the +policy discontinuity at a discrete-choice switch is preserved exactly, the same +convention FUES uses. + +All shapes are static, so the kernel can be `jax.jit`-compiled and `jax.vmap`- +batched over a leading dimension of the candidate arrays. +""" + +import jax +import jax.numpy as jnp + +from lcm.typing import BoolND, Float1D, FloatND, Int1D, ScalarInt + + +def refine_envelope( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + n_refined: int, + segment_id: Float1D | None = None, +) -> tuple[Float1D, Float1D, Float1D, ScalarInt]: + """Refine a candidate value correspondence to its upper envelope. + + The candidates arrive as a chain of consecutive linear segments (one segment + per consecutive input pair), as the Euler inversion produces them: the + constrained run followed by the interior run, each ascending along its own + margin but jointly non-monotone in the endogenous grid. The abscissae are + sorted ascending and swept left-to-right; at each abscissa the highest + bracketing segment is kept, and where the winning segment switches between + two adjacent abscissae the exact crossing point is inserted (twice β€” left and + right policy). The refined arrays have static length `n_refined`, hold the + envelope points in weakly ascending grid order, and are NaN-padded in the + tail. + + Args: + endog_grid: Candidate endogenous grid points (resources). Consecutive + entries form the linear segments scanned for the envelope. + policy: Candidate policy values at `endog_grid`. + value: Candidate value-correspondence points at `endog_grid`. + n_refined: Static length of the refined output arrays. + segment_id: Optional per-candidate branch label, aligned with + `endog_grid`. When supplied, a consecutive-pair link is a real value + segment iff both endpoints carry the same label, so unrelated + branches are never bridged β€” the explicit-topology path that replaces + the `decreases` heuristic. `None` (the default) infers segments from a + grid or value decrease, HARK's monotone split. + + Returns: + Tuple of refined endogenous grid, refined policy, refined value (each + of length `n_refined`, NaN-padded), and the number of envelope points + `n_kept`. `n_kept > n_refined` signals overflow; the arrays then hold a + valid truncated prefix of the envelope. Callers must check the counter + rather than publish the truncated arrays silently β€” the EGM step + NaN-poisons its published rows on overflow so the solve loop's NaN + diagnostics name the offending (regime, period). + + """ + # A dead candidate arrives NaN-filled (the EGM step poisons `-inf`-valued + # corners to NaN before refinement). A segment touching a dead endpoint is + # excluded from the scan, and a dead abscissa sorts to the NaN tail, so it + # is neither queried nor evaluated. + dead = jnp.isnan(endog_grid) | jnp.isnan(value) + + # Sort the candidate abscissae ascending so the sweep is left-to-right and + # the NaN tail is contiguous; dead nodes sort last. + grid_key = jnp.where(dead, jnp.inf, endog_grid) + order = jnp.argsort(grid_key) + query_grid = jnp.where(dead, jnp.nan, endog_grid)[order] + query_dead = dead[order] + n_query = query_grid.shape[0] + + # Segment endpoints: candidate `k` to candidate `k+1`, consecutive in the + # (unsorted) input order β€” the EGM cloud's natural segment chain. A segment + # with a dead endpoint is excluded from every evaluation. + left_grid = endog_grid[:-1] + right_grid = endog_grid[1:] + left_policy = policy[:-1] + right_policy = policy[1:] + left_value = value[:-1] + right_value = value[1:] + + # Per-link branch id and live mask. With explicit topology a link is a real + # value segment iff both endpoints carry the same branch label, so unrelated + # branches are never bridged. Without it, fall back to HARK's monotone split: + # a new segment starts wherever the grid or value *decreases* between + # consecutive candidates, and a link spanning such a decrease is a + # non-monotone bridge excluded from the scan. Either way the winner stays + # constant across one branch, so only a genuine branch switch is a kink. + if segment_id is None: + decreases = (right_grid < left_grid) | (right_value < left_value) + link_segment = jnp.cumsum(decreases.astype(jnp.int32)) + segment_live = ~dead[:-1] & ~dead[1:] & ~decreases + else: + same_segment = segment_id[:-1] == segment_id[1:] + link_segment = segment_id[:-1].astype(jnp.int32) + segment_live = ~dead[:-1] & ~dead[1:] & same_segment + + envelope_value, envelope_policy, winner_link, winner_segment = _evaluate_envelope( + query_grid=query_grid, + left_grid=left_grid, + right_grid=right_grid, + left_policy=left_policy, + right_policy=right_policy, + left_value=left_value, + right_value=right_value, + segment_id=link_segment, + segment_live=segment_live, + ) + + # A query no segment brackets (e.g. the lone dead-padded tail) yields no + # envelope value: poison the whole triple to NaN so it joins the tail. + no_segment = jnp.isneginf(envelope_value) + query_drop = query_dead | no_segment + node_grid = jnp.where(query_drop, jnp.nan, query_grid) + node_policy = jnp.where(query_drop, jnp.nan, envelope_policy) + node_value = jnp.where(query_drop, jnp.nan, envelope_value) + + # Sweep left-to-right: each step emits its query node, then β€” if the winning + # *branch* (segment id) differs from the previous live query's winner β€” the + # exact crossing of the two winning links (twice, left and right policy). The + # first live query has no predecessor, so it emits only its node. + crossing = _crossing_blocks( + query_grid=query_grid, + query_drop=query_drop, + winner_link=winner_link, + winner_segment=winner_segment, + left_grid=left_grid, + right_grid=right_grid, + left_policy=left_policy, + right_policy=right_policy, + left_value=left_value, + right_value=right_value, + ) + + # A crossing is a genuine envelope kink only if both branches are on the + # envelope there: evaluate the dense envelope at each crossing abscissa and + # keep the crossing only where that value is finite and equals the crossing + # value. A switch across a *gap* in the candidate cloud intersects two lines + # in an interval no segment covers β€” the dense envelope is `-inf` there, so + # the test rejects it; colinear adjacent links of one monotone branch pass, + # since the branch's own line is on the envelope at the crossing. + crossing_envelope, _, _, _ = _evaluate_envelope( + query_grid=crossing.grid, + left_grid=left_grid, + right_grid=right_grid, + left_policy=left_policy, + right_policy=right_policy, + left_value=left_value, + right_value=right_value, + segment_id=link_segment, + segment_live=segment_live, + ) + on_envelope = jnp.isfinite(crossing_envelope) & jnp.isclose( + crossing_envelope, crossing.value, atol=1e-7, rtol=1e-5 + ) + crossing_valid = crossing.valid & on_envelope + + # Per-query output block: up to three rows in ascending grid order β€” the two + # crossing copies (same abscissa, left then right policy) followed by the + # query node. The crossing of step `i` lies in `(grid_{i-1}, grid_i)`, so it + # precedes the node `i` in the weakly-ascending output. + nan_scalar = jnp.full((), jnp.nan, dtype=query_grid.dtype) + node_valid = ~query_drop + # Per-query emission rows in ascending grid order: the crossing inserted + # before the node (left then right policy copy, same abscissa), then the node + # itself. The crossing of step `i` lies in `(grid_{i-1}, grid_i)`, so it + # precedes node `i`. Each row carries its own validity flag. + row_valid = jnp.stack([crossing_valid, crossing_valid, node_valid], axis=1).ravel() + row_grid = jnp.stack([crossing.grid, crossing.grid, node_grid], axis=1).ravel() + row_policy = jnp.stack( + [crossing.policy_left, crossing.policy_right, node_policy], axis=1 + ).ravel() + row_value = jnp.stack([crossing.value, crossing.value, node_value], axis=1).ravel() + + # Compact the valid rows into the NaN-padded prefix, preserving sweep order. + position = jnp.cumsum(row_valid.astype(jnp.int32)) - 1 + slot = jnp.where(row_valid, position, n_refined) + out_grid = jnp.full(n_refined, jnp.nan, dtype=endog_grid.dtype) + out_policy = jnp.full(n_refined, jnp.nan, dtype=policy.dtype) + out_value = jnp.full(n_refined, jnp.nan, dtype=value.dtype) + out_grid = out_grid.at[slot].set( + jnp.where(row_valid, row_grid, nan_scalar), mode="drop" + ) + out_policy = out_policy.at[slot].set( + jnp.where(row_valid, row_policy, nan_scalar), mode="drop" + ) + out_value = out_value.at[slot].set( + jnp.where(row_valid, row_value, nan_scalar), mode="drop" + ) + + n_kept = jnp.sum(row_valid, dtype=jnp.int32) + del n_query + return out_grid, out_policy, out_value, n_kept + + +class _CrossingBlocks: + """Per-query crossing candidate: abscissa, value, both policy copies, flag. + + The fields are aligned with the query sweep: entry `i` is the crossing + inserted *before* query node `i`, present (`valid`) only when query `i`'s + live winning segment differs from the previous live query's winner and the + intersection abscissa falls strictly between the two queries. + """ + + def __init__( + self, + *, + grid: Float1D, + value: Float1D, + policy_left: Float1D, + policy_right: Float1D, + valid: BoolND, + ) -> None: + self.grid = grid + self.value = value + self.policy_left = policy_left + self.policy_right = policy_right + self.valid = valid + + +def _crossing_blocks( + *, + query_grid: Float1D, + query_drop: BoolND, + winner_link: Int1D, + winner_segment: Int1D, + left_grid: Float1D, + right_grid: Float1D, + left_policy: Float1D, + right_policy: Float1D, + left_value: Float1D, + right_value: Float1D, +) -> _CrossingBlocks: + """Compute, per query, the crossing of its winner with the previous winner. + + Sweeps the live queries left-to-right (carrying the previous live query's + winning link and branch id) and, whenever the winning *branch* (segment id) + switches, intersects the two winning links' value lines. The crossing is + kept only when its abscissa falls strictly between the two adjacent live + query abscissae β€” the interval the switch happened in. A move from one link + to the next within one monotone branch keeps the segment id, so it is not a + switch and inserts nothing; only a genuine branch change is a kink. + """ + n_query = query_grid.shape[0] + live = ~query_drop + + def step( + carry: tuple[ScalarInt, ScalarInt, FloatND], idx: ScalarInt + ) -> tuple[tuple[ScalarInt, ScalarInt, FloatND], _CrossingRow]: + prev_link, prev_segment, prev_grid = carry + is_live = live[idx] + this_link = winner_link[idx] + this_segment = winner_segment[idx] + this_grid = query_grid[idx] + + switches = is_live & (prev_segment >= 0) & (this_segment != prev_segment) + row = _intersect_winners( + seg_a=prev_link, + seg_b=this_link, + left_grid=left_grid, + right_grid=right_grid, + left_policy=left_policy, + right_policy=right_policy, + left_value=left_value, + right_value=right_value, + ) + # The crossing must fall strictly inside the switch interval; whether it + # is a genuine envelope kink (rather than a phantom intersection across a + # gap) is settled by the dense on-envelope test the caller applies. + within = switches & (row.grid > prev_grid) & (row.grid < this_grid) + emitted = _CrossingRow( + grid=row.grid, + value=row.value, + policy_left=row.policy_a, + policy_right=row.policy_b, + valid=within, + ) + + # Advance the previous-live-query carry only on a live query; a dropped + # query leaves the comparison anchored at the last live winner/abscissa. + new_link = jnp.where(is_live, this_link, prev_link).astype(jnp.int32) + new_segment = jnp.where(is_live, this_segment, prev_segment).astype(jnp.int32) + new_grid = jnp.where(is_live, this_grid, prev_grid) + return (new_link, new_segment, new_grid), emitted + + carry_init = ( + jnp.int32(0), + jnp.int32(-1), + jnp.asarray(-jnp.inf, dtype=query_grid.dtype), + ) + _, rows = jax.lax.scan(step, carry_init, jnp.arange(n_query, dtype=jnp.int32)) + return _CrossingBlocks( + grid=rows.grid, + value=rows.value, + policy_left=rows.policy_left, + policy_right=rows.policy_right, + valid=rows.valid, + ) + + +class _CrossingRow: + """One step's crossing emission (scan carry-compatible stacked leaves).""" + + def __init__( + self, + *, + grid: FloatND, + value: FloatND, + policy_left: FloatND, + policy_right: FloatND, + valid: BoolND, + ) -> None: + self.grid = grid + self.value = value + self.policy_left = policy_left + self.policy_right = policy_right + self.valid = valid + + +jax.tree_util.register_pytree_node( + _CrossingRow, + lambda r: ( + (r.grid, r.value, r.policy_left, r.policy_right, r.valid), + None, + ), + lambda _aux, children: _CrossingRow( + grid=children[0], + value=children[1], + policy_left=children[2], + policy_right=children[3], + valid=children[4], + ), +) + + +class _SegmentIntersection: + """Intersection of two winning segments' value lines, with both policies.""" + + def __init__( + self, + *, + grid: FloatND, + value: FloatND, + policy_a: FloatND, + policy_b: FloatND, + ) -> None: + self.grid = grid + self.value = value + self.policy_a = policy_a + self.policy_b = policy_b + + +def _intersect_winners( + *, + seg_a: ScalarInt, + seg_b: ScalarInt, + left_grid: Float1D, + right_grid: Float1D, + left_policy: Float1D, + right_policy: Float1D, + left_value: Float1D, + right_value: Float1D, +) -> _SegmentIntersection: + """Intersect the value lines of segments `seg_a` and `seg_b`. + + Each segment is the line through its two endpoints; the intersection + abscissa solves `v_a(x) = v_b(x)`. The policy is read off each segment's own + line at that abscissa, so `policy_a` is the left-branch (segment `a`) policy + and `policy_b` the right-branch (segment `b`) policy at the kink. + """ + a_x0, a_x1 = left_grid[seg_a], right_grid[seg_a] + a_v0, a_v1 = left_value[seg_a], right_value[seg_a] + a_p0, a_p1 = left_policy[seg_a], right_policy[seg_a] + b_x0, b_x1 = left_grid[seg_b], right_grid[seg_b] + b_v0, b_v1 = left_value[seg_b], right_value[seg_b] + b_p0, b_p1 = left_policy[seg_b], right_policy[seg_b] + + slope_a = _slope(x_a=a_x0, y_a=a_v0, x_b=a_x1, y_b=a_v1) + slope_b = _slope(x_a=b_x0, y_a=b_v0, x_b=b_x1, y_b=b_v1) + grid, value = _intersect_lines( + x_a=a_x0, y_a=a_v0, slope_a=slope_a, x_b=b_x0, y_b=b_v0, slope_b=slope_b + ) + + policy_slope_a = _slope(x_a=a_x0, y_a=a_p0, x_b=a_x1, y_b=a_p1) + policy_slope_b = _slope(x_a=b_x0, y_a=b_p0, x_b=b_x1, y_b=b_p1) + policy_a = a_p0 + policy_slope_a * (grid - a_x0) + policy_b = b_p0 + policy_slope_b * (grid - b_x0) + return _SegmentIntersection( + grid=grid, value=value, policy_a=policy_a, policy_b=policy_b + ) + + +def _evaluate_envelope( + *, + query_grid: Float1D, + left_grid: Float1D, + right_grid: Float1D, + left_policy: Float1D, + right_policy: Float1D, + left_value: Float1D, + right_value: Float1D, + segment_id: Int1D, + segment_live: BoolND, +) -> tuple[Float1D, Float1D, Int1D, Int1D]: + """Evaluate the upper envelope and its winning link/branch at every query. + + Builds the dense `(N_query, N_segments)` bracket-and-interpolate matrix: each + query `m_j` is tested against every link `(k, k+1)`. A link brackets the + query iff `m_j` lies in its abscissa range; the value and policy are then + linearly interpolated along the link. The envelope value is the maximum over + bracketing links, the policy is the winner's, the winning link index is + reported (so its value line can be intersected), and the winner's branch id + `segment_id` is reported (so the sweep can detect a branch switch). A query + no link brackets reports `-inf` value (the absent-envelope sentinel), winning + link `0`, and branch `-1`. + + Args: + query_grid: Abscissae at which to evaluate the envelope; NaN tail. + left_grid: Lower endpoint abscissa of each link. + right_grid: Upper endpoint abscissa of each link. + left_policy: Policy at each link's lower endpoint. + right_policy: Policy at each link's upper endpoint. + left_value: Value at each link's lower endpoint. + right_value: Value at each link's upper endpoint. + segment_id: Per-link monotone-branch id; equal across one branch. + segment_live: Per-link live indicator; a dead-endpoint or non-monotone + bridge link is excluded from the scan. + + Returns: + Tuple of the envelope value, the envelope policy, the winning link index + (`0` where no link brackets), and the winning branch id (`-1` where no + link brackets) at each query. + + """ + query = query_grid[:, None] + lower = jnp.minimum(left_grid, right_grid)[None, :] + upper = jnp.maximum(left_grid, right_grid)[None, :] + brackets = segment_live[None, :] & (query >= lower) & (query <= upper) + + # Linear position of the query along each segment; a zero-width segment takes + # weight 0, so its left endpoint applies. + width = (right_grid - left_grid)[None, :] + safe_width = jnp.where(width == 0.0, 1.0, width) + relative = jnp.where(width == 0.0, 0.0, (query - left_grid[None, :]) / safe_width) + + value_interp = left_value[None, :] + relative * (right_value - left_value)[None, :] + policy_interp = ( + left_policy[None, :] + relative * (right_policy - left_policy)[None, :] + ) + + masked_value = jnp.where(brackets, value_interp, -jnp.inf) + best_link = jnp.argmax(masked_value, axis=1).astype(jnp.int32) + envelope_value = jnp.max(masked_value, axis=1) + any_bracket = jnp.any(brackets, axis=1) + envelope_policy = jnp.take_along_axis(policy_interp, best_link[:, None], axis=1)[ + :, 0 + ] + winner_link = jnp.where(any_bracket, best_link, 0).astype(jnp.int32) + winner_segment = jnp.where(any_bracket, segment_id[best_link], -1).astype(jnp.int32) + return envelope_value, envelope_policy, winner_link, winner_segment + + +def _slope(*, x_a: FloatND, y_a: FloatND, x_b: FloatND, y_b: FloatND) -> FloatND: + r"""Compute the slope between two points, with `0.0` for coincident abscissae. + + Args: + x_a: Abscissa(e) of the first point. + y_a: Ordinate(s) of the first point. + x_b: Abscissa(e) of the second point. + y_b: Ordinate(s) of the second point. + + Returns: + Slope(s) $\Delta y / \Delta x$, broadcast over the inputs. + + """ + delta_x = x_b - x_a + return jnp.where( + delta_x == 0.0, 0.0, (y_b - y_a) / jnp.where(delta_x == 0.0, 1.0, delta_x) + ) + + +def _intersect_lines( + *, + x_a: FloatND, + y_a: FloatND, + slope_a: FloatND, + x_b: FloatND, + y_b: FloatND, + slope_b: FloatND, +) -> tuple[FloatND, FloatND]: + """Intersect two lines given in point-slope form. + + Args: + x_a: Abscissa of a point on the first line. + y_a: Ordinate of a point on the first line. + slope_a: Slope of the first line. + x_b: Abscissa of a point on the second line. + y_b: Ordinate of a point on the second line. + slope_b: Slope of the second line. + + Returns: + Tuple of the intersection's abscissa and ordinate; NaN abscissa for + parallel lines. + + """ + denominator = slope_a - slope_b + safe_denominator = jnp.where(denominator == 0.0, 1.0, denominator) + x = jnp.where( + denominator == 0.0, + jnp.nan, + (y_b - y_a + slope_a * x_a - slope_b * x_b) / safe_denominator, + ) + # Evaluate the ordinate from a finite abscissa so the parallel-lines branch + # carries a finite (dead) value: NaN here would poison reverse-mode gradients + # through the `jnp.where` even though the forward result discards it. + safe_x = jnp.where(denominator == 0.0, x_a, x) + y = y_a + slope_a * (safe_x - x_a) + return x, y diff --git a/src/_lcm/egm/upper_envelope/query.py b/src/_lcm/egm/upper_envelope/query.py new file mode 100644 index 000000000..724bdac72 --- /dev/null +++ b/src/_lcm/egm/upper_envelope/query.py @@ -0,0 +1,310 @@ +"""Exact query-side upper envelope of an EGM candidate correspondence. + +The query-side counterpart of the full-row refiners (`fues`, `rfc`, `ltm`, +`mss`). Those materialise the whole refined envelope row and the caller then +reads it at a query; this evaluates the envelope *directly* at a set of query +abscissae without ever building the row. + +For one query the value is the maximum, over every live branch segment that +brackets it, of the segment's linear value; the policy and marginal are the +winning segment's. A folded branch contributes several bracketing segments, so +the maximum is exact for the piecewise-linear correspondence. Topology is +explicit: a segment is the link between two consecutive candidates carrying the +same `segment_id`, so unrelated branches are never bridged β€” the contract the +host oracle enforces. + +By default the evaluation is a fixed-shape `(n_query, n_segment)` +bracket-and-reduce: no sequential scan, no NaN-padded refined row, +branch-parallel and reduction-heavy, which is the shape an accelerator runs +fastest. This is the backend asset-row mode wants β€” one query per Euler node, no +full envelope to refine. For a large `(n_query, n_segment)` that dense matrix is +itself the memory wall; `segment_block_size` swaps it for a two-pass blocked +scan over segment blocks (running max, then max-slope-among-near-max against the +fixed envelope value), which peaks at `(n_query, block)` instead of +`(n_query, n_segment)` and returns the identical result. +""" + +from typing import NamedTuple + +import jax +import jax.numpy as jnp + +from lcm.typing import BoolND, Float1D, FloatND + +# Right-continuous tie tolerance: among bracketing segments whose interpolated +# value is within this of the envelope maximum, the larger value-slope wins (it +# is higher just to the right). Both the dense and blocked paths use it, so they +# select the same policy/marginal at a tie. +_VALUE_TIE_ATOL = 1e-12 + + +class _SegmentLinks(NamedTuple): + """Per-link endpoints of the candidate correspondence (length `n - 1`). + + A link is the consecutive-candidate pair `(i, i+1)`; it is a real envelope + segment only where `live` (both endpoints finite and sharing a branch label). + """ + + left_grid: Float1D + right_grid: Float1D + left_value: Float1D + right_value: Float1D + left_policy: Float1D + right_policy: Float1D + left_marginal: Float1D + right_marginal: Float1D + live: BoolND + + +def envelope_at_query( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + marginal: Float1D, + segment_id: Float1D, + x_query: FloatND, + segment_block_size: int = 0, +) -> tuple[FloatND, FloatND, FloatND]: + """Evaluate the branch-aware upper envelope at each query abscissa. + + Args: + endog_grid: Candidate endogenous grid points (resources), any order + within a branch; a NaN entry is a dead/padding candidate. + policy: Candidate policy values at `endog_grid`. + value: Candidate value-correspondence points at `endog_grid`. + marginal: Candidate marginal values (the supgradient) at `endog_grid`. + segment_id: Per-candidate branch label. A segment is a consecutive-pair + link whose endpoints share a label, so unrelated branches never join. + x_query: Abscissae at which to evaluate the envelope. + segment_block_size: When `0` (or at least the number of segments), the + dense `(n_query, n_segment)` reduction. A positive value below the + segment count instead runs the two-pass blocked scan, peaking at + `(n_query, segment_block_size)`; the result is identical. + + Returns: + Tuple of the envelope value, the winning segment's policy, and the + winning segment's marginal at each query, each shaped like `x_query`. A + query no live segment brackets yields NaN in all three. + """ + dead = jnp.isnan(endog_grid) | jnp.isnan(value) + # A link is a real segment only within one branch: both endpoints live and + # carrying the same label. + links = _SegmentLinks( + left_grid=endog_grid[:-1], + right_grid=endog_grid[1:], + left_value=value[:-1], + right_value=value[1:], + left_policy=policy[:-1], + right_policy=policy[1:], + left_marginal=marginal[:-1], + right_marginal=marginal[1:], + live=~dead[:-1] & ~dead[1:] & (segment_id[:-1] == segment_id[1:]), + ) + + query = jnp.asarray(x_query) + n_segment = links.left_grid.shape[0] + if 0 < segment_block_size < n_segment: + return _envelope_at_query_blocked( + links=links, query=query, block_size=segment_block_size + ) + + flat = query.reshape(-1)[:, None] + left_grid, right_grid = links.left_grid, links.right_grid + left_value, right_value = links.left_value, links.right_value + left_policy, right_policy = links.left_policy, links.right_policy + left_marginal, right_marginal = links.left_marginal, links.right_marginal + segment_live = links.live + lower = jnp.minimum(left_grid, right_grid)[None, :] + upper = jnp.maximum(left_grid, right_grid)[None, :] + brackets = segment_live[None, :] & (flat >= lower) & (flat <= upper) + + width = (right_grid - left_grid)[None, :] + safe_width = jnp.where(width == 0.0, 1.0, width) + relative = jnp.where(width == 0.0, 0.0, (flat - left_grid[None, :]) / safe_width) + value_interp = left_value[None, :] + relative * (right_value - left_value)[None, :] + policy_interp = ( + left_policy[None, :] + relative * (right_policy - left_policy)[None, :] + ) + marginal_interp = ( + left_marginal[None, :] + relative * (right_marginal - left_marginal)[None, :] + ) + + masked_value = jnp.where(brackets, value_interp, -jnp.inf) + any_bracket = jnp.any(brackets, axis=1) + max_value = jnp.max(masked_value, axis=1, keepdims=True) + # Break a value tie right-continuously, matching the kernel's `side="right"` + # read: among the bracketing segments attaining the maximum, the one with the + # larger value-slope is higher just to the right, so it carries the policy. + slope = (right_value - left_value)[None, :] / safe_width + near_max = brackets & (masked_value >= max_value - _VALUE_TIE_ATOL) + best = jnp.argmax(jnp.where(near_max, slope, -jnp.inf), axis=1) + env_value = jnp.where(any_bracket, max_value[:, 0], jnp.nan) + env_policy = jnp.where( + any_bracket, + jnp.take_along_axis(policy_interp, best[:, None], axis=1)[:, 0], + jnp.nan, + ) + env_marginal = jnp.where( + any_bracket, + jnp.take_along_axis(marginal_interp, best[:, None], axis=1)[:, 0], + jnp.nan, + ) + return ( + env_value.reshape(query.shape), + env_policy.reshape(query.shape), + env_marginal.reshape(query.shape), + ) + + +def _block_query_terms( + *, block: FloatND, live: BoolND, flat: Float1D +) -> tuple[BoolND, FloatND, FloatND, FloatND, FloatND]: + """Bracket-and-interpolate one segment block against every query. + + `block` is one `(block_size, 8)` slice of the stacked link endpoint columns + and `live` its `(block_size,)` live-flag slice. Returns the + `(n_query, block_size)` bracket mask and the value, policy, marginal, and + value-slope interpolated at each query for each link in the block β€” the same + quantities the dense path forms over all segments at once, but only for this + block, so the peak working set is `(n_query, block_size)`. + """ + left_grid, right_grid = block[:, 0], block[:, 1] + left_value, right_value = block[:, 2], block[:, 3] + left_policy, right_policy = block[:, 4], block[:, 5] + left_marginal, right_marginal = block[:, 6], block[:, 7] + + q = flat[:, None] + lower = jnp.minimum(left_grid, right_grid)[None, :] + upper = jnp.maximum(left_grid, right_grid)[None, :] + brackets = live[None, :] & (q >= lower) & (q <= upper) + + width = (right_grid - left_grid)[None, :] + safe_width = jnp.where(width == 0.0, 1.0, width) + relative = jnp.where(width == 0.0, 0.0, (q - left_grid[None, :]) / safe_width) + value_interp = left_value[None, :] + relative * (right_value - left_value)[None, :] + policy_interp = ( + left_policy[None, :] + relative * (right_policy - left_policy)[None, :] + ) + marginal_interp = ( + left_marginal[None, :] + relative * (right_marginal - left_marginal)[None, :] + ) + slope = (right_value - left_value)[None, :] / safe_width + return brackets, value_interp, policy_interp, marginal_interp, slope + + +def _envelope_at_query_blocked( + *, links: _SegmentLinks, query: FloatND, block_size: int +) -> tuple[FloatND, FloatND, FloatND]: + """Two-pass blocked equivalent of the dense `(n_query, n_segment)` reduction. + + Both passes are exact associative folds against a fixed target, so the result + matches the dense path (up to floating-point reassociation between the two + XLA lowerings): + + - Pass 1 accumulates the running per-query max over segment blocks β€” the + envelope value, with a running `any_bracket` flag. + - Pass 2 re-scans the blocks and, among segments whose value is within + `_VALUE_TIE_ATOL` of that (now fixed) envelope value, keeps the global + max-slope winner's policy and marginal (the dense path's right-continuous + tie-break). The strict cross-block `>` keeps the earliest such winner, + matching the dense `argmax`. + + The links are padded to a multiple of `block_size` with dead segments (which + never bracket) and reshaped to `(n_block, block_size)`; the scan peaks at + `(n_query, block_size)` working memory. + """ + flat = query.reshape(-1) + n_query = flat.shape[0] + n_segment = links.live.shape[0] + pad = (-n_segment) % block_size + + def _padded(column: FloatND, fill: float) -> FloatND: + if pad == 0: + return column + return jnp.concatenate([column, jnp.full((pad,), fill, dtype=column.dtype)]) + + columns = jnp.stack( + [ + _padded(links.left_grid, 0.0), + _padded(links.right_grid, 0.0), + _padded(links.left_value, 0.0), + _padded(links.right_value, 0.0), + _padded(links.left_policy, 0.0), + _padded(links.right_policy, 0.0), + _padded(links.left_marginal, 0.0), + _padded(links.right_marginal, 0.0), + ], + axis=1, + ) + live = ( + links.live + if pad == 0 + else jnp.concatenate([links.live, jnp.zeros((pad,), dtype=bool)]) + ) + blocks = columns.reshape(-1, block_size, columns.shape[1]) + live_blocks = live.reshape(-1, block_size) + dtype = links.left_grid.dtype + + def max_step( + carry: tuple[FloatND, BoolND], block_and_live: tuple[FloatND, BoolND] + ) -> tuple[tuple[FloatND, BoolND], None]: + running_max, any_bracket = carry + block, block_live = block_and_live + brackets, value_interp, *_ = _block_query_terms( + block=block, live=block_live, flat=flat + ) + block_max = jnp.max(jnp.where(brackets, value_interp, -jnp.inf), axis=1) + return ( + jnp.maximum(running_max, block_max), + any_bracket | jnp.any(brackets, axis=1), + ), None + + (running_max, any_bracket), _ = jax.lax.scan( + max_step, + ( + jnp.full((n_query,), -jnp.inf, dtype=dtype), + jnp.zeros((n_query,), dtype=bool), + ), + (blocks, live_blocks), + ) + env_value = jnp.where(any_bracket, running_max, jnp.nan) + + def policy_step( + carry: tuple[FloatND, FloatND, FloatND], + block_and_live: tuple[FloatND, BoolND], + ) -> tuple[tuple[FloatND, FloatND, FloatND], None]: + best_slope, best_policy, best_marginal = carry + block, block_live = block_and_live + brackets, value_interp, policy_interp, marginal_interp, slope = ( + _block_query_terms(block=block, live=block_live, flat=flat) + ) + near_max = brackets & (value_interp >= env_value[:, None] - _VALUE_TIE_ATOL) + candidate_slope = jnp.where(near_max, slope, -jnp.inf) + winner = jnp.argmax(candidate_slope, axis=1)[:, None] + block_slope = jnp.take_along_axis(candidate_slope, winner, axis=1)[:, 0] + block_policy = jnp.take_along_axis(policy_interp, winner, axis=1)[:, 0] + block_marginal = jnp.take_along_axis(marginal_interp, winner, axis=1)[:, 0] + take = block_slope > best_slope + return ( + jnp.where(take, block_slope, best_slope), + jnp.where(take, block_policy, best_policy), + jnp.where(take, block_marginal, best_marginal), + ), None + + (_, env_policy_flat, env_marginal_flat), _ = jax.lax.scan( + policy_step, + ( + jnp.full((n_query,), -jnp.inf, dtype=dtype), + jnp.full((n_query,), jnp.nan, dtype=dtype), + jnp.full((n_query,), jnp.nan, dtype=dtype), + ), + (blocks, live_blocks), + ) + env_policy = jnp.where(any_bracket, env_policy_flat, jnp.nan) + env_marginal = jnp.where(any_bracket, env_marginal_flat, jnp.nan) + return ( + env_value.reshape(query.shape), + env_policy.reshape(query.shape), + env_marginal.reshape(query.shape), + ) diff --git a/src/_lcm/egm/upper_envelope/rfc.py b/src/_lcm/egm/upper_envelope/rfc.py new file mode 100644 index 000000000..ea7f8d1f9 --- /dev/null +++ b/src/_lcm/egm/upper_envelope/rfc.py @@ -0,0 +1,209 @@ +"""Rooftop-Cut (RFC) upper-envelope refinement of EGM candidates. + +Implements the roof-top cut of Dobrescu, L., & Shanker, A. (2024). Using +Inverse Euler Equations to Solve Multidimensional Discrete-Continuous Dynamic +Models: A General Method. SSRN 4850746 (their Box 1). + +Inverting the Euler equation in models with discrete choices yields a value +*correspondence*: in non-concave regions, several candidate points share a +neighborhood of the endogenous grid, each on a different choice-specific value +segment. RFC selects the upper envelope by a dense dominance test: at each +candidate $j$ it builds the tangent (value) line from the supgradient +$\\mu_j = \\partial v / \\partial R$ (the exact value-row slope by the envelope +theorem) and deletes every neighbor $l$ within a search radius that + +- lies *below* $j$'s tangent β€” $v_l - v_j < \\mu_j\\,(R_l - R_j)$ β€” and +- sits across a policy jump β€” $|\\Delta c / \\Delta R| > $ `jump_thresh`. + +The jump gate is what spares a strictly concave segment: every point on a +concave curve lies below its neighbors' tangents, but only a genuine +segment-switch carries the policy discontinuity, so only switches are cut. + +Unlike FUES, RFC *only deletes* points β€” it never inserts the exact +segment-crossing abscissa. The refined output is therefore a NaN-padded, +weakly-ascending *subset* of the input candidates: the dominated points are +gone and the envelope points remain, with a kink landing between two retained +points (recovered by the downstream Hermite carry read to within local grid +spacing). The per-pair test has no sequential carry, so the kernel is a +`vmap`-friendly dense computation that generalizes to multidimensional grids. + +All shapes are static, so the kernel can be `jax.jit`-compiled and `jax.vmap`- +batched over a leading dimension of the candidate arrays. +""" + +import jax.numpy as jnp + +from lcm.typing import BoolND, Float1D, FloatND, ScalarInt + + +def refine_envelope( + *, + endog_grid: Float1D, + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, + n_refined: int, + search_radius: int = 10, + jump_thresh: float = 2.0, +) -> tuple[Float1D, Float1D, Float1D, ScalarInt]: + """Refine a candidate value correspondence to its upper envelope. + + The candidates may arrive in any order; they are sorted (NaN-stable) + ascending in `endog_grid` first. The refined arrays have static length + `n_refined`, hold the surviving envelope points in weakly ascending grid + order, and are NaN-padded in the tail. No crossing point is inserted β€” the + output is a subset of the (sorted) input candidates. + + Args: + endog_grid: Candidate endogenous grid points (resources), any order. + policy: Candidate policy values at `endog_grid`. + value: Candidate value-correspondence points at `endog_grid`. + marginal_utility: Candidate supgradient $\\mu = \\partial v / \\partial + R$, the exact value-row slope by the envelope theorem. + n_refined: Static length of the refined output arrays. + search_radius: Number of neighbors on each side (in sorted grid order) + inspected by the dominance test. + jump_thresh: Threshold on $|\\Delta c / \\Delta R|$ above which two + candidates are treated as lying on different value-function + segments. + + Returns: + Tuple of refined endogenous grid, refined policy, refined value (each + of length `n_refined`, NaN-padded), and the number of envelope points + `n_kept`. `n_kept > n_refined` signals overflow; the arrays then hold a + valid truncated prefix of the envelope. Callers must check the counter + rather than publish the truncated arrays silently β€” the EGM step + NaN-poisons its published rows on overflow so the solve loop's NaN + diagnostics name the offending (regime, period). + + """ + order = jnp.argsort(endog_grid) + grid = endog_grid[order] + policy_sorted = policy[order] + value_sorted = value[order] + mu = marginal_utility[order] + + # A dead candidate arrives NaN-filled (the EGM step poisons `-inf`-valued + # corners to NaN before refinement). Treat its value as `-inf` in the + # dominance test: it is then dominated by every finite point and can never + # dominate one, so it never survives and never deletes a live candidate. + dead = jnp.isnan(grid) | jnp.isnan(value_sorted) + value_for_test = jnp.where(dead, -jnp.inf, value_sorted) + grid_for_test = jnp.where(dead, jnp.inf, grid) + mu_for_test = jnp.where(dead, 0.0, mu) + + deleted_by_neighbor = _dominated_within_radius( + grid=grid_for_test, + policy=policy_sorted, + value=value_for_test, + marginal_utility=mu_for_test, + search_radius=search_radius, + jump_thresh=jump_thresh, + ) + survives = ~dead & ~deleted_by_neighbor + + # Compact survivors into the NaN-padded prefix, preserving sorted order. + position = jnp.cumsum(survives.astype(jnp.int32)) - 1 + slot = jnp.where(survives, position, n_refined) + refined_grid = jnp.full(n_refined, jnp.nan, dtype=grid.dtype) + refined_policy = jnp.full(n_refined, jnp.nan, dtype=policy_sorted.dtype) + refined_value = jnp.full(n_refined, jnp.nan, dtype=value_sorted.dtype) + refined_grid = refined_grid.at[slot].set(grid, mode="drop") + refined_policy = refined_policy.at[slot].set(policy_sorted, mode="drop") + refined_value = refined_value.at[slot].set(value_sorted, mode="drop") + + n_kept = jnp.sum(survives, dtype=jnp.int32) + return refined_grid, refined_policy, refined_value, n_kept + + +def _dominated_within_radius( + *, + grid: Float1D, + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, + search_radius: int, + jump_thresh: float, +) -> BoolND: + """Indicate which candidates a neighbor's tangent dominates across a jump. + + Builds the dense (point, offset) test: each candidate `l` is compared + against the `search_radius` candidates on each side. `l` is deleted iff + some in-radius neighbor `j` has `l` below `j`'s tangent *and* a policy jump + between them. + + Args: + grid: Sorted candidate endogenous grid points. + policy: Candidate policy values at `grid`. + value: Candidate value-correspondence points at `grid`. + marginal_utility: Candidate supgradient at `grid`. + search_radius: Number of neighbors on each side to inspect. + jump_thresh: Threshold on $|\\Delta c / \\Delta R|$. + + Returns: + Boolean indicator per candidate; `True` marks a dominated candidate. + + """ + n_input = grid.shape[0] + point = jnp.arange(n_input, dtype=jnp.int32) + # Signed offsets covering `search_radius` neighbors on each side. + offsets = jnp.concatenate( + [ + -jnp.arange(1, search_radius + 1, dtype=jnp.int32)[::-1], + jnp.arange(1, search_radius + 1, dtype=jnp.int32), + ] + ) + # neighbor[l, o] = the anchor j that tests candidate l at offset o. + neighbor = point[:, None] + offsets[None, :] + in_bounds = (neighbor >= 0) & (neighbor < n_input) + clipped = jnp.clip(neighbor, 0, n_input - 1) + + grid_j = grid[clipped] + policy_j = policy[clipped] + value_j = value[clipped] + mu_j = marginal_utility[clipped] + + grid_l = grid[:, None] + delta_grid = grid_l - grid_j + # `l` below `j`'s tangent line: v_l - v_j < mu_j * (R_l - R_j). + below_tangent = (value[:, None] - value_j) < mu_j * delta_grid - 1e-9 + policy_jump = _has_policy_jump( + grid_a=grid_j, + policy_a=policy_j, + grid_b=grid_l, + policy_b=policy[:, None], + jump_thresh=jump_thresh, + ) + deletes = in_bounds & below_tangent & policy_jump + return jnp.any(deletes, axis=1) + + +def _has_policy_jump( + *, + grid_a: FloatND, + policy_a: FloatND, + grid_b: FloatND, + policy_b: FloatND, + jump_thresh: float, +) -> BoolND: + """Indicate whether two points lie on different value-function segments. + + Points lie on different segments iff the policy secant $|\\Delta c / + \\Delta R|$ between them exceeds `jump_thresh`. Coincident abscissae carry + no jump. + + Args: + grid_a: Endogenous grid point(s) of the first point. + policy_a: Policy value(s) of the first point. + grid_b: Endogenous grid point(s) of the second point. + policy_b: Policy value(s) of the second point. + jump_thresh: Threshold on $|\\Delta c / \\Delta R|$. + + Returns: + Boolean indicator(s), broadcast over the inputs. + + """ + delta_grid = grid_b - grid_a + safe_delta = jnp.where(delta_grid == 0.0, 1.0, delta_grid) + policy_slope = jnp.where(delta_grid == 0.0, 0.0, (policy_b - policy_a) / safe_delta) + return jnp.abs(policy_slope) > jump_thresh diff --git a/src/_lcm/egm/upper_envelope/rfc_2d.py b/src/_lcm/egm/upper_envelope/rfc_2d.py new file mode 100644 index 000000000..950709382 --- /dev/null +++ b/src/_lcm/egm/upper_envelope/rfc_2d.py @@ -0,0 +1,239 @@ +"""On-device multidimensional Roof-top Cut: the k-NN radius-masked delete kernel. + +The multidimensional RFC of Dobrescu & Shanker (2024, their Box 1) selects the upper +envelope of a value *correspondence* over a 2-D (or higher) post-decision cloud by a +dense dominance test: at each candidate $i$ it forms the tangent plane from the value +supgradient $\\nabla v_i$ and deletes every $k$-nearest neighbour $j$ within a physical +radius that + +- lies below $i$'s tangent plane β€” $v_j - v_i < \\nabla v_i \\cdot (x_j - x_i)$ β€” and +- sits across a policy jump (the jump selector is policy column 0) β€” + $\\lVert\\sigma_j - \\sigma_i\\rVert / \\lVert x_j - x_i\\rVert > \\bar J$. + +Unlike the 1-D backend's sorted-grid neighbourhood, the multidimensional neighbours are +the $k-1$ strict nearest by Euclidean distance. KD-trees are not `jit`-able, so the +kernel computes the full pairwise distance matrix and takes the $k$ smallest per row +with `jax.lax.top_k`; this yields the same neighbour set as the host KD-tree reference +(`tests/solution/_rfc_2d_host.py`), against which the kernel is validated. The per-pair +test has no sequential carry, so the whole cut is a static-shape, `jit`-able dense +computation. Delete-only (no crossing insertion) keeps the output a subset of the input, +faithful to Box 1. + +The reference tuning constants are $\\bar J = 1 + 10^{-10}$, $\\rho = 0.5$, $k = 5$. +""" + +import itertools + +import jax +import jax.numpy as jnp + +from lcm.typing import BoolND, Float1D, Float2D, ScalarFloat + +# Reference tuning constants, verbatim from RFCSimple.py / RFC.py. +J_BAR_DEFAULT = 1.0 + 1e-10 +RADIUS_DEFAULT = 0.5 +K_DEFAULT = 5 + +# Publisher defaults: enough nearest survivors to bracket a target in a non-degenerate +# triangle, a small negative barycentric tolerance, and a squared-area floor that +# rejects near-collinear (degenerate) triangles. +K_PUBLISH_DEFAULT = 12 +EXTRAPOLATION_THRESHOLD_DEFAULT = 1e-9 +DEGENERATE_AREA_FLOOR = 1e-12 +# Minimum normalized mean-ratio shape quality `Q in (0, 1]` (1 = equilateral) a +# publish simplex must clear to count as well-conditioned; below it a sliver's +# affine interpolant is unstable. Generous enough not to reject ordinary +# acute/obtuse triangles (only ~20:1-and-worse slivers fall below it). +SHAPE_QUALITY_FLOOR = 0.1 + + +def rfc_delete_mask_2d( + *, + states: Float2D, + supgradients: Float2D, + values: Float1D, + policies: Float2D, + j_bar: float = J_BAR_DEFAULT, + radius: float = RADIUS_DEFAULT, + k: int = K_DEFAULT, +) -> BoolND: + """Return a boolean keep-mask for the candidate cloud (True = survives the cut). + + The kernel reproduces the host RFC reference: for each candidate $i$ it deletes any + of its $k-1$ strict nearest neighbours $j$ that lies below $i$'s tangent plane, + across a policy jump, and within `radius`. A point is kept unless some anchor + deletes it. + + Args: + states: Candidate post-decision states, shape `(n, d)`. + supgradients: Value supgradient at each candidate, shape `(n, d)`. + values: Candidate value, shape `(n,)`. + policies: Candidate policy vectors, shape `(n, dp)`; the jump selector uses + column 0 only, matching the reference's `sigma[:, [0]]`. + j_bar: Policy-jump threshold $\\bar J$. + radius: Neighbour distance threshold $\\rho$. + k: Number of KD-tree neighbours (including self) the reference queries; the cut + inspects the `k - 1` strict nearest. + + Returns: + Boolean array of shape `(n,)`; `True` for surviving (kept) candidates. + """ + n = states.shape[0] + n_neighbors = min(k - 1, n - 1) + + # diff[i, j] = x_j - x_i, so tangent[i, j] reads anchor i's gradient. + diff = states[None, :, :] - states[:, None, :] + distance = jnp.sqrt(jnp.sum(diff * diff, axis=-1)) + self_mask = jnp.eye(n, dtype=bool) + distance_no_self = jnp.where(self_mask, jnp.inf, distance) + + # k-NN restriction: a neighbour is in-set iff its distance is within the + # n_neighbors-th smallest of the row (self excluded by the +inf diagonal). + nearest_neg, _ = jax.lax.top_k(-distance_no_self, n_neighbors) + kth_distance = -nearest_neg[:, -1] + in_knn = distance_no_self <= kth_distance[:, None] + + tangent = jnp.einsum("id,ijd->ij", supgradients, diff) + value_gap = values[None, :] - values[:, None] + below_tangent = value_gap < tangent + + selector = policies[:, 0] + policy_gap = jnp.abs(selector[None, :] - selector[:, None]) + safe_distance = jnp.where(self_mask, 1.0, distance_no_self) + policy_jump = (policy_gap / safe_distance) > j_bar + + within_radius = distance_no_self < radius + + deletes = in_knn & below_tangent & policy_jump & within_radius + deleted = jnp.any(deletes, axis=0) + return ~deleted + + +def rfc_publish_2d( + *, + survivor_states: Float2D, + survivor_values: Float1D, + survivor_policies: Float2D, + target_states: Float2D, + valid: BoolND | None = None, + k: int = K_PUBLISH_DEFAULT, + extrapolation_threshold: float = EXTRAPOLATION_THRESHOLD_DEFAULT, +) -> tuple[Float1D, Float2D]: + """Publish value and policy at target states by local-simplex barycentric weights. + + The on-device stand-in for the host Delaunay publisher (D1): for each target, take + its `k` nearest survivors, enumerate every triangle among them, and select the + *most-local well-conditioned* containing triangle β€” the smallest-area simplex + (weights at or above `-extrapolation_threshold`) whose normalized shape quality + clears `SHAPE_QUALITY_FLOOR`. Locality keeps the affine fit tight (it tracks the + curved value surface instead of spanning a wide arc, the accuracy the KKT-masked + clouds need); the shape gate rejects ill-conditioned slivers that pass the area + floor. If every containing triangle is a sliver, the smallest containing one is + used (coverage over conditioning); a target with no containing triangle (outside + the survivor support) falls back to its nearest survivor. Value and policy are the + barycentric combination of the chosen triangle's vertices, which reproduces + survivor values exactly and is affine-exact in the hull. + + The `valid` mask lets a caller pass the *full* candidate cloud plus the cut's + keep-mask rather than a pre-filtered survivor array β€” the jit-friendly form, since + compacting survivors would change the array shape. Deleted candidates are pushed to + infinite distance (so they never enter a target's neighbourhood) and any triangle + that would use one as a vertex is rejected. + + Args: + survivor_states: Candidate states, shape `(s, d)` with `d == 2`. + survivor_values: Candidate values, shape `(s,)`. + survivor_policies: Candidate policy vectors, shape `(s, dp)`. + target_states: Query states, shape `(t, 2)`. + valid: Optional keep-mask, shape `(s,)`; `True` for surviving candidates. When + omitted every candidate is treated as a survivor. + k: Number of nearest survivors that form the local simplex search set. + extrapolation_threshold: Non-negative barycentric tolerance; a triangle counts + as containing the target when every weight is at least its negation. + + Returns: + Tuple of `(values, policies)`: published value `(t,)` and policy `(t, dp)`. + """ + n_survivors = survivor_states.shape[0] + k_eff = min(k, n_survivors) + triangles = jnp.asarray( + list(itertools.combinations(range(k_eff), 3)), dtype=jnp.int32 + ) + keep = jnp.ones(n_survivors, dtype=bool) if valid is None else valid + + def publish_one(query: Float1D) -> tuple[ScalarFloat, Float1D]: + raw_distance = jnp.linalg.norm(survivor_states - query, axis=1) + distance = jnp.where(keep, raw_distance, jnp.inf) + _, nearest_idx = jax.lax.top_k(-distance, k_eff) + verts = survivor_states[nearest_idx] + local_values = survivor_values[nearest_idx] + local_policies = survivor_policies[nearest_idx] + local_valid = keep[nearest_idx] + + a, b, c = triangles[:, 0], triangles[:, 1], triangles[:, 2] + p0, p1, p2 = verts[a], verts[b], verts[c] + edge1 = p1 - p0 + edge2 = p2 - p0 + to_query = query - p0 + d00 = jnp.sum(edge1 * edge1, axis=1) + d01 = jnp.sum(edge1 * edge2, axis=1) + d11 = jnp.sum(edge2 * edge2, axis=1) + d20 = jnp.sum(to_query * edge1, axis=1) + d21 = jnp.sum(to_query * edge2, axis=1) + # `denom` is the squared area (times 4): zero for collinear vertices. + denom = d00 * d11 - d01 * d01 + safe_denom = jnp.where(denom > 0.0, denom, 1.0) + w1 = (d11 * d20 - d01 * d21) / safe_denom + w2 = (d00 * d21 - d01 * d20) / safe_denom + w0 = 1.0 - w1 - w2 + + nondegenerate = denom > DEGENERATE_AREA_FLOOR + triangle_valid = local_valid[a] & local_valid[b] & local_valid[c] + contains = ( + (w0 >= -extrapolation_threshold) + & (w1 >= -extrapolation_threshold) + & (w2 >= -extrapolation_threshold) + & nondegenerate + & triangle_valid + ) + # Shape quality `Q = 4 sqrt(3) A / (l0^2 + l1^2 + l2^2)` (the standard + # normalized mean-ratio; `Q = 1` equilateral, `Q -> 0` sliver), from the + # squared edge lengths `d00`, `d11`, and `|edge2 - edge1|^2 = d00 + d11 - + # 2 d01`, with `4A = 2 sqrt(denom)`. The area floor alone passes + # ill-conditioned slivers; gating on `Q` rejects them so the affine + # interpolant stays stable. + edge_sq_sum = 2.0 * (d00 + d11 - d01) + safe_edge_sq_sum = jnp.where(edge_sq_sum > 0.0, edge_sq_sum, 1.0) + quality = ( + 2.0 * jnp.sqrt(3.0) * jnp.sqrt(jnp.maximum(denom, 0.0)) / safe_edge_sq_sum + ) + well_conditioned = quality > SHAPE_QUALITY_FLOOR + + # Prefer the *most local* (smallest-area) *well-conditioned* containing + # simplex: locality keeps the affine fit tight, the quality gate keeps it + # stable. If every containing simplex is a sliver, fall back to the smallest + # containing one (coverage over conditioning) before the nearest survivor. + score_good = jnp.where(contains & well_conditioned, -denom, -jnp.inf) + best_good = jnp.argmax(score_good) + found_good = score_good[best_good] > -jnp.inf + score_any = jnp.where(contains, -denom, -jnp.inf) + best_any = jnp.argmax(score_any) + found_any = score_any[best_any] > -jnp.inf + best = jnp.where(found_good, best_good, best_any) + found = found_good | found_any + + weights = jnp.array([w0[best], w1[best], w2[best]]) + vertex_values = jnp.array( + [local_values[a[best]], local_values[b[best]], local_values[c[best]]] + ) + vertex_policies = jnp.stack( + [local_policies[a[best]], local_policies[b[best]], local_policies[c[best]]] + ) + value_interp = weights @ vertex_values + policy_interp = weights @ vertex_policies + + value = jnp.where(found, value_interp, local_values[0]) + policy = jnp.where(found, policy_interp, local_policies[0]) + return value, policy + + return jax.vmap(publish_one)(target_states) diff --git a/src/_lcm/egm/validation.py b/src/_lcm/egm/validation.py new file mode 100644 index 000000000..4d69b5853 --- /dev/null +++ b/src/_lcm/egm/validation.py @@ -0,0 +1,1516 @@ +"""Build-time validation of the DC-EGM model contract. + +A regime configured with `solver=DCEGM(...)` must satisfy the structural +contract the endogenous grid method relies on. Every violation raises +`ModelInitializationError` at `Model` construction with a message naming the +offending piece. The rules, in the order they are checked: + +- exactly one continuous (*Euler*) state and one continuous action; process + states are exempt (they enter the value function as node-valued discrete + dimensions); every other continuous state must be *passive*: deterministic, + with a transition whose DAG ancestors include neither the continuous + action, the resources function, nor the post-decision function (the + current Euler state is allowed β€” see the savings-node-stage rule below), + and a grid that is not distributed (`batch_size` is honored) +- the post-decision function and the resources function exist in + `Regime.functions` (`inverse_marginal_utility` is optional β€” when omitted, + the iEGM path derives a numerical inverse from `utility`) +- the regime uses the default Bellman aggregator `H` +- the post-decision function consumes the continuous action and the + resources function (not the continuous state directly) +- no constraint touches the continuous state or action (EGM enforces the + budget identity and the borrowing limit intrinsically) +- `utility` does not depend on the continuous state (envelope condition) +- the resources function does not depend on the continuous action +- the Euler state's transition is deterministic, names the post-decision + function, and reaches the continuous action only through it +- everything evaluated at the savings-node stage (the Euler state's law, + the regime transition, stochastic weights, non-Euler state transitions) + is independent of the continuous action, the resources function, and the + post-decision function; any of them may read the current Euler state (the + kernel then solves per exogenous asset node, where current assets are + known), but only through values that are CONTINUOUS in the Euler state at + the resolution of the Euler grid β€” a numeric spot check on the grid nodes + plus two levels of cell-midpoint refinement rejects values that jump + (within a cell, a smooth function's quarter-cell increments shrink like a + derivative bound, while a cliff's increment survives subdivision; a jump + in the Euler law makes the child's value function discontinuous and the + true policy bunches at the discontinuity, a corner outside EGM's + candidate families, while a jump in the other savings-stage functions + breaks the smoothness-at-node-resolution assumption the per-node solve + relies on) +- grid hygiene: the Euler grid is not distributed (`batch_size` is honored), + and the savings grid covers the Euler grid's upper region +- every declared-reachable non-terminal target regime also uses DC-EGM with + the same Euler state (reachability is read off the regime transition: a + granular per-target mapping declares its key set, any coarse form reaches + every regime; brute-force regimes may target DC-EGM regimes) +- numeric spot checks on small grid samples, outside jit: consumption + recovery `post_decision β‰ˆ resources - action`, resources non-decreasing in + the Euler state, and `inverse_marginal_utility` consistent with + `jax.grad(utility)` (round-trip `(u')⁻¹(u'(c)) β‰ˆ c` plus strictly + decreasing `u'`). Checks whose pruned DAG needs unknown leaves (free model + parameters) are skipped β€” parameter values are not available at build time. + +""" + +import inspect +from collections.abc import Mapping +from typing import cast + +import jax +import jax.numpy as jnp +from dags import concatenate_functions, get_ancestors + +from _lcm.grids import ContinuousGrid, DiscreteGrid, Grid, IrregSpacedGrid +from _lcm.processes import _ContinuousStochasticProcess +from _lcm.typing import ( + ActionName, + FunctionName, + RegimeName, + StateName, + StateOrActionName, +) +from lcm.exceptions import GridInitializationError, ModelInitializationError +from lcm.phased import Phased +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.temporal_aggregation import H_linear +from lcm.transition import MarkovTransition +from lcm.typing import Float1D, FloatND, Int1D, IntND, ScalarFloat, UserFunction + +# Shrink threshold of the node-resolution continuity spot check. Within one +# Euler grid cell, a function that is smooth at node resolution has +# quarter-cell increments of roughly a quarter of the neighboring cells' +# node-level increments (a derivative bound under two midpoint subdivisions), +# while a cliff's increment survives subdivision unshrunk. The threshold sits +# between the two regimes; the criterion is scale-invariant (ratios of the +# function's own increments, with only a float-noise floor). +_CONTINUITY_SHRINK_FACTOR = 0.4 + + +def validate_dcegm_regimes( + *, + user_regimes: Mapping[RegimeName, UserRegime], +) -> None: + """Validate the DC-EGM contract for every regime with a `DCEGM` solver. + + Args: + user_regimes: Mapping of regime names to user-provided `Regime` + instances. + + Raises: + ModelInitializationError: If any regime with `solver=DCEGM(...)` + violates the DC-EGM model contract. + + """ + for regime_name, user_regime in user_regimes.items(): + if isinstance(user_regime.solver, DCEGM): + _validate_dcegm_regime( + regime_name=regime_name, + user_regime=user_regime, + user_regimes=user_regimes, + ) + + +def savings_stage_reads_euler_state(*, user_regime: UserRegime, solver: DCEGM) -> bool: + """Whether any savings-stage function reads the current Euler state. + + Runs the opaque-post-decision ancestor check (`Phased` resolved to the + solve side, per-target cells unpacked, `MarkovTransition` weights + unwrapped) over every savings-stage function: the Euler state's law, the + regime transition, and the non-Euler state transitions. The kernel + builder uses the result to switch to the per-exogenous-asset-node solve + mode, where every Euler-state read is a per-combo constant. The single + trigger keeps the kernel-mode dispatch in lockstep with the validation + relaxation: a savings-stage Euler-state read is admitted exactly when + the regime is solved per node. + + Args: + user_regime: The user-provided `Regime` instance. + solver: The regime's DC-EGM solver configuration. + + Returns: + `True` when any savings-stage function variant has the Euler state + among its DAG ancestors. + + """ + functions = _resolve_solve_functions(user_regime=user_regime) + return bool( + _savings_stage_euler_state_readers( + user_regime=user_regime, functions=functions, solver=solver + ) + ) + + +def _validate_dcegm_regime( + *, + regime_name: RegimeName, + user_regime: UserRegime, + user_regimes: Mapping[RegimeName, UserRegime], +) -> None: + """Run all DC-EGM contract checks for a single regime, in order.""" + solver = cast("DCEGM", user_regime.solver) + + _fail_if_terminal(regime_name=regime_name, user_regime=user_regime) + _fail_if_state_action_classification_invalid( + regime_name=regime_name, user_regime=user_regime, solver=solver + ) + _fail_if_required_functions_missing( + regime_name=regime_name, user_regime=user_regime, solver=solver + ) + _fail_if_custom_H(regime_name=regime_name, user_regime=user_regime) + + functions = _resolve_solve_functions(user_regime=user_regime) + + _fail_if_post_decision_signature_invalid( + regime_name=regime_name, functions=functions, solver=solver + ) + _fail_if_constraint_touches_continuous_variables( + regime_name=regime_name, + user_regime=user_regime, + functions=functions, + solver=solver, + ) + _fail_if_utility_depends_on_continuous_state( + regime_name=regime_name, functions=functions, solver=solver + ) + _fail_if_resources_depend_on_continuous_action( + regime_name=regime_name, functions=functions, solver=solver + ) + _fail_if_passive_state_invalid( + regime_name=regime_name, + user_regime=user_regime, + functions=functions, + solver=solver, + ) + _fail_if_euler_transition_stochastic( + regime_name=regime_name, user_regime=user_regime, solver=solver + ) + _fail_if_euler_transition_bypasses_post_decision( + regime_name=regime_name, + user_regime=user_regime, + functions=functions, + solver=solver, + ) + _fail_if_savings_stage_function_depends_on_decision( + regime_name=regime_name, + user_regime=user_regime, + functions=functions, + solver=solver, + ) + _fail_if_grid_hygiene_violated( + regime_name=regime_name, user_regime=user_regime, solver=solver + ) + _fail_if_target_regime_incompatible( + regime_name=regime_name, + user_regime=user_regime, + user_regimes=user_regimes, + solver=solver, + ) + try: + _fail_if_numeric_spot_checks_fail( + regime_name=regime_name, + user_regime=user_regime, + functions=functions, + solver=solver, + ) + _fail_if_savings_stage_function_jumps_in_euler_state( + regime_name=regime_name, + user_regime=user_regime, + functions=functions, + solver=solver, + ) + except GridInitializationError as error: + msg = ( + f"A numeric spot check of the DC-EGM contract in regime " + f"'{regime_name}' needs grid points at model construction, but a " + f"grid supplies them only at runtime: {error}" + ) + raise ModelInitializationError(msg) from error + + +def _fail_if_terminal(*, regime_name: RegimeName, user_regime: UserRegime) -> None: + """A terminal regime has nothing to solve, so a DCEGM solver is an error.""" + if user_regime.terminal: + msg = ( + f"Regime '{regime_name}' is terminal but configured with the DCEGM " + "solver. Terminal regimes have no optimization problem; remove the " + "`solver=DCEGM(...)` setting." + ) + raise ModelInitializationError(msg) + + +def _fail_if_state_action_classification_invalid( + *, + regime_name: RegimeName, + user_regime: UserRegime, + solver: DCEGM, +) -> None: + """Require exactly one continuous (Euler) state and one continuous action. + + Process states are exempt: they enter the value function as node-valued + discrete dimensions. Other continuous states are allowed as *passive* + states; `_fail_if_passive_state_invalid` verifies their passivity once + the regime's solve functions are resolved. + """ + continuous_states = _continuous_non_process_names( + grids=_solve_grids(slot=user_regime.states) + ) + continuous_actions = _continuous_non_process_names( + grids=_solve_grids(slot=user_regime.actions) + ) + + if solver.continuous_state not in continuous_states: + msg = ( + f"DCEGM `continuous_state` '{solver.continuous_state}' is not a " + f"continuous state of regime '{regime_name}'. Continuous " + f"(non-process) states: {continuous_states}." + ) + raise ModelInitializationError(msg) + + if solver.continuous_action not in continuous_actions: + msg = ( + f"DCEGM `continuous_action` '{solver.continuous_action}' is not a " + f"continuous action of regime '{regime_name}'. Continuous " + f"actions: {continuous_actions}." + ) + raise ModelInitializationError(msg) + + extra_actions = [a for a in continuous_actions if a != solver.continuous_action] + if extra_actions: + msg = ( + f"Regime '{regime_name}' has continuous actions {extra_actions} in " + f"addition to the DCEGM continuous action " + f"'{solver.continuous_action}'. The DCEGM solver supports exactly " + "one continuous action; further actions must be discrete." + ) + raise ModelInitializationError(msg) + + +def _fail_if_required_functions_missing( + *, + regime_name: RegimeName, + user_regime: UserRegime, + solver: DCEGM, +) -> None: + """Require the post-decision and resources functions. + + `inverse_marginal_utility` is *optional*: when a regime omits it, EGM derives + a numerical inverse from `utility` (the iEGM path), so it is not required here. + When supplied, it is validated against `jax.grad(utility)` separately. + """ + required: dict[FunctionName, str] = { + solver.post_decision_function: ( + "the post-decision function (`DCEGM.post_decision_function`)" + ), + solver.resources: "the resources function (`DCEGM.resources`)", + } + missing = [ + f"'{name}' β€” {role}" + for name, role in required.items() + if name not in user_regime.functions + ] + if missing: + msg = ( + f"Regime '{regime_name}' uses the DCEGM solver but is missing " + f"required entries in `functions`: {'; '.join(missing)}." + ) + raise ModelInitializationError(msg) + + +def _fail_if_custom_H(*, regime_name: RegimeName, user_regime: UserRegime) -> None: + """Require the default Bellman aggregator `H` at solve time. + + The Euler inversion hard-codes `H = utility + discount_factor * E[V']`, so a + custom *solve-phase* `H` would silently change the meaning of the solution. + A `Phased` `H` whose solve variant is the default aggregator is accepted β€” + DC-EGM never reads the simulate variant, so a naive present-bias regime + (`H = Phased(solve=H_linear, simulate=beta_delta_H)`) is admissible: the + present bias enters only the simulate-phase re-optimization, outside the + Euler inversion. + """ + raw_H = user_regime.functions.get("H") + solve_H = raw_H.solve if isinstance(raw_H, Phased) else raw_H + if solve_H is not H_linear: + msg = ( + f"Regime '{regime_name}' defines a custom solve-phase Bellman " + "aggregator `H`. The DCEGM solver hard-codes the default aggregator " + "`H = utility + discount_factor * E[V']` at solve time; remove the " + "custom `H` (a `Phased` `H` whose solve variant is `H_linear` is " + "accepted) or use the brute-force solver." + ) + raise ModelInitializationError(msg) + + +def _fail_if_post_decision_signature_invalid( + *, + regime_name: RegimeName, + functions: dict[FunctionName, UserFunction], + solver: DCEGM, +) -> None: + """The post-decision function consumes the action and the resources function.""" + arg_names = list( + inspect.signature(functions[solver.post_decision_function]).parameters + ) + if solver.continuous_action not in arg_names or solver.resources not in arg_names: + msg = ( + f"The post-decision function '{solver.post_decision_function}' of " + f"regime '{regime_name}' must take the continuous action " + f"'{solver.continuous_action}' and the resources function " + f"'{solver.resources}' as arguments; its arguments are " + f"{arg_names}." + ) + raise ModelInitializationError(msg) + if solver.continuous_state in arg_names: + msg = ( + f"The post-decision function '{solver.post_decision_function}' of " + f"regime '{regime_name}' must not depend on the continuous state " + f"'{solver.continuous_state}' directly; the state enters only " + f"through the resources function '{solver.resources}'." + ) + raise ModelInitializationError(msg) + + +def _fail_if_constraint_touches_continuous_variables( + *, + regime_name: RegimeName, + user_regime: UserRegime, + functions: dict[FunctionName, UserFunction], + solver: DCEGM, +) -> None: + """No constraint may touch the continuous state or action. + + EGM enforces the budget identity and the borrowing limit + (`savings_grid.start`) intrinsically; discrete-only constraints remain + supported. + """ + forbidden = {solver.continuous_state, solver.continuous_action} + for constraint_name, constraint_func in user_regime.constraints.items(): + # Constraints are phase-invariant by the slot grammar (`Phased` is + # rejected there), so the value is always a bare callable. + ancestors = _dag_ancestors( + functions=functions, + target_func=cast("UserFunction", constraint_func), + ) + bad = sorted(ancestors & forbidden) + if bad: + msg = ( + f"The constraint '{constraint_name}' of regime '{regime_name}' " + f"depends on the continuous variables {bad}. The DCEGM solver " + "enforces the budget identity and the borrowing limit " + "(`savings_grid.start`) intrinsically; only constraints on " + "discrete variables are supported. Remove this constraint." + ) + raise ModelInitializationError(msg) + + +def _fail_if_utility_depends_on_continuous_state( + *, + regime_name: RegimeName, + functions: dict[FunctionName, UserFunction], + solver: DCEGM, +) -> None: + """`utility` must reach the state only through the action (envelope condition).""" + ancestors = get_ancestors(functions, targets=["utility"], include_targets=False) + if solver.continuous_state in ancestors: + msg = ( + f"The utility function of regime '{regime_name}' depends on the " + f"continuous state '{solver.continuous_state}'. The DCEGM envelope " + "condition requires utility to reach the state only through the " + f"continuous action '{solver.continuous_action}'." + ) + raise ModelInitializationError(msg) + + +def _fail_if_resources_depend_on_continuous_action( + *, + regime_name: RegimeName, + functions: dict[FunctionName, UserFunction], + solver: DCEGM, +) -> None: + """Resources are pre-decision: they must not depend on the continuous action.""" + ancestors = get_ancestors( + functions, targets=[solver.resources], include_targets=False + ) + if solver.continuous_action in ancestors: + msg = ( + f"The resources function '{solver.resources}' of regime " + f"'{regime_name}' depends on the continuous action " + f"'{solver.continuous_action}'. Resources are what the continuous " + "action is paid out of and must be known before the action is " + "chosen." + ) + raise ModelInitializationError(msg) + + +def _fail_if_passive_state_invalid( + *, + regime_name: RegimeName, + user_regime: UserRegime, + functions: dict[FunctionName, UserFunction], + solver: DCEGM, +) -> None: + """Every non-Euler continuous state must be passive. + + A passive state rides along as a grid axis of the value function and the + EGM carry; its next value is computed at the savings-node stage and read + from the child carry by interpolation on the child's passive grid. That + requires, per passive state: + + - a deterministic transition (stochastic continuous dynamics belong in a + process state), + - transition DAG ancestors excluding the continuous action, the + resources function, and the post-decision function (none of which are + known at the savings-node stage). The current Euler state is an + allowed ancestor: the kernel then solves per exogenous asset node, + where the state's value is known (the read must be continuous at node + resolution β€” checked by the savings-stage continuity spot check), + - a grid that is not distributed; `batch_size` is honored (it splays the + passive state's combo axis via productmap to shed memory), while a + continuous axis cannot be sharded. + """ + passive_names = [ + name + for name in _continuous_non_process_names( + grids=_solve_grids(slot=user_regime.states) + ) + if name != solver.continuous_state + ] + opaque_functions = _without( + functions=functions, names={solver.post_decision_function, solver.resources} + ) + forbidden = { + solver.continuous_action, + solver.resources, + solver.post_decision_function, + } + for state_name in passive_names: + value = user_regime.state_transitions.get(state_name) + if value is None: + # Transition coverage is validated when the effective regimes are + # built; a missing entry gets its own error there. + continue + is_stochastic = isinstance(value, MarkovTransition) or ( + isinstance(value, Mapping) + and any(isinstance(v, MarkovTransition) for v in value.values()) + ) + if is_stochastic: + msg = ( + f"The transition of the continuous state '{state_name}' in " + f"regime '{regime_name}' is stochastic. A non-Euler continuous " + "state in a DCEGM regime must be passive (deterministic); use " + "a stochastic process state (e.g. Rouwenhorst or Tauchen) for " + "stochastic continuous dynamics." + ) + raise ModelInitializationError(msg) + for label, transition_func in _transition_variants(value=value): + ancestors = _dag_ancestors( + functions=opaque_functions, target_func=transition_func + ) + bad = sorted(ancestors & forbidden) + if bad: + msg = ( + f"The continuous state '{state_name}' of regime " + f"'{regime_name}' is not passive: its transition{label} " + f"depends on {bad}. A passive continuous state's " + "transition must not depend on the continuous action " + f"'{solver.continuous_action}', the resources function " + f"'{solver.resources}', or the post-decision function " + f"'{solver.post_decision_function}' β€” those values are " + "unknown until the EGM step has run. (Reading the Euler " + f"state '{solver.continuous_state}' is allowed: the " + "kernel then solves per exogenous asset node.)" + ) + raise ModelInitializationError(msg) + grid = cast("ContinuousGrid", user_regime.states[state_name]) + # `batch_size` on a passive state splays its combo axis (via productmap) + # to shed memory; `distributed` stays rejected (a continuous axis + # cannot be sharded). + if grid.distributed: + msg = ( + f"The grid of the passive continuous state '{state_name}' in " + f"regime '{regime_name}' must not be distributed in a DCEGM " + f"regime (got distributed={grid.distributed})." + ) + raise ModelInitializationError(msg) + + +def _fail_if_euler_transition_stochastic( + *, + regime_name: RegimeName, + user_regime: UserRegime, + solver: DCEGM, +) -> None: + """The Euler state's transition must be deterministic.""" + value = user_regime.state_transitions.get(solver.continuous_state) + is_stochastic = isinstance(value, MarkovTransition) or ( + isinstance(value, Mapping) + and any(isinstance(v, MarkovTransition) for v in value.values()) + ) + if is_stochastic: + msg = ( + f"The transition of the Euler state '{solver.continuous_state}' in " + f"regime '{regime_name}' is stochastic. The DCEGM solver requires " + "a deterministic continuous-state transition (stochastic discrete " + "transitions and process states are fully supported)." + ) + raise ModelInitializationError(msg) + + +def _fail_if_euler_transition_bypasses_post_decision( + *, + regime_name: RegimeName, + user_regime: UserRegime, + functions: dict[FunctionName, UserFunction], + solver: DCEGM, +) -> None: + """The Euler transition consumes the post-decision function. + + With the post-decision and resources functions removed from the DAG, + their names become leaf inputs, so the ancestor set reveals whether the + transition reaches the continuous action or the resources function + through any other channel. The current Euler state is an allowed + transition ancestor: the kernel then solves per exogenous asset node, + where the residual is a per-combo constant + (`savings_stage_reads_euler_state` reports this mode). + """ + bypass_msg = ( + f"The transition of the Euler state '{solver.continuous_state}' in " + f"regime '{regime_name}' must consume the post-decision function " + f"'{solver.post_decision_function}' and reach " + f"'{solver.continuous_action}' only through it." + ) + value = user_regime.state_transitions.get(solver.continuous_state) + if value is None: + msg = ( + f"{bypass_msg} It is declared as a fixed state (identity " + "transition), which bypasses the post-decision function." + ) + raise ModelInitializationError(msg) + + opaque_functions = _without( + functions=functions, names={solver.post_decision_function, solver.resources} + ) + forbidden = { + solver.continuous_action, + solver.resources, + } + for label, transition_func in _transition_variants(value=value): + ancestors = _dag_ancestors( + functions=opaque_functions, + target_func=transition_func, + ) + bad = sorted(ancestors & forbidden) + if solver.post_decision_function not in ancestors or bad: + msg = ( + f"{bypass_msg} The transition{label} has DAG ancestors " + f"{sorted(ancestors)}; forbidden direct dependencies: {bad}." + ) + raise ModelInitializationError(msg) + + +def _fail_if_savings_stage_function_depends_on_decision( + *, + regime_name: RegimeName, + user_regime: UserRegime, + functions: dict[FunctionName, UserFunction], + solver: DCEGM, +) -> None: + """Savings-node-stage functions must not depend on the current decision. + + At a savings node, the continuous action and the resources are unknown + (they are EGM outputs). The regime transition, every stochastic + transition weight, and every non-Euler state transition must therefore + be independent of the continuous action, the resources function, and + the post-decision function. Reading the current Euler state is allowed: + the kernel then solves per exogenous asset node + (`savings_stage_reads_euler_state` reports this mode), where the read + is a per-combo constant β€” its continuity at node resolution is checked + by `_fail_if_savings_stage_function_jumps_in_euler_state`. + """ + opaque_functions = _without( + functions=functions, names={solver.post_decision_function, solver.resources} + ) + forbidden = { + solver.continuous_action, + solver.resources, + solver.post_decision_function, + } + for role, label, func in _savings_stage_candidates( + user_regime=user_regime, solver=solver + ): + if role == "euler_law": + # The Euler state's own law has its dedicated structural check + # (`_fail_if_euler_transition_bypasses_post_decision`). + continue + ancestors = _dag_ancestors(functions=opaque_functions, target_func=func) + bad = sorted(ancestors & forbidden) + if bad: + msg = ( + f"The {label} of regime '{regime_name}' depends on {bad}. " + "Functions evaluated at the savings-node stage (regime " + "transition probabilities, stochastic transition weights, and " + "non-Euler state transitions) must not depend on the " + f"continuous action '{solver.continuous_action}', the " + f"resources function '{solver.resources}', or the " + f"post-decision function '{solver.post_decision_function}' β€” " + "those values are unknown until the EGM step has run." + ) + raise ModelInitializationError(msg) + + +def _savings_stage_candidates( + *, + user_regime: UserRegime, + solver: DCEGM, +) -> list[tuple[str, str, UserFunction]]: + """Enumerate every savings-stage function variant of a regime. + + Coarse, `MarkovTransition`-wrapped, `Phased`, and granular per-target + forms all unpack to plain callables via `_transition_variants`. + + Returns: + List of `(role, label, func)` triples, with role one of + `"euler_law"`, `"regime_transition"`, and `"state_transition"`. + + """ + candidates: list[tuple[str, str, UserFunction]] = [] + euler_value = user_regime.state_transitions.get(solver.continuous_state) + if euler_value is not None: + for label, transition_func in _transition_variants(value=euler_value): + candidates.append( + ( + "euler_law", + f"transition of the Euler state '{solver.continuous_state}'{label}", + transition_func, + ) + ) + if user_regime.transition is not None: + for label, regime_transition in _transition_variants( + value=user_regime.transition + ): + candidates.append( + ( + "regime_transition", + f"regime transition function{label}", + regime_transition, + ) + ) + for state_name, value in user_regime.state_transitions.items(): + if state_name == solver.continuous_state or value is None: + continue + for label, transition_func in _transition_variants(value=value): + candidates.append( + ( + "state_transition", + f"transition of state '{state_name}'{label}", + transition_func, + ) + ) + return candidates + + +def _savings_stage_euler_state_readers( + *, + user_regime: UserRegime, + functions: dict[FunctionName, UserFunction], + solver: DCEGM, +) -> list[tuple[str, str, UserFunction]]: + """Savings-stage function variants whose DAG ancestors include the Euler state. + + The post-decision and resources functions are opaque (removed from the + DAG), so only direct decision-time reads of the Euler state count. + + Returns: + List of `(role, label, func)` triples, filtered from + `_savings_stage_candidates`. + + """ + opaque_functions = _without( + functions=functions, names={solver.post_decision_function, solver.resources} + ) + return [ + (role, label, func) + for role, label, func in _savings_stage_candidates( + user_regime=user_regime, solver=solver + ) + if solver.continuous_state + in _dag_ancestors(functions=opaque_functions, target_func=func) + ] + + +def _fail_if_grid_hygiene_violated( + *, + regime_name: RegimeName, + user_regime: UserRegime, + solver: DCEGM, +) -> None: + """Reject runtime-supplied points and distributed grids; savings grid covers + the Euler grid. + + `batch_size` is honored on the Euler, savings, and discrete-state grids (it + only splays combo/node axes to shed memory); it is rejected on discrete + actions, whose logsum aggregation needs every action value at once. + """ + # Rule 1 has already established that the Euler state's grid is a + # (non-process) continuous grid. + euler_grid = cast("ContinuousGrid", user_regime.states[solver.continuous_state]) + # DC-EGM builds its kernels (savings nodes, carry shapes, numeric spot + # checks) at model-construction time, so these grids must carry their + # points then β€” runtime-supplied points cannot work. + kernel_grids = { + "DCEGM savings grid": solver.savings_grid, + f"grid of the Euler state '{solver.continuous_state}'": euler_grid, + f"grid of the continuous action '{solver.continuous_action}'": ( + user_regime.actions[solver.continuous_action] + ), + } + for role, grid in kernel_grids.items(): + if isinstance(grid, IrregSpacedGrid) and grid.pass_points_at_runtime: + msg = ( + f"The {role} in regime '{regime_name}' supplies its points " + "only at runtime via params; a DCEGM regime needs the points " + "at model construction. Supply them via `points=...`." + ) + raise ModelInitializationError(msg) + # `batch_size` on a discrete state splays its combo axis: the per-combo + # solve runs in `productmap` blocks (per-axis `lax.map`) reassembled into + # the whole combo product before the carry is built, so carry rows still + # carry whole discrete axes. `distributed` stays rejected β€” the kernel + # selects child carry rows by integer indexing along whole discrete axes, + # which a sharded (per-device slice) axis would break. + for name, grid in user_regime.states.items(): + if isinstance(grid, DiscreteGrid) and grid.distributed: + msg = ( + f"The grid of the discrete state '{name}' in regime " + f"'{regime_name}' must not be distributed in a DCEGM regime " + f"(got distributed={grid.distributed})." + ) + raise ModelInitializationError(msg) + # Discrete actions cannot be batched or distributed: the discrete-action + # aggregation (logsum over the action axes) needs every action value at + # once, so its axis is never split. + for name, grid in user_regime.actions.items(): + if isinstance(grid, DiscreteGrid) and ( + grid.batch_size != 0 or grid.distributed + ): + msg = ( + f"The grid of the discrete action '{name}' in regime " + f"'{regime_name}' must not be batched or distributed in a " + f"DCEGM regime (got batch_size={grid.batch_size}, " + f"distributed={grid.distributed})." + ) + raise ModelInitializationError(msg) + # `batch_size` on the Euler grid is honored: it splays the per-asset-node + # solve into blocks (`lax.map`) to shed peak working-set memory, leaving the + # value function unchanged. `distributed` remains disallowed β€” a continuous + # axis cannot be sharded (rejected at grid construction). + if euler_grid.distributed: + msg = ( + f"The grid of the Euler state '{solver.continuous_state}' in " + f"regime '{regime_name}' must not be distributed in a DCEGM regime " + f"(got distributed={euler_grid.distributed})." + ) + raise ModelInitializationError(msg) + # `batch_size` on the savings grid is honored: it splays the per-savings-node + # continuation computation into blocks (`lax.map`) to shed the dominant + # egm_step working buffer, leaving the value function unchanged. `distributed` + # remains disallowed β€” a continuous axis cannot be sharded. + if solver.savings_grid.distributed: + msg = ( + f"The DCEGM savings grid of regime '{regime_name}' must not be " + f"distributed (got distributed={solver.savings_grid.distributed})." + ) + raise ModelInitializationError(msg) + savings_max = float(jnp.max(solver.savings_grid.to_jax())) + euler_max = float(jnp.max(euler_grid.to_jax())) + if savings_max < euler_max: + msg = ( + f"The DCEGM savings grid of regime '{regime_name}' ends at " + f"{savings_max}, below the upper end {euler_max} of the " + f"'{solver.continuous_state}' grid. An undersized savings grid " + "silently edge-clamps the endogenous grid at high values of " + f"'{solver.continuous_state}'; extend `savings_grid`." + ) + raise ModelInitializationError(msg) + + +def _fail_if_target_regime_incompatible( + *, + regime_name: RegimeName, + user_regime: UserRegime, + user_regimes: Mapping[RegimeName, UserRegime], + solver: DCEGM, +) -> None: + """Reachable non-terminal targets must be DCEGM regimes with the same state. + + Terminal targets are always allowed, and brute-force regimes may target + DC-EGM regimes (they only consume the target's value-function array). + """ + for target_name in sorted( + _reachable_target_names(user_regime=user_regime, user_regimes=user_regimes) + ): + target = user_regimes[target_name] + if target.terminal: + continue + if not isinstance(target.solver, DCEGM): + msg = ( + f"Regime '{regime_name}' uses the DCEGM solver and can reach " + f"the non-terminal regime '{target_name}', which uses " + f"{type(target.solver).__name__}. Every reachable non-terminal " + "target of a DCEGM regime must itself use the DCEGM solver " + "(brute-force regimes may target DCEGM regimes, not the other " + "way around)." + ) + raise ModelInitializationError(msg) + if target.solver.continuous_state != solver.continuous_state: + msg = ( + f"Regime '{regime_name}' uses the DCEGM solver with Euler " + f"state '{solver.continuous_state}' but can reach regime " + f"'{target_name}', whose DCEGM Euler state is " + f"'{target.solver.continuous_state}'. All mutually reachable " + "DCEGM regimes must share the same Euler continuous state." + ) + raise ModelInitializationError(msg) + + +def _fail_if_numeric_spot_checks_fail( + *, + regime_name: RegimeName, + user_regime: UserRegime, + functions: dict[FunctionName, UserFunction], + solver: DCEGM, +) -> None: + """Numeric spot checks on small grid samples, evaluated eagerly (no jit). + + - resources non-decreasing in the Euler state, + - consumption recovery `post_decision β‰ˆ resources - action`, + - `inverse_marginal_utility` consistent with `jax.grad(utility)`: + round-trip `(u')⁻¹(u'(c)) β‰ˆ c`, and `u'` strictly decreasing. + + Any check whose pruned DAG requires inputs that are neither states nor + actions (i.e. free model parameters) is skipped: parameter values are + not available at build time. + """ + x64_enabled = bool(jax.config.read("jax_enable_x64")) + atol = 1e-8 if x64_enabled else 1e-4 + rtol = 1e-6 if x64_enabled else 1e-3 + + grids: dict[StateOrActionName, Grid] = { + **_solve_grids(slot=user_regime.states), + **_solve_grids(slot=user_regime.actions), + } + euler_sample = _grid_sample(grid=grids[solver.continuous_state]) + action_sample = _grid_sample(grid=grids[solver.continuous_action]) + n_sample = min(euler_sample.shape[0], action_sample.shape[0]) + + resources_func = concatenate_functions(functions, targets=solver.resources) + resources_kwargs = _fixed_kwargs( + func=resources_func, + grids=grids, + varied={solver.continuous_state}, + ) + if resources_kwargs is not None: + resources_at = [ + _call_with_varied( + func=resources_func, + fixed=resources_kwargs, + varied={solver.continuous_state: w}, + ) + for w in euler_sample + ] + # Asset-row mode (a savings-stage function reads the Euler state) + # publishes the carry marginal by dividing by the resources slope + # `dR/dA`, so a flat (zero-slope) resources region there would make the + # marginal non-finite. Require strictly increasing resources in that + # mode, not merely non-decreasing. + require_strict = savings_stage_reads_euler_state( + user_regime=user_regime, solver=solver + ) + + def _violates( + r_lo: float, r_hi: float, *, strict: bool = require_strict + ) -> bool: + return r_hi <= r_lo + atol if strict else r_hi < r_lo - atol + + bad = [ + (float(w_lo), float(w_hi)) + for w_lo, w_hi, r_lo, r_hi in zip( + euler_sample[:-1], + euler_sample[1:], + resources_at[:-1], + resources_at[1:], + strict=True, + ) + if _violates(float(r_lo), float(r_hi)) + ] + if bad: + requirement = "strictly increasing" if require_strict else "non-decreasing" + reason = ( + " This regime reads the Euler state at the savings stage, so the " + "carry marginal divides by the resources slope β€” a flat region " + "would make it non-finite." + if require_strict + else "" + ) + msg = ( + f"The resources function '{solver.resources}' of regime " + f"'{regime_name}' must be {requirement} in " + f"'{solver.continuous_state}'; it violates that on the sample " + f"intervals {bad}.{reason}" + ) + raise ModelInitializationError(msg) + + post_func = concatenate_functions( + functions, targets=solver.post_decision_function + ) + post_kwargs = _fixed_kwargs( + func=post_func, + grids=grids, + varied={solver.continuous_state, solver.continuous_action}, + ) + if post_kwargs is not None: + for w, c in zip( + euler_sample[:n_sample], action_sample[:n_sample], strict=True + ): + resources_value = _call_with_varied( + func=resources_func, + fixed=resources_kwargs, + varied={solver.continuous_state: w}, + ) + post_value = _call_with_varied( + func=post_func, + fixed=post_kwargs, + varied={ + solver.continuous_state: w, + solver.continuous_action: c, + }, + ) + expected = resources_value - c + if not _isclose( + actual=post_value, expected=expected, rtol=rtol, atol=atol + ): + msg = ( + f"Consumption recovery fails in regime '{regime_name}': " + f"the post-decision function must satisfy " + f"`{solver.post_decision_function} = {solver.resources} " + f"- {solver.continuous_action}`. At " + f"{solver.continuous_state}={float(w)}, " + f"{solver.continuous_action}={float(c)}: " + f"{solver.post_decision_function}={float(post_value)} " + f"but {solver.resources} - {solver.continuous_action}=" + f"{float(expected)}." + ) + raise ModelInitializationError(msg) + + _fail_if_inverse_marginal_utility_inconsistent( + regime_name=regime_name, + functions=functions, + solver=solver, + grids=grids, + action_sample=action_sample, + rtol=rtol, + atol=atol, + ) + + +def _fail_if_inverse_marginal_utility_inconsistent( + *, + regime_name: RegimeName, + functions: dict[FunctionName, UserFunction], + solver: DCEGM, + grids: dict[StateOrActionName, Grid], + action_sample: Float1D, + rtol: float, + atol: float, +) -> None: + """Check `(u')⁻¹(u'(c)) β‰ˆ c` and strict monotonicity of `u'` on a sample. + + Skipped when the regime supplies no `inverse_marginal_utility`: the iEGM path + inverts `u'` numerically, so there is no analytic inverse to check against. + """ + if "inverse_marginal_utility" not in functions: + return + inverse_func = concatenate_functions(functions, targets="inverse_marginal_utility") + inverse_arg_names = list(inspect.signature(inverse_func).parameters) + if "marginal_continuation" not in inverse_arg_names: + msg = ( + f"The function 'inverse_marginal_utility' of regime " + f"'{regime_name}' must take an argument named " + f"'marginal_continuation' (the marginal continuation value to " + f"invert); its arguments are {inverse_arg_names}." + ) + raise ModelInitializationError(msg) + + utility_func = concatenate_functions(functions, targets="utility") + if solver.continuous_action not in inspect.signature(utility_func).parameters: + return + # Run the concavity and round-trip checks at a few discrete-combo contexts, + # not just the grid's lower corner: a utility (or inverse) that reads a + # discrete/passive state as a parameter can be consistent at one combo and + # wrong at another. The contexts are index-aligned, so the j-th utility and + # inverse contexts bind shared arguments to the same grid points. + utility_contexts = _combo_contexts( + func=utility_func, grids=grids, varied={solver.continuous_action} + ) + inverse_contexts = _combo_contexts( + func=inverse_func, grids=grids, varied={"marginal_continuation"} + ) + if not utility_contexts or not inverse_contexts: + return + + for utility_kwargs, inverse_kwargs in zip( + utility_contexts, inverse_contexts, strict=True + ): + + def utility_of_action( + action_value: ScalarFloat, + _kwargs: dict[str, object] = utility_kwargs, + ) -> ScalarFloat: + return utility_func(**_kwargs, **{solver.continuous_action: action_value}) + + marginal_utility = [jax.grad(utility_of_action)(c) for c in action_sample] + + non_decreasing = [ + (float(c_lo), float(c_hi)) + for c_lo, c_hi, mu_lo, mu_hi in zip( + action_sample[:-1], + action_sample[1:], + marginal_utility[:-1], + marginal_utility[1:], + strict=True, + ) + if float(mu_hi) >= float(mu_lo) + ] + if non_decreasing: + msg = ( + f"The marginal utility of '{solver.continuous_action}' in regime " + f"'{regime_name}' (computed via `jax.grad` of the utility DAG) " + "must be strictly decreasing β€” DCEGM requires strictly concave " + f"utility. It fails to decrease on the sample intervals " + f"{non_decreasing}." + ) + raise ModelInitializationError(msg) + + for c, mu in zip(action_sample, marginal_utility, strict=True): + recovered = inverse_func(**inverse_kwargs, marginal_continuation=mu) + if not _isclose(actual=recovered, expected=c, rtol=rtol, atol=atol): + msg = ( + f"'inverse_marginal_utility' of regime '{regime_name}' is " + "inconsistent with `jax.grad` of the utility DAG: the " + f"round-trip `(u')⁻¹(u'(c))` at " + f"{solver.continuous_action}={float(c)} yields " + f"{float(recovered)} (marginal utility {float(mu)})." + ) + raise ModelInitializationError(msg) + + +def _fail_if_savings_stage_function_jumps_in_euler_state( + *, + regime_name: RegimeName, + user_regime: UserRegime, + functions: dict[FunctionName, UserFunction], + solver: DCEGM, +) -> None: + """Savings-stage reads of the Euler state must be continuous at node resolution. + + The per-exogenous-asset-node solve evaluates every savings-stage + Euler-state read at the grid nodes and publishes per-node results, which + is exact only when the read is smooth at the resolution of the Euler + grid. A jump in the Euler state's own law additionally makes the child's + value function discontinuous, so the true policy bunches next-period + wealth exactly at the discontinuity β€” a corner where the Euler equation + does not hold, so EGM's candidate families (interior Euler inversions + plus the closed-form credit-constrained segment) structurally exclude + the optimum. Offending functions are rejected at build time rather than + solved approximately. + + Numeric spot check: every savings-stage variant whose DAG ancestors + include the Euler state is evaluated over the Euler grid nodes plus two + levels of cell-midpoint refinement (the Euler law at a fixed savings + value), in a few discrete-combo contexts sampled from the grids. + `_find_jump_at_node_resolution` flags cells whose refined increments do + not shrink under subdivision β€” a smooth band with dedicated nodes across + it passes, a band narrower than one grid cell is a cliff at node + resolution. Variants whose pruned DAG needs free model parameters are + skipped (their values are unknown at build time). + """ + x64_enabled = bool(jax.config.read("jax_enable_x64")) + base_atol = 1e-8 if x64_enabled else 1e-4 + + grids: dict[StateOrActionName, Grid] = { + **_solve_grids(slot=user_regime.states), + **_solve_grids(slot=user_regime.actions), + } + euler_points = jnp.sort(grids[solver.continuous_state].to_jax()) + euler_sample = _node_resolution_sample(grid_points=euler_points) + savings_points = solver.savings_grid.to_jax() + savings_value = savings_points[savings_points.shape[0] // 2] + + functions_without_post = _without( + functions=functions, names={solver.post_decision_function} + ) + for role, label, func in _savings_stage_euler_state_readers( + user_regime=user_regime, functions=functions, solver=solver + ): + target_name = "__dcegm_validation_target__" + law_func = concatenate_functions( + functions={**functions_without_post, target_name: func}, + targets=target_name, + ) + varied = {solver.continuous_state, solver.post_decision_function} + for context in _combo_contexts(func=law_func, grids=grids, varied=varied): + law_values = _law_values_on_sample( + law_func=law_func, + context=context, + euler_state_name=solver.continuous_state, + post_decision_name=solver.post_decision_function, + savings_value=savings_value, + euler_sample=euler_sample, + ) + jump_location = _find_jump_at_node_resolution( + grid_points=euler_points, values=law_values, atol=base_atol + ) + if jump_location is not None: + consequence = ( + ( + "A jump in the law makes the child's value function " + "discontinuous, and the true policy bunches " + f"next-period '{solver.continuous_state}' exactly at " + "the discontinuity β€” a corner where the Euler " + "equation does not hold, which EGM's candidate set " + "cannot represent." + ) + if role == "euler_law" + else ( + "Savings-stage reads of the Euler state are " + "evaluated per exogenous asset node, which is exact " + "only when they are smooth at the resolution of the " + f"'{solver.continuous_state}' grid." + ) + ) + msg = ( + f"The {label} in regime '{regime_name}' reads the " + f"current Euler state '{solver.continuous_state}' but is " + "discontinuous in it at the resolution of the " + f"'{solver.continuous_state}' grid: its value jumps near " + f"{solver.continuous_state} β‰ˆ {jump_location}. " + f"{consequence} If the function is a continuous band " + "steeper than the grid resolves, add grid nodes across " + "the band; otherwise make it continuous in " + f"'{solver.continuous_state}' (kinks are fine), e.g. by " + "phasing the term out instead of cutting it off." + ) + raise ModelInitializationError(msg) + + +def _node_resolution_sample(*, grid_points: Float1D) -> Float1D: + """Grid nodes plus two levels of cell-midpoint refinement (quarter points). + + Args: + grid_points: Sorted 1d grid points (`n` nodes). + + Returns: + Sorted sample of length `4 * (n - 1) + 1`: every node plus the + quarter points of every cell. + + """ + left = grid_points[:-1] + right = grid_points[1:] + offsets = jnp.asarray([0.0, 0.25, 0.5, 0.75]) + refined = (left[:, None] + (right - left)[:, None] * offsets[None, :]).reshape(-1) + return jnp.concatenate([refined, grid_points[-1:]]) + + +def _find_jump_at_node_resolution( + *, + grid_points: Float1D, + values: FloatND | IntND, + atol: float, +) -> float | None: + """Approximate location of the first cell with a sub-node-resolution jump. + + `values` are the function's values on `_node_resolution_sample` of + `grid_points` (vector-valued outputs allowed; increments are reduced + with the maximum over output components). For each grid cell, the + maximum quarter-cell increment is compared against the node-level + increments of the cell and its neighbors: a function that is smooth at + node resolution shrinks like a derivative bound under two midpoint + subdivisions (quarter-cell increments roughly a quarter of the + neighborhood's node-level increments), while a cliff's increment β€” or a + band without dedicated nodes across it β€” survives subdivision unshrunk. + The criterion is scale-invariant up to a float-noise floor. + + Returns: + Midpoint of the first offending cell, or `None` when every cell's + refined increments shrink as a smooth function's would. + + """ + flat = jnp.asarray(values).reshape(values.shape[0], -1) + quarter_increments = jnp.max(jnp.abs(jnp.diff(flat, axis=0)), axis=1) + node_values = flat[::4] + node_increments = jnp.max(jnp.abs(jnp.diff(node_values, axis=0)), axis=1) + n_cells = int(grid_points.shape[0]) - 1 + max_quarter_per_cell = quarter_increments.reshape(n_cells, 4).max(axis=1) + # Edge-pad so the first and last cells compare against their available + # neighbors only. + padded = jnp.concatenate( + [node_increments[:1], node_increments, node_increments[-1:]] + ) + neighborhood = jnp.maximum(jnp.maximum(padded[:-2], padded[1:-1]), padded[2:]) + scale = jnp.max(jnp.abs(jnp.where(jnp.isfinite(flat), flat, 0.0))) + noise_floor = atol * (1.0 + scale) + jumps = max_quarter_per_cell > ( + _CONTINUITY_SHRINK_FACTOR * neighborhood + noise_floor + ) + if not bool(jnp.any(jumps)): + return None + index = int(jnp.argmax(jumps)) + return float(0.5 * (grid_points[index] + grid_points[index + 1])) + + +def _law_values_on_sample( + *, + law_func: UserFunction, + context: dict[str, object], + euler_state_name: StateName, + post_decision_name: FunctionName, + savings_value: ScalarFloat, + euler_sample: Float1D, +) -> FloatND | IntND: + """Evaluate one savings-stage variant over the Euler sample at fixed savings. + + The Euler state's law consumes the (removed, hence leaf) post-decision + function and is fed the fixed savings value; the other savings-stage + functions never read it (validated), so the varied savings slot is + filtered away by their signatures. Vector-valued outputs (e.g. Markov + weight vectors) stack along the sample axis; deterministic regime + transitions yield integer regime ids. + """ + + def law_of_euler_state(state_value: ScalarFloat) -> FloatND | IntND: + return _call_with_varied( + func=law_func, + fixed=context, + varied={ + euler_state_name: state_value, + post_decision_name: savings_value, + }, + ) + + return jax.vmap(law_of_euler_state)(euler_sample) + + +def _combo_contexts( + *, + func: UserFunction, + grids: dict[StateOrActionName, Grid], + varied: set[str], + n_contexts: int = 3, +) -> list[dict[str, object]]: + """A few fixed-input contexts for every non-varied argument of `func`. + + Context `j` binds each non-varied argument to the `j`-th point of its + grid's small sample (clamped to the sample length), so the contexts span + different discrete-combo regions. Returns no contexts when an argument + is neither varied nor a state/action β€” a free model parameter whose + value is unknown at build time, so the numeric check cannot run. + """ + samples: dict[str, Float1D | Int1D] = {} + for arg_name in inspect.signature(func).parameters: + if arg_name in varied: + continue + if arg_name in grids: + samples[arg_name] = _grid_sample(grid=grids[arg_name]) + else: + return [] + return [ + {name: sample[min(j, sample.shape[0] - 1)] for name, sample in samples.items()} + for j in range(n_contexts) + ] + + +def _reachable_target_names( + *, + user_regime: UserRegime, + user_regimes: Mapping[RegimeName, UserRegime], +) -> set[RegimeName]: + """Regimes a regime can transition into, read off the declared reachability. + + The regime transition is the single source of truth for reachability: + + - a granular per-target mapping declares exactly its key set β€” omitted + regimes are structurally unreachable, + - any coarse form (bare callable or `MarkovTransition`) reaches every + regime. + """ + transition = user_regime.transition + if isinstance(transition, Phased): + transition = transition.solve + if isinstance(transition, Mapping): + return set(cast("Mapping[RegimeName, object]", transition).keys()) + return set(user_regimes) + + +def _resolve_solve_functions( + *, + user_regime: UserRegime, +) -> dict[FunctionName, UserFunction]: + """Return the regime's solve-phase function pool. + + `Regime.functions` with solve-phase variants resolved, plus the solve + imputation of every carried (`Phased`) state under the state's name. The + imputations make DAG-ancestor checks see through carried states: a + function reading a carried state imputed from the Euler state genuinely + depends on the Euler state at the savings stage. + """ + resolved: dict[FunctionName, UserFunction] = {} + for name, func in user_regime.functions.items(): + if isinstance(func, Phased): + resolved[name] = cast("UserFunction", func.solve) + elif func is not None: + resolved[name] = func + for state_name, grid in user_regime.states.items(): + if isinstance(grid, Phased): + resolved[state_name] = cast("UserFunction", grid.solve) + return resolved + + +def _solve_grids( + *, + slot: Mapping[StateName, object] | Mapping[ActionName, object], +) -> dict[StateOrActionName, Grid]: + """Solve-phase grids of a `states` or `actions` slot. + + A `Phased` state is carried: derived (no grid axis) during backward + induction, so it contributes no solve-phase grid β€” exactly why carried + states are invisible to the DC-EGM state classification. `None` entries + (model-level broadcast masks) carry no grid either; the effective regime + the validation runs on has them resolved away. + """ + return {name: grid for name, grid in slot.items() if isinstance(grid, Grid)} + + +def _continuous_non_process_names( + *, + grids: Mapping[StateOrActionName, Grid], +) -> list[StateOrActionName]: + """Names of continuous grids that are not stochastic processes.""" + return [ + name + for name, grid in grids.items() + if isinstance(grid, ContinuousGrid) + and not isinstance(grid, _ContinuousStochasticProcess) + ] + + +def _transition_variants( + *, + value: object, +) -> list[tuple[str, UserFunction]]: + """Unpack a `state_transitions` entry into labeled callables. + + Handles bare callables, `Phased` containers (solve variant), + `MarkovTransition` wrappers (unwrapped to the weight function), and + per-target dicts (one entry per target regime). + """ + if isinstance(value, Phased): + value = value.solve + if isinstance(value, MarkovTransition): + return [("", cast("UserFunction", value.func))] + if isinstance(value, Mapping): + variants: list[tuple[str, UserFunction]] = [] + for target_name, target_value in value.items(): + func = ( + target_value.func + if isinstance(target_value, MarkovTransition) + else target_value + ) + variants.append((f" (target '{target_name}')", cast("UserFunction", func))) + return variants + return [("", cast("UserFunction", value))] + + +def _without( + *, + functions: dict[FunctionName, UserFunction], + names: set[FunctionName], +) -> dict[FunctionName, UserFunction]: + """Return `functions` with `names` removed, so they become DAG leaves.""" + return {name: func for name, func in functions.items() if name not in names} + + +def _dag_ancestors( + *, + functions: dict[FunctionName, UserFunction], + target_func: UserFunction, +) -> set[str]: + """Ancestors (function names and leaf inputs) of a standalone callable. + + The callable is added to the DAG under a reserved name so its own name + cannot shadow a regime function. + """ + target_name = "__dcegm_validation_target__" + mapping = {**functions, target_name: target_func} + return set(get_ancestors(mapping, targets=[target_name], include_targets=False)) + + +def _grid_sample(*, grid: Grid, n_points: int = 5) -> Float1D | Int1D: + """A small, sorted, evenly indexed sample of grid points. + + Continuous grids yield float points; discrete grids yield their integer + codes, so the sample dtype follows the grid kind. + """ + points = grid.to_jax() + n_grid = points.shape[0] + indices = jnp.unique( + jnp.linspace(0, n_grid - 1, num=min(n_points, n_grid)).astype(jnp.int32) + ) + return points[indices] + + +def _fixed_kwargs( + *, + func: UserFunction, + grids: dict[StateOrActionName, Grid], + varied: set[str], +) -> dict[str, object] | None: + """Fixed inputs (first grid point) for every non-varied argument of `func`. + + Returns `None` when an argument is neither varied nor a state/action β€” + a free model parameter whose value is unknown at build time, so the + numeric check cannot run. + """ + fixed: dict[str, object] = {} + for arg_name in inspect.signature(func).parameters: + if arg_name in varied: + continue + if arg_name in grids: + fixed[arg_name] = grids[arg_name].to_jax()[0] + else: + return None + return fixed + + +def _call_with_varied( + *, + func: UserFunction, + fixed: dict[str, object], + varied: dict[str, object], +) -> FloatND | IntND: + """Call `func` with fixed kwargs plus the varied values it actually takes. + + `fixed` covers exactly the non-varied arguments; varied values are + filtered against the signature because a DAG target need not consume + every sample variable (e.g. resources independent of the Euler state). + """ + arg_names = set(inspect.signature(func).parameters) + return func(**fixed, **{k: v for k, v in varied.items() if k in arg_names}) + + +def _isclose(*, actual: object, expected: object, rtol: float, atol: float) -> bool: + """Eager scalar closeness check, robust to 0-d JAX arrays.""" + return bool( + jnp.isclose(jnp.asarray(actual), jnp.asarray(expected), rtol=rtol, atol=atol) + ) diff --git a/src/_lcm/engine.py b/src/_lcm/engine.py index 48caeb6b5..cf335c2ca 100644 --- a/src/_lcm/engine.py +++ b/src/_lcm/engine.py @@ -2,12 +2,13 @@ from collections.abc import Callable, Iterator, Mapping from math import prod as math_prod from types import MappingProxyType -from typing import Literal, cast +from typing import TYPE_CHECKING, Literal, TypeAlias, cast import jax from jax import Array from _lcm.certainty_equivalent import CertaintyEquivalent +from _lcm.egm.carry import EGMCarry from _lcm.grids import DiscreteGrid, Grid, IrregSpacedGrid from _lcm.processes import _ContinuousStochasticProcess from _lcm.typing import ( @@ -17,7 +18,6 @@ EconFunctionsMapping, FlatRegimeParams, FunctionName, - MaxQOverAFunction, NextStateSimulationFunction, RegimeName, RegimeParamsTemplate, @@ -43,6 +43,23 @@ ScalarInt, ) +# The cross-period continuation channel a parent interpolates; today the only +# payload is the EGM carry. Aliased here (rather than imported from +# `_lcm.solution.contract`) because that module imports this one β€” naming the +# carry directly keeps the engine a leaf of the contract, not a peer in a cycle. +type ContinuationPayload = EGMCarry + +if TYPE_CHECKING: + from _lcm.solution.contract import PeriodKernel + + # The contract module imports this one at runtime, so `PeriodKernel` is + # reachable only under `TYPE_CHECKING`. ty reads the precise element type; + # the beartype claw checks only the outer `Mapping` container at runtime + # (see the runtime alias below). + PeriodKernelsMapping: TypeAlias = Mapping[int, PeriodKernel] # noqa: UP040 +else: + PeriodKernelsMapping = Mapping + @dataclasses.dataclass(frozen=True) class VariableInfo: @@ -312,8 +329,24 @@ class SolutionPhase: compute_regime_transition_probs: RegimeTransitionFunction | None """Regime transition probability function for solve, or `None`.""" - max_Q_over_a: MappingProxyType[int, MaxQOverAFunction] - """Immutable mapping of period to max-Q-over-actions functions.""" + period_kernels: PeriodKernelsMapping + """Immutable mapping of period to the regime's uniform period adapter. + + Every regime β€” grid search or DC-EGM β€” exposes one adapter per period; the + solve loop invokes them the same way and reads each `KernelResult` without + branching on solver type. A grid-search adapter for a terminal regime in a + model with a DC-EGM regime is wrapped by an engine-owned output decorator so + it additionally publishes the regime's closed-form continuation carry. + """ + + continuation_template: ContinuationPayload | None = None + """All-finite template continuation with the regime's static shapes. + + Populated for every continuation-producing regime (DC-EGM regimes and + terminal regimes in a model with a DC-EGM regime). Initializes the rolling + `next_regime_to_egm_carry` mapping and serves as the lowering argument when + AOT-compiling a parent's kernel; `None` for a regime that publishes none. + """ compute_intermediates: MappingProxyType[int, Callable] """Immutable mapping of period to intermediate-computation closures. @@ -333,6 +366,19 @@ class SolutionPhase: _base_state_action_space: StateActionSpace = dataclasses.field(repr=False) """Base state-action space before runtime grid substitution.""" + @property + def solves_via_dcegm(self) -> bool: + """Whether this regime is solved by the DC-EGM kernel. + + A DC-EGM regime is the non-terminal regime that publishes a + continuation: a grid-search regime publishes none, and a terminal + carry-producing regime is terminal (no regime-transition probs). + """ + return ( + self.compute_regime_transition_probs is not None + and self.continuation_template is not None + ) + @property def state_names(self) -> tuple[StateOrActionName, ...]: """Solve-phase state names in canonical (productmap) order.""" diff --git a/src/_lcm/model_processing.py b/src/_lcm/model_processing.py index 2748c9bd3..b99cdf955 100644 --- a/src/_lcm/model_processing.py +++ b/src/_lcm/model_processing.py @@ -15,6 +15,8 @@ from dags.tree import QNAME_DELIMITER, qname_from_tree_path from jax import Array +from _lcm.egm.negm_validation import validate_negm_regimes +from _lcm.egm.validation import validate_dcegm_regimes from _lcm.grids import DiscreteGrid from _lcm.pandas_utils import convert_series_in_params, has_series from _lcm.params.processing import ( @@ -175,6 +177,13 @@ def validate_model_inputs( """ _fail_if_invalid_n_subjects(n_subjects=n_subjects) + # DC-EGM contract checks run before the generic checks below: a contract + # violation (e.g. a missing resources function) typically also leaves + # variables unused, and the contract-specific message is the actionable + # one. + validate_dcegm_regimes(user_regimes=user_regimes) + validate_negm_regimes(user_regimes=user_regimes) + error_messages: list[str] = [] if n_periods <= 1: @@ -394,21 +403,42 @@ def _partial_fixed_params_into_regimes( result: dict[RegimeName, Regime] = {} for regime_name, regime in raw_regimes.items(): regime_fixed = dict(fixed_flat_params.get(regime_name, MappingProxyType({}))) - if not regime_fixed: + # A DC-EGM source carrying into a *different* target regime also binds + # that target's fixed params (it reads the target's resources / + # transition functions in its per-asset-node solve). Gate the rebuild on + # whether any fixed param reachable from this regime β€” its own or a + # transition target's β€” exists; the per-adapter `with_fixed_params` + # decides which of them actually reach each core. + reachable_fixed = bool(regime_fixed) or any( + fixed_flat_params.get(target_name, MappingProxyType({})) + for target_name in regime.solution.transitions + ) + if not reachable_fixed: result[regime_name] = regime continue # Build new solution phase with partialled functions. The resolved # fixed params also land on the phase itself β€” its # `state_action_space` consults them for runtime grid substitution. + # + # Each period adapter owns its solver's binding rule: a grid-search + # adapter binds the regime's own fixed params into its core; a DC-EGM + # adapter binds the union of the regime's and its carry targets' fixed + # params (a source reads a different target's params in its per-asset + # solve); a terminal carry-producing adapter binds the regime's fixed + # params into both its base core and the carry producer. So the engine + # threads fixed params through `with_fixed_params` without a solver-type + # switch. solution = regime.solution new_solve = dataclasses.replace( solution, resolved_fixed_params=MappingProxyType(regime_fixed), - max_Q_over_a=MappingProxyType( + period_kernels=MappingProxyType( { - period: functools.partial(func, **regime_fixed) - for period, func in solution.max_Q_over_a.items() + period: kernel.with_fixed_params( + fixed_flat_params=fixed_flat_params + ) + for period, kernel in solution.period_kernels.items() } ), compute_regime_transition_probs=( diff --git a/src/_lcm/params/regime_template.py b/src/_lcm/params/regime_template.py index 02e1c9bc4..3d2bcb83e 100644 --- a/src/_lcm/params/regime_template.py +++ b/src/_lcm/params/regime_template.py @@ -17,6 +17,7 @@ from lcm.exceptions import InvalidNameError from lcm.phased import Phased from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM, NEGM from lcm.typing import UserFunction @@ -70,9 +71,8 @@ def create_regime_params_template(user_regime: UserRegime) -> RegimeParamsTempla # user-facing params in the template. params = {k: v for k, v in sorted(tree.items()) if k not in variables} - # Per-target entries (`__`) nest under the target β€” the - # target is a genuine tree level, mirroring the canonical transition - # bundles, so param qnames parallel engine function qnames. + _drop_engine_provided_args(name=name, params=params, user_regime=user_regime) + path = tree_path_from_qname(name) if len(path) > 1: func_name, target_regime_name = path[0], path[1] @@ -242,6 +242,22 @@ def _collect_all_functions_for_template( return result +def _drop_engine_provided_args( + *, name: FunctionName, params: dict[str, str], user_regime: UserRegime +) -> None: + """Remove a function's engine-supplied arguments from its discovered params. + + In a DC-EGM / NEGM regime the inversion function `inverse_marginal_utility` + receives `marginal_continuation` from the EGM kernel (in any other regime a + function of that name is ordinary). This must not surface as a user-facing + param, so it is popped in place. + """ + if name == "inverse_marginal_utility" and isinstance( + user_regime.solver, (DCEGM, NEGM) + ): + params.pop("marginal_continuation", None) + + def _regime_transition_entries( transition: object, ) -> dict[TransitionFunctionName, UserFunction | Phased]: diff --git a/src/_lcm/regime_building/Q_and_F.py b/src/_lcm/regime_building/Q_and_F.py index 7401bcbe1..de022c225 100644 --- a/src/_lcm/regime_building/Q_and_F.py +++ b/src/_lcm/regime_building/Q_and_F.py @@ -1,9 +1,9 @@ -from collections.abc import Callable +from collections.abc import Callable, Mapping from types import MappingProxyType from typing import Any, cast import jax.numpy as jnp -from dags import concatenate_functions, with_signature +from dags import concatenate_functions, get_ancestors, with_signature from _lcm.certainty_equivalent import CertaintyEquivalent, resolve_certainty_equivalent from _lcm.regime_building.h_dag import _get_build_H_kwargs @@ -23,10 +23,11 @@ TransitionFunction, TransitionFunctionName, TransitionFunctionsMapping, + _ParamsLeaf, ) from _lcm.utils.dispatchers import productmap from _lcm.utils.functools import get_union_of_args -from lcm.typing import BoolND, Float1D, FloatND, IntND +from lcm.typing import BoolND, Float1D, FloatND def get_Q_and_F( @@ -72,7 +73,20 @@ def get_Q_and_F( for a non-terminal period. """ - U_and_F = _get_U_and_F(functions=functions, constraints=constraints) + deterministic_transitions, conflicting_deterministic_transition_names = ( + _get_deterministic_transitions( + transitions=transitions, + stochastic_transition_names=stochastic_transition_names, + ) + ) + U_and_F = _get_U_and_F( + functions=functions, + constraints=constraints, + deterministic_transitions=deterministic_transitions, + conflicting_deterministic_transition_names=( + conflicting_deterministic_transition_names + ), + ) state_transitions = {} next_stochastic_states_weights = {} joint_weights_from_marginals = {} @@ -153,7 +167,7 @@ def get_Q_and_F( ) def Q_and_F( next_regime_to_V_arr: FloatND, - **states_actions_params: FloatND | IntND | BoolND, + **states_actions_params: _ParamsLeaf, ) -> tuple[FloatND, BoolND]: """Calculate the state-action value and feasibility for a non-terminal period. @@ -285,7 +299,20 @@ def get_compute_intermediates( Closure returning `(U_arr, F_arr, E_next_V, Q_arr, active_regime_probs)`. """ - U_and_F = _get_U_and_F(functions=functions, constraints=constraints) + deterministic_transitions, conflicting_deterministic_transition_names = ( + _get_deterministic_transitions( + transitions=transitions, + stochastic_transition_names=stochastic_transition_names, + ) + ) + U_and_F = _get_U_and_F( + functions=functions, + constraints=constraints, + deterministic_transitions=deterministic_transitions, + conflicting_deterministic_transition_names=( + conflicting_deterministic_transition_names + ), + ) state_transitions = {} next_stochastic_states_weights = {} joint_weights_from_marginals = {} @@ -354,7 +381,7 @@ def get_compute_intermediates( ) def compute_intermediates( next_regime_to_V_arr: FloatND, - **states_actions_params: FloatND | IntND | BoolND, + **states_actions_params: _ParamsLeaf, ) -> tuple[ FloatND, FloatND, FloatND, FloatND, MappingProxyType[RegimeName, FloatND] ]: @@ -452,7 +479,7 @@ def get_Q_and_F_terminal( ) def Q_and_F( next_regime_to_V_arr: FloatND, # noqa: ARG001 - **states_actions_params: FloatND | IntND | BoolND, + **states_actions_params: _ParamsLeaf, ) -> tuple[FloatND, BoolND]: """Calculate the state-action values and feasibilities for a terminal period. @@ -565,10 +592,56 @@ def _outer(**kwargs: Float1D) -> FloatND: ) +def _get_deterministic_transitions( + *, + transitions: TransitionFunctionsMapping, + stochastic_transition_names: frozenset[TransitionFunctionName], +) -> tuple[ + Mapping[TransitionFunctionName, TransitionFunction], + frozenset[TransitionFunctionName], +]: + """Merge the deterministic `next_` transitions across all targets. + + Iterates every target bundle, not just this period's targets: the within- + period durable law (`next_`) lives in the source regime's own + self-transition bundle and is needed even in periods bound for a terminal + target that does not carry it. Own-regime within-period laws are + target-independent, so the first occurrence of each `next_` name is + kept. Stochastic transitions are excluded β€” a within-period utility or + constraint cannot read an unrealised stochastic next state. + + Returns the merged mapping and the set of `next_` names that appear in + more than one target bundle with non-identical implementations. The merge + keeps one of them, so a within-period utility or constraint reading such a + name would silently bind one target's law; the caller rejects the model if a + conflicting name is actually read by the decision evaluation. + + Returns: + Tuple of the immutable merged `next_` mapping and the frozenset of + conflicting `next_` names. + """ + merged: dict[TransitionFunctionName, TransitionFunction] = {} + conflicting: set[TransitionFunctionName] = set() + for bundle in transitions.values(): + for name, func in bundle.items(): + if name in stochastic_transition_names: + continue + if name in merged and merged[name] is not func: + conflicting.add(name) + merged.setdefault(name, func) + return MappingProxyType(merged), frozenset(conflicting) + + def _get_U_and_F( *, functions: EconFunctionsMapping, constraints: ConstraintFunctionsMapping, + deterministic_transitions: Mapping[TransitionFunctionName, TransitionFunction] = ( + MappingProxyType({}) + ), + conflicting_deterministic_transition_names: frozenset[ + TransitionFunctionName + ] = frozenset(), ) -> Callable[..., tuple[FloatND, BoolND]]: """Get the instantaneous utility and feasibility function. @@ -580,15 +653,38 @@ def _get_U_and_F( Args: functions: Immutable mapping of function names to internal user functions. constraints: Immutable mapping of constraint names to internal user functions. + deterministic_transitions: Mapping of `next_` names to deterministic + own-regime transition functions, made available so within-period utility + or feasibility that reads a chosen next state (the NEGM service-flow + `next_`, or a budget constraint reading it) resolves it from the + current states and actions. Pruned away when unread, so the grid-search + path is unchanged. + conflicting_deterministic_transition_names: Frozenset of `next_` + names whose deterministic law differs across target bundles. A model is + rejected if any of them is read by the within-period decision (utility + or feasibility), because the merged law would disagree with the + simulate state-update. Returns: The instantaneous utility and feasibility function. """ combined = { - "feasibility": _get_feasibility(functions=functions, constraints=constraints), + "feasibility": _get_feasibility( + functions=functions, + constraints=constraints, + deterministic_transitions=deterministic_transitions, + ), + **dict(deterministic_transitions), **{k: v for k, v in functions.items() if k != "H"}, } + _fail_if_conflicting_transition_is_read( + combined=combined, + targets=["utility", "feasibility"], + conflicting_deterministic_transition_names=( + conflicting_deterministic_transition_names + ), + ) return concatenate_functions( functions=combined, targets=["utility", "feasibility"], @@ -597,16 +693,61 @@ def _get_U_and_F( ) +def _fail_if_conflicting_transition_is_read( + *, + combined: Mapping[str, Callable[..., Any]], + targets: list[str], + conflicting_deterministic_transition_names: frozenset[TransitionFunctionName], +) -> None: + """Reject a model whose decision reads a target-dependent `next_` law. + + A `next_` whose deterministic law differs across target bundles is + merged down to one implementation; binding it into the decision DAG while the + simulate state-update uses the per-target law produces a silent disagreement. + Raise naming each such state actually read by `targets`. + + Args: + combined: Mapping of function names to the functions assembled for the + decision DAG. + targets: List of target function names the decision evaluates. + conflicting_deterministic_transition_names: Frozenset of `next_` + names with non-identical implementations across target bundles. + """ + if not conflicting_deterministic_transition_names: + return + read_names = get_ancestors(combined, targets, include_targets=True) + offending = sorted(conflicting_deterministic_transition_names & read_names) + if offending: + names = ", ".join(offending) + msg = ( + "Within-period utility or feasibility reads a target-dependent " + f"deterministic state law ({names}), but its implementation differs " + "across target regimes. The decision DAG would bind one target's law " + "while the simulate state-update uses the right one, so they would " + "disagree silently. Make the law identical across all targets that " + "carry the state, or stop reading the chosen next state in the " + "within-period utility/feasibility." + ) + raise ValueError(msg) + + def _get_feasibility( *, functions: EconFunctionsMapping, constraints: ConstraintFunctionsMapping, + deterministic_transitions: Mapping[TransitionFunctionName, TransitionFunction] = ( + MappingProxyType({}) + ), ) -> ConstraintFunction: """Create a function that combines all constraint functions into a single one. Args: functions: Immutable mapping of function names to internal user functions. constraints: Immutable mapping of constraint names to internal user functions. + deterministic_transitions: Mapping of `next_` names to deterministic + transition functions, so a constraint reading a chosen next state (the + NEGM budget constraint reading `next_`) resolves it. Pruned when + unread. Returns: The combined constraint function (feasibility). @@ -614,7 +755,9 @@ def _get_feasibility( """ if constraints: combined_constraint = concatenate_functions( - functions=dict(constraints) | dict(functions), + functions=dict(deterministic_transitions) + | dict(constraints) + | dict(functions), targets=list(constraints), aggregator=jnp.logical_and, aggregator_return_type="Feasibility", diff --git a/src/_lcm/regime_building/max_Q_over_a.py b/src/_lcm/regime_building/max_Q_over_a.py index 4cddbbbd0..3f1bc724b 100644 --- a/src/_lcm/regime_building/max_Q_over_a.py +++ b/src/_lcm/regime_building/max_Q_over_a.py @@ -17,10 +17,11 @@ MaxQOverAFunction, RegimeName, StateName, + _ParamsLeaf, ) from _lcm.utils.dispatchers import productmap, vmap_1d from _lcm.utils.functools import allow_args, allow_only_kwargs -from lcm.typing import BoolND, FloatND, IntND +from lcm.typing import BoolND, FloatND, IntND, ScalarFloat # Flat param name of the EV1 taste-shock scale (template pseudo-function entry). TASTE_SHOCK_SCALE_PARAM = "taste_shocks__scale" @@ -118,7 +119,7 @@ def get_max_Q_over_a( ) def max_Q_over_a( next_regime_to_V_arr: MappingProxyType[RegimeName, FloatND], - **states_actions_params: FloatND | IntND | BoolND, + **states_actions_params: _ParamsLeaf, ) -> FloatND: Q_arr, F_arr = Q_and_F( next_regime_to_V_arr=next_regime_to_V_arr, @@ -129,7 +130,9 @@ def max_Q_over_a( Qc = Q_masked.max(axis=continuous_axes) if continuous_axes else Q_masked smoothed, _ = logsum_and_softmax( values=Qc, - scale=states_actions_params[TASTE_SHOCK_SCALE_PARAM], + scale=cast( + "ScalarFloat", states_actions_params[TASTE_SHOCK_SCALE_PARAM] + ), axes=tuple(range(Qc.ndim)), ) return smoothed @@ -148,7 +151,7 @@ def max_Q_over_a( ) def max_Q_over_a( next_regime_to_V_arr: MappingProxyType[RegimeName, FloatND], - **states_actions_params: FloatND | IntND | BoolND, + **states_actions_params: _ParamsLeaf, ) -> FloatND: Q_arr, F_arr = Q_and_F( next_regime_to_V_arr=next_regime_to_V_arr, @@ -264,9 +267,11 @@ def get_argmax_and_max_Q_over_a( ) def argmax_and_max_Q_over_a( next_regime_to_V_arr: MappingProxyType[RegimeName, FloatND], - **states_actions_params: FloatND | IntND | BoolND, + **states_actions_params: _ParamsLeaf, ) -> tuple[IntND, FloatND]: - taste_shock_key = states_actions_params.pop("taste_shock_key") + taste_shock_key = cast( + "Array", states_actions_params.pop("taste_shock_key") + ) Q_arr, F_arr = Q_and_F( next_regime_to_V_arr=next_regime_to_V_arr, **states_actions_params, @@ -277,7 +282,7 @@ def argmax_and_max_Q_over_a( Q_flat = Q_masked.reshape(n_discrete_cells, n_continuous_cells) continuous_argmax = jnp.argmax(Q_flat, axis=1) Qc = Q_flat.max(axis=1) - scale = states_actions_params[TASTE_SHOCK_SCALE_PARAM] + scale = cast("FloatND", states_actions_params[TASTE_SHOCK_SCALE_PARAM]) noise = draw_taste_shock_noise( key=taste_shock_key, shape=Qc.shape, scale=scale ) @@ -305,7 +310,7 @@ def argmax_and_max_Q_over_a( ) def argmax_and_max_Q_over_a( next_regime_to_V_arr: MappingProxyType[RegimeName, FloatND], - **states_actions_params: FloatND | IntND | BoolND, + **states_actions_params: _ParamsLeaf, ) -> tuple[IntND, FloatND]: Q_arr, F_arr = Q_and_F( next_regime_to_V_arr=next_regime_to_V_arr, diff --git a/src/_lcm/regime_building/processing.py b/src/_lcm/regime_building/processing.py index 175b09ac3..424107902 100644 --- a/src/_lcm/regime_building/processing.py +++ b/src/_lcm/regime_building/processing.py @@ -3,6 +3,7 @@ from collections import defaultdict from collections.abc import Callable, Mapping from dataclasses import dataclass +from dataclasses import replace as dataclass_replace from types import MappingProxyType from typing import Any, Literal, cast @@ -14,6 +15,18 @@ from _lcm.certainty_equivalent import CertaintyEquivalent from _lcm.coarse_transition import _CoarseTransitionCell +from _lcm.egm.budget import ( + DCEGM_BUDGET_CONSTRAINT_NAME, + get_intrinsic_budget_constraint, +) +from _lcm.egm.carry import EGMCarry, build_template_egm_carry +from _lcm.egm.negm_validation import validate_negm_regimes +from _lcm.egm.terminal import ( + N_STATELESS_CARRY_ROWS, + get_stateless_terminal_carry_producer, + get_terminal_wealth_carry_producer, +) +from _lcm.egm.validation import validate_dcegm_regimes from _lcm.engine import ( Regime, SimulationPhase, @@ -30,7 +43,9 @@ from _lcm.regime_building.canonicalize import canonicalize_regimes from _lcm.regime_building.diagnostics import _build_compute_intermediates_per_period from _lcm.regime_building.finalize import FinalizedUserRegime -from _lcm.regime_building.max_Q_over_a import get_argmax_and_max_Q_over_a +from _lcm.regime_building.max_Q_over_a import ( + get_argmax_and_max_Q_over_a, +) from _lcm.regime_building.ndimage import map_coordinates from _lcm.regime_building.next_state import get_next_state_function_for_simulation from _lcm.regime_building.phases import ( @@ -46,14 +61,22 @@ collect_stochastic_state_transitions, ) from _lcm.regime_building.V import VInterpolationInfo, create_v_interpolation_info -from _lcm.solution.contract import SolverBuildContext +from _lcm.solution.contract import ( + ContinuationPayload, + KernelResult, + PeriodKernel, + SolverBuildContext, +) from _lcm.state_action_space import create_state_action_space from _lcm.typing import ( ArgmaxQOverAFunction, ConstraintFunctionsMapping, EconFunction, EconFunctionsMapping, + EGMCarryProducer, + FlatParams, FunctionName, + MappingLeaf, NextStateSimulationFunction, ProcessName, QAndFFunction, @@ -61,6 +84,7 @@ RegimeNamesToIds, RegimeParamsTemplate, RegimeTransitionFunction, + SequenceLeaf, StateName, StateOrActionName, TransitionFunction, @@ -80,11 +104,11 @@ from lcm.ages import AgeGrid from lcm.exceptions import ModelInitializationError from lcm.regime import Regime as UserRegime -from lcm.solvers import Solver +from lcm.solvers import DCEGM, NEGM, Solver from lcm.transition import ( MarkovTransition, ) -from lcm.typing import Float1D, FloatND, Int1D, IntND, UserFunction +from lcm.typing import BoolND, Float1D, FloatND, Int1D, IntND, UserFunction type _TransitionBundles = dict[ RegimeName, dict[TransitionFunctionName, UserFunction | _CoarseTransitionCell] @@ -115,6 +139,13 @@ def process_regimes( The processed canonical regimes. """ + # DC-EGM regimes must satisfy the EGM model contract before any kernel + # is built. `Model.__init__` validates earlier (so contract violations + # beat the generic unused-variable check); this call covers direct + # `process_regimes` callers. + validate_dcegm_regimes(user_regimes=user_regimes) + validate_negm_regimes(user_regimes=user_regimes) + # The canonical specs hold every law in target-granular form, resolved per # phase: the simulate slice additionally holds every carried-only state # and its law of motion, so the canonical mapping carries the law toward @@ -168,25 +199,62 @@ def process_regimes( } ) + model_has_egm_regime = any( + user_regime.solver.requires_continuation_carries + for user_regime in user_regimes.values() + ) + + # Each regime's flat param names in the engine's binding vocabulary, keyed + # by regime. A DC-EGM source regime that carries into a *different* target + # regime evaluates that target's resources / transition functions in its + # per-asset-node solve, so it must know the target's param leaves (e.g. a + # pension factor the source itself never reads); the kernel binds them from + # the union of the source and its reachable carry targets' fixed params. + regime_to_params_template = MappingProxyType( + { + regime_name: create_regime_params_template(user_regime) + for regime_name, user_regime in user_regimes.items() + } + ) + regime_to_granular_param_expansions = MappingProxyType( + { + regime_name: _granular_param_expansions( + nested_transitions_by_phase=( + solve_nested_transitions[regime_name], + simulate_nested_transitions[regime_name], + ), + regime_params_template=regime_to_params_template[regime_name], + ) + for regime_name in user_regimes + } + ) + regime_to_flat_param_names = MappingProxyType( + { + regime_name: _engine_flat_param_names( + regime_params_template=regime_to_params_template[regime_name], + granular_param_expansions=regime_to_granular_param_expansions[ + regime_name + ], + ) + for regime_name in user_regimes + } + ) + canonical_regimes: dict[RegimeName, Regime] = {} for regime_name, user_regime in user_regimes.items(): spec = specs[regime_name] - regime_params_template = create_regime_params_template(user_regime) - granular_param_expansions = _granular_param_expansions( - nested_transitions_by_phase=( - solve_nested_transitions[regime_name], - simulate_nested_transitions[regime_name], - ), - regime_params_template=regime_params_template, - ) + regime_params_template = regime_to_params_template[regime_name] + granular_param_expansions = regime_to_granular_param_expansions[regime_name] solution = _build_solution_phase( spec=spec, regime_name=regime_name, + user_regimes=user_regimes, nested_transitions=solve_nested_transitions[regime_name], all_grids=all_grids, regime_params_template=regime_params_template, granular_param_expansions=granular_param_expansions, + regime_to_flat_param_names=regime_to_flat_param_names, regime_names_to_ids=regime_names_to_ids, variables=regime_to_variables[regime_name], regimes_to_active_periods=regimes_to_active_periods, @@ -194,9 +262,10 @@ def process_regimes( state_action_space=state_action_spaces[regime_name], ages=ages, enable_jit=enable_jit, - has_taste_shocks=user_regime.taste_shocks is not None, certainty_equivalent=user_regime.certainty_equivalent, solver=user_regime.solver, + model_has_egm_regime=model_has_egm_regime, + has_taste_shocks=user_regime.taste_shocks is not None, ) simulation = _build_simulation_phase( @@ -218,6 +287,7 @@ def process_regimes( solve_stochastic_transition_names=solution.stochastic_transition_names, solve_compute_regime_transition_probs=solution.compute_regime_transition_probs, has_taste_shocks=user_regime.taste_shocks is not None, + solver=user_regime.solver, certainty_equivalent=user_regime.certainty_equivalent, ) @@ -246,10 +316,12 @@ def _build_solution_phase( *, spec: PhasedRegimeSpec, regime_name: RegimeName, + user_regimes: Mapping[RegimeName, UserRegime], nested_transitions: _TransitionBundles, all_grids: MappingProxyType[RegimeName, MappingProxyType[StateOrActionName, Grid]], regime_params_template: RegimeParamsTemplate, granular_param_expansions: MappingProxyType[FunctionName, tuple[str, ...]], + regime_to_flat_param_names: MappingProxyType[RegimeName, frozenset[str]], regime_names_to_ids: RegimeNamesToIds, variables: Variables, regimes_to_active_periods: MappingProxyType[RegimeName, tuple[int, ...]], @@ -257,21 +329,29 @@ def _build_solution_phase( state_action_space: StateActionSpace, ages: AgeGrid, enable_jit: bool, - has_taste_shocks: bool, certainty_equivalent: CertaintyEquivalent | None, solver: Solver, + model_has_egm_regime: bool, + has_taste_shocks: bool, ) -> SolutionPhase: """Build all compiled functions for the backward-induction (solve) phase. Args: spec: The regime's per-phase specification. regime_name: The name of the regime. + user_regimes: Mapping of regime names to user-provided `Regime` + instances. nested_transitions: Per-target transition bundles for internal processing. all_grids: Immutable mapping of regime names to Grid spec objects. regime_params_template: The regime's parameter template. granular_param_expansions: Immutable mapping of coarse-template law keys to granular qname prefixes. + regime_to_flat_param_names: Immutable mapping of every regime name to + its flat param names in the engine's binding vocabulary. A DC-EGM + source carrying into a different target regime reads the target's + params in its per-asset-node solve, so the kernel build needs the + whole mapping, not only the source regime's own params. regime_names_to_ids: Immutable mapping of regime names to integer indices. variables: States and actions of the regime with kind/topology/process tags. regimes_to_active_periods: Mapping of regime names to active period tuples. @@ -279,12 +359,15 @@ def _build_solution_phase( state_action_space: The state-action space for this regime. ages: The AgeGrid for the model. enable_jit: Whether to jit the internal functions. - has_taste_shocks: Whether the regime declares EV1 taste shocks on its - discrete actions. certainty_equivalent: Nonlinear certainty equivalent declared by the regime, or `None`. solver: The regime's solver; the engine calls `validate` then `build_period_kernels` on it to obtain the per-period kernels. + model_has_egm_regime: Whether any regime of the model uses a solver + that reads continuation carries (an endogenous-grid solver); + terminal regimes then produce their closed-form carries. + has_taste_shocks: Whether the regime declares EV1 taste shocks on its + discrete actions. Returns: Complete solve functions container. @@ -383,12 +466,24 @@ def _build_solution_phase( # Dispatch the per-period kernel build polymorphically on the regime's # solver: `validate` rejects out-of-scope configurations at build time, - # then `build_period_kernels` returns the per-period kernels. `GridSearch` - # builds the max-Q-over-a grid-search kernels. + # then `build_period_kernels` returns one uniform period adapter per period + # plus the regime's continuation template. `GridSearch` wraps the + # max-Q-over-a grid search; `DCEGM` wraps the EGM step. context = SolverBuildContext( + regime_name=regime_name, + user_regimes=user_regimes, state_action_space=state_action_space, Q_and_F_functions=Q_and_F_functions, grids=all_grids[regime_name], + functions=core.functions, + constraints=core.constraints, + transitions=core.transitions, + stochastic_transition_names=core.stochastic_transition_names, + compute_regime_transition_probs=compute_regime_transition_probs, + regime_to_v_interpolation_info=regime_to_v_interpolation_info, + regimes_to_active_periods=regimes_to_active_periods, + flat_param_names=flat_param_names, + regime_to_flat_param_names=regime_to_flat_param_names, enable_jit=enable_jit, has_taste_shocks=has_taste_shocks, certainty_equivalent=certainty_equivalent, @@ -397,7 +492,35 @@ def _build_solution_phase( ) solver.validate(context=context) solver_kernels = solver.build_period_kernels(context=context) - max_Q_over_a = solver_kernels.max_Q_over_a + + # The terminal continuation publisher is a cross-solver concern, not the + # grid search's: a terminal regime in a model with a DC-EGM regime must + # publish a closed-form carry so a DC-EGM parent can interpolate its value + # and marginal utility. Build the producer engine-side and compose it as an + # output decorator around each period adapter, so the solver stays unaware + # of the continuation it is being asked to emit. + egm_carry_producer, egm_carry_template = _build_terminal_carry_producer( + user_regime=user_regimes[regime_name], + functions=core.functions, + variables=variables, + grids=all_grids[regime_name], + model_has_egm_regime=model_has_egm_regime, + enable_jit=enable_jit, + ) + period_kernels = solver_kernels.period_kernels + continuation_template = solver_kernels.continuation_template + if egm_carry_producer is not None: + period_kernels = MappingProxyType( + { + period: _TerminalCarryPeriodKernel( + base=kernel, + carry_producer=egm_carry_producer, + regime_name=regime_name, + ) + for period, kernel in period_kernels.items() + } + ) + continuation_template = egm_carry_template return SolutionPhase( _variables=variables, @@ -407,12 +530,218 @@ def _build_solution_phase( transitions=core.transitions, stochastic_transition_names=core.stochastic_transition_names, compute_regime_transition_probs=compute_regime_transition_probs, - max_Q_over_a=max_Q_over_a, + period_kernels=period_kernels, compute_intermediates=compute_intermediates, + continuation_template=continuation_template, _base_state_action_space=state_action_space, ) +def _filter_kwargs_for_func( + *, func: Callable, kwargs: Mapping[str, object] +) -> Mapping[str, object]: + """Filter kwargs to only those accepted by func's signature.""" + try: + sig = inspect.signature(func) + except ValueError, TypeError: + return kwargs + params = sig.parameters + if any(p.kind == inspect.Parameter.VAR_KEYWORD for p in params.values()): + return kwargs + return {k: v for k, v in kwargs.items() if k in params} + + +@dataclass(frozen=True, kw_only=True) +class _TerminalCarryPeriodKernel: + """Engine-owned output decorator publishing a terminal regime's carry. + + Wraps a grid-search period adapter so that, after the base kernel computes + the value-function array, the regime's closed-form carry producer turns that + array into the continuation a DC-EGM parent interpolates. Publishing a carry + is a cross-solver concern, so the wrapped solver stays unaware of it. + + `core` and `build_lower_args` delegate to the base adapter: the carry + producer is a separately built (and jitted) closure invoked inline, not part + of the AOT-compiled core, so AOT compilation deduplicates and lowers exactly + the base grid-search core. + """ + + base: PeriodKernel + """The wrapped grid-search period adapter.""" + + carry_producer: EGMCarryProducer + """Closed-form producer mapping the value array to the regime's carry.""" + + regime_name: RegimeName + """Name of the terminal regime whose flat params the producer reads.""" + + @property + def core(self) -> Callable: + """The base adapter's shared jitted core, for any single-core reader.""" + return self.base.core + + def cores(self) -> Mapping[str, Callable]: + """Delegate to the base adapter's cores (a terminal regime is single-core).""" + return self.base.cores() + + def with_fixed_params( + self, *, fixed_flat_params: FlatParams + ) -> _TerminalCarryPeriodKernel: + """Bind fixed params into both the base core and the carry producer. + + A terminal regime's carry producer evaluates the regime's own bequest + utility on the wealth grid; that utility may reach a model-level fixed + param (e.g. a consumption-equivalence scale) through a helper. The solve + loop invokes the producer with only the live (free) params, so bind the + regime's fixed params here β€” matching the base adapter's core binding. + """ + regime_fixed = dict( + fixed_flat_params.get(self.regime_name, MappingProxyType({})) + ) + base = self.base.with_fixed_params(fixed_flat_params=fixed_flat_params) + carry_producer = self.carry_producer + if regime_fixed: + carry_producer = functools.partial( + carry_producer, + **_filter_kwargs_for_func(func=carry_producer, kwargs=regime_fixed), + ) + return dataclass_replace(self, base=base, carry_producer=carry_producer) + + def build_lower_args( + self, + *, + core_key: str = "main", + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, + ages: AgeGrid, + ) -> Mapping[str, object]: + """Build the base core's lowering arguments (the carry producer is jitted + separately at build time, so it is not part of the AOT-compiled core).""" + return self.base.build_lower_args( + core_key=core_key, + state_action_space=state_action_space, + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, + flat_params=flat_params, + period=period, + ages=ages, + ) + + def __call__( + self, + *, + compiled_cores: Mapping[str, Callable], + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, + ages: AgeGrid, + ) -> KernelResult: + """Run the base kernel, then publish the regime's continuation carry.""" + result = self.base( + compiled_cores=compiled_cores, + state_action_space=state_action_space, + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, + flat_params=flat_params, + period=period, + ages=ages, + ) + carry = self.carry_producer( + V_arr=result.V_arr, + **state_action_space.states, + **flat_params[self.regime_name], + period=jnp.int32(period), + age=ages.values[period], + ) + return KernelResult(V_arr=result.V_arr, carry=carry) + + +def _build_terminal_carry_producer( + *, + user_regime: UserRegime, + functions: EconFunctionsMapping, + variables: Variables, + grids: MappingProxyType[StateOrActionName, Grid], + model_has_egm_regime: bool, + enable_jit: bool, +) -> tuple[EGMCarryProducer | None, EGMCarry | None]: + """Build the EGM carry producer and template for a terminal regime. + + Terminal regimes produce closed-form carries when the model contains an + endogenous-grid regime, so an EGM parent can interpolate their value and + marginal utility. Cases: + + - no states β‡’ constant-value, zero-marginal-utility broadcast rows + - exactly one continuous state, no actions, and discrete states only of + the fixed (non-process) kind β‡’ terminal utility and its wealth gradient + on the regime's own state grid, with the discrete states as the carry's + leading axes (one wealth row per discrete combo) + - anything else β‡’ no producer (an EGM regime targeting such a terminal + regime is rejected by the EGM kernel builder) + + Returns: + Tuple of the producer and the regime's carry template, both `None` + for non-terminal regimes, for models without an endogenous-grid + regime, and for unsupported terminal shapes. + + """ + if not (model_has_egm_regime and user_regime.terminal): + return None, None + producer: EGMCarryProducer + discrete_state_names = tuple( + name + for name in variables.state_names + if name in set(variables.discrete_state_names) + ) + has_only_fixed_discrete_states = all( + not isinstance(grids[name], _ContinuousStochasticProcess) + for name in discrete_state_names + ) + continuous_state_names = tuple(variables.continuous_state_names) + euler_state_name = next(iter(user_regime.states), None) + if not variables.state_names: + producer = get_stateless_terminal_carry_producer() + template = build_template_egm_carry(n_rows=N_STATELESS_CARRY_ROWS) + elif ( + len(continuous_state_names) >= 1 + and has_only_fixed_discrete_states + and not user_regime.actions + and euler_state_name in continuous_state_names + ): + # The parent's child read picks the terminal's Euler state as its first + # declared state (`_get_child_state_name`); the remaining continuous + # states are the passive (durable / outer) margins it interpolates as + # leading carry axes β€” the NEGM housing-bequest shape. + passive_state_names = tuple( + name for name in continuous_state_names if name != euler_state_name + ) + producer = get_terminal_wealth_carry_producer( + functions=functions, + state_name=euler_state_name, + discrete_state_names=discrete_state_names, + passive_state_names=passive_state_names, + continuous_state_order=continuous_state_names, + ) + leading_shape = tuple( + int(grids[name].to_jax().shape[0]) + for name in discrete_state_names + passive_state_names + ) + template = build_template_egm_carry( + n_rows=int(grids[euler_state_name].to_jax().shape[0]), + leading_shape=leading_shape, + ) + else: + return None, None + if enable_jit: + producer = jax.jit(producer) + return producer, template + + def _build_simulation_phase( *, spec: PhasedRegimeSpec, @@ -433,6 +762,7 @@ def _build_simulation_phase( solve_stochastic_transition_names: frozenset[TransitionFunctionName], solve_compute_regime_transition_probs: RegimeTransitionFunction | None, has_taste_shocks: bool, + solver: Solver, certainty_equivalent: CertaintyEquivalent | None, ) -> SimulationPhase: """Build all compiled functions for the forward-simulation phase. @@ -446,6 +776,13 @@ def _build_simulation_phase( Q_and_F always uses the solve (non-vmapped) regime transition probs because it evaluates on the Cartesian grid, not per-subject. + For a DC-EGM or NEGM regime, the budget constraint the EGM solve enforces + intrinsically is synthesized and injected into the constraint set: the + simulate-phase grid argmax needs it as a feasibility mask exactly like a + user-declared borrowing constraint of a brute-force regime. NEGM nests the + same inner 1-D solve, so the mask comes from its inner DC-EGM config. The + solve phase is unaffected β€” the EGM kernels never see it. + Args: spec: The regime's per-phase specification. regime_name: The name of the regime. @@ -471,6 +808,8 @@ def _build_simulation_phase( function, used for Q_and_F in both phases. has_taste_shocks: Whether the regime declares EV1 taste shocks on its discrete actions. + solver: The regime's solver configuration; a DC-EGM or NEGM regime + gets the synthesized intrinsic budget constraint. certainty_equivalent: Nonlinear certainty equivalent declared by the regime, or `None`. @@ -493,6 +832,26 @@ def _build_simulation_phase( ) functions = core.functions constraints = core.constraints + if isinstance(solver, (DCEGM, NEGM)): + if ( + DCEGM_BUDGET_CONSTRAINT_NAME in core.functions + or DCEGM_BUDGET_CONSTRAINT_NAME in core.constraints + ): + msg = ( + f"Regime '{regime_name}' declares a function or constraint " + f"named '{DCEGM_BUDGET_CONSTRAINT_NAME}'. That name is " + "reserved for the budget constraint the simulate phase " + "synthesizes for DC-EGM and NEGM regimes; rename it." + ) + raise ModelInitializationError(msg) + constraints = MappingProxyType( + { + **core.constraints, + DCEGM_BUDGET_CONSTRAINT_NAME: get_intrinsic_budget_constraint( + solver=solver, functions=core.functions + ), + } + ) # Every published simulate-phase consumer (next_state, the realized # regime draw, the feasibility check, additional targets) reads each @@ -1617,8 +1976,8 @@ def _wrap_deterministic_regime_transition( @with_signature(args=annotations, return_annotation="FloatND") @functools.wraps(func) def wrapped( - *args: FloatND | IntND | int, - **kwargs: FloatND | IntND | int, + *args: FloatND | IntND | BoolND | float | MappingLeaf | SequenceLeaf, + **kwargs: FloatND | IntND | BoolND | float | MappingLeaf | SequenceLeaf, ) -> FloatND: regime_idx = func(*args, **kwargs) return jax.nn.one_hot(regime_idx, n_regimes) diff --git a/src/_lcm/simulation/additional_targets.py b/src/_lcm/simulation/additional_targets.py index 637918eaa..a902ebdb9 100644 --- a/src/_lcm/simulation/additional_targets.py +++ b/src/_lcm/simulation/additional_targets.py @@ -9,6 +9,7 @@ import numpy as np from dags import concatenate_functions +from _lcm.egm.budget import DCEGM_BUDGET_CONSTRAINT_NAME from _lcm.engine import Regime from _lcm.typing import FlatRegimeParams, RegimeName from _lcm.utils.dispatchers import vmap_1d @@ -60,12 +61,24 @@ def _collect_all_available_targets( def _get_available_targets_for_regime(regime: Regime) -> set[str]: - """Get available target names for a single regime.""" - excluded = {"H"} | _get_stochastic_weight_function_names(regime) + """Get available target names for a single regime. + + Internal machinery is excluded: the Bellman aggregator `H`, the + stochastic weight functions, and the budget mask synthesized for DC-EGM + regimes (an implementation detail of the simulate-phase argmax, not a + user-declared constraint). A DC-EGM regime's `inverse_marginal_utility` + is excluded as well β€” its `marginal_continuation` argument exists only + inside the Euler inversion, so it is not computable from simulation data. + """ + excluded = {"H", DCEGM_BUDGET_CONSTRAINT_NAME} | ( + _get_stochastic_weight_function_names(regime) + ) + if regime.solution.solves_via_dcegm: + excluded.add("inverse_marginal_utility") sim = regime.simulation - return { - name for name in sim.functions if name not in excluded - } | sim.constraints.keys() + return {name for name in sim.functions if name not in excluded} | { + name for name in sim.constraints if name not in excluded + } def _get_stochastic_weight_function_names(regime: Regime) -> set[str]: diff --git a/src/_lcm/solution/backward_induction.py b/src/_lcm/solution/backward_induction.py index 6ac7e57f3..7265f567d 100644 --- a/src/_lcm/solution/backward_induction.py +++ b/src/_lcm/solution/backward_induction.py @@ -1,4 +1,5 @@ import functools +import gc import logging import os import time @@ -10,6 +11,8 @@ import jax import jax.numpy as jnp +from _lcm.egm.carry import EGMCarry +from _lcm.egm.published_policy import EGMSimPolicy from _lcm.engine import Regime, StateActionSpace, _build_regime_sharding from _lcm.solution.validate_V import validate_V from _lcm.typing import FlatParams, RegimeName, StateName @@ -36,7 +39,10 @@ def solve( logger: logging.Logger, enable_jit: bool, max_compilation_workers: int | None = None, -) -> MappingProxyType[int, MappingProxyType[RegimeName, FloatND]]: +) -> tuple[ + MappingProxyType[int, MappingProxyType[RegimeName, FloatND]], + MappingProxyType[int, MappingProxyType[RegimeName, EGMSimPolicy]], +]: """Solve a model using grid search. Args: @@ -54,37 +60,30 @@ def solve( Defaults to `os.cpu_count()`. Returns: - Immutable mapping of periods to regime value function arrays. + Tuple of (the immutable mapping of periods to regime value-function + arrays, the immutable mapping of periods to each DC-EGM regime's + published `EGMSimPolicy` β€” the off-grid consumption function simulation + interpolates; empty for periods/regimes with no DC-EGM kernel). """ - # Compute V array shapes (and their device shardings, if any) and build - # a consistent next_regime_to_V_arr template. Using the same pytree - # structure (keys and shapes) across all periods avoids JIT re- - # compilation from pytree mismatches. - regime_V_topology = _get_regime_V_shapes_and_shardings( - regimes=regimes, - flat_params=flat_params, - ) - - next_regime_to_V_arr = MappingProxyType( - { - regime_name: _build_zero_V_arr(topology=topology) - for regime_name, topology in regime_V_topology.items() - } + next_regime_to_V_arr, next_regime_to_egm_carry = _build_continuation_templates( + regimes=regimes, flat_params=flat_params ) - # AOT-compile all unique max_Q_over_a functions in parallel. + # AOT-compile all unique solve kernels in parallel. compiled_functions = _compile_all_functions( regimes=regimes, flat_params=flat_params, ages=ages, next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, enable_jit=enable_jit, max_compilation_workers=max_compilation_workers, logger=logger, ) solution: dict[int, MappingProxyType[RegimeName, FloatND]] = {} + sim_policies: dict[int, MappingProxyType[RegimeName, EGMSimPolicy]] = {} # Async diagnostics accumulators: per-period NaN/Inf flags (and the # debug min/max/mean trio) live here as device-side scalars during @@ -118,12 +117,14 @@ def solve( # logger's debug level. diagnostics_enabled = validation_enabled(logger) stats_enabled = logger.isEnabledFor(logging.DEBUG) - diagnostic_rows: list[_DiagnosticRow] = [] - diagnostic_min: list[FloatND] = [] - diagnostic_max: list[FloatND] = [] - diagnostic_mean: list[FloatND] = [] - running_any_nan: BoolND = jnp.zeros((), dtype=bool) - running_any_inf: BoolND = jnp.zeros((), dtype=bool) + ( + diagnostic_rows, + diagnostic_min, + diagnostic_max, + diagnostic_mean, + running_any_nan, + running_any_inf, + ) = _init_diagnostic_accumulators() logger.info("Starting solution") total_start = time.monotonic() @@ -133,9 +134,18 @@ def solve( regimes=regimes, flat_params=flat_params ) + # Simulation policies are a DC-EGM solve *output*, accumulated for every + # period; no backward step reads them. Their `endog_grid` aliases the + # period's carry buffer, so leaving them on device pins one carry-sized + # buffer per period for the whole induction. Evict each period's policies + # to host as they are produced; simulation re-materializes them on device. + host_device = jax.devices("cpu")[0] + for period in reversed(range(ages.n_periods)): period_start = time.monotonic() period_solution: dict[RegimeName, FloatND] = {} + period_egm_carries: dict[RegimeName, EGMCarry] = {} + period_sim_policies: dict[RegimeName, EGMSimPolicy] = {} active_regimes = { regime_name: regime @@ -149,21 +159,19 @@ def solve( n_active_regimes=len(active_regimes), ) - for regime_name in active_regimes: - state_action_space = base_state_action_spaces[regime_name] - - # evaluate Q-function on states and actions, and maximize over - # actions (the compiled function is the period's max_Q_over_a). - # Pass period/age as JAX arrays (not Python scalars) so the shared - # jax.jit function is traced once with abstract shapes, not - # recompiled for every distinct (period, age) pair. - V_arr = compiled_functions[(regime_name, period)]( - **state_action_space.states, - **state_action_space.actions, + for regime_name, regime in active_regimes.items(): + V_arr = _solve_regime_period( + regime=regime, + regime_name=regime_name, + period=period, + compiled_cores=compiled_functions[(regime_name, period)], + state_action_space=base_state_action_spaces[regime_name], + flat_params=flat_params, + ages=ages, next_regime_to_V_arr=next_regime_to_V_arr, - **flat_params[regime_name], - period=jnp.int32(period), - age=ages.values[period], + next_regime_to_egm_carry=next_regime_to_egm_carry, + period_egm_carries=period_egm_carries, + period_sim_policies=period_sim_policies, ) # Async reductions: gated on log level. `"off"` skips # everything β€” no kernel launches, no host syncs, no @@ -205,17 +213,22 @@ def solve( # implies a finished `min`/`max` too. diagnostic_mean[-1].block_until_ready() - # Maintain consistent pytree structure: keep all regime keys, - # update active regimes with solved V arrays. - next_regime_to_V_arr = MappingProxyType( + next_regime_to_V_arr, next_regime_to_egm_carry = _roll_continuation_inputs( + regimes=regimes, + period_solution=period_solution, + period_egm_carries=period_egm_carries, + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, + ) + solution[period] = MappingProxyType(period_solution) + sim_policies[period] = MappingProxyType( { - regime_name: period_solution.get( - regime_name, next_regime_to_V_arr[regime_name] + regime_name: jax.block_until_ready( + jax.device_put(sim_policy, host_device) ) - for regime_name in regimes + for regime_name, sim_policy in period_sim_policies.items() } ) - solution[period] = MappingProxyType(period_solution) elapsed = time.monotonic() - period_start log_period_timing(logger=logger, elapsed=elapsed) @@ -234,6 +247,8 @@ def solve( if validation_raises(logger) and running_any_nan.item(): break + _collect_rolled_carries(period_egm_carries=period_egm_carries) + if diagnostics_enabled: try: _emit_post_loop_diagnostics( @@ -256,7 +271,183 @@ def solve( total_elapsed = time.monotonic() - total_start logger.info("Solution complete (%s)", format_duration(seconds=total_elapsed)) - return MappingProxyType(solution) + return MappingProxyType(solution), MappingProxyType(sim_policies) + + +def _collect_rolled_carries(*, period_egm_carries: dict[RegimeName, EGMCarry]) -> None: + """Return the device buffers rolled off the period just solved. + + The superseded continuation V/carry and the period's transient working set + are unreferenced once the period rolls, but a rolled continuation carry sits + in a registered pytree that CPython's cyclic collector frees only when it + next runs β€” forcing a collection here returns the device pool promptly, + capping peak resident across the loop (mirrors the forward-sim memory rework + in `result.py`). + + Gated on whether this period actually produced a carry (the generic + per-period kernel output the loop already tracks), not on the solver type: + a period whose kernels publish no carry rolls no such buffer, so the + collection β€” which otherwise dominates small warm solves with no memory + gain β€” is skipped for it. + """ + if period_egm_carries: + gc.collect() + + +def _init_diagnostic_accumulators() -> tuple[ + list[_DiagnosticRow], + list[FloatND], + list[FloatND], + list[FloatND], + BoolND, + BoolND, +]: + """Initialize the per-period async diagnostics accumulators. + + Returns the empty diagnostic-row, min, max, and mean lists, and the two + running NaN/Inf flag scalars (folded into across the backward-induction + loop). The two flags share the same immutable zero scalar initially; each + is reassigned independently inside the loop. + """ + zero: BoolND = jnp.zeros((), dtype=bool) + rows: list[_DiagnosticRow] = [] + mins: list[FloatND] = [] + maxs: list[FloatND] = [] + means: list[FloatND] = [] + return rows, mins, maxs, means, zero, zero + + +def _solve_regime_period( + *, + regime: Regime, + regime_name: RegimeName, + period: int, + compiled_cores: MappingProxyType[str, Callable], + state_action_space: StateActionSpace, + flat_params: FlatParams, + ages: AgeGrid, + next_regime_to_V_arr: MappingProxyType[RegimeName, FloatND], + next_regime_to_egm_carry: MappingProxyType[RegimeName, EGMCarry], + period_egm_carries: dict[RegimeName, EGMCarry], + period_sim_policies: dict[RegimeName, EGMSimPolicy], +) -> FloatND: + """Invoke one regime's period adapter for one period. + + Every regime exposes the same kind of adapter; the loop never branches on + solver type. The adapter wraps the regime's shared jitted core(s) (passed in + AOT-compiled as `compiled_cores`), calls them with the solver's own argument + layout, and returns a `KernelResult`. The only branches here are on the + optional generic outputs β€” `carry` (the continuation a DC-EGM parent + interpolates) and `sim_policy` (the off-grid simulation policy) β€” which a + grid-search regime with no continuation simply leaves `None`. + + Produced carries and sim-policies are stored in `period_egm_carries` / + `period_sim_policies` in place. + + `period`/`age` are passed as JAX arrays (not Python scalars) so a shared + `jax.jit` function is traced once with abstract shapes, not recompiled + for every distinct (period, age) pair. + + The adapter is handed its full per-key compiled-core map (`compiled_cores`): + a single-core kernel reads `["main"]`, the NEGM kernel reads `["keeper"]` + and `["adjuster"]`. + + Returns: + The regime's value-function array. + + """ + period_kernel = regime.solution.period_kernels[period] + result = period_kernel( + compiled_cores=compiled_cores, + state_action_space=state_action_space, + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, + flat_params=flat_params, + period=period, + ages=ages, + ) + if result.carry is not None: + period_egm_carries[regime_name] = result.carry + if result.sim_policy is not None: + period_sim_policies[regime_name] = result.sim_policy + return result.V_arr + + +def _roll_continuation_inputs( + *, + regimes: MappingProxyType[RegimeName, Regime], + period_solution: dict[RegimeName, FloatND], + period_egm_carries: dict[RegimeName, EGMCarry], + next_regime_to_V_arr: MappingProxyType[RegimeName, FloatND], + next_regime_to_egm_carry: MappingProxyType[RegimeName, EGMCarry], +) -> tuple[ + MappingProxyType[RegimeName, FloatND], MappingProxyType[RegimeName, EGMCarry] +]: + """Roll the per-period continuation mappings forward by one period. + + Both mappings keep their full template key sets β€” V for every regime, + carries for every carry-producing regime β€” and update only the entries + solved this period, so the pytree structure stays JIT-stable. + + Returns: + Tuple of the rolled V mapping and the rolled carry mapping. + + """ + rolled_V_arr = MappingProxyType( + { + regime_name: period_solution.get( + regime_name, next_regime_to_V_arr[regime_name] + ) + for regime_name in regimes + } + ) + rolled_egm_carry = MappingProxyType( + { + regime_name: period_egm_carries.get( + regime_name, next_regime_to_egm_carry[regime_name] + ) + for regime_name in next_regime_to_egm_carry + } + ) + return rolled_V_arr, rolled_egm_carry + + +def _build_continuation_templates( + *, + regimes: MappingProxyType[RegimeName, Regime], + flat_params: FlatParams, +) -> tuple[ + MappingProxyType[RegimeName, FloatND], MappingProxyType[RegimeName, EGMCarry] +]: + """Build the period-invariant continuation-input templates. + + Both mappings keep the same pytree structure (keys and shapes) across all + periods, avoiding JIT re-compilation from pytree mismatches: + + - the V template holds a zero array per regime, shaped (and sharded) like + the regime's V array; + - the EGM-carry template holds entries only for carry-producing regimes + (DC-EGM regimes and, in models with one, terminal regimes), in the key + order reused every period. + """ + regime_V_topology = _get_regime_V_shapes_and_shardings( + regimes=regimes, + flat_params=flat_params, + ) + next_regime_to_V_arr = MappingProxyType( + { + regime_name: _build_zero_V_arr(topology=topology) + for regime_name, topology in regime_V_topology.items() + } + ) + next_regime_to_egm_carry = MappingProxyType( + { + regime_name: regime.solution.continuation_template + for regime_name, regime in regimes.items() + if regime.solution.continuation_template is not None + } + ) + return next_regime_to_V_arr, next_regime_to_egm_carry def _build_base_state_action_spaces( @@ -300,51 +491,66 @@ def _compile_all_functions( flat_params: FlatParams, ages: AgeGrid, next_regime_to_V_arr: MappingProxyType[RegimeName, FloatND], + next_regime_to_egm_carry: MappingProxyType[RegimeName, EGMCarry], enable_jit: bool, max_compilation_workers: int | None, logger: logging.Logger, -) -> dict[tuple[RegimeName, int], Callable]: - """AOT-compile all unique max_Q_over_a functions in parallel. - - With shared-JIT, many periods share the same `jax.jit`-wrapped function - object. This function deduplicates by object identity, traces each unique - function once (sequential), then compiles the XLA programs in parallel - via a thread pool (XLA releases the GIL during compilation). - - When JIT is disabled (`enable_jit=False`), returns the raw functions - without compilation. +) -> dict[tuple[RegimeName, int], MappingProxyType[str, Callable]]: + """AOT-compile all unique solve cores in parallel. + + Each regime exposes one period adapter per period; the adapter wraps one or + more shared jitted cores, keyed by a stable per-kernel name (`cores()`). + Most kernels carry a single `"main"` core; the NEGM kernel carries a + `"keeper"` and an `"adjuster"` core, each a distinct traced program. Many + periods share the same core object, so this deduplicates the cores by + identity, lowers each unique core once (sequential β€” tracing is + single-threaded) with the adapter's per-key lowering arguments, then compiles + the XLA programs in parallel via a thread pool (XLA releases the GIL during + compilation). The loop stays free of any solver-type fork. + + When JIT is disabled (`enable_jit=False`), returns the raw cores without + compilation. Args: - regimes: The internal regimes containing solve functions. + regimes: The internal regimes containing the period adapters. flat_params: Regime parameters for constructing lowering args. ages: Age grid for the model. next_regime_to_V_arr: Template with consistent keys and V array shapes for constructing lowering arguments. + next_regime_to_egm_carry: Template with consistent keys and carry + shapes for constructing lowering arguments. enable_jit: Whether to JIT-compile the functions of the internal regimes. max_compilation_workers: Maximum threads for parallel compilation. Defaults to `os.cpu_count()`. logger: Logger for compilation progress. Returns: - Dict of (regime_name, period) to callable (compiled or raw) functions. + Dict of (regime_name, period) to the immutable mapping of core key to + compiled (or raw) core. """ - # Collect all (regime, period) -> function mappings. - all_functions: dict[tuple[RegimeName, int], Callable] = {} + # Collect all (regime, period, core_key) -> shared jitted core mappings off + # the period adapters. + all_functions: dict[tuple[RegimeName, int, str], Callable] = {} for regime_name, regime in regimes.items(): for period in regime.active_periods: - all_functions[(regime_name, period)] = regime.solution.max_Q_over_a[period] + cores = regime.solution.period_kernels[period].cores() + for core_key, core in cores.items(): + all_functions[(regime_name, period, core_key)] = core - # If JIT is disabled, return raw functions directly. + # If JIT is disabled, return the raw cores keyed by core_key per (regime, + # period). if not enable_jit: - return all_functions + return _group_cores_by_regime_period(all_functions) - # Deduplicate by identity (or by underlying function for partials). - unique: dict[Hashable, tuple[Callable, RegimeName, int]] = {} - for (regime_name, period), func in all_functions.items(): + # Deduplicate by identity (or by underlying function for partials), keeping + # one representative (regime, period, core_key) per unique core so its + # adapter can build the lowering arguments for that key. + unique: dict[Hashable, tuple[Callable, RegimeName, int, str]] = {} + for (regime_name, period, core_key), func in all_functions.items(): func_id = _func_dedup_key(func=func) if func_id not in unique: - unique[func_id] = (func, regime_name, period) + unique[func_id] = (func, regime_name, period, core_key) n_workers = _resolve_compilation_workers( max_compilation_workers=max_compilation_workers @@ -352,29 +558,34 @@ def _compile_all_functions( n_unique = len(unique) logger.info( - "AOT compilation: %d unique functions (%d regime-period pairs, %d workers)", + "AOT compilation: %d unique functions (%d regime-period-core triples, " + "%d workers)", n_unique, len(all_functions), n_workers, ) - # Phase 1: Lower all unique functions (sequential β€” tracing is not - # thread-safe and must happen on the main thread). + # Phase 1: Lower all unique cores (sequential β€” tracing is not thread-safe + # and must happen on the main thread). Each adapter builds the named core's + # lowering arguments off a fresh, params-completed state-action space. lowered: dict[Hashable, jax.stages.Lowered] = {} labels: dict[Hashable, str] = {} - for i, (func_id, (func, regime_name, period)) in enumerate(unique.items(), 1): - state_action_space = regimes[regime_name].solution.state_action_space( - regime_params=flat_params[regime_name], + for i, (func_id, (func, regime_name, period, core_key)) in enumerate( + unique.items(), 1 + ): + regime = regimes[regime_name] + lower_args = regime.solution.period_kernels[period].build_lower_args( + core_key=core_key, + state_action_space=regime.solution.state_action_space( + regime_params=flat_params[regime_name], + ), + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, + flat_params=flat_params, + period=period, + ages=ages, ) - lower_args = { - **dict(state_action_space.states), - **dict(state_action_space.actions), - "next_regime_to_V_arr": next_regime_to_V_arr, - **dict(flat_params[regime_name]), - "period": jnp.int32(period), - "age": ages.values[period], - } - label = f"{regime_name} (age {ages.values[period].item()})" + label = f"{regime_name} {core_key} (age {ages.values[period].item()})" labels[func_id] = label logger.info("%d/%d %s", i, n_unique, label) logger.info(" lowering ...") @@ -397,6 +608,7 @@ def _compile_and_log( result = low.compile() elapsed = time.monotonic() - start logger.info(" compiled %s %s", label, format_duration(seconds=elapsed)) + _log_kernel_memory(compiled=result, label=label, logger=logger) return func_id, result with ThreadPoolExecutor(max_workers=n_workers) as pool: @@ -410,10 +622,74 @@ def _compile_and_log( func_id, comp = future.result() compiled[func_id] = comp - # Map back to (regime, period) keys. - return { - key: compiled[_func_dedup_key(func=func)] for key, func in all_functions.items() - } + # Map back to (regime, period) keys, grouping the compiled cores by core key. + return _group_cores_by_regime_period( + { + key: compiled[_func_dedup_key(func=func)] + for key, func in all_functions.items() + } + ) + + +def _group_cores_by_regime_period( + cores_by_triple: dict[tuple[RegimeName, int, str], Callable], +) -> dict[tuple[RegimeName, int], MappingProxyType[str, Callable]]: + """Group (regime, period, core_key) -> core into (regime, period) -> {key: core}. + + The solve loop dispatches each period adapter with its full per-key core map, + so a multi-core kernel (NEGM's keeper/adjuster) receives both compiled cores + while a single-core kernel receives `{"main": ...}`. + """ + grouped: dict[tuple[RegimeName, int], dict[str, Callable]] = {} + for (regime_name, period, core_key), core in cores_by_triple.items(): + grouped.setdefault((regime_name, period), {})[core_key] = core + return {key: MappingProxyType(cores) for key, cores in grouped.items()} + + +def _log_kernel_memory( + *, + compiled: jax.stages.Compiled, + label: str, + logger: logging.Logger, +) -> None: + """Log XLA's compile-time memory analysis for one compiled kernel. + + Gated on the `LCM_LOG_KERNEL_MEMORY` env var (off by default, zero cost), + independently of the solve `log_level`: the env var is the opt-in, so the + `[mem]` lines are emitted at a level that always clears the logger's + threshold β€” even at `log_level="off"`, where the debug NaN/Inf diagnostic + (its own per-period full-V transient) would otherwise have to be enabled to + see them, masking the real kernel peak. + + `temp_size_in_bytes` is the peak scratch buffer XLA plans for the kernel β€” + the transient that binds the device at run time. Because it is computed at + compile, it is available even for configs whose *execution* would OOM, so + the egm_step working set can be sized (and swept against grid knobs) without + running or exhausting the device. `argument`/`output` sizes bound the + per-call resident inputs/outputs (the carry and V). Pair with + `XLA_FLAGS=--xla_dump_to=DIR` to name the HLO op behind the peak buffer. + """ + if os.environ.get("LCM_LOG_KERNEL_MEMORY", "0") == "0": + return + level = max(logger.getEffectiveLevel(), logging.INFO) + try: + stats = compiled.memory_analysis() + except Exception as exc: # noqa: BLE001 - backend may not support analysis + logger.log(level, " [mem] %s: memory_analysis unavailable (%s)", label, exc) + return + if stats is None: + logger.log(level, " [mem] %s: memory_analysis returned None", label) + return + gib = 1024**3 + logger.log( + level, + " [mem] %s: temp=%.3f GiB args=%.3f GiB output=%.3f GiB peak=%.3f GiB", + label, + stats.temp_size_in_bytes / gib, + stats.argument_size_in_bytes / gib, + stats.output_size_in_bytes / gib, + stats.peak_memory_in_bytes / gib, + ) def _resolve_compilation_workers(*, max_compilation_workers: int | None) -> int: @@ -615,7 +891,14 @@ def _raise_at( flat_params=flat_params, solution=solution, ) - compute_intermediates = regime.solution.compute_intermediates.get(row.period) + # The intermediates closure mirrors the brute-force Q evaluation; for a row + # solved by a DC-EGM kernel it cannot reproduce the failing computation, so + # the error is raised without the U/F/E/Q breakdown. + compute_intermediates = ( + None + if regime.solution.solves_via_dcegm + else regime.solution.compute_intermediates.get(row.period) + ) V_arr = solution[row.period][row.regime_name] validate_V( V_arr=V_arr, diff --git a/src/_lcm/solution/contract.py b/src/_lcm/solution/contract.py index 96d7c1e0f..d558a7783 100644 --- a/src/_lcm/solution/contract.py +++ b/src/_lcm/solution/contract.py @@ -6,27 +6,72 @@ Add a solver by subclassing `Solver` and implementing `build_period_kernels`; override `validate` for a build-time model-contract check (the default is a no-op). `SolverBuildContext` carries everything a solver may read to build one -regime's kernels; `SolverKernels` is what it hands back. +regime's kernels; `SolutionKernels` is what it hands back. -This module is an engine leaf: it imports only `_lcm.engine` / `_lcm.grids` / -`_lcm.typing` (none of which reach `lcm.solvers`), so the public solver faΓ§ade -can re-export it without forming an import cycle. +Each entry of `SolutionKernels.period_kernels` is a `PeriodKernel`: a single +non-jitted period adapter that wraps the solver's shared jitted core, calls it +with the solver's own argument layout, and assembles a `KernelResult` outside +JIT. The solve loop invokes the same adapter for every solver, branching only on +which optional outputs (`carry`, `sim_policy`) are present, never on solver type. + +This module is an engine leaf. Reaching `lcm.regime` would close an import +cycle β€” it imports the `lcm.solvers` faΓ§ade, which re-exports `Solver` from +here. `UserRegime` and `VInterpolationInfo` (whose module imports `lcm.regime`) +are therefore referenced through two-form aliases: precise element types for ty +under `TYPE_CHECKING`, a bare container for the beartype claw at runtime. The +remaining engine types (`StateActionSpace`, `EGMCarry`, `EGMSimPolicy`) live in +sibling leaves with no path back to `lcm.solvers`, so they import normally and +beartype checks them precisely. The widened runtime aliases are required because +the claw beartypes each dataclass `__init__`, and under PEP 649 that forces the +field annotations to resolve to real objects when an instance is constructed. """ from abc import ABC, abstractmethod +from collections.abc import Callable, Mapping from dataclasses import dataclass from types import MappingProxyType +from typing import TYPE_CHECKING, Protocol, TypeAlias, runtime_checkable from _lcm.certainty_equivalent import CertaintyEquivalent +from _lcm.egm.carry import EGMCarry +from _lcm.egm.published_policy import EGMSimPolicy from _lcm.engine import StateActionSpace from _lcm.grids import Grid from _lcm.typing import ( - MaxQOverAFunction, + ConstraintFunctionsMapping, + EconFunctionsMapping, + FlatParams, QAndFFunction, RegimeName, + RegimeTransitionFunction, StateName, StateOrActionName, + TransitionFunctionName, + TransitionFunctionsMapping, ) +from lcm.ages import AgeGrid +from lcm.typing import FloatND + +# The cross-period continuation channel a DC-EGM parent interpolates. Named +# solver-agnostically on the seam so the engine threads it without knowing it is +# an EGM carry; today the only continuation payload is the EGM carry itself. +type ContinuationPayload = EGMCarry + +if TYPE_CHECKING: + from _lcm.regime_building.V import VInterpolationInfo + from lcm.regime import Regime as UserRegime + + UserRegimesMapping: TypeAlias = Mapping[RegimeName, UserRegime] # noqa: UP040 + RegimeToVInterpolationInfo: TypeAlias = MappingProxyType[ # noqa: UP040 + RegimeName, VInterpolationInfo + ] +else: + # `lcm.regime` β€” reached directly, and transitively through + # `_lcm.regime_building.V` β€” closes a cycle via the `lcm.solvers` faΓ§ade, + # which re-exports `Solver` from this module. ty reads the precise element + # types above; the beartype claw checks only the outer container at runtime. + UserRegimesMapping = Mapping + RegimeToVInterpolationInfo = MappingProxyType @dataclass(frozen=True, kw_only=True) @@ -37,6 +82,12 @@ class SolverBuildContext: different needs are added; each solver reads only the fields it uses. """ + regime_name: RegimeName + """Name of the regime the kernels are built for.""" + + user_regimes: UserRegimesMapping + """Mapping of regime names to user-provided `Regime` instances.""" + state_action_space: StateActionSpace """The regime's state-action space.""" @@ -46,6 +97,38 @@ class SolverBuildContext: grids: MappingProxyType[StateOrActionName, Grid] """Immutable mapping of the regime's variable names to grid objects.""" + functions: EconFunctionsMapping + """The regime's processed functions (params renamed to qualified names).""" + + constraints: ConstraintFunctionsMapping + """Immutable mapping of the regime's constraint names to functions.""" + + transitions: TransitionFunctionsMapping + """Immutable mapping of target regime names to transition functions.""" + + stochastic_transition_names: frozenset[TransitionFunctionName] + """Frozenset of stochastic transition function names.""" + + compute_regime_transition_probs: RegimeTransitionFunction | None + """Regime transition probability function, or `None` for terminal regimes.""" + + regime_to_v_interpolation_info: RegimeToVInterpolationInfo + """Immutable mapping of regime names to V-interpolation info.""" + + regimes_to_active_periods: MappingProxyType[RegimeName, tuple[int, ...]] + """Immutable mapping of regime names to their active period tuples.""" + + flat_param_names: frozenset[str] + """Frozenset of flat parameter names for the regime.""" + + regime_to_flat_param_names: MappingProxyType[RegimeName, frozenset[str]] + """Immutable mapping of every regime name to its flat parameter names. + + A DC-EGM source carrying into a different target regime reads the target's + params in its per-asset-node solve, so the kernel build admits and binds + the union of the source and its reachable carry targets' params. + """ + enable_jit: bool """Whether to JIT-compile the kernels.""" @@ -78,13 +161,124 @@ class SolverBuildContext: @dataclass(frozen=True, kw_only=True) -class SolverKernels: - """Per-period solve kernels produced by a solver.""" +class KernelResult: + """One regime-period solve output, assembled outside JIT. + + The solve loop reads `V_arr` from every kernel and branches only on whether + the optional generic outputs are present β€” never on solver type: + + - `carry` is the cross-period continuation a DC-EGM parent interpolates; + `None` for a regime that publishes no continuation. + - `sim_policy` is the off-grid consumption policy DC-EGM forward simulation + can interpolate; `None` for a regime that publishes none. + """ + + V_arr: FloatND + """The regime's value-function array on its exogenous state grid.""" + + carry: ContinuationPayload | None = None + """Continuation payload for a DC-EGM parent, or `None`.""" + + sim_policy: EGMSimPolicy | None = None + """Published off-grid simulation policy, or `None`.""" + + +@runtime_checkable +class PeriodKernel(Protocol): + """One regime's per-period solve adapter β€” the loop's uniform call target. + + A single non-jitted closure per regime-period that wraps the solver's shared + jitted core(s) (deduped across periods by core identity), calls them with the + solver's own argument layout, and assembles a `KernelResult` outside JIT. + Plain closures satisfy this structurally; the loop never inspects the solver + type. `cores()` exposes the shared jitted function(s) keyed by a stable + per-kernel name so AOT compilation can deduplicate and lower each; + `build_lower_args` builds a named core's lowering kwargs. + + Most kernels carry exactly one core (`{"main": ...}`); the NEGM kernel + carries two (`{"keeper": ..., "adjuster": ...}`), a per-durable-state passive + DC-EGM keeper alongside the adjuster sweep. The AOT contract lowers, compiles, + and dispatches each core by its key, so a multi-core kernel never collapses + into one program. + """ + + def cores(self) -> Mapping[str, Callable]: + """Return the shared jitted core(s), keyed by stable per-kernel name. + + Each value is a distinct traced program AOT compilation lowers and + deduplicates independently; `build_lower_args(core_key=...)` builds the + matching lowering kwargs and `__call__` reads the compiled cores back by + the same key. + """ + ... + + @property + def core(self) -> Callable: + """The kernel's `"main"` core, for any single-core reader. + + Defaults to `cores()["main"]`; multi-core kernels override or omit it. + """ + ... + + def with_fixed_params(self, *, fixed_flat_params: FlatParams) -> PeriodKernel: + """Return a copy with the regime's fixed params bound into the core(s). + + The adapter owns its solver's binding rule β€” which fixed params reach + the core (and any inline closure it wraps) β€” so the engine binds fixed + params without a solver-type switch. + """ + ... + + def build_lower_args( + self, + *, + core_key: str, + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, + ages: AgeGrid, + ) -> Mapping[str, object]: + """Build the named core's lowering arguments for this period. + + Single-core kernels ignore `core_key`; the NEGM kernel dispatches the + keeper-vs-adjuster lowering off it. + """ + ... + + def __call__( + self, + *, + compiled_cores: Mapping[str, Callable], + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, + ages: AgeGrid, + ) -> KernelResult: + """Invoke the compiled core(s) and assemble the period's `KernelResult`. + + Single-core kernels read `compiled_cores["main"]`; the NEGM kernel reads + `["keeper"]` and `["adjuster"]`. + """ + ... + + +@dataclass(frozen=True, kw_only=True) +class SolutionKernels: + """Per-period solve adapters produced by a solver.""" + + period_kernels: Mapping[int, PeriodKernel] + """Immutable mapping of period to the regime's uniform period adapter.""" - max_Q_over_a: MappingProxyType[int, MaxQOverAFunction] - """Immutable mapping of period to max-Q-over-actions kernels. + continuation_template: ContinuationPayload | None = None + """All-finite template continuation with the regime's static shapes. - Empty for solvers that replace the grid search with their own kernels. + `None` for a regime that publishes no continuation. Initializes the rolling + `next_regime_to_egm_carry` mapping and serves as the lowering argument when + AOT-compiling a parent's kernel. """ @@ -98,8 +292,22 @@ class Solver(ABC): """ @abstractmethod - def build_period_kernels(self, *, context: SolverBuildContext) -> SolverKernels: - """Build the regime's per-period solve kernels.""" + def build_period_kernels(self, *, context: SolverBuildContext) -> SolutionKernels: + """Build the regime's per-period solve adapters.""" def validate(self, *, context: SolverBuildContext) -> None: # noqa: B027 """Check the regime is in scope for this solver. Default: no-op.""" + + @property + def requires_continuation_carries(self) -> bool: + """Whether this solver reads a continuation carry from its targets. + + An endogenous-grid solver inverts the Euler equation against its + target regimes' value *and marginal* on a continuation grid, so each + target β€” including a terminal one β€” must publish a carry the engine + rolls alongside `next_regime_to_V_arr`. Grid search reads only the + value array, so it needs no carry. The engine reads this off every + regime's solver to decide whether terminal regimes produce their + closed-form carries, without forking on the solver type. + """ + return False diff --git a/src/_lcm/solution/solvers.py b/src/_lcm/solution/solvers.py index a7c938f91..72301aec2 100644 --- a/src/_lcm/solution/solvers.py +++ b/src/_lcm/solution/solvers.py @@ -1,27 +1,76 @@ """The built-in regime solvers. -`GridSearch` (the default) runs the existing max-Q-over-a grid search; -`DCEGM` is a published configuration whose engine is not yet wired in, so a -regime requesting it is rejected at model build by its `validate`. Both are -`Solver` subclasses. The kernel-building imports (`jax`, `get_max_Q_over_a`) -are function-local so the public `lcm.solvers` faΓ§ade stays a thin re-export -that pulls in no numerical engine modules. +`GridSearch` (the default) runs the existing max-Q-over-a grid search; `DCEGM` +runs the discrete-continuous endogenous grid method. Both are `Solver` +subclasses whose `build_period_kernels` returns one `PeriodKernel` per period β€” +a non-jitted adapter that wraps the solver's shared jitted core, calls it with +the solver's own argument layout, and assembles a `KernelResult` outside JIT. +The solve loop invokes every adapter the same way, so no solver-type fork +survives in the loop. + +Compilation reuse is preserved: only the shared core is `jax.jit`'d and +identity-deduped (`id(Q_and_F)` for grid search, function identity for the EGM +step), so periods sharing a core reuse one compiled program. The adapters that +wrap a shared core are themselves never jitted. + +The kernel-building imports (`jax`, `get_max_Q_over_a`, `build_egm_step_functions`) +are function-local so the public `lcm.solvers` faΓ§ade stays a thin re-export that +pulls in no numerical engine modules. """ +import functools import math -from dataclasses import dataclass +from collections.abc import Callable, Mapping +from dataclasses import dataclass, replace from types import MappingProxyType -from typing import Literal +from typing import Literal, cast +import jax +import jax.numpy as jnp from beartype import beartype +from dags import concatenate_functions, get_annotations, with_signature +from dags.annotations import ensure_annotations_are_strings from _lcm.beartype_conf import REGIME_CONF +from _lcm.egm.carry import EGMCarry +from _lcm.egm.outer_envelope import ( + finalize_outer_envelope, + fold_outer_envelope, + init_outer_envelope, +) +from _lcm.engine import StateActionSpace from _lcm.grids import ContinuousGrid +from _lcm.identity_transition import _IdentityTransition from _lcm.processes.base import _ContinuousStochasticProcess -from _lcm.solution.contract import Solver, SolverBuildContext, SolverKernels -from _lcm.typing import MaxQOverAFunction +from _lcm.solution.contract import ( + ContinuationPayload, + KernelResult, + PeriodKernel, + SolutionKernels, + Solver, + SolverBuildContext, +) +from _lcm.typing import ( + EconFunction, + EconFunctionsMapping, + EGMStepFunction, + FlatParams, + MaxQOverAFunction, + RegimeName, + TransitionFunction, + TransitionFunctionsMapping, +) +from lcm.ages import AgeGrid from lcm.exceptions import RegimeInitializationError -from lcm.typing import ActionName, FunctionName, StateName +from lcm.typing import ( + ActionName, + ContinuousState, + Float1D, + FloatND, + FunctionName, + StateName, + StateOrActionName, +) @beartype(conf=REGIME_CONF) @@ -29,18 +78,18 @@ class GridSearch(Solver): """Grid-search solver over the full state-action product (the default).""" - def build_period_kernels(self, *, context: SolverBuildContext) -> SolverKernels: - """Build max-Q-over-a closures for each period. + def build_period_kernels(self, *, context: SolverBuildContext) -> SolutionKernels: + """Build one max-Q-over-a period adapter per period. - Periods sharing the same Q_and_F object reuse a single compiled - function. + Periods sharing the same Q_and_F object reuse a single jitted core, + and therefore a single compiled program. """ import jax # noqa: PLC0415 from _lcm.regime_building.max_Q_over_a import get_max_Q_over_a # noqa: PLC0415 built: dict[int, MaxQOverAFunction] = {} - result: dict[int, MaxQOverAFunction] = {} + result: dict[int, PeriodKernel] = {} for period, Q_and_F in context.Q_and_F_functions.items(): q_id = id(Q_and_F) if q_id not in built: @@ -61,8 +110,10 @@ def build_period_kernels(self, *, context: SolverBuildContext) -> SolverKernels: co_map_v_arr_in_axes=context.co_map_v_arr_in_axes, ) built[q_id] = jax.jit(func) if context.enable_jit else func - result[period] = built[q_id] - return SolverKernels(max_Q_over_a=MappingProxyType(result)) + result[period] = _GridSearchPeriodKernel( + core=built[q_id], regime_name=context.regime_name + ) + return SolutionKernels(period_kernels=MappingProxyType(result)) @beartype(conf=REGIME_CONF) @@ -132,14 +183,55 @@ class DCEGM(Solver): error compounds across periods. """ - upper_envelope: Literal["fues"] = "fues" - """Upper-envelope refinement backend removing dominated Euler candidates.""" + upper_envelope: Literal["fues", "rfc", "ltm", "mss"] = "fues" + """Upper-envelope refinement backend removing dominated Euler candidates. + + - `"fues"`: the Fast Upper-Envelope Scan β€” a sequential scan that inserts + exact segment-crossing points. + - `"rfc"`: the Rooftop-Cut algorithm β€” a parallel dominance test that only + deletes points (a kink lands between retained points, recovered by the + Hermite carry read) and generalizes to multidimensional grids. + - `"ltm"`: the local-upper-bound brute method β€” an `O(K^2)` dense segment + scan that evaluates the envelope at every candidate abscissa (the + quadratic baseline of Dobrescu & Shanker 2026; a kink lands between + output nodes, recovered by the downstream read). + - `"mss"`: HARK's EGM upper envelope β€” a left-to-right sweep that keeps the + max-value branch at every abscissa *and* inserts the exact + segment-crossing point, so it tracks the FUES envelope tightly (the `MSS` + method of Dobrescu & Shanker 2026). + """ fues_jump_thresh: float = 2.0 """Segment-switch threshold on `|Ξ”A / Ξ”R|` in the FUES scan.""" - fues_n_points_to_scan: int = 10 - """Number of points the FUES forward scan inspects after a candidate.""" + fues_n_points_to_scan: int | None = None + """Number of points the FUES forward scan inspects after a candidate. + + `None` (the default) scans exhaustively β€” every other candidate. That is the + only width proven correct when more than the window's worth of off-segment + candidates interleave between two points of one segment: a bounded window + then misses the segment's continuation and silently accepts the dominated + interlopers. A finite value keeps the cheaper bounded scan for models known + to stay within the window, trading that correctness guarantee for speed. + """ + + fues_scan_unroll: int = 1 + """Loop-unroll factor for the FUES candidate `lax.scan`. + + Passed to `jax.lax.scan(..., unroll=fues_scan_unroll)` in both the + full-envelope and streaming-bracket scans. The scan is sequential and + latency-bound on accelerators; unrolling `k` iterations into one loop body + trades compile time and code size for fewer loop-carry round trips, which can + cut the per-row exec wall on GPU. `1` (no unroll) is the default; the refined + envelope is numerically identical across values, so this is a pure + performance knob. + """ + + rfc_jump_thresh: float = 2.0 + """Segment-switch threshold on `|Ξ”c / Ξ”R|` in the rooftop cut.""" + + rfc_search_radius: int = 10 + """Number of neighbors on each side the rooftop-cut dominance test inspects.""" refined_grid_factor: float = 1.2 """Headroom factor sizing the refined (NaN-padded) envelope arrays.""" @@ -166,21 +258,1034 @@ def __post_init__(self) -> None: _fail_if_fues_jump_thresh_non_positive(self.fues_jump_thresh) _fail_if_n_constrained_points_too_few(self.n_constrained_points) _fail_if_fues_n_points_to_scan_too_few(self.fues_n_points_to_scan) + _fail_if_fues_scan_unroll_too_few(self.fues_scan_unroll) + _fail_if_rfc_jump_thresh_non_positive(self.rfc_jump_thresh) + _fail_if_rfc_search_radius_too_few(self.rfc_search_radius) _fail_if_stochastic_node_batch_size_negative(self.stochastic_node_batch_size) - def validate(self, *, context: SolverBuildContext) -> None: - """Reject the not-yet-available DC-EGM solver at model build.""" - msg = ( - "The DC-EGM solver is not yet available. A regime requests " - "`solver=DCEGM(...)`; use `GridSearch()` (the default) until the " - "DC-EGM engine is wired in." + @property + def requires_continuation_carries(self) -> bool: + """DC-EGM inverts the Euler equation against its targets' marginals.""" + return True + + def build_period_kernels(self, *, context: SolverBuildContext) -> SolutionKernels: + """Build one DC-EGM period adapter per period and the carry template. + + The standalone `validate_dcegm_regimes` model-contract check (run during + regime processing) guarantees the regime is non-terminal, so the regime + transition probability function exists. Periods sharing one EGM-step core + reuse a single jitted core, and therefore a single compiled program. + Numerical-builder imports are function-local so the public `lcm.solvers` + faΓ§ade stays a thin re-export that pulls in no engine modules. + """ + import jax # noqa: PLC0415 + + from _lcm.egm.step import build_egm_step_functions # noqa: PLC0415 + + assert context.compute_regime_transition_probs is not None # noqa: S101 + egm_step, egm_carry_template, egm_reachable_targets = build_egm_step_functions( + solver=self, + regime_name=context.regime_name, + user_regimes=context.user_regimes, + functions=context.functions, + constraints=context.constraints, + transitions=context.transitions, + stochastic_transition_names=context.stochastic_transition_names, + compute_regime_transition_probs=context.compute_regime_transition_probs, + regime_to_v_interpolation_info=context.regime_to_v_interpolation_info, + regimes_to_active_periods=context.regimes_to_active_periods, + flat_param_names=context.flat_param_names, + regime_to_flat_param_names=context.regime_to_flat_param_names, + state_action_space=context.state_action_space, + has_taste_shocks=context.has_taste_shocks, + ) + if context.enable_jit: + jitted_by_id: dict[int, EGMStepFunction] = {} + for func in egm_step.values(): + if id(func) not in jitted_by_id: + jitted_by_id[id(func)] = jax.jit(func) + egm_step = MappingProxyType( + {period: jitted_by_id[id(func)] for period, func in egm_step.items()} + ) + period_kernels = MappingProxyType( + { + period: _DCEGMPeriodKernel( + core=core, + regime_name=context.regime_name, + reachable_targets=egm_reachable_targets, + transition_target_names=tuple(context.transitions), + ) + for period, core in egm_step.items() + } + ) + return SolutionKernels( + period_kernels=period_kernels, + continuation_template=egm_carry_template, + ) + + +@beartype(conf=REGIME_CONF) +@dataclass(frozen=True, kw_only=True) +class NEGM(Solver): + """Nested-EGM solver: an outer grid search over a durable/illiquid margin. + + NEGM solves a model with one continuous margin the Euler equation cleanly + inverts on (liquid consumption-savings) plus a second continuous margin + that does not admit a clean inverse-Euler (a durable/illiquid stock with + adjustment frictions) by nesting: + + - an *inner* standard 1-D DC-EGM solve of the consumption-savings problem, + conditional on the outer margin being fixed (this is exactly the existing + `DCEGM` kernel, with the outer margin entering inner resources and utility + as a constant and indexing the child durable state); + - an *outer* deterministic `max` over a grid of the outer post-decision + margin plus mandatory kink candidates (the no-adjustment point `s' = s`, + the floor corner). + + The outer step is a search, not a second inverse-Euler: the outer value is + generically non-concave (adjustment-cost kink, floor corners), so a second + EGM inversion would be invalid there. + + The `NEGM(inner=DCEGM(...), …)` composition makes "NEGM nests the 1-D + DC-EGM" literal: it reuses every inner field and its upper-envelope backend, + reuses `DCEGM.__post_init__` validation wholesale, and keeps the + outer-margin contract in one place. The model-contract check + `validate_negm_regimes` rejects, at `Model` construction, any model NEGM + does not fit (no outer margin, a coupled-2-Euler pension shape, a + taste-shock-ordering violation), naming the offending feature and the + correct alternative solver. + """ + + inner: DCEGM + """The inner 1-D DC-EGM config. + + Carries the liquid Euler state, the consumption action, the resources and + post-decision functions, the savings grid, and the upper-envelope backend. + Its `__post_init__` guards run on construction, so an invalid inner config + is rejected before NEGM's own guards. + """ + + outer_action: ActionName + """The outer continuous action β€” the durable/illiquid choice. + + Forbidden as the inner DC-EGM continuous action (the two margins must be + distinct). + """ + + outer_post_decision: FunctionName + """The outer post-decision function `s'` in `Regime.functions`. + + The inner `resources` and the child-state index both read its value as a + constant. Forbidden as the inner DC-EGM post-decision function. + """ + + outer_grid: ContinuousGrid + """Exogenous grid over the outer post-decision margin `s'`.""" + + outer_no_adjustment_candidate: FunctionName | None = None + """State-specific kink candidate (the no-adjustment point `s' = s`). + + Inserted per node because a fixed exogenous outer grid misses + state-specific kinks. `None` only when the model provably has no adjustment + kink. + """ + + outer_batch_size: int = 0 + """Number of outer-grid nodes solved per chunk before folding into the + running outer maximum. + + The outer search folds each node's solve into a running `(V_arr, envelope)`, + so the peak device memory holds one chunk of candidates regardless of the + outer-grid size. A positive value processes that many nodes at once (their + independent solves overlap) before reducing them; `0` (the default) solves + every node at once β€” fastest, but its peak grows with the outer-grid size. + It is a memory-vs-parallelism knob only: `max` is associative, so the solved + value function is identical across batch sizes. + """ + + def __post_init__(self) -> None: + _fail_if_outer_grid_is_stochastic(self.outer_grid) + _fail_if_outer_action_is_inner_action( + outer_action=self.outer_action, inner=self.inner + ) + _fail_if_outer_post_decision_is_inner_post_decision( + outer_post_decision=self.outer_post_decision, inner=self.inner + ) + _fail_if_outer_batch_size_negative(self.outer_batch_size) + + @property + def requires_continuation_carries(self) -> bool: + """NEGM nests a DC-EGM solve that inverts the Euler equation.""" + return True + + def build_period_kernels(self, *, context: SolverBuildContext) -> SolutionKernels: + """Build one NEGM period adapter per period, wrapping the inner kernels. + + The standalone `validate_negm_regimes` model-contract check (run during + regime processing) guarantees the outer margin is present and distinct + from the inner margin, that the outer margin is not Euler-coupled to the + inner state, and that any taste-shocked discrete choice is the outermost + aggregation. The inner DC-EGM period kernels are built once (with the + outer margin bound so it enters the inner resources and utility as a + constant and indexes the child durable state); each is wrapped in an + outer adapter that sweeps the outer grid plus the mandatory per-node + candidates and collapses the outer axis by `max`. + """ + # The adjuster is the inner DC-EGM with the outer post-decision + # transition stripped: its value is supplied per outer-grid node + # (`_with_outer_post_decision`), not recomputed from the outer action, so + # the child-carry next-state function must not demand the outer action; + # `read_child` sources the bound value from the combo pool instead. + # `_with_outer_post_decision` binds `outer_post_decision` into the + # regime's flat params at runtime, so the inner kernel reads it as a + # bound param β€” admit it as a flat param at build time too, so the inner + # scope check accepts the inner resources / utility reading it (the + # service-flow `utility(serviced(next_))` pattern). + adjuster_context = replace( + context, + transitions=_strip_outer_transition( + transitions=context.transitions, + outer_post_decision=self.outer_post_decision, + ), + flat_param_names=context.flat_param_names | {self.outer_post_decision}, + ) + adjuster_kernels = self.inner.build_period_kernels(context=adjuster_context) + # The keeper is a normal passive DC-EGM: the outer post-decision is held + # at its no-adjustment level (`next_ = keep()`), so the + # durable becomes a genuine decision-independent passive state and + # `credited(, keep()) = 0` makes keeping free. The keeper + # map is injected in two places that both read the outer post-decision: the + # transitions (so the child read indexes the kept durable) and the econ + # functions (so the inner resources DAG computes it from the durable leaf + # rather than demanding it as a bound param, as the adjuster does). With no + # `outer_no_adjustment_candidate`, `keep` is the identity (hold the stock); + # a depreciating `keep(d) = d (1 - delta)` lands the kept stock off the + # durable grid and the inner passive read blends it over the grid. + no_adjustment_func = ( + context.functions[self.outer_no_adjustment_candidate] + if self.outer_no_adjustment_candidate is not None + else None + ) + keeper_context = replace( + context, + transitions=_no_adjustment_outer_transition( + transitions=context.transitions, + outer_post_decision=self.outer_post_decision, + no_adjustment_func=no_adjustment_func, + ), + functions=_with_no_adjustment_outer_function( + functions=context.functions, + outer_post_decision=self.outer_post_decision, + no_adjustment_func=no_adjustment_func, + ), + ) + keeper_kernels = self.inner.build_period_kernels(context=keeper_context) + outer_grid_values = self.outer_grid.to_jax() + durable_state = self.outer_post_decision.removeprefix("next_") + coh_shift_func = _build_coh_shift_function( + functions=context.functions, + resources_name=self.inner.resources, + euler_state_name=self.inner.continuous_state, + durable_state_name=durable_state, + outer_post_decision=self.outer_post_decision, + ) + durable_grid_values = context.grids[durable_state].to_jax() + period_kernels = MappingProxyType( + { + period: _NEGMPeriodKernel( + keeper_kernel=keeper_kernels.period_kernels[period], + adjuster_kernel=adjuster_kernel, + regime_name=context.regime_name, + outer_grid_values=outer_grid_values, + outer_post_decision=self.outer_post_decision, + coh_shift_func=coh_shift_func, + durable_grid_values=durable_grid_values, + outer_batch_size=self.outer_batch_size, + ) + for period, adjuster_kernel in adjuster_kernels.period_kernels.items() + } + ) + return SolutionKernels( + period_kernels=period_kernels, + continuation_template=_widen_carry_template( + template=keeper_kernels.continuation_template, + n_extra=outer_grid_values.shape[0], + ), + ) + + +@dataclass(frozen=True, kw_only=True) +class _GridSearchPeriodKernel: + """The grid-search period adapter β€” wraps one max-Q-over-a core. + + Closes over the regime name (to project its flat params) and the shared + jitted core. Calling it evaluates Q on the full state-action product and + maximizes over the actions, returning a `KernelResult` whose only output is + the value-function array β€” no continuation, no simulation policy. + """ + + core: Callable + """The shared jitted max-Q-over-a core (`id`-deduped across periods).""" + + regime_name: RegimeName + """Name of the regime whose flat params this adapter projects.""" + + def cores(self) -> Mapping[str, Callable]: + """Return the single max-Q-over-a core under the `"main"` key.""" + return MappingProxyType({"main": self.core}) + + def with_fixed_params( + self, *, fixed_flat_params: FlatParams + ) -> _GridSearchPeriodKernel: + """Bind the regime's fixed params into the core. + + The core threads its `**kwargs` into the per-combo pool, so binding the + regime's own fixed params restores the values removed from the live + `flat_params`; the captured functions read only the keys they need. + """ + regime_fixed = dict( + fixed_flat_params.get(self.regime_name, MappingProxyType({})) + ) + if not regime_fixed: + return self + return replace(self, core=functools.partial(self.core, **regime_fixed)) + + def build_lower_args( + self, + *, + core_key: str = "main", # noqa: ARG002 + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], # noqa: ARG002 + flat_params: FlatParams, + period: int, + ages: AgeGrid, + ) -> Mapping[str, object]: + """Build the core's lowering arguments: the full state-action product.""" + return { + **dict(state_action_space.states), + **dict(state_action_space.actions), + "next_regime_to_V_arr": next_regime_to_V_arr, + **dict(flat_params[self.regime_name]), + "period": jnp.int32(period), + "age": ages.values[period], + } + + def __call__( + self, + *, + compiled_cores: Mapping[str, Callable], + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], # noqa: ARG002 + flat_params: FlatParams, + period: int, + ages: AgeGrid, + ) -> KernelResult: + """Evaluate the grid search and assemble the `KernelResult`.""" + V_arr = compiled_cores["main"]( + **state_action_space.states, + **state_action_space.actions, + next_regime_to_V_arr=next_regime_to_V_arr, + **flat_params[self.regime_name], + period=jnp.int32(period), + age=ages.values[period], + ) + return KernelResult(V_arr=V_arr) + + +@dataclass(frozen=True, kw_only=True) +class _DCEGMPeriodKernel: + """The DC-EGM period adapter β€” wraps one EGM-step core. + + Closes over the regime name, its reachable carry targets, and the names of + its transition targets (to union their params). Calling it inverts the Euler + equation on the savings grid and returns a `KernelResult` carrying the value + function, the continuation a parent interpolates, and the published off-grid + simulation policy. + """ + + core: Callable + """The shared jitted EGM-step core (`id`-deduped across periods).""" + + regime_name: RegimeName + """Name of the regime whose flat params this adapter projects.""" + + reachable_targets: frozenset[RegimeName] + """The carry keys the EGM core reads; the rolling carry is filtered to these.""" + + transition_target_names: tuple[RegimeName, ...] + """Names of the regime's transition targets, whose params are unioned in.""" + + def cores(self) -> Mapping[str, Callable]: + """Return the single EGM-step core under the `"main"` key.""" + return MappingProxyType({"main": self.core}) + + def with_fixed_params(self, *, fixed_flat_params: FlatParams) -> _DCEGMPeriodKernel: + """Bind the regime's and its carry targets' fixed params into the core. + + A DC-EGM source carrying into a *different* target regime evaluates that + target's resources / transition functions in its per-asset-node solve, + reading the target's fixed params. The core threads its `**kwargs` + straight into the per-combo pool those captured functions read, so + binding the union of the regime's and its carry targets' fixed params + restores the values removed from the live `flat_params` for all of them + at once. + """ + egm_fixed = dict(fixed_flat_params.get(self.regime_name, MappingProxyType({}))) + for target_name in self.transition_target_names: + for key, value in fixed_flat_params.get( + target_name, MappingProxyType({}) + ).items(): + egm_fixed.setdefault(key, value) + if not egm_fixed: + return self + return replace(self, core=functools.partial(self.core, **egm_fixed)) + + def build_lower_args( + self, + *, + core_key: str = "main", # noqa: ARG002 + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, + ages: AgeGrid, + ) -> Mapping[str, object]: + """Build the core's lowering arguments: states, carries, EGM params.""" + return { + **dict(state_action_space.states), + "next_regime_to_egm_carry": _reachable_carry_subset( + next_regime_to_egm_carry=next_regime_to_egm_carry, + reachable_targets=self.reachable_targets, + ), + "next_regime_to_V_arr": next_regime_to_V_arr, + **self._egm_kernel_params(flat_params=flat_params), + "period": jnp.int32(period), + "age": ages.values[period], + } + + def __call__( + self, + *, + compiled_cores: Mapping[str, Callable], + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, + ages: AgeGrid, + ) -> KernelResult: + """Run the DC-EGM step and assemble the `KernelResult`.""" + V_arr, egm_carry, sim_policy = compiled_cores["main"]( + **state_action_space.states, + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=_reachable_carry_subset( + next_regime_to_egm_carry=next_regime_to_egm_carry, + reachable_targets=self.reachable_targets, + ), + **self._egm_kernel_params(flat_params=flat_params), + period=jnp.int32(period), + age=ages.values[period], + ) + return KernelResult(V_arr=V_arr, carry=egm_carry, sim_policy=sim_policy) + + def _egm_kernel_params(self, *, flat_params: FlatParams) -> dict[str, object]: + """Flat params fed into the DC-EGM core: the source's plus its targets'. + + A DC-EGM source carrying into a *different* target regime evaluates that + target's resources / transition functions in its per-asset-node solve, + reading the target's params (e.g. a pension factor the source never + reads). These are model-level shared values, so the target's + `flat_params` entry carries the right value; union them in. The core + threads its `**kwargs` into the per-combo pool, and its captured + functions read only the keys they need, so a target's extra params are + harmless to the source functions that do not. Mirrors the fixed-param + binding done at model build (`_partial_fixed_params_into_regimes`) for + the free-param path. + """ + params: dict[str, object] = dict(flat_params[self.regime_name]) + for target_name in self.transition_target_names: + for key, value in flat_params.get( + target_name, MappingProxyType({}) + ).items(): + params.setdefault(key, value) + return params + + +@dataclass(frozen=True, kw_only=True) +class _NEGMPeriodKernel: + """The NEGM period adapter β€” a keeper plus an adjuster outer search. + + Holds two inner DC-EGM period adapters and the exogenous outer grid. The + outer durable choice splits into two distinct traced programs: + + - the *keeper* β€” a per-durable-state passive DC-EGM (`next_illiquid = + illiquid`, identity) that keeps the durable stock unchanged for free + (`credited(s, s) = 0`), run once over the full durable grid; and + - the *adjuster* β€” the inner DC-EGM with the outer transition stripped, run + once per exogenous outer-grid node with `outer_post_decision` bound to that + node as a constant. + + Calling it runs the keeper once and the adjuster once per outer-grid node, + then collapses the stacked outer axis by `V = max(V_keeper, V_adjuster_sweep)` + β€” the same shape brute would search, but with the inner consumption margin + off-grid (the accuracy win). The adapter is non-jitted: it calls the shared + jitted inner cores, matching `_DCEGMPeriodKernel`. + """ + + keeper_kernel: PeriodKernel + """The keeper inner adapter β€” a passive per-durable-state DC-EGM.""" + + adjuster_kernel: PeriodKernel + """The adjuster inner adapter whose shared jitted core is swept.""" + + regime_name: RegimeName + """Name of the regime whose flat params the outer node binds into.""" + + outer_grid_values: FloatND + """Exogenous grid over the outer post-decision margin `s'`.""" + + outer_post_decision: FunctionName + """Name of the outer post-decision function bound per outer-grid node.""" + + coh_shift_func: Callable[..., FloatND] + """Per-(durable, outer-node) cash-on-hand shift of each adjuster candidate. + + Maps the durable grid, the outer grid, and the regime's flat params to the + shift matrix `credited(z, z'_j)` that lifts each adjuster's endogenous grid + into the keeper's cash-on-hand axis. + """ + + durable_grid_values: FloatND + """The durable state's grid β€” the carry's last leading (passive) axis. + + Any discrete/process states precede the passive durable margin in the carry's + leading axes, so the durable is carry axis `-2`. + """ + + outer_batch_size: int + """Outer-grid nodes solved per chunk before folding into the running maximum. + + `0` solves every node at once; a positive value bounds the peak memory to one + chunk of candidates. A memory-vs-parallelism knob only β€” value-invariant. + """ + + @property + def core(self) -> Callable: + """The shared jitted adjuster core, exposed for any single-core reader.""" + return self.adjuster_kernel.core + + def cores(self) -> Mapping[str, Callable]: + """Return the keeper and adjuster inner cores, keyed independently. + + Each is a distinct traced DC-EGM program β€” the keeper is a passive + per-durable-state solve (`next_illiquid = illiquid`, identity), the + adjuster strips that transition and binds the outer node as a constant β€” + so AOT compilation lowers and compiles each under its own key rather than + collapsing both into one program. + """ + return MappingProxyType( + { + "keeper": self.keeper_kernel.core, + "adjuster": self.adjuster_kernel.core, + } + ) + + def with_fixed_params(self, *, fixed_flat_params: FlatParams) -> _NEGMPeriodKernel: + """Bind the regime's fixed params into both inner kernels and the shift. + + The cash-on-hand shift evaluates the regime's inner resources, which may + read a fixed param, so the same fixed params removed from the live + `flat_params` are bound into `coh_shift_func` as well. + """ + regime_fixed = dict( + fixed_flat_params.get(self.regime_name, MappingProxyType({})) + ) + coh_shift_func = self.coh_shift_func + if regime_fixed: + coh_shift_func = functools.partial(coh_shift_func, **regime_fixed) + return replace( + self, + keeper_kernel=self.keeper_kernel.with_fixed_params( + fixed_flat_params=fixed_flat_params + ), + adjuster_kernel=self.adjuster_kernel.with_fixed_params( + fixed_flat_params=fixed_flat_params + ), + coh_shift_func=coh_shift_func, + ) + + def build_lower_args( + self, + *, + core_key: str, + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, + ages: AgeGrid, + ) -> Mapping[str, object]: + """Delegate the named inner core's lowering arguments. + + The keeper is a normal passive DC-EGM, lowered straight off the inner + kernel with no outer-node binding (its `next_illiquid = illiquid` + identity sources the durable as a genuine passive state). The adjuster + binds `outer_post_decision` into the regime's flat params at the first + outer-grid node, so its lowered inner program matches the shape every + per-node call traces; the outer axis is added outside the jitted core by + the `__call__` sweep. + """ + if core_key == "keeper": + return self.keeper_kernel.build_lower_args( + core_key="main", + state_action_space=state_action_space, + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, + flat_params=flat_params, + period=period, + ages=ages, + ) + return self.adjuster_kernel.build_lower_args( + core_key="main", + state_action_space=state_action_space, + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, + flat_params=_with_outer_post_decision( + flat_params=flat_params, + regime_name=self.regime_name, + outer_post_decision=self.outer_post_decision, + value=self.outer_grid_values[0], + ), + period=period, + ages=ages, + ) + + def __call__( + self, + *, + compiled_cores: Mapping[str, Callable], + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, + ages: AgeGrid, + ) -> KernelResult: + """Run keeper and adjuster sweep, collapse by `max`, assemble the result. + + The keeper runs the passive DC-EGM once, yielding the value of leaving the + durable stock unchanged at every durable state. For each exogenous + outer-grid node `s'_j`, the adjuster runs with `outer_post_decision` bound + to `s'_j`, yielding `W_j`, the inner value over the liquid endogenous grid + at durable `s'_j`. The outer axis is collapsed by + `V = max(V_keeper, max_j W_j)`; the argmax over that stacked axis is the + outer simulation policy. + """ + keeper_result = self.keeper_kernel( + compiled_cores={"main": compiled_cores["keeper"]}, + state_action_space=state_action_space, + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, + flat_params=flat_params, + period=period, + ages=ages, + ) + # The published continuation is the genuine cash-on-hand upper envelope of + # the keeper and every adjuster candidate, so the parent period's + # keeper-identity continuation read sees the best durable choice at every + # coh β€” not only the keeper's, and an adjuster that wins strictly between + # keeper nodes survives. + coh_shifts = self.coh_shift_func( + durable_values=self.durable_grid_values, + outer_values=self.outer_grid_values, + **flat_params[self.regime_name], + ) + # Fold the adjuster outer-grid nodes into a running outer maximum β€” `V = + # max_j W_j` on the state grid and the coh-space envelope carry β€” in chunks + # of `outer_batch_size`, rather than materialising every node's solve at + # once. Each chunk's independent solves overlap; reducing them into the + # running `(V_arr, envelope)` bounds the peak to one chunk of candidates. + # `max` is associative and the envelope's shared coh grid is fixed at the + # keeper's, so the chunked fold is value-identical to a single stacked + # maximum regardless of the chunk size. The keeper and every adjuster are + # DC-EGM kernels, so each always publishes a continuation carry. + keeper_carry = cast("EGMCarry", keeper_result.carry) + V_arr = keeper_result.V_arr + nodes = self._outer_nodes() + envelope = init_outer_envelope(keeper_carry, len(nodes)) + chunk_size = self.outer_batch_size or len(nodes) + for chunk_start in range(0, len(nodes), chunk_size): + chunk_results = [ + self.adjuster_kernel( + compiled_cores={"main": compiled_cores["adjuster"]}, + state_action_space=state_action_space, + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, + flat_params=_with_outer_post_decision( + flat_params=flat_params, + regime_name=self.regime_name, + outer_post_decision=self.outer_post_decision, + value=node, + ), + period=period, + ages=ages, + ) + for node in nodes[chunk_start : chunk_start + chunk_size] + ] + for offset, adjuster_result in enumerate(chunk_results): + V_arr = jnp.maximum(V_arr, adjuster_result.V_arr) + envelope = fold_outer_envelope( + envelope, + cast("EGMCarry", adjuster_result.carry), + coh_shifts[:, chunk_start + offset], + chunk_start + offset, + ) + # Force the running maximum to device before the next chunk. Without + # this the lazy fold accumulates a dependency on every chunk's solves + # at once β€” the peak would grow with the whole outer grid rather than + # one chunk β€” and the chunk's independent solves could not overlap. + V_arr, envelope = jax.block_until_ready((V_arr, envelope)) + carry = finalize_outer_envelope(envelope) + # The simulate phase re-optimizes the outer durable action by grid argmax + # over the next-period value array, so the published `sim_policy` (the + # keeper's off-grid inner consumption function) is not the channel that + # drives simulated durable choice; it rides through unchanged. + return KernelResult( + V_arr=V_arr, + carry=carry, + sim_policy=keeper_result.sim_policy, + ) + + def _outer_nodes(self) -> list[FloatND]: + """The exogenous outer post-decision nodes, each a scalar `s'_j`. + + The state-specific no-adjustment kink `s' = s` a fixed exogenous grid + would miss is covered by the keeper, not appended here. + """ + return [ + self.outer_grid_values[index] + for index in range(self.outer_grid_values.shape[0]) + ] + + +def _widen_carry_template( + *, template: EGMCarry | None, n_extra: int +) -> EGMCarry | None: + """Widen a keeper carry template by `n_extra` trailing island-peak slots. + + The NEGM outer envelope publishes the keeper's shared-grid envelope plus one + spliced island-peak slot per adjuster, so the published carry is `n_extra` + nodes wider than the keeper's. The parent period's kernel is AOT-compiled + against this template, so the template's last axis must match the published + width. The padding is `NaN` (trailing dead nodes), consistent with the + interpolator's first-finite-node search. + """ + if template is None: + return None + pad = [(0, 0)] * (template.endog_grid.ndim - 1) + [(0, n_extra)] + widen = lambda arr: jnp.pad(arr, pad, constant_values=jnp.nan) # noqa: E731 + return EGMCarry( + endog_grid=widen(template.endog_grid), + value=widen(template.value), + marginal_utility=widen(template.marginal_utility), + taste_shock_scale=template.taste_shock_scale, + ) + + +def _build_coh_shift_function( + *, + functions: EconFunctionsMapping, + resources_name: FunctionName, + euler_state_name: StateName, + durable_state_name: StateName, + outer_post_decision: FunctionName, +) -> Callable[..., FloatND]: + """Build the per-(durable, outer-node) cash-on-hand shift of each adjuster. + + Adjuster `j`'s inner endogenous grid lives in resources space `R_j = coh - + credited(z, z'_j)`; mapping it into the keeper's cash-on-hand axis adds back + `credited(z, z'_j)`. That credited cost is the keeper-minus-adjuster + difference of the regime's own inner resources at any fixed liquid wealth + (`resources` is affine in wealth, so wealth cancels): + + `shift(z, z'_j) = resources(w0, z, next=z) - resources(w0, z, next=z'_j)`. + + The returned callable takes the durable grid (`durable_values`), the outer + grid (`outer_values`), and the regime's flat params, and returns the shift + matrix of shape `(n_durable, n_outer)`. + """ + resources_func = concatenate_functions( + functions={name: func for name, func in functions.items() if name != "H"}, + targets=resources_name, + enforce_signature=False, + set_annotations=True, + ) + resources_arg_names = set(get_annotations(resources_func)) - {"return"} + bound_arg_names = {euler_state_name, durable_state_name, outer_post_decision} + + def coh_shifts( + *, durable_values: FloatND, outer_values: FloatND, **params: object + ) -> FloatND: + zero_reference = jnp.zeros((), dtype=durable_values.dtype) + # Every resources leaf other than the Euler state, the durable state, the + # outer post-decision, and the regime params is constant in the outer + # choice (the credited cost reads only the durable margin), so it appears + # identically in the keeper and adjuster legs and cancels in their + # difference. Hold each at a fixed reference β€” exactly as the Euler state + # is held at zero β€” so the shift is the pure credited-cost difference. + separable_arg_names = resources_arg_names - bound_arg_names - set(params) + separable_references = dict.fromkeys(separable_arg_names, zero_reference) + + def shift_one(durable: FloatND, outer: FloatND) -> FloatND: + # The keeper reference holds the outer post-decision at the durable + # itself (`next = durable`), not at the keeper core's no-adjustment + # level `keep(durable)`. For an identity keeper (`keep(d) = d`) the two + # coincide and this is the exact credited-cost lift. Under a + # depreciating keeper (`keep(d) = d(1 - delta)`) the design-exact + # reference would be `keep(durable)`, but using it in isolation lifts + # each adjuster to a coh that the fixed keeper-grid envelope reads by + # extrapolation and the one-island-per-adjuster splice then over-counts + # β€” empirically regressing the DS-2024 delta=0.10 oracle agreement from + # a converging ~0.08 to a plateaued ~0.18. The identity reference and + # the island splice are tuned together; correcting both belongs with + # the segment-topology outer-envelope redesign, not here. + keeper_resources = resources_func( + **{ + euler_state_name: zero_reference, + durable_state_name: durable, + outer_post_decision: durable, + }, + **separable_references, + **params, + ) + adjuster_resources = resources_func( + **{ + euler_state_name: zero_reference, + durable_state_name: durable, + outer_post_decision: outer, + }, + **separable_references, + **params, + ) + return keeper_resources - adjuster_resources + + return jax.vmap( + lambda durable: jax.vmap(lambda outer: shift_one(durable, outer))( + outer_values + ) + )(durable_values) + + return coh_shifts + + +def _strip_outer_transition( + *, + transitions: TransitionFunctionsMapping, + outer_post_decision: FunctionName, +) -> TransitionFunctionsMapping: + """Drop the outer post-decision transition from every target's transitions. + + The adjuster supplies the outer post-decision value per outer-grid node, so + its child-carry next-state function must not demand the outer action; + `read_child` sources the bound value from the combo pool instead. + """ + return MappingProxyType( + { + target: MappingProxyType( + { + name: func + for name, func in target_transitions.items() + if name != outer_post_decision + } + ) + for target, target_transitions in transitions.items() + } + ) + + +def _no_adjustment_outer_transition( + *, + transitions: TransitionFunctionsMapping, + outer_post_decision: FunctionName, + no_adjustment_func: EconFunction | None, +) -> TransitionFunctionsMapping: + """Replace the outer post-decision transition with the keeper's durable map. + + The keeper holds the durable at its no-adjustment level + (`next_ = keep()`), so each target's outer transition + becomes that law on the durable state. The durable state name is the + transition name with the `next_` prefix removed, mirroring the engine's + `next_` auto-naming. The durable then reads as a genuine + decision-independent passive state in the inner DC-EGM. + + With no `no_adjustment_func` the keeper holds the stock unchanged via the + auto-identity transition (`next_ = `), and `read_child` + indexes the unchanged durable on its grid. A depreciating + `keep(d) = d (1 - delta)` lands the kept stock off the durable grid; the + inner passive read blends the child value over the grid's neighbouring nodes. + """ + durable_state = outer_post_decision.removeprefix("next_") + if no_adjustment_func is None: + keeper_transition = cast( + "TransitionFunction", + _IdentityTransition(durable_state, annotation=ContinuousState), ) - raise NotImplementedError(msg) + else: + keeper_transition = _durable_keeper_transition( + no_adjustment_func=no_adjustment_func, + durable_state=durable_state, + outer_post_decision=outer_post_decision, + ) + return MappingProxyType( + { + target: MappingProxyType( + { + name: (keeper_transition if name == outer_post_decision else func) + for name, func in target_transitions.items() + } + ) + for target, target_transitions in transitions.items() + } + ) + + +def _with_no_adjustment_outer_function( + *, + functions: EconFunctionsMapping, + outer_post_decision: FunctionName, + no_adjustment_func: EconFunction | None, +) -> EconFunctionsMapping: + """Add the keeper's outer post-decision to the econ-function DAG. + + The inner resources function reads the outer post-decision (`next_`) + by name. The adjuster binds it as a per-node param; the keeper instead holds + it at its no-adjustment level, so the resources DAG computes + `next_ = keep()` from the durable leaf state. The injected + function declares the durable state as its single parameter, so DAG + concatenation wires the durable combo value into resources. With no + `no_adjustment_func`, `keep` is the identity (hold the stock). + """ + durable_state = outer_post_decision.removeprefix("next_") + # Copy the durable's annotation (and the outer post-decision's consumer + # annotation) off the existing functions so the DAG's annotation-consistency + # check, which requires every consumer of a leaf to agree, stays satisfied. + durable_annotation = _annotation_of_arg(functions=functions, arg_name=durable_state) + outer_annotation = _annotation_of_arg( + functions=functions, arg_name=outer_post_decision + ) + + @with_signature( + args={durable_state: durable_annotation}, + return_annotation=outer_annotation, + ) + def keep_outer_post_decision(**kwargs: FloatND) -> FloatND: + if no_adjustment_func is None: + return kwargs[durable_state] + return no_adjustment_func(**{durable_state: kwargs[durable_state]}) + + keep_outer_post_decision.__name__ = outer_post_decision + return MappingProxyType( + { + **dict(functions), + outer_post_decision: cast("EconFunction", keep_outer_post_decision), + } + ) + + +def _durable_keeper_transition( + *, + no_adjustment_func: EconFunction, + durable_state: StateName, + outer_post_decision: FunctionName, +) -> TransitionFunction: + """Wrap the no-adjustment map as the keeper's durable transition. + + The map reads the durable state alone and returns the kept next stock, so it + is a decision-independent passive law `next_ = keep()`. The + wrapper carries the `next_` name and a `ContinuousState` signature so + the engine's transition collector classifies it like any passive durable law. + """ + + @with_signature( + args={durable_state: "ContinuousState"}, + return_annotation="ContinuousState", + ) + def keeper_transition(**kwargs: ContinuousState) -> ContinuousState: + return no_adjustment_func(**{durable_state: kwargs[durable_state]}) + + keeper_transition.__name__ = outer_post_decision + return cast("TransitionFunction", keeper_transition) + + +def _annotation_of_arg( + *, functions: EconFunctionsMapping, arg_name: StateOrActionName +) -> str: + """Return the annotation the regime's functions use for one argument. + + The DAG's annotation-consistency check requires every consumer of a leaf to + agree on its annotation, so the injected keeper function copies it from the + first regime function that declares the argument. Falls back to `"FloatND"` + when no function annotates it. + """ + for func in functions.values(): + annotations = ensure_annotations_are_strings(get_annotations(func)) + annotation = annotations.get(arg_name, "no_annotation_found") + if annotation != "no_annotation_found": + return annotation + return "FloatND" + + +def _with_outer_post_decision( + *, + flat_params: FlatParams, + regime_name: RegimeName, + outer_post_decision: FunctionName, + value: FloatND, +) -> FlatParams: + """Bind the outer post-decision value into the regime's flat params. + + The inner DC-EGM core threads its per-combo pool from `flat_params`, so + binding `outer_post_decision` there makes the inner resources and the + child-state index read the fixed outer node as a constant. + """ + regime_params = {**dict(flat_params[regime_name]), outer_post_decision: value} + return MappingProxyType( + { + name: ( + MappingProxyType(regime_params) if name == regime_name else regime_pool + ) + for name, regime_pool in flat_params.items() + } + ) - def build_period_kernels(self, *, context: SolverBuildContext) -> SolverKernels: - """Unreachable β€” `validate` rejects DC-EGM before the kernel build.""" - msg = "The DC-EGM solver is not yet available." - raise NotImplementedError(msg) + +def _reachable_carry_subset( + *, + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + reachable_targets: frozenset[RegimeName], +) -> MappingProxyType[RegimeName, EGMCarry]: + """The carries a regime's EGM core actually reads. + + Each core only ever indexes `next_regime_to_egm_carry[target]` for its + reachable targets, so the full all-regimes mapping is needlessly large. + Filtering to the reachable subset keeps the core's carry pytree input + minimal β€” only this subset is passed per call rather than every regime's + carry at once. + + Iterates the source mapping's key order (stable across rolls) so the + filtered pytree structure matches between lowering and call. Membership is + tested defensively; reachable targets are always carry-producing. + """ + return MappingProxyType( + { + name: next_regime_to_egm_carry[name] + for name in next_regime_to_egm_carry + if name in reachable_targets + } + ) def _fail_if_savings_grid_is_stochastic(savings_grid: ContinuousGrid) -> None: @@ -219,6 +1324,28 @@ def _fail_if_fues_jump_thresh_non_positive(fues_jump_thresh: float) -> None: raise RegimeInitializationError(msg) +def _fail_if_rfc_jump_thresh_non_positive(rfc_jump_thresh: float) -> None: + # `not (x > 0.0)` rejects NaN too: `nan <= 0.0` is False, so the segment- + # switch comparison would silently misbehave on a non-finite threshold. + if not (math.isfinite(rfc_jump_thresh) and rfc_jump_thresh > 0.0): + msg = ( + f"DCEGM.rfc_jump_thresh must be a finite positive value, got " + f"{rfc_jump_thresh}. It is the segment-switch threshold on " + "`|Ξ”c / Ξ”R|` in the rooftop cut." + ) + raise RegimeInitializationError(msg) + + +def _fail_if_rfc_search_radius_too_few(rfc_search_radius: int) -> None: + if rfc_search_radius < 1: + msg = ( + f"DCEGM.rfc_search_radius must be at least 1, got " + f"{rfc_search_radius}. The rooftop-cut dominance test must inspect " + "at least one neighbor on each side of a candidate." + ) + raise RegimeInitializationError(msg) + + def _fail_if_n_constrained_points_too_few(n_constrained_points: int) -> None: if n_constrained_points < 2: # noqa: PLR2004 msg = ( @@ -229,8 +1356,9 @@ def _fail_if_n_constrained_points_too_few(n_constrained_points: int) -> None: raise RegimeInitializationError(msg) -def _fail_if_fues_n_points_to_scan_too_few(fues_n_points_to_scan: int) -> None: - if fues_n_points_to_scan < 1: +def _fail_if_fues_n_points_to_scan_too_few(fues_n_points_to_scan: int | None) -> None: + # `None` requests the exhaustive scan; only an explicit finite width is bounded. + if fues_n_points_to_scan is not None and fues_n_points_to_scan < 1: msg = ( f"DCEGM.fues_n_points_to_scan must be at least 1, got " f"{fues_n_points_to_scan}. The FUES forward scan must inspect at " @@ -239,6 +1367,16 @@ def _fail_if_fues_n_points_to_scan_too_few(fues_n_points_to_scan: int) -> None: raise RegimeInitializationError(msg) +def _fail_if_fues_scan_unroll_too_few(fues_scan_unroll: int) -> None: + if fues_scan_unroll < 1: + msg = ( + f"DCEGM.fues_scan_unroll must be at least 1, got " + f"{fues_scan_unroll}. It is the `lax.scan` unroll factor for the " + "FUES candidate scan; 1 means no unrolling." + ) + raise RegimeInitializationError(msg) + + def _fail_if_stochastic_node_batch_size_negative( stochastic_node_batch_size: int, ) -> None: @@ -250,3 +1388,648 @@ def _fail_if_stochastic_node_batch_size_negative( "fused vmap." ) raise RegimeInitializationError(msg) + + +@beartype(conf=REGIME_CONF) +@dataclass(frozen=True, kw_only=True) +class OneAssetEGM(Solver): + """Endogenous-grid solver for a 1-D consumption--saving regime. + + A regime with exactly one continuous state (the liquid wealth), one + continuous consumption action, and no discrete choice is a plain + consumption--saving problem. The single continuous state needs no upper + envelope: inverting the consumption Euler equation on the post-decision + savings grid and mapping the resulting endogenous wealth back onto the + regular grid solves the period exactly. The step carries the marginal + value of liquid backward (the envelope theorem makes it exact, unlike a + finite difference of a coarse value array), so each period both reads its + continuation's marginal and publishes its own. + """ + + savings_grid: ContinuousGrid + """Exogenous post-decision savings grid `s = liquid - consumption` (>= 0).""" + + @property + def requires_continuation_carries(self) -> bool: + """The 1-D EGM step reads its continuation's marginal value of liquid.""" + return True + + def build_period_kernels(self, *, context: SolverBuildContext) -> SolutionKernels: + """Build one 1-D EGM period adapter per active period. + + Each period's adapter knows the single deterministic continuation + target (the transition target whose regime is active next period), so + it reads that target's value array and marginal-utility carry. + """ + import jax # noqa: PLC0415 + + savings_grid = self.savings_grid.to_jax() + liquid_grid = context.grids[context.state_action_space.state_names[0]].to_jax() + + period_to_target = _period_to_continuation_target(context=context) + cores: dict[RegimeName, Callable] = {} + period_kernels: dict[int, PeriodKernel] = {} + for period, target in period_to_target.items(): + if target not in cores: + core = _build_one_asset_core(savings_grid=savings_grid, target=target) + cores[target] = jax.jit(core) if context.enable_jit else core + period_kernels[period] = _OneAssetEGMPeriodKernel( + core=cores[target], + regime_name=context.regime_name, + continuation_target=target, + transition_target_names=tuple(context.transitions), + ) + return SolutionKernels( + period_kernels=MappingProxyType(period_kernels), + continuation_template=_build_one_asset_carry_template( + liquid_grid=liquid_grid + ), + ) + + +@beartype(conf=REGIME_CONF) +@dataclass(frozen=True, kw_only=True) +class TwoDimEGM(Solver): + """Two-asset G2EGM solver for a regime with two continuous Euler states. + + The working phase of the DS pension model couples a liquid state `m` and a + pension state `n` through the budget, with two continuous actions + (consumption and a one-directional pension deposit). The G2EGM step builds + the four KKT constraint segments on the post-decision `(a, b)` and + `(consumption, b)` grids, triangulates each into the current `(m, n)` + plane, and selects the best feasible policy by the recomputed Bellman + objective. + + A working->working period reads the regime's own next-period value on the + `(m, n)` grid; the single working->retired boundary period reads the 1-D + retired continuation (value and marginal) through the lump-sum pension + payout. The continuation target per period is resolved at build time from + the active-period structure, so the right step is selected without a + runtime fork. + """ + + a_grid: ContinuousGrid + """Liquid post-decision grid for the `ucon`/`dcon` segments (include 0).""" + + b_grid: ContinuousGrid + """Pension post-decision grid shared by all segments.""" + + consumption_grid: ContinuousGrid + """Consumption sweep for the `acon`/`con` segments at `a = 0`.""" + + threshold: float = 0.25 + """Barycentric extrapolation tolerance for triangle admissibility.""" + + upper_envelope: Literal["g2egm", "rfc"] = "g2egm" + """Multidimensional upper-envelope backend. + + `"g2egm"` triangulates each KKT segment and takes within- then across-segment + maxima; `"rfc"` merges the segment clouds and selects by the Dobrescu-Shanker + rooftop-cut delete plus a single local-simplex publish. The retirement-boundary + period always uses the G2EGM step (the RFC step has no retiring variant yet). + """ + + @property + def requires_continuation_carries(self) -> bool: + """The boundary step reads the retired regime's marginal value of liquid.""" + return True + + def build_period_kernels(self, *, context: SolverBuildContext) -> SolutionKernels: + """Build one G2EGM period adapter per active period. + + Periods whose next period stays in this regime use the working->working + step; the single period whose next period leaves it (the retirement + boundary) uses the retiring step reading the 1-D retired continuation. + All periods share one jitted core (the boundary branch is selected by a + static Python flag), so they reuse a single compiled program. + """ + import jax # noqa: PLC0415 + + a_grid = self.a_grid.to_jax() + b_grid = self.b_grid.to_jax() + consumption_grid = self.consumption_grid.to_jax() + + period_to_target = _period_to_continuation_target(context=context) + own_name = context.regime_name + boundary_targets = { + target for target in period_to_target.values() if target != own_name + } + boundary_prefix = next(iter(boundary_targets), own_name) + cores: dict[bool, Callable] = {} + period_kernels: dict[int, PeriodKernel] = {} + for period, target in period_to_target.items(): + is_boundary = target != own_name + if is_boundary not in cores: + core = _build_two_dim_core( + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + threshold=self.threshold, + is_boundary=is_boundary, + interior_prefix=own_name, + boundary_prefix=boundary_prefix, + upper_envelope=self.upper_envelope, + ) + cores[is_boundary] = jax.jit(core) if context.enable_jit else core + period_kernels[period] = _TwoDimEGMPeriodKernel( + core=cores[is_boundary], + regime_name=own_name, + continuation_target=target, + is_boundary=is_boundary, + transition_target_names=tuple(context.transitions), + ) + return SolutionKernels(period_kernels=MappingProxyType(period_kernels)) + + +@dataclass(frozen=True, kw_only=True) +class _OneAssetEGMPeriodKernel: + """The 1-D EGM period adapter β€” wraps the shared `egm_one_asset_step` core. + + Closes over the regime name, the period's single deterministic + continuation target (whose value array and marginal carry feed the Euler + inversion), and the transition target names (to union their params). + Returns a `KernelResult` carrying the value array and the marginal-value + carry a parent EGM regime interpolates. + """ + + core: Callable + """The shared jitted 1-D EGM-step core.""" + + regime_name: RegimeName + """Name of the regime whose flat params this adapter projects.""" + + continuation_target: RegimeName + """The regime active next period; its value and marginal continue this one.""" + + transition_target_names: tuple[RegimeName, ...] + """Names of the regime's transition targets, whose params are unioned in.""" + + def cores(self) -> Mapping[str, Callable]: + """Return the single EGM-step core under the `"main"` key.""" + return MappingProxyType({"main": self.core}) + + def with_fixed_params( + self, *, fixed_flat_params: FlatParams + ) -> _OneAssetEGMPeriodKernel: + """Bind the regime's and its targets' fixed params into the core.""" + bound = _union_fixed_params( + fixed_flat_params=fixed_flat_params, + regime_name=self.regime_name, + transition_target_names=self.transition_target_names, + ) + if not bound: + return self + return replace(self, core=functools.partial(self.core, **bound)) + + def build_lower_args( + self, + *, + core_key: str = "main", # noqa: ARG002 + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, # noqa: ARG002 + ages: AgeGrid, # noqa: ARG002 + ) -> Mapping[str, object]: + """Build the core's lowering arguments: state, continuation, params.""" + return { + **dict(state_action_space.states), + "next_value": next_regime_to_V_arr[self.continuation_target], + "next_marginal": next_regime_to_egm_carry[ + self.continuation_target + ].marginal_utility, + **_union_free_params( + flat_params=flat_params, + regime_name=self.regime_name, + transition_target_names=self.transition_target_names, + ), + } + + def __call__( + self, + *, + compiled_cores: Mapping[str, Callable], + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, # noqa: ARG002 + ages: AgeGrid, # noqa: ARG002 + ) -> KernelResult: + """Run the 1-D EGM step and assemble the `KernelResult`.""" + V_arr, carry = compiled_cores["main"]( + **state_action_space.states, + next_value=next_regime_to_V_arr[self.continuation_target], + next_marginal=next_regime_to_egm_carry[ + self.continuation_target + ].marginal_utility, + **_union_free_params( + flat_params=flat_params, + regime_name=self.regime_name, + transition_target_names=self.transition_target_names, + ), + ) + return KernelResult(V_arr=V_arr, carry=carry) + + +@dataclass(frozen=True, kw_only=True) +class _TwoDimEGMPeriodKernel: + """The two-asset G2EGM period adapter β€” wraps one G2EGM-step core. + + Closes over the regime name, the period's continuation target, and the + transition target names. The working->working core reads the regime's own + next-period value on `(m, n)`; the boundary core additionally reads the + retired continuation's value and marginal carry. Returns a `KernelResult` + whose only output is the value array β€” a working parent reads it directly + as its 2-D continuation, so no carry is published. + """ + + core: Callable + """The shared jitted G2EGM-step core (one per boundary/interior branch).""" + + regime_name: RegimeName + """Name of the regime whose flat params this adapter projects.""" + + continuation_target: RegimeName + """The regime active next period; equals this regime except at the boundary.""" + + is_boundary: bool + """Whether next period leaves this regime (the retirement boundary step).""" + + transition_target_names: tuple[RegimeName, ...] + """Names of the regime's transition targets, whose params are unioned in.""" + + def cores(self) -> Mapping[str, Callable]: + """Return the single EGM-step core under the `"main"` key.""" + return MappingProxyType({"main": self.core}) + + def with_fixed_params( + self, *, fixed_flat_params: FlatParams + ) -> _TwoDimEGMPeriodKernel: + """Bind the regime's and its targets' fixed params into the core.""" + bound = _union_fixed_params( + fixed_flat_params=fixed_flat_params, + regime_name=self.regime_name, + transition_target_names=self.transition_target_names, + ) + if not bound: + return self + return replace(self, core=functools.partial(self.core, **bound)) + + def build_lower_args( + self, + *, + core_key: str = "main", # noqa: ARG002 + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, # noqa: ARG002 + ages: AgeGrid, # noqa: ARG002 + ) -> Mapping[str, object]: + """Build the core's lowering arguments: states, continuation, params.""" + return self._core_args( + state_action_space=state_action_space, + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, + flat_params=flat_params, + ) + + def __call__( + self, + *, + compiled_cores: Mapping[str, Callable], + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + period: int, # noqa: ARG002 + ages: AgeGrid, # noqa: ARG002 + ) -> KernelResult: + """Run the G2EGM step and assemble the `KernelResult`.""" + V_arr = compiled_cores["main"]( + **self._core_args( + state_action_space=state_action_space, + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=next_regime_to_egm_carry, + flat_params=flat_params, + ) + ) + return KernelResult(V_arr=V_arr) + + def _core_args( + self, + *, + state_action_space: StateActionSpace, + next_regime_to_V_arr: Mapping[RegimeName, FloatND], + next_regime_to_egm_carry: Mapping[RegimeName, ContinuationPayload], + flat_params: FlatParams, + ) -> dict[str, object]: + """Assemble the core's keyword arguments for one period. + + The state grids come from the state-action space. The interior step + reads the regime's own next-period value on `(m, n)`; the boundary step + reads the retired continuation's value and marginal-utility carry. Each + branch's core takes only the continuation it consumes, so the two + signatures differ and a working continuation (which carries no marginal) + is never demanded at the boundary. + """ + states = dict(state_action_space.states) + continuation: dict[str, object] + if self.is_boundary: + continuation = { + "next_value_retired": next_regime_to_V_arr[self.continuation_target], + "next_marginal_retired": next_regime_to_egm_carry[ + self.continuation_target + ].marginal_utility, + } + else: + continuation = { + "next_value_working": next_regime_to_V_arr[self.continuation_target], + } + return { + "liquid": states["liquid"], + "pension": states["pension"], + **continuation, + **_union_free_params( + flat_params=flat_params, + regime_name=self.regime_name, + transition_target_names=self.transition_target_names, + ), + } + + +def _build_one_asset_core(*, savings_grid: Float1D, target: RegimeName) -> Callable: + """Build the jitted-able 1-D EGM core closing over the savings grid. + + The core reads the state grid (`liquid`), the continuation value and + marginal, and the regime's scalar params, runs `egm_one_asset_step`, and + returns the value array and the marginal-value carry on the liquid grid. + The liquid law params are qualified by the continuation target's transition + (`{target}__next_liquid__...`). + """ + from _lcm.egm.one_asset_egm_step import egm_one_asset_step # noqa: PLC0415 + + def core( + *, + liquid: Float1D, + next_value: Float1D, + next_marginal: Float1D, + **params: FloatND, + ) -> tuple[Float1D, EGMCarry]: + step = egm_one_asset_step( + next_value=next_value, + next_marginal=next_marginal, + liquid_grid=liquid, + savings_grid=savings_grid, + discount_factor=params["H__discount_factor"], + crra=params["utility__crra"], + return_liquid=params[f"{target}__next_liquid__return_liquid"], + income=params[f"{target}__next_liquid__retirement_income"], + ) + carry = EGMCarry( + endog_grid=liquid, + value=step.value, + marginal_utility=step.marginal, + taste_shock_scale=jnp.asarray(0.0, dtype=step.value.dtype), + ) + return step.value, carry + + return core + + +def _build_two_dim_core( + *, + a_grid: Float1D, + b_grid: Float1D, + consumption_grid: Float1D, + threshold: float, + is_boundary: bool, + interior_prefix: RegimeName, + boundary_prefix: RegimeName, + upper_envelope: Literal["g2egm", "rfc"] = "g2egm", +) -> Callable: + """Build the jitted-able two-asset core for one branch (interior or boundary). + + The interior branch reads the regime's own next-period working value on the + `(m, n)` grid; the boundary branch reads the 1-D retired value and marginal + through the lump-sum payout. Both subtract the additive work disutility the + generic envelope objective omits, so the returned value matches the engine's + working value (whose utility carries the disutility). Transition params are + qualified by the regime's own name (interior) or the retirement target + (boundary), since the boundary reads the retired liquid law. + + `upper_envelope` selects the interior step's envelope β€” the G2EGM mesh or the + combined-cloud RFC. The boundary (retiring) step is always G2EGM. + """ + from _lcm.egm.rfc_two_asset_step import rfc_two_asset_step # noqa: PLC0415 + from _lcm.egm.two_asset_g2egm_step import ( # noqa: PLC0415 + g2egm_retiring_step, + g2egm_step, + ) + + def boundary_core( + *, + liquid: Float1D, + pension: Float1D, + next_value_retired: Float1D, + next_marginal_retired: Float1D, + **params: FloatND, + ) -> FloatND: + result = g2egm_retiring_step( + next_value_retired=next_value_retired, + next_marginal_retired=next_marginal_retired, + liquid_grid=liquid, + m_grid=liquid, + n_grid=pension, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + discount_factor=params["H__discount_factor"], + crra=params["utility__crra"], + match_rate=params[f"{boundary_prefix}__next_liquid__match_rate"], + return_liquid=params[f"{boundary_prefix}__next_liquid__return_liquid"], + pension_payout_return=params[ + f"{boundary_prefix}__next_liquid__pension_payout_return" + ], + retirement_income=params[ + f"{boundary_prefix}__next_liquid__retirement_income" + ], + threshold=threshold, + ) + return result.value - params["utility__work_disutility"] + + def interior_core( + *, + liquid: Float1D, + pension: Float1D, + next_value_working: FloatND, + **params: FloatND, + ) -> FloatND: + discount_factor = params["H__discount_factor"] + crra = params["utility__crra"] + match_rate = params[f"{interior_prefix}__next_pension__match_rate"] + return_liquid = params[f"{interior_prefix}__next_liquid__return_liquid"] + return_pension = params[f"{interior_prefix}__next_pension__return_pension"] + wage = params[f"{interior_prefix}__next_liquid__wage"] + if upper_envelope == "rfc": + result = rfc_two_asset_step( + next_value=next_value_working, + m_grid=liquid, + n_grid=pension, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + return_liquid=return_liquid, + return_pension=return_pension, + wage=wage, + ) + else: + result = g2egm_step( + next_value=next_value_working, + m_grid=liquid, + n_grid=pension, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + discount_factor=discount_factor, + crra=crra, + match_rate=match_rate, + return_liquid=return_liquid, + return_pension=return_pension, + wage=wage, + threshold=threshold, + ) + return result.value - params["utility__work_disutility"] + + return boundary_core if is_boundary else interior_core + + +def _build_one_asset_carry_template(*, liquid_grid: Float1D) -> EGMCarry: + """Build the all-finite 1-D EGM carry template on the liquid grid.""" + return EGMCarry( + endog_grid=liquid_grid, + value=jnp.zeros_like(liquid_grid), + marginal_utility=jnp.zeros_like(liquid_grid), + taste_shock_scale=jnp.asarray(0.0, dtype=liquid_grid.dtype), + ) + + +def _period_to_continuation_target( + *, context: SolverBuildContext +) -> dict[int, RegimeName]: + """Resolve each active period's single deterministic continuation target. + + The model's deterministic lifecycle transition reaches exactly one target + next period: the regime among this regime's transition targets that is + active at `period + 1`. The last active period continues into the target + active at the period beyond the horizon's interior (the terminal regime). + """ + own_active = set(context.regimes_to_active_periods[context.regime_name]) + target_active = { + target: set(context.regimes_to_active_periods[target]) + for target in context.transitions + } + result: dict[int, RegimeName] = {} + for period in sorted(own_active): + reached = [ + target for target, active in target_active.items() if (period + 1) in active + ] + if len(reached) != 1: + msg = ( + f"Regime '{context.regime_name}' does not reach exactly one " + f"active target at period {period + 1}: candidates {reached}. " + "The endogenous-grid solvers require a deterministic " + "lifecycle transition (one active target per period)." + ) + raise RegimeInitializationError(msg) + result[period] = reached[0] + return result + + +def _union_free_params( + *, + flat_params: FlatParams, + regime_name: RegimeName, + transition_target_names: tuple[RegimeName, ...], +) -> dict[str, object]: + """Union the regime's free params with its transition targets' free params. + + The boundary step evaluates the target regime's transition params (e.g. the + pension payout factor the source never reads), so the core needs the union; + captured functions read only the keys they need. + """ + params: dict[str, object] = dict(flat_params[regime_name]) + for target_name in transition_target_names: + for key, value in flat_params.get(target_name, MappingProxyType({})).items(): + params.setdefault(key, value) + return params + + +def _union_fixed_params( + *, + fixed_flat_params: FlatParams, + regime_name: RegimeName, + transition_target_names: tuple[RegimeName, ...], +) -> dict[str, object]: + """Union the regime's and its targets' fixed params for core binding.""" + bound = dict(fixed_flat_params.get(regime_name, MappingProxyType({}))) + for target_name in transition_target_names: + for key, value in fixed_flat_params.get( + target_name, MappingProxyType({}) + ).items(): + bound.setdefault(key, value) + return bound + + +def _fail_if_outer_batch_size_negative(outer_batch_size: int) -> None: + if outer_batch_size < 0: + msg = ( + f"NEGM.outer_batch_size must be non-negative, got {outer_batch_size}. " + "Use 0 to solve every outer-grid node at once, or a positive value to " + "fold the outer search in chunks of that many nodes." + ) + raise RegimeInitializationError(msg) + + +def _fail_if_outer_grid_is_stochastic(outer_grid: ContinuousGrid) -> None: + if isinstance(outer_grid, _ContinuousStochasticProcess): + msg = ( + "NEGM.outer_grid must be a deterministic continuous grid, not a " + f"stochastic process ({type(outer_grid).__name__}). The outer grid " + "is the exogenous search grid over the durable post-decision margin; " + "it carries no transition. A stochastic durable margin belongs in a " + "process state, not the NEGM outer search." + ) + raise RegimeInitializationError(msg) + + +def _fail_if_outer_action_is_inner_action( + *, outer_action: ActionName, inner: DCEGM +) -> None: + if outer_action == inner.continuous_action: + msg = ( + f"NEGM.outer_action '{outer_action}' coincides with the inner " + f"DC-EGM continuous action '{inner.continuous_action}'. The outer " + "durable/illiquid margin and the inner consumption margin must be " + "distinct actions." + ) + raise RegimeInitializationError(msg) + + +def _fail_if_outer_post_decision_is_inner_post_decision( + *, outer_post_decision: FunctionName, inner: DCEGM +) -> None: + if outer_post_decision == inner.post_decision_function: + msg = ( + f"NEGM.outer_post_decision '{outer_post_decision}' coincides with " + f"the inner DC-EGM post-decision function " + f"'{inner.post_decision_function}'. The outer post-decision (the " + "next-period durable stock) and the inner post-decision (the liquid " + "savings) must be distinct functions." + ) + raise RegimeInitializationError(msg) diff --git a/src/_lcm/typing.py b/src/_lcm/typing.py index afcedba55..2671aca3f 100644 --- a/src/_lcm/typing.py +++ b/src/_lcm/typing.py @@ -14,6 +14,8 @@ from jax import Array from jaxtyping import Key +from _lcm.egm.carry import EGMCarry +from _lcm.egm.published_policy import EGMSimPolicy from _lcm.params.mapping_leaf import MappingLeaf from _lcm.params.sequence_leaf import SequenceLeaf @@ -98,6 +100,12 @@ # Type aliases for value function arrays type PeriodToRegimeToVArr = MappingProxyType[int, MappingProxyType[RegimeName, FloatND]] +# Sparse over regimes: the inner mapping carries an entry only for regimes +# solved by DC-EGM. Brute-force and terminal regimes publish no `EGMSimPolicy`, +# so their names are absent β€” callers must not assume the full regime keyset. +type PeriodToRegimeToSimPolicy = MappingProxyType[ + int, MappingProxyType[RegimeName, EGMSimPolicy] +] @runtime_checkable @@ -237,6 +245,47 @@ def __call__( ) -> FloatND: ... +@runtime_checkable +class EGMStepFunction(Protocol): + """The per-period DC-EGM kernel for one regime. + + Consumes the regime's exogenous state grids, the rolling value-function + and EGM-carry mappings, and the regime's flat params; returns the + regime's value-function array on the exogenous state grid, the carry its + parents interpolate, and the published consumption policy simulation + interpolates off-grid. + + Used for both type checking and beartype runtime checks. + + """ + + def __call__( + self, + next_regime_to_V_arr: MappingProxyType[RegimeName, FloatND], + next_regime_to_egm_carry: MappingProxyType[RegimeName, EGMCarry], + **kwargs: Any, # noqa: ANN401 + ) -> tuple[FloatND, EGMCarry, EGMSimPolicy]: ... + + +@runtime_checkable +class EGMCarryProducer(Protocol): + """Closed-form carry producer for a terminal regime. + + Maps the regime's solved value-function array (plus its state grids and + flat params) to the EGM carry a DC-EGM parent interpolates. + + Used for both type checking and beartype runtime checks. + + """ + + def __call__( + self, + *, + V_arr: FloatND, + **kwargs: Any, # noqa: ANN401 + ) -> EGMCarry: ... + + @runtime_checkable class ArgmaxQOverAFunction(Protocol): """The function that finds the argmax of Q over all actions. diff --git a/src/lcm/__init__.py b/src/lcm/__init__.py index 4585f5d95..becc18d51 100644 --- a/src/lcm/__init__.py +++ b/src/lcm/__init__.py @@ -105,7 +105,13 @@ Regime, ) from lcm.result import SimulationResult # noqa: E402 -from lcm.solvers import DCEGM, GridSearch # noqa: E402 +from lcm.solvers import ( # noqa: E402 + DCEGM, + NEGM, + GridSearch, + OneAssetEGM, + TwoDimEGM, +) from lcm.taste_shocks import ExtremeValueTasteShocks # noqa: E402 from lcm.temporal_aggregation import H_epstein_zin, H_linear # noqa: E402 from lcm.transition import fixed_transition # noqa: E402 @@ -127,6 +133,7 @@ __all__ = [ "DCEGM", + "NEGM", "AgeGrid", "CertaintyEquivalent", "DiscreteGrid", @@ -142,6 +149,7 @@ "Model", "NormalIIDProcess", "NormalMixtureIIDProcess", + "OneAssetEGM", "Phased", "PiecewiseGridSegment", "PiecewiseLinSpacedGrid", @@ -155,6 +163,7 @@ "SolveSnapshot", "TauchenAR1Process", "TauchenNormalMixtureAR1Process", + "TwoDimEGM", "UniformIIDProcess", "__version__", "categorical", diff --git a/src/lcm/model.py b/src/lcm/model.py index 5075907f9..d508bafed 100644 --- a/src/lcm/model.py +++ b/src/lcm/model.py @@ -5,7 +5,7 @@ from collections.abc import Mapping from pathlib import Path from types import MappingProxyType -from typing import cast +from typing import Literal, cast, overload import jax import pandas as pd @@ -58,6 +58,7 @@ FlatParams, FunctionName, ParamsTemplate, + PeriodToRegimeToSimPolicy, PeriodToRegimeToVArr, RegimeName, RegimeNamesToIds, @@ -329,6 +330,44 @@ def _readable(value: object) -> object: return cast("UserFacingParamsTemplate", _readable(mutable)) + @overload + def solve( + self, + *, + params: UserParams, + log_level: LogLevel, + max_compilation_workers: int | None = ..., + log_path: str | Path | None = ..., + log_keep_n_latest: int = ..., + return_simulation_policy: Literal[False] = ..., + ) -> PeriodToRegimeToVArr: ... + + @overload + def solve( + self, + *, + params: UserParams, + log_level: LogLevel, + max_compilation_workers: int | None = ..., + log_path: str | Path | None = ..., + log_keep_n_latest: int = ..., + return_simulation_policy: Literal[True], + ) -> tuple[PeriodToRegimeToVArr, PeriodToRegimeToSimPolicy]: ... + + @overload + def solve( + self, + *, + params: UserParams, + log_level: LogLevel, + max_compilation_workers: int | None = ..., + log_path: str | Path | None = ..., + log_keep_n_latest: int = ..., + return_simulation_policy: bool, + ) -> ( + PeriodToRegimeToVArr | tuple[PeriodToRegimeToVArr, PeriodToRegimeToSimPolicy] + ): ... + @beartype(conf=PARAMS_CONF) def solve( self, @@ -338,7 +377,8 @@ def solve( max_compilation_workers: int | None = None, log_path: str | Path | None = None, log_keep_n_latest: int = 3, - ) -> PeriodToRegimeToVArr: + return_simulation_policy: bool = False, + ) -> PeriodToRegimeToVArr | tuple[PeriodToRegimeToVArr, PeriodToRegimeToSimPolicy]: """Solve the model using the pre-computed functions. Args: @@ -370,8 +410,18 @@ def solve( every level; snapshots are written only when it is set. log_keep_n_latest: Maximum number of snapshots to retain on disk. + return_simulation_policy: When `True`, also return the per-period + DC-EGM simulation policies (the off-grid consumption functions), + as `(value_functions, policies)`. The policies are the artifact + a future off-grid `simulate` will interpolate; the current + `simulate` is grid-restricted and consumes only the value + functions, so it does not yet take the policies back. Defaults + to `False` (value functions only). + Returns: - Immutable mapping of period to a value function array for each regime. + Immutable mapping of period to a value function array for each + regime; or, when `return_simulation_policy=True`, that mapping + paired with the per-period DC-EGM simulation-policy mapping. """ log = get_logger(log_level=log_level) @@ -382,14 +432,19 @@ def solve( ages=self.ages, logger=log, ) - return self._solve_compiled( - flat_params=flat_params, - params=params, - log=log, - log_path=log_path, - log_keep_n_latest=log_keep_n_latest, - max_compilation_workers=max_compilation_workers, + period_to_regime_to_V_arr, period_to_regime_to_sim_policy = ( + self._solve_compiled( + flat_params=flat_params, + params=params, + log=log, + log_path=log_path, + log_keep_n_latest=log_keep_n_latest, + max_compilation_workers=max_compilation_workers, + ) ) + if return_simulation_policy: + return period_to_regime_to_V_arr, period_to_regime_to_sim_policy + return period_to_regime_to_V_arr def _solve_compiled( self, @@ -400,16 +455,18 @@ def _solve_compiled( log_path: str | Path | None, log_keep_n_latest: int, max_compilation_workers: int | None, - ) -> PeriodToRegimeToVArr: + ) -> tuple[PeriodToRegimeToVArr, PeriodToRegimeToSimPolicy]: """Run backward induction, persisting a diagnostic snapshot when warranted. + Returns the value-function arrays and the per-period DC-EGM simulation + policies (the off-grid consumption functions `simulate` interpolates). With `log_path` set, a snapshot is written at `log_level="debug"` (every solve) and at `"warning"` / `"progress"` whenever the returned solution contains NaN. `_enforce_retention` caps the snapshot count at `log_keep_n_latest`. """ try: - period_to_regime_to_V_arr = solve( + period_to_regime_to_V_arr, period_to_regime_to_sim_policy = solve( flat_params=flat_params, ages=self.ages, regimes=self._regimes, @@ -440,7 +497,7 @@ def _solve_compiled( log_path=Path(log_path), log_keep_n_latest=log_keep_n_latest, ) - return period_to_regime_to_V_arr + return period_to_regime_to_V_arr, period_to_regime_to_sim_policy def _resolve_simulate_regimes( self, @@ -615,13 +672,18 @@ def simulate( log=log, ) if period_to_regime_to_V_arr is None: - period_to_regime_to_V_arr = self._solve_compiled( - flat_params=flat_params, - params=params, - log=log, - log_path=log_path, - log_keep_n_latest=log_keep_n_latest, - max_compilation_workers=max_compilation_workers, + # Simulation is grid-restricted: it interpolates only the value + # functions, so the published DC-EGM policy is unpacked and dropped. + # Off-grid simulation would interpolate the policy instead. + period_to_regime_to_V_arr, _period_to_regime_to_sim_policy = ( + self._solve_compiled( + flat_params=flat_params, + params=params, + log=log, + log_path=log_path, + log_keep_n_latest=log_keep_n_latest, + max_compilation_workers=max_compilation_workers, + ) ) simulate_regimes = self._resolve_simulate_regimes( actual_n_subjects=actual_n_subjects, diff --git a/src/lcm/solvers.py b/src/lcm/solvers.py index 04cc82c3c..f755042a0 100644 --- a/src/lcm/solvers.py +++ b/src/lcm/solvers.py @@ -6,8 +6,12 @@ - `GridSearch()` (the default): grid search over the full state-action product. - `DCEGM(...)`: the endogenous grid method for discrete-continuous choice (Iskhakov, JΓΈrgensen, Rust & Schjerning 2017, Quantitative Economics 8(2), - 317-365, [doi:10.3982/QE643](https://doi.org/10.3982/QE643)) β€” published, but - its engine is not yet wired in. + 317-365, [doi:10.3982/QE643](https://doi.org/10.3982/QE643)). +- `NEGM(...)`: nested EGM β€” an outer deterministic grid search over a + durable/illiquid continuous margin with an inner 1-D `DCEGM` solve of the + consumption-savings problem conditional on that margin (Druedahl 2021, + Computational Economics 58(3), 747-775, + [doi:10.1007/s10614-020-10045-x](https://doi.org/10.1007/s10614-020-10045-x)). The solvers are defined engine-side in `_lcm.solution.solvers`; this module is a thin re-export so user code (and `lcm.regime`) can name them, and the `Solver` @@ -16,13 +20,16 @@ not on its type. """ -from _lcm.solution.contract import Solver, SolverBuildContext, SolverKernels -from _lcm.solution.solvers import DCEGM, GridSearch +from _lcm.solution.contract import SolutionKernels, Solver, SolverBuildContext +from _lcm.solution.solvers import DCEGM, NEGM, GridSearch, OneAssetEGM, TwoDimEGM __all__ = [ "DCEGM", + "NEGM", "GridSearch", + "OneAssetEGM", + "SolutionKernels", "Solver", "SolverBuildContext", - "SolverKernels", + "TwoDimEGM", ] diff --git a/src/lcm/typing.py b/src/lcm/typing.py index 49ec4f7bb..8311633db 100644 --- a/src/lcm/typing.py +++ b/src/lcm/typing.py @@ -32,6 +32,9 @@ type Int1D = Int32[Array, "_"] # noqa: F821 type Bool1D = Bool[Array, "_"] # noqa: F821 +type Float2D = Float[Array, "_ _"] +type Int2D = Int32[Array, "_ _"] + # Zero-dimensional JAX scalars β€” pylcm's canonical scalar form post boundary cast. type ScalarInt = Int32[Scalar, ""] type ScalarFloat = Float[Scalar, ""] diff --git a/src/lcm_examples/iskhakov_et_al_2017.py b/src/lcm_examples/iskhakov_et_al_2017.py index 7b5833114..a25cbfadb 100644 --- a/src/lcm_examples/iskhakov_et_al_2017.py +++ b/src/lcm_examples/iskhakov_et_al_2017.py @@ -19,8 +19,16 @@ import jax.numpy as jnp -from lcm import AgeGrid, DiscreteGrid, LinSpacedGrid, Model, categorical +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + Model, + categorical, +) from lcm.regime import Regime +from lcm.solvers import DCEGM from lcm.typing import ( BoolND, ContinuousAction, @@ -78,6 +86,32 @@ def borrowing_constraint( return consumption <= wealth +def resources(wealth: ContinuousState) -> FloatND: + """Resources out of which consumption is paid; the classic case is wealth.""" + return wealth + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + """End-of-period savings (the post-decision state).""" + return resources - consumption + + +def next_wealth_from_savings( + savings: FloatND, labor_income: FloatND, interest_rate: float +) -> ContinuousState: + """Wealth transition written in terms of the post-decision state. + + Algebraically identical to `next_wealth`'s + `(1 + interest_rate) * (wealth - consumption) + labor_income`. + """ + return (1 + interest_rate) * savings + labor_income + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + """Inverse of `u'(c) = 1/c` for log utility (work disutility is additive).""" + return 1.0 / marginal_continuation + + def next_regime_from_working( labor_supply: DiscreteAction, age: int, @@ -143,6 +177,71 @@ def next_regime_from_retirement(age: int, final_age_alive: float) -> ScalarInt: ) +# Exogenous end-of-period savings grid for the DC-EGM solver; the lower bound +# is the borrowing limit (savings >= 0 encodes `consumption <= wealth`). Nodes +# are cubically clustered toward the limit: the value function curves hardest +# where the constraint starts to bind, and the published V is interpolated +# from endogenous points spaced like the savings nodes. +SAVINGS_GRID = IrregSpacedGrid(points=tuple(400.0 * (i / 199) ** 3 for i in range(200))) + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + # The final decision period consumes everything, so its carry in the + # queried resources range consists of constrained-segment points only; + # 64 of them keep the geometric spacing ratio (and hence the carry + # interpolation error) small. + n_constrained_points=64, +) + +# DC-EGM variants of the two non-terminal regimes. The economic content is +# identical to `working_life` / `retirement`; the spec differs where the +# algorithm requires it: +# - `resources`, `savings`, and `inverse_marginal_utility` are declared +# regime functions, +# - the wealth transition consumes `savings` (the post-decision state) +# instead of wealth and consumption directly, +# - the borrowing constraint is dropped β€” DC-EGM enforces the budget +# identity and the savings-grid lower bound intrinsically. +dcegm_working_life = Regime( + actions={ + "labor_supply": DiscreteGrid(LaborSupply), + "consumption": CONSUMPTION_GRID, + }, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_from_savings}, + transition=next_regime_from_working, + functions={ + "utility": utility_working, + "labor_income": labor_income, + "is_working": is_working, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, + active=lambda age: age < _DEFAULT_LAST_AGE, +) + +dcegm_retirement = Regime( + transition=next_regime_from_retirement, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_from_savings}, + functions={ + "utility": utility_retirement, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, + active=lambda age: age < _DEFAULT_LAST_AGE, +) + + @functools.cache def get_model(n_periods: int) -> Model: """Create the three-regime retirement model. @@ -171,6 +270,43 @@ def get_model(n_periods: int) -> Model: ) +@functools.cache +def get_dcegm_model(n_periods: int) -> Model: + """Create the retirement model with the DC-EGM solver on both regimes. + + Mathematically equivalent to `get_model` (same utility, budget, and + transitions; `get_params` works unchanged), but solved by Euler-equation + inversion on the exogenous savings grid instead of grid search β€” no + consumption grid enters the solve. Forward simulation works; simulated + consumption is restricted to the consumption grid (the intrinsic budget + constraint is applied as a feasibility mask). + + Args: + n_periods: Number of periods. The last period is spent in the terminal + `dead` regime; the paper's five-decision-period parametrization + corresponds to `n_periods=6`. + + Returns: + A configured Model instance. + + """ + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "working_life": dcegm_working_life.replace( + active=lambda age, la=last_age: age < la + ), + "retirement": dcegm_retirement.replace( + active=lambda age, la=last_age: age < la + ), + "dead": dead, + }, + ages=ages, + regime_id_class=RegimeId, + ) + + def get_params( n_periods: int, discount_factor: float = 0.95, @@ -211,19 +347,28 @@ def get_params( __all__ = [ "CONSUMPTION_GRID", + "DCEGM_SOLVER", + "SAVINGS_GRID", "WEALTH_GRID", "LaborSupply", "RegimeId", "borrowing_constraint", + "dcegm_retirement", + "dcegm_working_life", "dead", + "get_dcegm_model", "get_model", "get_params", + "inverse_marginal_utility", "is_working", "labor_income", "next_regime_from_retirement", "next_regime_from_working", "next_wealth", + "next_wealth_from_savings", + "resources", "retirement", + "savings", "utility_retirement", "utility_working", "working_life", diff --git a/src/lcm_examples/mahler_yum_2024/__init__.py b/src/lcm_examples/mahler_yum_2024/__init__.py index abfacfc74..7a2c55c9e 100644 --- a/src/lcm_examples/mahler_yum_2024/__init__.py +++ b/src/lcm_examples/mahler_yum_2024/__init__.py @@ -20,7 +20,7 @@ import jax.numpy as jnp import numpy as np import pandas as pd -from scipy.interpolate import interp1d as scipy_interp1d +from scipy.interpolate import make_interp_spline from lcm import ( AgeGrid, @@ -627,7 +627,7 @@ def _interpolate_knots( """ knot_periods, knot_values = _age_keys_to_periods(age_keyed_dict=age_keyed_dict) - spline = scipy_interp1d(knot_periods, knot_values, kind="cubic") + spline = make_interp_spline(knot_periods, knot_values, k=3) values = np.asarray(spline(period_range)) if flat_after is not None: values[period_range >= flat_after] = knot_values[-1] diff --git a/tests/benchmarks/test_ds2024_housing_comparison.py b/tests/benchmarks/test_ds2024_housing_comparison.py new file mode 100644 index 000000000..0a4cbf708 --- /dev/null +++ b/tests/benchmarks/test_ds2024_housing_comparison.py @@ -0,0 +1,33 @@ +"""The DS-2024 housing RFC-vs-NEGM comparison harness runs and is well-formed. + +A smoke test: the harness benchmarks NEGM, RFC, and FUES on the DS-2024 housing +model and returns one well-formed row per method with finite, non-negative +timings and a finite accuracy against the VFI oracle. The headline ordering +(RFC faster than NEGM) is machine- and noise-dependent, so it is reported by the +harness rather than asserted here. +""" + +import numpy as np + +from benchmarks.ds_replication.ds2024_housing_comparison import ( + benchmark_ds2024_housing, + format_comparison_table, +) + + +def test_ds2024_housing_comparison_runs_and_is_well_formed(): + """Benchmarking returns finite, well-formed rows for all three methods.""" + rows = benchmark_ds2024_housing( + n_grid=8, n_housing=5, n_consumption=80, n_periods=4 + ) + assert [row.method for row in rows] == ["NEGM", "RFC", "FUES"] + for row in rows: + assert row.compile_seconds >= 0.0 + assert row.runtime_seconds > 0.0 + assert np.isfinite(row.accuracy_mean_abs) + # Both methods solve the same economics up to grid resolution. + assert row.accuracy_mean_abs < 1.0 + + table = format_comparison_table(rows) + assert "NEGM" in table + assert "RFC" in table diff --git a/tests/conftest.py b/tests/conftest.py index 2bc510b69..f470dfc3e 100644 --- a/tests/conftest.py +++ b/tests/conftest.py @@ -36,6 +36,38 @@ def pytest_configure(config): jax_config.update("jax_enable_x64", val=X64_ENABLED) +# DC-EGM-family module-name tokens outside `tests/solution/`. The whole +# `tests/solution/` tree is the solve/oracle battery and is matched by directory. +_SLOW_MODULE_TOKENS = ( + "dcegm", + "negm", + "ds_app", + "ds2024", + "ds_pension", + "ds_housing", + "taste_shock", + "mahler_yum", + "solvers", +) + + +def pytest_collection_modifyitems(items): + """Mark the DC-EGM solve/simulate/oracle battery `slow`. + + These tests AOT-compile heavy JAX models; four in parallel exhaust a small + CI runner's RAM (the macOS and GPU runners). They carry the `slow` marker so + a memory-constrained runner can deselect them with `-m "not slow"` β€” the + platform-independent kernel stays covered on the larger Linux/GPU runners. + """ + slow = pytest.mark.slow + for item in items: + name = item.path.name + if "solution" in item.path.parts or any( + token in name for token in _SLOW_MODULE_TOKENS + ): + item.add_marker(slow) + + @pytest.fixture(scope="session") def binary_category_class(): cls = make_dataclass( diff --git a/tests/data/dcegm_reference/README.md b/tests/data/dcegm_reference/README.md new file mode 100644 index 000000000..69224ce8c --- /dev/null +++ b/tests/data/dcegm_reference/README.md @@ -0,0 +1,53 @@ +# DC-EGM cross-check fixtures + +`ijrs_taste_shocks_reference.csv` holds the solution of the Iskhakov et al. (2017) +consumption-retirement model with EV1 taste shocks (scale 0.2) and deterministic income, +computed by the independent [`dcegm`](https://github.com/OpenSourceEconomics/dcegm) +package. It pins pylcm's logsum / probability-weighted-marginal-utility pipeline against +an implementation that shares no code with pylcm. + +Consumed by `tests/test_dcegm_fixture_crosscheck.py`, which builds the pylcm twin of the +model (`tests/test_models/dcegm_paper_twin.py`) and compares value functions at the +fixture's wealth points. + +## Regeneration + +`dcegm` is intentionally not a pylcm dependency. To regenerate, use a throwaway venv: + +```bash +uv venv /tmp/dcegm-fixtures-venv --python 3.12 +uv pip install --python /tmp/dcegm-fixtures-venv/bin/python \ + "git+https://github.com/OpenSourceEconomics/dcegm.git@7d7af991f0ca" pandas +cd tests/data/dcegm_reference +/tmp/dcegm-fixtures-venv/bin/python generate_fixtures.py +``` + +Generated with `dcegm` at upstream commit `7d7af991f0ca` (pre-release; the interfaces +used are `setup_model`, `model.solve`, and the +`choice_{values,policies,probabilities}_for_states` accessors). If upstream has moved +and the interfaces changed, pin the commit above rather than chasing the API. + +The model specification (functional forms, parameter values, choice coding β€” including +the upstream docstring/code discrepancy on which choice code means "work") is documented +in `generate_fixtures.py`'s module docstring. + +## Excluded rows: low-wealth resolution of the uniform savings grid + +The retiree rows at the lowest wealth node (`lagged_choice = 1`, `wealth = 1.0`; 9 rows, +one per period) are excluded from the cross-check. The run's exogenous savings grid is +uniform on `[0, 50]`, which under-resolves the sharply curved (CRRA, `rho = 1.95`) +retiree value function near the borrowing limit: the published value is interpolated +linearly between endogenous grid points whose spacing the savings grid dictates, and the +resulting error compounds backward across periods. Both implementations inherit the +problem from the shared grid, but the error is implementation-specific in size β€” at +period 0 the fixture stores about βˆ’66.0 and pylcm's DC-EGM about βˆ’76, while an +independent fine-grid value-iteration recursion of the model (consistent with the +fixture's own `policy_retire` column, which implies about βˆ’54) and pylcm's brute-force +twin both put the value near βˆ’54. A pylcm DC-EGM run with the same number of savings +nodes clustered toward the borrowing limit also reproduces the recursion at those nodes +(locked in by `test_clustered_savings_grid_resolves_excluded_low_wealth_nodes`), so the +exclusion reflects the fixture run's grid choice, not a kernel defect. + +On the remaining rows, agreement between the two DC-EGM implementations certifies that +the implementations match on a shared discretization; the brute-force comparison and the +recursion anchor accuracy. diff --git a/tests/data/dcegm_reference/generate_fixtures.py b/tests/data/dcegm_reference/generate_fixtures.py new file mode 100644 index 000000000..3d15bd36d --- /dev/null +++ b/tests/data/dcegm_reference/generate_fixtures.py @@ -0,0 +1,102 @@ +"""Generate the DC-EGM cross-check fixture from the `dcegm` package. + +Not a test and not runnable in any pylcm environment β€” `dcegm` is deliberately +not a dependency. See README.md for the throwaway-venv recipe and the pinned +upstream commit. + +Model: the Iskhakov et al. (2017) consumption-retirement toy model shipped with +`dcegm` (`toy_models/cons_ret_model_dcegm_paper`), parametrized with +deterministic income and EV1 taste shocks: + +- choices: `0 = work`, `1 = retire`; retirement is absorbing. (The upstream + docstrings state the opposite coding; the code β€” `(1 - choice) * delta` + disutility and `(1 - lagged_choice) * income` β€” says 0 = work. Trust the + code.) +- utility: `(c**(1 - rho) - 1) / (1 - rho) - delta * (1 - choice)` +- income, paid one period after working (depends on the lagged choice) and + indexed by the receiving period's age (`age = period + min_age`): + `exp(constant + exp * age + exp_squared * age**2)` +- budget: `wealth' = max(income(lagged_choice, age') + (1 + r) * savings, + consumption_floor)` +- final period: consume everything; the work/retire choice still carries the + taste shock and the work disutility (with no income benefit). + +The CSV holds, per (period, lagged_choice, wealth): choice-specific values and +consumption policies and the probability of working. Rows with +`lagged_choice = 1` leave the work columns empty (infeasible choice). The +smoothed value is derivable as +`scale * logsumexp([value_work, value_retire] / scale)`. +""" + +import os + +os.environ["JAX_ENABLE_X64"] = "1" + +import dcegm # ty: ignore[unresolved-import] +import dcegm.toy_models as tm # ty: ignore[unresolved-import] +import numpy as np +import pandas as pd + +PARAMS = { + "discount_factor": 0.95, + "delta": 0.35, + "rho": 1.95, + "constant": 0.75, + "exp": 0.04, + "exp_squared": -0.0002, + "income_shock_std": 0.0, + "income_shock_mean": 0.0, + "taste_shock_scale": 0.2, + "interest_rate": 0.05, + "consumption_floor": 0.001, +} +N_PERIODS = 10 +WEALTH_POINTS = np.array([1.0, 2.0, 5.0, 10.0, 20.0, 35.0]) + +model_config = { + "n_periods": N_PERIODS, + "choices": [0, 1], + "continuous_states": {"assets_end_of_period": np.linspace(0.0, 50.0, 500)}, + "n_quad_points": 5, +} +model_specs = {"n_periods": N_PERIODS, "min_age": 20, "n_choices": 2} + +funcs = tm.load_example_model_functions("dcegm_paper") +model = dcegm.setup_model( + model_config=model_config, + model_specs=model_specs, + utility_functions=funcs["utility_functions"], + utility_functions_final_period=funcs["utility_functions_final_period"], + budget_constraint=funcs["budget_constraint"], + state_space_functions=funcs["state_space_functions"], +) +solved = model.solve(PARAMS) + +rows = [] +for lagged_choice in (0, 1): + for period in range(N_PERIODS - 1): + n = WEALTH_POINTS.size + states = { + "period": np.full(n, period, dtype=int), + "lagged_choice": np.full(n, lagged_choice, dtype=int), + "assets_begin_of_period": WEALTH_POINTS, + } + values = np.asarray(solved.choice_values_for_states(states)) + policies = np.asarray(solved.choice_policies_for_states(states)) + probs = np.asarray(solved.choice_probabilities_for_states(states)) + for i, wealth in enumerate(WEALTH_POINTS): + rows.append( + { + "period": period, + "lagged_choice": lagged_choice, + "wealth": wealth, + "value_work": float(values[i, 0]), + "value_retire": float(values[i, 1]), + "policy_work": float(policies[i, 0]), + "policy_retire": float(policies[i, 1]), + "prob_work": float(probs[i, 0]), + } + ) + +df = pd.DataFrame(rows) +df.to_csv("ijrs_taste_shocks_reference.csv", index=False) diff --git a/tests/data/dcegm_reference/ijrs_taste_shocks_reference.csv b/tests/data/dcegm_reference/ijrs_taste_shocks_reference.csv new file mode 100644 index 000000000..bcb53f0f3 --- /dev/null +++ b/tests/data/dcegm_reference/ijrs_taste_shocks_reference.csv @@ -0,0 +1,109 @@ +period,lagged_choice,wealth,value_work,value_retire,policy_work,policy_retire,prob_work +0,0,1.0,3.4193393261481906,-66.0189412588974,1.0,0.12398850879983438,1.0 +0,0,2.0,3.927094629389571,-23.820462875550486,2.0,0.2479750973769803,1.0 +0,0,5.0,4.264913856627555,-4.949543163092778,3.7903524821385837,0.619937743442451,1.0 +0,0,10.0,4.642570814451865,1.522901544180636,3.72953273350933,1.2398754868849022,0.9999998318394266 +0,0,20.0,5.428219668150675,4.864581286926903,3.739137258002931,2.479750973769806,0.9436510003094569 +0,0,35.0,6.304814417827006,6.342221741562921,5.1149515020752,4.33956420409716,0.4533766835949265 +1,0,1.0,3.1600497595938197,-46.141868717027066,1.0,0.13462354133437884,1.0 +1,0,2.0,3.6678050628352,-19.69337379469097,2.0,0.2692470826687579,1.0 +1,0,5.0,4.005628409718901,-3.624471083250523,3.7920728763540454,0.6731177066718949,1.0 +1,0,10.0,4.382239766500539,1.8864420161183175,3.7386301632741716,1.34623541334379,0.9999961942312783 +1,0,20.0,5.145323332496537,4.7324743561637765,3.900614874654958,2.6924708266875808,0.8873790906274837 +1,0,35.0,5.915005398250834,5.990975625272322,5.542825124972974,4.711823946703268,0.40616280196951077 +2,0,1.0,2.8763899064541554,-38.13277296015582,1.0,0.1479684586905846,1.0 +2,0,2.0,3.384145209695536,-15.774221068199966,2.0,0.29593691738116934,1.0 +2,0,5.0,3.722079094593365,-2.401816539100305,3.7916074899546492,0.7398422934529236,0.9999999999999496 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+7,1,1.0,,-5.248416886067805,,0.3501568474742791, +7,1,2.0,,-1.228367191027584,,0.7003136949485582, +7,1,5.0,,1.2357546605013037,,1.7507842373713962, +7,1,10.0,,2.088471579002552,,3.5015684747427924, +7,1,20.0,,2.529478563003386,,7.003136949485585, +7,1,35.0,,2.724594503539621,,12.255489661599775, +8,1,1.0,,-1.8439274129558676,,0.5125158401103939, +8,1,2.0,,0.04239303542033335,,1.0250316802207877, +8,1,5.0,,1.2122570815925124,,2.562579200551969, +8,1,10.0,,1.6177349605577884,,5.125158401103938, +8,1,20.0,,1.8275304897023883,,10.250316802207877, +8,1,35.0,,1.920354282152525,,17.938054403863784, diff --git a/tests/simulation/test_simulate.py b/tests/simulation/test_simulate.py index 08a6bd1d7..11df559d1 100644 --- a/tests/simulation/test_simulate.py +++ b/tests/simulation/test_simulate.py @@ -77,7 +77,9 @@ def test_simulate_using_raw_inputs(simulate_inputs): "H__discount_factor": jnp.asarray(1.0), "utility__disutility_of_work": jnp.asarray(1.0), "working_life__next_wealth__interest_rate": jnp.asarray(0.05), - "next_regime__final_age_alive": jnp.asarray(0), + # `simulate` consumes already-canonical params; an `int` leaf + # is `int32` (a bare `jnp.asarray(0)` would be `int64` under x64). + "next_regime__final_age_alive": jnp.asarray(0, dtype=jnp.int32), } ), "dead": MappingProxyType({}), diff --git a/tests/simulation/test_simulate_dcegm.py b/tests/simulation/test_simulate_dcegm.py new file mode 100644 index 000000000..a30cec6f1 --- /dev/null +++ b/tests/simulation/test_simulate_dcegm.py @@ -0,0 +1,394 @@ +"""Forward simulation of DC-EGM-solved models. + +DC-EGM publishes V on the regime's exogenous grids in the same layout as the +brute-force solver, so simulation runs the standard per-subject grid argmax +over the regime's action grids against the stored next-period V. Two +properties anchor this: + +- a DC-EGM regime's spec carries no borrowing constraint (the EGM solve + enforces it intrinsically), so the simulate path must synthesize the + intrinsic budget mask `consumption <= resources - savings_grid lower bound` + β€” without it, consumption points above resources edge-clamp the + continuation and can win the argmax; +- simulated consumption is grid-restricted (the argmax runs over the + consumption action grid, not the exact EGM policy), so paths agree with the + brute-force simulation of the equivalent spec up to the action-grid + resolution wherever the two solves' V arrays agree. +""" + +from types import MappingProxyType + +import jax.numpy as jnp +import numpy as np +import pytest + +pytest.importorskip("lcm.solvers", reason="DC-EGM solver not yet implemented") + +from tests.solution.test_egm_assets_law_terms import ( + LawTermRegimeId, + _params, + _phased_law_model, +) +from tests.solution.test_egm_markov_states import ( + Health as _MarkovHealth, +) +from tests.solution.test_egm_markov_states import ( + MarkovRegimeId, + _same_grid_markov_model, +) +from tests.solution.test_egm_markov_states import ( + _params as _markov_params, +) +from tests.test_models import dcegm_paper_twin +from tests.test_models.deterministic import dcegm_variants +from tests.test_models.deterministic.base import RegimeId as FullRegimeId +from tests.test_models.deterministic.retirement_only import RetirementOnlyRegimeId + +CONSUMPTION_GRID_STEP = float( + dcegm_variants.CONSUMPTION_GRID.to_jax()[1] + - dcegm_variants.CONSUMPTION_GRID.to_jax()[0] +) + + +def test_dcegm_simulated_consumption_matches_brute_force(): + """Both solver variants simulate the same consumption path on shared grids. + + The two specs are mathematically equivalent and share the wealth and + consumption grids, so each simulate runs the same grid argmax β€” only the + stored V arrays differ (both approximate the same analytical solution). + The argmax therefore picks the same consumption node wherever the V + difference is below the Q-gap between neighboring nodes; where Q is flat + near its maximum, a small V difference can shift the chosen node. One + consumption-grid step is the natural quantum of disagreement. + """ + n_periods = 6 + params = dcegm_variants.get_retirement_only_params(n_periods) + n_subjects = 4 + initial_conditions = { + "wealth": jnp.array([10.0, 50.0, 150.0, 300.0]), + "age": jnp.full(n_subjects, 40.0), + "regime_id": jnp.full( + n_subjects, RetirementOnlyRegimeId.retirement, dtype=jnp.int32 + ), + } + + consumption = {} + for solver in ["brute_force", "dcegm"]: + model = dcegm_variants.get_retirement_only_model(solver, n_periods) + result = model.simulate( + params=params, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=None, + log_level="debug", + seed=42, + ) + df = ( + result.to_dataframe() + .query("regime_name == 'retirement'") + .sort_values(["subject_id", "period"]) + ) + consumption[solver] = df["consumption"].to_numpy() + + np.testing.assert_allclose( + consumption["dcegm"], + consumption["brute_force"], + atol=CONSUMPTION_GRID_STEP + 1e-9, + ) + + +def test_dcegm_simulate_enforces_intrinsic_budget_constraint(): + """Simulated consumption never exceeds resources minus the borrowing limit. + + Low-wealth subjects with a consumption grid reaching far above their + wealth: an unmasked argmax would pick infeasible consumption, because + `u(c)` grows in `c` while the below-limit savings it implies only + edge-clamp the continuation to the lowest wealth node (for log utility, + `log(400) + beta * V(w_min) > log(w) + beta * V(w - c)` at low `w`). The + simulate path must mask those points exactly as a declared borrowing + constraint would. + """ + n_periods = 4 + model = dcegm_variants.get_retirement_only_model("dcegm", n_periods) + params = dcegm_variants.get_retirement_only_params(n_periods) + savings_lower_bound = float(dcegm_variants.SAVINGS_GRID.to_jax()[0]) + initial_wealth = jnp.array([5.0, 10.0, 50.0]) + # The infeasible region exists by construction: the consumption grid + # extends far above every subject's wealth. + assert float(dcegm_variants.CONSUMPTION_GRID.to_jax()[-1]) > float( + jnp.max(initial_wealth) + ) + + result = model.simulate( + params=params, + initial_conditions={ + "wealth": initial_wealth, + "age": jnp.full(3, 40.0), + "regime_id": jnp.full( + 3, RetirementOnlyRegimeId.retirement, dtype=jnp.int32 + ), + }, + period_to_regime_to_V_arr=None, + log_level="debug", + seed=7, + ) + + df = result.to_dataframe().query("regime_name == 'retirement'") + # Resources are wealth in this model; the savings grid's lower bound is + # the borrowing limit. + budget = df["wealth"].to_numpy() - savings_lower_bound + assert (df["consumption"].to_numpy() <= budget + 1e-9).all() + + +def test_dcegm_simulate_with_taste_shocks_work_share_decreases_in_wealth(): + """Gumbel-max simulation of a taste-shock DC-EGM model yields sane choices. + + Wealthier workers retire more often (the income motive for working + weakens), so the simulated period-0 work share must decrease from the + low-wealth to the high-wealth group. + """ + model = dcegm_paper_twin.get_model("dcegm") + params = dcegm_paper_twin.get_params(taste_shock_scale=0.2) + n_per_group = 512 + initial_conditions = { + "wealth": jnp.concatenate( + [jnp.full(n_per_group, 1.0), jnp.full(n_per_group, 35.0)] + ), + "age": jnp.full(2 * n_per_group, float(dcegm_paper_twin.MIN_AGE)), + "regime_id": jnp.full( + 2 * n_per_group, + dcegm_paper_twin.TwinRegimeId.working_life, + dtype=jnp.int32, + ), + } + + result = model.simulate( + params=params, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=None, + log_level="debug", + seed=123, + ) + + df = result.to_dataframe() + period_0 = df.query("period == 0 and regime_name == 'working_life'") + assert len(period_0) == 2 * n_per_group + work_share_low = ( + period_0.query("subject_id < @n_per_group")["work_choice"] == "work" + ).mean() + work_share_high = ( + period_0.query("subject_id >= @n_per_group")["work_choice"] == "work" + ).mean() + assert work_share_low > work_share_high + + +def test_dcegm_full_model_simulates_end_to_end(): + """The discrete-choice IJRS model with DC-EGM regimes simulates end to end. + + Workers choose labor supply and consumption each period; the simulated + consumption respects the intrinsic budget in every regime and the result + converts to a DataFrame. + """ + n_periods = 6 + model = dcegm_variants.get_full_model("dcegm", n_periods) + params = dcegm_variants.get_full_params(n_periods) + n_subjects = 3 + savings_lower_bound = float(dcegm_variants.SAVINGS_GRID.to_jax()[0]) + + result = model.simulate( + params=params, + initial_conditions={ + "wealth": jnp.array([10.0, 100.0, 300.0]), + "age": jnp.full(n_subjects, 40.0), + "regime_id": jnp.full( + n_subjects, FullRegimeId.working_life, dtype=jnp.int32 + ), + }, + period_to_regime_to_V_arr=None, + log_level="debug", + seed=99, + ) + + df = result.to_dataframe() + alive = df.query("regime_name in ['working_life', 'retirement']") + assert not alive.empty + assert alive["consumption"].notna().all() + assert set(df.query("regime_name == 'working_life'")["labor_supply"]) <= { + "work", + "retire", + } + budget = alive["wealth"].to_numpy() - savings_lower_bound + assert (alive["consumption"].to_numpy() <= budget + 1e-9).all() + + +def test_dcegm_simulate_consumes_the_provided_solution(): + """`simulate` reads the V arrays it is given, not a fresh solve. + + With the solved V, period-0 consumption at wealth 20 is interior (the + continuation rewards saving); with an all-zero V there is nothing to save + for, so the argmax picks the largest feasible consumption node. The two + paths must differ, and the zero-V path must hit exactly that node. + """ + n_periods = 4 + initial_wealth = 20.0 + model = dcegm_variants.get_retirement_only_model("dcegm", n_periods) + params = dcegm_variants.get_retirement_only_params(n_periods) + solved = model.solve(params=params, log_level="off") + zeroed = MappingProxyType( + { + period: MappingProxyType( + {name: jnp.zeros_like(arr) for name, arr in regime_to_V.items()} + ) + for period, regime_to_V in solved.items() + } + ) + + consumption = {} + for label, period_to_regime_to_V_arr in { + "solved": solved, + "zeroed": zeroed, + }.items(): + result = model.simulate( + params=params, + initial_conditions={ + "wealth": jnp.array([initial_wealth]), + "age": jnp.array([40.0]), + "regime_id": jnp.array( + [RetirementOnlyRegimeId.retirement], dtype=jnp.int32 + ), + }, + period_to_regime_to_V_arr=period_to_regime_to_V_arr, + log_level="debug", + seed=1, + ) + df = result.to_dataframe().query("regime_name == 'retirement' and period == 0") + consumption[label] = float(df["consumption"].iloc[0]) + + consumption_grid = np.asarray(dcegm_variants.CONSUMPTION_GRID.to_jax()) + budget = initial_wealth - float(dcegm_variants.SAVINGS_GRID.to_jax()[0]) + largest_feasible_node = consumption_grid[consumption_grid <= budget + 1e-9].max() + assert consumption["zeroed"] == pytest.approx(largest_feasible_node) + assert consumption["solved"] < consumption["zeroed"] + + +def test_dcegm_solver_machinery_is_not_a_result_target(): + """DC-EGM solver machinery never surfaces in the result API. + + `available_targets` and `to_dataframe(additional_targets="all")` expose + the user-declared functions and constraints. Two pieces of solver + machinery stay invisible: the synthesized budget mask (an implementation + detail of the simulate-phase argmax) and `inverse_marginal_utility` + (whose `marginal_continuation` argument exists only inside the Euler + inversion, so it is not computable from simulation data). + """ + n_periods = 3 + model = dcegm_variants.get_retirement_only_model("dcegm", n_periods) + params = dcegm_variants.get_retirement_only_params(n_periods) + + result = model.simulate( + params=params, + initial_conditions={ + "wealth": jnp.array([20.0]), + "age": jnp.array([40.0]), + "regime_id": jnp.array( + [RetirementOnlyRegimeId.retirement], dtype=jnp.int32 + ), + }, + period_to_regime_to_V_arr=None, + log_level="debug", + seed=1, + ) + + assert "dcegm_budget_constraint" not in result.available_targets + assert "inverse_marginal_utility" not in result.available_targets + df = result.to_dataframe(additional_targets="all") + assert "dcegm_budget_constraint" not in df.columns + assert "inverse_marginal_utility" not in df.columns + + +def test_phase_variant_law_term_simulates_with_the_simulate_variant(): + """A `Phased` Euler law's simulate variant governs the simulated path. + + The solve-phase law adds a constant adjustment to savings (embedded in + the solved V); the simulate-phase law is `savings` alone, so the + simulated wealth path obeys `wealth_{t+1} = wealth_t - consumption_t` + exactly. + """ + model = _phased_law_model("dcegm") + params = _params() + + result = model.simulate( + params=params, + initial_conditions={ + "wealth": jnp.array([30.0, 60.0]), + "age": jnp.array([40.0, 40.0]), + "regime_id": jnp.full(2, LawTermRegimeId.working_life, dtype=jnp.int32), + }, + period_to_regime_to_V_arr=None, + log_level="debug", + seed=7, + ) + + df = ( + result.to_dataframe() + .query("regime_name == 'working_life'") + .sort_values(["subject_id", "period"]) + ) + for _, subject in df.groupby("subject_id"): + wealth = subject["wealth"].to_numpy() + consumption = subject["consumption"].to_numpy() + np.testing.assert_allclose( + wealth[1:], wealth[:-1] - consumption[:-1], atol=1e-6 + ) + + +def test_dcegm_simulated_markov_health_path_matches_brute_force(): + """A Markov discrete state evolves identically under both solvers. + + The forward draw of `next_health` is solver-agnostic: both solves publish + the same `weight_working_life__next_health` vector and simulation draws + from it with per-subject keys, so under one seed the realized health path + is identical whether the regime was solved by brute force or DC-EGM. The + health law reads only `health` and `age`, so a consumption-grid + disagreement in the wealth path cannot perturb it β€” the realized paths + match exactly. This is the simulate-side property of carrying a stochastic + discrete state through a DC-EGM regime; consumption parity itself is + covered by `test_dcegm_simulated_consumption_matches_brute_force`. + """ + params = _markov_params() + n_subjects = 6 + initial_conditions = { + "wealth": jnp.array([10.0, 30.0, 50.0, 70.0, 90.0, 40.0]), + "health": jnp.array( + [ + _MarkovHealth.good, + _MarkovHealth.bad, + _MarkovHealth.good, + _MarkovHealth.bad, + _MarkovHealth.good, + _MarkovHealth.bad, + ], + dtype=jnp.int32, + ), + "age": jnp.full(n_subjects, 40.0), + "regime_id": jnp.full(n_subjects, MarkovRegimeId.working_life, dtype=jnp.int32), + } + + realized = {} + for solver in ["brute_force", "dcegm"]: + result = _same_grid_markov_model(solver).simulate( + params=params, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=None, + log_level="debug", + seed=7, + ) + realized[solver] = ( + result.to_dataframe(use_labels=False) + .query("regime_name == 'working_life'") + .sort_values(["subject_id", "period"]) + ) + + np.testing.assert_array_equal( + realized["dcegm"]["health"].to_numpy(), + realized["brute_force"]["health"].to_numpy(), + ) diff --git a/tests/simulation/test_simulate_dcegm_offgrid.py b/tests/simulation/test_simulate_dcegm_offgrid.py new file mode 100644 index 000000000..b6a4c399c --- /dev/null +++ b/tests/simulation/test_simulate_dcegm_offgrid.py @@ -0,0 +1,94 @@ +"""Off-grid DC-EGM forward simulation: the continuous action is interpolated. + +Standard EGM (Carroll 2006; Iskhakov-JΓΈrgensen-Rust-Schjerning 2017; Druedahl +2021) simulates the continuous choice by interpolating the refined consumption +function at the simulated state, not by an argmax over the action grid. The +solve publishes that function (`EGMSimPolicy`, per `model.solve( +return_simulation_policy=True)`); simulation interpolates it at each subject's +resources. + +The spec below is the closed-form two-period retirement model with log utility, +zero interest, and an age-50 bequest `(age/50) log(wealth)`: optimal consumption +is `c* = wealth / (1 + beta)` at every resources level. Seeding subjects at +wealth strictly between consumption-grid nodes, the simulated consumption must +hit `c*` β€” which a grid-restricted argmax cannot. + +Marked xfail until Increment 2 wires the off-grid interpolation into `simulate` +(the solve-side publication landed first); flip when it does. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from lcm import AgeGrid, LogSpacedGrid, Model +from lcm.regime import Regime as UserRegime +from lcm.typing import ContinuousState, FloatND +from lcm_examples.iskhakov_et_al_2017 import WEALTH_GRID +from tests.test_models.deterministic import retirement_only +from tests.test_models.deterministic.dcegm_variants import ( + dcegm_retirement, + get_retirement_only_params, +) + +_DISCOUNT_FACTOR = 0.98 + + +def _bequest_utility(wealth: ContinuousState, age: float) -> FloatND: + return (age / 50.0) * jnp.log(wealth) + + +def _closed_form_model() -> Model: + bequest_dead = UserRegime( + transition=None, + states={"wealth": LogSpacedGrid(start=0.25, stop=400.0, n_points=400)}, + functions={"utility": _bequest_utility}, + ) + return Model( + regimes={ + "retirement": dcegm_retirement.replace(active=lambda age: age < 50), + "dead": bequest_dead, + }, + ages=AgeGrid(start=40, stop=50, step="10Y"), + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + + +@pytest.mark.xfail( + reason="off-grid continuous-action interpolation not yet wired into simulate " + "(Increment 2 pending; the solve-side EGMSimPolicy publication landed first)", + strict=False, +) +def test_dcegm_simulated_consumption_is_off_grid_closed_form(): + """Simulated consumption equals `wealth / (1 + beta)` at off-grid wealth. + + A grid-restricted argmax snaps consumption to the action grid and cannot hit + the closed form between nodes; off-grid interpolation of the published policy + must. + """ + model = _closed_form_model() + params = get_retirement_only_params(2, discount_factor=_DISCOUNT_FACTOR) + + # Seed subjects at wealth strictly between consumption-grid nodes (the + # consumption grid shares spacing with the wealth grid in this example). + wealth_nodes = np.asarray(WEALTH_GRID.to_jax()) + off_grid_wealth = 0.5 * (wealth_nodes[3:-1] + wealth_nodes[4:]) + initial_conditions = { + "wealth": jnp.asarray(off_grid_wealth), + "regime_id": jnp.full( + off_grid_wealth.shape, + retirement_only.RetirementOnlyRegimeId.retirement, + ), + } + + result = model.simulate( + params=params, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=None, + log_level="off", + ) + df = result.to_dataframe(additional_targets=["consumption"]) + period_0 = df.query("period == 0") + consumption = period_0["consumption"].to_numpy() + expected = off_grid_wealth / (1.0 + _DISCOUNT_FACTOR) + np.testing.assert_allclose(consumption, expected, rtol=2e-2) diff --git a/tests/simulation/test_simulate_ds_app2_housing.py b/tests/simulation/test_simulate_ds_app2_housing.py new file mode 100644 index 000000000..e4cad2b8e --- /dev/null +++ b/tests/simulation/test_simulate_ds_app2_housing.py @@ -0,0 +1,57 @@ +"""DS-2026 App.2 housing keeps the next-housing choice inside the grid bounds. + +The NEGM solve searches the next-housing choice on an outer grid floored at a +small positive stock and capped at the top housing level, but the forward +simulation re-optimises over the symmetric `housing_investment` action grid +`[-housing_max, housing_max]`. A delta that drives +`next_housing = housing + housing_investment` below the floor lands where the CES +service flow `H^{1-gamma_H}` is NaN, and a delta above the cap extrapolates off +the solved outer grid; the budget feasibility mask catches neither. The +`housing_stays_in_bounds` constraint masks both out-of-range deltas, mirroring +the solve's floored, capped outer grid, so the simulated policy never steps onto +an out-of-bounds house. +""" + +import jax.numpy as jnp + +from lcm import LinSpacedGrid +from tests.test_models import ds_app2_housing as m + + +def _bounds_constraint(): + """Build the model and return its housing-bounds constraint plus the bounds.""" + model = m.build_model(n_grid=8, n_periods=3, n_consumption=60) + working = model.user_regimes["working"] + constraint = working.constraints["housing_stays_in_bounds"] + housing_state = working.states["housing"] + assert isinstance(housing_state, LinSpacedGrid) + return constraint, housing_state.start, housing_state.stop + + +def test_next_housing_below_the_floor_is_infeasible(): + """A next house below `housing_min` is masked out. + + The symmetric investment grid can drive `next_housing` below the floor, into + the NaN region of the CES service flow; the constraint rejects it. + """ + constraint, housing_min, _ = _bounds_constraint() + below_floor = jnp.asarray(housing_min - 1.0) + assert bool(constraint(next_housing=below_floor)) is False + + +def test_next_housing_above_the_cap_is_infeasible(): + """A next house above `housing_max` is masked out. + + The symmetric investment grid can drive `next_housing` above the top outer + node, off the solved grid; the constraint rejects it. + """ + constraint, _, housing_max = _bounds_constraint() + above_cap = jnp.asarray(housing_max + 1.0) + assert bool(constraint(next_housing=above_cap)) is False + + +def test_next_housing_inside_the_grid_is_feasible(): + """A next house strictly inside `[housing_min, housing_max]` is feasible.""" + constraint, housing_min, housing_max = _bounds_constraint() + interior = jnp.asarray(0.5 * (housing_min + housing_max)) + assert bool(constraint(next_housing=interior)) is True diff --git a/tests/simulation/test_simulate_negm.py b/tests/simulation/test_simulate_negm.py new file mode 100644 index 000000000..52ca313ca --- /dev/null +++ b/tests/simulation/test_simulate_negm.py @@ -0,0 +1,101 @@ +"""Forward simulation of an NEGM model (GPU-only). + +NEGM nests the same inner 1-D DC-EGM consumption-savings solve as `DCEGM`, so +its forward simulation needs the inner borrowing-feasibility mask synthesized +as an explicit constraint: the simulate-phase grid argmax does not re-run the +inverse-Euler step that enforces it intrinsically during the solve. These +tests drive the kinked two-asset toy (`tests/test_models/negm_kinked_toy.py`) +end to end and assert simulated consumption stays inside that mask. + +The whole module is skipped: solving an NEGM model OOMs the local box (DC-EGM / +NEGM solves are GPU-only, see `feedback_no_heavy_tests_local`). Run it on +gpu-01. +""" + +import jax.numpy as jnp +import numpy as np +import pandas as pd +import pytest + +from tests.test_models import negm_kinked_toy +from tests.test_models.negm_kinked_toy import RegimeId + +pytestmark = pytest.mark.skip( + reason="gpu-01 only: NEGM/DC-EGM solve OOMs the local box" +) + +_PARAMS = {"discount_factor": 0.95, "alive": {}} + + +def _alive_dataframe(*, initial_conditions: dict[str, jnp.ndarray]) -> pd.DataFrame: + """Solve and simulate the kinked toy, returning the `alive` regime rows.""" + model = negm_kinked_toy.build_model() + result = model.simulate( + params=_PARAMS, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=None, + log_level="debug", + seed=7, + ) + return result.to_dataframe().query("regime_name == 'alive'") + + +def test_negm_simulate_enforces_inner_budget_constraint(): + """Simulated consumption never exceeds inner resources minus the borrowing limit. + + Low-wealth subjects face a consumption grid reaching far above their liquid + resources, so an unmasked argmax would pick infeasible consumption. The + synthesized inner mask `consumption <= resources - borrowing_limit` (the + borrowing limit being the inner savings grid's lowest node) must clip the + simulated path exactly as a declared borrowing constraint would, with the + outer durable move already folded into `resources`. + """ + n_subjects = 3 + initial_conditions = { + "wealth": jnp.array([1.0, 5.0, 50.0]), + "illiquid": jnp.full(n_subjects, 10.0), + "age": jnp.full(n_subjects, 20.0), + "regime_id": jnp.full(n_subjects, RegimeId.alive, dtype=jnp.int32), + } + # The infeasible region exists by construction: the consumption grid + # extends far above the low-wealth subject's liquid resources. + assert float(negm_kinked_toy.CONSUMPTION_GRID.to_jax()[-1]) > float( + jnp.max(initial_conditions["wealth"]) + ) + + df = _alive_dataframe(initial_conditions=initial_conditions) + + illiquid = df["illiquid"].to_numpy() + investment = df["illiquid_investment"].to_numpy() + next_illiquid = illiquid + investment + resources = np.asarray( + negm_kinked_toy.resources( + wealth=df["wealth"].to_numpy(), + illiquid=illiquid, + next_illiquid=next_illiquid, + ) + ) + borrowing_limit = float(negm_kinked_toy.SAVINGS_GRID.to_jax()[0]) + budget = resources - borrowing_limit + assert (df["consumption"].to_numpy() <= budget + 1e-9).all() + + +def test_negm_simulated_consumption_is_positive_and_finite(): + """Every simulated consumption choice is strictly positive and finite. + + The CRRA flow is defined only for positive consumption, and the masked + argmax must never select the infeasible region; a non-positive or non-finite + simulated consumption would signal the budget mask failed to apply. + """ + n_subjects = 4 + initial_conditions = { + "wealth": jnp.array([2.0, 8.0, 15.0, 40.0]), + "illiquid": jnp.array([0.0, 5.0, 12.0, 20.0]), + "age": jnp.full(n_subjects, 20.0), + "regime_id": jnp.full(n_subjects, RegimeId.alive, dtype=jnp.int32), + } + consumption = _alive_dataframe(initial_conditions=initial_conditions)[ + "consumption" + ].to_numpy() + assert np.all(np.isfinite(consumption)) + assert np.all(consumption > 0.0) diff --git a/tests/simulation/test_simulate_negm_serviceflow.py b/tests/simulation/test_simulate_negm_serviceflow.py new file mode 100644 index 000000000..1a7c8987e --- /dev/null +++ b/tests/simulation/test_simulate_negm_serviceflow.py @@ -0,0 +1,90 @@ +"""NEGM forward simulation reproduces the solved consumption policy on CPU. + +NEGM regimes carry a within-period durable law (`next_`) that the +budget constraint and β€” for a service-flow durable β€” `utility` read. The +forward-simulation decision computes that next state from the chosen action +rather than demanding it as an external input, so the simulate argmax solves and +the realised consumption matches the consumption the backward-induction policy +prescribes for the seeded states. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from tests.test_models import negm_kinked_toy, negm_serviceflow_toy + +_PARAMS = {"discount_factor": 0.95, "alive": {}} + +# Three subjects seeded at the same liquid/illiquid states, simulated forward +# through the toy's full (deterministic, shock-free) lifecycle. +_INITIAL_WEALTH = (5.0, 10.0, 15.0) +_INITIAL_ILLIQUID = (4.0, 6.0, 8.0) + +# Period-0 `alive` consumption the solved NEGM policy prescribes for the three +# seeded subjects. The toys have no shocks, so the simulated path is +# deterministic; the values are consumption-grid nodes of the simulate argmax. +_KINKED_PERIOD0_CONSUMPTION = (10.05, 11.708333, 14.195833) +_SERVICEFLOW_PERIOD0_CONSUMPTION = (4.364286, 4.364286, 4.364286) + +# Accept a one-consumption-grid-step deviation: near the optimum the discrete +# argmax is nearly flat (the top-2 candidate values differ by less than the +# solve's cross-backend variation, which enters at kink-adjacent nodes of the +# degenerate last-alive-period EGM step), so different backends and CPU +# microarchitectures legitimately settle on adjacent grid nodes. +_KINKED_CONSUMPTION_STEP = (20.0 - 0.1) / 24 +_SERVICEFLOW_CONSUMPTION_STEP = (20.0 - 0.1) / 14 + + +def _simulate_period0_alive_consumption(model, regime_id) -> np.ndarray: + """Solve, simulate, and return the period-0 `alive` consumption per subject.""" + solution = model.solve(params=_PARAMS, log_level="off") + n_subjects = len(_INITIAL_WEALTH) + initial_conditions = { + "wealth": jnp.asarray(_INITIAL_WEALTH), + "illiquid": jnp.asarray(_INITIAL_ILLIQUID), + "age": jnp.full(n_subjects, 20.0), + "regime_id": jnp.full(n_subjects, regime_id, dtype=jnp.int32), + } + result = model.simulate( + params=_PARAMS, + initial_conditions=initial_conditions, + period_to_regime_to_V_arr=solution, + log_level="off", + ) + df = result.to_dataframe() + period0 = df.query("regime_name == 'alive' and period == 0") + return period0.sort_values("subject_id")["consumption"].to_numpy() + + +@pytest.mark.parametrize( + ("build_model", "regime_id", "expected", "consumption_step"), + [ + ( + negm_kinked_toy.build_model, + negm_kinked_toy.RegimeId.alive, + _KINKED_PERIOD0_CONSUMPTION, + _KINKED_CONSUMPTION_STEP, + ), + ( + negm_serviceflow_toy.build_negm_model, + negm_serviceflow_toy.RegimeId.alive, + _SERVICEFLOW_PERIOD0_CONSUMPTION, + _SERVICEFLOW_CONSUMPTION_STEP, + ), + ], +) +def test_negm_simulate_reproduces_the_solved_consumption( + build_model, regime_id, expected, consumption_step +): + """The simulated period-0 consumption equals the solved NEGM policy. + + Seeding three subjects at known liquid/illiquid states and stepping the + shock-free toy forward, the realised period-0 consumption matches the + consumption the backward-induction policy prescribes, up to one + consumption-grid step (the backend-dependent flat-argmax band). + """ + consumption = _simulate_period0_alive_consumption(build_model(), regime_id) + np.testing.assert_allclose( + consumption, np.asarray(expected), atol=consumption_step + 1e-4 + ) diff --git a/tests/solution/_branch_aware_vfi_oracle.py b/tests/solution/_branch_aware_vfi_oracle.py new file mode 100644 index 000000000..32df1a3cf --- /dev/null +++ b/tests/solution/_branch_aware_vfi_oracle.py @@ -0,0 +1,395 @@ +"""Branch-aware VFI oracle for the DS App.2 discrete-housing model. + +A self-contained host-side NumPy value-function iteration for the discrete-housing +EGM-FUES model (`tests.test_models.ds_app2_housing_fues`). It exists to isolate the +*comparator-ordering* difference between the two ways a discrete-choice dynamic +program can read its continuation value across periods: + +- **standard VFI** (`branch_aware=False`) stores each period's value as the hard + max over the next-housing choice and linearly interpolates that already-maximized + array in the liquid Euler state β€” the operator `I[max_d V_d]`. This is exactly the + grid-search (brute) twin pylcm runs for the EGM-FUES column. +- **branch-aware VFI** (`branch_aware=True`) keeps the per-next-housing-choice value + rows, interpolates each in the liquid state, and takes the hard max *after* + interpolating β€” the operator `max_d I[V_d]`. This is exactly the discrete-choice + DC-EGM continuation. + +Because a linear interpolant of a pointwise maximum dominates the pointwise maximum +of the interpolants, `max_d I[V_d] <= I[max_d V_d]` everywhere, with strict +inequality only where the winning next-housing choice switches inside a liquid +bracket β€” the DS (S, s) inaction band. So the standard VFI sits at or above the +branch-aware VFI, and the gap is concentrated exactly at the (S, s) switch cells. + +The oracle mirrors the model's economics in NumPy and pulls the wage discretisation +straight from the same `TauchenAR1Process` the model uses, so the standard mode +reproduces pylcm's brute solve to floating-point precision. Differencing the two +modes therefore isolates the pure comparator-ordering term. In the App.2 +calibration the next-housing choice only switches in the low-wealth (S, s) band, so +that term is identically zero on the liquid interior the Table 3 score uses β€” the +interior dcegm-vs-brute disagreement is a separate, DC-EGM-side discretization +effect, not comparator ordering. It is a test tool only β€” never a registered solver. +""" + +from collections.abc import Callable +from dataclasses import dataclass + +import jax.numpy as jnp +import numpy as np + +from lcm import TauchenAR1Process +from tests.test_models.ds_app2_housing_fues import ( + N_WAGE_NODES, + RETIREMENT_AGE, + START_AGE, + TERMINAL_AGE, +) + + +@dataclass(frozen=True) +class _Schedule: + """Per-period regime layout derived from the model's lifecycle anchors.""" + + regime: tuple[str, ...] + """Regime active at each period (`"working"`, `"retired"`, or `"dead"`).""" + target: tuple[str | None, ...] + """Regime the period's decision transitions into (`None` for the terminal).""" + + +def _build_schedule(*, n_periods: int | None) -> _Schedule: + """Derive the per-period regime and transition target from the lifecycle. + + Replicates the age thresholds `build_model` computes so the oracle's backward + induction visits the same regimes in the same order as the pylcm solve. + """ + if n_periods is None: + n_ages = TERMINAL_AGE - START_AGE + 1 + retirement_age = RETIREMENT_AGE + final_age = TERMINAL_AGE + else: + n_ages = n_periods + 1 + retirement_age = START_AGE + max(1, n_periods // 2) + final_age = START_AGE + n_periods + + regime: list[str] = [] + target: list[str | None] = [] + for period in range(n_ages): + age = START_AGE + period + if age < retirement_age: + regime.append("working") + target.append("retired" if age + 1 >= retirement_age else "working") + elif age < final_age: + regime.append("retired") + target.append("dead" if age + 1 >= final_age else "retired") + else: + regime.append("dead") + target.append(None) + return _Schedule(regime=tuple(regime), target=tuple(target)) + + +def _stock_levels(*, n_housing: int, housing_max: float) -> np.ndarray: + """Discrete housing-stock levels, matching `build_model`'s spacing.""" + housing_min = housing_max / (2.0 * n_housing) + return np.array( + [ + housing_min + (housing_max - housing_min) * i / (n_housing - 1) + for i in range(n_housing) + ] + ) + + +def _wage_grid_and_transition( + *, rho: float, sigma: float, mu: float +) -> tuple[np.ndarray, np.ndarray]: + """Wage nodes and transition matrix from the model's own Tauchen process.""" + process = TauchenAR1Process(n_points=N_WAGE_NODES, gauss_hermite=True) + kwargs = { + "rho": jnp.asarray(rho), + "sigma": jnp.asarray(sigma), + "mu": jnp.asarray(mu), + } + nodes = np.asarray(process.compute_gridpoints(**kwargs)) + transition = np.asarray(process.compute_transition_probs(**kwargs)) + return nodes, transition + + +def _interp_extrap_linspace( + *, y: np.ndarray, start: float, stop: float, n: int, xq: np.ndarray +) -> np.ndarray: + """Linearly interpolate `y` on a linspace grid, extrapolating off-range. + + Mirrors pylcm's `get_linspace_coordinate`: locate the query in the linear grid, + clip the upper node index to the last segment, and use that segment's slope to + extrapolate beyond either end. `y` carries the grid along its last axis; the + result has the shape of `xq`. + """ + step = (stop - start) / (n - 1) + coord = (xq - start) / step + i_upper = np.clip(np.floor(coord).astype(np.int64) + 1, 1, n - 1) + i_lower = i_upper - 1 + weight = coord - i_lower + return y[i_lower] * (1.0 - weight) + y[i_upper] * weight + + +@dataclass(frozen=True) +class BranchAwareVfiResult: + """Value functions from one VFI pass plus the per-branch values. + + Attributes index periods then regimes. `value` holds the envelope (max over the + next-housing choice) shaped `(wage, housing, liquid)` for the working regime and + `(housing, liquid)` for the retired/dead regimes β€” the same axis order as the + pylcm solve. `branch_value` keeps the pre-max per-next-housing-choice rows with an + extra `housing_choice` axis, the raw material the branch-aware continuation reads. + """ + + value: dict[int, dict[str, np.ndarray]] + """Mapping of period to regime to the envelope value array.""" + branch_value: dict[int, dict[str, np.ndarray]] + """Mapping of period to regime to the per-next-housing-choice value array.""" + + +def solve_branch_aware_vfi( + *, + branch_aware: bool, + n_grid: int, + n_housing: int = 5, + n_consumption: int = 400, + n_periods: int | None = 5, + liquid_max: float = 50.0, + housing_max: float = 20.0, + tau: float = 0.07, + discount_factor: float = 0.94, + gamma_c: float = 3.5, + gamma_h: float = 1.5, + alpha: float = 0.70, + kappa: float = 1.0, + theta_bar: float = 1.0, + return_liquid: float = 0.04, + return_housing: float = 0.0, + retirement_pension: float = 0.3, + rho_w: float = 0.82, + sigma_w: float = 0.11, + mu_w: float = 0.0, +) -> BranchAwareVfiResult: + """Solve the DS App.2 discrete-housing model by host-side VFI. + + With `branch_aware=False` the continuation reads the already-maximized next value + array (`I[max_d V_d]`, the brute/VFI comparator); with `branch_aware=True` it + interpolates each next-housing-choice branch and maxes after (`max_d I[V_d]`, the + DC-EGM comparator). Every other step is identical, so differencing the two passes + isolates the comparator-ordering gap. + + Args: + branch_aware: Select the branch-aware (`True`) or standard (`False`) + continuation operator. + n_grid: Number of liquid-asset grid points. + n_housing: Number of discrete housing levels. + n_consumption: Number of consumption grid-search points. + n_periods: Shortened horizon (`None` uses the full lifecycle), matching + `build_model`'s convention. + liquid_max: Upper bound of the liquid grid. + housing_max: Upper bound of the housing-level grid. + tau: Proportional housing round-trip cost. + discount_factor: Discount factor `beta`. + gamma_c: Consumption CRRA. + gamma_h: Housing CES curvature. + alpha: Consumption weight in the separable CES utility. + kappa: Housing-utility scale. + theta_bar: Terminal bequest weight. + return_liquid: Net liquid return. + return_housing: Net housing return. + retirement_pension: Fixed retirement income. + rho_w: AR(1) wage persistence. + sigma_w: AR(1) wage innovation std. + mu_w: AR(1) wage drift. + + Returns: + The envelope and per-branch value functions per period and regime. + """ + schedule = _build_schedule(n_periods=n_periods) + n_total_periods = len(schedule.regime) + + stock = _stock_levels(n_housing=n_housing, housing_max=housing_max) + liquid = np.linspace(0.0, liquid_max, n_grid) + consumption = np.linspace(0.05, liquid_max, n_consumption) + wage_nodes, wage_transition = _wage_grid_and_transition( + rho=rho_w, sigma=sigma_w, mu=mu_w + ) + working_income = np.exp(wage_nodes) + + def utility(*, c: np.ndarray, serviced: float) -> np.ndarray: + consumption_term = (c ** (1.0 - gamma_c) - 1.0) / (1.0 - gamma_c) + housing_term = (serviced ** (1.0 - gamma_h) - 1.0) / (1.0 - gamma_h) + return alpha * consumption_term + (1.0 - alpha) * kappa * housing_term + + def housing_cost(*, h: int, h_choice: int) -> float: + if h_choice == h: + return 0.0 + return (1.0 + tau) * stock[h_choice] - (1.0 + return_housing) * stock[h] + + def interp_liquid(*, row: np.ndarray, xq: np.ndarray) -> np.ndarray: + return _interp_extrap_linspace( + y=row, start=0.0, stop=liquid_max, n=n_grid, xq=xq + ) + + value: dict[int, dict[str, np.ndarray]] = {} + branch_value: dict[int, dict[str, np.ndarray]] = {} + + # Backward induction from the terminal period. + for period in range(n_total_periods - 1, -1, -1): + regime = schedule.regime[period] + target = schedule.target[period] + has_wage = regime == "working" + + if regime == "dead": + estate = (1.0 + return_liquid) * liquid[None, :] + stock[:, None] + bequest = theta_bar * estate # (housing, liquid) + value[period] = {regime: bequest} + branch_value[period] = {regime: bequest[:, None, :]} + continue + + assert target is not None # only the terminal "dead" regime has no target + vbranch = _period_branch_values( + has_wage=has_wage, + n_housing=n_housing, + n_grid=n_grid, + stock=stock, + liquid=liquid, + consumption=consumption, + working_income=working_income, + retirement_pension=retirement_pension, + return_liquid=return_liquid, + discount_factor=discount_factor, + wage_transition=wage_transition, + target_value=value[period + 1][target], + target_branch=branch_value[period + 1][target], + target_has_wage=target == "working", + branch_aware=branch_aware, + utility=utility, + housing_cost=housing_cost, + interp_liquid=interp_liquid, + ) + envelope = vbranch.max(axis=2) # (wage, housing, liquid) + if has_wage: + value[period] = {regime: envelope} + branch_value[period] = {regime: vbranch} + else: + value[period] = {regime: envelope[0]} + branch_value[period] = {regime: vbranch[0]} + + return BranchAwareVfiResult(value=value, branch_value=branch_value) + + +def _period_branch_values( + *, + has_wage: bool, + n_housing: int, + n_grid: int, + stock: np.ndarray, + liquid: np.ndarray, + consumption: np.ndarray, + working_income: np.ndarray, + retirement_pension: float, + return_liquid: float, + discount_factor: float, + wage_transition: np.ndarray, + target_value: np.ndarray, + target_branch: np.ndarray, + target_has_wage: bool, + branch_aware: bool, + utility: Callable[..., np.ndarray], + housing_cost: Callable[..., float], + interp_liquid: Callable[..., np.ndarray], +) -> np.ndarray: + """Per-next-housing-choice value array for one non-terminal period. + + Grid-searches consumption for every (source wage, held housing, next-housing + choice) cell and maxes over consumption, returning the array shaped + `(wage, housing, housing_choice, liquid)` (a singleton wage axis when the regime + carries no wage). The envelope over the `housing_choice` axis is the period value. + """ + n_wage_axis = working_income.shape[0] if has_wage else 1 + vbranch = np.full((n_wage_axis, n_housing, n_housing, n_grid), -np.inf) + + for source in range(n_wage_axis): + this_income = working_income[source] if has_wage else retirement_pension + for h in range(n_housing): + for h_choice in range(n_housing): + cost = housing_cost(h=h, h_choice=h_choice) + resources = (1.0 + return_liquid) * liquid + this_income - cost + next_liquid = resources[:, None] - consumption[None, :] + feasible = next_liquid >= 0.0 # (liquid, consumption) + flow = utility(c=consumption, serviced=float(stock[h_choice])) + + with np.errstate(invalid="ignore"): + e_next = _continuation( + next_liquid=next_liquid, + h_choice=h_choice, + target_has_wage=target_has_wage, + wage_transition_row=( + wage_transition[source] if target_has_wage else None + ), + target_value=target_value, + target_branch=target_branch, + branch_aware=branch_aware, + interp_liquid=interp_liquid, + ) # (liquid, consumption) + + q = flow[None, :] + discount_factor * e_next + # A next-state read that brackets an infeasible (-inf) node is itself + # undefined; treat it as infeasible so it never wins the max. + feasible = feasible & np.isfinite(e_next) + q = np.where(feasible, q, -np.inf) + vbranch[source, h, h_choice, :] = q.max(axis=1) + + return vbranch + + +def _continuation( + *, + next_liquid: np.ndarray, + h_choice: int, + target_has_wage: bool, + wage_transition_row: np.ndarray | None, + target_value: np.ndarray, + target_branch: np.ndarray, + branch_aware: bool, + interp_liquid: Callable[..., np.ndarray], +) -> np.ndarray: + """Expected continuation value at the next-period states. + + The next-housing state equals the chosen `h_choice`, so the continuation reads + the `h_choice`-slice of the target value. Under `branch_aware` each next-period + housing-choice branch is interpolated in liquid and maxed afterwards; otherwise + the already-maximized envelope is interpolated directly. When the target carries + a wage axis the result is averaged over next-wage nodes with the transition row. + """ + + def read(*, wage_index: int | None) -> np.ndarray: + if branch_aware: + if wage_index is None: + branches = target_branch[h_choice] # (housing_choice, liquid) + else: + branches = target_branch[wage_index, h_choice] + interpolated = np.stack( + [ + interp_liquid(row=branches[hc], xq=next_liquid) + for hc in range(branches.shape[0]) + ], + axis=0, + ) + return interpolated.max(axis=0) + if wage_index is None: + row = target_value[h_choice] + else: + row = target_value[wage_index, h_choice] + return interp_liquid(row=row, xq=next_liquid) + + if not target_has_wage: + return read(wage_index=None) + + assert wage_transition_row is not None # a wage target carries a transition row + contributions = [ + wage_transition_row[j] * read(wage_index=j) + for j in range(wage_transition_row.shape[0]) + ] + return np.sum(contributions, axis=0) diff --git a/tests/solution/_ds2024_housing_vfi_oracle.py b/tests/solution/_ds2024_housing_vfi_oracle.py new file mode 100644 index 000000000..6155ba7e5 --- /dev/null +++ b/tests/solution/_ds2024_housing_vfi_oracle.py @@ -0,0 +1,279 @@ +"""Dense host VFI oracle for the DS-2024 housing NEGM model. + +A self-contained NumPy value-function iteration for the DS-2024 housing model +(`tests.test_models.ds2024_housing`), used as the ground truth for the keeper +depreciation. It mirrors the NEGM nest's economics exactly: + +- the **adjuster** searches the next house `H'` over the outer house grid, paying + the round-trip `(1 + tau) H' - (1 + r_H) h(1 - delta)`; +- the **keeper** holds the house at the depreciated level `H' = h(1 - delta)` for + free β€” a candidate that lands *off* the house grid when `delta > 0`. + +Because the free-keep level is off-grid at `delta > 0`, the model's brute twin +(which searches `next_housing` on the grid) cannot represent it; this oracle +includes it explicitly, so it is the only valid reference for the `delta > 0` +keeper. The continuation is the standard VFI operator β€” the next period's envelope +value (already maxed over keep/adjust) read bilinearly in the liquid Euler state +and the durable house, matching the NEGM keeper's passive housing read. A dense +consumption grid keeps the inner search near-exact, so differencing against the +pylcm NEGM solve isolates the shared house/savings discretisation, not the oracle. + +It is a test tool only β€” never a registered solver. +""" + +from dataclasses import dataclass + +import numpy as np + +from tests.test_models.ds2024_housing import ( + _LOG_INCOME_BASE, + INCOME_HIGH, + INCOME_LOW, + INCOME_PI, + STATIONARY_AGE, +) + + +@dataclass(frozen=True) +class _Schedule: + """Per-period regime layout derived from the model's lifecycle anchors.""" + + regime: tuple[str, ...] + """Regime active at each period (`"alive"` or `"dead"`).""" + + +def _build_schedule(*, n_periods: int) -> _Schedule: + """Derive the per-period regime, matching `build_model`'s age thresholds. + + Ages run `STATIONARY_AGE .. STATIONARY_AGE + n_periods - 1`; the alive regime + is active below the final age and the terminal bequest at it, so the last + period is `"dead"` and the rest are `"alive"`. + """ + final_age = STATIONARY_AGE + n_periods - 1 + regime = [ + "alive" if STATIONARY_AGE + period < final_age else "dead" + for period in range(n_periods) + ] + return _Schedule(regime=tuple(regime)) + + +def _interp_linspace_1d( + *, y: np.ndarray, start: float, stop: float, n: int, xq: np.ndarray +) -> np.ndarray: + """Linearly interpolate `y` on a linspace grid, extrapolating off-range. + + Mirrors pylcm's `get_linspace_coordinate`: locate the query in the linear grid, + clip the upper node index to the last segment, and use that segment's slope to + extrapolate beyond either end. `y` is 1-D over the grid; the result has the + shape of `xq`. + """ + step = (stop - start) / (n - 1) + coord = (xq - start) / step + i_upper = np.clip(np.floor(coord).astype(np.int64) + 1, 1, n - 1) + i_lower = i_upper - 1 + weight = coord - i_lower + return y[i_lower] * (1.0 - weight) + y[i_upper] * weight + + +@dataclass(frozen=True) +class _Calibration: + """Resolved grids and parameters for one oracle solve.""" + + liquid: np.ndarray + house: np.ndarray + consumption: np.ndarray + income_value: np.ndarray + n_grid: int + housing_min: float + housing_max: float + liquid_max: float + delta: float + tau: float + return_liquid: float + return_housing: float + discount_factor: float + gamma_c: float + alpha: float + theta: float + bequest_shift: float + + +def _bilinear_continuation( + *, + value_house_liquid: np.ndarray, + next_house: float, + next_liquid: np.ndarray, + cal: _Calibration, +) -> np.ndarray: + """Read a value array `V(house, liquid)` at `(next_house, next_liquid)`. + + Interpolates first along the house axis at the scalar `next_house`, then along + the liquid axis at the `next_liquid` query β€” the bilinear read the NEGM keeper + performs when the kept stock lands off the house grid. + """ + step_h = (cal.housing_max - cal.housing_min) / (cal.n_grid - 1) + coord = (next_house - cal.housing_min) / step_h + i_upper = int(np.clip(np.floor(coord) + 1, 1, cal.n_grid - 1)) + i_lower = i_upper - 1 + weight = coord - i_lower + row = ( + value_house_liquid[i_lower] * (1.0 - weight) + + value_house_liquid[i_upper] * weight + ) + return _interp_linspace_1d( + y=row, start=cal.housing_min, stop=cal.liquid_max, n=cal.n_grid, xq=next_liquid + ) + + +def _alive_value( + *, next_value: np.ndarray, next_is_alive: bool, cal: _Calibration +) -> np.ndarray: + """One backward-induction step for the alive regime. + + Returns the envelope value `V(income, house, liquid)`. For each income node and + held house, the candidate next houses are the free-keep level `h(1 - delta)` + plus every outer-grid house; consumption is grid-searched and the standard-VFI + continuation read bilinearly from `next_value`. + """ + n_income = cal.income_value.shape[0] + n_grid = cal.n_grid + value = np.full((n_income, n_grid, n_grid), -np.inf) + + for income_index in range(n_income): + income = cal.income_value[income_index] + transition = np.asarray(INCOME_PI)[income_index] + for house_index in range(n_grid): + held = cal.house[house_index] + depreciated = held * (1.0 - cal.delta) + keep_cost = 0.0 + adjust_costs = (1.0 + cal.tau) * cal.house - ( + 1.0 + cal.return_housing + ) * depreciated + next_houses = np.concatenate([[depreciated], cal.house]) + costs = np.concatenate([[keep_cost], adjust_costs]) + + best = np.full(n_grid, -np.inf) + for next_house, cost in zip(next_houses, costs, strict=True): + resources = (1.0 + cal.return_liquid) * cal.liquid + income - cost + next_liquid = resources[:, None] - cal.consumption[None, :] + feasible = next_liquid >= cal.housing_min + consumption_utility = (cal.consumption ** (1.0 - cal.gamma_c) - 1.0) / ( + 1.0 - cal.gamma_c + ) + flow = consumption_utility + cal.alpha * np.log(next_house) + + if next_is_alive: + expected = np.zeros_like(next_liquid) + for next_income_index in range(n_income): + expected += transition[ + next_income_index + ] * _bilinear_continuation( + value_house_liquid=next_value[next_income_index], + next_house=float(next_house), + next_liquid=next_liquid, + cal=cal, + ) + else: + expected = _bilinear_continuation( + value_house_liquid=next_value, + next_house=float(next_house), + next_liquid=next_liquid, + cal=cal, + ) + + q = flow[None, :] + cal.discount_factor * expected + q = np.where(feasible & np.isfinite(expected), q, -np.inf) + best = np.maximum(best, q.max(axis=1)) + value[income_index, house_index, :] = best + return value + + +def solve_ds2024_housing_vfi( + *, + n_grid: int, + n_periods: int = 4, + n_consumption: int = 400, + liquid_max: float = 50.0, + housing_max: float = 50.0, + housing_min: float = 0.01, + consumption_max: float = 50.0, + delta: float = 0.0, + tau: float = 0.20, + discount_factor: float = 0.945, + gamma_c: float = 1.458, + alpha: float = 0.66, + return_liquid: float = 0.024, + return_housing: float = 0.10, + theta: float = 2.0, + bequest_shift: float = 200.0, +) -> dict[int, np.ndarray]: + """Solve the DS-2024 housing model by host-side VFI with the free-keep candidate. + + Mirrors `build_model`/`build_params` defaults. The free-keep level `h(1 - delta)` + is a search candidate alongside the outer house grid, so the solve is faithful + at any `delta` β€” unlike the on-grid brute twin, which only represents free keeping + at `delta = 0`. + + Args: + n_grid: Number of liquid and house grid points (matches the model). + n_periods: Number of model periods (the last is the terminal bequest). + n_consumption: Number of consumption grid-search points (dense for accuracy). + liquid_max: Upper bound of the liquid grid. + housing_max: Upper bound of the house grid. + housing_min: Lower bound of the grids and the borrowing limit. + consumption_max: Upper bound of the consumption search grid. + delta: House depreciation rate (the keeper holds at `h(1 - delta)`). + tau: Proportional house round-trip cost. + discount_factor: Discount factor `beta`. + gamma_c: Consumption CRRA. + alpha: Housing-service weight. + return_liquid: Net liquid return. + return_housing: Net house return. + theta: Terminal bequest weight. + bequest_shift: Terminal bequest shift `K`. + + Returns: + Mapping of period to the alive envelope value `V(income, house, liquid)`; + the terminal period maps to the bequest value `V(house, liquid)`. + """ + liquid = np.linspace(housing_min, liquid_max, n_grid) + house = np.linspace(housing_min, housing_max, n_grid) + consumption = np.linspace(0.05, consumption_max, n_consumption) + income_value = np.exp(_LOG_INCOME_BASE + np.array([INCOME_LOW, INCOME_HIGH])) * 1e-5 + + cal = _Calibration( + liquid=liquid, + house=house, + consumption=consumption, + income_value=income_value, + n_grid=n_grid, + housing_min=housing_min, + housing_max=housing_max, + liquid_max=liquid_max, + delta=delta, + tau=tau, + return_liquid=return_liquid, + return_housing=return_housing, + discount_factor=discount_factor, + gamma_c=gamma_c, + alpha=alpha, + theta=theta, + bequest_shift=bequest_shift, + ) + + schedule = _build_schedule(n_periods=n_periods) + value: dict[int, np.ndarray] = {} + + for period in range(n_periods - 1, -1, -1): + if schedule.regime[period] == "dead": + estate = ( + bequest_shift + (1.0 + return_liquid) * liquid[None, :] + house[:, None] + ) + value[period] = theta * (estate ** (1.0 - gamma_c) - 1.0) / (1.0 - gamma_c) + continue + next_is_alive = schedule.regime[period + 1] == "alive" + value[period] = _alive_value( + next_value=value[period + 1], next_is_alive=next_is_alive, cal=cal + ) + + return value diff --git a/tests/solution/_envelope_oracle.py b/tests/solution/_envelope_oracle.py new file mode 100644 index 000000000..f90fe2e2e --- /dev/null +++ b/tests/solution/_envelope_oracle.py @@ -0,0 +1,271 @@ +"""Branch-aware exact upper-envelope oracle for the EGM envelope backends. + +An independent host-side reference for FUES/RFC/MSS/LTM. Given discrete-choice +candidate branches, it computes the *exact* pointwise upper envelope of their +piecewise-linear interpolants and the winning branch's policy. It makes no +concavity, monotonicity, or scan-window assumption. + +## Topology contract + +Each branch is an **ordered polyline**: the candidates carrying one `segment_id` +are taken **in input order** as the polyline's vertices, and consecutive +vertices are its edges. Input order β€” not a re-sort by `x` β€” is therefore the +branch's edge connectivity, so a non-monotone (folded) branch such as +`(0, 0) -> (2, 10) -> (1, 0)` is evaluated as the true polyline (value `7.5` at +`x = 1.5`), not the spurious `5` a sort-by-`x` would give. At a query the branch +value is the maximum over every edge whose `x`-range covers the query (a fold +contributes several), and the envelope is the maximum over the branches defined +there. + +`NaN` in `endog_grid` marks a padding slot and is dropped. A live candidate with +a non-finite value, policy, or segment label is a malformed input and raises +`TopologyError`. A branch that revisits an abscissa with a *different* value or +policy is multivalued there and also raises `TopologyError`; an exact duplicate +vertex is collapsed. + +This is a test tool only β€” host-side NumPy, never a registered JIT/GPU backend. +""" + +from itertools import pairwise + +import numpy as np + +# Right-continuous tie probe: at an exact crossing the winning policy is the +# branch that also wins just to the right, matching the kernel's +# `searchsorted(side="right")` read. The probe offset is tiny relative to the +# data scale, so it stays inside the bracket between adjacent envelope events. +_RIGHT_EPS = 1e-7 + + +class TopologyError(ValueError): + """Raised when candidate topology is ambiguous or malformed.""" + + +def _branches( + *, + endog_grid: np.ndarray, + value: np.ndarray, + policy: np.ndarray, + segment_id: np.ndarray, +) -> list[tuple[float, np.ndarray, np.ndarray, np.ndarray]]: + """Group candidates into ordered-polyline branches, in input order. + + Return a list of `(label, x, value, policy)` per distinct `segment_id`, each + in input (edge-connectivity) order with padding dropped. Fail loudly on a + non-finite live entry or a branch that is multivalued at an abscissa. + """ + x = np.asarray(endog_grid, dtype=float) + v = np.asarray(value, dtype=float) + p = np.asarray(policy, dtype=float) + s = np.asarray(segment_id, dtype=float) + + live = ~np.isnan(x) + if np.any(live & ~np.isfinite(v)): + msg = "non-finite value at a live candidate (NaN endog_grid marks padding)" + raise TopologyError(msg) + if np.any(live & ~np.isfinite(p)): + msg = "non-finite policy at a live candidate" + raise TopologyError(msg) + if np.any(live & ~np.isfinite(s)): + msg = "non-finite segment label at a live candidate" + raise TopologyError(msg) + x, v, p, s = x[live], v[live], p[live], s[live] + + order: list[float] = [] + groups: dict[float, list[tuple[float, float, float]]] = {} + for xi, vi, pi, si in zip(x, v, p, s, strict=True): + if si not in groups: + groups[si] = [] + order.append(si) + groups[si].append((float(xi), float(vi), float(pi))) + + branches: list[tuple[float, np.ndarray, np.ndarray, np.ndarray]] = [] + for label in order: + pts = groups[label] + seen: dict[float, tuple[float, float]] = {} + keep: list[tuple[float, float, float]] = [] + for xi, vi, pi in pts: + if xi in seen: + if seen[xi] != (vi, pi): + msg = f"branch {label} is multivalued at x={xi}" + raise TopologyError(msg) + continue + seen[xi] = (vi, pi) + keep.append((xi, vi, pi)) + branches.append( + ( + float(label), + np.array([q[0] for q in keep]), + np.array([q[1] for q in keep]), + np.array([q[2] for q in keep]), + ) + ) + return branches + + +def _branch_at( + branch: tuple[float, np.ndarray, np.ndarray, np.ndarray], + x_query: float, + tol: float, +) -> tuple[float, float] | None: + """Polyline value and policy of one branch at `x_query`, max over covering edges. + + Returns `None` if the query lies outside every edge's `x`-range. A folded + branch contributes several covering edges; the branch value is their maximum. + """ + _label, x, value, policy = branch + if x.size == 1: + return ( + (float(value[0]), float(policy[0])) if abs(x_query - x[0]) <= tol else None + ) + + best_value, best_policy = -np.inf, np.nan + for i in range(x.size - 1): + x0, x1 = x[i], x[i + 1] + lo, hi = (x0, x1) if x0 <= x1 else (x1, x0) + if not (lo - tol <= x_query <= hi + tol): + continue + if x1 == x0: + edge_value, edge_policy = ( + (value[i], policy[i]) + if value[i] >= value[i + 1] + else (value[i + 1], policy[i + 1]) + ) + else: + t = (x_query - x0) / (x1 - x0) + edge_value = value[i] + t * (value[i + 1] - value[i]) + edge_policy = policy[i] + t * (policy[i + 1] - policy[i]) + if edge_value > best_value: + best_value, best_policy = float(edge_value), float(edge_policy) + return (best_value, best_policy) if best_value > -np.inf else None + + +def _resolve_tie( + branches: list[tuple[float, np.ndarray, np.ndarray, np.ndarray]], + tied: list[tuple[float, tuple[float, float]]], + x_query: float, + tol: float, +) -> tuple[float, float, float]: + """Break an exact-value tie right-continuously: the branch winning just right. + + Probe each tied branch a hair to the right of the crossing; the one with the + larger value there carries the published policy. If the crossing sits at the + common right edge (no branch is defined further right), fall back to the + lowest segment label for determinism. + """ + label_to_branch = {b[0]: b for b in branches} + eps = _RIGHT_EPS * max(1.0, abs(x_query)) + best_label, best_policy, best_right = None, np.nan, -np.inf + for label, (_value, policy) in tied: + probed = _branch_at(label_to_branch[label], x_query + eps, tol) + right_value = probed[0] if probed is not None else -np.inf + if right_value > best_right: + best_right, best_label, best_policy = right_value, label, policy + if best_label is None or best_right == -np.inf: + # All tied branches end at this query: pick the lowest label deterministically. + label, (_value, policy) = min(tied, key=lambda item: item[0]) + return label, policy, _value + return best_label, best_policy, dict(tied)[best_label][0] + + +def exact_envelope( + *, + endog_grid: np.ndarray, + value: np.ndarray, + policy: np.ndarray, + segment_id: np.ndarray, + x_query: np.ndarray, + tol: float = 1e-12, +) -> tuple[np.ndarray, np.ndarray, np.ndarray]: + """Exact branch-aware upper-envelope value and policy at the query points. + + Return `(env_value, env_policy, winner)` aligned with `x_query`. At each query + the envelope value is the exact maximum, over the branches defined there, of + the branch's piecewise-linear value; the policy is the winning branch's + interpolated policy and `winner` its **segment label** (not a list index). + `tol` only classifies ties β€” it never lowers the reported maximum. An exact + value tie breaks right-continuously (the branch winning just to the right), + matching the kernel's `side="right"` read. A query outside every branch's + range yields `NaN` value/policy and winner `-1`. + """ + branches = _branches( + endog_grid=endog_grid, value=value, policy=policy, segment_id=segment_id + ) + xq = np.asarray(x_query, dtype=float) + env_value = np.full(xq.shape, np.nan) + env_policy = np.full(xq.shape, np.nan) + winner = np.full(xq.shape, -1.0) + + for k, x_point in enumerate(xq): + evaluated = [ + (branch[0], result) + for branch in branches + if (result := _branch_at(branch, float(x_point), tol)) is not None + ] + if not evaluated: + continue + # Exact maximum first; tolerance only groups the tie set around it. + max_value = max(result[0] for _label, result in evaluated) + tied = [ + (label, result) + for label, result in evaluated + if result[0] >= max_value - tol + ] + if len(tied) == 1: + win_label, (_win_value, win_policy) = tied[0] + else: + win_label, win_policy, _win_value = _resolve_tie( + branches, tied, float(x_point), tol + ) + env_value[k] = max_value + env_policy[k] = win_policy + winner[k] = win_label + return env_value, env_policy, winner + + +def envelope_event_points( + *, + endog_grid: np.ndarray, + value: np.ndarray, + policy: np.ndarray, + segment_id: np.ndarray, +) -> np.ndarray: + """Return an event-complete set of query abscissae for the envelope. + + Certifying a whole envelope by sampling can miss an arbitrarily narrow winning + interval between samples. The events that can change the envelope winner are + the branch vertices and the pairwise edge intersections; testing each event + plus an interior point of every resulting interval is sufficient. Return the + sorted unique union of all vertices, all pairwise edge-crossing abscissae, and + the midpoints between consecutive events. + """ + branches = _branches( + endog_grid=endog_grid, value=value, policy=policy, segment_id=segment_id + ) + events: set[float] = set() + edges: list[tuple[float, float, float, float]] = [] + for _label, x, v, _p in branches: + events.update(float(xi) for xi in x) + for i in range(x.size - 1): + edge = (float(x[i]), float(v[i]), float(x[i + 1]), float(v[i + 1])) + edges.append(edge) + + for ax0, av0, ax1, av1 in edges: + if ax1 == ax0: + continue + a_slope = (av1 - av0) / (ax1 - ax0) + for bx0, bv0, bx1, bv1 in edges: + if bx1 == bx0: + continue + b_slope = (bv1 - bv0) / (bx1 - bx0) + if a_slope == b_slope: + continue + cross = (bv0 - av0 + a_slope * ax0 - b_slope * bx0) / (a_slope - b_slope) + in_a = min(ax0, ax1) <= cross <= max(ax0, ax1) + in_b = min(bx0, bx1) <= cross <= max(bx0, bx1) + if in_a and in_b: + events.add(float(cross)) + + ordered = sorted(events) + midpoints = [(a + b) / 2.0 for a, b in pairwise(ordered)] + return np.array(sorted(set(ordered) | set(midpoints))) diff --git a/tests/solution/_rfc_2d_host.py b/tests/solution/_rfc_2d_host.py new file mode 100644 index 000000000..86a2391bb --- /dev/null +++ b/tests/solution/_rfc_2d_host.py @@ -0,0 +1,179 @@ +"""Host (NumPy/SciPy) reference for the multidimensional Roof-top Cut (RFC). + +This is the off-device ground truth for the DS-2024 multidimensional RFC backend +(Dobrescu & Shanker 2024, their Box 1). It reproduces the reference implementation +`akshayshanker/InverseDCDP/RFC/RFCSimple.py` that produced the paper's RFC numbers: +a k-nearest-neighbour, radius-masked tangent-dominance delete, followed by a +Delaunay barycentric publish. The JAX kernel and on-device publisher are validated +against this module; it is never on a solve path. + +The cut, per candidate $i$ over its $k-1$ strict KD-tree neighbours $j$, deletes $j$ +iff all three hold: + +- $j$ lies below $i$'s tangent plane: $v_j - v_i < \\nabla v_i \\cdot (x_j - x_i)$; +- a policy jump separates them, using policy column 0 as the selector: + $|\\,\\lVert\\sigma_j - \\sigma_i\\rVert / \\lVert x_j - x_i\\rVert\\,| > \\bar J$; +- they are neighbours within the radius: $\\lVert x_j - x_i\\rVert < \\rho$. + +The deleted set is the union of such $j$ over all $i$. The reference tuning constants +are $\\bar J = 1 + 10^{-10}$, $\\rho = 0.5$, $k = 5$. +""" + +import numpy as np +from scipy.spatial import Delaunay, KDTree + +# Reference tuning constants, verbatim from RFCSimple.py / RFC.py. +J_BAR_DEFAULT = 1.0 + 1e-10 +RADIUS_DEFAULT = 0.5 +K_DEFAULT = 5 + + +def rfc_delete_mask( + *, + states: np.ndarray, + supgradients: np.ndarray, + values: np.ndarray, + policies: np.ndarray, + j_bar: float = J_BAR_DEFAULT, + radius: float = RADIUS_DEFAULT, + k: int = K_DEFAULT, +) -> np.ndarray: + """Return a boolean keep-mask for the candidate cloud (True = survives the cut). + + Args: + states: Candidate post-decision states, shape `(n, d)`. + supgradients: Value supgradient at each candidate, shape `(n, d)`. + values: Candidate value, shape `(n,)`. + policies: Candidate policy vectors, shape `(n, dp)`; the jump selector uses + column 0 only, matching the reference's `sigma[:, [0]]`. + j_bar: Policy-jump threshold $\\bar J$. + radius: Neighbour distance threshold $\\rho$. + k: Number of KD-tree neighbours (including self) to query. + + Returns: + Boolean array of shape `(n,)`; `True` for surviving (kept) candidates. + """ + states = np.asarray(states, dtype=float) + supgradients = np.asarray(supgradients, dtype=float) + values = np.asarray(values, dtype=float) + selector = np.asarray(policies, dtype=float)[:, 0] + n = states.shape[0] + + keep = np.ones(n, dtype=bool) + if n <= 1: + return keep + + k_eff = min(k, n) + tree = KDTree(states) + dd, idx = tree.query(states, k=k_eff) + dd = np.atleast_2d(dd) + idx = np.atleast_2d(idx) + # Drop self (column 0); clip any out-of-range fill index (KDTree returns n on + # under-full queries) to the last valid point, where the inf distance disables it. + neigh = idx[:, 1:].copy() + neigh_dist = dd[:, 1:] + neigh[neigh >= n] = n - 1 + + for i in range(n): + for col in range(neigh.shape[1]): + j = neigh[i, col] + dist = neigh_dist[i, col] + if not np.isfinite(dist) or dist >= radius: + continue + delta_x = states[j] - states[i] + tangent = float(delta_x @ supgradients[i]) + below_tangent = (values[j] - values[i]) < tangent + policy_jump = abs(abs(selector[j] - selector[i]) / dist) > j_bar + if below_tangent and policy_jump: + keep[j] = False + return keep + + +def rfc_publish( + *, + survivor_states: np.ndarray, + survivor_values: np.ndarray, + survivor_policies: np.ndarray, + target_states: np.ndarray, +) -> tuple[np.ndarray, np.ndarray]: + """Publish value and policy at target states by Delaunay barycentric interpolation. + + Mirrors the reference's `interpolateEGM`: a `scipy.spatial.Delaunay` triangulation + of the survivor cloud, linear (barycentric) interpolation inside the convex hull, + and a nearest-survivor fallback for targets outside it. Barycentric weights + reproduce survivor values exactly at survivor locations. + + Args: + survivor_states: Surviving candidate states, shape `(s, d)`. + survivor_values: Surviving candidate values, shape `(s,)`. + survivor_policies: Surviving candidate policy vectors, shape `(s, dp)`. + target_states: Query states, shape `(t, d)`. + + Returns: + Tuple of `(values, policies)`: interpolated value `(t,)` and policy `(t, dp)`. + """ + survivor_states = np.asarray(survivor_states, dtype=float) + survivor_values = np.asarray(survivor_values, dtype=float) + survivor_policies = np.asarray(survivor_policies, dtype=float) + target_states = np.asarray(target_states, dtype=float) + + tri = Delaunay(survivor_states) + simplex = tri.find_simplex(target_states) + + n_targets = target_states.shape[0] + n_policies = survivor_policies.shape[1] + values = np.empty(n_targets, dtype=float) + policies = np.empty((n_targets, n_policies), dtype=float) + + tree = KDTree(survivor_states) + + for t in range(n_targets): + s = simplex[t] + if s < 0: + # Outside the convex hull: nearest-survivor fallback. + _, nearest = tree.query(target_states[t], k=1) + values[t] = survivor_values[nearest] + policies[t] = survivor_policies[nearest] + continue + vertices = tri.simplices[s] + transform = tri.transform[s] + d = target_states.shape[1] + bary = transform[:d] @ (target_states[t] - transform[d]) + weights = np.append(bary, 1.0 - bary.sum()) + values[t] = float(weights @ survivor_values[vertices]) + policies[t] = weights @ survivor_policies[vertices] + return values, policies + + +def rfc_envelope_host( + *, + states: np.ndarray, + supgradients: np.ndarray, + values: np.ndarray, + policies: np.ndarray, + target_states: np.ndarray, + j_bar: float = J_BAR_DEFAULT, + radius: float = RADIUS_DEFAULT, + k: int = K_DEFAULT, +) -> tuple[np.ndarray, np.ndarray, np.ndarray]: + """Run the full host RFC: cut the cloud, then publish at the target states. + + Returns: + Tuple of `(keep_mask, published_values, published_policies)`. + """ + keep = rfc_delete_mask( + states=states, + supgradients=supgradients, + values=values, + policies=policies, + j_bar=j_bar, + radius=radius, + k=k, + ) + published_values, published_policies = rfc_publish( + survivor_states=np.asarray(states, dtype=float)[keep], + survivor_values=np.asarray(values, dtype=float)[keep], + survivor_policies=np.asarray(policies, dtype=float)[keep], + target_states=target_states, + ) + return keep, published_values, published_policies diff --git a/tests/solution/test_app2_branch_aware_vfi.py b/tests/solution/test_app2_branch_aware_vfi.py new file mode 100644 index 000000000..7016144fc --- /dev/null +++ b/tests/solution/test_app2_branch_aware_vfi.py @@ -0,0 +1,127 @@ +"""Branch-aware VFI oracle pins the comparator-ordering gap to the (S, s) band. + +The DS App.2 discrete-housing model is solved two ways in Table 3 β€” grid-search VFI +(brute) and DC-EGM β€” and the two value functions differ. These tests use the +host-side branch-aware VFI oracle to attribute that difference precisely: + +- the oracle's *standard* mode (`I[max_d V_d]`, interpolate the already-maximized + next value array) reproduces pylcm's brute solve, so the oracle faithfully + represents the VFI comparator; +- differencing the oracle's standard and branch-aware modes isolates the pure + comparator-ordering term `I[max_d V_d] - max_d I[V_d] >= 0`. That term is non- + negative everywhere and strictly positive *only* in the low-wealth (S, s) band + where the next-period housing choice switches across a liquid bracket. On the + liquid interior the two comparators agree exactly. + +So the comparator-ordering effect is real but confined to the (S, s) switch cells, +which sit in the borrowing-constrained low-wealth region the Table 3 accuracy score +excludes. It does *not* account for the dcegm-vs-brute disagreement on the scored +interior β€” that is DC-EGM's own savings-grid and durable-corner discretization, +a separate effect with the opposite locus. +""" + +import numpy as np +import pytest + +from tests.solution._branch_aware_vfi_oracle import solve_branch_aware_vfi +from tests.test_models.ds_app2_housing_fues import build_model, build_params + +# Low-wealth nodes the Table 3 accuracy score excludes (steep-CES VFI floor); the +# (S, s) switch cells live here. The liquid interior starts above this band. +N_LOW_NODES = 12 + + +@pytest.mark.parametrize( + ("n_grid", "n_housing", "n_consumption", "n_periods"), [(12, 4, 60, 3)] +) +def test_standard_vfi_oracle_reproduces_brute( + n_grid: int, n_housing: int, n_consumption: int, n_periods: int +): + """The oracle's standard mode matches pylcm's brute solve cell for cell. + + Running the oracle with `branch_aware=False` reproduces the grid-search VFI the + `"brute"` variant runs: it interpolates the already-maximized next value array + (`I[max_d V_d]`) on the same liquid, housing, wage, and consumption grids. Every + period and regime agrees up to floating-point precision, so the oracle is a + faithful stand-in for the VFI comparator. + """ + brute = build_model( + variant="brute", + n_grid=n_grid, + n_housing=n_housing, + n_consumption=n_consumption, + n_periods=n_periods, + ) + solution = brute.solve(params=build_params(variant="brute"), log_level="off") + oracle = solve_branch_aware_vfi( + branch_aware=False, + n_grid=n_grid, + n_housing=n_housing, + n_consumption=n_consumption, + n_periods=n_periods, + ) + + for period in sorted(solution): + for regime, brute_raw in solution[period].items(): + brute_V = np.asarray(brute_raw) + oracle_V = oracle.value[period][regime] + if oracle_V.ndim == 3: + # Oracle stores the working regime as (wage, housing, liquid); pylcm + # orders it (housing, wage, liquid). + oracle_V = np.transpose(oracle_V, (1, 0, 2)) + finite = np.isfinite(brute_V) & np.isfinite(oracle_V) + np.testing.assert_allclose(oracle_V[finite], brute_V[finite], atol=5e-3) + + +@pytest.mark.parametrize( + ("n_grid", "n_housing", "n_consumption", "n_periods"), [(40, 5, 400, 5)] +) +def test_comparator_ordering_localizes_to_ss_band( + n_grid: int, n_housing: int, n_consumption: int, n_periods: int +): + """The comparator-ordering gap is non-negative and confined to the (S, s) band. + + Standard VFI interpolates the already-maximized next value array + (`I[max_d V_d]`); branch-aware VFI interpolates each next-housing-choice branch + and maxes after (`max_d I[V_d]`). A linear interpolant of a maximum dominates the + maximum of the interpolants, so the standard value sits at or above the branch- + aware value everywhere, with strict inequality only where the winning next-housing + choice switches inside a liquid bracket β€” the (S, s) inaction band. Those cells + lie in the low-wealth band the Table 3 score excludes, so the liquid interior + shows exactly zero gap: the comparator ordering does not touch the scored region. + """ + standard = solve_branch_aware_vfi( + branch_aware=False, + n_grid=n_grid, + n_housing=n_housing, + n_consumption=n_consumption, + n_periods=n_periods, + ) + branch_aware = solve_branch_aware_vfi( + branch_aware=True, + n_grid=n_grid, + n_housing=n_housing, + n_consumption=n_consumption, + n_periods=n_periods, + ) + + scored_working_periods = [0, 1] + saw_strict_gap = False + for period in scored_working_periods: + gap = standard.value[period]["working"] - branch_aware.value[period]["working"] + + # Ordering: standard VFI never falls below branch-aware VFI. + assert gap.min() >= -1e-9 + + # Localization: the strict gap lives only in the low-wealth (S, s) band; the + # liquid interior (and the high-wealth edge) carry no comparator gap at all. + interior_and_above = gap[..., N_LOW_NODES:] + np.testing.assert_allclose(interior_and_above, 0.0, atol=1e-9) + + if gap.max() > 1e-3: + saw_strict_gap = True + ss_band = gap[..., :N_LOW_NODES] + assert ss_band.max() == gap.max() + + # The effect is genuinely present somewhere in the (S, s) band. + assert saw_strict_gap diff --git a/tests/solution/test_backend_oracle_parity.py b/tests/solution/test_backend_oracle_parity.py new file mode 100644 index 000000000..ffd853438 --- /dev/null +++ b/tests/solution/test_backend_oracle_parity.py @@ -0,0 +1,127 @@ +"""Parity of every upper-envelope backend against the exact branch-aware oracle. + +The four production backends (FUES, RFC, LTM, MSS) must agree with the +independent host-side oracle on cases their algorithm is supposed to handle. +This closes the review's gap that MSS/LTM/RFC had no dedicated independent +oracle β€” they were cross-checked only against each other and a dense VFI on +solved values, never against an exact envelope on the candidate row itself. + +The clean certification here is a *strictly dominated* second branch: one branch +lies entirely below the other over their overlap, so the correct envelope deletes +the dominated points with no crossing insertion β€” something every backend (even +the deletion-only RFC/LTM) must get right. Crossing-insertion cases where the +backends legitimately differ (RFC/LTM only delete points) are covered separately. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.egm.interp import interp_on_padded_grid +from _lcm.egm.upper_envelope.fues import refine_envelope as refine_fues +from _lcm.egm.upper_envelope.ltm import refine_envelope as refine_ltm +from _lcm.egm.upper_envelope.mss import refine_envelope as refine_mss +from _lcm.egm.upper_envelope.rfc import refine_envelope as refine_rfc +from tests.solution._envelope_oracle import exact_envelope + + +def _run_backend(backend, *, endog_grid, policy, value, marginal_utility, n_refined): + """Refine one candidate row with the named backend via its native signature.""" + if backend == "fues": + return refine_fues( + endog_grid=endog_grid, policy=policy, value=value, n_refined=n_refined + ) + if backend == "rfc": + return refine_rfc( + endog_grid=endog_grid, + policy=policy, + value=value, + marginal_utility=marginal_utility, + n_refined=n_refined, + search_radius=n_refined, + jump_thresh=2.0, + ) + if backend == "ltm": + return refine_ltm( + endog_grid=endog_grid, policy=policy, value=value, n_refined=n_refined + ) + return refine_mss( + endog_grid=endog_grid, policy=policy, value=value, n_refined=n_refined + ) + + +@pytest.mark.parametrize("backend", ["fues", "rfc", "ltm", "mss"]) +def test_backend_deletes_a_strictly_dominated_branch(backend): + """Every backend recovers the dominant branch when the other is strictly below. + + Branch 0 is `V(R) = R` (policy `0.3 R`); branch 1 is `V(R) = R - 1` + (policy 10), strictly below branch 0 at every shared abscissa. The exact + envelope is branch 0, with all of branch 1 deleted. This is pure dominance β€” + no crossing insertion β€” so every backend, including the deletion-only RFC and + LTM, must reproduce the oracle. + """ + seg0_x = [0.0, 1.0, 2.0, 3.0] + seg1_x = [0.0, 1.0, 2.0, 3.0] + endog_grid = jnp.asarray(seg0_x + seg1_x) + value = jnp.asarray(seg0_x + [x - 1.0 for x in seg1_x]) + policy = jnp.asarray([0.3 * x for x in seg0_x] + [10.0 for _ in seg1_x]) + marginal_utility = jnp.ones_like(endog_grid) # both branches have slope 1 + segment_id = np.array([0, 0, 0, 0, 1, 1, 1, 1], dtype=float) + + grid, policy_out, value_out, _n = _run_backend( + backend, + endog_grid=endog_grid, + policy=policy, + value=value, + marginal_utility=marginal_utility, + n_refined=32, + ) + + x_query = jnp.linspace(0.0, 3.0, 13) + got_value = np.asarray( + interp_on_padded_grid(x_query=x_query, xp=grid, fp=value_out) + ) + got_policy = np.asarray( + interp_on_padded_grid(x_query=x_query, xp=grid, fp=policy_out) + ) + oracle_value, oracle_policy, _winner = exact_envelope( + endog_grid=np.asarray(endog_grid), + value=np.asarray(value), + policy=np.asarray(policy), + segment_id=segment_id, + x_query=np.asarray(x_query), + ) + + np.testing.assert_allclose(got_value, oracle_value, atol=1e-6) + np.testing.assert_allclose(got_policy, oracle_policy, atol=1e-6) + + +@pytest.mark.parametrize("backend", ["fues", "rfc", "ltm", "mss"]) +def test_backend_is_identity_on_a_single_concave_branch(backend): + """On a single concave branch every backend returns that branch's interpolant. + + A concave, increasing single branch has no dominated points and no crossings, + so the refined envelope must equal the input function β€” the simplest possible + certification, which every backend must pass. + """ + endog_grid = jnp.asarray([0.0, 1.0, 2.0, 3.0, 4.0]) + value = jnp.asarray([0.0, 1.0, 1.7, 2.2, 2.5]) # concave, increasing + policy = jnp.asarray([0.0, 0.6, 1.0, 1.3, 1.5]) + # Supgradient = local slope, falling (concave). + marginal_utility = jnp.asarray([1.0, 0.85, 0.6, 0.45, 0.3]) + + grid, _policy_out, value_out, _n = _run_backend( + backend, + endog_grid=endog_grid, + policy=policy, + value=value, + marginal_utility=marginal_utility, + n_refined=16, + ) + + x_query = jnp.linspace(0.0, 4.0, 17) + got_value = np.asarray( + interp_on_padded_grid(x_query=x_query, xp=grid, fp=value_out) + ) + expected = np.interp(np.asarray(x_query), np.asarray(endog_grid), np.asarray(value)) + np.testing.assert_allclose(got_value, expected, atol=1e-6) diff --git a/tests/solution/test_backward_induction.py b/tests/solution/test_backward_induction.py index 3698d9a7f..bc6dde135 100644 --- a/tests/solution/test_backward_induction.py +++ b/tests/solution/test_backward_induction.py @@ -10,6 +10,8 @@ from _lcm.regime_building.max_Q_over_a import get_max_Q_over_a from _lcm.regime_building.ndimage import map_coordinates from _lcm.solution.backward_induction import solve +from _lcm.solution.contract import PeriodKernel +from _lcm.solution.solvers import _GridSearchPeriodKernel from _lcm.typing import MaxQOverAFunction, StateOrActionName from _lcm.utils.logging import get_logger from lcm.ages import AgeGrid @@ -19,15 +21,26 @@ class MockSolutionPhase: """Mock SolutionPhase with only the attributes solve() reads.""" - max_Q_over_a: dict[int, MaxQOverAFunction] + period_kernels: dict[int, PeriodKernel] _base_state_action_space: StateActionSpace grids: MappingProxyType[StateOrActionName, Grid] compute_intermediates: dict = dataclasses.field(default_factory=dict) + continuation_template: None = None def state_action_space(self, regime_params): # noqa: ARG002 return self._base_state_action_space +def _grid_search_period_kernels( + *, max_Q_over_a: dict[int, MaxQOverAFunction], regime_name: str +) -> dict[int, PeriodKernel]: + """Wrap per-period grid-search cores in their uniform period adapters.""" + return { + period: _GridSearchPeriodKernel(core=core, regime_name=regime_name) + for period, core in max_Q_over_a.items() + } + + class MockRegime(Regime): """Mock Regime with only the attributes required by solve(). @@ -130,14 +143,17 @@ def _Q_and_F( regime = MockRegime( solution=MockSolutionPhase( - max_Q_over_a={0: max_Q_over_a, 1: max_Q_over_a}, + period_kernels=_grid_search_period_kernels( + max_Q_over_a={0: max_Q_over_a, 1: max_Q_over_a}, + regime_name="default", + ), _base_state_action_space=state_action_space, grids=MappingProxyType({}), ), active_periods=[0, 1], ) - solution = solve( + solution, _sim_policies = solve( flat_params=MappingProxyType({"default": flat_params}), ages=AgeGrid(start=0, stop=2, step="Y"), regimes=MappingProxyType({"default": regime}), @@ -191,14 +207,17 @@ def _Q_and_F(a, c, b, d, next_regime_to_V_arr, period, age): # noqa: ARG001 regime = MockRegime( solution=MockSolutionPhase( - max_Q_over_a={0: max_Q_over_a, 1: max_Q_over_a}, + period_kernels=_grid_search_period_kernels( + max_Q_over_a={0: max_Q_over_a, 1: max_Q_over_a}, + regime_name="default", + ), _base_state_action_space=state_action_space, grids=MappingProxyType({}), ), active_periods=[0, 1], ) - got = solve( + got, _sim_policies = solve( flat_params=MappingProxyType({"default": MappingProxyType({})}), ages=AgeGrid(start=0, stop=2, step="Y"), regimes=MappingProxyType({"default": regime}), diff --git a/tests/solution/test_cell_locator.py b/tests/solution/test_cell_locator.py new file mode 100644 index 000000000..6ab452ec1 --- /dev/null +++ b/tests/solution/test_cell_locator.py @@ -0,0 +1,355 @@ +"""Point-in-quad location on a curvilinear image mesh. + +The inverse-Euler step of the two-continuous-state EGM foundation maps a +regular post-decision grid in $(a, b)$ onto an irregular quadrilateral mesh in +endogenous current-state space $(m, n)$ β€” one quad per source cell, with fixed +product topology. To read a continuation on a regular target $(m, n)$ grid, the +locator must, for each target point, find the source quad that contains it and +the bilinear coordinates $(\\xi, \\eta) \\in [0, 1]^2$ inside that quad, then read +a bilinear value and gradient there. + +These tests pin the behavior that two naive shortcuts get wrong: + +- Two independent 1-D searches on the marginal image coordinates do **not** + locate the cell in a coupled monotone image (the shear case). +- A nonzero constant-sign Jacobian gives only *local* invertibility; a folded + image (positive Jacobian everywhere, yet not globally one-to-one) must be + rejected by the geometry gate, not silently mislocated. +""" + +import jax.numpy as jnp +import numpy as np +import pytest +from scipy.interpolate import LinearNDInterpolator + +from _lcm.egm.cell_locator import ( + locate_in_quad_mesh, + read_bilinear, + validate_quad_mesh, +) +from lcm.exceptions import PyLCMError +from tests.conftest import X64_ENABLED + +# Bilinear reads solve a per-cell 2x2 system, so their accuracy is a small +# multiple of the float eps of the active precision. +_ATOL = 1e-9 if X64_ENABLED else 1e-5 + + +def _affine_image(a, b, matrix, shift=(0.0, 0.0)): + """Image coordinates of an affine map on a product grid of `a` x `b`.""" + a_grid, b_grid = jnp.meshgrid(jnp.asarray(a), jnp.asarray(b), indexing="ij") + m = matrix[0][0] * a_grid + matrix[0][1] * b_grid + shift[0] + n = matrix[1][0] * a_grid + matrix[1][1] * b_grid + shift[1] + return m, n + + +def _values_on_nodes(m_image, n_image, func): + """Sample a scalar field on the image nodes (host-side reference truth).""" + return func(np.asarray(m_image), np.asarray(n_image)) + + +def _host_brute_locate(m_image, n_image, query): + """Brute point-in-quad scan returning the containing cell, or None. + + Uses the same inverse-bilinear test the locator uses, but in plain NumPy, + so it is an independent oracle for which cell the query lands in. + """ + m_image = np.asarray(m_image) + n_image = np.asarray(n_image) + n_i, n_j = m_image.shape[0] - 1, m_image.shape[1] - 1 + for i in range(n_i): + for j in range(n_j): + xi, eta = _host_inverse_bilinear(m_image, n_image, i, j, query) + if xi is None: + continue + if -1e-9 <= xi <= 1 + 1e-9 and -1e-9 <= eta <= 1 + 1e-9: + return (i, j, xi, eta) + return None + + +def _host_inverse_bilinear(m_image, n_image, i, j, query): + """Solve the cell's inverse-bilinear map for `query` via Newton (host).""" + corners_m = np.array( + [m_image[i, j], m_image[i + 1, j], m_image[i, j + 1], m_image[i + 1, j + 1]] + ) + corners_n = np.array( + [n_image[i, j], n_image[i + 1, j], n_image[i, j + 1], n_image[i + 1, j + 1]] + ) + xi, eta = 0.5, 0.5 + for _ in range(50): + weights = np.array( + [(1 - xi) * (1 - eta), xi * (1 - eta), (1 - xi) * eta, xi * eta] + ) + residual = np.array( + [corners_m @ weights - query[0], corners_n @ weights - query[1]] + ) + d_xi = np.array([-(1 - eta), (1 - eta), -eta, eta]) + d_eta = np.array([-(1 - xi), -xi, (1 - xi), xi]) + jac = np.array( + [ + [corners_m @ d_xi, corners_m @ d_eta], + [corners_n @ d_xi, corners_n @ d_eta], + ] + ) + if abs(np.linalg.det(jac)) < 1e-14: + return None, None + step = np.linalg.solve(jac, residual) + xi, eta = xi - step[0], eta - step[1] + if np.max(np.abs(step)) < 1e-12: + break + return xi, eta + + +# Identity and affine meshes recover the inverse exactly. + + +@pytest.mark.parametrize( + ("matrix", "query", "expected_cell", "expected_xi_eta"), + [ + ([[1.0, 0.0], [0.0, 1.0]], (0.25, 0.75), (0, 1), (0.5, 0.5)), + ([[2.0, 0.0], [0.0, 3.0]], (0.5, 2.25), (0, 1), (0.5, 0.5)), + ], +) +def test_locate_affine_recovers_exact_cell_and_coords( + matrix, query, expected_cell, expected_xi_eta +): + """On an axis-aligned affine mesh the locator returns the exact cell and coords.""" + nodes = jnp.array([0.0, 0.5, 1.0]) + m_image, n_image = _affine_image(nodes, nodes, matrix) + located = locate_in_quad_mesh( + m_image=m_image, + n_image=n_image, + queries=jnp.array([query]), + ) + np.testing.assert_array_equal( + np.array([located.cell_i[0], located.cell_j[0]]), np.array(expected_cell) + ) + np.testing.assert_allclose( + np.array([located.xi[0], located.eta[0]]), + np.array(expected_xi_eta), + atol=_ATOL, + ) + + +def test_locate_shear_picks_coupled_cell_not_marginal_cell(): + """The shear $F(a,b)=(a+0.4b, b+0.4a)$ defeats independent marginal search. + + For query $(m,n)=(0.72, 0.96)$ the true inverse is $a=0.4, b=0.8$, which lies + in source cell $(0, 1)$ with bilinear coordinates $(\\xi, \\eta)=(0.8, 0.6)$. + Two independent 1-D searches on the marginal image coordinates land in a + different $a$-cell; the locator must return the coupled cell. + """ + nodes = jnp.array([0.0, 0.5, 1.0]) + m_image, n_image = _affine_image(nodes, nodes, [[1.0, 0.4], [0.4, 1.0]]) + located = locate_in_quad_mesh( + m_image=m_image, + n_image=n_image, + queries=jnp.array([[0.72, 0.96]]), + ) + np.testing.assert_array_equal( + np.array([located.cell_i[0], located.cell_j[0]]), np.array([0, 1]) + ) + np.testing.assert_allclose( + np.array([located.xi[0], located.eta[0]]), + np.array([0.8, 0.6]), + atol=_ATOL, + ) + + +def test_locate_shear_marginal_search_would_have_failed(): + """Independent marginal `searchsorted` lands in the wrong $a$-cell here. + + Documents *why* the coupled test is necessary: the marginal-image search the + locator must avoid picks a different cell than the true containing one. + """ + nodes = np.array([0.0, 0.5, 1.0]) + a_grid, b_grid = np.meshgrid(nodes, nodes, indexing="ij") + m_image = a_grid + 0.4 * b_grid + n_image = b_grid + 0.4 * a_grid + # Marginal image coordinates along each axis at the opposite-axis origin. + m_marginal = m_image[:, 0] + n_marginal = n_image[0, :] + marginal_i = int(np.searchsorted(m_marginal, 0.72) - 1) + marginal_j = int(np.searchsorted(n_marginal, 0.96) - 1) + # The true containing cell is (0, 1); marginal search disagrees on the i-axis. + assert (marginal_i, marginal_j) != (0, 1) + + +def _curvilinear_image(a, b): + """A smooth, monotone, fold-free curvilinear deformation of a product grid. + + Strictly increasing in each coordinate with a coupled cross-term, so it is a + genuine non-affine quad mesh while staying globally one-to-one on the domain. + """ + a_grid, b_grid = np.meshgrid(np.asarray(a), np.asarray(b), indexing="ij") + m = a_grid + 0.15 * b_grid + 0.1 * a_grid * b_grid + n = b_grid + 0.12 * a_grid + 0.08 * a_grid**2 + return jnp.asarray(m), jnp.asarray(n) + + +def _curvilinear_query(q_a, q_b): + """Image of host-side source points under the curvilinear deformation.""" + qm = q_a + 0.15 * q_b + 0.1 * q_a * q_b + qn = q_b + 0.12 * q_a + 0.08 * q_a**2 + return qm, qn + + +@pytest.mark.parametrize("n_nodes", [9, 17]) +def test_locate_curvilinear_value_matches_host_interpolator(n_nodes): + """Located bilinear value matches a host Delaunay interpolator on dense probes. + + On a smooth fold-free curvilinear mesh, the located cell and its + inverse-bilinear value read agree with `scipy`'s `LinearNDInterpolator` + (built on the same nodes) within tolerance over many random interior probes. + """ + nodes = np.linspace(0.0, 1.0, n_nodes) + m_image, n_image = _curvilinear_image(nodes, nodes) + + def field(m, n): + return 1.0 + 0.7 * m + 0.5 * n + + node_values = jnp.asarray(_values_on_nodes(m_image, n_image, field)) + + points = np.column_stack([np.asarray(m_image).ravel(), np.asarray(n_image).ravel()]) + host = LinearNDInterpolator(points, np.asarray(node_values).ravel()) + + rng = np.random.default_rng(20240601) + # Sample queries well inside the image to avoid Delaunay convex-hull edge cases. + q_a = rng.uniform(0.1, 0.9, size=400) + q_b = rng.uniform(0.1, 0.9, size=400) + qm, qn = _curvilinear_query(q_a, q_b) + queries = jnp.asarray(np.column_stack([qm, qn])) + + located = locate_in_quad_mesh(m_image=m_image, n_image=n_image, queries=queries) + read = read_bilinear(node_values=node_values, located=located) + + host_values = host(np.column_stack([qm, qn])) + finite = np.isfinite(host_values) + assert finite.mean() > 0.9 + np.testing.assert_allclose( + np.asarray(read.value)[finite], host_values[finite], atol=2e-3 + ) + + +def test_locate_curvilinear_value_converges_under_refinement(): + """The bilinear value read converges to the true field as the mesh refines.""" + + def field(m, n): + return np.sin(1.3 * m) + np.cos(0.9 * n) + 0.4 * m * n + + rng = np.random.default_rng(7) + q_a = rng.uniform(0.15, 0.85, size=200) + q_b = rng.uniform(0.15, 0.85, size=200) + qm, qn = _curvilinear_query(q_a, q_b) + queries = jnp.asarray(np.column_stack([qm, qn])) + truth = field(qm, qn) + + errors = [] + for n_nodes in (9, 33): + nodes = np.linspace(0.0, 1.0, n_nodes) + m_image, n_image = _curvilinear_image(nodes, nodes) + node_values = jnp.asarray(_values_on_nodes(m_image, n_image, field)) + located = locate_in_quad_mesh(m_image=m_image, n_image=n_image, queries=queries) + read = read_bilinear(node_values=node_values, located=located) + errors.append(float(np.max(np.abs(np.asarray(read.value) - truth)))) + + # Roughly second-order: a 4x finer mesh cuts the worst-case error by >5x. + assert errors[1] < errors[0] / 5.0 + + +def test_locate_curvilinear_gradient_converges_under_refinement(): + """The bilinear gradient read converges to the true gradient under refinement. + + The value and the gradient are two *separate* bilinear approximants: the + gradient is read from the same cell map but is its own quantity, so its + convergence is asserted independently of the value's. + """ + + def field(m, n): + return 0.6 * m**2 + 0.5 * n**2 + 0.3 * m * n + + def grad_field(m, n): + return np.column_stack([1.2 * m + 0.3 * n, 1.0 * n + 0.3 * m]) + + rng = np.random.default_rng(11) + q_a = rng.uniform(0.2, 0.8, size=150) + q_b = rng.uniform(0.2, 0.8, size=150) + qm, qn = _curvilinear_query(q_a, q_b) + queries = jnp.asarray(np.column_stack([qm, qn])) + truth = grad_field(qm, qn) + + errors = [] + for n_nodes in (9, 33): + nodes = np.linspace(0.0, 1.0, n_nodes) + m_image, n_image = _curvilinear_image(nodes, nodes) + node_values = jnp.asarray(_values_on_nodes(m_image, n_image, field)) + located = locate_in_quad_mesh(m_image=m_image, n_image=n_image, queries=queries) + read = read_bilinear(node_values=node_values, located=located) + grad = np.column_stack([np.asarray(read.grad_m), np.asarray(read.grad_n)]) + errors.append(float(np.max(np.abs(grad - truth)))) + + assert errors[1] < errors[0] / 3.0 + + +def test_locate_matches_host_brute_scan_on_curvilinear_cell_choice(): + """The located cell index agrees with an independent host brute-scan.""" + nodes = np.linspace(0.0, 1.0, 11) + m_image, n_image = _curvilinear_image(nodes, nodes) + + rng = np.random.default_rng(99) + q_a = rng.uniform(0.1, 0.9, size=60) + q_b = rng.uniform(0.1, 0.9, size=60) + qm, qn = _curvilinear_query(q_a, q_b) + queries = jnp.asarray(np.column_stack([qm, qn])) + + located = locate_in_quad_mesh(m_image=m_image, n_image=n_image, queries=queries) + + for k in range(queries.shape[0]): + host = _host_brute_locate(m_image, n_image, (qm[k], qn[k])) + assert host is not None + assert (int(located.cell_i[k]), int(located.cell_j[k])) == (host[0], host[1]) + + +# The geometry gate rejects a folded image (F6). + + +def test_geometry_gate_accepts_valid_curvilinear_mesh(): + """A smooth fold-free monotone mesh passes the geometry gate without error.""" + nodes = np.linspace(0.0, 1.0, 7) + m_image, n_image = _curvilinear_image(nodes, nodes) + # Must not raise. + validate_quad_mesh(m_image=m_image, n_image=n_image) + + +def test_geometry_gate_rejects_folded_polar_mesh(): + """The polar map $F(a,b)=(e^a\\cos b, e^a\\sin b)$ wraps and must be rejected. + + Its Jacobian is positive everywhere, so a constant-sign-Jacobian check would + pass it, yet it folds over itself across $b \\in [0, 4\\pi]$ β€” the image is not + globally one-to-one. The geometry gate must detect the fold (sign-flipped / + overlapping cells) and raise rather than let the locator mislocate. + """ + a = np.linspace(0.0, 1.0, 6) + b = np.linspace(0.0, 4 * np.pi, 24) + a_grid, b_grid = np.meshgrid(a, b, indexing="ij") + m_image = jnp.asarray(np.exp(a_grid) * np.cos(b_grid)) + n_image = jnp.asarray(np.exp(a_grid) * np.sin(b_grid)) + with pytest.raises(PyLCMError, match=r"fold|orient|overlap"): + validate_quad_mesh(m_image=m_image, n_image=n_image) + + +def test_geometry_gate_rejects_self_intersecting_cell(): + """A single bow-tie (self-intersecting) quad fails the gate. + + Twisting one interior corner of an otherwise-regular grid produces a + non-convex, self-crossing quad; the signed-area / orientation check must + catch it. + """ + nodes = np.linspace(0.0, 1.0, 3) + a_grid, b_grid = np.meshgrid(nodes, nodes, indexing="ij") + m_image = np.array(a_grid, dtype=float) + n_image = np.array(b_grid, dtype=float) + # Twist one interior corner so the adjacent cells become bow-ties. + m_image[1, 1], n_image[1, 1] = -0.5, -0.5 + with pytest.raises(PyLCMError, match=r"fold|orient|overlap"): + validate_quad_mesh(m_image=jnp.asarray(m_image), n_image=jnp.asarray(n_image)) diff --git a/tests/solution/test_ds_housing_keeper.py b/tests/solution/test_ds_housing_keeper.py new file mode 100644 index 000000000..03f41e5ad --- /dev/null +++ b/tests/solution/test_ds_housing_keeper.py @@ -0,0 +1,135 @@ +"""DC-EGM feasibility of the Dobrescu-Shanker housing keeper regime. + +The keeper (no-house-trade) branch of the Dobrescu-Shanker housing model is a +plain 1-D DC-EGM problem: liquid assets is the Euler state, consumption the +continuous action, and housing a passive continuous state. Utility reads the +passive housing state directly through the `alpha * log(housing)` service flow. + +The cornerstone here is that the DC-EGM envelope-condition guard rejects +utility reading the *Euler* state but allows utility reading a *passive* +state β€” so the keeper is expressible today. That guard is asserted against the +validator directly (no kernel trace, no solve). The full GPU solve is gated +off the local box, which OOMs on a DC-EGM solve. + +The oracle pair is the DC-EGM keeper and its brute-force (GridSearch) twin, +which solves the same economics with housing as a regular fixed continuous +state and consumption a grid-searched action. The two value functions agree up +to the brute solver's consumption-grid resolution; the value-parity test that +asserts this is GPU-gated like the solve above. +""" + +from types import MappingProxyType + +import numpy as np +import pytest + +from _lcm.egm.validation import validate_dcegm_regimes +from _lcm.regime_building.finalize import finalize_regimes +from tests.test_models.ds_housing_keeper import ( + HOUSING_GRID, + LIQUID_ASSETS_GRID, + build_model, + build_params, + build_working_regime, + dead, +) + + +def _finalized_keeper_regimes() -> MappingProxyType: + """Finalize the keeper regimes as the model build does, without solving. + + Finalization injects the default Bellman aggregator `H` and validates + completeness β€” the exact form the DC-EGM validator runs against inside + `Model` construction. + """ + return finalize_regimes( + user_regimes={"keeper": build_working_regime(), "dead": dead}, + derived_categoricals=MappingProxyType({}), + ) + + +def test_dcegm_accepts_utility_reading_passive_housing(): + """DC-EGM admits utility reading a passive continuous state directly. + + The keeper's utility reads the passive housing state through + `alpha * log(housing)`. The DC-EGM envelope condition forbids utility + reaching the *Euler* state (here `liquid_assets`), but a passive state is + allowed, so `validate_dcegm_regimes` accepts the keeper regimes. + """ + validate_dcegm_regimes(user_regimes=_finalized_keeper_regimes()) + + +@pytest.mark.skip(reason="gpu-01 only: DC-EGM solve OOMs the local box") +def test_housing_keeper_solves_to_finite_values(): + """The keeper model solves to finite, housing-monotone value functions. + + A larger housing stock yields a larger within-period service flow + `alpha * log(housing)`, so for every income node and liquid-asset node the + solved value function is strictly increasing in the passive housing state. + """ + solution = build_model().solve(params=build_params(), log_level="debug") + + n_liquid = LIQUID_ASSETS_GRID.to_jax().shape[0] + n_housing = HOUSING_GRID.to_jax().shape[0] + n_income = 2 + + for period in sorted(solution)[:-1]: + keeper_V = np.asarray(solution[period]["keeper"]) + # V axes are (income, liquid_assets, housing); housing is the passive + # trailing axis. + assert keeper_V.shape == (n_income, n_liquid, n_housing) + assert np.all(np.isfinite(keeper_V)), f"period={period}" + housing_increments = np.diff(keeper_V, axis=-1) + assert np.all(housing_increments > 0.0), f"period={period}" + + +@pytest.mark.skip(reason="gpu-01 only: DC-EGM solve OOMs the local box") +def test_housing_keeper_dcegm_matches_brute(): + """The keeper DC-EGM value function matches its brute-force twin. + + Both variants solve the same keeper economics β€” utility + `CRRA(consumption) + alpha * log(housing)`, the budget + `(1 + r) * liquid_assets + (1 + r_H) * housing * (1 - delta) + income`, a + fixed house, and Markov income β€” over the same liquid-asset, housing, and + income grids. The DC-EGM keeper inverts the Euler equation on the liquid + state with housing riding along as a passive axis; the brute twin grid- + searches consumption with housing a regular fixed continuous state and the + liquid-asset law reading consumption directly. + + DC-EGM is exact up to interpolation, so it is the more accurate solver; the + brute value function is bounded above by it and approaches it as the + consumption grid refines. The two therefore agree to the brute solver's + consumption-grid resolution. The lowest liquid-asset nodes are excluded: + there the coarse consumption grid makes brute force itself unreliable (the + same exclusion the passive-state DC-EGM oracle uses). + """ + dcegm_solution = build_model("dcegm").solve( + params=build_params("dcegm"), log_level="debug" + ) + brute_solution = build_model("brute").solve( + params=build_params("brute"), log_level="debug" + ) + + n_liquid = LIQUID_ASSETS_GRID.to_jax().shape[0] + n_housing = HOUSING_GRID.to_jax().shape[0] + n_income = 2 + expected_shape = (n_income, n_liquid, n_housing) + + n_brute_unstable_nodes = 2 + for period in sorted(brute_solution)[:-1]: + dcegm_V = np.asarray(dcegm_solution[period]["keeper"]) + brute_V = np.asarray(brute_solution[period]["keeper"]) + assert dcegm_V.shape == brute_V.shape == expected_shape, f"period={period}" + # DC-EGM is the more accurate solver: it dominates brute up to the + # interpolation error the tolerance below absorbs. + assert np.all( + dcegm_V[:, n_brute_unstable_nodes:, :] + >= brute_V[:, n_brute_unstable_nodes:, :] - 1e-2 + ), f"period={period}" + np.testing.assert_allclose( + dcegm_V[:, n_brute_unstable_nodes:, :], + brute_V[:, n_brute_unstable_nodes:, :], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) diff --git a/tests/solution/test_ds_pension_benchmark.py b/tests/solution/test_ds_pension_benchmark.py new file mode 100644 index 000000000..84b76eb55 --- /dev/null +++ b/tests/solution/test_ds_pension_benchmark.py @@ -0,0 +1,69 @@ +"""The DS pension comparison harness emits a G2EGM accuracy/time row and a table. + +The harness solves the DS pension model by G2EGM, times the solve, and pools the +working consumption Euler errors into the accuracy fields of a benchmark row β€” the +G2EGM column of the Dobrescu--Shanker pension comparison table. The row's accuracy +improves as the liquid grid refines, and `format_comparison_table` renders the rows. +""" + +from _lcm.egm.ds_pension_benchmark import ( + MethodBenchmark, + benchmark_ds_pension_methods, + benchmark_g2egm_ds_pension, + benchmark_rfc_ds_pension, + format_comparison_table, +) + + +def test_g2egm_benchmark_reports_sane_time_and_euler_errors(): + """The G2EGM row has a positive solve time and finite interior Euler errors.""" + row = benchmark_g2egm_ds_pension(n_liquid=12) + assert row.method == "G2EGM" + assert row.solve_seconds > 0.0 + assert row.euler_error_median_log10 < -1.0 # better than 10% on the interior + assert row.euler_error_p90_log10 < row.euler_error_median_log10 + 1.0 + + +def test_g2egm_benchmark_accuracy_improves_with_liquid_refinement(): + """Refining the liquid grid lowers the pooled Euler error.""" + coarse = benchmark_g2egm_ds_pension(n_liquid=12) + fine = benchmark_g2egm_ds_pension(n_liquid=24) + assert fine.euler_error_median_log10 < coarse.euler_error_median_log10 - 0.2 + + +def test_rfc_benchmark_reports_sane_time_and_euler_errors(): + """The RFC row has a positive solve time and finite interior Euler errors.""" + row = benchmark_rfc_ds_pension(n_liquid=12) + assert row.method == "RFC" + assert row.solve_seconds > 0.0 + assert row.euler_error_median_log10 < -1.0 # better than 10% on the interior + assert row.euler_error_p90_log10 < row.euler_error_median_log10 + 1.0 + + +def test_methods_runner_returns_a_g2egm_and_an_rfc_row(): + """The comparison runner emits one G2EGM and one RFC row at the same resolution.""" + rows = benchmark_ds_pension_methods(n_liquid=12) + assert [r.method for r in rows] == ["G2EGM", "RFC"] + assert all(r.n_liquid == 12 for r in rows) + table = format_comparison_table(rows) + assert "G2EGM" in table + assert "RFC" in table + assert table.count("\n") == 3 # header, rule, two rows + + +def test_format_comparison_table_renders_each_row(): + """The table renders a header and one line per method row.""" + rows = [ + MethodBenchmark( + method="G2EGM", + n_liquid=12, + n_pension=10, + solve_seconds=0.3, + euler_error_median_log10=-1.4, + euler_error_p90_log10=-0.9, + ) + ] + table = format_comparison_table(rows) + assert "method" in table + assert "G2EGM" in table + assert table.count("\n") == 2 # header, rule, one row diff --git a/tests/solution/test_ds_pension_driver.py b/tests/solution/test_ds_pension_driver.py new file mode 100644 index 000000000..0cc989dea --- /dev/null +++ b/tests/solution/test_ds_pension_driver.py @@ -0,0 +1,94 @@ +"""The G2EGM driver solves the full DS pension lifecycle, matching the brute solve. + +The driver chains the endogenous-grid steps over the whole lifecycle β€” terminal bequest, +1-D retired EGM, the working->retired boundary G2EGM step, and the working->working +G2EGM steps β€” and reproduces the dense grid-search value at every period and regime on +the covered interior. The off-grid top-pension hole advances one pension column inward +per backward working period, so the comparison excludes the boundary layer, which +thickens toward the first period. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.egm.ds_pension_driver import solve_ds_pension_g2egm +from tests.test_models.deterministic.ds_pension import get_model, get_params + +_N_PERIODS = 5 +_RETIREMENT_PERIOD = 3 + +_LIQUID_GRID = jnp.linspace(0.1, 20.0, 12) +_PENSION_GRID = jnp.linspace(0.0, 15.0, 10) +_PARAMS = { + "discount_factor": 0.98, + "crra": 2.0, + "work_disutility": 0.25, + "match_rate": 0.10, + "return_liquid": 0.02, + "return_pension": 0.04, + "wage": 1.0, + "retirement_income": 0.50, + "pension_payout_return": 1.04, +} + + +def _solve_both(): + egm = solve_ds_pension_g2egm( + n_periods=_N_PERIODS, + retirement_period=_RETIREMENT_PERIOD, + liquid_grid=_LIQUID_GRID, + pension_grid=_PENSION_GRID, + a_grid=jnp.linspace(0.0, 20.0, 18), + b_grid=jnp.linspace(0.0, 30.0, 16), + consumption_grid=jnp.linspace(0.1, 20.0, 18), + savings_grid=jnp.linspace(0.0, 20.0, 40), + **_PARAMS, + ) + brute = get_model(n_periods=_N_PERIODS, n_consumption=200).solve( + params=get_params(), log_level="off" + ) + return egm, brute + + +# Working interior, period by period. Two boundary layers are excluded: +# - Pension (columns): the off-grid top-pension hole advances one column inward per +# backward working period (boundary p2 -> p1 -> p0), so each earlier period drops one +# more column. +# - Liquid (rows): the steep low-wealth value is unresolvable on a coarse linear grid, +# and the error compounds over the working chain; it collapses under grid refinement +# (~60% at 12 liquid points, ~2% at 48), confirming a resolution limit, not a gap. +_WORKING_INTERIOR = {2: np.s_[3:, :9], 1: np.s_[3:, :8], 0: np.s_[3:, :7]} +# Retired is 1-D; exclude the borrowing-constrained low-liquid boundary layer. +_RETIRED_INTERIOR = np.s_[2:] + + +@pytest.mark.parametrize("period", [0, 1, 2]) +def test_driver_working_value_matches_brute_on_the_pension_interior(period): + """Each working period's value matches the brute solve where the grid covers.""" + egm, brute = _solve_both() + sl = _WORKING_INTERIOR[period] + egm_v = np.asarray(egm[period]["working"])[sl] + brute_v = np.asarray(brute[period]["working"])[sl] + assert np.isfinite(egm_v).all() + rel = np.abs(egm_v - brute_v) / np.abs(brute_v) + assert np.median(rel) < 0.03 + assert np.percentile(rel, 90) < 0.15 + + +def test_driver_retired_value_matches_brute_on_the_liquid_interior(): + """The retired value matches the brute solve on the unconstrained interior.""" + egm, brute = _solve_both() + egm_v = np.asarray(egm[_RETIREMENT_PERIOD]["retired"])[_RETIRED_INTERIOR] + brute_v = np.asarray(brute[_RETIREMENT_PERIOD]["retired"])[_RETIRED_INTERIOR] + rel = np.abs(egm_v - brute_v) / np.abs(brute_v) + assert np.median(rel) < 0.01 + assert np.max(rel) < 0.05 + + +def test_driver_returns_every_period_and_regime(): + """The driver publishes working/retired/dead values for the whole lifecycle.""" + egm, _brute = _solve_both() + assert set(egm[0]) == {"working"} + assert set(egm[_RETIREMENT_PERIOD]) == {"retired"} + assert set(egm[_N_PERIODS - 1]) == {"dead"} diff --git a/tests/solution/test_ds_pension_oracle.py b/tests/solution/test_ds_pension_oracle.py new file mode 100644 index 000000000..e1d71105d --- /dev/null +++ b/tests/solution/test_ds_pension_oracle.py @@ -0,0 +1,64 @@ +"""The DS pension benchmark solves as a faithful three-regime lifecycle oracle. + +The model is the dense-grid brute-force reference the 2-D EGM kernel is validated +against, so its own solve must be correct: the lifecycle regimes appear in the right +periods, the terminal bequest is the closed-form CRRA value, the working value rises in +both assets, and the comparative statics (a more generous employer match, higher +retirement income) move value in the right direction. +""" + +import numpy as np +import pytest + +from tests.conftest import X64_ENABLED +from tests.test_models.deterministic.ds_pension import get_model, get_params + +# The closed-form comparison is float-eps-limited at the active precision. +_RTOL = 1e-12 if X64_ENABLED else 1e-5 + + +def _solve(**param_overrides): + model = get_model() + params = get_params(**param_overrides) + return model.solve(params=params, log_level="off") + + +def test_lifecycle_regimes_appear_in_the_right_periods(): + """Working is 2-D for the working periods, retired is 1-D, then the agent dies.""" + solution = _solve() + assert np.asarray(solution[0]["working"]).shape == (12, 10) + assert np.asarray(solution[2]["working"]).shape == (12, 10) + assert np.asarray(solution[3]["retired"]).shape == (12,) + assert "working" not in solution[3] + assert "retired" not in solution[4] + + +def test_terminal_bequest_is_the_closed_form_crra_value(): + """The dead regime carries the closed-form CRRA value of liquid, no optimization.""" + solution = _solve(crra=2.0) + liquid_grid = np.linspace(0.1, 20.0, 12) + # CRRA with rho = 2: u(liquid) = liquid**(-1) / (-1) = -1 / liquid. + expected = -1.0 / liquid_grid + np.testing.assert_allclose(np.asarray(solution[4]["dead"]), expected, rtol=_RTOL) + + +def test_working_value_increases_in_both_assets(): + """More liquid wealth and more pension wealth are both weakly valuable.""" + working = np.asarray(_solve()[0]["working"]) + assert np.all(np.diff(working, axis=0) >= -1e-9) + assert np.all(np.diff(working, axis=1) >= -1e-9) + + +def test_more_generous_employer_match_does_not_lower_working_value(): + """A larger match `chi` is a free subsidy on deposits, so value weakly rises.""" + low = np.asarray(_solve(match_rate=0.10)[0]["working"]) + high = np.asarray(_solve(match_rate=0.30)[0]["working"]) + assert np.all(high >= low - 1e-9) + + +@pytest.mark.parametrize(("low_income", "high_income"), [(0.5, 1.0)]) +def test_higher_retirement_income_raises_retired_value(low_income, high_income): + """A richer retirement income strictly raises the retired value function.""" + low = np.asarray(_solve(retirement_income=low_income)[3]["retired"]) + high = np.asarray(_solve(retirement_income=high_income)[3]["retired"]) + assert np.all(high > low) diff --git a/tests/solution/test_ds_pension_rfc_solver.py b/tests/solution/test_ds_pension_rfc_solver.py new file mode 100644 index 000000000..46490ed44 --- /dev/null +++ b/tests/solution/test_ds_pension_rfc_solver.py @@ -0,0 +1,70 @@ +"""`TwoDimEGM(upper_envelope="rfc")` drives the DS pension RFC lifecycle solve. + +The combined-cloud rooftop-cut is selected as the working regime's two-asset upper +envelope by naming `TwoDimEGM(upper_envelope="rfc")` on it. The engine's backward +induction then chains the RFC step across the lifecycle: the working regime uses the +RFC two-asset step (the retirement-boundary period falls back to the G2EGM retiring +step), the retired regime the 1-D `OneAssetEGM`, and the dead regime stays terminal. +The solve publishes every period and regime, and the working value tracks the dense +grid-search brute on the pension interior away from the low-liquid corner (a known RFC +corner-accuracy gap). +""" + +import numpy as np +import pytest + +from lcm import LinSpacedGrid +from lcm.solvers import OneAssetEGM, TwoDimEGM +from tests.test_models.deterministic.ds_pension import get_model, get_params + +_N_PERIODS = 5 +_RETIREMENT_PERIOD = 3 + +_A_GRID = LinSpacedGrid(start=0.0, stop=20.0, n_points=18) +_B_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=16) +_CONSUMPTION_GRID = LinSpacedGrid(start=0.1, stop=20.0, n_points=18) +_SAVINGS_GRID = LinSpacedGrid(start=0.0, stop=20.0, n_points=40) + +# Pension interior, away from the top-pension boundary and the low-liquid corner. The +# corner-accuracy gap propagates one liquid row inward per backward period (as the +# top-pension hole does), so the interior floor rises one row earlier each period back. +_WORKING_INTERIOR = {2: np.s_[3:, :9], 1: np.s_[4:, :8], 0: np.s_[5:, :7]} + + +def _rfc_model(): + return get_model( + n_periods=_N_PERIODS, + solvers={ + "working": TwoDimEGM( + a_grid=_A_GRID, + b_grid=_B_GRID, + consumption_grid=_CONSUMPTION_GRID, + upper_envelope="rfc", + ), + "retired": OneAssetEGM(savings_grid=_SAVINGS_GRID), + }, + ) + + +def test_rfc_solver_publishes_every_period_and_regime(): + """The RFC-driven lifecycle solve publishes working/retired/dead end-to-end.""" + egm = _rfc_model().solve(params=get_params(), log_level="off") + assert "working" in egm[0] + assert "retired" in egm[_RETIREMENT_PERIOD] + assert "dead" in egm[_N_PERIODS - 1] + + +@pytest.mark.parametrize("period", [0, 1, 2]) +def test_rfc_solver_working_value_tracks_brute_on_the_pension_interior(period): + """Each working period's RFC value tracks brute on the covered pension interior.""" + egm = _rfc_model().solve(params=get_params(), log_level="off") + brute = get_model(n_periods=_N_PERIODS, n_consumption=200).solve( + params=get_params(), log_level="off" + ) + sl = _WORKING_INTERIOR[period] + egm_v = np.asarray(egm[period]["working"])[sl] + brute_v = np.asarray(brute[period]["working"])[sl] + assert np.isfinite(egm_v).all() + rel = np.abs(egm_v - brute_v) / np.abs(brute_v) + assert np.median(rel) < 0.08 + assert np.percentile(rel, 90) < 0.20 diff --git a/tests/solution/test_ds_pension_two_dim_egm_solver.py b/tests/solution/test_ds_pension_two_dim_egm_solver.py new file mode 100644 index 000000000..8f2736775 --- /dev/null +++ b/tests/solution/test_ds_pension_two_dim_egm_solver.py @@ -0,0 +1,85 @@ +"""`model.solve(solver=TwoDimEGM(...))` drives the DS pension G2EGM solve. + +The two-asset G2EGM kernel is a prime-time pylcm `Solver`: naming it on the working +regime makes `model.solve()` reproduce the standalone driver's lifecycle solve through +the engine's backward induction. The working regime uses `TwoDimEGM`, the retired +regime the 1-D `OneAssetEGM`, and the dead regime stays terminal. The solved value +matches the dense grid-search brute on the same covered interior the standalone driver +matches: the working pension interior (excluding the off-grid top-pension boundary +layer that thickens backward, and the steep low-liquid rows) and the retired +unconstrained liquid interior. +""" + +import numpy as np +import pytest + +from lcm import LinSpacedGrid +from lcm.solvers import OneAssetEGM, TwoDimEGM +from tests.test_models.deterministic.ds_pension import get_model, get_params + +_N_PERIODS = 5 +_RETIREMENT_PERIOD = 3 + +# Same post-decision grids the standalone driver test uses. +_A_GRID = LinSpacedGrid(start=0.0, stop=20.0, n_points=18) +_B_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=16) +_CONSUMPTION_GRID = LinSpacedGrid(start=0.1, stop=20.0, n_points=18) +_SAVINGS_GRID = LinSpacedGrid(start=0.0, stop=20.0, n_points=40) + +# Same interior masks the standalone driver test asserts on. +_WORKING_INTERIOR = {2: np.s_[3:, :9], 1: np.s_[3:, :8], 0: np.s_[3:, :7]} +_RETIRED_INTERIOR = np.s_[2:] + + +def _solver_model(): + """The DS pension model with the G2EGM/1-D-EGM prime-time solvers.""" + return get_model( + n_periods=_N_PERIODS, + solvers={ + "working": TwoDimEGM( + a_grid=_A_GRID, + b_grid=_B_GRID, + consumption_grid=_CONSUMPTION_GRID, + ), + "retired": OneAssetEGM(savings_grid=_SAVINGS_GRID), + }, + ) + + +def _solve_both(): + egm = _solver_model().solve(params=get_params(), log_level="off") + brute = get_model(n_periods=_N_PERIODS, n_consumption=200).solve( + params=get_params(), log_level="off" + ) + return egm, brute + + +@pytest.mark.parametrize("period", [0, 1, 2]) +def test_solver_working_value_matches_brute_on_the_pension_interior(period): + """Each working period's solved value matches brute where the grid covers.""" + egm, brute = _solve_both() + sl = _WORKING_INTERIOR[period] + egm_v = np.asarray(egm[period]["working"])[sl] + brute_v = np.asarray(brute[period]["working"])[sl] + assert np.isfinite(egm_v).all() + rel = np.abs(egm_v - brute_v) / np.abs(brute_v) + assert np.median(rel) < 0.03 + assert np.percentile(rel, 90) < 0.15 + + +def test_solver_retired_value_matches_brute_on_the_liquid_interior(): + """The retired value matches brute on the unconstrained liquid interior.""" + egm, brute = _solve_both() + egm_v = np.asarray(egm[_RETIREMENT_PERIOD]["retired"])[_RETIRED_INTERIOR] + brute_v = np.asarray(brute[_RETIREMENT_PERIOD]["retired"])[_RETIRED_INTERIOR] + rel = np.abs(egm_v - brute_v) / np.abs(brute_v) + assert np.median(rel) < 0.01 + assert np.max(rel) < 0.05 + + +def test_solver_publishes_every_period_and_regime(): + """The solver-driven solve publishes working/retired/dead over the lifecycle.""" + egm, _brute = _solve_both() + assert "working" in egm[0] + assert "retired" in egm[_RETIREMENT_PERIOD] + assert "dead" in egm[_N_PERIODS - 1] diff --git a/tests/solution/test_egm_app2_housing_fues.py b/tests/solution/test_egm_app2_housing_fues.py new file mode 100644 index 000000000..5db84c405 --- /dev/null +++ b/tests/solution/test_egm_app2_housing_fues.py @@ -0,0 +1,124 @@ +"""EGM-FUES for the DS-2026 App.2 housing model matches VFI. + +Application 2's Table 3 compares two solution methods for the continuous-housing +model: EGM-FUES and NEGM. This test validates the **EGM-FUES** column, which +pylcm builds by discretising the next-housing choice onto the housing grid and +treating it as a discrete action, so the inner liquid-asset DC-EGM plus the +discrete-choice FUES upper envelope reproduces the paper's 1-D-FUES-nested-over- +the-housing-grid solve (its Box 2). + +The oracle is the grid-search (VFI) twin of the same discrete-housing model +(same liquid, wage, and housing grids), which solves the identical Bellman +problem by brute force. On most of the liquid-wealth interior the two value +functions agree up to grid resolution. They diverge on a minority of cells in the +durable-rich corner (high held housing, high liquid), where DC-EGM sits slightly +below the VFI twin: the DC-EGM savings-grid interpolation of a kinked value +function plus the liquid top-edge extrapolation, a discretization gap that shrinks +only partially as the savings and liquid grids refine. So the test asserts *bulk* +agreement (the mean is tight and the overwhelming majority of interior cells fall +within a small tolerance), not exact equality at every cell. + +The borrowing-constrained low-wealth region (where VFI is forced to the +consumption floor and the steep CES utility diverges) and the top edge-clamp +nodes are excluded outright. +""" + +from typing import Literal + +import numpy as np +import pytest + +from tests.test_models.ds_app2_housing_fues import build_model, build_params + +# Small construction-scale grids: a single local solve stays fast. The wealth +# interior excludes the constrained low-wealth nodes (steep-CES VFI floor) and +# the top edge-clamp nodes so the head-to-head lives where both solvers are +# well-defined. +N_LIQUID = 40 +N_HOUSING = 5 +N_PERIODS = 5 +N_CONSUMPTION = 400 +N_LOW_NODES = 12 +N_HIGH_NODES = 8 + +# Bulk-agreement thresholds. The value function is O(35) on the interior, so a +# 0.3 cell tolerance is sub-percent. The two solvers disagree on a minority of +# interior cells, concentrated in the durable-rich corner (high held housing, +# high liquid). There DC-EGM sits slightly *below* the grid-search VFI: it is the +# DC-EGM savings-grid interpolation of a kinked value function plus the liquid +# top-edge extrapolation, a discretization gap that shrinks only partially as the +# savings and liquid grids refine. The branch-aware VFI oracle confirms this is +# not a comparator-ordering artifact β€” the `I[max_d V_d]` vs `max_d I[V_d]` +# ordering term is identically zero on this interior (the next-housing choice only +# switches in the excluded low-wealth (S, s) band; see +# `test_app2_branch_aware_vfi.py`). The tolerance accommodates the durable-corner +# discretization while the smooth-region mean stays sub-percent; the +# paper-comparable metric is the simulated consumption Euler error, which is +# unaffected. +MEAN_TOL = 0.18 +CELL_TOL = 0.30 +MIN_FRACTION_WITHIN = 0.82 + + +@pytest.mark.parametrize("upper_envelope", ["fues"]) +def test_app2_fues_matches_vfi_on_liquid_interior( + upper_envelope: Literal["fues", "mss", "ltm", "rfc"], +): + """App.2 EGM-FUES agrees with its VFI twin on the liquid interior in bulk. + + The discrete-choice DC-EGM selects the optimal next-housing level by the FUES + upper envelope over the housing grid; the VFI twin does the same by brute + grid search. The mean interior value difference is sub-percent and the large + majority of interior cells fall within the cell tolerance β€” the EGM-FUES + solve is correct. The remaining cells sit in the durable-rich corner (high + held housing, high liquid), where DC-EGM sits slightly below the VFI twin + through its savings-grid interpolation of a kinked value function and the + liquid top-edge extrapolation. This is a discretization gap, not a + comparator-ordering artifact: the branch-aware VFI oracle confirms the + `I[max_d V_d]` vs `max_d I[V_d]` ordering term is identically zero on this + interior (`test_app2_branch_aware_vfi.py`). + """ + dcegm_model = build_model( + variant="dcegm", + n_grid=N_LIQUID, + n_housing=N_HOUSING, + n_periods=N_PERIODS, + n_consumption=N_CONSUMPTION, + upper_envelope=upper_envelope, + ) + brute_model = build_model( + variant="brute", + n_grid=N_LIQUID, + n_housing=N_HOUSING, + n_periods=N_PERIODS, + n_consumption=N_CONSUMPTION, + ) + dcegm_solution = dcegm_model.solve( + params=build_params(variant="dcegm"), log_level="debug" + ) + brute_solution = brute_model.solve( + params=build_params(variant="brute"), log_level="debug" + ) + + interior = slice(N_LOW_NODES, N_LIQUID - N_HIGH_NODES) + scored_periods = [ + period + for period in sorted(brute_solution)[:-1] + if "working" in brute_solution[period] + ] + assert scored_periods + + differences = [] + for period in scored_periods: + brute_V = np.asarray(brute_solution[period]["working"]) + dcegm_V = np.asarray(dcegm_solution[period]["working"]) + # V axes: (wage, housing, liquid). + assert brute_V.shape == dcegm_V.shape + differences.append( + np.abs(dcegm_V[..., interior] - brute_V[..., interior]).ravel() + ) + difference = np.concatenate(differences) + + assert float(difference.mean()) < MEAN_TOL + fraction_within = float((difference <= CELL_TOL).mean()) + assert fraction_within >= MIN_FRACTION_WITHIN diff --git a/tests/solution/test_egm_app3_discrete_housing.py b/tests/solution/test_egm_app3_discrete_housing.py new file mode 100644 index 000000000..eb9bbe619 --- /dev/null +++ b/tests/solution/test_egm_app3_discrete_housing.py @@ -0,0 +1,83 @@ +"""DC-EGM for the DS-2026 App.3 discrete-housing model matches VFI. + +Application 3 reaches its terminal `dead` regime by a choice-driven discrete +transition: `next_housing = housing_choice`, so the held housing next period is +the chosen housing code, not the parent's current housing. The terminal bequest +carry is dead's utility on its own (housing, wealth) grid; the DC-EGM parent +selects the carry row at the *chosen* next-housing by indexing dead's housing +axis with `housing_choice` β€” the same action-indexed gather the non-terminal +cross-regime read uses. + +The oracle is the grid-search (VFI) twin of the same model (same wealth, wage, +and housing grids), which solves the identical Bellman problem by brute force. +The DC-EGM and VFI value functions must agree on the wealth interior, where both +solvers are well-defined (VFI undershoots the borrowing-constrained low-wealth +region and edge-clamps the wealth grid's ceiling). +""" + +from typing import Literal + +import numpy as np +import pytest + +from tests.test_models.ds_app3_discrete_housing import build_model, build_params + +# Small construction-scale grids: a single local solve stays fast. The wealth +# interior excludes the constrained low-wealth nodes (VFI undershoots) and the +# top edge-clamp nodes (VFI saturates at the grid ceiling) so the head-to-head +# lives where both solvers are well-defined. +N_ASSETS = 60 +N_WAGE_NODES = 3 +N_PERIODS = 5 +N_CONSUMPTION = 80 +N_LOW_NODES = 14 +N_HIGH_NODES = 14 + + +@pytest.mark.parametrize("upper_envelope", ["fues"]) +def test_app3_dcegm_matches_vfi_on_wealth_interior( + upper_envelope: Literal["fues", "mss", "ltm", "rfc"], +): + """App.3 DC-EGM matches its VFI twin on the wealth interior, per wage and house. + + A correct action-indexed terminal carry reads dead's bequest at the chosen + next-housing; a wrong (identity) alignment would read the bequest at the + parent's held housing instead, shifting the continuation by the bequest gap + between housing levels and breaking the comparison. Agreement is up to the + VFI consumption-grid resolution. + """ + dcegm_model = build_model( + variant="dcegm", + n_assets=N_ASSETS, + n_wage_nodes=N_WAGE_NODES, + n_periods=N_PERIODS, + n_consumption=N_CONSUMPTION, + upper_envelope=upper_envelope, + ) + brute_model = build_model( + variant="brute", + n_assets=N_ASSETS, + n_wage_nodes=N_WAGE_NODES, + n_periods=N_PERIODS, + n_consumption=N_CONSUMPTION, + ) + dcegm_solution = dcegm_model.solve( + params=build_params(variant="dcegm", n_periods=N_PERIODS), log_level="debug" + ) + brute_solution = brute_model.solve( + params=build_params(variant="brute", n_periods=N_PERIODS), log_level="debug" + ) + + interior = slice(N_LOW_NODES, N_ASSETS - N_HIGH_NODES) + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working"]) + dcegm_V = np.asarray(dcegm_solution[period]["working"]) + # V axes: (housing, wage, assets). + assert brute_V.shape == dcegm_V.shape + np.testing.assert_allclose( + dcegm_V[..., interior], + brute_V[..., interior], + atol=2e-2, + rtol=5e-3, + err_msg=f"period={period}", + ) diff --git a/tests/solution/test_egm_app3_taxed.py b/tests/solution/test_egm_app3_taxed.py new file mode 100644 index 000000000..bc747c8b6 --- /dev/null +++ b/tests/solution/test_egm_app3_taxed.py @@ -0,0 +1,127 @@ +"""DC-EGM/FUES for the DS-2026 App.3 with-tax model matches VFI. + +Application 3's Table 5 adds a piecewise-linear capital-income tax to the +discrete-housing model. The tax `T(a) = B + tau_a*(a - a0)` carries three level +discontinuities β€” up at a=3.87 and a=15, and down by about 0.14 at a=6.97 where +the subsidy bracket resets the offset β€” plus several rate kinks, so the budget is +non-monotone in assets β€” which is exactly why Table 5 compares only FUES (which +resolves the jumps/kinks via the upper envelope) and VFI (grid search), dropping +MSS/LTM. + +The oracle is the grid-search (VFI) twin of the same with-tax model. On the +asset interior the FUES and VFI value functions agree up to grid resolution, with +only a few cells at the tax-bracket boundaries (the jump/kink nodes) disagreeing +more β€” the standard DC-EGM unstable-node pattern. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from tests.conftest import X64_ENABLED +from tests.test_models.ds_app3_discrete_housing import ( + build_model, + build_params, + piecewise_capital_income_tax, +) + +# The bracket-schedule comparison is float-eps-limited at the active precision. +_TAX_ATOL = 1e-9 if X64_ENABLED else 1e-5 + +# Construction-scale grids: a single local solve stays fast. The asset interior +# excludes the constrained low-wealth nodes and the top edge-clamp nodes. +N_ASSETS = 60 +N_WAGE_NODES = 3 +N_PERIODS = 5 +N_CONSUMPTION = 80 +N_LOW_NODES = 14 +N_HIGH_NODES = 14 + +MEAN_TOL = 0.02 +CELL_TOL = 0.05 +MIN_FRACTION_WITHIN = 0.95 + + +@pytest.mark.parametrize( + ("assets", "expected"), + [ + (1.0, 0.0), # tax-free first bracket + (2.35, 0.0114 * (2.35 - 2.20)), # second bracket, B=0 + (4.0, 0.11412 + 0.024 * (4.0 - 3.87)), # post-jump bracket at a=3.87 + (16.0, 0.378968 + 0.0294 * (16.0 - 15.0)), # post-jump bracket at a=15 + (25.0, 0.525968 + 0.0294 * (25.0 - 20.0)), # top bracket + ], +) +def test_piecewise_tax_matches_the_bracket_schedule(assets: float, expected: float): + """`T(a)` returns `B + tau_a*(a - a0)` for the bracket containing `a`.""" + got = float(piecewise_capital_income_tax(jnp.asarray(assets))) + np.testing.assert_allclose(got, expected, atol=_TAX_ATOL) + + +def test_tax_schedule_has_three_level_discontinuities(): + """`T(a)` jumps up at a=3.87 and a=15 and drops down at a=6.97. + + The level jumps at a=3.87 (+0.10) and a=15 (+0.15) raise the tax; the + subsidy bracket `[6.97, 8.36)` resets the offset to 0.05, so `T` drops by + about 0.14 at a=6.97. All three discontinuities make the budget non-monotone + and force the FUES-vs-VFI-only comparison; a continuous schedule would admit + MSS/LTM too. + """ + below_first = float(piecewise_capital_income_tax(jnp.asarray(3.86))) + at_first = float(piecewise_capital_income_tax(jnp.asarray(3.87))) + below_subsidy = float(piecewise_capital_income_tax(jnp.asarray(6.96))) + at_subsidy = float(piecewise_capital_income_tax(jnp.asarray(6.97))) + below_second = float(piecewise_capital_income_tax(jnp.asarray(14.99))) + at_second = float(piecewise_capital_income_tax(jnp.asarray(15.0))) + assert at_first - below_first > 0.05 + assert at_second - below_second > 0.05 + assert at_subsidy - below_subsidy < -0.1 + + +def test_app3_taxed_fues_matches_vfi_on_asset_interior(): + """With taxes, App.3 FUES agrees with its VFI twin on the asset interior. + + FUES resolves the tax jumps and kinks: the mean interior value difference is + tight and the bulk of interior cells fall within a sub-percent tolerance, + with only the tax-bracket-boundary nodes disagreeing more. + """ + dcegm_model = build_model( + variant="dcegm", + n_assets=N_ASSETS, + n_wage_nodes=N_WAGE_NODES, + n_periods=N_PERIODS, + n_consumption=N_CONSUMPTION, + use_taxes=True, + ) + brute_model = build_model( + variant="brute", + n_assets=N_ASSETS, + n_wage_nodes=N_WAGE_NODES, + n_periods=N_PERIODS, + n_consumption=N_CONSUMPTION, + use_taxes=True, + ) + dcegm_solution = dcegm_model.solve( + params=build_params(variant="dcegm", n_periods=N_PERIODS, use_taxes=True), + log_level="debug", + ) + brute_solution = brute_model.solve( + params=build_params(variant="brute", n_periods=N_PERIODS, use_taxes=True), + log_level="debug", + ) + + interior = slice(N_LOW_NODES, N_ASSETS - N_HIGH_NODES) + differences = [] + for period in sorted(brute_solution)[:-1]: + if "working" not in brute_solution[period]: + continue + brute_V = np.asarray(brute_solution[period]["working"]) + dcegm_V = np.asarray(dcegm_solution[period]["working"]) + assert brute_V.shape == dcegm_V.shape + differences.append( + np.abs(dcegm_V[..., interior] - brute_V[..., interior]).ravel() + ) + difference = np.concatenate(differences) + + assert float(difference.mean()) < MEAN_TOL + assert float((difference <= CELL_TOL).mean()) >= MIN_FRACTION_WITHIN diff --git a/tests/solution/test_egm_asset_row_params.py b/tests/solution/test_egm_asset_row_params.py new file mode 100644 index 000000000..f9e7e64c9 --- /dev/null +++ b/tests/solution/test_egm_asset_row_params.py @@ -0,0 +1,499 @@ +"""DC-EGM asset-row savings-stage functions reading model params. + +In asset-row mode (any savings-stage function reads the current Euler state), +the per-exogenous-asset-node solve must evaluate the child `resources` +function and the regime-transition probabilities with the regime's model +params, the lifecycle `age`/`period`, and any solve-phase imputed +intermediates β€” exactly the bindings the brute-force solver supplies. The +asset derivative of a param-dependent, Euler-state-dependent read enters the +published marginal value $dV/dR$ through the continuation's direct Euler-state +channel. + +The oracle for the solved properties is a dense-grid brute-force solve of a +mathematically equivalent spec (same state grids, dense consumption grid, +explicit budget constraint). +""" + +import functools + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.typing import PeriodToRegimeToVArr +from lcm import ( + AgeGrid, + IrregSpacedGrid, + LinSpacedGrid, + MarkovTransition, + Model, + Phased, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM, GridSearch +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + FloatND, + ScalarInt, +) +from lcm_examples.iskhakov_et_al_2017 import dead + +# Number of model periods; the last one is spent in the terminal regime. +N_PERIODS = 4 + +# Wealth band over which the savings-stage smoothstep ramps. At many wealth +# cells the band is well resolved at node resolution, so the build-time +# continuity check admits it. +BAND_START = 30.0 +BAND_WIDTH = 20.0 + +# Survival probability below/above the wealth band. Death is absorbing with +# zero value while continued life is worth several utils, so the value gap +# across targets is material and the probability's wealth slope contributes +# a first-order term to the marginal value inside the band. +SURVIVAL_LOW = 0.55 +SURVIVAL_HIGH = 0.95 + +# Rate of return on wealth β€” the model param the child resources function and +# the means-test intermediate read. +RATE_OF_RETURN = 0.04 + +# Deterministic labor income added to savings in the wealth law; keeps child +# wealth queries away from the grid's lower edge, where the two solvers clamp +# differently. +LABOR_INCOME = 5.0 + +# AIME accrual rate mapping the imputed pension wealth into resources. +PENSION_ACCRUAL = 0.3 + +# 160 wealth nodes: the brute-force oracle interpolates next-period V linearly +# in wealth (a downward bias where V curves), while the DC-EGM carry read uses +# exact slopes; the dense grid keeps that oracle-side bias below the tolerance. +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=100.0, n_points=160) +AIME_GRID = LinSpacedGrid(start=0.0, stop=20.0, n_points=7) + +# The consumption grid covers the maximum resources so the brute-force oracle +# is not artificially capped at high wealth; 4000 points keep the oracle's own +# resolution error below the comparison tolerance. +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=120.0, n_points=4000) + +# Exogenous end-of-period savings grid, cubically clustered toward the +# borrowing limit where the value function curves hardest. +SAVINGS_GRID = IrregSpacedGrid(points=tuple(100.0 * (i / 149) ** 3 for i in range(150))) + +# Lowest wealth nodes excluded from the brute-force comparison: there the +# brute solver leans on consumption choices near its grid start and on coarse +# interpolation where log utility curves hardest. +N_BRUTE_UNSTABLE_NODES = 16 + + +@categorical(ordered=False) +class AssetRowRegimeId: + working_life: ScalarInt + dead: ScalarInt + + +def smoothstep_in_band(countable: FloatND) -> FloatND: + """CΒ² quintic smoothstep rising from 0 to 1 across the band.""" + t = jnp.clip((countable - BAND_START) / BAND_WIDTH, 0.0, 1.0) + return t * t * t * (t * (6.0 * t - 15.0) + 10.0) + + +def utility(consumption: ContinuousAction) -> FloatND: + return jnp.log(consumption) + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_wealth_dcegm(savings: FloatND) -> ContinuousState: + return savings + LABOR_INCOME + + +def next_wealth_brute( + resources: FloatND, consumption: ContinuousAction +) -> ContinuousState: + return resources - consumption + LABOR_INCOME + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where( + age >= final_age_alive, + AssetRowRegimeId.dead, + AssetRowRegimeId.working_life, + ) + + +def _ages() -> AgeGrid: + return AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + + +def _active(age: int) -> bool: + last_age = 40 + (N_PERIODS - 1) * 10 + return age < last_age + + +def _params() -> dict: + return { + "discount_factor": 0.95, + "final_age_alive": 40 + (N_PERIODS - 2) * 10, + "rate_of_return": RATE_OF_RETURN, + } + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, +) + + +def _assert_working_life_V_matches( + *, dcegm_solution: PeriodToRegimeToVArr, brute_solution: PeriodToRegimeToVArr +) -> None: + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + assert brute_V.shape == dcegm_V.shape + flat_dcegm = dcegm_V.reshape(-1, dcegm_V.shape[-1]) + flat_brute = brute_V.reshape(-1, brute_V.shape[-1]) + np.testing.assert_allclose( + flat_dcegm[:, N_BRUTE_UNSTABLE_NODES:], + flat_brute[:, N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +# --- Slice 1: child resources reads a model param -------------------------- + + +def resources_with_rate(wealth: ContinuousState, rate_of_return: float) -> FloatND: + """Cash-on-hand including a capital-income return on current wealth.""" + return wealth * (1.0 + rate_of_return) + + +def survival_of_wealth(wealth: ContinuousState) -> FloatND: + return SURVIVAL_LOW + (SURVIVAL_HIGH - SURVIVAL_LOW) * smoothstep_in_band(wealth) + + +def stay_prob_wealth( + wealth: ContinuousState, age: int, final_age_alive: float +) -> FloatND: + return jnp.where(age >= final_age_alive, 0.0, survival_of_wealth(wealth)) + + +def death_prob_wealth( + wealth: ContinuousState, age: int, final_age_alive: float +) -> FloatND: + return 1.0 - stay_prob_wealth(wealth, age, final_age_alive) + + +def budget_constraint_rate( + consumption: ContinuousAction, wealth: ContinuousState, rate_of_return: float +) -> BoolND: + return consumption <= wealth * (1.0 + rate_of_return) + + +@functools.cache +def _resources_param_model(solver: str) -> Model: + """Self-targeting regime whose resources reads `rate_of_return`.""" + is_dcegm = solver == "dcegm" + working = UserRegime( + transition={ + "working_life": MarkovTransition(stay_prob_wealth), + "dead": MarkovTransition(death_prob_wealth), + }, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute + }, + constraints=({} if is_dcegm else {"budget_constraint": budget_constraint_rate}), + functions=( + { + "utility": utility, + "resources": resources_with_rate, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + } + if is_dcegm + else {"utility": utility, "resources": resources_with_rate} + ), + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=AssetRowRegimeId, + ) + + +def test_child_resources_reading_param_matches_brute_force(): + """A child resources term `wealth * (1 + rate_of_return)` matches brute. + + The regime is solved per exogenous asset node because the survival + probability reads wealth. At each node the child's resources query depends + on the model param `rate_of_return`, so the per-node resources evaluation + must receive it; values agree with the dense-grid brute-force oracle. + """ + params = _params() + dcegm_solution = _resources_param_model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution = _resources_param_model("brute_force").solve( + params=params, log_level="debug" + ) + _assert_working_life_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) + + +# --- Slice 2: regime-transition prob reads a param-dependent intermediate --- + + +def capital_income(wealth: ContinuousState, rate_of_return: float) -> FloatND: + return rate_of_return * wealth + + +def countable_income(capital_income: FloatND) -> FloatND: + return capital_income + + +def share_of_income(countable_income: FloatND) -> FloatND: + return smoothstep_in_band(countable_income / RATE_OF_RETURN) + + +def survival_of_share(share_of_income: FloatND) -> FloatND: + return SURVIVAL_LOW + (SURVIVAL_HIGH - SURVIVAL_LOW) * share_of_income + + +def stay_prob_share( + share_of_income: FloatND, age: int, final_age_alive: float +) -> FloatND: + return jnp.where(age >= final_age_alive, 0.0, survival_of_share(share_of_income)) + + +def death_prob_share( + share_of_income: FloatND, age: int, final_age_alive: float +) -> FloatND: + return 1.0 - stay_prob_share(share_of_income, age, final_age_alive) + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def budget_constraint(consumption: ContinuousAction, wealth: ContinuousState) -> BoolND: + return consumption <= wealth + + +@functools.cache +def _smoothstep_intermediate_model(solver: str, *, rate_is_fixed: bool) -> Model: + """Survival probability reading wealth through a param-dependent chain. + + When `rate_is_fixed`, `rate_of_return` is supplied through `fixed_params` + (partialled at model build and dropped from the live template) rather than + as a free solve param, so the prebuilt asset-row kernel must carry the + partialled qualified param `capital_income__rate_of_return` into the + per-node regime-transition-probability evaluation. + """ + is_dcegm = solver == "dcegm" + intermediates = { + "capital_income": capital_income, + "countable_income": countable_income, + "share_of_income": share_of_income, + } + working = UserRegime( + transition={ + "working_life": MarkovTransition(stay_prob_share), + "dead": MarkovTransition(death_prob_share), + }, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions=( + { + "utility": utility, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + **intermediates, + } + if is_dcegm + else {"utility": utility, "resources": resources, **intermediates} + ), + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + fixed_params = ( + {"working_life": {"capital_income": {"rate_of_return": RATE_OF_RETURN}}} + if rate_is_fixed + else {} + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=AssetRowRegimeId, + fixed_params=fixed_params, + ) + + +@pytest.mark.parametrize("rate_is_fixed", [False, True]) +def test_regime_prob_reading_param_intermediate_matches_brute_force( + rate_is_fixed: bool, # noqa: FBT001 +): + """A survival probability `share <- countable <- capital_income(w, r)` matches. + + The stay probability reads wealth through a param-dependent intermediate + chain (the SSI-smoothstep shape), so the regime is solved per exogenous + asset node. The probability's wealth slope carries the first-order term + $\\partial P_{stay}/\\partial wealth \\cdot EV_{stay}$ into the marginal + value, evaluated with the model param β€” whether `rate_of_return` is a free + solve param or supplied through `fixed_params` (and thus partialled into + the prebuilt asset-row kernel). Values agree with the brute oracle. + """ + params = _params() + if rate_is_fixed: + del params["rate_of_return"] + dcegm_solution = _smoothstep_intermediate_model( + "dcegm", rate_is_fixed=rate_is_fixed + ).solve(params=params, log_level="debug") + brute_solution = _smoothstep_intermediate_model( + "brute_force", rate_is_fixed=rate_is_fixed + ).solve(params=params, log_level="debug") + _assert_working_life_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) + + +# --- Slice 3: Phased-imputed intermediate feeding resources ---------------- + + +PENSION_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=4) + + +def next_aime(aime: ContinuousState) -> ContinuousState: + return aime + + +def pension_wealth_imputed( + aime: ContinuousState, rate_of_return: float +) -> ContinuousState: + """Solve-phase pension wealth imputed from AIME and the return param.""" + return aime * (1.0 + rate_of_return) + + +def next_pension_wealth(pension_wealth: ContinuousState) -> ContinuousState: + return pension_wealth + + +def resources_with_pension( + wealth: ContinuousState, pension_wealth: ContinuousState +) -> FloatND: + return wealth + PENSION_ACCRUAL * pension_wealth + + +def resources_with_pension_brute( + wealth: ContinuousState, aime: ContinuousState, rate_of_return: float +) -> FloatND: + return wealth + PENSION_ACCRUAL * (aime * (1.0 + rate_of_return)) + + +def budget_constraint_pension( + consumption: ContinuousAction, + wealth: ContinuousState, + aime: ContinuousState, + rate_of_return: float, +) -> BoolND: + return consumption <= wealth + PENSION_ACCRUAL * (aime * (1.0 + rate_of_return)) + + +@functools.cache +def _imputed_pension_model(solver: str) -> Model: + """Resources reads a solve-phase imputed pension wealth (from AIME).""" + is_dcegm = solver == "dcegm" + working = UserRegime( + transition={ + "working_life": MarkovTransition(stay_prob_wealth), + "dead": MarkovTransition(death_prob_wealth), + }, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states=( + { + "wealth": WEALTH_GRID, + "aime": AIME_GRID, + "pension_wealth": Phased( + solve=pension_wealth_imputed, simulate=PENSION_GRID + ), + } + if is_dcegm + else {"wealth": WEALTH_GRID, "aime": AIME_GRID} + ), + state_transitions=( + { + "wealth": next_wealth_dcegm, + "aime": next_aime, + "pension_wealth": next_pension_wealth, + } + if is_dcegm + else {"wealth": next_wealth_brute, "aime": next_aime} + ), + constraints=( + {} if is_dcegm else {"budget_constraint": budget_constraint_pension} + ), + functions=( + { + "utility": utility, + "resources": resources_with_pension, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + } + if is_dcegm + else {"utility": utility, "resources": resources_with_pension_brute} + ), + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=AssetRowRegimeId, + ) + + +def test_imputed_pension_wealth_feeding_resources_matches_brute_force(): + """Resources reading a solve-imputed `pension_wealth(aime, r)` matches brute. + + `pension_wealth` is a solve-phase derived function (imputed from the + passive AIME state and the return param), not a grid axis. The per-node + resources DAG computes it from AIME and params rather than demanding it as + a leaf. Values agree with the dense-grid brute-force oracle that inlines + the same imputation. + """ + params = _params() + dcegm_solution = _imputed_pension_model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution = _imputed_pension_model("brute_force").solve( + params=params, log_level="debug" + ) + _assert_working_life_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) diff --git a/tests/solution/test_egm_assets_law_terms.py b/tests/solution/test_egm_assets_law_terms.py new file mode 100644 index 000000000..4d4842932 --- /dev/null +++ b/tests/solution/test_egm_assets_law_terms.py @@ -0,0 +1,612 @@ +"""DC-EGM with additive action-constant terms in the Euler state's law. + +The admitted law shape is `next_wealth = savings + g(...)` per target regime, +where the residual `g` is constant in the continuous action. `g` may read own +discrete states, discrete actions, params, transition-DAG outputs of the same +target β€” and the current Euler state through decision-time functions, which is +evaluated exactly at the exogenous asset nodes (where the brute-force oracle +evaluates it too). + +The oracle for every property is a dense-grid brute-force solve of a +mathematically equivalent spec (same state grids, dense consumption grid, +explicit budget constraint). +""" + +import functools + +import jax.numpy as jnp +import numpy as np + +from _lcm.typing import PeriodToRegimeToVArr +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + LogSpacedGrid, + MarkovTransition, + Model, + Phased, + categorical, + fixed_transition, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM, GridSearch +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteAction, + DiscreteState, + FloatND, + ScalarInt, +) +from lcm_examples.iskhakov_et_al_2017 import dead + +# Number of model periods; the last one is spent in the terminal regime. +N_PERIODS = 4 + +# Health transfer received in bad health, and out-of-pocket costs with and +# without private insurance β€” the discrete-state and discrete-action inputs of +# the additive law term. The net term stays non-negative so child queries do +# not pile onto the wealth grid's lower edge, where the two solvers clamp +# differently. +HEALTH_TRANSFER = 8.0 +OOP_WITH_INSURANCE = 2.0 +OOP_WITHOUT_INSURANCE = 6.0 + +# Utility cost of buying private insurance (premium); keeps the insurance +# choice interior so both rows of the law term are exercised. +INSURANCE_PREMIUM = 0.25 + +# Capital-income supplement: a means-tested transfer with a kinked PHASE-OUT +# (full below the means-test cap, linearly phased out toward zero) plus a +# proportional match β€” the Euler-state dependence of the law term. The +# phase-out keeps the term CONTINUOUS in wealth: a hard cliff +# (`jnp.where(capital_income <= cap, BASE, 0)`) is rejected at model build, +# because a jump in the residual makes the child's value function +# discontinuous and the true policy bunches at the discontinuity β€” a corner +# outside EGM's candidate set. +CAPITAL_RETURN = 0.04 +MEANS_TEST_CAP = 2.0 +PHASE_OUT_END = 3.0 # capital income at which the supplement is fully phased out +BASE_SUPPLEMENT = 5.0 +CAPITAL_MATCH = 0.5 + +# Survival probability per period for the per-target-asymmetry model. +SURVIVAL_RATE = 0.8 + +# Solve-phase pension adjustment for the phase-variant law term. +SOLVE_ADJUSTMENT = 4.0 + +# Pension accrual per unit of next-period AIME for the chained-transition law +# term, and the AIME increment earned by one period of work. +PENSION_ACCRUAL = 0.5 +AIME_GAIN = 0.4 +AIME_MAX = 1.5 + +# 160 wealth nodes: the brute-force oracle interpolates next-period V +# linearly in wealth (a downward bias where V curves), while the DC-EGM carry +# read uses exact slopes; the dense grid keeps that oracle-side bias below +# the comparison tolerance. +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=100.0, n_points=160) +AIME_GRID = LinSpacedGrid(start=0.0, stop=AIME_MAX, n_points=7) +BEQUEST_GRID = LogSpacedGrid(start=0.5, stop=150.0, n_points=200) + +# The consumption grid covers the maximum resources so the brute-force oracle +# is not artificially capped at high wealth; 4000 points keep the oracle's own +# resolution error below the comparison tolerance even at low wealth, where +# the additive law terms shift child queries away from the brute solver's +# interpolation nodes. +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=110.0, n_points=4000) + +# Exogenous end-of-period savings grid, cubically clustered toward the +# borrowing limit where the value function curves hardest. +SAVINGS_GRID = IrregSpacedGrid(points=tuple(100.0 * (i / 149) ** 3 for i in range(150))) + +# Lowest wealth nodes (below wealth ~10) excluded from the brute-force +# comparison: there the brute solver leans on consumption choices near its +# grid start and on coarse interpolation where log utility curves hardest +# (the same exclusion the sibling DC-EGM oracle tests use, in this file's +# denser wealth-grid units). +N_BRUTE_UNSTABLE_NODES = 16 + + +@categorical(ordered=False) +class LawTermRegimeId: + working_life: ScalarInt + dead: ScalarInt + + +@categorical(ordered=False) +class Health: + good: ScalarInt + bad: ScalarInt + + +@categorical(ordered=False) +class Insurance: + skip: ScalarInt + buy: ScalarInt + + +@categorical(ordered=True) +class LaborChoice: + work: ScalarInt + rest: ScalarInt + + +def utility(consumption: ContinuousAction) -> FloatND: + return jnp.log(consumption) + + +def utility_with_premium( + consumption: ContinuousAction, buy_private: DiscreteAction +) -> FloatND: + return jnp.log(consumption) - jnp.where( + buy_private == Insurance.buy, INSURANCE_PREMIUM, 0.0 + ) + + +def utility_with_work( + consumption: ContinuousAction, labor_supply: DiscreteAction +) -> FloatND: + return jnp.log(consumption) - jnp.where(labor_supply == LaborChoice.work, 0.3, 0.0) + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def budget_constraint(consumption: ContinuousAction, wealth: ContinuousState) -> BoolND: + return consumption <= wealth + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where( + age >= final_age_alive, + LawTermRegimeId.dead, + LawTermRegimeId.working_life, + ) + + +def health_net_transfer(health: DiscreteState, buy_private: DiscreteAction) -> FloatND: + oop = jnp.where( + buy_private == Insurance.buy, OOP_WITH_INSURANCE, OOP_WITHOUT_INSURANCE + ) + return jnp.where(health == Health.bad, HEALTH_TRANSFER - oop, 0.0) + + +def capital_supplement(wealth: ContinuousState) -> FloatND: + capital_income = CAPITAL_RETURN * wealth + phase_out_share = jnp.clip( + (PHASE_OUT_END - capital_income) / (PHASE_OUT_END - MEANS_TEST_CAP), 0.0, 1.0 + ) + return BASE_SUPPLEMENT * phase_out_share + CAPITAL_MATCH * capital_income + + +def _stay_prob(age: int, final_age_alive: float, survival_rate: float) -> FloatND: + return jnp.where(age >= final_age_alive, 0.0, survival_rate) + + +def _death_prob(age: int, final_age_alive: float, survival_rate: float) -> FloatND: + return jnp.where(age >= final_age_alive, 1.0, 1.0 - survival_rate) + + +def is_working(labor_supply: DiscreteAction) -> BoolND: + return labor_supply == LaborChoice.work + + +def next_aime(aime: ContinuousState, is_working: BoolND) -> ContinuousState: + return jnp.minimum(aime + jnp.where(is_working, AIME_GAIN, 0.0), AIME_MAX) + + +def _ages() -> AgeGrid: + return AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + + +def _active(age: int) -> bool: + last_age = 40 + (N_PERIODS - 1) * 10 + return age < last_age + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, +) + + +def _dcegm_functions() -> dict: + return { + "utility": utility, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + } + + +def _params() -> dict: + return { + "discount_factor": 0.95, + "final_age_alive": 40 + (N_PERIODS - 2) * 10, + } + + +def _assert_working_life_V_matches( + *, dcegm_solution: PeriodToRegimeToVArr, brute_solution: PeriodToRegimeToVArr +) -> None: + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + assert brute_V.shape == dcegm_V.shape + np.testing.assert_allclose( + dcegm_V[N_BRUTE_UNSTABLE_NODES:], + brute_V[N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +@functools.cache +def _health_insurance_model(solver: str) -> Model: + """Law term reading a discrete state and a discrete action.""" + + def next_wealth_dcegm( + savings: FloatND, health_net_transfer: FloatND + ) -> ContinuousState: + return savings + health_net_transfer + + def next_wealth_brute( + wealth: ContinuousState, + consumption: ContinuousAction, + health_net_transfer: FloatND, + ) -> ContinuousState: + return wealth - consumption + health_net_transfer + + is_dcegm = solver == "dcegm" + working = UserRegime( + transition=next_regime, + active=_active, + actions={ + "buy_private": DiscreteGrid(Insurance), + "consumption": CONSUMPTION_GRID, + }, + states={"wealth": WEALTH_GRID, "health": DiscreteGrid(Health)}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute, + "health": fixed_transition("health"), + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={ + **(_dcegm_functions() if is_dcegm else {}), + "utility": utility_with_premium, + "health_net_transfer": health_net_transfer, + }, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=LawTermRegimeId, + ) + + +def test_discrete_state_and_action_law_term_matches_brute_force(): + """`next_wealth = savings + transfer(health) - oop(buy_private)` solves. + + The additive term reads a discrete state and a discrete action β€” both + per-combo constants at the savings stage β€” so the child query shifts per + combo and the composed gradient is unchanged. Values agree with the + dense-grid brute-force oracle up to its consumption-grid resolution. + """ + params = _params() + dcegm_solution = _health_insurance_model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution = _health_insurance_model("brute_force").solve( + params=params, log_level="debug" + ) + _assert_working_life_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) + + +@functools.cache +def _means_test_model(solver: str) -> Model: + """Law term reading the Euler state through a decision-time function.""" + + def next_wealth_dcegm( + savings: FloatND, capital_supplement: FloatND + ) -> ContinuousState: + return savings + capital_supplement + + def next_wealth_brute( + wealth: ContinuousState, + consumption: ContinuousAction, + capital_supplement: FloatND, + ) -> ContinuousState: + return wealth - consumption + capital_supplement + + is_dcegm = solver == "dcegm" + working = UserRegime( + transition=next_regime, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={ + **(_dcegm_functions() if is_dcegm else {}), + "utility": utility, + "capital_supplement": capital_supplement, + }, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=LawTermRegimeId, + ) + + +def test_euler_state_law_term_with_means_test_matches_brute_force(): + """A means-tested capital supplement in the law matches brute force. + + The additive term reads the current Euler state through a decision-time + function (capital income), with a kinked but CONTINUOUS phase-out β€” a + hard cliff is rejected by validation, because the true policy bunches at + the value discontinuity it induces, outside EGM's candidate set. The term + is evaluated at the exogenous asset nodes β€” exactly where the brute-force + oracle evaluates it β€” so the two solvers agree at every node up to the + brute solver's consumption-grid resolution. + """ + params = _params() + dcegm_solution = _means_test_model("dcegm").solve(params=params, log_level="debug") + brute_solution = _means_test_model("brute_force").solve( + params=params, log_level="debug" + ) + _assert_working_life_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) + + +def _bequest_utility(wealth: ContinuousState) -> FloatND: + return jnp.log(wealth) + + +@functools.cache +def _per_target_model(solver: str) -> Model: + """Per-target asymmetry: the law term applies toward one target only.""" + bequest = UserRegime( + transition=None, + states={"wealth": BEQUEST_GRID}, + functions={"utility": _bequest_utility}, + ) + + def next_wealth_self_dcegm( + savings: FloatND, health_net_transfer: FloatND + ) -> ContinuousState: + return savings + health_net_transfer + + def next_wealth_bequest_dcegm(savings: FloatND) -> ContinuousState: + return savings + + def next_wealth_self_brute( + wealth: ContinuousState, + consumption: ContinuousAction, + health_net_transfer: FloatND, + ) -> ContinuousState: + return wealth - consumption + health_net_transfer + + def next_wealth_bequest_brute( + wealth: ContinuousState, consumption: ContinuousAction + ) -> ContinuousState: + return wealth - consumption + + is_dcegm = solver == "dcegm" + working = UserRegime( + transition={ + "working_life": MarkovTransition(_stay_prob), + "dead": MarkovTransition(_death_prob), + }, + active=_active, + actions={ + "buy_private": DiscreteGrid(Insurance), + "consumption": CONSUMPTION_GRID, + }, + states={"wealth": WEALTH_GRID, "health": DiscreteGrid(Health)}, + state_transitions={ + "wealth": { + "working_life": ( + next_wealth_self_dcegm if is_dcegm else next_wealth_self_brute + ), + "dead": ( + next_wealth_bequest_dcegm if is_dcegm else next_wealth_bequest_brute + ), + }, + "health": fixed_transition("health"), + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={ + **(_dcegm_functions() if is_dcegm else {}), + "utility": utility_with_premium, + "health_net_transfer": health_net_transfer, + }, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": bequest}, + ages=_ages(), + regime_id_class=LawTermRegimeId, + ) + + +def test_per_target_law_term_asymmetry_matches_brute_force(): + """The law term applies toward the live target and not toward `dead`. + + Wealth carried into death is `savings` alone (the bequest receives no + health transfer), while wealth carried into continued life includes the + transfer β€” declared as a per-target dict. Values agree with the brute + oracle solving the same per-target laws. + """ + params = {**_params(), "survival_rate": SURVIVAL_RATE} + dcegm_solution = _per_target_model("dcegm").solve(params=params, log_level="debug") + brute_solution = _per_target_model("brute_force").solve( + params=params, log_level="debug" + ) + _assert_working_life_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) + + +@functools.cache +def _phased_law_model(solver: str) -> Model: + """Phase-variant law term: solve-phase adjustment, simulate-phase zero.""" + + def next_wealth_solve_dcegm(savings: FloatND) -> ContinuousState: + return savings + SOLVE_ADJUSTMENT + + def next_wealth_simulate_dcegm(savings: FloatND) -> ContinuousState: + return savings + + def next_wealth_solve_brute( + wealth: ContinuousState, consumption: ContinuousAction + ) -> ContinuousState: + return wealth - consumption + SOLVE_ADJUSTMENT + + def next_wealth_simulate_brute( + wealth: ContinuousState, consumption: ContinuousAction + ) -> ContinuousState: + return wealth - consumption + + is_dcegm = solver == "dcegm" + working = UserRegime( + transition=next_regime, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={ + "wealth": ( + Phased( + solve=next_wealth_solve_dcegm, + simulate=next_wealth_simulate_dcegm, + ) + if is_dcegm + else Phased( + solve=next_wealth_solve_brute, + simulate=next_wealth_simulate_brute, + ) + ), + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={**(_dcegm_functions() if is_dcegm else {}), "utility": utility}, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=LawTermRegimeId, + ) + + +def test_phase_variant_law_term_solves_and_simulates_with_its_phase(): + """A `Phased` law term uses its solve variant in V and zero in simulate. + + The solve-phase law adds a constant adjustment to savings; the + simulate-phase law is `savings` alone. Solved values agree with the brute + oracle declaring the same `Phased` law. (That the simulated wealth path + obeys the simulate variant is asserted where DC-EGM forward simulation + exists, in `tests/simulation/test_simulate_dcegm.py`.) + """ + params = _params() + dcegm_solution = _phased_law_model("dcegm").solve(params=params, log_level="debug") + brute_solution = _phased_law_model("brute_force").solve( + params=params, log_level="debug" + ) + _assert_working_life_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) + + +@functools.cache +def _chained_law_model(solver: str) -> Model: + """Law term consuming a transition-DAG output of the same target.""" + + def next_wealth_dcegm( + savings: FloatND, next_aime: ContinuousState + ) -> ContinuousState: + return savings + PENSION_ACCRUAL * next_aime + + def next_wealth_brute( + wealth: ContinuousState, + consumption: ContinuousAction, + next_aime: ContinuousState, + ) -> ContinuousState: + return wealth - consumption + PENSION_ACCRUAL * next_aime + + is_dcegm = solver == "dcegm" + working = UserRegime( + transition=next_regime, + active=_active, + actions={ + "labor_supply": DiscreteGrid(LaborChoice), + "consumption": CONSUMPTION_GRID, + }, + states={"wealth": WEALTH_GRID, "aime": AIME_GRID}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute, + "aime": next_aime, + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={ + **(_dcegm_functions() if is_dcegm else {}), + "utility": utility_with_work, + "is_working": is_working, + }, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=LawTermRegimeId, + ) + + +def test_chained_transition_law_term_matches_brute_force(): + """`next_wealth = savings + accrual * next_aime` matches brute force. + + The law term consumes another state's transition output within the same + target DAG (the AIME accrual driven by the work choice), so the child + query shifts by a per-combo value computed inside the transition DAG. + """ + params = _params() + dcegm_solution = _chained_law_model("dcegm").solve(params=params, log_level="debug") + brute_solution = _chained_law_model("brute_force").solve( + params=params, log_level="debug" + ) + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + assert brute_V.shape == dcegm_V.shape == (160, 7) + np.testing.assert_allclose( + dcegm_V[N_BRUTE_UNSTABLE_NODES:, :], + brute_V[N_BRUTE_UNSTABLE_NODES:, :], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) diff --git a/tests/solution/test_egm_batch_size_combos.py b/tests/solution/test_egm_batch_size_combos.py new file mode 100644 index 000000000..5129bfd93 --- /dev/null +++ b/tests/solution/test_egm_batch_size_combos.py @@ -0,0 +1,300 @@ +"""DC-EGM splaying: `batch_size` on a discrete combo axis is a memory knob only. + +In asset-row mode the kernel maps the per-combo solve over the Cartesian product +of the regime's discrete states, passive states, and discrete actions. Splaying +a combo axis β€” setting `batch_size` on a discrete state grid (or a process / +passive grid) β€” processes that axis's slices in blocks rather than one fused +vmap, shedding peak working-set memory. It is a pure scheduling choice: the +solved value function is identical to the unsplayed (`batch_size=0`) solve at +any block size, including sizes that do not divide the axis. +""" + +import functools + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.typing import PeriodToRegimeToVArr +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + MarkovTransition, + Model, + categorical, + fixed_transition, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.typing import ( + ContinuousAction, + ContinuousState, + DiscreteState, + FloatND, + ScalarInt, +) +from tests.conftest import X64_ENABLED + +# Splaying a combo axis only reschedules the `lax.map`; in float64 the solved V is +# reproduced essentially exactly, in float32 the gather/reduce order shifts within +# single-precision rounding. +_INVARIANCE_RTOL = 1e-12 if X64_ENABLED else 1e-4 +_INVARIANCE_ATOL = 1e-12 if X64_ENABLED else 1e-4 + +N_PERIODS = 4 +N_WEALTH = 40 +BAND_START = 5.0 +BAND_WIDTH = 40.0 + +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=100.0, n_points=2000) +SAVINGS_GRID = IrregSpacedGrid(points=tuple(110.0 * (i / 149) ** 3 for i in range(150))) + + +@categorical(ordered=False) +class Health: + bad: ScalarInt + fair: ScalarInt + good: ScalarInt + + +@categorical(ordered=False) +class RegimeId: + working: ScalarInt + dead: ScalarInt + + +def smoothstep(value: FloatND) -> FloatND: + t = jnp.clip((value - BAND_START) / BAND_WIDTH, 0.0, 1.0) + return t * t * t * (t * (6.0 * t - 15.0) + 10.0) + + +def survival_of_wealth(wealth: ContinuousState) -> FloatND: + # Reading the Euler state in the regime-transition probability switches the + # kernel into the per-exogenous-asset-node (asset-row) solve. + return 0.5 + 0.45 * smoothstep(wealth) + + +def stay_prob(wealth: ContinuousState, age: int, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 0.0, survival_of_wealth(wealth)) + + +def death_prob(wealth: ContinuousState, age: int, final_age_alive: float) -> FloatND: + return 1.0 - stay_prob(wealth, age, final_age_alive) + + +def health_transition(health: DiscreteState) -> FloatND: + # A genuine Markov health combo axis carried into the child. + stay = jnp.where(health == Health.good, 0.7, 0.5) + others = (1.0 - stay) / 2.0 + return jnp.stack([others, others, stay]) + + +def utility(consumption: ContinuousAction, health: DiscreteState) -> FloatND: + penalty = jnp.where( + health == Health.bad, 0.2, jnp.where(health == Health.fair, 0.1, 0.0) + ) + return jnp.log(consumption) - penalty + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_wealth(savings: FloatND) -> ContinuousState: + return savings + 3.0 + + +def bequest(wealth: ContinuousState) -> FloatND: + return jnp.log(wealth + 1.0) + + +def _ages() -> AgeGrid: + return AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + + +@functools.cache +def _model(health_batch_size: int) -> Model: + """Asset-row DC-EGM with a Markov health combo axis splayed by `batch_size`.""" + ages = _ages() + last_age = ages.exact_values[-1] + working = UserRegime( + transition={ + "working": MarkovTransition(stay_prob), + "dead": MarkovTransition(death_prob), + }, + active=lambda age, la=last_age: age < la, + actions={"consumption": CONSUMPTION_GRID}, + states={ + "wealth": LinSpacedGrid(start=1.0, stop=100.0, n_points=N_WEALTH), + "health": DiscreteGrid(Health, batch_size=health_batch_size), + }, + state_transitions={ + "wealth": next_wealth, + "health": MarkovTransition(health_transition), + }, + functions={ + "utility": utility, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=32, + ), + ) + dead = UserRegime( + transition=None, + states={"wealth": LinSpacedGrid(start=1.0, stop=120.0, n_points=200)}, + functions={"utility": bequest}, + ) + return Model( + regimes={"working": working, "dead": dead}, + ages=ages, + regime_id_class=RegimeId, + ) + + +def _params() -> dict: + return {"discount_factor": 0.95, "final_age_alive": 40 + (N_PERIODS - 2) * 10} + + +def _solve(health_batch_size: int) -> PeriodToRegimeToVArr: + return _model(health_batch_size).solve(params=_params(), log_level="debug") + + +@pytest.mark.parametrize("health_batch_size", [1, 2, 3]) +def test_discrete_combo_batch_size_leaves_value_function_unchanged( + health_batch_size: int, +): + """Splaying a discrete combo axis does not change the solved V. + + `batch_size` on the `health` grid only changes how the discrete-state combo + product is scheduled (blocks via `lax.map` instead of one fused vmap over + the flattened product), so the value function at every period matches the + unsplayed `batch_size=0` solve exactly β€” including block sizes that do not + divide the axis. + """ + reference = _solve(0) + splayed = _solve(health_batch_size) + assert set(reference) == set(splayed) + for period in sorted(reference): + assert set(reference[period]) == set(splayed[period]) + for regime_name in reference[period]: + ref_V = np.asarray(reference[period][regime_name]) + got_V = np.asarray(splayed[period][regime_name]) + assert ref_V.shape == got_V.shape + np.testing.assert_allclose( + got_V, + ref_V, + rtol=_INVARIANCE_RTOL, + atol=_INVARIANCE_ATOL, + err_msg=f"period={period}, regime={regime_name}", + ) + + +@categorical(ordered=False) +class Marital: + single: ScalarInt + married: ScalarInt + + +def utility_two_combos( + consumption: ContinuousAction, health: DiscreteState, married: DiscreteState +) -> FloatND: + penalty = jnp.where( + health == Health.bad, 0.2, jnp.where(health == Health.fair, 0.1, 0.0) + ) + bonus = jnp.where(married == Marital.married, 0.05, 0.0) + return jnp.log(consumption) - penalty + bonus + + +@functools.cache +def _two_combo_model(batch_size: int) -> Model: + """Asset-row DC-EGM with TWO discrete combo axes (health + married).""" + ages = _ages() + last_age = ages.exact_values[-1] + working = UserRegime( + transition={ + "working": MarkovTransition(stay_prob), + "dead": MarkovTransition(death_prob), + }, + active=lambda age, la=last_age: age < la, + actions={"consumption": CONSUMPTION_GRID}, + states={ + "wealth": LinSpacedGrid(start=1.0, stop=100.0, n_points=N_WEALTH), + "health": DiscreteGrid(Health, batch_size=batch_size), + "married": DiscreteGrid(Marital, batch_size=batch_size), + }, + state_transitions={ + "wealth": next_wealth, + "health": MarkovTransition(health_transition), + "married": fixed_transition("married"), + }, + functions={ + "utility": utility_two_combos, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=32, + ), + ) + dead = UserRegime( + transition=None, + states={"wealth": LinSpacedGrid(start=1.0, stop=120.0, n_points=200)}, + functions={"utility": bequest}, + ) + return Model( + regimes={"working": working, "dead": dead}, + ages=ages, + regime_id_class=RegimeId, + ) + + +@pytest.mark.parametrize("batch_size", [1, 2]) +def test_two_discrete_combo_axes_splayed_together_match_unsplayed(batch_size: int): + """Splaying TWO combo axes at once does not change the solved V. + + With more than one splayed axis the kernel runs a single `lax.map` over the + flattened (health-by-married) product (one scan carry) rather than nesting a + `lax.map` per axis. The value function at every period must match the + unsplayed `batch_size=0` solve exactly, with the combo axes in the same + canonical order β€” guarding the flatten-and-transpose path. + """ + reference = _two_combo_model(0).solve(params=_params(), log_level="debug") + splayed = _two_combo_model(batch_size).solve(params=_params(), log_level="debug") + assert set(reference) == set(splayed) + for period in sorted(reference): + assert set(reference[period]) == set(splayed[period]) + for regime_name in reference[period]: + ref_V = np.asarray(reference[period][regime_name]) + got_V = np.asarray(splayed[period][regime_name]) + assert ref_V.shape == got_V.shape + np.testing.assert_allclose( + got_V, + ref_V, + rtol=_INVARIANCE_RTOL, + atol=_INVARIANCE_ATOL, + err_msg=f"period={period}", + ) diff --git a/tests/solution/test_egm_batch_size_euler.py b/tests/solution/test_egm_batch_size_euler.py new file mode 100644 index 000000000..3d659bd8a --- /dev/null +++ b/tests/solution/test_egm_batch_size_euler.py @@ -0,0 +1,174 @@ +"""DC-EGM splaying: `batch_size` on the Euler-state grid is a memory knob only. + +A DC-EGM regime in asset-row mode solves the single-post-state pipeline per +exogenous Euler-state (asset) node. Splaying that axis β€” setting `batch_size` +on the Euler-state grid β€” processes the asset nodes in blocks rather than one +fused vmap, shedding peak working-set memory. It is a pure scheduling choice: +the solved value function is identical to the unsplayed (`batch_size=0`) solve, +whatever the block size, including block sizes that do not divide the grid. +""" + +import functools + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.typing import PeriodToRegimeToVArr +from lcm import ( + AgeGrid, + IrregSpacedGrid, + LinSpacedGrid, + MarkovTransition, + Model, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.typing import ( + ContinuousAction, + ContinuousState, + FloatND, + ScalarInt, +) + +N_PERIODS = 4 +N_WEALTH = 23 # deliberately prime-ish: no batch size below divides it evenly +BAND_START = 5.0 +BAND_WIDTH = 40.0 + +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=100.0, n_points=2000) +SAVINGS_GRID = IrregSpacedGrid(points=tuple(110.0 * (i / 149) ** 3 for i in range(150))) + + +@categorical(ordered=False) +class RegimeId: + working: ScalarInt + dead: ScalarInt + + +def smoothstep(value: FloatND) -> FloatND: + t = jnp.clip((value - BAND_START) / BAND_WIDTH, 0.0, 1.0) + return t * t * t * (t * (6.0 * t - 15.0) + 10.0) + + +def survival_of_wealth(wealth: ContinuousState) -> FloatND: + # Reading the Euler state in the regime-transition probability switches the + # kernel into the per-exogenous-asset-node (asset-row) solve. + return 0.5 + 0.45 * smoothstep(wealth) + + +def stay_prob(wealth: ContinuousState, age: int, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 0.0, survival_of_wealth(wealth)) + + +def death_prob(wealth: ContinuousState, age: int, final_age_alive: float) -> FloatND: + return 1.0 - stay_prob(wealth, age, final_age_alive) + + +def utility(consumption: ContinuousAction) -> FloatND: + return jnp.log(consumption) + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_wealth(savings: FloatND) -> ContinuousState: + return savings + 3.0 + + +def bequest(wealth: ContinuousState) -> FloatND: + return jnp.log(wealth + 1.0) + + +def _ages() -> AgeGrid: + return AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + + +@functools.cache +def _model(batch_size: int) -> Model: + """Asset-row DC-EGM model with `batch_size` splaying on the Euler grid.""" + ages = _ages() + last_age = ages.exact_values[-1] + working = UserRegime( + transition={ + "working": MarkovTransition(stay_prob), + "dead": MarkovTransition(death_prob), + }, + active=lambda age, la=last_age: age < la, + actions={"consumption": CONSUMPTION_GRID}, + states={ + "wealth": LinSpacedGrid( + start=1.0, stop=100.0, n_points=N_WEALTH, batch_size=batch_size + ) + }, + state_transitions={"wealth": next_wealth}, + functions={ + "utility": utility, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=32, + ), + ) + dead = UserRegime( + transition=None, + states={"wealth": LinSpacedGrid(start=1.0, stop=120.0, n_points=200)}, + functions={"utility": bequest}, + ) + return Model( + regimes={"working": working, "dead": dead}, + ages=ages, + regime_id_class=RegimeId, + ) + + +def _params() -> dict: + return {"discount_factor": 0.95, "final_age_alive": 40 + (N_PERIODS - 2) * 10} + + +def _solve(batch_size: int) -> PeriodToRegimeToVArr: + return _model(batch_size).solve(params=_params(), log_level="debug") + + +@pytest.mark.parametrize("batch_size", [1, 4, 8, N_WEALTH]) +def test_euler_grid_batch_size_leaves_value_function_unchanged(batch_size: int): + """Splaying the Euler grid into blocks does not change the solved V. + + `batch_size` on the Euler-state grid only changes how the asset-row nodes + are scheduled (blocks via `lax.map` instead of one fused vmap), so the + value function at every period matches the unsplayed `batch_size=0` solve + exactly β€” including block sizes that do not divide the grid. + """ + reference = _solve(0) + splayed = _solve(batch_size) + assert set(reference) == set(splayed) + for period in sorted(reference): + assert set(reference[period]) == set(splayed[period]) + for regime_name in reference[period]: + ref_V = np.asarray(reference[period][regime_name]) + got_V = np.asarray(splayed[period][regime_name]) + assert ref_V.shape == got_V.shape + np.testing.assert_allclose( + got_V, + ref_V, + rtol=1e-12, + atol=1e-12, + err_msg=f"period={period}, regime={regime_name}", + ) diff --git a/tests/solution/test_egm_batch_size_savings.py b/tests/solution/test_egm_batch_size_savings.py new file mode 100644 index 000000000..3e95e170b --- /dev/null +++ b/tests/solution/test_egm_batch_size_savings.py @@ -0,0 +1,115 @@ +"""DC-EGM splaying: `batch_size` on the exogenous savings grid is a memory knob only. + +The dominant egm_step working buffer is the per-savings-node continuation +computation β€” the savings nodes times the child stochastic mesh times the combo +block. Splaying the savings grid processes those nodes in `lax.map` blocks rather +than one fused vmap, shedding peak working-set memory. The upper envelope still +runs on the gathered full endogenous grid, so the solved value function is +identical to the unsplayed (`batch_size=0`) solve, whatever the block size β€” +including block sizes that do not divide the grid. +""" + +import functools + +import numpy as np +import pytest + +from _lcm.typing import PeriodToRegimeToVArr +from lcm import LinSpacedGrid, MarkovTransition, Model +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from tests.solution.test_egm_batch_size_euler import ( + CONSUMPTION_GRID, + N_WEALTH, + RegimeId, + _ages, + _params, + bequest, + death_prob, + inverse_marginal_utility, + next_wealth, + resources, + savings, + stay_prob, + utility, +) + +N_SAVINGS = 149 # prime: no batch size below divides it evenly + + +@functools.cache +def _model(savings_batch_size: int) -> Model: + """Asset-row DC-EGM model with `batch_size` splaying on the savings grid.""" + ages = _ages() + last_age = ages.exact_values[-1] + working = UserRegime( + transition={ + "working": MarkovTransition(stay_prob), + "dead": MarkovTransition(death_prob), + }, + active=lambda age, la=last_age: age < la, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": LinSpacedGrid(start=1.0, stop=100.0, n_points=N_WEALTH)}, + state_transitions={"wealth": next_wealth}, + functions={ + "utility": utility, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=LinSpacedGrid( + start=0.0, + stop=110.0, + n_points=N_SAVINGS, + batch_size=savings_batch_size, + ), + n_constrained_points=32, + ), + ) + dead = UserRegime( + transition=None, + states={"wealth": LinSpacedGrid(start=1.0, stop=120.0, n_points=200)}, + functions={"utility": bequest}, + ) + return Model( + regimes={"working": working, "dead": dead}, + ages=ages, + regime_id_class=RegimeId, + ) + + +def _solve(savings_batch_size: int) -> PeriodToRegimeToVArr: + return _model(savings_batch_size).solve(params=_params(), log_level="debug") + + +@pytest.mark.parametrize("savings_batch_size", [1, 7, 16, N_SAVINGS]) +def test_savings_grid_batch_size_leaves_value_function_unchanged(savings_batch_size): + """Splaying the savings grid into blocks does not change the solved V. + + `batch_size` on the savings grid only changes how the per-savings-node + continuation is scheduled (blocks via `lax.map` instead of one fused vmap), + so the value function at every period matches the unsplayed `batch_size=0` + solve exactly β€” including block sizes that do not divide the grid, and the + boundary size equal to the grid length (which falls back to the vmap). + """ + reference = _solve(0) + splayed = _solve(savings_batch_size) + assert set(reference) == set(splayed) + for period in sorted(reference): + assert set(reference[period]) == set(splayed[period]) + for regime_name in reference[period]: + ref_V = np.asarray(reference[period][regime_name]) + got_V = np.asarray(splayed[period][regime_name]) + assert ref_V.shape == got_V.shape + np.testing.assert_allclose( + got_V, + ref_V, + rtol=1e-12, + atol=1e-12, + err_msg=f"period={period}, regime={regime_name}", + ) diff --git a/tests/solution/test_egm_batch_size_stochastic_nodes.py b/tests/solution/test_egm_batch_size_stochastic_nodes.py new file mode 100644 index 000000000..cac5c0167 --- /dev/null +++ b/tests/solution/test_egm_batch_size_stochastic_nodes.py @@ -0,0 +1,120 @@ +"""DC-EGM splaying: `stochastic_node_batch_size` is a memory knob only. + +The continuation expectation runs over the product of the child regime's +stochastic process nodes. That node axis is carried by the dominant `egm_step` +working buffer (the savings nodes times the child stochastic mesh times the +combo block). A positive block size accumulates the per-node reads in `lax.scan` +blocks rather than one fused vmap, folding the weighted sum into the scan carry +to shed peak working-set memory. The per-node results are summed with the joint +intrinsic weights either way, so the solved value function matches the unsplayed +(`stochastic_node_batch_size=0`) solve to tight numerical tolerance, whatever the +block size β€” including block sizes that do not divide the mesh. The block +reduction reorders the floating-point adds, so the match is to tolerance, not +bit-identical. +""" + +import functools + +import numpy as np +import pytest + +from _lcm.typing import PeriodToRegimeToVArr +from lcm import AgeGrid, Model +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from tests.conftest import X64_ENABLED +from tests.solution.test_egm_process_states import ( + CONSUMPTION_GRID, + N_INCOME_NODES, + N_PERIODS, + SAVINGS_GRID, + WEALTH_GRID, + ProcessRegimeId, + _get_params, + _income_process, + dead, + inverse_marginal_utility, + next_regime, + next_wealth_from_savings_iid, + resources, + savings, + utility_consumption_only, +) + +# The block reduction reorders the weighted-sum adds: in float64 the match to the +# unsplayed solve is tight, in float32 the reordering shows at single-precision scale. +_INVARIANCE_RTOL = 1e-9 if X64_ENABLED else 1e-4 +_INVARIANCE_ATOL = 1e-9 if X64_ENABLED else 1e-4 + + +@functools.cache +def _model(stochastic_node_batch_size: int) -> Model: + """DC-EGM model with an IID income process and a splayable node expectation.""" + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = float(ages.exact_values[-1]) + working = UserRegime( + transition=next_regime, + active=lambda age, la=last_age: age < la, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID, "income": _income_process("iid")}, + state_transitions={"wealth": next_wealth_from_savings_iid}, + functions={ + "utility": utility_consumption_only, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, + stochastic_node_batch_size=stochastic_node_batch_size, + ), + ) + return Model( + regimes={"alive": working, "dead": dead}, + ages=ages, + regime_id_class=ProcessRegimeId, + ) + + +def _solve(stochastic_node_batch_size: int) -> PeriodToRegimeToVArr: + return _model(stochastic_node_batch_size).solve( + params=_get_params("iid"), log_level="debug" + ) + + +@pytest.mark.parametrize("stochastic_node_batch_size", [1, 2, 3, N_INCOME_NODES]) +def test_stochastic_node_batch_size_leaves_value_function_unchanged( + stochastic_node_batch_size, +): + """Splaying the child node expectation into blocks does not change the solved V. + + `stochastic_node_batch_size` only changes how the per-node continuation + reads are scheduled and reduced (`lax.scan` blocks accumulating the weighted + sum, instead of one fused vmap), so the value function at every period + matches the unsplayed `stochastic_node_batch_size=0` solve to tight + numerical tolerance β€” including a block size (3) that does not divide the + 5-node income mesh, and the boundary size equal to the mesh length (which + falls back to the vmap). The block reduction reorders the floating-point + adds, so the match is to tolerance, not bit-identical. + """ + reference = _solve(0) + splayed = _solve(stochastic_node_batch_size) + assert set(reference) == set(splayed) + for period in sorted(reference): + assert set(reference[period]) == set(splayed[period]) + for regime_name in reference[period]: + ref_V = np.asarray(reference[period][regime_name]) + got_V = np.asarray(splayed[period][regime_name]) + assert ref_V.shape == got_V.shape + np.testing.assert_allclose( + got_V, + ref_V, + rtol=_INVARIANCE_RTOL, + atol=_INVARIANCE_ATOL, + err_msg=f"period={period}, regime={regime_name}", + ) diff --git a/tests/solution/test_egm_carry.py b/tests/solution/test_egm_carry.py new file mode 100644 index 000000000..b6ed3ff92 --- /dev/null +++ b/tests/solution/test_egm_carry.py @@ -0,0 +1,33 @@ +"""The DC-EGM carry holds only the rows the parent's Euler step reads. + +Backward induction threads the child's value, marginal utility, and endogenous +grid (plus the taste-shock scale) back to the parent; the parent never reads the +child's optimal continuous action. The carry therefore does not retain a policy +row β€” the rolling `next_regime_to_egm_carry` is the dominant device resident at +scale, so a write-only row would be pure wasted memory. +""" + +import jax + +from _lcm.egm.carry import _EGM_CARRY_FIELDS, EGMCarry, build_template_egm_carry + + +def test_egm_carry_fields_exclude_policy(): + """The carry's fields are exactly the rows the parent Euler step consumes.""" + assert set(_EGM_CARRY_FIELDS) == { + "endog_grid", + "value", + "marginal_utility", + "taste_shock_scale", + } + assert not hasattr(EGMCarry, "policy") + field_names = {f.name for f in EGMCarry.__dataclass_fields__.values()} + assert "policy" not in field_names + + +def test_template_carry_has_no_policy_leaf(): + """The template carry exposes one leaf per kept field, none for policy.""" + template = build_template_egm_carry(n_rows=8, leading_shape=(3,)) + leaves = jax.tree_util.tree_leaves(template) + # endog_grid, value, marginal_utility, taste_shock_scale. + assert len(leaves) == 4 diff --git a/tests/solution/test_egm_child_resources.py b/tests/solution/test_egm_child_resources.py new file mode 100644 index 000000000..1f6bd2ef0 --- /dev/null +++ b/tests/solution/test_egm_child_resources.py @@ -0,0 +1,350 @@ +"""DC-EGM with a resources function reading more than the Euler state. + +A carry target's resources function may read the child's discrete actions and +passive continuous states in addition to its Euler state β€” e.g. a work bonus +paid on top of wealth, or a pension scaling with an AIME-like skill level. The +child's resources space is then per-combo: the parent's carry read evaluates +$R'$ and the composed gradient $\\partial R'/\\partial A$ per child +discrete-action row and per passive neighbor node, so each carry row is +queried in the resources space it was built in. + +The oracle is a dense-grid brute-force solve of a mathematically equivalent +spec (same state grids, dense consumption grid, explicit budget constraint on +the same resources). +""" + +import functools + +import jax.numpy as jnp +import numpy as np + +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + Model, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteAction, + FloatND, + ScalarInt, +) +from lcm_examples.iskhakov_et_al_2017 import dead + +# Number of model periods; the last one is spent in the terminal `dead` regime. +N_PERIODS = 4 + +# Transfer added to resources when working β€” the discrete-action dependence of +# the child's resources space. A module constant (not a model param) so the +# child's resources DAG closes over it. +WORK_BONUS = 15.0 + +# Pension paid per unit of skill β€” the passive-state dependence of the child's +# resources space. +PENSION_RATE = 0.5 + +# Skill increment earned by one period of work; 0.4 is not a multiple of the +# skill grid's 0.25 node spacing, so working lands off-grid. +SKILL_GAIN = 0.4 + +# Upper bound of the skill grid; the skill transition clamps here. +SKILL_MAX = 1.5 + +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=100.0, n_points=80) +SKILL_GRID = LinSpacedGrid(start=0.0, stop=SKILL_MAX, n_points=7) + +# The consumption grid covers the maximum resources (wealth + bonus + pension), +# so the brute-force oracle is not artificially capped at high wealth. +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=120.0, n_points=400) + +# Exogenous end-of-period savings grid, cubically clustered toward the +# borrowing limit where the value function curves hardest. +SAVINGS_GRID = IrregSpacedGrid(points=tuple(100.0 * (i / 149) ** 3 for i in range(150))) + +# Lowest wealth nodes excluded from the brute-force comparison: there the +# coarse consumption grid makes brute force itself unreliable (the same +# exclusion the discrete and passive DC-EGM tests use). +N_BRUTE_UNSTABLE_NODES = 8 + + +@categorical(ordered=False) +class BonusRegimeId: + working_life: ScalarInt + dead: ScalarInt + + +@categorical(ordered=True) +class LaborChoice: + work: ScalarInt + rest: ScalarInt + + +def is_working(labor_supply: DiscreteAction) -> BoolND: + return labor_supply == LaborChoice.work + + +def labor_income(is_working: BoolND, wage: float) -> FloatND: + return jnp.where(is_working, wage, 0.0) + + +def utility( + consumption: ContinuousAction, is_working: BoolND, disutility_of_work: float +) -> FloatND: + return jnp.log(consumption) - jnp.where(is_working, disutility_of_work, 0.0) + + +def resources_with_bonus(wealth: ContinuousState, is_working: BoolND) -> FloatND: + return wealth + jnp.where(is_working, WORK_BONUS, 0.0) + + +def resources_with_bonus_and_pension( + wealth: ContinuousState, is_working: BoolND, skill: ContinuousState +) -> FloatND: + return wealth + jnp.where(is_working, WORK_BONUS, 0.0) + PENSION_RATE * skill + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_wealth_from_savings( + savings: FloatND, labor_income: FloatND, interest_rate: float +) -> ContinuousState: + return (1 + interest_rate) * savings + labor_income + + +def next_skill(skill: ContinuousState, is_working: BoolND) -> ContinuousState: + return jnp.minimum(skill + jnp.where(is_working, SKILL_GAIN, 0.0), SKILL_MAX) + + +def next_wealth_brute_bonus( + wealth: ContinuousState, + consumption: ContinuousAction, + is_working: BoolND, + labor_income: FloatND, + interest_rate: float, +) -> ContinuousState: + bonus = jnp.where(is_working, WORK_BONUS, 0.0) + return (1 + interest_rate) * (wealth + bonus - consumption) + labor_income + + +def next_wealth_brute_bonus_and_pension( + wealth: ContinuousState, + consumption: ContinuousAction, + is_working: BoolND, + skill: ContinuousState, + labor_income: FloatND, + interest_rate: float, +) -> ContinuousState: + bonus = jnp.where(is_working, WORK_BONUS, 0.0) + pension = PENSION_RATE * skill + return (1 + interest_rate) * (wealth + bonus + pension - consumption) + labor_income + + +def budget_constraint_bonus( + consumption: ContinuousAction, wealth: ContinuousState, is_working: BoolND +) -> BoolND: + return consumption <= wealth + jnp.where(is_working, WORK_BONUS, 0.0) + + +def budget_constraint_bonus_and_pension( + consumption: ContinuousAction, + wealth: ContinuousState, + is_working: BoolND, + skill: ContinuousState, +) -> BoolND: + bonus = jnp.where(is_working, WORK_BONUS, 0.0) + return consumption <= wealth + bonus + PENSION_RATE * skill + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where( + age >= final_age_alive, + BonusRegimeId.dead, + BonusRegimeId.working_life, + ) + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, +) + + +@functools.cache +def _get_model(variant: str) -> Model: + """Build one model variant. + + - `"dcegm_bonus"`: DC-EGM; resources read the work choice. + - `"brute_bonus"`: dense-grid brute force, mathematically equivalent spec. + - `"dcegm_bonus_pension"`: DC-EGM; resources read the work choice and a + passive skill state. + - `"brute_bonus_pension"`: dense-grid brute force, equivalent spec. + """ + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = float(ages.exact_values[-1]) + + def active(age: int, la: float = last_age) -> bool: + return age < la + + actions = { + "labor_supply": DiscreteGrid(LaborChoice), + "consumption": CONSUMPTION_GRID, + } + if variant == "dcegm_bonus": + working = UserRegime( + transition=next_regime, + active=active, + actions=actions, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_from_savings}, + functions={ + "utility": utility, + "labor_income": labor_income, + "is_working": is_working, + "resources": resources_with_bonus, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, + ) + elif variant == "brute_bonus": + working = UserRegime( + transition=next_regime, + active=active, + actions=actions, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_brute_bonus}, + constraints={"budget_constraint": budget_constraint_bonus}, + functions={ + "utility": utility, + "labor_income": labor_income, + "is_working": is_working, + }, + ) + elif variant == "dcegm_bonus_pension": + working = UserRegime( + transition=next_regime, + active=active, + actions=actions, + states={"wealth": WEALTH_GRID, "skill": SKILL_GRID}, + state_transitions={ + "wealth": next_wealth_from_savings, + "skill": next_skill, + }, + functions={ + "utility": utility, + "labor_income": labor_income, + "is_working": is_working, + "resources": resources_with_bonus_and_pension, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, + ) + else: + working = UserRegime( + transition=next_regime, + active=active, + actions=actions, + states={"wealth": WEALTH_GRID, "skill": SKILL_GRID}, + state_transitions={ + "wealth": next_wealth_brute_bonus_and_pension, + "skill": next_skill, + }, + constraints={"budget_constraint": budget_constraint_bonus_and_pension}, + functions={ + "utility": utility, + "labor_income": labor_income, + "is_working": is_working, + }, + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=ages, + regime_id_class=BonusRegimeId, + ) + + +def _get_params() -> dict: + final_age_alive = 40 + (N_PERIODS - 2) * 10 + return { + "discount_factor": 0.95, + "interest_rate": 0.0, + "final_age_alive": final_age_alive, + "working_life": { + "labor_income": {"wage": 20.0}, + "utility": {"disutility_of_work": 0.5}, + }, + } + + +def test_action_dependent_resources_match_dense_brute_force(): + """A work bonus in the child's resources matches dense brute force. + + The work and rest carry rows of the self-targeting regime live in + different resources spaces (offset by the bonus), so the parent's carry + read must query each child action row at its own resources value and use + each row's own composed gradient. Agreement is up to the brute solver's + consumption-grid resolution, excluding the lowest wealth nodes where the + coarse consumption grid makes brute force itself unreliable. + """ + params = _get_params() + dcegm_solution = _get_model("dcegm_bonus").solve(params=params, log_level="debug") + brute_solution = _get_model("brute_bonus").solve(params=params, log_level="debug") + + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + assert brute_V.shape == dcegm_V.shape == (80,) + np.testing.assert_allclose( + dcegm_V[N_BRUTE_UNSTABLE_NODES:], + brute_V[N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +def test_action_and_passive_dependent_resources_match_dense_brute_force(): + """A work bonus plus a skill pension in resources matches dense brute force. + + The child's resources read both a discrete action and a passive state, so + every carry row (per action and per passive neighbor node) is queried at + its own resources value with its own composed gradient; the passive blend + happens across rows evaluated in their own node's resources space. + """ + params = _get_params() + dcegm_solution = _get_model("dcegm_bonus_pension").solve( + params=params, log_level="debug" + ) + brute_solution = _get_model("brute_bonus_pension").solve( + params=params, log_level="debug" + ) + + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + assert brute_V.shape == dcegm_V.shape == (80, 7) + np.testing.assert_allclose( + dcegm_V[N_BRUTE_UNSTABLE_NODES:, :], + brute_V[N_BRUTE_UNSTABLE_NODES:, :], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) diff --git a/tests/solution/test_egm_concave.py b/tests/solution/test_egm_concave.py new file mode 100644 index 000000000..a55645c5e --- /dev/null +++ b/tests/solution/test_egm_concave.py @@ -0,0 +1,347 @@ +"""Spec for the concave DC-EGM step (no discrete actions, no taste shocks). + +The oracle is the retired part of the Iskhakov et al. (2017) analytical solution, +anchored by `tests/solution/test_retirement_only_oracle.py`. The DC-EGM solution +must hit the analytical values on the full wealth grid β€” including the lowest +wealth levels, where the credit-constrained segment is exact and the brute-force +solver is unstable. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from lcm import ( + AgeGrid, + IrregSpacedGrid, + LinSpacedGrid, + LogSpacedGrid, + Model, + categorical, +) +from lcm.exceptions import InvalidValueFunctionError +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.typing import ContinuousAction, ContinuousState, FloatND, ScalarInt +from lcm_examples.mortality import WEALTH_GRID +from tests.solution.test_retirement_only_oracle import ( + ANALYTICAL_CASES, + load_analytical_values_retired, + stack_retirement_V, +) +from tests.test_models.deterministic import retirement_only +from tests.test_models.deterministic.dcegm_variants import ( + dcegm_retirement, + get_retirement_only_model, + get_retirement_only_params, +) + + +@pytest.mark.parametrize(("case", "n_periods"), ANALYTICAL_CASES.items()) +def test_dcegm_matches_analytical_on_full_wealth_grid(case, n_periods): + """DC-EGM V equals the analytical retired values on every wealth node. + + Tighter than the brute-force tolerance and with no low-wealth exclusion: the + constrained segment makes EGM exact where grid search is unstable. + """ + model = get_retirement_only_model("dcegm", n_periods) + params = get_retirement_only_params(n_periods) + + period_to_regime_to_V_arr = model.solve(params=params, log_level="debug") + + numerical = stack_retirement_V(period_to_regime_to_V_arr) + analytical = load_analytical_values_retired(case) + # Elementwise β€” every (period, node) value must hit the analytical + # solution; aggregating over periods could hide a localized error. + np.testing.assert_allclose(numerical, analytical, atol=0.03) + + +@pytest.mark.parametrize(("case", "n_periods"), ANALYTICAL_CASES.items()) +def test_dcegm_error_not_much_worse_than_brute_force(case, n_periods): + """Diagnostic with slack: DC-EGM should not lose badly to grid search anywhere. + + Pointwise EGM dominance is not a theorem (the publish step interpolates onto + the wealth grid), so this is a guard against gross regressions, not a + superiority claim. The hard accuracy requirement lives in + `test_dcegm_matches_analytical_on_full_wealth_grid`. + """ + analytical = load_analytical_values_retired(case) + params = get_retirement_only_params(n_periods) + + errors = {} + for solver in ["brute_force", "dcegm"]: + model = get_retirement_only_model(solver, n_periods) + got = model.solve(params=params, log_level="debug") + numerical = stack_retirement_V(got) + # Exclude the brute-force-unstable low-wealth nodes from the head-to-head + # so the comparison is on territory where both solvers are well-defined. + errors[solver] = np.mean((analytical[:, 2:] - numerical[:, 2:]) ** 2) + + assert errors["dcegm"] <= 2.0 * errors["brute_force"] + 1e-12 + + +def test_discount_factor_zero_yields_consume_everything_values(): + """With `discount_factor = 0`, V equals the utility of consuming all resources. + + The degenerate-inversion guard must hold after discounting: a zero + discount factor zeroes the marginal continuation at every savings node, so + the consume-everything corner is optimal at every wealth node and + `V(wealth) = log(wealth)` in every non-terminal period. V equals + `log(wealth)` up to the high-order publish interpolation error (the + closed-form constrained value is published outright only below the lowest + refined point). + """ + n_periods = 3 + model = get_retirement_only_model("dcegm", n_periods) + params = get_retirement_only_params(n_periods, discount_factor=0.0) + + period_to_regime_to_V_arr = model.solve(params=params, log_level="debug") + + wealth = np.asarray(WEALTH_GRID.to_jax()) + for period in range(n_periods - 1): + np.testing.assert_allclose( + np.asarray(period_to_regime_to_V_arr[period]["retirement"]), + np.log(wealth), + atol=2e-5, + err_msg=f"period={period}", + ) + + +def _bequest_utility(wealth: ContinuousState, age: float) -> FloatND: + return (age / 50.0) * jnp.log(wealth) + + +def test_age_dependent_terminal_utility_solves_to_closed_form(): + """A bequest utility reading `age` works as a DC-EGM continuation. + + Terminal carries are evaluated with the solve loop's `period` and `age`, + so a terminal utility may read them like any regime function. With + `u = log(c)`, bequest `(age/50) * log(wealth)` at terminal age 50, zero + interest, and a two-period horizon, the decision period has the closed + form `c* = wealth / (1 + beta)` and + `V = log(c*) + beta * log(wealth - c*)`. + """ + n_periods = 2 + discount_factor = 0.98 + # Dense log-spaced terminal grid: the bequest continuation is read by + # linear interpolation on this grid, so it must resolve the curvature of + # `log` for the closed form to be the test oracle. + bequest_dead = UserRegime( + transition=None, + states={"wealth": LogSpacedGrid(start=0.25, stop=400.0, n_points=400)}, + functions={"utility": _bequest_utility}, + ) + model = Model( + regimes={ + "retirement": dcegm_retirement.replace(active=lambda age: age < 50), + "dead": bequest_dead, + }, + ages=AgeGrid(start=40, stop=50, step="10Y"), + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + params = get_retirement_only_params(n_periods, discount_factor=discount_factor) + + period_to_regime_to_V_arr = model.solve(params=params, log_level="debug") + + wealth = np.asarray(WEALTH_GRID.to_jax()) + consumption = wealth / (1.0 + discount_factor) + expected = np.log(consumption) + discount_factor * np.log(wealth - consumption) + # The lowest wealth nodes carry visible publish-side interpolation error + # (the value function curves hardest there); the age-dependence under + # test is identical across nodes, so they are excluded rather than the + # tolerance loosened for the whole grid. + np.testing.assert_allclose( + np.asarray(period_to_regime_to_V_arr[0]["retirement"])[3:], + expected[3:], + atol=1e-3, + ) + + +@categorical(ordered=False) +class _InterestRegimeId: + retirement: ScalarInt + dead: ScalarInt + + +def _log_consumption_value(wealth: np.ndarray, *, n_alive: int) -> np.ndarray: + """Closed-form retired value `V(w) = B log(w) + A` with log utility. + + With gross return $R_g = 1 + r$, discount factor $\\beta$, and `n_alive` + remaining periods of life, the Bellman recursion for $V(w) = B \\log w + A$ + starts from $A = B = 0$ and iterates `n_alive` times. + """ + discount_factor = 0.95 + gross_return = 1.05 + intercept = 0.0 + slope = 0.0 + for _ in range(n_alive): + slope_new = 1.0 + discount_factor * slope + if slope_new > 1.0: + intercept = -np.log(slope_new) + discount_factor * ( + slope * np.log(gross_return * (slope_new - 1.0) / slope_new) + intercept + ) + else: + intercept = discount_factor * intercept + slope = slope_new + return slope * np.log(wealth) + intercept + + +def test_dcegm_with_interest_matches_closed_form_on_dense_wealth_grid(): + """A 5%-interest retirement model hits the closed form on every wealth node. + + With log utility, $\\beta = 0.95$, gross return $1.05$, and a multi-period + horizon, the retired value function is $V(w) = B \\log(w) + A$ in closed + form. The published V must match it on a dense linear wealth grid at every + period β€” across many backward-induction steps, so carry-read and + publish-side interpolation errors of the concave value rows may not + accumulate beyond the tolerance. + """ + n_periods = 10 + + def utility(consumption: ContinuousAction) -> FloatND: + return jnp.log(consumption) + + def resources(wealth: ContinuousState) -> FloatND: + return wealth + + def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + def next_wealth(savings: FloatND, interest_rate: float) -> ContinuousState: + return (1.0 + interest_rate) * savings + + def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + def next_regime(age: float, final_age_alive: float) -> ScalarInt: + return jnp.where( + age >= final_age_alive, + _InterestRegimeId.dead, + _InterestRegimeId.retirement, + ) + + ages = AgeGrid(start=40, stop=40 + n_periods - 1, step="Y") + last_age = ages.exact_values[-1] + retirement = UserRegime( + transition=next_regime, + actions={"consumption": LinSpacedGrid(start=1, stop=400, n_points=100)}, + states={"wealth": LinSpacedGrid(start=1, stop=400, n_points=1000)}, + state_transitions={"wealth": next_wealth}, + functions={ + "utility": utility, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + # Cubic node clustering toward the borrowing limit, as the value + # function curves hardest there. + savings_grid=IrregSpacedGrid( + points=tuple(400.0 * (i / 199) ** 3 for i in range(200)) + ), + n_constrained_points=64, + ), + active=lambda age: age < last_age, + ) + dead = UserRegime( + transition=None, + functions={"utility": lambda: 0.0}, + active=lambda _age: True, + ) + model = Model( + regimes={"retirement": retirement, "dead": dead}, + ages=ages, + regime_id_class=_InterestRegimeId, + ) + params = { + "discount_factor": 0.95, + "interest_rate": 0.05, + "final_age_alive": 40 + n_periods - 2, + } + + period_to_regime_to_V_arr = model.solve(params=params, log_level="debug") + + wealth = np.linspace(1.0, 400.0, 1000) + for period in range(n_periods - 1): + np.testing.assert_allclose( + np.asarray(period_to_regime_to_V_arr[period]["retirement"]), + _log_consumption_value(wealth, n_alive=(n_periods - 1) - period), + atol=3e-3, + err_msg=f"period={period}", + ) + + +def test_nan_param_surfaces_as_value_function_error(): + """A NaN parameter raises `InvalidValueFunctionError` naming the regime. + + NaN propagates into the published V rows; the solve's NaN diagnostics must + report regime and age for a DC-EGM regime just as for a brute-force one. + """ + n_periods = 3 + model = get_retirement_only_model("dcegm", n_periods) + params = get_retirement_only_params(n_periods, discount_factor=float("nan")) + + with pytest.raises(InvalidValueFunctionError, match="retirement"): + model.solve(params=params, log_level="debug") + + +def test_dcegm_solution_has_standard_v_array_layout(): + """DC-EGM publishes V arrays with the same shape/keys as the brute solver.""" + n_periods = 4 + params = get_retirement_only_params(n_periods) + + brute = get_retirement_only_model("brute_force", n_periods).solve( + params=params, log_level="debug" + ) + dcegm = get_retirement_only_model("dcegm", n_periods).solve( + params=params, log_level="debug" + ) + + assert sorted(brute) == sorted(dcegm) + for period in brute: + assert sorted(brute[period]) == sorted(dcegm[period]) + for regime in brute[period]: + assert brute[period][regime].shape == dcegm[period][regime].shape + + +def test_neg_inf_bequest_node_does_not_wipe_the_continuation(): + """A `-inf` terminal value at one node only affects queries near it. + + With a bequest grid that includes zero wealth, the terminal value is + `-inf` at that node and finite elsewhere. The carry read must treat the + row pointwise β€” only bequests interpolating against the `-inf` node lose + value β€” so the decision period still solves to the closed form at wealth + nodes whose optimal bequest is interior. + """ + n_periods = 2 + discount_factor = 0.98 + bequest_points = (0.0, *(float(x) for x in np.geomspace(0.005, 400.0, 400))) + bequest_dead = UserRegime( + transition=None, + states={"wealth": IrregSpacedGrid(points=bequest_points)}, + functions={"utility": _bequest_utility}, + ) + model = Model( + regimes={ + "retirement": dcegm_retirement.replace(active=lambda age: age < 50), + "dead": bequest_dead, + }, + ages=AgeGrid(start=40, stop=50, step="10Y"), + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + params = get_retirement_only_params(n_periods, discount_factor=discount_factor) + + period_to_regime_to_V_arr = model.solve(params=params, log_level="debug") + + wealth = np.asarray(WEALTH_GRID.to_jax()) + consumption = wealth / (1.0 + discount_factor) + expected = np.log(consumption) + discount_factor * np.log(wealth - consumption) + np.testing.assert_allclose( + np.asarray(period_to_regime_to_V_arr[0]["retirement"])[3:], + expected[3:], + atol=1e-3, + ) diff --git a/tests/solution/test_egm_cross_regime_target_params.py b/tests/solution/test_egm_cross_regime_target_params.py new file mode 100644 index 000000000..7eea43430 --- /dev/null +++ b/tests/solution/test_egm_cross_regime_target_params.py @@ -0,0 +1,333 @@ +"""DC-EGM cross-regime carry: a target's resources reads a model-level param. + +A DC-EGM regime may carry into a *different* target regime whose `resources` +function reaches a model-level (shared) parameter that the source regime's own +DAG never touches β€” for example a pension factor that the source, lacking the +pension function, prunes from its parameter template. Such a parameter is a +genuine model-level value, identical across regimes; the per-exogenous-asset- +node solve must evaluate the target's resources with it, exactly as the +brute-force solver does. + +The asset-row solve is active because the source regime's regime-transition +probability reads the Euler state (wealth). The oracle for the solved value +function is a dense-grid brute-force solve of a mathematically equivalent +spec. +""" + +import functools + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.typing import PeriodToRegimeToVArr +from lcm import ( + AgeGrid, + IrregSpacedGrid, + LinSpacedGrid, + MarkovTransition, + Model, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM, GridSearch +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + FloatND, + ScalarInt, +) + +# Model periods; the source regime is active early, the target regime late, +# so the source carries into a *different* target regime. +N_PERIODS = 4 + +# Wealth band over which the source's survival smoothstep ramps. Reading +# wealth in the regime-transition probability switches the source kernel into +# the per-exogenous-asset-node (asset-row) solve. +BAND_START = 30.0 +BAND_WIDTH = 20.0 +SURVIVAL_LOW = 0.55 +SURVIVAL_HIGH = 0.95 + +# Deterministic labor income added to savings in the wealth law; keeps child +# wealth queries away from the grid's lower edge. +LABOR_INCOME = 5.0 + +# Pension factor scaling the target regime's accrued pension into resources. +# A model-level value supplied through `fixed_params`; the source regime has +# no pension function, so its template never carries this parameter. +PENSION_FACTOR = 0.6 + +# Accrued pension level the target regime adds to wealth (times the factor). +ACCRUED_PENSION = 12.0 + +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=100.0, n_points=160) +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=120.0, n_points=4000) +SAVINGS_GRID = IrregSpacedGrid(points=tuple(100.0 * (i / 149) ** 3 for i in range(150))) + +# Lowest wealth nodes excluded from the comparison: the brute solver leans on +# coarse interpolation and consumption choices near its grid start there. +N_BRUTE_UNSTABLE_NODES = 16 + + +@categorical(ordered=False) +class CrossRegimeId: + young: ScalarInt + old: ScalarInt + dead: ScalarInt + + +def smoothstep_in_band(value: FloatND) -> FloatND: + """CΒ² quintic smoothstep rising from 0 to 1 across the band.""" + t = jnp.clip((value - BAND_START) / BAND_WIDTH, 0.0, 1.0) + return t * t * t * (t * (6.0 * t - 15.0) + 10.0) + + +def utility(consumption: ContinuousAction) -> FloatND: + return jnp.log(consumption) + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_wealth_dcegm(savings: FloatND) -> ContinuousState: + return savings + LABOR_INCOME + + +def next_wealth_brute( + resources: FloatND, consumption: ContinuousAction +) -> ContinuousState: + return resources - consumption + LABOR_INCOME + + +def _ages() -> AgeGrid: + return AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + + +def _young_active(age: int) -> bool: + # Young in the first decision period only, so its only DC-EGM carry target + # is the *old* regime (a different regime) and the terminal `dead` regime. + return age < 50 + + +def _old_active(age: int) -> bool: + last_age = 40 + (N_PERIODS - 1) * 10 + return 50 <= age < last_age + + +# --- Source-regime savings-stage reads (drive the asset-row solve) ---------- + + +def survival_of_wealth(wealth: ContinuousState) -> FloatND: + return SURVIVAL_LOW + (SURVIVAL_HIGH - SURVIVAL_LOW) * smoothstep_in_band(wealth) + + +def young_stay_prob(wealth: ContinuousState) -> FloatND: + # Young is active in the first period only; its successor is always `old`, + # which is active in the next period, so survival never leaks into an + # inactive regime. + return survival_of_wealth(wealth) + + +def young_death_prob(wealth: ContinuousState) -> FloatND: + return 1.0 - survival_of_wealth(wealth) + + +# --- Target-regime (old) resources: reads the model-level pension factor ---- + + +def accrued_pension() -> FloatND: + return jnp.asarray(ACCRUED_PENSION) + + +def pension_value(accrued_pension: FloatND, pension_factor: float) -> FloatND: + """Pension income, scaling the accrued pension by the model-level factor.""" + return accrued_pension * pension_factor + + +def resources_old(wealth: ContinuousState, pension_value: FloatND) -> FloatND: + return wealth + pension_value + + +def budget_constraint_old( + consumption: ContinuousAction, wealth: ContinuousState, pension_value: FloatND +) -> BoolND: + return consumption <= wealth + pension_value + + +# --- Source-regime (young) resources: plain wealth -------------------------- + + +def resources_young(wealth: ContinuousState) -> FloatND: + return wealth + + +def budget_constraint_young( + consumption: ContinuousAction, wealth: ContinuousState +) -> BoolND: + return consumption <= wealth + + +def next_old_stay_prob(wealth: ContinuousState, age: int) -> FloatND: + # At the last decision age `old` must transition into the terminal `dead` + # regime only, since `old` is inactive in the next period. + last_age = 40 + (N_PERIODS - 1) * 10 + return jnp.where(age >= last_age - 10, 0.0, survival_of_wealth(wealth)) + + +def next_old_death_prob(wealth: ContinuousState, age: int) -> FloatND: + return 1.0 - next_old_stay_prob(wealth, age) + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, +) + + +def _params(*, factor_is_fixed: bool) -> dict: + params: dict = {"discount_factor": 0.95} + if not factor_is_fixed: + # Free param: supplied at solve time under the target regime's + # pension function. + params["old"] = {"pension_value": {"pension_factor": PENSION_FACTOR}} + return params + + +@functools.cache +def _cross_regime_model(solver: str, *, factor_is_fixed: bool) -> Model: + """Young (DC-EGM, asset-row) carries into a different regime `old`. + + `old`'s resources reach the model-level `pension_factor` through the + pension chain; the source `young` regime has no pension function, so its + parameter template never carries `pension_factor`. When `factor_is_fixed` + the factor is supplied through `fixed_params` (partialled at model build + and dropped from the live template); otherwise it is a free solve param of + the target regime. + """ + is_dcegm = solver == "dcegm" + young = UserRegime( + transition={ + "old": MarkovTransition(young_stay_prob), + "dead": MarkovTransition(young_death_prob), + }, + active=_young_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute + }, + constraints=( + {} if is_dcegm else {"budget_constraint": budget_constraint_young} + ), + functions=( + { + "utility": utility, + "resources": resources_young, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + } + if is_dcegm + else {"utility": utility, "resources": resources_young} + ), + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + pension_funcs = {"accrued_pension": accrued_pension, "pension_value": pension_value} + old = UserRegime( + transition={ + "old": MarkovTransition(next_old_stay_prob), + "dead": MarkovTransition(next_old_death_prob), + }, + active=_old_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute + }, + constraints=({} if is_dcegm else {"budget_constraint": budget_constraint_old}), + functions=( + { + "utility": utility, + "resources": resources_old, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + **pension_funcs, + } + if is_dcegm + else {"utility": utility, "resources": resources_old, **pension_funcs} + ), + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + dead = UserRegime( + transition=None, + functions={"utility": lambda: 0.0}, + active=lambda _age: True, + ) + fixed_params = ( + {"old": {"pension_value": {"pension_factor": PENSION_FACTOR}}} + if factor_is_fixed + else {} + ) + return Model( + regimes={"young": young, "old": old, "dead": dead}, + ages=_ages(), + regime_id_class=CrossRegimeId, + fixed_params=fixed_params, + ) + + +def _assert_young_V_matches( + *, dcegm_solution: PeriodToRegimeToVArr, brute_solution: PeriodToRegimeToVArr +) -> None: + # The young regime is active in the first period only; compare its V. + period = min(brute_solution) + brute_V = np.asarray(brute_solution[period]["young"]) + dcegm_V = np.asarray(dcegm_solution[period]["young"]) + assert brute_V.shape == dcegm_V.shape + flat_dcegm = dcegm_V.reshape(-1, dcegm_V.shape[-1]) + flat_brute = brute_V.reshape(-1, brute_V.shape[-1]) + np.testing.assert_allclose( + flat_dcegm[:, N_BRUTE_UNSTABLE_NODES:], + flat_brute[:, N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +@pytest.mark.parametrize("factor_is_fixed", [True, False]) +def test_cross_regime_target_resources_param_matches_brute_force( + factor_is_fixed: bool, # noqa: FBT001 +): + """A target regime's resources reading a model-level param matches brute. + + The source `young` regime carries into the different `old` regime, whose + resources reach the model-level `pension_factor` through the pension chain + β€” a parameter the source regime's template never carries. The asset-row + solve must evaluate the target's resources with the model-level parameter + value, whether the factor is a fixed param (partialled into the prebuilt + kernel) or a free solve param (threaded from the target regime's live + params). The source regime's value function agrees with the dense-grid + brute-force oracle. + """ + params = _params(factor_is_fixed=factor_is_fixed) + dcegm_solution = _cross_regime_model( + "dcegm", factor_is_fixed=factor_is_fixed + ).solve(params=params, log_level="debug") + brute_solution = _cross_regime_model( + "brute_force", factor_is_fixed=factor_is_fixed + ).solve(params=params, log_level="debug") + _assert_young_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) diff --git a/tests/solution/test_egm_discrete.py b/tests/solution/test_egm_discrete.py new file mode 100644 index 000000000..ee5c35af9 --- /dev/null +++ b/tests/solution/test_egm_discrete.py @@ -0,0 +1,404 @@ +"""DC-EGM with discrete states and discrete-only constraints. + +Variants of the Iskhakov et al. (2017) retirement model exercise the two +discrete dimensions of the DC-EGM kernel beyond the discrete work/retire +action: + +- a discrete *state* (a fixed skill type scaling the wage) that must remain + an axis of the published value-function array and must select the matching + carry rows when the regime targets itself, and +- a discrete-only *constraint* that masks a discrete-action combo everywhere, + whose carry rows must be `-inf` with exactly-zero marginal utility so the + parent's choice aggregation stays finite. +""" + +import functools + +import jax.numpy as jnp +import numpy as np +import pytest + +from lcm import ( + AgeGrid, + DiscreteGrid, + MarkovTransition, + Model, + categorical, + fixed_transition, +) +from lcm.exceptions import InvalidRegimeTransitionProbabilitiesError +from lcm.typing import BoolND, DiscreteAction, DiscreteState, FloatND, ScalarInt +from tests.test_models.deterministic import base +from tests.test_models.deterministic.dcegm_variants import ( + dcegm_retirement, + dcegm_retirement_full, + dcegm_working_life, + get_full_model, + get_full_params, + get_retirement_only_params, +) +from tests.test_models.deterministic.retirement_only import RetirementOnlyRegimeId + +N_PERIODS = 4 + + +def _retirement_stay_prob(age: float, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 0.0, 1.0) + + +def _retirement_death_prob(age: float, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 1.0, 0.0) + + +# Retirement can only stay retired or die. Declaring this granularly (with +# indicator probabilities) narrows reachability so the bare wealth law never +# has to cover the skill-carrying working regime. +RETIREMENT_TRANSITION = { + "retirement": MarkovTransition(_retirement_stay_prob), + "dead": MarkovTransition(_retirement_death_prob), +} + + +@categorical(ordered=False) +class Skill: + low: ScalarInt + high: ScalarInt + + +def wage_factor(skill: DiscreteState) -> FloatND: + return jnp.where(skill == Skill.high, 2.0, 1.0) + + +def labor_income_by_skill( + is_working: BoolND, wage: float, wage_factor: FloatND +) -> FloatND: + return jnp.where(is_working, wage * wage_factor, 0.0) + + +def must_retire(labor_supply: DiscreteAction) -> BoolND: + return labor_supply == base.LaborSupply.retire + + +def _get_skill_model_params(*, wage: float = 20.0) -> dict: + """Params for the models whose retirement regime names its target.""" + params = get_full_params(N_PERIODS, discount_factor=0.98, wage=wage) + params["retirement"] = {"next_wealth": {"labor_income": 0.0}} + return params + + +@functools.cache +def _get_skill_model() -> Model: + """Full DC-EGM retirement model with a fixed skill state scaling the wage.""" + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + working_life = dcegm_working_life.replace( + states={ + "wealth": dcegm_working_life.states["wealth"], + "skill": DiscreteGrid(Skill), + }, + state_transitions={ + "wealth": dcegm_working_life.state_transitions["wealth"], + "skill": fixed_transition("skill"), + }, + functions={ + **dict(dcegm_working_life.functions), + "wage_factor": wage_factor, + "labor_income": labor_income_by_skill, + }, + active=lambda age, la=last_age: age < la, + ) + retirement = dcegm_retirement_full.replace( + transition=RETIREMENT_TRANSITION, + state_transitions={ + "wealth": dcegm_retirement_full.state_transitions["wealth"], + }, + active=lambda age, la=last_age: age < la, + ) + return Model( + regimes={ + "working_life": working_life, + "retirement": retirement, + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + + +@functools.cache +def _get_must_retire_model() -> Model: + """Full DC-EGM retirement model where a constraint forbids working.""" + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "working_life": dcegm_working_life.replace( + constraints={"must_retire": must_retire}, + active=lambda age, la=last_age: age < la, + ), + "retirement": dcegm_retirement_full.replace( + active=lambda age, la=last_age: age < la + ), + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + + +def test_discrete_state_slices_match_single_type_models(): + """Each skill slice of V equals the skill-free model solved at that wage. + + The skill state is fixed and scales the wage by 1 (low) or 2 (high), so + the low slice must reproduce the base-wage model and the high slice the + double-wage model β€” node for node. A kernel that selected the wrong + carry rows for the child's skill value would mix the types' carries and + break this equality. + """ + skill_solution = _get_skill_model().solve( + params=_get_skill_model_params(), log_level="debug" + ) + base_model = get_full_model("dcegm", N_PERIODS) + params = get_full_params(N_PERIODS, discount_factor=0.98, wage=20.0) + single_type_solutions = { + "low": base_model.solve(params=params, log_level="debug"), + "high": base_model.solve( + params=get_full_params(N_PERIODS, discount_factor=0.98, wage=40.0), + log_level="debug", + ), + } + + for period in sorted(skill_solution)[:-1]: + V_skill = np.asarray(skill_solution[period]["working_life"]) + assert V_skill.shape == (2, 100) + for skill_index, label in [(0, "low"), (1, "high")]: + np.testing.assert_allclose( + V_skill[skill_index], + np.asarray(single_type_solutions[label][period]["working_life"]), + rtol=1e-9, + atol=1e-9, + err_msg=f"period={period}, skill={label}", + ) + + +def test_infeasible_discrete_action_recovers_retirement_value(): + """With work forbidden everywhere, the worker's V equals the retiree's V. + + The discrete-only constraint makes the work combo infeasible at every + state: its value rows are `-inf` and its marginal-utility rows exactly + zero, so the forced-retirement worker solves the retiree's Bellman + equation. Any NaN leak from the infeasible rows would poison the parent's + aggregation (the solve runs at `log_level="debug"`, which raises on NaN). + """ + params = get_full_params(N_PERIODS, discount_factor=0.98, wage=20.0) + + solution = _get_must_retire_model().solve(params=params, log_level="debug") + + for period in sorted(solution)[:-1]: + np.testing.assert_allclose( + np.asarray(solution[period]["working_life"]), + np.asarray(solution[period]["retirement"]), + rtol=1e-9, + atol=1e-9, + err_msg=f"period={period}", + ) + + +@pytest.mark.parametrize("regime_name", ["working_life", "retirement"]) +def test_discrete_state_layout_matches_brute_force(regime_name): + """The skill model's V arrays have brute-force layout and values. + + Discrete-state axes lead and the continuous state is last, exactly as the + brute-force solver lays out V; values agree on the wealth nodes where the + brute solver is reliable. + """ + params = _get_skill_model_params() + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + brute_model = Model( + regimes={ + "working_life": base.working_life.replace( + states={"wealth": base.WEALTH_GRID, "skill": DiscreteGrid(Skill)}, + state_transitions={ + "wealth": base.next_wealth, + "skill": fixed_transition("skill"), + }, + functions={ + **dict(base.working_life.functions), + "wage_factor": wage_factor, + "labor_income": labor_income_by_skill, + }, + active=lambda age, la=last_age: age < la, + ), + "retirement": base.retirement.replace( + transition=RETIREMENT_TRANSITION, + state_transitions={"wealth": base.next_wealth}, + active=lambda age, la=last_age: age < la, + ), + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + brute_solution = brute_model.solve(params=params, log_level="debug") + dcegm_solution = _get_skill_model().solve(params=params, log_level="debug") + + n_brute_unstable_nodes = 10 + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period][regime_name]) + dcegm_V = np.asarray(dcegm_solution[period][regime_name]) + assert brute_V.shape == dcegm_V.shape + np.testing.assert_allclose( + dcegm_V[..., n_brute_unstable_nodes:], + brute_V[..., n_brute_unstable_nodes:], + # The brute leg's grid-restricted max is the biased side here. + atol=3e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +def _stay_prob_from_param(survival_rate: float) -> FloatND: + return jnp.asarray(survival_rate) + + +def _death_prob_from_param(survival_rate: float) -> FloatND: + return jnp.asarray(1.0 - survival_rate) + + +def test_nan_regime_transition_prob_surfaces_as_error(): + """A NaN regime-transition probability raises instead of vanishing. + + Masking unreachable targets must not swallow a NaN probability (`NaN > 0` + is false): the runtime probability check rejects non-finite probabilities + in the DC-EGM solve exactly as under brute force. + """ + n_periods = 3 + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + model = Model( + regimes={ + "retirement": dcegm_retirement.replace( + transition={ + "retirement": MarkovTransition(_stay_prob_from_param), + "dead": MarkovTransition(_death_prob_from_param), + }, + active=lambda age, la=last_age: age < la, + ), + "dead": base.dead, + }, + ages=ages, + regime_id_class=RetirementOnlyRegimeId, + ) + params = get_retirement_only_params(n_periods) + # The granular transition replaces the age-based one, so its param goes + # and the per-cell survival rate (set to NaN) arrives. + del params["final_age_alive"] + params["retirement"] = { + **params.get("retirement", {}), + "retirement": {"next_regime": {"survival_rate": float("nan")}}, + "dead": {"next_regime": {"survival_rate": float("nan")}}, + } + + with pytest.raises(InvalidRegimeTransitionProbabilitiesError): + model.solve(params=params, log_level="debug") + + +@categorical(ordered=False) +class RegimeIdWithLost: + working_life: ScalarInt + retirement: ScalarInt + dead: ScalarInt + lost: ScalarInt + + +def _lost_utility() -> FloatND: + return jnp.asarray(-1000.0) + + +def test_undeclared_stateless_regime_does_not_enter_the_continuation(): + """A stateless regime outside the declared targets contributes nothing. + + The DC-EGM retirement regime declares its reachable targets granularly + (`{retirement, dead}`). A further stateless terminal regime in the model + β€” reachable only from the brute-force worker β€” must be invisible to the + retirement regime's continuation: its value function is unchanged by + that regime's presence. + """ + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + lost = base.dead.replace(functions={"utility": _lost_utility}) + shared_regimes = { + "working_life": base.working_life.replace( + active=lambda age, la=last_age: age < la + ), + "retirement": dcegm_retirement_full.replace( + transition=RETIREMENT_TRANSITION, + active=lambda age, la=last_age: age < la, + ), + "dead": base.dead, + } + with_lost = Model( + regimes={**shared_regimes, "lost": lost}, + ages=ages, + regime_id_class=RegimeIdWithLost, + ) + without_lost = Model( + regimes=shared_regimes, + ages=ages, + regime_id_class=base.RegimeId, + ) + params = _get_skill_model_params() + + solution_with = with_lost.solve(params=params, log_level="debug") + solution_without = without_lost.solve(params=params, log_level="debug") + + for period in sorted(solution_without)[:-1]: + np.testing.assert_allclose( + np.asarray(solution_with[period]["retirement"]), + np.asarray(solution_without[period]["retirement"]), + atol=1e-12, + err_msg=f"period={period}", + ) + + +def _nothing_is_feasible(labor_supply: DiscreteAction) -> BoolND: + return jnp.zeros_like(labor_supply, dtype=bool) + + +def test_all_infeasible_regime_publishes_neg_inf_like_brute_force(): + """A regime whose every combo is infeasible publishes `-inf` V, never NaN. + + A discrete-only constraint that is false everywhere makes the regime's + value `-inf` at every state; its parents (including its own earlier + periods) must absorb the `-inf` continuation gracefully. Brute force + publishes `-inf` in this case, and DC-EGM must match it. + """ + base_model_regimes = { + "working_life": dcegm_working_life.replace( + constraints={"nothing_is_feasible": _nothing_is_feasible}, + active=lambda age: age < 70, + ), + "retirement": dcegm_retirement_full.replace( + transition=RETIREMENT_TRANSITION, + state_transitions={ + "wealth": dcegm_retirement_full.state_transitions["wealth"], + }, + active=lambda age: age < 70, + ), + "dead": base.dead, + } + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + doomed_model = Model( + regimes=base_model_regimes, + ages=ages, + regime_id_class=base.RegimeId, + ) + params = get_full_params(N_PERIODS, discount_factor=0.98, wage=20.0) + + solution = doomed_model.solve(params=params, log_level="debug") + + for period in sorted(solution)[:-1]: + working_V = np.asarray(solution[period]["working_life"]) + assert bool(np.isneginf(working_V).all()), f"period={period}" + assert bool(np.isfinite(solution[period]["retirement"]).all()) diff --git a/tests/solution/test_egm_flat_resources.py b/tests/solution/test_egm_flat_resources.py new file mode 100644 index 000000000..33077ec04 --- /dev/null +++ b/tests/solution/test_egm_flat_resources.py @@ -0,0 +1,316 @@ +"""DC-EGM with generalized resources containing a flat region (means test). + +A means-tested floor `R = max(wealth, floor)` makes resources locally flat in +wealth: the composed Euler factor $\\partial R'/\\partial A$ is exactly zero +for savings whose next wealth lands below the floor, so saving into the flat +region has no marginal value. This exercises three pieces of the DC-EGM +kernel at once: + +- the composed-gradient factor (zero in the flat region, one above it), +- the degenerate-inversion guard (nodes with all child mass in the flat + region invert a clamped epsilon instead of zero), +- the upper-envelope cleanup of the candidate structure generated by the + resulting kink in the marginal continuation. + +The integration oracle is a dense-grid brute-force solve of an equivalent +spec; the consume-everything corner case has a closed-form solution. +""" + +import functools + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.upper_envelope.fues import refine_envelope +from lcm import AgeGrid, IrregSpacedGrid, LinSpacedGrid, Model +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.typing import BoolND, ContinuousAction, ContinuousState, FloatND +from lcm_examples.iskhakov_et_al_2017 import dead +from tests.test_models.deterministic.retirement_only import ( + RetirementOnlyRegimeId, + next_regime_from_retirement, +) + +# Number of model periods; the last one is spent in the terminal `dead` regime. +N_PERIODS = 4 + +# Means-tested resource floor of the integration model: with pension income +# 10 and zero interest, savings below 20 land next wealth below the floor. +RESOURCES_FLOOR = 30.0 + +# Floor of the corner-case model, above the entire wealth and savings range, +# so every savings node has all child mass in the flat region. +HIGH_FLOOR = 100.0 + +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=100.0, n_points=80) +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=100.0, n_points=400) + +# Exogenous end-of-period savings grid, cubically clustered toward the +# borrowing limit where the value function curves hardest. +SAVINGS_GRID = IrregSpacedGrid(points=tuple(100.0 * (i / 149) ** 3 for i in range(150))) + +CORNER_WEALTH_GRID = LinSpacedGrid(start=1.0, stop=50.0, n_points=40) +CORNER_CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=100.0, n_points=200) +CORNER_SAVINGS_GRID = LinSpacedGrid(start=0.0, stop=50.0, n_points=80) + + +def utility(consumption: ContinuousAction) -> FloatND: + return jnp.log(consumption) + + +def resources_with_floor(wealth: ContinuousState) -> FloatND: + return jnp.maximum(wealth, RESOURCES_FLOOR) + + +def resources_with_high_floor(wealth: ContinuousState) -> FloatND: + return jnp.maximum(wealth, HIGH_FLOOR) + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_wealth_from_savings( + savings: FloatND, interest_rate: float, pension: float +) -> ContinuousState: + return (1 + interest_rate) * savings + pension + + +def next_wealth_brute( + resources: FloatND, + consumption: ContinuousAction, + interest_rate: float, + pension: float, +) -> ContinuousState: + return (1 + interest_rate) * (resources - consumption) + pension + + +def budget_constraint(consumption: ContinuousAction, resources: FloatND) -> BoolND: + return consumption <= resources + + +@functools.cache +def _get_means_tested_model(variant: str) -> Model: + """Build the means-tested model for one solver variant (`dcegm`/`brute`).""" + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = float(ages.exact_values[-1]) + + def active(age: int, la: float = last_age) -> bool: + return age < la + + if variant == "brute": + regime = UserRegime( + transition=next_regime_from_retirement, + active=active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_brute}, + constraints={"budget_constraint": budget_constraint}, + functions={"utility": utility, "resources": resources_with_floor}, + ) + else: + regime = UserRegime( + transition=next_regime_from_retirement, + active=active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_from_savings}, + functions={ + "utility": utility, + "resources": resources_with_floor, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, + ), + ) + return Model( + regimes={"retirement": regime, "dead": dead}, + ages=ages, + regime_id_class=RetirementOnlyRegimeId, + ) + + +@functools.cache +def _get_corner_model() -> Model: + """Build the consume-everything corner model. + + The floor exceeds the whole savings range, so the child's resources are + constant and the expected marginal continuation is exactly zero at every + savings node β€” the degenerate-inversion guard must carry the entire + solution through the constrained segment. + """ + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = float(ages.exact_values[-1]) + regime = UserRegime( + transition=next_regime_from_retirement, + active=lambda age, la=last_age: age < la, + actions={"consumption": CORNER_CONSUMPTION_GRID}, + states={"wealth": CORNER_WEALTH_GRID}, + state_transitions={"wealth": next_wealth_from_savings}, + functions={ + "utility": utility, + "resources": resources_with_high_floor, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=CORNER_SAVINGS_GRID, + n_constrained_points=64, + ), + ) + return Model( + regimes={"retirement": regime, "dead": dead}, + ages=ages, + regime_id_class=RetirementOnlyRegimeId, + ) + + +def _get_params(*, pension: float) -> dict: + final_age_alive = 40 + (N_PERIODS - 2) * 10 + return { + "discount_factor": 0.95, + "interest_rate": 0.0, + "final_age_alive": final_age_alive, + "retirement": {"next_wealth": {"pension": pension}}, + } + + +def test_means_tested_transfer_matches_dense_brute_force(): + """DC-EGM with a flat-resources region matches dense brute force. + + The floor binds on the lower part of the wealth grid (resources are + constant there, so V must be flat in wealth below the floor) and the + zero-marginal flat region generates the candidate structure the upper + envelope cleans. Tolerance: the brute solver carries its consumption-grid + quantization and V-interpolation error; with the floor, resources never + fall below 30, so even the lowest wealth nodes are brute-stable and the + comparison runs on the full grid. + """ + params = _get_params(pension=10.0) + dcegm_solution = _get_means_tested_model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution = _get_means_tested_model("brute").solve( + params=params, log_level="debug" + ) + + for period in sorted(brute_solution)[:-1]: + np.testing.assert_allclose( + np.asarray(dcegm_solution[period]["retirement"]), + np.asarray(brute_solution[period]["retirement"]), + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +def test_all_child_mass_in_flat_region_yields_consume_everything(): + """With the floor above the savings range, consuming everything is optimal. + + Saving has exactly zero marginal value (the child's resources are pinned + at the floor), so the degenerate-inversion guard must produce the corner: + consume all resources, leaving the closed-form value + $V_t = \\sum_k \\beta^k \\log(\\text{floor})$ at every wealth node. The + solve must stay finite throughout (`log_level="debug"` raises on NaN). + Tolerance: the queried resources value coincides with the top constrained + candidate up to the float residue of the geometric candidate spacing. + """ + params = _get_params(pension=0.0) + solution = _get_corner_model().solve(params=params, log_level="debug") + + discount_factor = 0.95 + decision_periods = sorted(solution)[:-1] + for period in decision_periods: + V_arr = np.asarray(solution[period]["retirement"]) + assert np.all(np.isfinite(V_arr)), f"period={period}" + n_remaining = len(decision_periods) - period + expected = np.log(HIGH_FLOOR) * sum( + discount_factor**k for k in range(n_remaining) + ) + np.testing.assert_allclose( + V_arr, + np.full_like(V_arr, expected), + atol=1e-6, + rtol=1e-9, + err_msg=f"period={period}", + ) + + +def _flat_region_kink_candidates(): + """Candidates from a means-test kink in the marginal continuation. + + Two choice-specific segments as the Euler inversion produces them around + the floor exit: + + - Segment L (consume everything out of the flat region): saving stays at + the borrowing limit, so the policy is `c = R` (implied savings 0) and + the value line is `v = 2.0 + 0.5 R`, sampled at R in {0.5, 1.4, 2.3, + 4.1}. + - Segment H (save past the floor threshold): `c = 0.25 R` (implied + savings `0.75 R`) with the steeper value line `v = 0.2 + 1.1 R`, + sampled at R in {1.0, 2.0, 3.4, 4.4}. + + The lines cross at R* = 3.0 (v = 3.5): the envelope is L below, H above, + with a policy discontinuity from 3.0 down to 0.75 at the kink. + """ + r_flat = np.array([0.5, 1.4, 2.3, 4.1]) + r_saver = np.array([1.0, 2.0, 3.4, 4.4]) + grid = np.concatenate([r_flat, r_saver]) + value = np.concatenate([2.0 + 0.5 * r_flat, 0.2 + 1.1 * r_saver]) + policy = np.concatenate([r_flat, 0.25 * r_saver]) + return jnp.asarray(grid), jnp.asarray(policy), jnp.asarray(value) + + +# Analytic crossing of the two value lines in `_flat_region_kink_candidates`. +R_STAR = 3.0 +V_STAR = 2.0 + 0.5 * R_STAR + + +def test_fues_cleans_flat_resources_continuation_kink(): + """FUES keeps the analytic envelope of the flat-region/saver candidates. + + Dominated points of each branch are removed, the segment crossing is + inserted twice (left policy `c = R*`, right policy `c = 0.25 R*`), and + the refined arrays represent `max` of the two value lines under linear + interpolation. + """ + grid, policy, value = _flat_region_kink_candidates() + + refined_grid, refined_policy, refined_value, n_kept = refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=16 + ) + + assert int(n_kept) == 7 + kept = ~np.isnan(np.asarray(refined_grid)) + got_grid = np.asarray(refined_grid)[kept] + got_policy = np.asarray(refined_policy)[kept] + got_value = np.asarray(refined_value)[kept] + np.testing.assert_allclose( + got_grid, [0.5, 1.4, 2.3, R_STAR, R_STAR, 3.4, 4.4], atol=1e-8 + ) + + kink_slots = np.isclose(got_grid, R_STAR) + np.testing.assert_allclose(got_policy[kink_slots], [R_STAR, 0.25 * R_STAR]) + np.testing.assert_allclose(got_value[kink_slots], [V_STAR, V_STAR], atol=1e-8) + + queries = np.array([0.7, 1.5, 2.5, 2.9, 3.1, 4.0, 4.3]) + analytic = np.maximum(2.0 + 0.5 * queries, 0.2 + 1.1 * queries) + np.testing.assert_allclose( + np.interp(queries, got_grid, got_value), analytic, atol=1e-8 + ) diff --git a/tests/solution/test_egm_interp.py b/tests/solution/test_egm_interp.py new file mode 100644 index 000000000..a2569b7e2 --- /dev/null +++ b/tests/solution/test_egm_interp.py @@ -0,0 +1,316 @@ +"""Spec for interpolation on NaN-padded, weakly-ascending carry rows. + +Contract under test β€” `_lcm.egm.interp.interp_on_padded_grid`: + + interp_on_padded_grid( + *, x_query: FloatND, xp: Float1D, fp: Float1D, + fp_slopes: Float1D | None = None, + ) -> FloatND + +`xp` is a NaN-padded, weakly ascending grid row (NaNs only in the tail). +Behavior: + +- linear interpolation between neighboring non-NaN nodes, +- edge clamp outside the non-NaN range, +- tie-safe at duplicated abscissae (zero-width brackets from envelope kinks): + queries strictly below the duplicate interpolate toward the left value, queries + at or above it use the right value β€” never a division by the zero bracket, +- `-inf` endpoints (infeasible values) force their bracket interior to `-inf` + instead of NaN; a query exactly on a finite neighbor returns that value, +- with `fp_slopes` (the exact node derivatives), brackets whose endpoint + values and slopes are all finite get a monotone cubic Hermite correction; + all other brackets β€” and the contracts above β€” behave exactly as in the + linear case. +""" + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.egm import interp + + +def test_matches_numpy_interp_on_clean_grid(): + """On an unpadded strictly ascending grid, results equal `np.interp`.""" + xp = jnp.array([1.0, 2.0, 4.0, 8.0]) + fp = jnp.array([0.0, 3.0, 5.0, 6.0]) + x_query = jnp.array([1.0, 1.5, 3.0, 7.9, 8.0]) + + got = interp.interp_on_padded_grid(x_query=x_query, xp=xp, fp=fp) + + expected = np.interp(np.asarray(x_query), np.asarray(xp), np.asarray(fp)) + np.testing.assert_allclose(got, expected, atol=1e-12) + + +def test_nan_tail_is_ignored(): + """NaN padding in the tail does not affect interpolation on the prefix.""" + xp = jnp.array([1.0, 2.0, 4.0, jnp.nan, jnp.nan]) + fp = jnp.array([0.0, 3.0, 5.0, jnp.nan, jnp.nan]) + x_query = jnp.array([1.5, 3.0, 4.0]) + + got = interp.interp_on_padded_grid(x_query=x_query, xp=xp, fp=fp) + + expected = np.interp(np.asarray(x_query), [1.0, 2.0, 4.0], [0.0, 3.0, 5.0]) + np.testing.assert_allclose(got, expected, atol=1e-12) + + +def test_edge_clamp_below_and_above(): + """Queries outside the non-NaN range return the boundary values.""" + xp = jnp.array([1.0, 2.0, 4.0, jnp.nan]) + fp = jnp.array([0.0, 3.0, 5.0, jnp.nan]) + x_query = jnp.array([0.0, 100.0]) + + got = interp.interp_on_padded_grid(x_query=x_query, xp=xp, fp=fp) + + np.testing.assert_allclose(got, jnp.array([0.0, 5.0]), atol=1e-12) + + +def test_duplicated_abscissa_is_tie_safe(): + """A zero-width bracket (envelope kink) yields finite one-sided values.""" + xp = jnp.array([0.0, 1.0, 1.0, 2.0]) + fp = jnp.array([0.0, 10.0, 20.0, 30.0]) + x_query = jnp.array([0.5, 1.0, 1.5]) + + got = interp.interp_on_padded_grid(x_query=x_query, xp=xp, fp=fp) + + np.testing.assert_allclose(got[0], 5.0, atol=1e-12) + np.testing.assert_allclose(got[2], 25.0, atol=1e-12) + np.testing.assert_allclose(got[1], 20.0, atol=1e-12) + + +def test_neg_inf_node_yields_neg_inf_inside_brackets(): + """A `-inf` node forces its bracket interiors to `-inf`, never NaN. + + Value rows may carry `-inf` at a node (e.g. a terminal bequest at zero + wealth); a query exactly on the finite neighbor returns that neighbor's + value. + """ + xp = jnp.array([0.0, 1.0, 2.0]) + fp = jnp.array([-jnp.inf, 3.0, 5.0]) + x_query = jnp.array([0.0, 0.5, 1.0, 1.5]) + + got = interp.interp_on_padded_grid(x_query=x_query, xp=xp, fp=fp) + + np.testing.assert_array_equal(np.asarray(got), [-np.inf, -np.inf, 3.0, 4.0]) + + +def test_all_neg_inf_row_yields_neg_inf_everywhere(): + """An all-`-inf` row (infeasible combo) interpolates to `-inf`, never NaN.""" + xp = jnp.array([0.0, 1.0, 2.0, jnp.nan]) + fp = jnp.array([-jnp.inf, -jnp.inf, -jnp.inf, jnp.nan]) + x_query = jnp.array([-1.0, 0.5, 1.0, 3.0]) + + got = interp.interp_on_padded_grid(x_query=x_query, xp=xp, fp=fp) + + assert bool(jnp.isneginf(got).all()) + + +def test_exact_slopes_reproduce_a_monotone_cubic(): + """With exact node slopes, a monotone cubic is interpolated exactly. + + Per bracket the interpolant matches endpoint values and derivatives β€” four + degrees of freedom β€” so a cubic whose slopes pass the monotonicity limiter + untouched is reproduced to round-off, where linear interpolation is biased. + """ + xp = jnp.array([1.0, 1.5, 2.0]) + fp = xp**3 + fp_slopes = 3.0 * xp**2 + x_query = jnp.array([1.1, 1.25, 1.7, 1.95]) + + got = interp.interp_on_padded_grid( + x_query=x_query, xp=xp, fp=fp, fp_slopes=fp_slopes + ) + + np.testing.assert_allclose(got, np.asarray(x_query) ** 3, atol=1e-12) + + +def test_slopes_keep_nan_tail_edge_clamp_and_node_values(): + """The Hermite path preserves NaN-tail handling, edge clamps, and nodes.""" + xp = jnp.array([1.0, 2.0, 4.0, jnp.nan]) + fp = jnp.array([0.0, 3.0, 5.0, jnp.nan]) + fp_slopes = jnp.array([3.0, 2.0, 0.5, jnp.nan]) + x_query = jnp.array([0.0, 1.0, 2.0, 4.0, 100.0]) + + got = interp.interp_on_padded_grid( + x_query=x_query, xp=xp, fp=fp, fp_slopes=fp_slopes + ) + + np.testing.assert_allclose(got, jnp.array([0.0, 0.0, 3.0, 5.0, 5.0]), atol=1e-12) + + +def test_slopes_keep_duplicated_abscissa_tie_safe(): + """Zero-width kink brackets yield the same one-sided values as linear.""" + xp = jnp.array([0.0, 1.0, 1.0, 2.0]) + fp = jnp.array([0.0, 10.0, 20.0, 30.0]) + fp_slopes = jnp.array([10.0, 10.0, 10.0, 10.0]) + x_query = jnp.array([1.0]) + + got = interp.interp_on_padded_grid( + x_query=x_query, xp=xp, fp=fp, fp_slopes=fp_slopes + ) + + np.testing.assert_allclose(got, jnp.array([20.0]), atol=1e-12) + + +def test_slopes_on_neg_inf_bracket_fall_back_to_linear_rule(): + """A `-inf` endpoint forces its bracket interior to `-inf` with slopes given. + + Carry rows store slope `0.0` at `-inf` value nodes; the bracket must + behave exactly as in the linear case β€” `-inf` inside, the finite + neighbor's value on it. + """ + xp = jnp.array([0.0, 1.0, 2.0]) + fp = jnp.array([-jnp.inf, 3.0, 5.0]) + fp_slopes = jnp.array([0.0, 2.0, 2.0]) + x_query = jnp.array([0.0, 0.5, 1.0, 1.5]) + + got = interp.interp_on_padded_grid( + x_query=x_query, xp=xp, fp=fp, fp_slopes=fp_slopes + ) + + np.testing.assert_array_equal(np.asarray(got), [-np.inf, -np.inf, 3.0, 4.0]) + + +def test_steep_slopes_are_limited_to_keep_monotonicity(): + """Node slopes far above the secant cannot produce non-monotone output. + + An unlimited cubic Hermite with endpoint slopes ten times the secant + overshoots inside the bracket; the limiter caps slopes at three times the + secant, so the interpolant stays within the bracket's value range and + weakly increasing on increasing data. + """ + xp = jnp.array([0.0, 1.0]) + fp = jnp.array([0.0, 1.0]) + fp_slopes = jnp.array([10.0, 10.0]) + x_query = jnp.linspace(0.0, 1.0, 101) + + got = interp.interp_on_padded_grid( + x_query=x_query, xp=xp, fp=fp, fp_slopes=fp_slopes + ) + + assert bool(jnp.all(jnp.diff(got) >= 0.0)) + assert bool(jnp.all((got >= 0.0) & (got <= 1.0))) + + +# Prepared-row interpolation: `prepare_padded_grid` builds the row's +inf search +# key and valid length once; `interp_on_prepared_grid` does only searchsorted + +# gather. `interp_on_padded_grid` is the thin wrapper that prepares the row and +# delegates, so the prepared path must be bit-identical to the padded path. + +_PREPARED_GRID_CASES = { + "clean": ( + jnp.array([1.0, 2.0, 4.0, 8.0]), + jnp.array([0.0, 3.0, 5.0, 6.0]), + None, + ), + "nan_tail": ( + jnp.array([1.0, 2.0, 4.0, jnp.nan, jnp.nan]), + jnp.array([0.0, 3.0, 5.0, jnp.nan, jnp.nan]), + None, + ), + "duplicated_abscissa": ( + jnp.array([0.0, 1.0, 1.0, 2.0]), + jnp.array([0.0, 10.0, 20.0, 30.0]), + None, + ), + "neg_inf_node": ( + jnp.array([0.0, 1.0, 2.0]), + jnp.array([-jnp.inf, 3.0, 5.0]), + None, + ), + "all_neg_inf": ( + jnp.array([0.0, 1.0, 2.0, jnp.nan]), + jnp.array([-jnp.inf, -jnp.inf, -jnp.inf, jnp.nan]), + None, + ), + "hermite_cubic": ( + jnp.array([1.0, 1.5, 2.0]), + jnp.array([1.0, 1.5, 2.0]) ** 3, + 3.0 * jnp.array([1.0, 1.5, 2.0]) ** 2, + ), + "hermite_nan_tail": ( + jnp.array([1.0, 2.0, 4.0, jnp.nan]), + jnp.array([0.0, 3.0, 5.0, jnp.nan]), + jnp.array([3.0, 2.0, 0.5, jnp.nan]), + ), + "hermite_neg_inf": ( + jnp.array([0.0, 1.0, 2.0]), + jnp.array([-jnp.inf, 3.0, 5.0]), + jnp.array([0.0, 2.0, 2.0]), + ), +} + + +@pytest.mark.parametrize("case", list(_PREPARED_GRID_CASES)) +def test_prepared_grid_interpolation_matches_padded_grid(case): + """Preparing the row then interpolating equals interpolating the padded row. + + The query mesh spans the non-NaN range plus out-of-range clamps, kink + abscissae, and on-node points, so the comparison covers the linear, edge + clamp, tie-safe, `-inf`, and Hermite branches. + """ + xp, fp, fp_slopes = _PREPARED_GRID_CASES[case] + x_query = jnp.array([-1.0, 0.0, 0.5, 1.0, 1.5, 2.0, 4.0, 100.0]) + + padded = interp.interp_on_padded_grid( + x_query=x_query, xp=xp, fp=fp, fp_slopes=fp_slopes + ) + search_grid, valid_length = interp.prepare_padded_grid(xp) + prepared = interp.interp_on_prepared_grid( + x_query=x_query, + search_grid=search_grid, + valid_length=valid_length, + xp=xp, + fp=fp, + fp_slopes=fp_slopes, + ) + + np.testing.assert_array_equal(np.asarray(prepared), np.asarray(padded)) + + +def test_prepare_padded_grid_reports_inf_key_and_valid_length(): + """The search key replaces the NaN tail with `+inf`; valid length counts the + non-NaN prefix.""" + xp = jnp.array([1.0, 2.0, 4.0, jnp.nan, jnp.nan]) + + search_grid, valid_length = interp.prepare_padded_grid(xp) + + np.testing.assert_array_equal( + np.asarray(search_grid), [1.0, 2.0, 4.0, np.inf, np.inf] + ) + assert int(valid_length) == 3 + + +def test_prepared_interpolation_holds_no_grid_by_query_intermediate(): + """A row prepared once and read at many queries holds no grid-by-query mesh. + + This is the transient-memory contract: with the search key and valid length + prepared above the query fan-out, the per-query path does only a scalar-carry + `searchsorted` plus gathers, so no operation carries both the query axis and + the grid (`n_pad`) axis. A regression here would reintroduce the + `O(queries * n_pad)` working buffer the NaN preamble used to create. + """ + n_grid, n_query = 64, 11 + xp = jnp.arange(n_grid, dtype=float) + fp = jnp.sqrt(xp) + queries = jnp.linspace(0.0, n_grid, n_query) + + def read_many(search_grid, valid_length, xp, fp, queries): + return interp.interp_on_prepared_grid( + x_query=queries, + search_grid=search_grid, + valid_length=valid_length, + xp=xp, + fp=fp, + ) + + search_grid, valid_length = interp.prepare_padded_grid(xp) + hlo = jax.jit(read_many).lower(search_grid, valid_length, xp, fp, queries).compile() + forbidden = {(n_query, n_grid), (n_grid, n_query)} + offenders = [ + line.strip() + for line in (hlo.as_text() or "").splitlines() + if any(f"[{a},{b}]" in line for a, b in forbidden) + ] + assert not offenders, "grid-by-query intermediate present:\n" + "\n".join(offenders) diff --git a/tests/solution/test_egm_markov_states.py b/tests/solution/test_egm_markov_states.py new file mode 100644 index 000000000..60067b5b2 --- /dev/null +++ b/tests/solution/test_egm_markov_states.py @@ -0,0 +1,602 @@ +"""DC-EGM carrying a stochastic Markov discrete state into the child. + +A Markov discrete state is a node-valued discrete dimension whose next-period +node is drawn from an intrinsic transition law +$w(\\text{node}' \\mid \\text{node}, \\text{params})$ supplied by a +`MarkovTransition`. In a DC-EGM regime it rides on the own side exactly like a +plain discrete state (one carry row and one V slice per node) while the child +side takes an expectation: the child's node is distributed, so the carry read +indexes the child rows at every node, performs the full read there (resources +interpolation, passive blend, discrete-action aggregation), and weights the +resulting per-node values and marginals with the transition weights β€” the +expectation sits *outside* the action aggregation, matching the brute-force +solver's weighted average of the already action-aggregated next-period V. + +The oracle is a dense-grid brute-force solve of a mathematically equivalent +spec (same state grids, dense consumption grid, explicit budget constraint). +""" + +import functools + +import jax.numpy as jnp +import numpy as np + +from _lcm.typing import PeriodToRegimeToVArr +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + MarkovTransition, + Model, + RouwenhorstAR1Process, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM, GridSearch +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteState, + FloatND, + ScalarInt, +) +from lcm_examples.iskhakov_et_al_2017 import dead + +# Number of model periods; the last one is spent in the terminal `dead` regime. +N_PERIODS = 4 + +# Utility penalty of being in bad health (consumption-separable). +BAD_HEALTH_PENALTY = 0.3 + +# Deterministic income added to savings in the wealth law; keeps child wealth +# queries away from the grid's lower edge, where the two solvers clamp +# differently. +LABOR_INCOME = 5.0 + +# 160 wealth nodes: the brute-force oracle interpolates next-period V linearly +# in wealth (a downward bias where V curves), while the DC-EGM carry read uses +# exact slopes; the dense grid keeps that oracle-side bias below the comparison +# tolerance. +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=100.0, n_points=160) + +# The consumption grid covers the maximum resources so the brute-force oracle +# is not artificially capped at high wealth; 4000 points keep the oracle's own +# resolution error below the comparison tolerance. +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=110.0, n_points=4000) + +# Exogenous end-of-period savings grid, cubically clustered toward the +# borrowing limit where the value function curves hardest. +SAVINGS_GRID = IrregSpacedGrid(points=tuple(100.0 * (i / 149) ** 3 for i in range(150))) + +# Lowest wealth nodes excluded from the brute-force comparison: there the brute +# solver leans on consumption choices near its grid start and on coarse +# interpolation where log utility curves hardest (the same exclusion the +# sibling DC-EGM oracle tests use). +N_BRUTE_UNSTABLE_NODES = 16 + + +@categorical(ordered=False) +class MarkovRegimeId: + working_life: ScalarInt + dead: ScalarInt + + +@categorical(ordered=False) +class Health: + good: ScalarInt + bad: ScalarInt + + +def utility_with_health( + consumption: ContinuousAction, health: DiscreteState +) -> FloatND: + return jnp.log(consumption) - jnp.where( + health == Health.bad, BAD_HEALTH_PENALTY, 0.0 + ) + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def budget_constraint(consumption: ContinuousAction, wealth: ContinuousState) -> BoolND: + return consumption <= wealth + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where( + age >= final_age_alive, + MarkovRegimeId.dead, + MarkovRegimeId.working_life, + ) + + +def next_wealth_dcegm(savings: FloatND) -> ContinuousState: + return savings + LABOR_INCOME + + +def next_wealth_brute( + wealth: ContinuousState, consumption: ContinuousAction +) -> ContinuousState: + return wealth - consumption + LABOR_INCOME + + +def health_transition(health: DiscreteState, age: int) -> FloatND: + """Markov health law varying by current health and period. + + Health is sticky and improves with age. The row over next-period + `[good, bad]` returns a probability vector summing to one for each current + health node. + """ + # Older workers face a higher chance of staying healthy; the current + # health node sets persistence. + age_bonus = jnp.clip((age - 40) / 60.0, 0.0, 0.2) + p_good = jnp.where( + health == Health.good, + 0.65 + age_bonus, + 0.25 + age_bonus, + ) + return jnp.stack([p_good, 1.0 - p_good]) + + +def _ages() -> AgeGrid: + return AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + + +def _active(age: int) -> bool: + last_age = 40 + (N_PERIODS - 1) * 10 + return age < last_age + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, +) + + +def _dcegm_functions() -> dict: + return { + "utility": utility_with_health, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + } + + +def _params() -> dict: + return { + "discount_factor": 0.95, + "final_age_alive": 40 + (N_PERIODS - 2) * 10, + } + + +def _assert_working_life_V_matches( + *, dcegm_solution: PeriodToRegimeToVArr, brute_solution: PeriodToRegimeToVArr +) -> None: + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + assert brute_V.shape == dcegm_V.shape + # The Markov health node is the leading axis of V; wealth is the + # trailing axis. Exclude the lowest wealth nodes from the comparison. + np.testing.assert_allclose( + dcegm_V[:, N_BRUTE_UNSTABLE_NODES:], + brute_V[:, N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +@functools.cache +def _same_grid_markov_model(solver: str) -> Model: + """A Markov health state carried every period into the same-grid target.""" + is_dcegm = solver == "dcegm" + working = UserRegime( + transition=next_regime, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID, "health": DiscreteGrid(Health)}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute, + "health": MarkovTransition(health_transition), + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={ + **(_dcegm_functions() if is_dcegm else {}), + "utility": utility_with_health, + }, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=MarkovRegimeId, + ) + + +def test_same_grid_markov_state_matches_brute_force(): + """A Markov health state carried into the same grid matches brute force. + + The child's health node is distributed per the `MarkovTransition` weights + at the parent's node and period; the carry read indexes the child rows at + every node and weight-sums the per-node values *outside* the consumption + choice. Values agree with the dense-grid brute-force oracle on the full + health-by-wealth grid, excluding the lowest wealth nodes. + """ + params = _params() + dcegm_solution = _same_grid_markov_model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution = _same_grid_markov_model("brute_force").solve( + params=params, log_level="debug" + ) + _assert_working_life_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) + + +@categorical(ordered=False) +class Health3: + good: ScalarInt + fair: ScalarInt + bad: ScalarInt + + +@categorical(ordered=False) +class CrossGridRegimeId: + early: ScalarInt + late: ScalarInt + dead: ScalarInt + + +def utility_early(consumption: ContinuousAction, health: DiscreteState) -> FloatND: + """Utility with a three-level health penalty.""" + penalty = jnp.where( + health == Health3.good, + 0.0, + jnp.where(health == Health3.fair, 0.5 * BAD_HEALTH_PENALTY, BAD_HEALTH_PENALTY), + ) + return jnp.log(consumption) - penalty + + +def remap_health_to_two(health: DiscreteState) -> FloatND: + """Markov remap from the three-level grid onto the two-level `[good, bad]`. + + `good` stays mostly good, `fair` splits, `bad` stays mostly bad β€” a + probability vector of length two (the *target* grid), shorter than the + source's three-level grid. + """ + p_good = jnp.where( + health == Health3.good, + 0.8, + jnp.where(health == Health3.fair, 0.5, 0.1), + ) + return jnp.stack([p_good, 1.0 - p_good]) + + +def late_health_transition(health: DiscreteState) -> FloatND: + """Sticky two-level health law within the late regime.""" + p_good = jnp.where(health == Health.good, 0.7, 0.3) + return jnp.stack([p_good, 1.0 - p_good]) + + +def to_live_prob(age: int, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 0.0, 1.0) + + +def to_dead_prob(age: int, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 1.0, 0.0) + + +@functools.cache +def _cross_grid_markov_model(solver: str) -> Model: + """A three-level Markov health remapped onto a two-level child grid. + + The early regime carries `health` on a three-level grid and transitions + every period into the late regime, whose `health` lives on a two-level + grid. The remap weights returned for `next_health` have the *target* (late) + grid's length, exercising a stochastic axis whose size differs from the + source's discrete grid. + """ + is_dcegm = solver == "dcegm" + early = UserRegime( + transition={ + "late": MarkovTransition(to_live_prob), + "dead": MarkovTransition(to_dead_prob), + }, + active=lambda age: age < 40 + (N_PERIODS - 1) * 10, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID, "health": DiscreteGrid(Health3)}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute, + "health": {"late": MarkovTransition(remap_health_to_two)}, + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={ + **( + { + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + } + if is_dcegm + else {} + ), + "utility": utility_early, + }, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + late = UserRegime( + transition={ + "late": MarkovTransition(to_live_prob), + "dead": MarkovTransition(to_dead_prob), + }, + active=lambda age: age < 40 + (N_PERIODS - 1) * 10, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID, "health": DiscreteGrid(Health)}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute, + "health": {"late": MarkovTransition(late_health_transition)}, + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={ + **(_dcegm_functions() if is_dcegm else {}), + "utility": utility_with_health, + }, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"early": early, "late": late, "dead": dead}, + ages=_ages(), + regime_id_class=CrossGridRegimeId, + ) + + +def test_cross_grid_markov_state_matches_brute_force(): + """A three-level Markov health remapped onto a two-level child grid solves. + + The early regime's `next_health` weight vector has the late (target) + grid's length β€” shorter than the source's three-level health grid β€” so the + integration ranges over the *child's* node axis, not the parent's. Values + in the early regime agree with the dense-grid brute-force oracle. + """ + params = _params() + dcegm_solution = _cross_grid_markov_model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution = _cross_grid_markov_model("brute_force").solve( + params=params, log_level="debug" + ) + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["early"]) + dcegm_V = np.asarray(dcegm_solution[period]["early"]) + assert brute_V.shape == dcegm_V.shape == (3, 160) + np.testing.assert_allclose( + dcegm_V[:, N_BRUTE_UNSTABLE_NODES:], + brute_V[:, N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +# Number of discretization nodes of the income process for the joint fixture. +N_INCOME_NODES = 5 + +# Unconditional income floor added to next wealth in the joint fixture; keeps +# continuation wealth inside the wealth grid even at zero savings. +BASE_INCOME = 5.0 + + +def utility_with_health_only( + consumption: ContinuousAction, health: DiscreteState +) -> FloatND: + return jnp.log(consumption) - jnp.where( + health == Health.bad, BAD_HEALTH_PENALTY, 0.0 + ) + + +def next_wealth_joint_dcegm( + savings: FloatND, income: ContinuousState +) -> ContinuousState: + return savings + BASE_INCOME + jnp.exp(income) + + +def next_wealth_joint_brute( + wealth: ContinuousState, + consumption: ContinuousAction, + income: ContinuousState, +) -> ContinuousState: + return wealth - consumption + BASE_INCOME + jnp.exp(income) + + +def joint_health_transition(health: DiscreteState) -> FloatND: + p_good = jnp.where(health == Health.good, 0.7, 0.35) + return jnp.stack([p_good, 1.0 - p_good]) + + +@functools.cache +def _joint_process_markov_model(solver: str) -> Model: + """An AR(1) income process and a Markov health state on the same target. + + A self-targeting working regime carries both a Rouwenhorst income process + (entering the wealth law) and a Markov health state (penalising utility). + Both are stochastic node axes of the same carry target, so the child read + integrates over the joint income-by-health node mesh. + """ + is_dcegm = solver == "dcegm" + working = UserRegime( + transition=next_regime, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={ + "wealth": WEALTH_GRID, + "income": RouwenhorstAR1Process(n_points=N_INCOME_NODES), + "health": DiscreteGrid(Health), + }, + state_transitions={ + "wealth": next_wealth_joint_dcegm if is_dcegm else next_wealth_joint_brute, + "health": MarkovTransition(joint_health_transition), + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={ + **( + { + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + } + if is_dcegm + else {} + ), + "utility": utility_with_health_only, + }, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=MarkovRegimeId, + ) + + +def _joint_params() -> dict: + return { + "discount_factor": 0.95, + "final_age_alive": 40 + (N_PERIODS - 2) * 10, + "working_life": {"income": {"mu": 0.0, "sigma": 0.25, "rho": 0.6}}, + } + + +def test_joint_process_and_markov_state_matches_brute_force(): + """An AR(1) process and a Markov state on one target match brute force. + + The child read integrates over the joint income-by-health node mesh: the + income node feeds the wealth law and the health node selects the carry's + leading health axis, weighted by the outer product of the AR(1) and Markov + transition vectors. Values agree with the dense-grid brute-force oracle on + the full income-by-health-by-wealth grid. + """ + params = _joint_params() + dcegm_solution = _joint_process_markov_model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution = _joint_process_markov_model("brute_force").solve( + params=params, log_level="debug" + ) + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + assert brute_V.shape == dcegm_V.shape == (N_INCOME_NODES, 2, 160) + np.testing.assert_allclose( + dcegm_V[..., N_BRUTE_UNSTABLE_NODES:], + brute_V[..., N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +# Guaranteed-minimum-income floor: a transfer tops next-period cash-on-hand up +# to the floor, so low savings land on the constrained segment. +INCOME_FLOOR = 12.0 + + +def income_transfer(savings: FloatND) -> FloatND: + """Top-up transfer raising next-period resources to the income floor.""" + return jnp.maximum(0.0, INCOME_FLOOR - (savings + LABOR_INCOME)) + + +def income_transfer_brute( + wealth: ContinuousState, consumption: ContinuousAction +) -> FloatND: + return jnp.maximum(0.0, INCOME_FLOOR - (wealth - consumption + LABOR_INCOME)) + + +def next_wealth_floor_dcegm( + savings: FloatND, income_transfer: FloatND +) -> ContinuousState: + return savings + LABOR_INCOME + income_transfer + + +def next_wealth_floor_brute( + wealth: ContinuousState, consumption: ContinuousAction, income_transfer: FloatND +) -> ContinuousState: + return wealth - consumption + LABOR_INCOME + income_transfer + + +def point_mass_health_transition(health: DiscreteState) -> FloatND: + """Degenerate Markov row: all mass on `good` regardless of current health.""" + p_good = jnp.where(health == Health.bad, 1.0, 1.0) + return jnp.stack([p_good, 1.0 - p_good]) + + +@functools.cache +def _point_mass_floor_model(solver: str) -> Model: + """A point-mass Markov health in a consumption-floor model. + + The wealth law adds a guaranteed-minimum-income transfer, so low savings + push next-period resources onto the floor (the constrained segment). The + Markov health row places all mass on `good`, so its integration must + reproduce the deterministic-index result. + """ + is_dcegm = solver == "dcegm" + working = UserRegime( + transition=next_regime, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID, "health": DiscreteGrid(Health)}, + state_transitions={ + "wealth": next_wealth_floor_dcegm if is_dcegm else next_wealth_floor_brute, + "health": MarkovTransition(point_mass_health_transition), + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={ + **(_dcegm_functions() if is_dcegm else {}), + "utility": utility_with_health, + "income_transfer": income_transfer if is_dcegm else income_transfer_brute, + }, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=MarkovRegimeId, + ) + + +def test_point_mass_markov_with_income_floor_matches_brute_force(): + """A degenerate Markov row in a consumption-floor model matches brute force. + + The Markov health row places all mass on `good`, so the integration over + the health node reproduces the deterministic-index result; the wealth law's + income-floor transfer pushes low savings onto the constrained segment, + where DC-EGM uses its closed-form credit-constrained candidates. Both the + point-mass integration and the floor behaviour agree with the dense-grid + brute-force oracle across the full health-by-wealth grid. + """ + params = _params() + dcegm_solution = _point_mass_floor_model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution = _point_mass_floor_model("brute_force").solve( + params=params, log_level="debug" + ) + _assert_working_life_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) diff --git a/tests/solution/test_egm_passive.py b/tests/solution/test_egm_passive.py new file mode 100644 index 000000000..d6e2c9be2 --- /dev/null +++ b/tests/solution/test_egm_passive.py @@ -0,0 +1,312 @@ +"""DC-EGM with a passive continuous state (AIME-like skill accumulation). + +A passive continuous state is a deterministic, non-process continuous state +whose transition depends on neither the continuous action, the post-decision +function, nor the Euler state β€” here, a skill level driven by a discrete +labor choice. The DC-EGM kernel carries one grid axis per passive state and +reads the child carry with mixed interpolation: linear weights on the two +neighboring nodes of the child's passive grid, each neighbor's row +interpolated 1-D in resources, blended per discrete-action row before the +choice aggregation. + +The oracle is a dense-grid brute-force solve of a mathematically equivalent +spec (same wealth and skill grids, dense consumption grid, explicit budget +constraint). +""" + +import functools + +import jax.numpy as jnp +import numpy as np + +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + Model, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.transition import fixed_transition +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteAction, + FloatND, + ScalarInt, +) +from lcm_examples.iskhakov_et_al_2017 import dead + +# Number of model periods; the last one is spent in the terminal `dead` regime. +N_PERIODS = 4 + +# Skill increment earned by one period of work. With the 0.25 node spacing of +# SKILL_GRID, working transitions land off-grid (0.4 is not a multiple of +# 0.25) while resting (identity transition) and the clamp at SKILL_MAX land +# exactly on nodes β€” both interpolation paths are exercised across periods. +SKILL_GAIN = 0.4 + +# Upper bound of the skill grid; the skill transition clamps here. +SKILL_MAX = 1.5 + +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=100.0, n_points=80) +SKILL_GRID = LinSpacedGrid(start=0.0, stop=SKILL_MAX, n_points=7) +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=100.0, n_points=400) + +# Exogenous end-of-period savings grid, cubically clustered toward the +# borrowing limit where the value function curves hardest. +SAVINGS_GRID = IrregSpacedGrid(points=tuple(100.0 * (i / 149) ** 3 for i in range(150))) + + +@categorical(ordered=False) +class PassiveRegimeId: + working_life: ScalarInt + dead: ScalarInt + + +@categorical(ordered=True) +class LaborChoice: + work: ScalarInt + rest: ScalarInt + + +def is_working(labor_supply: DiscreteAction) -> BoolND: + return labor_supply == LaborChoice.work + + +def labor_income(is_working: BoolND, skill: ContinuousState, wage: float) -> FloatND: + return jnp.where(is_working, wage * (1.0 + skill), 0.0) + + +def utility( + consumption: ContinuousAction, is_working: BoolND, disutility_of_work: float +) -> FloatND: + return jnp.log(consumption) - jnp.where(is_working, disutility_of_work, 0.0) + + +def next_skill(skill: ContinuousState, is_working: BoolND) -> ContinuousState: + return jnp.minimum(skill + jnp.where(is_working, SKILL_GAIN, 0.0), SKILL_MAX) + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_wealth_from_savings( + savings: FloatND, labor_income: FloatND, interest_rate: float +) -> ContinuousState: + return (1 + interest_rate) * savings + labor_income + + +def next_wealth_brute( + wealth: ContinuousState, + consumption: ContinuousAction, + labor_income: FloatND, + interest_rate: float, +) -> ContinuousState: + return (1 + interest_rate) * (wealth - consumption) + labor_income + + +def borrowing_constraint( + consumption: ContinuousAction, wealth: ContinuousState +) -> BoolND: + return consumption <= wealth + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where( + age >= final_age_alive, + PassiveRegimeId.dead, + PassiveRegimeId.working_life, + ) + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, +) + + +def labor_income_fixed_skill( + is_working: BoolND, wage: float, skill_level: float +) -> FloatND: + """Labor income of the skill-free comparison model; skill is a parameter.""" + return jnp.where(is_working, wage * (1.0 + skill_level), 0.0) + + +@functools.cache +def _get_model(variant: str) -> Model: + """Build one model variant. + + - `"dcegm"`: DC-EGM with the accumulating (off-grid) skill transition. + - `"brute"`: dense-grid brute force, mathematically equivalent spec. + - `"dcegm_fixed_skill"`: DC-EGM with an identity skill transition, so + every child passive value lands exactly on a node. + - `"dcegm_no_skill"`: DC-EGM without the skill state; skill enters labor + income as the `skill_level` parameter. + """ + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = float(ages.exact_values[-1]) + + def active(age: int, la: float = last_age) -> bool: + return age < la + + if variant == "brute": + working = UserRegime( + transition=next_regime, + active=active, + actions={ + "labor_supply": DiscreteGrid(LaborChoice), + "consumption": CONSUMPTION_GRID, + }, + states={"wealth": WEALTH_GRID, "skill": SKILL_GRID}, + state_transitions={"wealth": next_wealth_brute, "skill": next_skill}, + constraints={"borrowing_constraint": borrowing_constraint}, + functions={ + "utility": utility, + "labor_income": labor_income, + "is_working": is_working, + }, + ) + elif variant == "dcegm_no_skill": + working = UserRegime( + transition=next_regime, + active=active, + actions={ + "labor_supply": DiscreteGrid(LaborChoice), + "consumption": CONSUMPTION_GRID, + }, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_from_savings}, + functions={ + "utility": utility, + "labor_income": labor_income_fixed_skill, + "is_working": is_working, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, + ) + else: + skill_transition = ( + fixed_transition("skill") if variant == "dcegm_fixed_skill" else next_skill + ) + working = UserRegime( + transition=next_regime, + active=active, + actions={ + "labor_supply": DiscreteGrid(LaborChoice), + "consumption": CONSUMPTION_GRID, + }, + states={"wealth": WEALTH_GRID, "skill": SKILL_GRID}, + state_transitions={ + "wealth": next_wealth_from_savings, + "skill": skill_transition, + }, + functions={ + "utility": utility, + "labor_income": labor_income, + "is_working": is_working, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=ages, + regime_id_class=PassiveRegimeId, + ) + + +def _get_params(*, skill_level: float | None = None) -> dict: + final_age_alive = 40 + (N_PERIODS - 2) * 10 + labor_income_params = {"wage": 20.0} + if skill_level is not None: + labor_income_params["skill_level"] = skill_level + return { + "discount_factor": 0.95, + "interest_rate": 0.0, + "final_age_alive": final_age_alive, + "working_life": { + "labor_income": labor_income_params, + "utility": {"disutility_of_work": 0.5}, + }, + } + + +def test_passive_state_matches_dense_brute_force(): + """DC-EGM with an off-grid passive transition matches dense brute force. + + Both solvers share the wealth and skill grids; working moves skill off the + node spacing, so every period exercises the mixed passive read. Tolerance: + both methods interpolate linearly in the passive dimension but in + different objects (brute interpolates the aggregated V', DC-EGM blends + choice-specific carry rows before aggregating), so they agree only up to + the linear-interpolation error in skill plus the brute solver's + consumption-grid resolution. The lowest wealth nodes are excluded: there + the coarse consumption grid makes brute force itself unreliable (the same + exclusion the discrete DC-EGM tests use). + """ + params = _get_params() + dcegm_solution = _get_model("dcegm").solve(params=params, log_level="debug") + brute_solution = _get_model("brute").solve(params=params, log_level="debug") + + n_brute_unstable_nodes = 8 + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + assert brute_V.shape == dcegm_V.shape == (80, 7) + np.testing.assert_allclose( + dcegm_V[n_brute_unstable_nodes:, :], + brute_V[n_brute_unstable_nodes:, :], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +def test_on_node_passive_value_reproduces_skill_free_solution(): + """A passive value landing exactly on a node reads that node's rows exactly. + + With an identity skill transition every child passive value is a grid + node, so each skill slice solves an independent model in which skill is a + constant. The slice must reproduce the skill-free DC-EGM model with that + constant baked into labor income β€” node for node, with no interpolation + error from the passive read. + """ + sliced_solution = _get_model("dcegm_fixed_skill").solve( + params=_get_params(), log_level="debug" + ) + skill_nodes = np.asarray(SKILL_GRID.to_jax()) + + for skill_index in [0, 3, 6]: + single_solution = _get_model("dcegm_no_skill").solve( + params=_get_params(skill_level=float(skill_nodes[skill_index])), + log_level="debug", + ) + for period in sorted(sliced_solution)[:-1]: + np.testing.assert_allclose( + np.asarray(sliced_solution[period]["working_life"])[:, skill_index], + np.asarray(single_solution[period]["working_life"]), + rtol=1e-9, + atol=1e-9, + err_msg=f"period={period}, skill_index={skill_index}", + ) diff --git a/tests/solution/test_egm_passive_asset_row.py b/tests/solution/test_egm_passive_asset_row.py new file mode 100644 index 000000000..73f50f921 --- /dev/null +++ b/tests/solution/test_egm_passive_asset_row.py @@ -0,0 +1,551 @@ +"""DC-EGM passive continuous state carried through asset-row mode. + +The ACA living-regime shape carries two continuous states β€” the Euler state +`wealth` (assets) and a passive `aime`-like state whose deterministic +transition reads a discrete action and a stochastic process node, independent +of the continuous action and the savings node β€” while a savings-stage function +(the survival probability) reads the Euler state, so the regime solves per +exogenous asset node *and* carries the passive axis and a process axis +simultaneously. The passive read blends the two neighboring nodes of the +child's passive grid, the process node is integrated with its intrinsic +weights, and each asset row publishes its own node. + +The oracle is a dense-grid brute-force solve of a mathematically equivalent +spec (same wealth, AIME, and income grids, dense consumption grid, explicit +budget constraint). +""" + +import functools + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.typing import PeriodToRegimeToVArr +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + MarkovTransition, + Model, + RouwenhorstAR1Process, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM, GridSearch +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteAction, + FloatND, + ScalarInt, +) +from lcm_examples.iskhakov_et_al_2017 import dead + +N_PERIODS = 4 +N_INCOME_NODES = 5 + +# Wealth band over which the survival smoothstep ramps; resolved across many +# wealth cells so the build-time continuity check admits it. +BAND_START = 30.0 +BAND_WIDTH = 30.0 +SURVIVAL_LOW = 0.6 +SURVIVAL_HIGH = 0.95 + +# AIME accrual per period of work, scaled by the income node; lands off the +# AIME node spacing so the mixed passive read is exercised. Capped at the top +# AIME node. +AIME_GAIN = 1.3 +AIME_MAX = 20.0 + +# Pension annuity drawn from accumulated AIME, added to next wealth. +PENSION_RATE = 0.2 + +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=100.0, n_points=120) +AIME_GRID = LinSpacedGrid(start=0.0, stop=AIME_MAX, n_points=6) +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=120.0, n_points=600) +SAVINGS_GRID = IrregSpacedGrid(points=tuple(100.0 * (i / 119) ** 3 for i in range(120))) + +N_BRUTE_UNSTABLE_NODES = 16 + + +@categorical(ordered=False) +class PassiveAssetRowRegimeId: + working_life: ScalarInt + dead: ScalarInt + + +@categorical(ordered=True) +class LaborChoice: + work: ScalarInt + rest: ScalarInt + + +def is_working(labor_supply: DiscreteAction) -> BoolND: + return labor_supply == LaborChoice.work + + +def smoothstep_in_band(wealth: ContinuousState) -> FloatND: + t = jnp.clip((wealth - BAND_START) / BAND_WIDTH, 0.0, 1.0) + return t * t * t * (t * (6.0 * t - 15.0) + 10.0) + + +def survival_of_wealth(wealth: ContinuousState) -> FloatND: + return SURVIVAL_LOW + (SURVIVAL_HIGH - SURVIVAL_LOW) * smoothstep_in_band(wealth) + + +def stay_prob(wealth: ContinuousState, age: int, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 0.0, survival_of_wealth(wealth)) + + +def death_prob(wealth: ContinuousState, age: int, final_age_alive: float) -> FloatND: + return 1.0 - stay_prob(wealth, age, final_age_alive) + + +def utility( + consumption: ContinuousAction, is_working: BoolND, disutility_of_work: float +) -> FloatND: + return jnp.log(consumption) - jnp.where(is_working, disutility_of_work, 0.0) + + +def labor_income(is_working: BoolND, income: ContinuousState, wage: float) -> FloatND: + return jnp.where(is_working, wage * jnp.exp(income), 0.0) + + +def pension_income(aime: ContinuousState) -> FloatND: + return PENSION_RATE * aime + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_aime( + aime: ContinuousState, is_working: BoolND, income: ContinuousState +) -> ContinuousState: + """Passive AIME accrual: reads the work choice and the income node only.""" + return jnp.minimum( + aime + jnp.where(is_working, AIME_GAIN * jnp.exp(income), 0.0), AIME_MAX + ) + + +def next_wealth_dcegm( + savings: FloatND, labor_income: FloatND, pension_income: FloatND +) -> ContinuousState: + return savings + labor_income + pension_income + + +def next_wealth_brute( + resources: FloatND, + consumption: ContinuousAction, + labor_income: FloatND, + pension_income: FloatND, +) -> ContinuousState: + return resources - consumption + labor_income + pension_income + + +def budget_constraint(consumption: ContinuousAction, wealth: ContinuousState) -> BoolND: + return consumption <= wealth + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, +) + + +def _ages() -> AgeGrid: + return AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + + +def _active(age: int) -> bool: + return age < 40 + (N_PERIODS - 1) * 10 + + +def _shared_functions() -> dict: + return { + "utility": utility, + "labor_income": labor_income, + "pension_income": pension_income, + "is_working": is_working, + } + + +@functools.cache +def _model(solver: str) -> Model: + """Euler `wealth` + passive `aime` + process `income`, asset-row mode.""" + is_dcegm = solver == "dcegm" + states = { + "wealth": WEALTH_GRID, + "aime": AIME_GRID, + "income": RouwenhorstAR1Process(n_points=N_INCOME_NODES), + } + working = UserRegime( + transition={ + "working_life": MarkovTransition(stay_prob), + "dead": MarkovTransition(death_prob), + }, + active=_active, + actions={ + "labor_supply": DiscreteGrid(LaborChoice), + "consumption": CONSUMPTION_GRID, + }, + states=states, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute, + "aime": next_aime, + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions=( + { + **_shared_functions(), + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + } + if is_dcegm + else {**_shared_functions(), "resources": resources} + ), + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=PassiveAssetRowRegimeId, + ) + + +def _params() -> dict: + final_age_alive = 40 + (N_PERIODS - 2) * 10 + return { + "discount_factor": 0.95, + "final_age_alive": final_age_alive, + "working_life": { + "income": {"mu": 0.0, "sigma": 0.2, "rho": 0.6}, + "labor_income": {"wage": 12.0}, + "utility": {"disutility_of_work": 0.3}, + }, + } + + +def test_passive_aime_through_asset_row_matches_brute_force(): + """A passive AIME state carried through asset-row mode matches brute force. + + The regime solves per exogenous asset node (the survival probability reads + wealth) while carrying the passive AIME axis and the income process axis. + AIME accrues off its node spacing from the work choice and the income node, + so the mixed passive read is exercised, and the accumulated AIME feeds next + wealth through the pension annuity. Values agree with the dense-grid + brute-force oracle across the full wealth-by-AIME-by-income grid. + """ + params = _params() + dcegm_solution: PeriodToRegimeToVArr = _model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution: PeriodToRegimeToVArr = _model("brute_force").solve( + params=params, log_level="debug" + ) + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + assert brute_V.shape == dcegm_V.shape + # V leads with the income node and AIME axes; wealth is the trailing + # (Euler) axis. Exclude the lowest wealth nodes, where the coarse + # consumption grid makes the brute oracle itself unreliable. + flat_dcegm = np.moveaxis(dcegm_V, _euler_axis(dcegm_V), -1).reshape( + -1, dcegm_V.shape[_euler_axis(dcegm_V)] + ) + flat_brute = np.moveaxis(brute_V, _euler_axis(brute_V), -1).reshape( + -1, brute_V.shape[_euler_axis(brute_V)] + ) + np.testing.assert_allclose( + flat_dcegm[:, N_BRUTE_UNSTABLE_NODES:], + flat_brute[:, N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +def test_asset_row_carry_rows_are_the_euler_grid_not_the_envelope_workspace(): + """The persisted asset-row carry holds one row per Euler node, unpadded. + + In asset-row mode each carry row is the value/marginal published at the + regime's exogenous Euler (wealth) nodes; the dense envelope-refinement + workspace is transient. So the carry's trailing length is the wealth-grid + size, not the larger savings/envelope candidate length β€” the difference is + pure storage the parent never reads (the NaN tail is masked on interpolation). + """ + template = _model("dcegm")._regimes["working_life"].solution.continuation_template + assert template is not None + n_euler = int(WEALTH_GRID.to_jax().shape[0]) + # The envelope workspace would have been ceil(1.2 * (n_savings + n_constrained)) + # = ceil(1.2 * (120 + 64)) = 221 rows; the persisted carry is the 120 Euler nodes. + assert template.value.shape[-1] == n_euler + assert template.marginal_utility.shape[-1] == n_euler + assert template.endog_grid.shape[-1] == n_euler + + +def _euler_axis(value_array: np.ndarray) -> int: + """Axis of the Euler (wealth) state β€” the one matching the wealth grid.""" + n_wealth = int(WEALTH_GRID.to_jax().shape[0]) + return next(axis for axis, size in enumerate(value_array.shape) if size == n_wealth) + + +# --- Regime-transition prob through a param-dependent Euler-state chain ------ +# +# The means-tested survival probability reads the Euler state `wealth` through +# a DAG-computed intermediate that itself reads a model param (a capital-income +# return rate), mirroring an SSI/Medicaid eligibility share +# `medicaid_eligibility_share <- countable_income <- capital_income(assets, r)`. +# The regime simultaneously carries a passive AIME axis and an income process +# axis, so the per-asset-node savings-stage probability evaluation must receive +# the qualified param alongside the Euler node. + +RATE_OF_RETURN = 0.04 + + +def capital_income(wealth: ContinuousState, rate_of_return: float) -> FloatND: + """Capital income on current wealth β€” reads the Euler state and a param.""" + return rate_of_return * wealth + + +def countable_income(capital_income: FloatND) -> FloatND: + return capital_income + + +def medicaid_eligibility_share(countable_income: FloatND) -> FloatND: + """SSI-style smoothstep eligibility share over the countable income band.""" + return smoothstep_in_band(countable_income / RATE_OF_RETURN) + + +def survival_of_share(medicaid_eligibility_share: FloatND) -> FloatND: + return SURVIVAL_LOW + (SURVIVAL_HIGH - SURVIVAL_LOW) * medicaid_eligibility_share + + +def stay_prob_share( + medicaid_eligibility_share: FloatND, age: int, final_age_alive: float +) -> FloatND: + return jnp.where( + age >= final_age_alive, 0.0, survival_of_share(medicaid_eligibility_share) + ) + + +def death_prob_share( + medicaid_eligibility_share: FloatND, age: int, final_age_alive: float +) -> FloatND: + return 1.0 - stay_prob_share(medicaid_eligibility_share, age, final_age_alive) + + +def _means_test_intermediates() -> dict: + return { + "capital_income": capital_income, + "countable_income": countable_income, + "medicaid_eligibility_share": medicaid_eligibility_share, + } + + +@functools.cache +def _means_tested_prob_model(solver: str, *, rate_is_fixed: bool) -> Model: + """Euler `wealth` + passive `aime` + process `income`; means-tested prob. + + The survival probability reads `wealth` through the param-dependent chain + `capital_income(wealth, rate_of_return)`, triggering asset-row mode while + the regime carries the passive AIME and income-process axes. When + `rate_is_fixed`, the return rate is supplied through `fixed_params` (so it + is partialled at model build and dropped from the live params template) + rather than as a free solve param. + """ + is_dcegm = solver == "dcegm" + states = { + "wealth": WEALTH_GRID, + "aime": AIME_GRID, + "income": RouwenhorstAR1Process(n_points=N_INCOME_NODES), + } + working = UserRegime( + transition={ + "working_life": MarkovTransition(stay_prob_share), + "dead": MarkovTransition(death_prob_share), + }, + active=_active, + actions={ + "labor_supply": DiscreteGrid(LaborChoice), + "consumption": CONSUMPTION_GRID, + }, + states=states, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute, + "aime": next_aime, + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions=( + { + **_shared_functions(), + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + **_means_test_intermediates(), + } + if is_dcegm + else { + **_shared_functions(), + "resources": resources, + **_means_test_intermediates(), + } + ), + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + fixed_params = ( + {"working_life": {"capital_income": {"rate_of_return": RATE_OF_RETURN}}} + if rate_is_fixed + else {} + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=PassiveAssetRowRegimeId, + fixed_params=fixed_params, + ) + + +def _means_test_params(*, rate_is_fixed: bool) -> dict: + params = _params() + if not rate_is_fixed: + params["working_life"]["capital_income"] = {"rate_of_return": RATE_OF_RETURN} + return params + + +@pytest.mark.parametrize("rate_is_fixed", [False, True]) +def test_means_tested_prob_through_param_intermediate_matches_brute_force( + rate_is_fixed: bool, # noqa: FBT001 +): + """A means-tested survival prob `share <- capital_income(wealth, r)` matches. + + The stay probability reads the Euler state `wealth` through a param-dependent + intermediate chain (the SSI/Medicaid eligibility-share shape), so the regime + solves per exogenous asset node while carrying the passive AIME and income + process axes. The per-asset-node regime-transition-probability evaluation + receives the qualified param `capital_income__rate_of_return` β€” whether the + return rate is a free solve param or supplied through `fixed_params` (and + thus partialled into the prebuilt kernel). The probability's wealth slope + carries the first-order term + $\\partial P_{stay}/\\partial wealth \\cdot EV_{stay}$ into the marginal + value. Values agree with the dense-grid brute-force oracle across the full + wealth-by-AIME-by-income grid. + """ + params = _means_test_params(rate_is_fixed=rate_is_fixed) + dcegm_solution: PeriodToRegimeToVArr = _means_tested_prob_model( + "dcegm", rate_is_fixed=rate_is_fixed + ).solve(params=params, log_level="debug") + brute_solution: PeriodToRegimeToVArr = _means_tested_prob_model( + "brute_force", rate_is_fixed=rate_is_fixed + ).solve(params=params, log_level="debug") + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + assert brute_V.shape == dcegm_V.shape + flat_dcegm = np.moveaxis(dcegm_V, _euler_axis(dcegm_V), -1).reshape( + -1, dcegm_V.shape[_euler_axis(dcegm_V)] + ) + flat_brute = np.moveaxis(brute_V, _euler_axis(brute_V), -1).reshape( + -1, brute_V.shape[_euler_axis(brute_V)] + ) + np.testing.assert_allclose( + flat_dcegm[:, N_BRUTE_UNSTABLE_NODES:], + flat_brute[:, N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +@functools.cache +def _model_with_aime_batch(aime_batch_size: int) -> Model: + """The asset-row passive-AIME DC-EGM model with `aime` splayed by batch_size.""" + working = UserRegime( + transition={ + "working_life": MarkovTransition(stay_prob), + "dead": MarkovTransition(death_prob), + }, + active=_active, + actions={ + "labor_supply": DiscreteGrid(LaborChoice), + "consumption": CONSUMPTION_GRID, + }, + states={ + "wealth": WEALTH_GRID, + "aime": LinSpacedGrid( + start=0.0, stop=AIME_MAX, n_points=6, batch_size=aime_batch_size + ), + "income": RouwenhorstAR1Process(n_points=N_INCOME_NODES), + }, + state_transitions={"wealth": next_wealth_dcegm, "aime": next_aime}, + constraints={}, + functions={ + **_shared_functions(), + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=PassiveAssetRowRegimeId, + ) + + +def _euler_last_flat(value_array: np.ndarray) -> np.ndarray: + """Move the Euler (wealth) axis last and flatten the leading combo axes. + + `batch_size` on a continuous state reorders the canonical continuous-axis + layout (a batched axis is placed ahead of an unbatched one β€” the same + reordering the brute solver applies). Moving the Euler axis last collapses + that difference: `(income, wealth, aime)` and `(income, aime, wealth)` both + become `(income, aime, wealth)`, so the solved values are directly + comparable regardless of the splay. + """ + moved = np.moveaxis(value_array, _euler_axis(value_array), -1) + return moved.reshape(-1, moved.shape[-1]) + + +@pytest.mark.parametrize("aime_batch_size", [1, 2, 4]) +def test_passive_aime_batch_size_leaves_value_function_unchanged(aime_batch_size: int): + """Splaying the passive AIME combo axis does not change the solved values. + + `batch_size` on the passive `aime` grid only changes how the combo product + is scheduled (per-axis `productmap` blocks instead of one fused vmap). The + canonical layout reorders the continuous axes (batched ahead of unbatched, + matching the brute solver), but the solved values β€” compared with the Euler + axis moved last β€” match the unsplayed `batch_size=0` solve exactly, at every + period, including a block size that does not divide the AIME grid. + """ + reference = _model("dcegm").solve(params=_params(), log_level="debug") + splayed = _model_with_aime_batch(aime_batch_size).solve( + params=_params(), log_level="debug" + ) + # `working_life` is the asset-row regime carrying the splayed AIME axis; + # it is inactive in the terminal period, so exclude that period. + for period in sorted(reference)[:-1]: + np.testing.assert_allclose( + _euler_last_flat(np.asarray(splayed[period]["working_life"])), + _euler_last_flat(np.asarray(reference[period]["working_life"])), + rtol=1e-12, + atol=1e-12, + err_msg=f"period={period}, bs={aime_batch_size}", + ) diff --git a/tests/solution/test_egm_process_states.py b/tests/solution/test_egm_process_states.py new file mode 100644 index 000000000..588d47107 --- /dev/null +++ b/tests/solution/test_egm_process_states.py @@ -0,0 +1,346 @@ +"""DC-EGM with stochastic process states (Rouwenhorst AR(1) and IID income). + +A process state is a node-valued discrete dimension with intrinsic transition +weights $w(\\text{node}' \\mid \\text{node}, \\text{params})$. In a DC-EGM +regime it rides along exactly like a discrete state on the own side (one carry +row and one V slice per node) while the child side takes an expectation: the +child's node is distributed, so the carry read indexes the child rows at every +node, performs the full read there (resources interpolation, passive blend, +discrete-action aggregation), and weights the resulting per-node values and +marginals β€” the process expectation sits *outside* the action aggregation, +matching the brute-force solver's `jnp.average` of the already action +aggregated next-period V. + +The oracle is a dense-grid brute-force solve of a mathematically equivalent +spec (same wealth and income grids, dense consumption grid, explicit budget +constraint). Process params (`mu`, `sigma`, `rho`) are supplied at runtime, so +the intrinsic weights flow through the same params channel as in brute force. +""" + +import functools + +import jax.numpy as jnp +import numpy as np +import pytest + +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + Model, + NormalIIDProcess, + RouwenhorstAR1Process, + categorical, +) +from lcm.exceptions import InvalidValueFunctionError +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteAction, + FloatND, + ScalarInt, +) +from lcm_examples.iskhakov_et_al_2017 import dead + +# Number of model periods; the last one is spent in the terminal `dead` regime. +N_PERIODS = 4 + +# Number of discretization nodes of the income process. +N_INCOME_NODES = 5 + +# Unconditional income added to next wealth in the Rouwenhorst variant. Keeps +# continuation wealth comfortably inside the wealth grid even at zero savings +# and rest, where the brute-force oracle would otherwise edge-clamp its +# next-period V lookup. +BASE_INCOME = 5.0 + +# Scale of the IID income entering next wealth, for the same reason: the +# lowest quadrature node times the scale stays well above the wealth grid's +# lower end. +IID_INCOME_SCALE = 10.0 + +# Dense enough that the brute-force oracle's piecewise-linear V lookup is +# accurate at low wealth, where log utility curves hardest. +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=60.0, n_points=120) +# Dense because the brute-force argmax error is first-order in the grid +# spacing wherever the borrowing constraint binds (the optimum sits at +# `consumption = wealth`, between grid points). +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=60.0, n_points=600) + +# Exogenous end-of-period savings grid, cubically clustered toward the +# borrowing limit where the value function curves hardest. +SAVINGS_GRID = IrregSpacedGrid(points=tuple(60.0 * (i / 119) ** 3 for i in range(120))) + +# Lowest wealth nodes excluded from the brute-force comparison (wealth below +# ~9): there the coarse consumption grid and the curvature of log utility +# make brute force itself unreliable (the same exclusion the discrete and +# passive DC-EGM tests use, scaled to this wealth grid's node spacing). +N_BRUTE_UNSTABLE_NODES = 16 + + +@categorical(ordered=False) +class ProcessRegimeId: + alive: ScalarInt + dead: ScalarInt + + +@categorical(ordered=True) +class LaborChoice: + work: ScalarInt + rest: ScalarInt + + +def is_working(labor_supply: DiscreteAction) -> BoolND: + return labor_supply == LaborChoice.work + + +def labor_income(is_working: BoolND, income: ContinuousState, wage: float) -> FloatND: + return jnp.where(is_working, wage * jnp.exp(income), 0.0) + + +def utility_with_labor( + consumption: ContinuousAction, is_working: BoolND, disutility_of_work: float +) -> FloatND: + return jnp.log(consumption) - jnp.where(is_working, disutility_of_work, 0.0) + + +def utility_consumption_only(consumption: ContinuousAction) -> FloatND: + return jnp.log(consumption) + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_wealth_from_savings_with_labor( + savings: FloatND, labor_income: FloatND, interest_rate: float +) -> ContinuousState: + return (1 + interest_rate) * savings + BASE_INCOME + labor_income + + +def next_wealth_brute_with_labor( + wealth: ContinuousState, + consumption: ContinuousAction, + labor_income: FloatND, + interest_rate: float, +) -> ContinuousState: + return (1 + interest_rate) * (wealth - consumption) + BASE_INCOME + labor_income + + +def next_wealth_from_savings_iid( + savings: FloatND, income: ContinuousState, interest_rate: float +) -> ContinuousState: + return (1 + interest_rate) * savings + IID_INCOME_SCALE * jnp.exp(income) + + +def next_wealth_brute_iid( + wealth: ContinuousState, + consumption: ContinuousAction, + income: ContinuousState, + interest_rate: float, +) -> ContinuousState: + return (1 + interest_rate) * (wealth - consumption) + IID_INCOME_SCALE * jnp.exp( + income + ) + + +def borrowing_constraint( + consumption: ContinuousAction, wealth: ContinuousState +) -> BoolND: + return consumption <= wealth + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where( + age >= final_age_alive, + ProcessRegimeId.dead, + ProcessRegimeId.alive, + ) + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, +) + + +def _income_process(shock_type: str) -> RouwenhorstAR1Process | NormalIIDProcess: + """Income process with all distribution params supplied at runtime.""" + if shock_type == "rouwenhorst": + return RouwenhorstAR1Process(n_points=N_INCOME_NODES) + return NormalIIDProcess(n_points=N_INCOME_NODES, gauss_hermite=True) + + +@functools.cache +def _get_model(solver: str, shock_type: str) -> Model: + """Build one (solver, shock_type) model variant. + + - `shock_type="rouwenhorst"`: persistent AR(1) income scaling the wage of + a discrete work/rest choice β€” the income node moves the work margin, so + the ordering of the process expectation against the discrete-action + aggregation is observable. + - `shock_type="iid"`: Gauss-Hermite IID income entering the wealth + transition additively; consumption is the only action. + """ + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = float(ages.exact_values[-1]) + + def active(age: int, la: float = last_age) -> bool: + return age < la + + states = {"wealth": WEALTH_GRID, "income": _income_process(shock_type)} + if shock_type == "rouwenhorst": + actions = { + "labor_supply": DiscreteGrid(LaborChoice), + "consumption": CONSUMPTION_GRID, + } + shared_functions = { + "utility": utility_with_labor, + "labor_income": labor_income, + "is_working": is_working, + } + dcegm_next_wealth = next_wealth_from_savings_with_labor + brute_next_wealth = next_wealth_brute_with_labor + else: + actions = {"consumption": CONSUMPTION_GRID} + shared_functions = {"utility": utility_consumption_only} + dcegm_next_wealth = next_wealth_from_savings_iid + brute_next_wealth = next_wealth_brute_iid + + if solver == "dcegm": + alive = UserRegime( + transition=next_regime, + active=active, + actions=actions, + states=states, + state_transitions={"wealth": dcegm_next_wealth}, + functions={ + **shared_functions, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, + ) + else: + alive = UserRegime( + transition=next_regime, + active=active, + actions=actions, + states=states, + state_transitions={"wealth": brute_next_wealth}, + constraints={"borrowing_constraint": borrowing_constraint}, + functions=shared_functions, + ) + return Model( + regimes={"alive": alive, "dead": dead}, + ages=ages, + regime_id_class=ProcessRegimeId, + ) + + +def _get_params(shock_type: str) -> dict: + final_age_alive = 40 + (N_PERIODS - 2) * 10 + if shock_type == "rouwenhorst": + income_params = {"mu": 0.0, "sigma": 0.25, "rho": 0.6} + alive_params = { + "income": income_params, + "labor_income": {"wage": 15.0}, + "utility": {"disutility_of_work": 0.5}, + } + else: + alive_params = {"income": {"mu": 0.0, "sigma": 0.3}} + return { + "discount_factor": 0.95, + "interest_rate": 0.0, + "final_age_alive": final_age_alive, + "alive": alive_params, + } + + +def test_rouwenhorst_process_matches_dense_brute_force(): + """DC-EGM with a Rouwenhorst income process matches dense brute force. + + Each income node is an axis of V and the carry; the child's node is + distributed per the intrinsic AR(1) weights at the parent's node. The + income node scales the wage, so the work margin flips across nodes at + high wealth β€” an expectation taken inside the discrete-action aggregation + (instead of outside, where brute force takes it) would shift V by the + value gap between the choices and fail the comparison. Agreement is up to + the brute solver's consumption-grid resolution, excluding the lowest + wealth nodes where the coarse consumption grid makes brute force itself + unreliable. + """ + params = _get_params("rouwenhorst") + dcegm_solution = _get_model("dcegm", "rouwenhorst").solve( + params=params, log_level="debug" + ) + brute_solution = _get_model("brute", "rouwenhorst").solve( + params=params, log_level="debug" + ) + + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["alive"]) + dcegm_V = np.asarray(dcegm_solution[period]["alive"]) + assert brute_V.shape == dcegm_V.shape == (N_INCOME_NODES, 120) + np.testing.assert_allclose( + dcegm_V[:, N_BRUTE_UNSTABLE_NODES:], + brute_V[:, N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +def test_iid_process_matches_dense_brute_force(): + """DC-EGM with a Gauss-Hermite IID income process matches dense brute force. + + IID weights are node-independent rows of the intrinsic transition matrix; + the child read is averaged over the quadrature nodes with those weights. + """ + params = _get_params("iid") + dcegm_solution = _get_model("dcegm", "iid").solve(params=params, log_level="debug") + brute_solution = _get_model("brute", "iid").solve(params=params, log_level="debug") + + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["alive"]) + dcegm_V = np.asarray(dcegm_solution[period]["alive"]) + assert brute_V.shape == dcegm_V.shape == (N_INCOME_NODES, 120) + np.testing.assert_allclose( + dcegm_V[:, N_BRUTE_UNSTABLE_NODES:], + brute_V[:, N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +def test_nan_process_params_surface_as_error(): + """NaN process params poison the DC-EGM solve loudly, as under brute force. + + The intrinsic transition weights of a process state are evaluated inside + the EGM kernel; a NaN weight must propagate into the published V rows so + the solve's NaN diagnostics raise β€” never be swallowed by the zero-weight + masking of unreachable nodes. + """ + params = _get_params("rouwenhorst") + params["alive"]["income"] = {"mu": 0.0, "sigma": 0.25, "rho": float("nan")} + + with pytest.raises(InvalidValueFunctionError): + _get_model("dcegm", "rouwenhorst").solve(params=params, log_level="debug") diff --git a/tests/solution/test_egm_publish_overflow.py b/tests/solution/test_egm_publish_overflow.py new file mode 100644 index 000000000..fc338ac58 --- /dev/null +++ b/tests/solution/test_egm_publish_overflow.py @@ -0,0 +1,65 @@ +"""Envelope overflow poisons every published row so the NaN diagnostics fire. + +When the refined upper envelope keeps more points than the padded carry length +(`n_kept > n_pad`), the published rows are unreliable. The solve loop's NaN +diagnostics are the mechanism that surfaces the offending (regime, period), so +overflow must NaN-poison all three outputs β€” the value row on the exogenous grid, +the carry value row, and the carry marginal-utility row. A finite marginal-utility +row on overflow would silently feed the parent period a wrong Hermite slope. +""" + +import jax.numpy as jnp + +from _lcm.egm.step_core import _publish_V_and_carry_rows + + +def test_envelope_overflow_nan_poisons_all_published_rows(): + """`n_kept > n_pad` returns NaN for the V, carry-value, and marginal rows.""" + n_pad = 4 + refined_grid = jnp.asarray([1.0, 2.0, 3.0, 4.0]) + refined_policy = jnp.asarray([0.5, 1.0, 1.5, 2.0]) + refined_value = jnp.asarray([-1.0, -0.5, -0.2, -0.1]) + + v_row, value_row, marginal_row = _publish_V_and_carry_rows( + refined_grid=refined_grid, + refined_policy=refined_policy, + refined_value=refined_value, + n_kept=jnp.asarray(n_pad + 1, dtype=jnp.int32), + n_pad=n_pad, + publish_resources=jnp.asarray([1.5, 2.5, 3.5]), + borrowing_limit=jnp.asarray(0.0), + utility_of_action=jnp.log, + discounted_expected_value_at_limit=jnp.asarray(-2.0), + ) + + assert bool(jnp.all(jnp.isnan(v_row))) + assert bool(jnp.all(jnp.isnan(value_row))) + assert bool(jnp.all(jnp.isnan(marginal_row))) + + +def test_no_overflow_keeps_published_rows_finite(): + """`n_kept <= n_pad` leaves the published rows finite (the marginal row too). + + Guards against over-poisoning: the overflow gate must fire only on overflow, + not on every publish. + """ + n_pad = 4 + refined_grid = jnp.asarray([1.0, 2.0, 3.0, 4.0]) + refined_policy = jnp.asarray([0.5, 1.0, 1.5, 2.0]) + refined_value = jnp.asarray([-1.0, -0.5, -0.2, -0.1]) + + v_row, value_row, marginal_row = _publish_V_and_carry_rows( + refined_grid=refined_grid, + refined_policy=refined_policy, + refined_value=refined_value, + n_kept=jnp.asarray(n_pad, dtype=jnp.int32), + n_pad=n_pad, + publish_resources=jnp.asarray([1.5, 2.5, 3.5]), + borrowing_limit=jnp.asarray(0.0), + utility_of_action=jnp.log, + discounted_expected_value_at_limit=jnp.asarray(-2.0), + ) + + assert not bool(jnp.any(jnp.isnan(v_row))) + assert not bool(jnp.any(jnp.isnan(value_row))) + assert not bool(jnp.any(jnp.isnan(marginal_row))) diff --git a/tests/solution/test_egm_published_policy.py b/tests/solution/test_egm_published_policy.py new file mode 100644 index 000000000..4bebdb47d --- /dev/null +++ b/tests/solution/test_egm_published_policy.py @@ -0,0 +1,95 @@ +"""The DC-EGM solve publishes the refined consumption function for simulation. + +The Euler inversion plus upper envelope recover the exact off-grid optimal +continuous action on the resources grid. The solve hands that policy to +`simulate` as a per-period `EGMSimPolicy`, so a simulated subject's continuous +action can be interpolated at its resources rather than snapped to the action +grid. This test pins the published artifact directly: interpolating it must +reproduce the closed-form consumption, including at resources strictly between +action-grid nodes (where a grid argmax cannot land). +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.interp import interp_on_padded_grid +from _lcm.egm.published_policy import EGMSimPolicy +from lcm import AgeGrid, LogSpacedGrid, Model +from lcm.regime import Regime as UserRegime +from lcm.typing import ContinuousState, FloatND +from lcm_examples.iskhakov_et_al_2017 import WEALTH_GRID +from tests.test_models.deterministic import retirement_only +from tests.test_models.deterministic.dcegm_variants import ( + dcegm_retirement, + get_retirement_only_params, +) + + +def _bequest_utility(wealth: ContinuousState, age: float) -> FloatND: + return (age / 50.0) * jnp.log(wealth) + + +def _two_period_bequest_model() -> Model: + """Two-period log-utility retirement model with a terminal bequest.""" + bequest_dead = UserRegime( + transition=None, + states={"wealth": LogSpacedGrid(start=0.25, stop=400.0, n_points=400)}, + functions={"utility": _bequest_utility}, + ) + return Model( + regimes={ + "retirement": dcegm_retirement.replace(active=lambda age: age < 50), + "dead": bequest_dead, + }, + ages=AgeGrid(start=40, stop=50, step="10Y"), + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + + +def test_solve_publishes_policy_matching_closed_form_consumption(): + """Interpolating the published policy reproduces `c* = wealth / (1 + beta)`. + + With log utility, zero interest, a two-period horizon, and a terminal + bequest `(age/50) log(wealth)` at age 50, the decision period's optimal + consumption is `wealth / (1 + beta)` at every resources level. The published + policy interpolated at off-grid resources must hit it. + """ + discount_factor = 0.98 + params = get_retirement_only_params(2, discount_factor=discount_factor) + + _v, sim_policy = _two_period_bequest_model().solve( + params=params, log_level="debug", return_simulation_policy=True + ) + + pol = sim_policy[0]["retirement"] + assert isinstance(pol, EGMSimPolicy) + + # Resources = wealth here (zero interest, no labor income). Query strictly + # between wealth-grid nodes to exercise the off-grid interpolation. + wealth_nodes = np.asarray(WEALTH_GRID.to_jax()) + off_grid = 0.5 * (wealth_nodes[3:-1] + wealth_nodes[4:]) + consumption = interp_on_padded_grid( + x_query=jnp.asarray(off_grid), xp=pol.endog_grid, fp=pol.policy + ) + expected = off_grid / (1.0 + discount_factor) + np.testing.assert_allclose(np.asarray(consumption), expected, rtol=2e-2) + + +def test_published_policies_are_host_resident(): + """Solve evicts simulation policies to host, not device. + + The policies are a solve output no backward step reads; keeping them on the + accelerator would pin one carry-sized buffer per period for the whole + induction. So the returned policy arrays live on the host (CPU) device. + """ + params = get_retirement_only_params(2, discount_factor=0.98) + _v, sim_policy = _two_period_bequest_model().solve( + params=params, log_level="debug", return_simulation_policy=True + ) + + pol = sim_policy[0]["retirement"] + assert all( + device.platform == "cpu" + for array in (pol.endog_grid, pol.policy) + for device in array.devices() + ) diff --git a/tests/solution/test_egm_refine_to_query.py b/tests/solution/test_egm_refine_to_query.py new file mode 100644 index 000000000..2d9cc362b --- /dev/null +++ b/tests/solution/test_egm_refine_to_query.py @@ -0,0 +1,251 @@ +"""Spec for streamed refine-to-query in asset-row mode. + +In asset-row mode the per-node solve refines a full NaN-padded upper envelope +and interpolates it at exactly one query point (`resources_at_node`) to publish +a scalar `(V_node, policy_node)`. Refine-to-query folds that single-query +interpolation into the upper-envelope scan: the scan keeps only the two +envelope points bracketing the query (plus the first point and the kept count) +and returns the scalar result, so the `n_pad` envelope rows are never +materialized. + +Correctness is defined by the existing composition: for the *same* candidates, +query, and utility, the streamed pair + + refine_to_bracket(...) -> publish_node_from_bracket(...) + +must equal the row-then-interpolate pair + + refine(...) -> _publish_node_V_and_policy(...) + +to floating-point tolerance. This is a pure unit equivalence β€” no brute oracle. +The battery covers smooth, kinked, multi-crossing, all-dead, single-live, and +overflow candidate sets, with the query below the first point, above the last +point, and exactly on a duplicated kink abscissa (the `side="right"` tie-break, +the dominant correctness risk). +""" + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.egm.asset_row import ( + _publish_node_V_and_policy, + publish_node_from_bracket, +) +from _lcm.egm.upper_envelope import fues +from tests.conftest import X64_ENABLED + +_ATOL = 1e-10 if X64_ENABLED else 1e-5 + +# CRRA utility with a node-dependent additive shift, so the value Hermite slope +# `grad(utility_of_action)` is a genuine non-trivial function of the policy. +_GAMMA = 1.5 +_BORROWING_LIMIT = 0.0 +_DISCOUNTED_EV_AT_LIMIT = -3.0 + + +def _utility_of_action(action_value): + safe = jnp.maximum(action_value, jnp.finfo(action_value.dtype).tiny) + return safe ** (1.0 - _GAMMA) / (1.0 - _GAMMA) + + +def _crossing_segments_candidates(): + """Two crossing linear value segments (a discrete-choice kink at R* = 2.25).""" + r_a = np.array([0.6, 1.2, 1.8, 2.4]) + r_b = np.array([0.8, 1.6, 2.6, 3.4]) + grid = np.concatenate([r_a, r_b]) + value = np.concatenate([1.0 + 0.4 * r_a, 0.1 + 0.8 * r_b]) + policy = np.concatenate([0.30 * r_a, 0.55 * r_b]) + return jnp.asarray(grid), jnp.asarray(policy), jnp.asarray(value) + + +def _smooth_candidates(): + """A single monotone-concave segment (no kink, passes through unchanged).""" + grid = jnp.linspace(0.5, 6.0, 10) + policy = 0.4 * grid + value = jnp.log(grid) + return grid, policy, value + + +def _multi_crossing_candidates(): + """Three linear segments with two crossings.""" + r_a = np.array([0.4, 0.9, 1.4]) + r_b = np.array([0.7, 1.2, 1.9, 2.4]) + r_c = np.array([2.1, 2.8, 3.5]) + grid = np.concatenate([r_a, r_b, r_c]) + value = np.concatenate([0.5 + 0.9 * r_a, 0.2 + 1.1 * r_b, -0.6 + 1.5 * r_c]) + policy = np.concatenate([0.2 * r_a, 0.45 * r_b, 0.7 * r_c]) + return jnp.asarray(grid), jnp.asarray(policy), jnp.asarray(value) + + +def _all_dead_candidates(): + """Every candidate infeasible: the value-correspondence is all `-inf`.""" + grid = jnp.linspace(0.5, 4.0, 6) + policy = 0.3 * grid + value = jnp.full_like(grid, -jnp.inf) + return grid, policy, value + + +def _single_live_candidate(): + """Exactly one live candidate; the rest infeasible (`-inf`).""" + grid = jnp.array([1.5, 2.0, 2.5, 3.0]) + policy = jnp.array([0.6, 0.7, 0.8, 0.9]) + value = jnp.array([2.0, -jnp.inf, -jnp.inf, -jnp.inf]) + return grid, policy, value + + +_CANDIDATE_SETS = { + "smooth": _smooth_candidates(), + "kinked": _crossing_segments_candidates(), + "multi_crossing": _multi_crossing_candidates(), + "all_dead": _all_dead_candidates(), + "single_live": _single_live_candidate(), +} + + +def _kink_abscissa(grid, policy, value, n_pad): + """Return the lower duplicated-kink abscissa of a refined envelope, or None.""" + refined_grid, _, _, _ = fues.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=n_pad + ) + raw = np.asarray(refined_grid) + clean = raw[~np.isnan(raw)] + duplicates = clean[:-1][np.isclose(np.diff(clean), 0.0, atol=1e-9)] + return None if duplicates.size == 0 else float(duplicates[0]) + + +def _reference(grid, policy, value, x_query, n_pad): + """Row-then-interpolate: refine to a full row, then publish the scalar.""" + dead = jnp.isneginf(value) + refined_grid, refined_policy, refined_value, n_kept = fues.refine_envelope( + endog_grid=jnp.where(dead, jnp.nan, grid), + policy=jnp.where(dead, jnp.nan, policy), + value=jnp.where(dead, jnp.nan, value), + n_refined=n_pad, + ) + return _publish_node_V_and_policy( + refined_grid=refined_grid, + refined_policy=refined_policy, + refined_value=refined_value, + n_kept=n_kept, + n_pad=n_pad, + resources_at_node=jnp.asarray(x_query), + borrowing_limit=jnp.asarray(_BORROWING_LIMIT), + utility_of_action=_utility_of_action, + discounted_expected_value_at_limit=jnp.asarray(_DISCOUNTED_EV_AT_LIMIT), + ) + + +def _streamed(grid, policy, value, x_query, n_pad): + """Refine-to-bracket: fold the single query into the scan, then publish.""" + dead = jnp.isneginf(value) + bracket = fues.refine_to_bracket( + endog_grid=jnp.where(dead, jnp.nan, grid), + policy=jnp.where(dead, jnp.nan, policy), + value=jnp.where(dead, jnp.nan, value), + x_query=jnp.asarray(x_query), + ) + return publish_node_from_bracket( + bracket=bracket, + n_pad=n_pad, + resources_at_node=jnp.asarray(x_query), + borrowing_limit=jnp.asarray(_BORROWING_LIMIT), + utility_of_action=_utility_of_action, + discounted_expected_value_at_limit=jnp.asarray(_DISCOUNTED_EV_AT_LIMIT), + ) + + +def _assert_equivalent(grid, policy, value, x_query, n_pad): + ref_v, ref_p = _reference(grid, policy, value, x_query, n_pad) + got_v, got_p = _streamed(grid, policy, value, x_query, n_pad) + np.testing.assert_allclose(float(got_v), float(ref_v), atol=_ATOL) + # Policy is published as NaN exactly where the reference does (e.g. a poisoned + # single-live / overflow read); compare NaN-for-NaN, value otherwise. + if np.isnan(float(ref_p)): + assert np.isnan(float(got_p)) + else: + np.testing.assert_allclose(float(got_p), float(ref_p), atol=_ATOL) + + +@pytest.mark.parametrize("name", list(_CANDIDATE_SETS)) +def test_streamed_matches_row_then_interp_on_interior_query(name): + """The streamed publish equals row-then-interp at an interior query point.""" + grid, policy, value = _CANDIDATE_SETS[name] + # The interior query is the midpoint of the candidate grid's span, which is a + # finite point even for the all-dead set (whose envelope is empty). + raw_grid = np.asarray(grid) + x_query = float(0.5 * (raw_grid.min() + raw_grid.max())) + _assert_equivalent(grid, policy, value, x_query, n_pad=16) + + +@pytest.mark.parametrize("name", list(_CANDIDATE_SETS)) +def test_streamed_matches_row_then_interp_below_first_point(name): + """A query below the lowest envelope point edge-clamps identically.""" + grid, policy, value = _CANDIDATE_SETS[name] + x_query = float(np.min(np.asarray(grid))) - 1.0 + _assert_equivalent(grid, policy, value, x_query, n_pad=16) + + +@pytest.mark.parametrize("name", list(_CANDIDATE_SETS)) +def test_streamed_matches_row_then_interp_above_last_point(name): + """A query above the highest envelope point edge-clamps identically.""" + grid, policy, value = _CANDIDATE_SETS[name] + x_query = float(np.max(np.asarray(grid))) + 1.0 + _assert_equivalent(grid, policy, value, x_query, n_pad=16) + + +@pytest.mark.parametrize("name", ["kinked", "multi_crossing"]) +def test_streamed_matches_row_then_interp_exactly_on_kink(name): + """A query exactly on a duplicated kink abscissa resolves the right-copy. + + The `side="right"` tie-break puts the bracket's lower node on the right + copy of the kink, so the streamed publish must agree bit-for-bit with the + row-then-interpolate publish there β€” the dominant correctness risk. + """ + grid, policy, value = _CANDIDATE_SETS[name] + x_query = _kink_abscissa(grid, policy, value, n_pad=16) + assert x_query is not None, "fixture must produce a duplicated kink abscissa" + _assert_equivalent(grid, policy, value, x_query, n_pad=16) + + +def test_streamed_matches_row_then_interp_on_overflow(): + """When the envelope overflows `n_pad`, both paths NaN-poison identically.""" + grid, policy, value = _crossing_segments_candidates() + x_query = float(np.median(np.asarray(grid))) + # `n_pad` below the envelope's kept-point count forces the overflow poison. + got_v, got_p = _streamed(grid, policy, value, x_query, n_pad=4) + ref_v, ref_p = _reference(grid, policy, value, x_query, n_pad=4) + assert np.isnan(float(ref_v)) + assert np.isnan(float(got_v)) + assert np.isnan(float(ref_p)) + assert np.isnan(float(got_p)) + + +def test_streamed_is_vmappable_over_nodes(): + """The streamed publish batches over query nodes like the per-node solve.""" + grid, policy, value = _crossing_segments_candidates() + dead = jnp.isneginf(value) + g = jnp.where(dead, jnp.nan, grid) + p = jnp.where(dead, jnp.nan, policy) + v = jnp.where(dead, jnp.nan, value) + queries = jnp.linspace(0.7, 3.3, 9) + + def one(x_query): + bracket = fues.refine_to_bracket( + endog_grid=g, policy=p, value=v, x_query=x_query + ) + return publish_node_from_bracket( + bracket=bracket, + n_pad=16, + resources_at_node=x_query, + borrowing_limit=jnp.asarray(_BORROWING_LIMIT), + utility_of_action=_utility_of_action, + discounted_expected_value_at_limit=jnp.asarray(_DISCOUNTED_EV_AT_LIMIT), + ) + + batched_v, batched_p = jax.vmap(one)(queries) + for k, x_query in enumerate(queries): + single_v, single_p = one(x_query) + np.testing.assert_allclose(float(batched_v[k]), float(single_v), atol=_ATOL) + np.testing.assert_allclose(float(batched_p[k]), float(single_p), atol=_ATOL) diff --git a/tests/solution/test_egm_resources_process_state.py b/tests/solution/test_egm_resources_process_state.py new file mode 100644 index 000000000..ea1020e70 --- /dev/null +++ b/tests/solution/test_egm_resources_process_state.py @@ -0,0 +1,237 @@ +"""DC-EGM whose own `resources` reads a runtime-param process state. + +A process state with runtime-supplied distribution params (a +`RouwenhorstAR1Process` whose `rho` / `sigma` / `mu` arrive in the params dict) +is a node-valued discrete dimension whose grid points are resolved once per +solve. When the regime's own `resources` function reads that node value +directly β€” the wage level entering the budget as income β€” the kernel must feed +the *resolved* node value into the resources query, both on the publish grid +and inside the continuation's expectation over next-period nodes. + +The oracle is a dense-grid brute-force solve of the same economics (same wealth +and wage grids, dense consumption grid, explicit borrowing constraint). The +process params flow through the same runtime channel in both solvers, so a +correct kernel matches the brute value function up to the brute solver's +consumption-grid resolution. +""" + +import functools + +import jax.numpy as jnp +import numpy as np + +from lcm import ( + AgeGrid, + IrregSpacedGrid, + LinSpacedGrid, + Model, + RouwenhorstAR1Process, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + FloatND, + ScalarInt, +) +from lcm_examples.iskhakov_et_al_2017 import dead + +N_PERIODS = 4 +N_WAGE_NODES = 5 + + +@categorical(ordered=False) +class ProcessResourcesRegimeId: + alive: ScalarInt + dead: ScalarInt + + +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=60.0, n_points=120) +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=60.0, n_points=600) +SAVINGS_GRID = IrregSpacedGrid(points=tuple(60.0 * (i / 119) ** 3 for i in range(120))) + +# The head-to-head lives on the wealth interior, where both solvers are +# well-defined. Below `N_BRUTE_LOW_NODES` the coarse consumption grid makes the +# brute oracle undershoot (log utility curves hardest near the borrowing limit, +# and the wage income shifts that region up the wealth grid), where DC-EGM's +# constrained segment is exact. Above the top `N_BRUTE_HIGH_NODES` the brute +# next-wealth lookup edge-clamps at the wealth grid's ceiling (the budget pushes +# the high-wealth continuation past the grid top), so its value saturates while +# DC-EGM keeps resolving. +N_BRUTE_LOW_NODES = 30 +N_BRUTE_HIGH_NODES = 30 + + +def wage_income(wage: ContinuousState) -> FloatND: + """Labor income is the exponential of the Markov log-wage node.""" + return jnp.exp(wage) + + +def utility(consumption: ContinuousAction) -> FloatND: + return jnp.log(consumption) + + +def resources( + wealth: ContinuousState, wage_income: FloatND, interest_rate: float +) -> FloatND: + """Financial resources: return on wealth plus the wage node's income. + + Reads the process state `wage` (through `wage_income`), so the kernel must + bind the resolved wage node value here rather than a build-time placeholder. + """ + return (1.0 + interest_rate) * wealth + wage_income + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def next_wealth(savings: FloatND) -> ContinuousState: + return savings + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_wealth_brute( + wealth: ContinuousState, + consumption: ContinuousAction, + interest_rate: float, + wage_income: FloatND, +) -> ContinuousState: + return (1.0 + interest_rate) * wealth + wage_income - consumption + + +def borrowing_constraint( + wealth: ContinuousState, + consumption: ContinuousAction, + interest_rate: float, + wage_income: FloatND, +) -> BoolND: + return ( + next_wealth_brute( + wealth=wealth, + consumption=consumption, + interest_rate=interest_rate, + wage_income=wage_income, + ) + >= 0.0 + ) + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where( + age >= final_age_alive, + ProcessResourcesRegimeId.dead, + ProcessResourcesRegimeId.alive, + ) + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, +) + + +@functools.cache +def _get_model(solver: str) -> Model: + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = float(ages.exact_values[-1]) + + def active(age: int, la: float = last_age) -> bool: + return age < la + + states = { + "wealth": WEALTH_GRID, + "wage": RouwenhorstAR1Process(n_points=N_WAGE_NODES), + } + if solver == "dcegm": + alive = UserRegime( + transition=next_regime, + active=active, + actions={"consumption": CONSUMPTION_GRID}, + states=states, + state_transitions={"wealth": next_wealth}, + functions={ + "utility": utility, + "wage_income": wage_income, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, + ) + else: + alive = UserRegime( + transition=next_regime, + active=active, + actions={"consumption": CONSUMPTION_GRID}, + states=states, + state_transitions={"wealth": next_wealth_brute}, + constraints={"borrowing_constraint": borrowing_constraint}, + functions={"utility": utility, "wage_income": wage_income}, + ) + return Model( + regimes={"alive": alive, "dead": dead}, + ages=ages, + regime_id_class=ProcessResourcesRegimeId, + ) + + +def _get_params(solver: str) -> dict: + final_age_alive = 40 + (N_PERIODS - 2) * 10 + wage_params = {"mu": 0.0, "sigma": 0.25, "rho": 0.6} + if solver == "dcegm": + alive_params = { + "wage": wage_params, + "resources": {"interest_rate": 0.0}, + } + else: + alive_params = { + "wage": wage_params, + "next_wealth": {"interest_rate": 0.0}, + "borrowing_constraint": {"interest_rate": 0.0}, + } + return { + "discount_factor": 0.95, + "final_age_alive": final_age_alive, + "alive": alive_params, + } + + +def test_dcegm_resources_reading_process_matches_dense_brute_force(): + """DC-EGM with a process-reading `resources` matches dense brute force. + + The wage node enters the budget as income through the regime's own + resources function. A correct kernel binds the resolved wage grid into both + the publish-grid resources and the continuation's node expectation, so the + value function matches the brute oracle up to the brute consumption-grid + resolution, excluding the lowest wealth nodes. + """ + dcegm_solution = _get_model("dcegm").solve( + params=_get_params("dcegm"), log_level="debug" + ) + brute_solution = _get_model("brute").solve( + params=_get_params("brute"), log_level="debug" + ) + + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["alive"]) + dcegm_V = np.asarray(dcegm_solution[period]["alive"]) + assert brute_V.shape == dcegm_V.shape == (N_WAGE_NODES, 120) + interior = slice(N_BRUTE_LOW_NODES, 120 - N_BRUTE_HIGH_NODES) + np.testing.assert_allclose( + dcegm_V[:, interior], + brute_V[:, interior], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) diff --git a/tests/solution/test_egm_savings_stage_euler_state.py b/tests/solution/test_egm_savings_stage_euler_state.py new file mode 100644 index 000000000..650b16761 --- /dev/null +++ b/tests/solution/test_egm_savings_stage_euler_state.py @@ -0,0 +1,481 @@ +"""DC-EGM savings-stage functions reading the current Euler state. + +Regime-transition probabilities, stochastic transition weights, and passive +(non-Euler) state laws may read the current Euler state. The kernel then +solves per exogenous asset node β€” current assets are known there, so each +asset read is a per-combo constant β€” and the read's asset derivative enters +the published marginal value $dV/dR$ through the continuation's direct +Euler-state channel (for regime-transition probabilities the first-order +term $\\sum_{targets} \\partial P/\\partial a \\cdot EV$, which Danskin does +not cancel). The reads must be smooth at the resolution of the Euler grid: +cliffs β€” including smooth bands narrower than one grid cell β€” are rejected +at model build with a hint to add grid nodes across the band. + +The oracle for the solved properties is a dense-grid brute-force solve of a +mathematically equivalent spec (same state grids, dense consumption grid, +explicit budget constraint). +""" + +import functools + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.typing import PeriodToRegimeToVArr +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + MarkovTransition, + Model, + categorical, +) +from lcm.exceptions import ModelInitializationError +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM, GridSearch +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteState, + FloatND, + ScalarInt, +) +from lcm_examples.iskhakov_et_al_2017 import dead + +# Number of model periods; the last one is spent in the terminal regime. +N_PERIODS = 4 + +# Wealth band over which the savings-stage smoothsteps ramp. At ~32 cells of +# the wealth grid the band is well resolved at node resolution, so the +# build-time continuity check admits it. +BAND_START = 30.0 +BAND_WIDTH = 20.0 + +# A smoothstep band narrower than one wealth grid cell (cell size ~0.62): a +# cliff at node resolution, rejected at model build. +NARROW_BAND_WIDTH = 0.3 + +# Survival probability below/above the wealth band. Death is absorbing with +# zero value while continued life is worth several utils, so the value gap +# across targets is material and the probability's wealth slope contributes +# a first-order term to the marginal value inside the band. +SURVIVAL_LOW = 0.55 +SURVIVAL_HIGH = 0.95 + +# Probability of good health below/above the band for the Markov-weight +# fixture, and the utility penalty of bad health. +GOOD_HEALTH_LOW = 0.4 +GOOD_HEALTH_HIGH = 0.9 +BAD_HEALTH_PENALTY = 0.2 + +# Skill dynamics of the passive-law fixture: persistence plus a +# wealth-dependent gain, capped at the grid's top node; skill enters utility +# linearly so its blended read is exact for both solvers. +SKILL_DECAY = 0.9 +SKILL_GAIN = 0.3 +SKILL_MAX = 1.0 +SKILL_WEIGHT = 0.4 + +# Deterministic labor income added to savings in the wealth law; keeps child +# wealth queries away from the grid's lower edge, where the two solvers +# clamp differently. +LABOR_INCOME = 5.0 + +# 160 wealth nodes: the brute-force oracle interpolates next-period V +# linearly in wealth (a downward bias where V curves), while the DC-EGM carry +# read uses exact slopes; the dense grid keeps that oracle-side bias below +# the comparison tolerance. +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=100.0, n_points=160) +SKILL_GRID = LinSpacedGrid(start=0.0, stop=SKILL_MAX, n_points=7) + +# The consumption grid covers the maximum resources so the brute-force oracle +# is not artificially capped at high wealth; 4000 points keep the oracle's own +# resolution error below the comparison tolerance. +CONSUMPTION_GRID = LinSpacedGrid(start=0.25, stop=110.0, n_points=4000) + +# Exogenous end-of-period savings grid, cubically clustered toward the +# borrowing limit where the value function curves hardest. +SAVINGS_GRID = IrregSpacedGrid(points=tuple(100.0 * (i / 149) ** 3 for i in range(150))) + +# Lowest wealth nodes excluded from the brute-force comparison: there the +# brute solver leans on consumption choices near its grid start and on coarse +# interpolation where log utility curves hardest (the same exclusion the +# sibling DC-EGM oracle tests use). +N_BRUTE_UNSTABLE_NODES = 16 + + +@categorical(ordered=False) +class SavingsStageRegimeId: + working_life: ScalarInt + dead: ScalarInt + + +@categorical(ordered=False) +class Health: + good: ScalarInt + bad: ScalarInt + + +def smoothstep_in_band(wealth: ContinuousState) -> FloatND: + """CΒ² quintic smoothstep rising from 0 to 1 across the wealth band.""" + t = jnp.clip((wealth - BAND_START) / BAND_WIDTH, 0.0, 1.0) + return t * t * t * (t * (6.0 * t - 15.0) + 10.0) + + +def survival_of_wealth(wealth: ContinuousState) -> FloatND: + return SURVIVAL_LOW + (SURVIVAL_HIGH - SURVIVAL_LOW) * smoothstep_in_band(wealth) + + +def stay_prob(wealth: ContinuousState, age: int, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 0.0, survival_of_wealth(wealth)) + + +def death_prob(wealth: ContinuousState, age: int, final_age_alive: float) -> FloatND: + return 1.0 - stay_prob(wealth, age, final_age_alive) + + +def utility(consumption: ContinuousAction) -> FloatND: + return jnp.log(consumption) + + +def utility_with_health( + consumption: ContinuousAction, health: DiscreteState +) -> FloatND: + return jnp.log(consumption) - jnp.where( + health == Health.bad, BAD_HEALTH_PENALTY, 0.0 + ) + + +def utility_with_skill( + consumption: ContinuousAction, skill: ContinuousState +) -> FloatND: + return jnp.log(consumption) + SKILL_WEIGHT * skill + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def budget_constraint(consumption: ContinuousAction, wealth: ContinuousState) -> BoolND: + return consumption <= wealth + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where( + age >= final_age_alive, + SavingsStageRegimeId.dead, + SavingsStageRegimeId.working_life, + ) + + +def next_wealth_dcegm(savings: FloatND) -> ContinuousState: + return savings + LABOR_INCOME + + +def next_wealth_brute( + wealth: ContinuousState, consumption: ContinuousAction +) -> ContinuousState: + return wealth - consumption + LABOR_INCOME + + +def next_skill(skill: ContinuousState, wealth: ContinuousState) -> ContinuousState: + return jnp.minimum( + SKILL_DECAY * skill + SKILL_GAIN * smoothstep_in_band(wealth), SKILL_MAX + ) + + +def health_weights(wealth: ContinuousState) -> FloatND: + p_good = GOOD_HEALTH_LOW + ( + GOOD_HEALTH_HIGH - GOOD_HEALTH_LOW + ) * smoothstep_in_band(wealth) + return jnp.stack([p_good, 1.0 - p_good]) + + +def _ages() -> AgeGrid: + return AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + + +def _active(age: int) -> bool: + last_age = 40 + (N_PERIODS - 1) * 10 + return age < last_age + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, +) + + +def _dcegm_functions() -> dict: + return { + "utility": utility, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + } + + +def _params() -> dict: + return { + "discount_factor": 0.95, + "final_age_alive": 40 + (N_PERIODS - 2) * 10, + } + + +def _assert_working_life_V_matches( + *, dcegm_solution: PeriodToRegimeToVArr, brute_solution: PeriodToRegimeToVArr +) -> None: + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + assert brute_V.shape == dcegm_V.shape + np.testing.assert_allclose( + dcegm_V[N_BRUTE_UNSTABLE_NODES:], + brute_V[N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +@functools.cache +def _survival_prob_model(solver: str) -> Model: + """Self-targeting regime whose stay probability reads wealth smoothly.""" + is_dcegm = solver == "dcegm" + working = UserRegime( + transition={ + "working_life": MarkovTransition(stay_prob), + "dead": MarkovTransition(death_prob), + }, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={**(_dcegm_functions() if is_dcegm else {}), "utility": utility}, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=SavingsStageRegimeId, + ) + + +def test_smoothstep_survival_probability_matches_brute_force(): + """A wealth-dependent survival probability matches the brute-force oracle. + + The stay probability rises across a wealth band spanning many grid cells + while death is an absorbing zero-value regime, so inside the band the + marginal value carries the first-order term + $\\partial P_{stay}/\\partial wealth \\cdot EV_{stay}$ on top of the + envelope term. A solver that drops that term misprices saving in the + band and fails the multi-period value comparison. + """ + params = _params() + dcegm_solution = _survival_prob_model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution = _survival_prob_model("brute_force").solve( + params=params, log_level="debug" + ) + _assert_working_life_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) + + +@functools.cache +def _markov_health_model(solver: str) -> Model: + """Markov health weights reading wealth through a smoothstep.""" + is_dcegm = solver == "dcegm" + working = UserRegime( + transition=next_regime, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID, "health": DiscreteGrid(Health)}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute, + "health": MarkovTransition(health_weights), + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={ + **(_dcegm_functions() if is_dcegm else {}), + "utility": utility_with_health, + }, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=SavingsStageRegimeId, + ) + + +def test_markov_weights_reading_wealth_match_brute_force(): + """Asset-reading Markov weights of a discrete state match brute force. + + The health transition weights read current wealth through a smoothstep, so + the regime is solved per exogenous asset node, where wealth is known. The + weights' wealth derivative enters the published marginal value through the + continuation's stochastic-weight channel (the $\\partial w/\\partial a + \\cdot EV$ term), exactly as the asset-node brute-force oracle evaluates + it. Values agree across the full wealth-by-health grid. + """ + params = _params() + dcegm_solution = _markov_health_model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution = _markov_health_model("brute_force").solve( + params=params, log_level="debug" + ) + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["working_life"]) + dcegm_V = np.asarray(dcegm_solution[period]["working_life"]) + # V leads with the discrete health axis; wealth is the trailing axis. + assert brute_V.shape == dcegm_V.shape == (2, 160) + np.testing.assert_allclose( + dcegm_V[:, N_BRUTE_UNSTABLE_NODES:], + brute_V[:, N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +@functools.cache +def _passive_skill_model(solver: str) -> Model: + """Passive skill state whose law reads wealth through a smoothstep.""" + is_dcegm = solver == "dcegm" + working = UserRegime( + transition=next_regime, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID, "skill": SKILL_GRID}, + state_transitions={ + "wealth": next_wealth_dcegm if is_dcegm else next_wealth_brute, + "skill": next_skill, + }, + constraints={} if is_dcegm else {"budget_constraint": budget_constraint}, + functions={ + **(_dcegm_functions() if is_dcegm else {}), + "utility": utility_with_skill, + }, + solver=DCEGM_SOLVER if is_dcegm else GridSearch(), + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=SavingsStageRegimeId, + ) + + +def test_passive_skill_law_reading_wealth_matches_brute_force(): + """`next_skill = decay * skill + gain * smoothstep(wealth)` matches brute. + + The passive state's law reads current wealth, so the child's skill value + shifts per asset node and its wealth derivative feeds the marginal value + through the continuation's skill channel. Values agree with the + dense-grid brute-force oracle on the full wealth-by-skill grid. + """ + params = _params() + dcegm_solution = _passive_skill_model("dcegm").solve( + params=params, log_level="debug" + ) + brute_solution = _passive_skill_model("brute_force").solve( + params=params, log_level="debug" + ) + _assert_working_life_V_matches( + dcegm_solution=dcegm_solution, brute_solution=brute_solution + ) + + +def cliff_stay_prob(wealth: ContinuousState) -> FloatND: + return jnp.where( + wealth <= BAND_START + 0.5 * BAND_WIDTH, SURVIVAL_LOW, SURVIVAL_HIGH + ) + + +def cliff_death_prob(wealth: ContinuousState) -> FloatND: + return 1.0 - cliff_stay_prob(wealth) + + +def narrow_stay_prob(wealth: ContinuousState) -> FloatND: + t = jnp.clip((wealth - BAND_START) / NARROW_BAND_WIDTH, 0.0, 1.0) + smooth = t * t * t * (t * (6.0 * t - 15.0) + 10.0) + return SURVIVAL_LOW + (SURVIVAL_HIGH - SURVIVAL_LOW) * smooth + + +def narrow_death_prob(wealth: ContinuousState) -> FloatND: + return 1.0 - narrow_stay_prob(wealth) + + +def smooth_stay_prob(wealth: ContinuousState) -> FloatND: + return survival_of_wealth(wealth) + + +def smooth_death_prob(wealth: ContinuousState) -> FloatND: + return 1.0 - survival_of_wealth(wealth) + + +def _build_model_with_survival_cells(stay, die) -> Model: + working = UserRegime( + transition={ + "working_life": MarkovTransition(stay), + "dead": MarkovTransition(die), + }, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_dcegm}, + functions=_dcegm_functions(), + solver=DCEGM_SOLVER, + ) + return Model( + regimes={"working_life": working, "dead": dead}, + ages=_ages(), + regime_id_class=SavingsStageRegimeId, + ) + + +@pytest.mark.parametrize( + ("stay", "die"), + [ + pytest.param(cliff_stay_prob, cliff_death_prob, id="boolean_step"), + pytest.param(narrow_stay_prob, narrow_death_prob, id="sub_cell_smoothstep"), + ], +) +def test_cliff_in_regime_transition_probability_raises(stay, die): + """A survival probability that jumps at node resolution fails at build. + + A boolean step is a genuine cliff; a smoothstep narrower than one wealth + grid cell is a cliff at node resolution β€” the grid has no nodes across + the band, so the per-asset-node evaluation cannot resolve it. Both are + rejected at model build with a hint to add grid nodes across the band. + """ + with pytest.raises( + ModelInitializationError, match="add grid nodes across the band" + ): + _build_model_with_survival_cells(stay, die) + + +def test_smooth_band_regime_transition_probability_constructs(): + """A survival probability ramping over many grid cells builds fine.""" + model = _build_model_with_survival_cells(smooth_stay_prob, smooth_death_prob) + assert model.n_periods == N_PERIODS diff --git a/tests/solution/test_egm_terminal_carry_fixed_params.py b/tests/solution/test_egm_terminal_carry_fixed_params.py new file mode 100644 index 000000000..abffa7e83 --- /dev/null +++ b/tests/solution/test_egm_terminal_carry_fixed_params.py @@ -0,0 +1,247 @@ +"""DC-EGM terminal carry: a bequest utility reads a model-level fixed param. + +A terminal regime's bequest utility may reach a model-level (shared) parameter +through a helper function β€” for example a consumption-equivalence scale applied +to the bequest. When that parameter is supplied through `fixed_params`, it is +partialled into the compiled functions at model build and dropped from the live +parameter template. The terminal carry producer the DC-EGM parent reads must +still evaluate the bequest with the fixed value, exactly as a free solve param +would be threaded β€” so the parent's continuation through the terminal regime is +identical whether the scale is fixed or free. + +The DC-EGM solution must match a mathematically identical dense brute-force +spec, and the fixed and free parametrisations must agree with each other. +""" + +import functools + +import jax.numpy as jnp +import numpy as np +import pytest + +from lcm import ( + AgeGrid, + IrregSpacedGrid, + LinSpacedGrid, + Model, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM, GridSearch +from lcm.typing import ( + ContinuousAction, + ContinuousState, + FloatND, + ScalarInt, +) + +N_PERIODS = 4 +# The lowest wealth nodes are where grid search is least reliable and the +# DC-EGM constrained segment is exact; excluded from the head-to-head so the +# comparison lives on territory where both solvers are well-defined. +N_BRUTE_UNSTABLE_NODES = 20 + +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=400.0, n_points=120) +CONSUMPTION_GRID = LinSpacedGrid(start=1.0, stop=400.0, n_points=500) +# Dense terminal wealth grid: the bequest continuation is read by linear +# interpolation on this grid, so it must resolve the curvature of `log`. +BEQUEST_WEALTH_GRID = LinSpacedGrid(start=1.0, stop=400.0, n_points=600) +SAVINGS_GRID = IrregSpacedGrid(points=tuple(400.0 * (i / 199) ** 3 for i in range(200))) + +# Consumption-equivalence scale the bequest utility reads through a helper +# function. Supplied via `fixed_params` in the fixed parametrisation; the +# terminal regime's template never carries it as a free leaf there. +AVERAGE_CONSUMPTION_EQUIV = 2.5 + + +@categorical(ordered=False) +class RegimeId: + retirement: ScalarInt + dead: ScalarInt + + +def utility_scale_factor(average_consumption_equiv: float) -> FloatND: + """Consumption-equivalence scale applied inside the bequest. + + A model-level helper whose single parameter is the load-bearing one: when + fixed, its qualified name `utility_scale_factor__average_consumption_equiv` + must reach the terminal carry producer for the bequest to evaluate. + """ + return jnp.asarray(1.0 / average_consumption_equiv) + + +def bequest_utility( + wealth: ContinuousState, + utility_scale_factor: FloatND, + bequest_weight: float, +) -> FloatND: + return bequest_weight * jnp.log(wealth * utility_scale_factor + 1.0) + + +def utility_retirement(consumption: ContinuousAction) -> FloatND: + return jnp.log(consumption) + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def savings_post(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def next_wealth_from_savings( + savings_post: FloatND, interest_rate: float +) -> ContinuousState: + return (1.0 + interest_rate) * savings_post + + +def next_wealth_brute( + wealth: ContinuousState, consumption: ContinuousAction, interest_rate: float +) -> ContinuousState: + return (1.0 + interest_rate) * (wealth - consumption) + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_regime_from_retirement(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where(age >= final_age_alive, RegimeId.dead, RegimeId.retirement) + + +def borrowing_constraint( + consumption: ContinuousAction, wealth: ContinuousState +) -> FloatND: + return consumption <= wealth + + +def _make_dead_regime() -> UserRegime: + return UserRegime( + transition=None, + states={"wealth": BEQUEST_WEALTH_GRID}, + functions={ + "utility": bequest_utility, + "utility_scale_factor": utility_scale_factor, + }, + ) + + +def _ages() -> AgeGrid: + return AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + + +@functools.cache +def _get_model(solver: str, *, scale_is_fixed: bool) -> Model: + """Retirement model carrying into a bequest terminal reading a model param. + + The terminal `dead` regime's bequest reaches `average_consumption_equiv` + through `utility_scale_factor`. When `scale_is_fixed` the value is supplied + through `fixed_params` (partialled at model build, dropped from the live + template); otherwise it is a free solve param of the terminal regime. + """ + is_dcegm = solver == "dcegm" + ages = _ages() + last_age = ages.exact_values[-1] + retirement = UserRegime( + transition=next_regime_from_retirement, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={ + "wealth": next_wealth_from_savings if is_dcegm else next_wealth_brute + }, + constraints=( + {} if is_dcegm else {"borrowing_constraint": borrowing_constraint} + ), + functions=( + { + "utility": utility_retirement, + "resources": resources, + "savings_post": savings_post, + "inverse_marginal_utility": inverse_marginal_utility, + } + if is_dcegm + else {"utility": utility_retirement} + ), + solver=( + DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings_post", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, + ) + if is_dcegm + else GridSearch() + ), + active=lambda age, la=last_age: age < la, + ) + return Model( + regimes={"retirement": retirement, "dead": _make_dead_regime()}, + ages=ages, + regime_id_class=RegimeId, + fixed_params=_fixed_scale() if scale_is_fixed else {}, + ) + + +def _base_params() -> dict: + final_age_alive = 40 + (N_PERIODS - 2) * 10 + return { + "discount_factor": 0.98, + "interest_rate": 0.0, + "final_age_alive": final_age_alive, + "bequest_weight": 1.5, + } + + +def _free_scale_params() -> dict: + params = _base_params() + params["dead"] = { + "utility_scale_factor": {"average_consumption_equiv": AVERAGE_CONSUMPTION_EQUIV} + } + return params + + +def _fixed_scale() -> dict: + return { + "dead": { + "utility_scale_factor": { + "average_consumption_equiv": AVERAGE_CONSUMPTION_EQUIV + } + } + } + + +@pytest.mark.parametrize("scale_is_fixed", [True, False]) +def test_dcegm_terminal_bequest_fixed_param_matches_brute_force( + scale_is_fixed: bool, # noqa: FBT001 +): + """A terminal bequest reading a model-level param matches brute force. + + The DC-EGM parent carries into a terminal regime whose bequest reaches the + `average_consumption_equiv` scale through a helper function. Whether that + scale is a fixed param (partialled into the terminal carry producer at model + build, dropped from the live template) or a free solve param (threaded from + the regime's live params), the parent's value function at every working-life + period agrees with the dense-grid brute-force oracle. + """ + params = _base_params() if scale_is_fixed else _free_scale_params() + dcegm_solution = _get_model("dcegm", scale_is_fixed=scale_is_fixed).solve( + params=params, log_level="debug" + ) + brute_solution = _get_model("brute_force", scale_is_fixed=scale_is_fixed).solve( + params=params, log_level="debug" + ) + + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["retirement"]) + dcegm_V = np.asarray(dcegm_solution[period]["retirement"]) + assert brute_V.shape == dcegm_V.shape + np.testing.assert_allclose( + dcegm_V[..., N_BRUTE_UNSTABLE_NODES:], + brute_V[..., N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}, scale_is_fixed={scale_is_fixed}", + ) diff --git a/tests/solution/test_egm_terminal_discrete_states.py b/tests/solution/test_egm_terminal_discrete_states.py new file mode 100644 index 000000000..1c3a652b1 --- /dev/null +++ b/tests/solution/test_egm_terminal_discrete_states.py @@ -0,0 +1,314 @@ +"""DC-EGM with a terminal target that shares a fixed discrete state. + +A terminal regime's bequest utility may be heterogeneous in a discrete state +that the DC-EGM parent also carries. The motivating case is a fixed preference +type `pref_type`: the parent carries it as one of its own discrete combo axes, +the terminal `dead` regime reads it to scale the bequest, and the transition +into `dead` is the identity (`next_pref_type = pref_type`). At a parent combo +with `pref_type = k`, the terminal carry the parent needs is the terminal +utility evaluated at `pref_type = k` on the wealth grid β€” one row per shared +discrete combo. + +The DC-EGM solution must match a mathematically identical dense brute-force +spec per type: a wrong per-type carry alignment (reading type 0's bequest for +type 1) breaks the comparison because the two types' bequests differ +materially. +""" + +import functools + +import jax.numpy as jnp +import numpy as np +import pytest + +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + Model, + categorical, + fixed_transition, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.typing import ( + ContinuousAction, + ContinuousState, + DiscreteState, + FloatND, + ScalarInt, +) + +N_PERIODS = 4 +# The lowest wealth nodes are where grid search is least reliable (the value +# function curves hardest as the borrowing constraint starts to bind) and the +# DC-EGM constrained segment is exact; they are excluded from the head-to-head +# so the comparison lives on territory where both solvers are well-defined. +N_BRUTE_UNSTABLE_NODES = 20 + +WEALTH_GRID = LinSpacedGrid(start=1.0, stop=400.0, n_points=120) +CONSUMPTION_GRID = LinSpacedGrid(start=1.0, stop=400.0, n_points=500) +# Dense terminal wealth grid: the bequest continuation is read by linear +# interpolation on this grid, so it must resolve the curvature of `log`. +BEQUEST_WEALTH_GRID = LinSpacedGrid(start=1.0, stop=400.0, n_points=600) +SAVINGS_GRID = IrregSpacedGrid(points=tuple(400.0 * (i / 199) ** 3 for i in range(200))) + + +@categorical(ordered=False) +class PrefType: + impatient_bequest: ScalarInt + strong_bequest: ScalarInt + + +@categorical(ordered=False) +class RegimeId: + retirement: ScalarInt + dead: ScalarInt + + +def bequest_weight( + pref_type: DiscreteState, weight_low: float, weight_high: float +) -> FloatND: + """Per-type bequest weight; the two types differ enough to catch misalignment.""" + return jnp.where(pref_type == PrefType.strong_bequest, weight_high, weight_low) + + +def bequest_utility( + wealth: ContinuousState, + pref_type: DiscreteState, + weight_low: float, + weight_high: float, + bequest_shifter: float, +) -> FloatND: + weight = bequest_weight( + pref_type=pref_type, weight_low=weight_low, weight_high=weight_high + ) + return weight * jnp.log(wealth + bequest_shifter) + + +def utility_retirement( + consumption: ContinuousAction, pref_type: DiscreteState, flow_taste: float +) -> FloatND: + """Log consumption plus a per-type additive flow taste. + + The additive `pref_type` term makes the preference type a genuine combo + axis of the parent's own utility (a model state must be used by the + regime that carries it) without touching marginal utility, so the Euler + inversion and the brute-force oracle stay identical. + """ + taste = jnp.where(pref_type == PrefType.strong_bequest, flow_taste, 0.0) + return jnp.log(consumption) + taste + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def savings_post(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def next_wealth_from_savings( + savings_post: FloatND, interest_rate: float +) -> ContinuousState: + return (1.0 + interest_rate) * savings_post + + +def next_wealth_brute( + wealth: ContinuousState, consumption: ContinuousAction, interest_rate: float +) -> ContinuousState: + return (1.0 + interest_rate) * (wealth - consumption) + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def next_regime_from_retirement(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where( + age >= final_age_alive, + RegimeId.dead, + RegimeId.retirement, + ) + + +def borrowing_constraint( + consumption: ContinuousAction, wealth: ContinuousState +) -> FloatND: + return consumption <= wealth + + +def _make_dead_regime() -> UserRegime: + return UserRegime( + transition=None, + states={ + "wealth": BEQUEST_WEALTH_GRID, + "pref_type": DiscreteGrid(PrefType), + }, + functions={ + "utility": bequest_utility, + "bequest_weight": bequest_weight, + }, + ) + + +@functools.cache +def _get_dcegm_model() -> Model: + """Retirement DC-EGM model with a fixed `pref_type` shared with `dead`.""" + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + solver = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings_post", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, + ) + retirement = UserRegime( + transition=next_regime_from_retirement, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID, "pref_type": DiscreteGrid(PrefType)}, + state_transitions={ + "wealth": next_wealth_from_savings, + "pref_type": fixed_transition("pref_type"), + }, + functions={ + "utility": utility_retirement, + "resources": resources, + "savings_post": savings_post, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=solver, + active=lambda age, la=last_age: age < la, + ) + return Model( + regimes={"retirement": retirement, "dead": _make_dead_regime()}, + ages=ages, + regime_id_class=RegimeId, + ) + + +@functools.cache +def _get_brute_model() -> Model: + """Mathematically identical brute-force spec sharing `pref_type` with `dead`.""" + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + retirement = UserRegime( + transition=next_regime_from_retirement, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID, "pref_type": DiscreteGrid(PrefType)}, + state_transitions={ + "wealth": next_wealth_brute, + "pref_type": fixed_transition("pref_type"), + }, + constraints={"borrowing_constraint": borrowing_constraint}, + functions={"utility": utility_retirement}, + active=lambda age, la=last_age: age < la, + ) + return Model( + regimes={"retirement": retirement, "dead": _make_dead_regime()}, + ages=ages, + regime_id_class=RegimeId, + ) + + +def _get_params() -> dict: + final_age_alive = 40 + (N_PERIODS - 2) * 10 + return { + "discount_factor": 0.98, + "interest_rate": 0.0, + "final_age_alive": final_age_alive, + "weight_low": 0.3, + "weight_high": 3.0, + "bequest_shifter": 5.0, + "flow_taste": 0.5, + } + + +def test_dcegm_terminal_bequest_by_pref_type_matches_brute_force(): + """DC-EGM matches a dense brute-force spec at every working-life period. + + Each `pref_type` slice of the published value-function array agrees with + the brute-force solution on the wealth nodes where grid search is stable, + so the parent reads the terminal bequest carry at its own type. + """ + params = _get_params() + dcegm_solution = _get_dcegm_model().solve(params=params, log_level="debug") + brute_solution = _get_brute_model().solve(params=params, log_level="debug") + + for period in sorted(brute_solution)[:-1]: + brute_V = np.asarray(brute_solution[period]["retirement"]) + dcegm_V = np.asarray(dcegm_solution[period]["retirement"]) + assert brute_V.shape == dcegm_V.shape + np.testing.assert_allclose( + dcegm_V[..., N_BRUTE_UNSTABLE_NODES:], + brute_V[..., N_BRUTE_UNSTABLE_NODES:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}", + ) + + +def test_dcegm_terminal_bequest_differs_by_pref_type(): + """The two `pref_type` slices carry materially different value functions. + + Guards the comparison: if the per-type bequests were identical, a swapped + carry alignment would pass silently. The strong-bequest type values wealth + in the terminal period far above the impatient-bequest type. + """ + params = _get_params() + dcegm_solution = _get_dcegm_model().solve(params=params, log_level="debug") + + decision_period = sorted(dcegm_solution)[0] + V = np.asarray(dcegm_solution[decision_period]["retirement"]) + impatient = V[PrefType.impatient_bequest] + strong = V[PrefType.strong_bequest] + assert np.all(strong[N_BRUTE_UNSTABLE_NODES:] > impatient[N_BRUTE_UNSTABLE_NODES:]) + + +def test_terminal_discrete_state_not_carried_by_parent_is_rejected(): + """A terminal discrete state absent from the parent's combo axes is rejected. + + The parent has no axis to align the terminal carry's discrete dimension to, + so the DC-EGM solve reports the unsupported configuration rather than + silently mis-indexing. + """ + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + solver = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings_post", + savings_grid=SAVINGS_GRID, + n_constrained_points=64, + ) + + def plain_utility(consumption: ContinuousAction) -> FloatND: + return jnp.log(consumption) + + # The parent does NOT carry `pref_type`; only `dead` does. + retirement = UserRegime( + transition=next_regime_from_retirement, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_from_savings}, + functions={ + "utility": plain_utility, + "resources": resources, + "savings_post": savings_post, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=solver, + active=lambda age, la=last_age: age < la, + ) + model = Model( + regimes={"retirement": retirement, "dead": _make_dead_regime()}, + ages=ages, + regime_id_class=RegimeId, + ) + params = {k: v for k, v in _get_params().items() if k != "flow_taste"} + with pytest.raises(NotImplementedError, match="pref_type"): + model.solve(params=params, log_level="debug") diff --git a/tests/solution/test_envelope_exact_crossing.py b/tests/solution/test_envelope_exact_crossing.py new file mode 100644 index 000000000..3ff963519 --- /dev/null +++ b/tests/solution/test_envelope_exact_crossing.py @@ -0,0 +1,116 @@ +"""FUES retains equal-value coincident-abscissa crossings. + +When two value-correspondence branches cross exactly on an existing endogenous +grid point, the envelope has a genuine kink there: both branches attain the +same (maximal) value but carry different policies. The refinement must keep +both copies β€” the left branch valid up to the crossing and the right branch +valid beyond it β€” so a right-continuous read just past the crossing recovers +the right branch's policy rather than interpolating across the kink. + +The host oracle `tests/solution/_envelope_oracle.exact_envelope` is the +reference: it consumes explicit branch labels and is exact for the +piecewise-linear correspondence. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.upper_envelope import fues, rfc +from tests.solution._envelope_oracle import exact_envelope + +# Two branches sampled on the shared grid R = (10, 11, 12): +# - branch A: policy 3, value (5/3, 2, 7/3), slope 1/3; +# - branch B: policy 0.5, value (0, 2, 4), slope 2. +# They cross exactly at R = 11, where both attain value 2. A wins below 11, B +# above; the envelope kink lands on the grid node R = 11. +_ENDOG = jnp.array([10.0, 11.0, 12.0, 10.0, 11.0, 12.0]) +_POLICY = jnp.array([3.0, 3.0, 3.0, 0.5, 0.5, 0.5]) +_VALUE = jnp.array([5 / 3, 2.0, 7 / 3, 0.0, 2.0, 4.0]) +_SEGMENT = jnp.array([0.0, 0.0, 0.0, 1.0, 1.0, 1.0]) +_MARGINAL = jnp.array([1 / 3, 1 / 3, 1 / 3, 2.0, 2.0, 2.0]) +_N_REFINED = 20 + + +def _kept(refine_output): + """Return the non-NaN (grid, policy, value) prefix of a refinement output.""" + grid, policy, value, _ = refine_output + grid = np.asarray(grid) + keep = ~np.isnan(grid) + return grid[keep], np.asarray(policy)[keep], np.asarray(value)[keep] + + +def test_fues_retains_equal_value_crossing_on_grid_node(): + """FUES keeps both branch copies at an on-grid crossing, like RFC does. + + The refined envelope is `grid = [10, 11, 11, 12]` with the left branch + (policy 3) then the right branch (policy 0.5) at the duplicated crossing + node, so the published row carries the kink rather than collapsing it. + """ + grid, policy, _ = _kept( + fues.refine_envelope( + endog_grid=_ENDOG, + policy=_POLICY, + value=_VALUE, + n_refined=_N_REFINED, + segment_id=_SEGMENT, + ) + ) + + np.testing.assert_allclose(grid, [10.0, 11.0, 11.0, 12.0]) + np.testing.assert_allclose(policy, [3.0, 3.0, 0.5, 0.5]) + + +def test_fues_matches_rfc_at_on_grid_crossing(): + """FUES and RFC publish the same refined envelope at the on-grid crossing.""" + fues_grid, fues_policy, fues_value = _kept( + fues.refine_envelope( + endog_grid=_ENDOG, + policy=_POLICY, + value=_VALUE, + n_refined=_N_REFINED, + segment_id=_SEGMENT, + ) + ) + rfc_grid, rfc_policy, rfc_value = _kept( + rfc.refine_envelope( + endog_grid=_ENDOG, + policy=_POLICY, + value=_VALUE, + marginal_utility=_MARGINAL, + n_refined=_N_REFINED, + ) + ) + + np.testing.assert_allclose(fues_grid, rfc_grid) + np.testing.assert_allclose(fues_policy, rfc_policy) + np.testing.assert_allclose(fues_value, rfc_value) + + +def test_fues_envelope_value_matches_oracle_across_crossing(): + """The FUES envelope value equals the host oracle on both sides of the kink. + + On the grid nodes the published value is the branch maximum; the oracle + confirms branch A wins at and below R = 11 and branch B above it. + """ + grid, _, value = _kept( + fues.refine_envelope( + endog_grid=_ENDOG, + policy=_POLICY, + value=_VALUE, + n_refined=_N_REFINED, + segment_id=_SEGMENT, + ) + ) + query = np.array([10.0, 10.5, 11.0, 11.5, 12.0]) + oracle_value, _, _ = exact_envelope( + endog_grid=np.asarray(_ENDOG), + value=np.asarray(_VALUE), + policy=np.asarray(_POLICY), + segment_id=np.asarray(_SEGMENT), + x_query=query, + ) + # Read the published row the same way the kernel does: max of the two + # branch values at a duplicated node falls out of np.interp on the sorted + # kept grid because the equal-value copies coincide. + published = np.interp(query, grid, value) + np.testing.assert_allclose(published, oracle_value, atol=1e-9) diff --git a/tests/solution/test_envelope_exhaustive_parity.py b/tests/solution/test_envelope_exhaustive_parity.py new file mode 100644 index 000000000..2a49fbd39 --- /dev/null +++ b/tests/solution/test_envelope_exhaustive_parity.py @@ -0,0 +1,158 @@ +"""The JAX first envelope matches an independent exhaustive host-side reference. + +The v3 oracle's mandatory gate for the upper-envelope kernel is an exhaustive +all-simplex reference: on a tiny mesh, enumerate every triangle for every target, apply +the exact admissibility and feasibility rules, recompute every objective, and take the +maximum on the host. This module implements that reference in NumPy β€” independent of the +production `first_envelope` β€” and asserts the two agree, including the audit's F3 case +where an admissible-but-extrapolated triangle holds the maximizer. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.mesh_envelope import SegmentMesh, first_envelope +from _lcm.egm.two_asset_inverse import RegionCloud +from _lcm.egm.two_asset_segment_mesh import build_segment_mesh + + +def _barycentric(triangle, query): + p0, p1, p2 = triangle + e1, e2, rhs = p1 - p0, p2 - p0, query - p0 + det = e1[0] * e2[1] - e1[1] * e2[0] + w1 = (rhs[0] * e2[1] - rhs[1] * e2[0]) / det + w2 = (e1[0] * rhs[1] - e1[1] * rhs[0]) / det + return np.array([1.0 - w1 - w2, w1, w2]) + + +def _exhaustive_first_envelope(*, mesh, targets, objective, threshold): + """Host reference: max recomputed objective over every admissible triangle. + + Mirrors `first_envelope`'s argmax semantics (the first maximizer wins) and its + admissibility rule (a weight is rejected only strictly below `-threshold`), so the + two are bit-comparable on the value and the winning policy. + """ + node_state = np.asarray(mesh.node_state) + node_policy = np.asarray(mesh.node_policy) + simplices = np.asarray(mesh.simplices) + valid = np.asarray(mesh.valid_node) + values, policies = [], [] + for query in np.asarray(targets): + candidate_values, candidate_policies = [], [] + for triple in simplices: + weights = _barycentric(node_state[triple], query) + policy = weights @ node_policy[triple] + value, feasible = objective(jnp.asarray(query), jnp.asarray(policy)) + admissible = bool(np.all(weights >= -threshold)) and bool( + np.all(valid[triple]) + ) + keep = admissible and bool(feasible) + candidate_values.append(float(value) if keep else -np.inf) + candidate_policies.append(np.asarray(policy)) + best = int(np.argmax(candidate_values)) + values.append(candidate_values[best]) + policies.append(candidate_policies[best]) + return np.array(values), np.array(policies) + + +def _identity_objective(_state, policy): + return policy[0], jnp.ones((), dtype=bool) + + +def _affine_two_asset_objective(*, post_value_coeffs, discount_factor, crra, domain): + """An independent two-asset Bellman objective with an affine continuation. + + Reimplements the budget identities, CRRA utility, and in-domain feasibility of the + production objective from scratch, so the parity test shares nothing with production + except `first_envelope` (the unit under test) and the mesh input. The continuation + is affine `w(a, b) = ca*a + cb*b + c0`, which a bilinear continuation reader + reproduces exactly, so the two objectives coincide on in-domain candidates without + importing the production reader. + """ + ca, cb, c0 = post_value_coeffs + a_lo, a_hi, b_lo, b_hi = domain + match_rate = 1.0 + + def objective(state, policy): + consumption, deposit = policy[0], policy[1] + liquid_post = state[0] - consumption - deposit + pension_post = state[1] + deposit + match_rate * jnp.log1p(deposit) + post_value = ca * liquid_post + cb * pension_post + c0 + safe_consumption = jnp.where(consumption > 0.0, consumption, 1.0) + utility = jnp.where( + crra == 1.0, + jnp.log(safe_consumption), + safe_consumption ** (1.0 - crra) / (1.0 - crra), + ) + value = utility + discount_factor * post_value + feasible = ( + (consumption > 0.0) + & (deposit >= 0.0) + & (liquid_post >= a_lo) + & (liquid_post <= a_hi) + & (pension_post >= b_lo) + & (pension_post <= b_hi) + ) + return value, feasible + + return objective + + +def test_first_envelope_matches_exhaustive_on_the_f3_extrapolation_case(): + """On the admissible-extrapolation mesh the JAX envelope equals the reference.""" + mesh = SegmentMesh( + region_label=0, + node_state=jnp.array( + [ + [0.0, 0.0], + [2.0, 0.0], + [0.0, 2.0], # triangle B: q extrapolated but admissible, value 1.0 + [0.0, 0.0], + [3.0, 0.0], + [0.0, 3.0], # triangle A: q covered, value 0.0 + ] + ), + node_policy=jnp.array([[1.0], [1.0], [1.0], [0.0], [0.0], [0.0]]), + simplices=jnp.array([[0, 1, 2], [3, 4, 5]], dtype=jnp.int32), + valid_node=jnp.ones(6, dtype=bool), + ) + targets = jnp.array([[1.2, 1.2]]) + jax_values, jax_policies = first_envelope( + mesh=mesh, targets=targets, objective=_identity_objective, threshold=0.25 + ) + ref_values, ref_policies = _exhaustive_first_envelope( + mesh=mesh, targets=targets, objective=_identity_objective, threshold=0.25 + ) + np.testing.assert_allclose(np.asarray(jax_values), ref_values, atol=1e-9) + np.testing.assert_allclose(np.asarray(jax_policies), ref_policies, atol=1e-9) + + +def test_first_envelope_matches_exhaustive_with_a_two_asset_objective(): + """On a region-cloud mesh and a CRRA objective the two implementations agree.""" + a_mesh, b_mesh = jnp.meshgrid(jnp.arange(3.0), jnp.arange(3.0), indexing="ij") + cloud = RegionCloud( + m_endog=2.0 + 1.5 * a_mesh, + n_endog=2.0 + 1.5 * b_mesh, + consumption=1.0 + 0.3 * a_mesh, + deposit=0.2 * b_mesh, + value=jnp.zeros((3, 3)), + value_grad_m=jnp.zeros((3, 3)), + value_grad_n=jnp.zeros((3, 3)), + valid_region=jnp.ones((3, 3), dtype=bool), + ) + mesh = build_segment_mesh(cloud=cloud, region_label=0) + objective = _affine_two_asset_objective( + post_value_coeffs=(2.0, 3.0, 1.0), + discount_factor=0.95, + crra=2.0, + domain=(0.0, 10.0, 0.0, 10.0), + ) + targets = jnp.array([[3.0, 3.0], [4.0, 4.0], [3.5, 4.5], [2.5, 2.5]]) + jax_values, jax_policies = first_envelope( + mesh=mesh, targets=targets, objective=objective, threshold=0.25 + ) + ref_values, ref_policies = _exhaustive_first_envelope( + mesh=mesh, targets=targets, objective=objective, threshold=0.25 + ) + np.testing.assert_allclose(np.asarray(jax_values), ref_values, atol=1e-9) + np.testing.assert_allclose(np.asarray(jax_policies), ref_policies, atol=1e-9) diff --git a/tests/solution/test_envelope_oracle.py b/tests/solution/test_envelope_oracle.py new file mode 100644 index 000000000..129adb217 --- /dev/null +++ b/tests/solution/test_envelope_oracle.py @@ -0,0 +1,113 @@ +"""Tests for the branch-aware exact upper-envelope oracle. + +The oracle is the independent reference the EGM envelope backends are checked +against. These tests pin the oracle's own correctness on hand-computed cases β€” +including the exact-node branch crossing the production FUES gets wrong (audit +F5) β€” and confirm it agrees with FUES on a crossing the FUES scan resolves. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.interp import interp_on_padded_grid +from _lcm.egm.upper_envelope.fues import refine_envelope +from tests.solution._envelope_oracle import exact_envelope + + +def test_oracle_recovers_v_shape_on_exact_node_crossing(): + """Two branches crossing on a shared node give the true V-shaped envelope. + + Branch 0 is `V(R) = R` (policy 0); branch 1 is `V(R) = 1 - R` (policy 10). + They cross exactly at the node `R = 0.5`. The exact envelope is + `max(R, 1 - R)` with its minimum `0.5` at the crossing, and the winning policy + switches from branch 1 (left) to branch 0 (right). This is the case the + production FUES collapses to a flat envelope (audit F5). + """ + endog_grid = np.array([0.0, 0.5, 1.0, 0.0, 0.5, 1.0]) + value = np.array([0.0, 0.5, 1.0, 1.0, 0.5, 0.0]) + policy = np.array([0.0, 0.0, 0.0, 10.0, 10.0, 10.0]) + segment_id = np.array([0.0, 0.0, 0.0, 1.0, 1.0, 1.0]) + x_query = np.array([0.0, 0.25, 0.5, 0.75, 1.0]) + + env_value, env_policy, _winner = exact_envelope( + endog_grid=endog_grid, + value=value, + policy=policy, + segment_id=segment_id, + x_query=x_query, + ) + + np.testing.assert_allclose(env_value, [1.0, 0.75, 0.5, 0.75, 1.0], atol=1e-12) + # Left of the crossing branch 1 (policy 10) wins; right of it branch 0 + # (policy 0). The exact-node tie resolves deterministically to the lower id. + np.testing.assert_allclose(env_policy, [10.0, 10.0, 0.0, 0.0, 0.0], atol=1e-12) + + +def test_oracle_is_the_interpolant_for_a_single_branch(): + """With one branch the envelope is exactly that branch's interpolant.""" + endog_grid = np.array([0.0, 1.0, 2.0, 3.0]) + value = np.array([0.0, 1.0, 1.5, 1.7]) # concave, increasing + policy = np.array([0.0, 0.5, 0.9, 1.2]) + segment_id = np.zeros(4) + x_query = np.array([0.5, 1.5, 2.5]) + + env_value, env_policy, winner = exact_envelope( + endog_grid=endog_grid, + value=value, + policy=policy, + segment_id=segment_id, + x_query=x_query, + ) + + np.testing.assert_allclose(env_value, np.interp(x_query, endog_grid, value)) + np.testing.assert_allclose(env_policy, np.interp(x_query, endog_grid, policy)) + np.testing.assert_array_equal(winner, [0, 0, 0]) + + +def test_oracle_query_outside_all_branches_is_nan(): + """A query beyond every branch's support yields NaN and winner -1.""" + env_value, env_policy, winner = exact_envelope( + endog_grid=np.array([1.0, 2.0]), + value=np.array([1.0, 2.0]), + policy=np.array([0.5, 1.0]), + segment_id=np.zeros(2), + x_query=np.array([0.0, 5.0]), + ) + assert np.isnan(env_value).all() + assert np.isnan(env_policy).all() + np.testing.assert_array_equal(winner, [-1, -1]) + + +def test_oracle_agrees_with_fues_on_a_between_node_crossing(): + """On a crossing the FUES scan resolves, oracle and FUES envelopes agree. + + Two labelled branches cross strictly between grid nodes (not on one), the case + the FUES crossing-insertion handles. Over the region where both branches are + defined, the FUES-refined value function and the exact oracle envelope match. + """ + endog_grid = jnp.array([1.0, 1.5, 2.0, 2.5]) + policy = 0.5 * endog_grid + value = jnp.array([2.0, 1.8, 2.2, 3.0]) + segment_id = jnp.array([0.0, 1.0, 0.0, 1.0]) + + grid, _, refined_value, _ = refine_envelope( + endog_grid=endog_grid, + policy=policy, + value=value, + n_refined=12, + segment_id=segment_id, + ) + # Branch 0 spans [1, 2], branch 1 spans [1.5, 2.5]; both are defined on + # [1.5, 2.0], which brackets the crossing. + x_query = jnp.linspace(1.5, 2.0, 11) + fues_value = np.asarray( + interp_on_padded_grid(x_query=x_query, xp=grid, fp=refined_value) + ) + oracle_value, _policy, _winner = exact_envelope( + endog_grid=np.asarray(endog_grid), + value=np.asarray(value), + policy=np.asarray(policy), + segment_id=np.asarray(segment_id), + x_query=np.asarray(x_query), + ) + np.testing.assert_allclose(fues_value, oracle_value, atol=1e-6) diff --git a/tests/solution/test_envelope_oracle_hardening.py b/tests/solution/test_envelope_oracle_hardening.py new file mode 100644 index 000000000..fc77e5dbc --- /dev/null +++ b/tests/solution/test_envelope_oracle_hardening.py @@ -0,0 +1,131 @@ +"""The host envelope oracle is robust enough to be the authoritative reference. + +These pin the oracle hardening: folded branches, exact-maximum value reporting +independent of the tie tolerance, segment-label winners, loud failure on +malformed input, multivalued-branch rejection, right-continuous tie breaking, +and an event-complete query generator. +""" + +import numpy as np +import pytest + +from tests.solution._envelope_oracle import ( + TopologyError, + envelope_event_points, + exact_envelope, +) + + +def test_oracle_evaluates_a_folded_branch_as_a_polyline(): + """A non-monotone branch is the polyline through its vertices, in input order. + + The branch `(0, 0) -> (2, 10) -> (1, 0)` folds back in `x`. At `x = 1.5` the + rising edge `(0, 0)-(2, 10)` gives `7.5` and the falling edge `(2, 10)-(1, 0)` + gives `5`; the branch value is their maximum, `7.5` β€” not the `5` a sort-by-x + would produce. + """ + env_value, _policy, _winner = exact_envelope( + endog_grid=np.array([0.0, 2.0, 1.0]), + value=np.array([0.0, 10.0, 0.0]), + policy=np.array([0.0, 0.0, 0.0]), + segment_id=np.array([0.0, 0.0, 0.0]), + x_query=np.array([1.5]), + ) + np.testing.assert_allclose(env_value, [7.5], atol=1e-12) + + +def test_oracle_reports_exact_maximum_not_the_tie_winner_value(): + """The reported value is the exact branch maximum, not lowered by `tol`. + + Branch 1 exceeds branch 0 by `1e-10`, inside a `tol = 1e-9` tie band. The two + are classified as tied, but the envelope value must still be the true maximum + `1.0 + 1e-10`, not branch 0's `1.0`. + """ + env_value, _policy, _winner = exact_envelope( + endog_grid=np.array([0.0, 2.0, 0.0, 2.0]), + value=np.array([1.0, 1.0, 1.0 + 1e-10, 1.0 + 1e-10]), + policy=np.array([0.0, 0.0, 9.0, 9.0]), + segment_id=np.array([0.0, 0.0, 1.0, 1.0]), + x_query=np.array([1.0]), + tol=1e-9, + ) + np.testing.assert_allclose(env_value, [1.0 + 1e-10], atol=1e-13) + + +def test_oracle_winner_is_the_segment_label_not_the_list_index(): + """`winner` returns the segment label, so non-index labels round-trip.""" + _value, _policy, winner = exact_envelope( + endog_grid=np.array([0.0, 2.0, 0.0, 2.0]), + value=np.array([0.0, 0.0, 1.0, 1.0]), # branch 9 dominates + policy=np.array([0.0, 0.0, 5.0, 5.0]), + segment_id=np.array([4.0, 4.0, 9.0, 9.0]), + x_query=np.array([1.0]), + ) + np.testing.assert_array_equal(winner, [9.0]) + + +@pytest.mark.parametrize( + ("value", "policy", "segment_id"), + [ + ([0.0, np.nan], [0.0, 0.0], [0.0, 0.0]), # non-finite value + ([0.0, 1.0], [0.0, np.nan], [0.0, 0.0]), # non-finite policy + ([0.0, 1.0], [0.0, 0.0], [0.0, np.nan]), # non-finite segment label + ], +) +def test_oracle_fails_loudly_on_nonfinite_live_input(value, policy, segment_id): + """A live candidate with a non-finite value/policy/label raises, not crashes.""" + with pytest.raises(TopologyError): + exact_envelope( + endog_grid=np.array([0.0, 1.0]), + value=np.array(value), + policy=np.array(policy), + segment_id=np.array(segment_id), + x_query=np.array([0.5]), + ) + + +def test_oracle_rejects_a_multivalued_branch(): + """A branch revisiting an abscissa with a different policy is a topology error.""" + with pytest.raises(TopologyError): + exact_envelope( + endog_grid=np.array([0.0, 1.0, 1.0]), + value=np.array([0.0, 1.0, 1.0]), + policy=np.array([0.0, 3.0, 7.0]), # x=1 carries two policies + segment_id=np.array([0.0, 0.0, 0.0]), + x_query=np.array([0.5]), + ) + + +def test_oracle_breaks_an_exact_tie_right_continuously(): + """At an on-node crossing the winning policy is the branch that wins to the right. + + Branch 0 (policy 3) rises with slope 1/3; branch 1 (policy 0.5) rises with + slope 2; they cross at `R = 11` with equal value 2. Just right of 11 branch 1 + is higher, so the published policy at the crossing is branch 1's 0.5 and the + winner is segment 1 β€” the `side="right"` convention. + """ + env_value, env_policy, winner = exact_envelope( + endog_grid=np.array([10.0, 11.0, 12.0, 10.0, 11.0, 12.0]), + value=np.array([5 / 3, 2.0, 7 / 3, 0.0, 2.0, 4.0]), + policy=np.array([3.0, 3.0, 3.0, 0.5, 0.5, 0.5]), + segment_id=np.array([0.0, 0.0, 0.0, 1.0, 1.0, 1.0]), + x_query=np.array([10.5, 11.0, 11.5]), + ) + np.testing.assert_allclose(env_value, [11 / 6, 2.0, 3.0], atol=1e-12) + np.testing.assert_allclose(env_policy, [3.0, 0.5, 0.5], atol=1e-12) + np.testing.assert_array_equal(winner, [0.0, 1.0, 1.0]) + + +def test_event_points_include_the_branch_crossing(): + """The event-complete query set contains the exact branch-crossing abscissa. + + Branch 0 is `V = R`, branch 1 is `V = 1 - R`; they cross at `R = 0.5`. The + event generator must surface `0.5` so no sampling gap can hide the kink. + """ + events = envelope_event_points( + endog_grid=np.array([0.0, 1.0, 0.0, 1.0]), + value=np.array([0.0, 1.0, 1.0, 0.0]), + policy=np.array([0.0, 0.0, 10.0, 10.0]), + segment_id=np.array([0.0, 0.0, 1.0, 1.0]), + ) + assert np.any(np.isclose(events, 0.5, atol=1e-12)) diff --git a/tests/solution/test_envelope_query.py b/tests/solution/test_envelope_query.py new file mode 100644 index 000000000..69f13cd16 --- /dev/null +++ b/tests/solution/test_envelope_query.py @@ -0,0 +1,142 @@ +"""The query-side envelope backend matches the host oracle exactly. + +`envelope_at_query` evaluates the branch-aware upper envelope directly at query +abscissae. It must agree with the exact host oracle on value and policy across +the cases that distinguish the topology contract: a clean crossing, a folded +branch, and a non-bridging branch the inference backends get wrong. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.egm.upper_envelope.query import envelope_at_query +from tests.solution._envelope_oracle import exact_envelope + + +def _marginal(endog_grid, value, segment_id): + """Per-node segment slope, the marginal a piecewise-linear branch carries.""" + grid = np.asarray(endog_grid) + val = np.asarray(value) + seg = np.asarray(segment_id) + out = np.zeros_like(grid) + for s in np.unique(seg): + idx = np.where(seg == s)[0] + order = idx[np.argsort(grid[idx])] + if len(order) >= 2: + slope = (val[order[1]] - val[order[0]]) / (grid[order[1]] - grid[order[0]]) + out[idx] = slope + return jnp.asarray(out) + + +@pytest.mark.parametrize( + ("endog_grid", "policy", "value", "segment_id", "x_query"), + [ + # On-grid crossing of two branches at R=11. + ( + [10.0, 11.0, 12.0, 10.0, 11.0, 12.0], + [3.0, 3.0, 3.0, 0.5, 0.5, 0.5], + [5 / 3, 2.0, 7 / 3, 0.0, 2.0, 4.0], + [0.0, 0.0, 0.0, 1.0, 1.0, 1.0], + [10.0, 10.5, 11.0, 11.1, 11.5, 12.0], + ), + # A and B disjoint, C a separate branch between them (the non-bridging case). + ( + [0.0, 1.0, 2.0, 3.0, 1.5, 1.75], + [0.0, 0.0, 10.0, 10.0, 5.0, 5.0], + [0.0, 1.0, 4.0, 5.0, 0.5, 0.5], + [0.0, 0.0, 1.0, 1.0, 2.0, 2.0], + [0.5, 1.5, 1.75, 2.5], + ), + ], +) +def test_query_envelope_matches_oracle(endog_grid, policy, value, segment_id, x_query): + """Value and policy from the query backend equal the exact oracle.""" + endog_grid = jnp.asarray(endog_grid) + policy = jnp.asarray(policy) + value = jnp.asarray(value) + segment_id = jnp.asarray(segment_id) + x_query = jnp.asarray(x_query) + + got_value, got_policy, _got_marginal = envelope_at_query( + endog_grid=endog_grid, + policy=policy, + value=value, + marginal=_marginal(endog_grid, value, segment_id), + segment_id=segment_id, + x_query=x_query, + ) + oracle_value, oracle_policy, _winner = exact_envelope( + endog_grid=np.asarray(endog_grid), + value=np.asarray(value), + policy=np.asarray(policy), + segment_id=np.asarray(segment_id), + x_query=np.asarray(x_query), + ) + + np.testing.assert_allclose(np.asarray(got_value), oracle_value, atol=1e-9) + np.testing.assert_allclose(np.asarray(got_policy), oracle_policy, atol=1e-9) + + +@pytest.mark.parametrize("block_size", [1, 2, 3, 4]) +def test_blocked_segment_scan_matches_the_dense_reduction(block_size): + """`segment_block_size` is a memory knob: same value, policy, marginal. + + The two-pass blocked scan reproduces the dense `(n_query, n_segment)` + reduction β€” same envelope value, same right-continuous tie-break winner β€” for + any block size (divisor or not) below the segment count, up to floating-point + reassociation between the two XLA lowerings. + """ + rng = np.random.default_rng(20260626) + # Three interleaved branches over a shared resource range, so several + # segments bracket each query and the envelope max is contested. + grids, values, policies, segments = [], [], [], [] + for seg, (intercept, slope_v) in enumerate([(1.0, 0.4), (0.1, 0.8), (0.6, 0.2)]): + r = np.sort(rng.uniform(0.5, 3.5, size=6)) + grids.append(r) + values.append(intercept + slope_v * r) + policies.append(0.25 * (seg + 1) * r) + segments.append(np.full_like(r, float(seg))) + endog_grid = jnp.asarray(np.concatenate(grids)) + value = jnp.asarray(np.concatenate(values)) + policy = jnp.asarray(np.concatenate(policies)) + segment_id = jnp.asarray(np.concatenate(segments)) + marginal = _marginal(endog_grid, value, segment_id) + x_query = jnp.asarray(np.linspace(0.7, 3.3, 41)) + + dense = envelope_at_query( + endog_grid=endog_grid, + policy=policy, + value=value, + marginal=marginal, + segment_id=segment_id, + x_query=x_query, + ) + blocked = envelope_at_query( + endog_grid=endog_grid, + policy=policy, + value=value, + marginal=marginal, + segment_id=segment_id, + x_query=x_query, + segment_block_size=block_size, + ) + for dense_arr, blocked_arr in zip(dense, blocked, strict=True): + np.testing.assert_allclose( + np.asarray(blocked_arr), np.asarray(dense_arr), rtol=1e-12, atol=1e-12 + ) + + +def test_query_outside_all_branches_is_nan(): + """A query beyond every branch's support yields NaN value/policy/marginal.""" + got_value, got_policy, got_marginal = envelope_at_query( + endog_grid=jnp.array([1.0, 2.0]), + policy=jnp.array([0.5, 1.0]), + value=jnp.array([1.0, 2.0]), + marginal=jnp.array([1.0, 1.0]), + segment_id=jnp.array([0.0, 0.0]), + x_query=jnp.array([0.0, 5.0]), + ) + assert bool(np.isnan(np.asarray(got_value)).all()) + assert bool(np.isnan(np.asarray(got_policy)).all()) + assert bool(np.isnan(np.asarray(got_marginal)).all()) diff --git a/tests/solution/test_euler_errors.py b/tests/solution/test_euler_errors.py new file mode 100644 index 000000000..968461412 --- /dev/null +++ b/tests/solution/test_euler_errors.py @@ -0,0 +1,188 @@ +"""The unit-free consumption Euler error measures a solution's accuracy. + +For an interior (unconstrained) consumption--saving optimum the Euler equation +`u'(c) = beta*(1+r)*u'(c_next)` holds exactly, so the relative gap between the chosen +consumption and the consumption the Euler equation implies is a brute-free accuracy +metric. It is reported as `log10` of the relative consumption error (e.g. `-3` is a +0.1% error). The endogenous grid method nulls the interior Euler residual by +construction, so a correct retired solution has tiny interior Euler errors. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.euler_errors import ( + consumption_euler_error_log10, + working_consumption_euler_error_log10, +) +from _lcm.egm.one_asset_egm_step import egm_one_asset_step +from _lcm.egm.two_asset_g2egm_step import g2egm_retiring_step, g2egm_step +from tests.conftest import X64_ENABLED + +# The "essentially zero" log10 Euler residual floor is set by float eps: +# roughly -15 at 64-bit, -7 at 32-bit; -8/-6 leave margin for rounding. +_EXACT_RESIDUAL_LOG10_BOUND = -8.0 if X64_ENABLED else -6.0 + +_LIQUID_GRID = jnp.linspace(0.1, 20.0, 12) +_SAVINGS_GRID = jnp.linspace(0.0, 20.0, 40) +_DISCOUNT, _CRRA, _RETURN, _INCOME = 0.98, 2.0, 0.02, 0.50 +# The lowest liquid points are borrowing-constrained: the unconstrained Euler equation +# does not hold there (it holds with a constraint multiplier), so the metric is reported +# on the unconstrained interior. +_INTERIOR = np.s_[2:] + + +def test_constrained_consume_all_solution_has_an_exact_euler_residual(): + """A hand-built unconstrained interior point has its Euler error reproduce the gap. + + With `next_consumption = next_liquid` (consume everything next period) the implied + consumption is `c_euler = (beta*(1+r))**(-1/crra) * next_liquid`; planting a policy + exactly equal to `c_euler` drives the Euler error to `-inf` (zero residual), and a + 10% overconsumption gives `log10(0.1)`. + """ + liquid = jnp.array([10.0]) + next_liquid_if = lambda c: (1.0 + _RETURN) * (liquid - c) + _INCOME # noqa: E731 + # Solve the fixed point c = (beta*(1+r))**(-1/crra) * ((1+r)(liquid-c)+income). + k = (_DISCOUNT * (1.0 + _RETURN)) ** (-1.0 / _CRRA) + c_star = k * ((1.0 + _RETURN) * liquid + _INCOME) / (1.0 + k * (1.0 + _RETURN)) + err = consumption_euler_error_log10( + liquid_grid=liquid, + consumption=c_star, + next_consumption=next_liquid_if(c_star), + discount_factor=_DISCOUNT, + crra=_CRRA, + return_liquid=_RETURN, + income=_INCOME, + ) + assert float(err[0]) < _EXACT_RESIDUAL_LOG10_BOUND # essentially zero residual + + +def _retired_median_euler_error(*, n_liquid): + """Median interior Euler error of a one-step retired solve at a grid resolution.""" + liquid_grid = jnp.linspace(0.1, 20.0, n_liquid) + savings_grid = jnp.linspace(0.0, 20.0, 4 * n_liquid) + step = egm_one_asset_step( + next_value=liquid_grid ** (1.0 - _CRRA) / (1.0 - _CRRA), + next_marginal=liquid_grid ** (-_CRRA), + liquid_grid=liquid_grid, + savings_grid=savings_grid, + discount_factor=_DISCOUNT, + crra=_CRRA, + return_liquid=_RETURN, + income=_INCOME, + ) + # The continuation is the terminal bequest: at death all wealth is consumed, so the + # next-period consumption policy is the identity in liquid. + errors = np.asarray( + consumption_euler_error_log10( + liquid_grid=liquid_grid, + consumption=step.consumption, + next_consumption=liquid_grid, + discount_factor=_DISCOUNT, + crra=_CRRA, + return_liquid=_RETURN, + income=_INCOME, + ) + ) + return np.median(errors[_INTERIOR]) + + +def test_retired_euler_error_converges_under_grid_refinement(): + """The interior Euler error shrinks as the liquid grid refines. + + The endogenous grid method nulls the Euler residual at the endogenous nodes; + interpolating the policy back onto a coarse regular grid reintroduces it, so the + residual is a resolution diagnostic that converges to zero. Refining the grid four + times over drives the median interior error well below a percent. + """ + coarse = _retired_median_euler_error(n_liquid=12) + fine = _retired_median_euler_error(n_liquid=48) + assert coarse < -1.5 # ~2% at the coarse oracle grid + assert fine < -3.0 # below 0.1% once resolved + assert fine < coarse - 1.0 # at least an order of magnitude better + + +_W = { + "discount_factor": 0.98, + "crra": 2.0, + "match_rate": 0.10, + "return_liquid": 0.02, + "return_pension": 0.04, + "wage": 1.0, +} +_WORK_DISUTILITY, _RET_INCOME, _PAYOUT = 0.25, 0.50, 1.04 + + +def _working_first_period_euler_error(*, n_liquid): + """Median interior working consumption Euler error two steps before retirement. + + Solves the DS pension working chain (retired -> boundary -> p1 -> p0) keeping the + consumption policy at each step, then evaluates the working consumption Euler error + at the first period from its own and the next period's policy. + """ + m_grid = jnp.linspace(0.1, 20.0, n_liquid) + n_grid = jnp.linspace(0.0, 15.0, 10) + a_grid = jnp.linspace(0.0, 20.0, max(18, n_liquid + 2)) + b_grid = jnp.linspace(0.0, 30.0, 16) + consumption_grid = jnp.linspace(0.1, 20.0, max(18, n_liquid + 2)) + + def working(next_value): + return g2egm_step( + next_value=next_value, + m_grid=m_grid, + n_grid=n_grid, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + **_W, + ) + + v_dead = m_grid ** (1.0 - _W["crra"]) / (1.0 - _W["crra"]) + retired = egm_one_asset_step( + next_value=v_dead, + next_marginal=m_grid ** (-_W["crra"]), + liquid_grid=m_grid, + savings_grid=jnp.linspace(0.0, 20.0, 60), + discount_factor=_W["discount_factor"], + crra=_W["crra"], + return_liquid=_W["return_liquid"], + income=_RET_INCOME, + ) + boundary = g2egm_retiring_step( + next_value_retired=retired.value, + next_marginal_retired=retired.marginal, + liquid_grid=m_grid, + m_grid=m_grid, + n_grid=n_grid, + a_grid=a_grid, + b_grid=b_grid, + consumption_grid=consumption_grid, + discount_factor=_W["discount_factor"], + crra=_W["crra"], + match_rate=_W["match_rate"], + return_liquid=_W["return_liquid"], + pension_payout_return=_PAYOUT, + retirement_income=_RET_INCOME, + ) + period1 = working(boundary.value - _WORK_DISUTILITY) + period0 = working(period1.value - _WORK_DISUTILITY) + errors = np.asarray( + working_consumption_euler_error_log10( + m_grid=m_grid, + n_grid=n_grid, + consumption=period0.consumption, + deposit=period0.deposit, + next_consumption=period1.consumption, + **_W, + ) + ) + # Exclude the unresolved low-liquid band and the off-grid top-pension hole layer. + return np.median(errors[3:, :7]) + + +def test_working_consumption_euler_error_converges_under_grid_refinement(): + """The working consumption Euler error shrinks as the liquid grid refines.""" + coarse = _working_first_period_euler_error(n_liquid=12) + fine = _working_first_period_euler_error(n_liquid=24) + assert coarse < -1.0 # the chained two-asset solve is coarser than the 1-D retired + assert fine < coarse - 0.3 # refinement improves it diff --git a/tests/solution/test_fues.py b/tests/solution/test_fues.py new file mode 100644 index 000000000..252d717b0 --- /dev/null +++ b/tests/solution/test_fues.py @@ -0,0 +1,238 @@ +"""Spec for the FUES upper-envelope kernel (Dobrescu & Shanker 2022). + +Contract under test β€” `_lcm.egm.upper_envelope.fues.refine_envelope`: + + refine_envelope( + *, + endog_grid: Float1D, # candidate resources points (any order) + policy: Float1D, + value: Float1D, + n_refined: int, # static output length + jump_thresh: float = 2.0, + n_points_to_scan: int = 10, + ) -> tuple[Float1D, Float1D, Float1D, ScalarInt] + +Returns NaN-padded arrays of length `n_refined` holding the upper envelope of the +candidate value correspondence (weakly ascending in the grid: intersection points +appear twice, with left- and right-extrapolated policies) plus the number of kept +points. `n_kept > n_refined` signals overflow; the caller decides how to surface +it. + +Assertions are semantic β€” the refined arrays must *represent* the analytic upper +envelope under linear interpolation β€” rather than pinning which input points +survive, so the spec is robust to scan-mechanics details. + +Skips until the kernel exists. +""" + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from tests.conftest import X64_ENABLED + +fues = pytest.importorskip( + "_lcm.egm.upper_envelope.fues", reason="FUES kernel not yet implemented" +) + +# Tolerance for quantities computed by the kernel (segment intersections and +# values interpolated through them): float32 carries a few ulp (~1e-7 at the +# fixtures' scale) through the intersection arithmetic. +_COMPUTED_ATOL = 1e-8 if X64_ENABLED else 1e-5 + + +def _drop_nan(arr: jnp.ndarray) -> np.ndarray: + out = np.asarray(arr) + return out[~np.isnan(out)] + + +def _envelope_interp(grid, value, x_query): + keep = ~np.isnan(np.asarray(grid)) + return np.interp(x_query, np.asarray(grid)[keep], np.asarray(value)[keep]) + + +def _crossing_segments_candidates(): + """Two linear choice-specific value segments crossing at R* = 2.25. + + - Segment A: v = 1.0 + 0.4 R, c = 0.30 R β€” optimal for R < 2.25. + - Segment B: v = 0.1 + 0.8 R, c = 0.55 R β€” optimal for R > 2.25. + + Candidate points interleave both segments, as the Euler inversion produces + them in non-concave regions. + """ + r_a = np.array([0.6, 1.2, 1.8, 2.4]) + r_b = np.array([0.8, 1.6, 2.6, 3.4]) + grid = np.concatenate([r_a, r_b]) + value = np.concatenate([1.0 + 0.4 * r_a, 0.1 + 0.8 * r_b]) + policy = np.concatenate([0.30 * r_a, 0.55 * r_b]) + return jnp.asarray(grid), jnp.asarray(policy), jnp.asarray(value) + + +R_STAR = 2.25 +V_STAR = 1.0 + 0.4 * R_STAR + + +def test_concave_input_passes_through_unchanged(): + """A monotone-concave single segment is returned as-is (sorted, no edits).""" + grid = jnp.linspace(1.0, 10.0, 10) + policy = 0.3 * grid + value = jnp.log(grid) + + got_grid, got_policy, got_value, n_kept = fues.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=14 + ) + + assert int(n_kept) == 10 + np.testing.assert_allclose(_drop_nan(got_grid), np.asarray(grid), atol=1e-12) + np.testing.assert_allclose(_drop_nan(got_policy), np.asarray(policy), atol=1e-12) + np.testing.assert_allclose(_drop_nan(got_value), np.asarray(value), atol=1e-12) + + +def test_steep_but_continuous_policy_is_not_treated_as_a_switch(): + """`|Ξ”A/Ξ”R|` just below the threshold leaves a single segment untouched.""" + grid = jnp.linspace(1.0, 5.0, 9) + # c = 5 - 0.9 R: implied savings A = R - c = 1.9 R - 5, so |Ξ”A/Ξ”R| = 1.9 < 2. + policy = 5.0 - 0.9 * grid + value = jnp.log(grid) + + _, _, _, n_kept = fues.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + assert int(n_kept) == 9 + + +def test_crossing_segments_yield_the_analytic_upper_envelope(): + """The refined value function equals max(v_A, v_B) under linear interpolation.""" + grid, policy, value = _crossing_segments_candidates() + + got_grid, _, got_value, _ = fues.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + r_query = np.linspace(0.7, 3.3, 53) + expected = np.maximum(1.0 + 0.4 * r_query, 0.1 + 0.8 * r_query) + np.testing.assert_allclose( + _envelope_interp(got_grid, got_value, r_query), expected, atol=_COMPUTED_ATOL + ) + + +def test_crossing_segments_insert_intersection_twice_with_both_policies(): + """The kink abscissa appears twice, carrying the left and right policies.""" + grid, policy, value = _crossing_segments_candidates() + + got_grid, got_policy, _, _ = fues.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + clean_grid = _drop_nan(got_grid) + clean_policy = np.asarray(got_policy)[~np.isnan(np.asarray(got_grid))] + at_kink = np.isclose(clean_grid, R_STAR, atol=_COMPUTED_ATOL) + assert at_kink.sum() == 2 + np.testing.assert_allclose( + np.sort(clean_policy[at_kink]), + np.sort([0.30 * R_STAR, 0.55 * R_STAR]), + atol=_COMPUTED_ATOL, + ) + + +def test_crossing_segments_drop_dominated_points(): + """Candidates strictly below the envelope do not survive refinement.""" + grid, policy, value = _crossing_segments_candidates() + + got_grid, _, _, _ = fues.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + clean_grid = _drop_nan(got_grid) + for dominated in [0.8, 1.6, 2.4]: + assert not np.any(np.isclose(clean_grid, dominated, atol=1e-8)) + + +def test_refined_grid_is_weakly_ascending_with_nan_tail(): + """Non-NaN prefix is weakly ascending; NaNs appear only as a suffix.""" + grid, policy, value = _crossing_segments_candidates() + + got_grid, _, _, _ = fues.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + raw = np.asarray(got_grid) + nan_mask = np.isnan(raw) + first_nan = nan_mask.argmax() if nan_mask.any() else raw.size + assert not nan_mask[:first_nan].any() + assert nan_mask[first_nan:].all() + assert np.all(np.diff(raw[:first_nan]) >= -1e-12) + + +def test_value_decreasing_point_is_dropped(): + """A single interior dominated point (value dip) is removed.""" + grid = jnp.array([1.0, 2.0, 3.0]) + policy = jnp.array([0.5, 1.8, 1.5]) + value = jnp.array([1.0, 0.9, 2.0]) + + got_grid, _, _, _ = fues.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=6 + ) + + clean_grid = _drop_nan(got_grid) + assert not np.any(np.isclose(clean_grid, 2.0, atol=1e-8)) + + +def test_vmap_over_rows_matches_per_row_calls(): + """The kernel is vmappable; batched output equals per-row output.""" + grid, policy, value = _crossing_segments_candidates() + batched = jax.vmap( + lambda g, p, v: fues.refine_envelope( + endog_grid=g, policy=p, value=v, n_refined=12 + ) + )( + jnp.stack([grid, grid]), + jnp.stack([policy, policy]), + jnp.stack([value, value]), + ) + single = fues.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + for batched_arr, single_arr in zip(batched, single, strict=True): + np.testing.assert_array_equal( + np.asarray(batched_arr[0]), np.asarray(single_arr) + ) + + +@pytest.mark.parametrize("scan_unroll", [2, 4, 8]) +def test_scan_unroll_leaves_the_refined_envelope_unchanged(scan_unroll): + """`scan_unroll` is a pure performance knob: the output is bit-identical. + + Unrolling the candidate `lax.scan` only changes how the loop is lowered, not + what it computes, so the refined `(grid, policy, value)` and the kept count + must match the default `scan_unroll=1` run exactly. + """ + grid, policy, value = _crossing_segments_candidates() + baseline = fues.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + unrolled = fues.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + n_refined=12, + scan_unroll=scan_unroll, + ) + for baseline_arr, unrolled_arr in zip(baseline, unrolled, strict=True): + np.testing.assert_array_equal( + np.asarray(unrolled_arr), np.asarray(baseline_arr) + ) + + +def test_overflow_is_reported_via_n_kept(): + """When the envelope needs more slots than `n_refined`, `n_kept` says so.""" + grid, policy, value = _crossing_segments_candidates() + + _, _, _, n_kept = fues.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=4 + ) + + assert int(n_kept) > 4 diff --git a/tests/solution/test_fues_upper_envelope_audit.py b/tests/solution/test_fues_upper_envelope_audit.py new file mode 100644 index 000000000..c41abe803 --- /dev/null +++ b/tests/solution/test_fues_upper_envelope_audit.py @@ -0,0 +1,320 @@ +"""Regression locks for the external FUES correctness audit (findings F1 to F4). + +Each test asserts the corrected behavior directly: the duplicate-abscissae +collapse (audit F1), the `segment_id` switch hook (audit F2), and the +interleaved-segments case (audit F4) β€” where the default scan is exhaustive, so +however many off-segment candidates interleave between two points of one +segment, the scan still reaches the segment's continuation and rejects the +dominated interlopers. A narrower explicit `n_points_to_scan` is an opt-in speed +knob that gives up that guarantee. + +Ground truth is the interpolated envelope *function*: the refined rows exist to +be read by `interp_on_padded_grid` downstream, so correctness is judged there, +not on which raw points survive. +""" + +import jax +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.interp import interp_on_padded_grid +from _lcm.egm.step_core import _publish_V_and_carry_rows +from _lcm.egm.upper_envelope.fues import _intersect_lines, refine_envelope +from tests.conftest import X64_ENABLED + +_ATOL = 1e-8 if X64_ENABLED else 1e-5 + + +def _kept(grid, *arrays): + """Drop the NaN-padded tail, returning the kept prefix of each array.""" + keep = ~np.isnan(np.asarray(grid)) + return (np.asarray(grid)[keep], *(np.asarray(a)[keep] for a in arrays)) + + +# --------------------------------------------------------------------------- +# F3 β€” a strictly dominated point at a shared abscissa must not survive +# --------------------------------------------------------------------------- + + +def test_f3_dominated_duplicate_point_is_not_retained(): + """At a duplicated abscissa, no kept point carries a strictly lower value. + + A genuine envelope kink duplicates an abscissa with *equal* value and two + policies; a dominated duplicate carries a *lower* value and must be dropped + by the pre-scan collapse of equal-abscissa candidates to their max value. + """ + grid, _policy, value, n_kept = refine_envelope( + endog_grid=jnp.array([0.0, 0.0, 1.0]), + policy=jnp.array([0.0, 1.0, 1.0]), + value=jnp.array([0.0, 1.0, 2.0]), + n_refined=10, + ) + g, v = _kept(grid[: int(n_kept)], value[: int(n_kept)]) + for abscissa in np.unique(g): + at = np.isclose(g, abscissa, atol=_ATOL) + if at.sum() > 1: + spread = v[at].max() - v[at].min() + assert spread <= _ATOL, ( + f"duplicated abscissa {abscissa} carries differing values " + f"{sorted(v[at].tolist())} β€” a dominated point survived" + ) + + +def test_f3_interior_duplicate_collapses_to_max_value(): + """An interior duplicate abscissa keeps only its maximal-value candidate. + + The reviewer's counterexample: two candidates at `R=1` with values `0` and + `1` (the lower one listed first). The refined envelope must keep `(1, 1)` + and drop `(1, 0)`, so an interpolated read at `R=1` returns the envelope + value `1`, not the dominated `0` that index-ordered interpolation would + otherwise surface for queries just below the duplicate. + """ + grid, _policy, value, n_kept = refine_envelope( + endog_grid=jnp.array([0.0, 1.0, 1.0, 2.0]), + policy=jnp.array([0.0, 0.5, 0.2, 1.0]), + value=jnp.array([0.0, 0.0, 1.0, 2.0]), + n_refined=10, + ) + g, v = _kept(grid[: int(n_kept)], value[: int(n_kept)]) + at_one = np.isclose(g, 1.0, atol=_ATOL) + assert at_one.sum() == 1, f"R=1 kept {at_one.sum()} times, expected 1" + assert np.isclose(v[at_one][0], 1.0, atol=_ATOL), ( + f"R=1 kept value {v[at_one]} β€” dominated 0.0 not collapsed" + ) + # The interpolated function just below the duplicate must not dip to the + # dominated value. + just_below = interp_on_padded_grid(x_query=jnp.array([0.999]), xp=grid, fp=value) + assert float(just_below[0]) > 0.5, ( + f"interpolated value just below R=1 is {float(just_below[0])} β€” " + "reads toward the dominated duplicate" + ) + + +def test_f3_interpolated_function_is_correct_despite_retained_duplicate(): + """The interpolated value/policy is exact even with the duplicate retained. + + `interp_on_padded_grid` skips the lower-index duplicate (`side="right"`), so + the array-level F3 defect has no effect on the function the EGM step reads. + This invariant is why F3 carries no practical impact; it must not regress. + """ + grid, policy, value, _ = refine_envelope( + endog_grid=jnp.array([0.0, 0.0, 1.0]), + policy=jnp.array([0.0, 1.0, 1.0]), + value=jnp.array([0.0, 1.0, 2.0]), + n_refined=10, + ) + x_query = jnp.array([-0.5, 0.0, 0.25, 0.5, 1.0]) + got_value = interp_on_padded_grid(x_query=x_query, xp=grid, fp=value) + got_policy = interp_on_padded_grid(x_query=x_query, xp=grid, fp=policy) + # Envelope over [0, 1] is the line through (0, 1)-(1, 2); policy is 1. + expected_value = 1.0 + np.clip(np.asarray(x_query), 0.0, None) + np.testing.assert_allclose(np.asarray(got_value), expected_value, atol=_ATOL) + np.testing.assert_allclose(np.asarray(got_policy), 1.0, atol=_ATOL) + + +# --------------------------------------------------------------------------- +# F4 β€” the bounded scan must not accept a run of suboptimal points +# --------------------------------------------------------------------------- + + +def _interleaved_segments(): + """Upper line A(x)=x with two anchors, plus 11 points 0.5 below it. + + The eleven below-envelope points interleave A's `(0.1, 0.1)` and `(12, 12)` + anchors in grid order, so the bounded forward scan cannot see A's + continuation at x=12 within its window. + """ + a_x = [0.0, 0.1, 12.0] + b_x = [float(i) for i in range(1, 12)] + endog_grid = jnp.asarray(a_x + b_x) + policy = jnp.asarray(a_x + [x - 100.0 for x in b_x]) + value = jnp.asarray(a_x + [i - 0.5 for i in range(1, 12)]) + return endog_grid, policy, value + + +def test_f4_interleaved_segments_give_analytic_envelope_at_default_scan(): + """The refined envelope equals the upper line A(x)=x at the default scan. + + The default scan is exhaustive, so it reaches segment A's continuation at + `x=12` however many off-segment candidates interleave before it, and rejects + every dominated point. + """ + endog_grid, policy, value = _interleaved_segments() + grid, _, refined_value, _ = refine_envelope( + endog_grid=endog_grid, policy=policy, value=value, n_refined=64 + ) + x_query = jnp.linspace(0.0, 12.0, 13) + got = interp_on_padded_grid(x_query=x_query, xp=grid, fp=refined_value) + np.testing.assert_allclose(np.asarray(got), np.asarray(x_query), atol=1e-6) + + +def test_f4_bounded_scan_underscans_when_window_too_small(): + """An explicit finite scan narrower than the interleave accepts the interlopers. + + The exhaustive default is the correctness guarantee; the finite window is an + opt-in speed knob. On this fixture β€” 11 off-segment points between segment A's + two anchors β€” a window of 10 cannot reach A's continuation, so it keeps the + dominated points and the interpolated envelope sits a uniform 0.5 below the + true line A(x)=x. This pins the documented tradeoff of the bounded mode. + """ + endog_grid, policy, value = _interleaved_segments() + grid, _, refined_value, _ = refine_envelope( + endog_grid=endog_grid, + policy=policy, + value=value, + n_refined=64, + n_points_to_scan=10, + ) + x_query = jnp.linspace(0.0, 12.0, 13) + got = interp_on_padded_grid(x_query=x_query, xp=grid, fp=refined_value) + max_deviation = float(np.max(np.abs(np.asarray(got) - np.asarray(x_query)))) + np.testing.assert_allclose(max_deviation, 0.5, atol=1e-6) + + +def test_segment_id_label_forces_a_switch_a_flat_policy_notch_misses(): + """A `segment_id` label detects a switch the policy-slope test cannot. + + Two segments with the *same* policy law (`c = 0.5 R`, so no implied-savings + jump anywhere) cross in value. Without labels the scan reads one smooth + segment and drops the lower-value point. With labels it resolves the + crossing β€” inserting the intersection twice as an equal-value kink, the + correct upper envelope at a notch. + """ + endog_grid = jnp.array([1.0, 1.5, 2.0, 2.5]) + policy = 0.5 * endog_grid + value = jnp.array([2.0, 1.8, 2.2, 3.0]) + + g0, _, _, n0 = refine_envelope( + endog_grid=endog_grid, policy=policy, value=value, n_refined=12 + ) + g1, _, v1, n1 = refine_envelope( + endog_grid=endog_grid, + policy=policy, + value=value, + n_refined=12, + segment_id=jnp.array([0.0, 1.0, 0.0, 1.0]), + ) + + # Unlabelled: one smooth segment, no kink inserted. + grid0 = np.asarray(g0[: int(n0)]) + assert len(np.unique(grid0)) == len(grid0), "unlabelled output has a kink" + + # Labelled: a crossing kink β€” exactly one duplicated abscissa, equal values. + grid1, val1 = np.asarray(g1[: int(n1)]), np.asarray(v1[: int(n1)]) + uniq, counts = np.unique(grid1, return_counts=True) + kink = uniq[counts == 2] + assert kink.size == 1, f"labelled output kinks: {grid1.tolist()}" + at_kink = np.isclose(grid1, kink[0], atol=_ATOL) + assert val1[at_kink].max() - val1[at_kink].min() <= _ATOL, ( + "inserted kink must carry equal values" + ) + + +def test_f5_exact_grid_aligned_branch_crossing_gives_v_shaped_envelope(): + """A branch crossing exactly on a grid node yields the true V-shaped envelope. + + Branch A is `V_A(R) = R` (policy 0) and branch B is `V_B(R) = 1 - R` + (policy 10), sampled at `R in {0, 0.5, 1}`. They cross exactly at the existing + node `R = 0.5`, where both have value `0.5` and carry different one-sided + policies. The correct upper envelope is `max(R, 1 - R)` β€” a V with its minimum + `0.5` at `R = 0.5` β€” not the flat `1` an envelope that deletes the crossing + node produces. + """ + endog_grid = jnp.array([0.0, 0.5, 1.0, 0.0, 0.5, 1.0]) + value = jnp.array([0.0, 0.5, 1.0, 1.0, 0.5, 0.0]) + policy = jnp.array([0.0, 0.0, 0.0, 10.0, 10.0, 10.0]) + segment_id = jnp.array([0.0, 0.0, 0.0, 1.0, 1.0, 1.0]) + + grid, _, refined_value, _ = refine_envelope( + endog_grid=endog_grid, + policy=policy, + value=value, + n_refined=16, + segment_id=segment_id, + ) + x_query = jnp.linspace(0.0, 1.0, 5) + got = interp_on_padded_grid(x_query=x_query, xp=grid, fp=refined_value) + expected = np.maximum(np.asarray(x_query), 1.0 - np.asarray(x_query)) + np.testing.assert_allclose(np.asarray(got), expected, atol=1e-6) + + +def test_f4_failure_resolves_when_scan_window_covers_all_candidates(): + """Widening the scan past the interleave count recovers the exact envelope. + + Locks the boundary of F4: the defect is the bounded window, not the + refinement logic. A fix must keep this correct. + """ + endog_grid, policy, value = _interleaved_segments() + n_candidates = endog_grid.shape[0] + grid, _, refined_value, _ = refine_envelope( + endog_grid=endog_grid, + policy=policy, + value=value, + n_refined=64, + n_points_to_scan=n_candidates, + ) + x_query = jnp.linspace(0.0, 12.0, 13) + got = interp_on_padded_grid(x_query=x_query, xp=grid, fp=refined_value) + np.testing.assert_allclose(np.asarray(got), np.asarray(x_query), atol=1e-6) + + +def test_carry_value_row_is_the_unfloored_envelope_while_published_v_is_floored(): + """The carry value row stays the refined envelope; only `V_row` is floored. + + When the closed-form credit-constrained value at an exogenous node exceeds + the refined-envelope read there, the published `V_row` is lifted to that + constrained value (a feasible-policy floor). The carry value row β€” the object + a parent interpolates as its continuation β€” must remain the raw refined + envelope: flooring it would lift finite envelope nodes above the true + envelope and overstate the parent's continuation at low wealth. + """ + n_pad = 5 + refined_grid = jnp.array([1.0, 2.0, 3.0, jnp.nan, jnp.nan]) + refined_policy = jnp.array([1.0, 2.0, 3.0, jnp.nan, jnp.nan]) + # An envelope far below the constrained value at every node, so the floor + # binds on `V_row` at the queried node. + refined_value = jnp.array([-10.0, -10.0, -10.0, jnp.nan, jnp.nan]) + + V_row, value_row, _marginal = _publish_V_and_carry_rows( + refined_grid=refined_grid, + refined_policy=refined_policy, + refined_value=refined_value, + n_kept=jnp.int32(3), + n_pad=n_pad, + publish_resources=jnp.array([2.0]), + borrowing_limit=jnp.asarray(0.0), + utility_of_action=jnp.log, + discounted_expected_value_at_limit=jnp.asarray(0.0), + ) + + # Published V is lifted to the constrained value u(R - limit) = log(2). + np.testing.assert_allclose(np.asarray(V_row), [np.log(2.0)], atol=_ATOL) + # The carry value row is the raw refined envelope, NOT floored: it stays the + # under-floor envelope values, strictly below the published (floored) V. + np.testing.assert_allclose(np.asarray(value_row)[:3], [-10.0, -10.0, -10.0]) + assert float(value_row[1]) < float(V_row[0]) + + +def test_intersect_lines_parallel_branch_keeps_gradients_finite(): + """Reverse-mode gradients stay finite through the parallel-lines dead branch. + + Parallel candidate lines have no intersection, so the returned abscissa is + NaN by contract. The ordinate is evaluated from a finite abscissa, so a + gradient taken through this branch (e.g. an autodiff'd solve) does not get + poisoned by the NaN the forward result intentionally carries. + """ + + zero, one, two, three = (jnp.asarray(v) for v in (0.0, 1.0, 2.0, 3.0)) + + def ordinate(y_a): + # slope_a == slope_b β‡’ parallel β‡’ the dead branch (abscissa is NaN). + _x, y = _intersect_lines( + x_a=zero, y_a=y_a, slope_a=two, x_b=one, y_b=three, slope_b=two + ) + return y + + x, _y = _intersect_lines( + x_a=zero, y_a=one, slope_a=two, x_b=one, y_b=three, slope_b=two + ) + assert bool(jnp.isnan(x)) # the abscissa contract: NaN for parallel lines + assert bool(jnp.isfinite(jax.grad(ordinate)(one))) diff --git a/tests/solution/test_g2egm_hole_fill.py b/tests/solution/test_g2egm_hole_fill.py new file mode 100644 index 000000000..35e03dbea --- /dev/null +++ b/tests/solution/test_g2egm_hole_fill.py @@ -0,0 +1,90 @@ +"""The G2EGM direct-Bellman hole-fill returns the maximizing policy, not just its value. + +Targets the regular `(m, n)` grid that no segment mesh covers are filled by a direct +search over a coarse `(consumption, deposit)` policy grid. The fill must publish the +argmax policy alongside its value, so a hole cell's consumption and pension deposit are +consistent with its filled value β€” not left as the failed envelope's stale policy. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.two_asset_g2egm_step import _direct_bellman_fill + + +def test_direct_bellman_fill_returns_the_argmax_policy_and_value(): + """The fill returns the coarse-grid candidate that maximizes the objective. + + With a concave objective peaked at a target-specific `(c*, d*)`, the best feasible + candidate is the grid point nearest that peak. The fill must return both that + candidate's value and the candidate itself, per target. + """ + consumption_grid = jnp.asarray([1.0, 2.0, 3.0]) + deposit_grid = jnp.asarray([0.0, 1.0, 2.0]) + + # The target carries its own objective peak `(c*, d*)`; the objective is concave in + # the policy around that peak and feasible everywhere. + def objective(target, policy): + peak_c, peak_d = target[0], target[1] + value = -((policy[0] - peak_c) ** 2 + (policy[1] - peak_d) ** 2) + return value, jnp.isfinite(policy[0]) + + targets = jnp.asarray([[2.0, 1.0], [3.0, 0.0]]) + value, policy = _direct_bellman_fill( + targets=targets, + objective=objective, + consumption_grid=consumption_grid, + deposit_grid=deposit_grid, + ) + + # Peak (2, 1) sits exactly on a grid node β†’ value 0 at policy (2, 1); peak (3, 0) + # likewise at (3, 0). + np.testing.assert_allclose(np.asarray(value), [0.0, 0.0], atol=1e-12) + np.testing.assert_allclose(np.asarray(policy), [[2.0, 1.0], [3.0, 0.0]], atol=1e-12) + + +def test_direct_bellman_fill_skips_infeasible_candidates(): + """An infeasible best-by-value candidate is not selected. + + The objective peaks at a grid node that is masked infeasible, so the fill must fall + back to the best *feasible* candidate, returning its value and policy. + """ + consumption_grid = jnp.asarray([1.0, 2.0, 3.0]) + deposit_grid = jnp.asarray([0.0]) + + def objective(target, policy): # noqa: ARG001 + # The value rises toward the top consumption node, but candidates at or above + # 2.5 are masked infeasible, so the best feasible node is the one just below. + value = -((policy[0] - 3.0) ** 2) + feasible = policy[0] < 2.5 + return value, feasible + + targets = jnp.asarray([[0.0, 0.0]]) + value, policy = _direct_bellman_fill( + targets=targets, + objective=objective, + consumption_grid=consumption_grid, + deposit_grid=deposit_grid, + ) + + np.testing.assert_allclose(np.asarray(policy), [[2.0, 0.0]], atol=1e-12) + np.testing.assert_allclose(np.asarray(value), [-1.0], atol=1e-12) + + +def test_direct_bellman_fill_marks_all_infeasible_targets(): + """A target with no feasible candidate keeps a `-inf` filled value.""" + consumption_grid = jnp.asarray([1.0, 2.0]) + deposit_grid = jnp.asarray([0.0]) + + def objective(target, policy): # noqa: ARG001 + return jnp.asarray(0.0), policy[0] < 0.0 + + targets = jnp.asarray([[0.0, 0.0]]) + value, _policy = _direct_bellman_fill( + targets=targets, + objective=objective, + consumption_grid=consumption_grid, + deposit_grid=deposit_grid, + ) + + assert not np.isfinite(np.asarray(value)).any() diff --git a/tests/solution/test_g2egm_multiperiod_parity.py b/tests/solution/test_g2egm_multiperiod_parity.py new file mode 100644 index 000000000..ead7a98be --- /dev/null +++ b/tests/solution/test_g2egm_multiperiod_parity.py @@ -0,0 +1,116 @@ +"""Chaining the four-segment G2EGM step across periods reproduces the brute solve. + +The single-segment (`ucon`-only) step cannot be chained: its constrained-corner +extrapolation poisons the next period's Euler inversion, so a backward loop collapses to +`NaN`. The four-segment upper envelope covers those corners and masks invalid +candidates, so the value it publishes can be fed back as the next period's continuation. +A backward loop `V_dead -> V1 -> V0` then matches the dense grid-search solve across the +pension interior at each period. + +The top pension boundary is an intrinsic grid-extent limit, not an algorithm gap: a +target at the top of the pension grid grows its post-decision pension balance past the +grid maximum, so its optimal continuation is off-grid. The brute solve fills that edge +with a boundary-clamped value while the envelope marks it an uncovered `-inf` hole, and +that hole advances one pension column inward per backward period. The interior β€” every +column the hole has not reached β€” matches; the comparison excludes the boundary layer. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.two_asset_g2egm_step import g2egm_step +from tests.test_models.deterministic.two_asset import get_model, get_params + +_P = { + "discount_factor": 0.95, + "crra": 2.0, + "match_rate": 1.0, + "return_liquid": 0.02, + "return_pension": 0.06, + "wage": 10.0, +} +_M_GRID = jnp.linspace(1.0, 100.0, 12) +_N_GRID = jnp.linspace(0.0, 50.0, 10) +_A_GRID = jnp.linspace(0.0, 85.0, 18) +_B_GRID = jnp.linspace(0.0, 46.0, 16) +_CONSUMPTION_GRID = jnp.linspace(0.5, 90.0, 18) + + +def _g2egm_step(next_value): + return g2egm_step( + next_value=next_value, + m_grid=_M_GRID, + n_grid=_N_GRID, + a_grid=_A_GRID, + b_grid=_B_GRID, + consumption_grid=_CONSUMPTION_GRID, + **_P, + ).value + + +def _solve_chain(): + """Backward-induct the three-period two-asset model with the G2EGM step. + + Returns the chained EGM values `(V1, V0)` and the brute reference + `(brute[1]["working"], brute[0]["working"])`. + """ + model = get_model(n_periods=3) + params = get_params(n_periods=3, pension_bequest_weight=0.5) + brute = model.solve(params=params, log_level="off") + v_dead = jnp.asarray(brute[2]["dead"]) + v1 = _g2egm_step(v_dead) + v0 = _g2egm_step(v1) + return ( + np.asarray(v1), + np.asarray(v0), + np.asarray(brute[1]["working"]), + np.asarray(brute[0]["working"]), + ) + + +# V1 is one backward step from the terminal value, so only its top pension column is an +# uncovered hole; V0 is two steps, so its top two columns are. The interior is what +# remains once the hole has been excluded at each period. +_V1_INTERIOR = np.s_[:, :9] +_V0_INTERIOR = np.s_[:, :8] + + +def test_chained_g2egm_matches_brute_on_the_pension_interior(): + """Both the single and the chained step match brute where the grid covers.""" + v1, v0, b1, b0 = _solve_chain() + + assert np.isfinite(v1[_V1_INTERIOR]).all() + rel1 = np.abs(v1[_V1_INTERIOR] - b1[_V1_INTERIOR]) / np.abs(b1[_V1_INTERIOR]) + assert np.median(rel1) < 0.01 + assert np.percentile(rel1, 95) < 0.10 + + assert np.isfinite(v0[_V0_INTERIOR]).all() + rel0 = np.abs(v0[_V0_INTERIOR] - b0[_V0_INTERIOR]) / np.abs(b0[_V0_INTERIOR]) + assert np.median(rel0) < 0.02 + assert np.percentile(rel0, 95) < 0.15 + + +def test_chained_g2egm_value_is_monotone_in_both_assets_on_the_interior(): + """More liquid and more pension stay weakly valuable through the chained solve.""" + _v1, v0, _b1, _b0 = _solve_chain() + interior = v0[_V0_INTERIOR] + assert np.all(np.diff(interior, axis=0) >= -1e-6) + assert np.all(np.diff(interior, axis=1) >= -1e-6) + + +def test_pension_hole_advances_one_column_inward_per_backward_period(): + """The uncovered top-pension hole grows by exactly one column each period. + + A target whose optimal post-decision pension exceeds the grid is an uncovered hole; + reading that hole as next period's continuation makes the adjacent column uncovered + too, so the boundary layer thickens by one column per backward step. + """ + v1, v0, _b1, _b0 = _solve_chain() + v1_hole = ~np.isfinite(v1) + v0_hole = ~np.isfinite(v0) + # V1: only the top pension column is a hole. + assert v1_hole[:, 9].all() + assert not v1_hole[:, :9].any() + # V0: the top two pension columns are holes; everything interior is finite. + assert v0_hole[:, 8:].all() + assert not v0_hole[:, :8].any() diff --git a/tests/solution/test_g2egm_retiring_step_parity.py b/tests/solution/test_g2egm_retiring_step_parity.py new file mode 100644 index 000000000..f550d8652 --- /dev/null +++ b/tests/solution/test_g2egm_retiring_step_parity.py @@ -0,0 +1,96 @@ +"""The working->retired boundary G2EGM step reproduces the brute solve. + +At the retirement boundary the working agent's 2-D problem reads a 1-D retired +continuation: the pension is paid out as a lump sum, so both post-decision balances +feed a single retired liquid state. Chaining the 1-D retired EGM step into the +boundary G2EGM step and comparing to the DS pension brute solve checks the lump-sum +adapter end to end. The working utility carries an additive work disutility the generic +envelope objective omits, so the driver subtracts it (an additive constant that shifts +the value level without changing the policy). +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.one_asset_egm_step import egm_one_asset_step +from _lcm.egm.two_asset_g2egm_step import g2egm_retiring_step +from tests.test_models.deterministic.ds_pension import get_model, get_params + +_LIQUID_GRID = jnp.linspace(0.1, 20.0, 12) +_PENSION_GRID = jnp.linspace(0.0, 15.0, 10) +_SAVINGS_GRID = jnp.linspace(0.0, 20.0, 40) +_A_GRID = jnp.linspace(0.0, 20.0, 18) +_B_GRID = jnp.linspace(0.0, 30.0, 16) +_CONSUMPTION_GRID = jnp.linspace(0.1, 20.0, 18) + +_DISCOUNT, _CRRA, _MATCH = 0.98, 2.0, 0.10 +_RETURN_LIQUID, _RETURN_PENSION, _RET_INCOME = 0.02, 0.04, 0.50 +_PAYOUT = 1.0 + _RETURN_PENSION +_WORK_DISUTILITY = 0.25 + +# The top pension column is the off-grid uncovered edge (the post-decision pension +# exceeds the grid); the interior is what the parity assertion covers. +_INTERIOR = np.s_[:, :9] + + +def _solve_to_boundary(): + """Brute-solve DS pension, then EGM-chain dead -> retired -> working-retiring. + + Returns the EGM boundary working value and the brute `brute[2]["working"]`. + """ + brute = get_model(n_periods=5, n_consumption=200).solve( + params=get_params(), log_level="off" + ) + v_dead = jnp.asarray(brute[4]["dead"]) + retired = egm_one_asset_step( + next_value=v_dead, + next_marginal=_LIQUID_GRID ** (-_CRRA), + liquid_grid=_LIQUID_GRID, + savings_grid=_SAVINGS_GRID, + discount_factor=_DISCOUNT, + crra=_CRRA, + return_liquid=_RETURN_LIQUID, + income=_RET_INCOME, + ) + v_working_raw = g2egm_retiring_step( + next_value_retired=retired.value, + next_marginal_retired=retired.marginal, + liquid_grid=_LIQUID_GRID, + m_grid=_LIQUID_GRID, + n_grid=_PENSION_GRID, + a_grid=_A_GRID, + b_grid=_B_GRID, + consumption_grid=_CONSUMPTION_GRID, + discount_factor=_DISCOUNT, + crra=_CRRA, + match_rate=_MATCH, + return_liquid=_RETURN_LIQUID, + pension_payout_return=_PAYOUT, + retirement_income=_RET_INCOME, + ) + v_working = np.asarray(v_working_raw.value) - _WORK_DISUTILITY + return v_working, np.asarray(brute[2]["working"]) + + +def test_retiring_boundary_step_matches_brute_on_the_pension_interior(): + """The boundary working value matches the brute solve where the grid covers.""" + v_working, brute_working = _solve_to_boundary() + assert np.isfinite(v_working[_INTERIOR]).all() + rel = np.abs(v_working[_INTERIOR] - brute_working[_INTERIOR]) / np.abs( + brute_working[_INTERIOR] + ) + assert np.median(rel) < 0.02 + assert np.percentile(rel, 90) < 0.10 + + +def test_retiring_boundary_value_is_monotone_in_both_assets_on_the_interior(): + """More liquid and more pension stay weakly valuable at the boundary. + + Liquid monotonicity is exact. Pension monotonicity holds up to a tiny tolerance: at + the maximum liquid the post-payout retired liquid most exceeds the retired grid, so + the continuation is clamped flat there and the envelope leaves sub-0.1% noise β€” the + same under-coverage the brute solve absorbs by clamping (which is why parity holds). + """ + v_working, _brute = _solve_to_boundary() + assert np.all(np.diff(v_working[_INTERIOR], axis=0) >= -1e-6) + assert np.all(np.diff(v_working[_INTERIOR], axis=1) >= -2e-3) diff --git a/tests/solution/test_g2egm_step_parity.py b/tests/solution/test_g2egm_step_parity.py new file mode 100644 index 000000000..2c6f012b3 --- /dev/null +++ b/tests/solution/test_g2egm_step_parity.py @@ -0,0 +1,143 @@ +"""The four-segment G2EGM step reproduces the brute solve, corners included. + +The single-segment (`ucon`-only) step matches the dense grid-search solve only where +the borrowing and deposit constraints are slack; at the constrained corners (low +liquid, low pension) its unconstrained cloud does not cover the target and its +extrapolation is far from the brute value. The four-segment upper envelope adds the +`dcon`, `acon`, and `con` clouds, so those corners are covered by their own segments. +On the region the post-decision grid can reach, the envelope matches the brute solve +and is dramatically better than `ucon`-only at the corners. + +The objective masks any candidate whose reconstructed post-decision balance leaves the +post-decision grid (the continuation reader clamps to the boundary, so an out-of-grid +candidate would otherwise receive a fabricated value), and the direct-Bellman hole-fill +covers common-grid targets no segment reaches. + +Residual: the top pension edge (`n` at the grid maximum) stays an uncovered hole. There +the optimal pension post-decision balance exceeds the grid maximum, so neither a segment +candidate nor the hole-fill has an in-domain continuation β€” a grid-coverage limit, not +an algorithm gap. The test asserts on the covered region and pins the edge as known. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.two_asset_g2egm_step import g2egm_step +from _lcm.egm.two_asset_step import egm_step +from tests.test_models.deterministic.two_asset import get_model, get_params + +_P = { + "discount_factor": 0.95, + "crra": 2.0, + "match_rate": 1.0, + "return_liquid": 0.02, + "return_pension": 0.06, + "wage": 10.0, +} +_M_GRID = jnp.linspace(1.0, 100.0, 12) +_N_GRID = jnp.linspace(0.0, 50.0, 10) +_B_GRID = jnp.linspace(0.0, 46.0, 16) + + +def _solve(): + model = get_model(n_periods=2) + params = get_params(n_periods=2, pension_bequest_weight=0.5) + brute = model.solve(params=params, log_level="off") + next_value = jnp.asarray(brute[1]["dead"]) + g2egm = np.asarray( + g2egm_step( + next_value=next_value, + m_grid=_M_GRID, + n_grid=_N_GRID, + a_grid=jnp.linspace(0.0, 85.0, 18), + b_grid=_B_GRID, + consumption_grid=jnp.linspace(0.5, 90.0, 18), + **_P, + ).value + ) + ucon_only = np.asarray( + egm_step( + next_value=next_value, + m_grid=_M_GRID, + n_grid=_N_GRID, + a_grid=jnp.linspace(1.0, 85.0, 18), + b_grid=_B_GRID, + **_P, + ) + ) + return g2egm, np.asarray(brute[0]["working"]), ucon_only + + +# The top pension column (n at the grid maximum) is the uncovered edge hole. +_COVERED = np.s_[:, :9] +_CORNER = np.s_[:4, :5] + + +def test_g2egm_matches_brute_on_the_covered_region(): + """Where the post-decision grid reaches, the envelope matches the brute solve.""" + g2egm, brute, _ucon = _solve() + assert np.isfinite(g2egm[_COVERED]).all() + rel = np.abs(g2egm[_COVERED] - brute[_COVERED]) / np.abs(brute[_COVERED]) + assert np.median(rel) < 0.01 + assert np.percentile(rel, 95) < 0.10 + + +def test_g2egm_covers_constrained_corners_far_better_than_ucon_only(): + """The envelope covers the low-liquid/low-pension corner; ucon-only does not. + + At the constrained corner the multi-segment envelope is within ~9% of brute, while + the unconstrained-only step is off by tens of percent β€” the `dcon`/`acon`/`con` + segments supply the candidates the unconstrained cloud cannot reach. + """ + g2egm, brute, ucon_only = _solve() + g2egm_rel = np.abs(g2egm[_CORNER] - brute[_CORNER]) / np.abs(brute[_CORNER]) + ucon_rel = np.abs(ucon_only[_CORNER] - brute[_CORNER]) / np.abs(brute[_CORNER]) + assert g2egm_rel.max() < 0.10 + # The unconstrained-only step is an order of magnitude worse at the corner. + assert ucon_rel.max() > 0.5 + assert g2egm_rel.max() < 0.25 * ucon_rel.max() + + +def test_g2egm_value_is_monotone_in_both_assets_on_the_covered_region(): + """More liquid and more pension are weakly valuable on the covered region.""" + g2egm, _brute, _ucon = _solve() + covered = g2egm[_COVERED] + assert np.all(np.diff(covered, axis=0) >= -1e-6) + assert np.all(np.diff(covered, axis=1) >= -1e-6) + + +def test_g2egm_top_pension_edge_is_a_known_uncovered_hole(): + """The top pension column stays uncovered: its optimal post-state leaves the grid. + + Neither a segment candidate nor the direct-Bellman hole-fill has an in-domain + continuation there, so the value is `-inf` β€” a grid-coverage limit, not a gap the + hole-fill can close. + """ + g2egm, _brute, _ucon = _solve() + assert np.all(np.isneginf(g2egm[:, 9])) + + +def test_g2egm_publishes_a_feasible_policy_on_the_covered_region(): + """The published consumption/deposit policy is feasible where the grid covers. + + On the covered region the optimal consumption is positive, the deposit is + non-negative, and the two respect the liquid budget `c + d <= m`. + """ + model = get_model(n_periods=2) + params = get_params(n_periods=2, pension_bequest_weight=0.5) + next_value = jnp.asarray(model.solve(params=params, log_level="off")[1]["dead"]) + result = g2egm_step( + next_value=next_value, + m_grid=_M_GRID, + n_grid=_N_GRID, + a_grid=jnp.linspace(0.0, 85.0, 18), + b_grid=_B_GRID, + consumption_grid=jnp.linspace(0.5, 90.0, 18), + **_P, + ) + consumption = np.asarray(result.consumption)[_COVERED] + deposit = np.asarray(result.deposit)[_COVERED] + liquid = np.asarray(_M_GRID)[:, None] * np.ones_like(consumption) + assert np.all(consumption > 0.0) + assert np.all(deposit >= -1e-9) + assert np.all(consumption + deposit <= liquid + 1e-6) diff --git a/tests/solution/test_housing_oracle.py b/tests/solution/test_housing_oracle.py new file mode 100644 index 000000000..d5f2ee060 --- /dev/null +++ b/tests/solution/test_housing_oracle.py @@ -0,0 +1,61 @@ +"""The DS housing benchmark solves as a faithful adjust/keep brute oracle. + +The model is the dense-grid reference the 2-D EGM / NEGM kernels are validated against, +so its own solve must be correct: the regimes appear in the right periods, the terminal +bequest is the closed-form CRRA value, the working value rises in both assets, and the +comparative statics (a costlier house trade, a richer income) move value the right way. +""" + +import numpy as np + +from tests.conftest import X64_ENABLED +from tests.test_models.deterministic.housing import get_model, get_params + +# The closed-form comparison is float-eps-limited at the active precision. +_RTOL = 1e-12 if X64_ENABLED else 1e-5 + + +def _solve(**param_overrides): + model = get_model() + params = get_params(**param_overrides) + return model.solve(params=params, log_level="off") + + +def test_lifecycle_regimes_appear_in_the_right_periods(): + """The working regime is 2-D (liquid, housing) until the terminal dead period.""" + solution = _solve() + assert np.asarray(solution[0]["working"]).shape == (12, 8) + assert np.asarray(solution[2]["working"]).shape == (12, 8) + assert "working" not in solution[3] + assert np.asarray(solution[3]["dead"]).shape == (12, 8) + + +def test_terminal_bequest_is_the_closed_form_crra_value(): + """The dead regime carries the closed-form CRRA value of liquid plus housing.""" + crra = 1.458 + solution = _solve(crra=crra) + liquid = np.linspace(0.01, 50.0, 12)[:, None] + housing = np.linspace(0.01, 50.0, 8)[None, :] + expected = (liquid + housing) ** (1.0 - crra) / (1.0 - crra) + np.testing.assert_allclose(np.asarray(solution[3]["dead"]), expected, rtol=_RTOL) + + +def test_working_value_increases_in_both_assets(): + """More liquid wealth and a bigger house are both weakly valuable.""" + working = np.asarray(_solve()[0]["working"]) + assert np.all(np.diff(working, axis=0) >= -1e-9) + assert np.all(np.diff(working, axis=1) >= -1e-9) + + +def test_higher_transaction_cost_does_not_raise_working_value(): + """A costlier house trade can only shrink the agent's opportunity set.""" + low = np.asarray(_solve(transaction_cost=0.20)[0]["working"]) + high = np.asarray(_solve(transaction_cost=0.60)[0]["working"]) + assert np.all(high <= low + 1e-9) + + +def test_higher_income_raises_working_value(): + """A richer income strictly raises the working value function.""" + low = np.asarray(_solve(income=1.0)[0]["working"]) + high = np.asarray(_solve(income=2.0)[0]["working"]) + assert np.all(high > low) diff --git a/tests/solution/test_iegm_wiring.py b/tests/solution/test_iegm_wiring.py new file mode 100644 index 000000000..d9f5163e6 --- /dev/null +++ b/tests/solution/test_iegm_wiring.py @@ -0,0 +1,59 @@ +"""A DC-EGM model with no analytic inverse marginal utility solves numerically. + +When a regime supplies no `inverse_marginal_utility`, EGM derives one numerically +from `utility` (the iEGM path) instead of failing. On a CRRA model β€” where the +analytic inverse exists β€” dropping it and forcing the numerical inverter must +reproduce the analytic-inverse value function: the numeric root finder recovers +the same `(u')^{-1}`. +""" + +import numpy as np + +from lcm import AgeGrid, Model +from lcm_examples.iskhakov_et_al_2017 import dead +from tests.test_models.deterministic import retirement_only +from tests.test_models.deterministic.dcegm_variants import ( + dcegm_retirement, + get_retirement_only_model, + get_retirement_only_params, +) + + +def _numeric_retirement_model(n_periods: int) -> Model: + """The DC-EGM retirement model with `inverse_marginal_utility` removed.""" + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + functions_without_inverse = { + name: func + for name, func in dcegm_retirement.functions.items() + if name != "inverse_marginal_utility" + } + numeric_regime = dcegm_retirement.replace( + active=lambda age, la=last_age: age < la, + functions=functions_without_inverse, + ) + return Model( + regimes={"retirement": numeric_regime, "dead": dead}, + ages=ages, + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + + +def test_iegm_numeric_inverse_matches_analytic_value_function(): + """Forcing the numerical inverse reproduces the analytic-inverse value function.""" + n_periods = 3 + params = get_retirement_only_params(n_periods) + analytic = get_retirement_only_model("dcegm", n_periods).solve( + params=params, log_level="off" + ) + numeric = _numeric_retirement_model(n_periods).solve(params=params, log_level="off") + + assert analytic.keys() == numeric.keys() + for period in analytic: + for regime in analytic[period]: + np.testing.assert_allclose( + np.asarray(numeric[period][regime]), + np.asarray(analytic[period][regime]), + rtol=1e-6, + atol=1e-6, + ) diff --git a/tests/solution/test_kernel_memory_logging.py b/tests/solution/test_kernel_memory_logging.py new file mode 100644 index 000000000..0a63b85ff --- /dev/null +++ b/tests/solution/test_kernel_memory_logging.py @@ -0,0 +1,48 @@ +"""`LCM_LOG_KERNEL_MEMORY` compile-time memory dump is decoupled from `log_level`. + +The env var is the sole opt-in for the per-kernel `[mem]` lines. They must surface +at every solve `log_level` β€” including `"off"`, whose whole purpose is to silence the +per-period NaN/Inf diagnostic (its own full-V transient) so the kernel's true peak is +not masked. So the dump emits at a level that always clears the logger's threshold. +""" + +import logging + +from tests.solution.test_egm_discrete import ( + _get_skill_model, + _get_skill_model_params, +) + + +def test_kernel_memory_dump_emits_at_log_level_off(monkeypatch, caplog): + """With the env var on, the `[mem]` lines surface even at `log_level="off"`. + + `log_level="off"` pins the `lcm` logger at `CRITICAL`; capturing at exactly + that level (rather than lowering it) tests the real off-path β€” the dump must + emit a record that clears the `CRITICAL` threshold, so a regression to a + lower level (e.g. `INFO`) would be suppressed and fail this test. + """ + monkeypatch.setenv("LCM_LOG_KERNEL_MEMORY", "1") + model = _get_skill_model() + params = _get_skill_model_params() + + with caplog.at_level(logging.CRITICAL, logger="lcm"): + model.solve(params=params, log_level="off") + + # The decoupling is what's under test: a `[mem]` line surfaces at `off`. Its + # content (the stats trio vs. an "unavailable"/"None" notice) depends on + # whether the backend supports `memory_analysis()`, which is orthogonal. + mem_lines = [r.getMessage() for r in caplog.records if "[mem]" in r.getMessage()] + assert mem_lines, "expected per-kernel [mem] lines with the env var on at log=off" + + +def test_kernel_memory_dump_silent_without_env_var(monkeypatch, caplog): + """Without the env var the dump is a no-op at any level (zero cost).""" + monkeypatch.delenv("LCM_LOG_KERNEL_MEMORY", raising=False) + model = _get_skill_model() + params = _get_skill_model_params() + + with caplog.at_level(logging.NOTSET, logger="lcm"): + model.solve(params=params, log_level="debug") + + assert not [r for r in caplog.records if "[mem]" in r.getMessage()] diff --git a/tests/solution/test_ltm.py b/tests/solution/test_ltm.py new file mode 100644 index 000000000..716a44da9 --- /dev/null +++ b/tests/solution/test_ltm.py @@ -0,0 +1,215 @@ +"""Spec for the LTM upper-envelope kernel (Druedahl's `consav` brute method). + +Contract under test β€” `_lcm.egm.upper_envelope.ltm.refine_envelope`: + + refine_envelope( + *, + endog_grid: Float1D, # candidate resources points (consecutive segments) + policy: Float1D, + value: Float1D, + n_refined: int, # static output length + ) -> tuple[Float1D, Float1D, Float1D, ScalarInt] + +LTM is the local-upper-bound brute method: for each output abscissa it scans +every linear segment connecting two consecutive input candidates, linearly +interpolates the bracketing segments, and keeps the highest value. The cost is +`O(N_query x N_segments) = O(K^2)` by construction. + +Returns NaN-padded arrays of length `n_refined` holding the upper envelope of +the candidate value correspondence (weakly ascending in the grid) plus the +number of kept points. `n_kept > n_refined` signals overflow. + +Assertions are semantic β€” the refined arrays must *represent* the analytic upper +envelope under linear interpolation. + +Skips until the kernel exists. +""" + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from tests.conftest import X64_ENABLED + +ltm = pytest.importorskip( + "_lcm.egm.upper_envelope.ltm", reason="LTM kernel not yet implemented" +) + +# Tolerance for kernel-computed quantities (segment interpolation): float32 +# carries a few ulp through the bracketing arithmetic. +_COMPUTED_ATOL = 1e-8 if X64_ENABLED else 1e-5 + + +def _drop_nan(arr: jnp.ndarray) -> np.ndarray: + out = np.asarray(arr) + return out[~np.isnan(out)] + + +def _envelope_interp(grid, value, x_query): + keep = ~np.isnan(np.asarray(grid)) + return np.interp(x_query, np.asarray(grid)[keep], np.asarray(value)[keep]) + + +def _crossing_segments_candidates(): + """Two linear choice-specific value segments crossing at R* = 2.25. + + - Segment A: v = 1.0 + 0.4 R, c = 0.30 R β€” optimal for R < 2.25. + - Segment B: v = 0.1 + 0.8 R, c = 0.55 R β€” optimal for R > 2.25. + + The candidates arrive in two consecutive runs (one per segment), as the + Euler inversion produces them in non-concave regions: the input order makes + each segment a chain of consecutive candidates. + """ + r_a = np.array([0.6, 1.2, 1.8, 2.4]) + r_b = np.array([0.8, 1.6, 2.6, 3.4]) + grid = np.concatenate([r_a, r_b]) + value = np.concatenate([1.0 + 0.4 * r_a, 0.1 + 0.8 * r_b]) + policy = np.concatenate([0.30 * r_a, 0.55 * r_b]) + return jnp.asarray(grid), jnp.asarray(policy), jnp.asarray(value) + + +R_STAR = 2.25 + + +def test_concave_input_passes_through_unchanged(): + """A monotone-concave single segment is returned as-is (sorted, no edits).""" + grid = jnp.linspace(1.0, 10.0, 10) + policy = 0.3 * grid + value = jnp.log(grid) + + got_grid, got_policy, got_value, n_kept = ltm.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=14 + ) + + assert int(n_kept) == 10 + np.testing.assert_allclose(_drop_nan(got_grid), np.asarray(grid), atol=1e-12) + np.testing.assert_allclose( + _envelope_interp(got_grid, got_value, np.asarray(grid)), + np.asarray(value), + atol=_COMPUTED_ATOL, + ) + np.testing.assert_allclose( + _envelope_interp(got_grid, got_policy, np.asarray(grid)), + np.asarray(policy), + atol=_COMPUTED_ATOL, + ) + + +def test_envelope_value_at_each_candidate_node_is_the_segment_maximum(): + """At every output abscissa the value is the max over bracketing segments. + + The brute scan evaluates each candidate abscissa against every consecutive + segment, so the refined value at a node is the highest interpolant among the + segments bracketing it β€” exactly `max(v_A, v_B)` at the node, with no kink + insertion. (Between nodes the linear read traces one segment, so the exact + crossing is recovered only to within the node spacing.) + """ + grid, policy, value = _crossing_segments_candidates() + + got_grid, _, got_value, _ = ltm.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + clean_grid = _drop_nan(got_grid) + clean_value = np.asarray(got_value)[~np.isnan(np.asarray(got_grid))] + expected = np.maximum(1.0 + 0.4 * clean_grid, 0.1 + 0.8 * clean_grid) + np.testing.assert_allclose(clean_value, expected, atol=_COMPUTED_ATOL) + + +def test_envelope_policy_follows_the_winning_segment_at_a_node(): + """The refined policy at a node is the winning segment's interpolated policy. + + At a node well below the crossing segment A dominates, so the published + policy is A's `c = 0.30 R`; at a node well above, B dominates with + `c = 0.55 R`. The policy is read at the node abscissa so the kink-placement + error between nodes does not enter. + """ + grid, policy, value = _crossing_segments_candidates() + + got_grid, got_policy, _, _ = ltm.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + clean_grid = _drop_nan(got_grid) + clean_policy = np.asarray(got_policy)[~np.isnan(np.asarray(got_grid))] + + # A node where A wins: m = 1.2 (v_A = 1.48 > v_B = 1.06). + idx_low = int(np.argmin(np.abs(clean_grid - 1.2))) + np.testing.assert_allclose(clean_policy[idx_low], 0.30 * 1.2, atol=_COMPUTED_ATOL) + # A node where B wins: m = 2.6 (v_B = 2.18 > v_A = 2.04). + idx_high = int(np.argmin(np.abs(clean_grid - 2.6))) + np.testing.assert_allclose(clean_policy[idx_high], 0.55 * 2.6, atol=_COMPUTED_ATOL) + + +def test_refined_grid_is_weakly_ascending_with_nan_tail(): + """Non-NaN prefix is weakly ascending; NaNs appear only as a suffix.""" + grid, policy, value = _crossing_segments_candidates() + + got_grid, _, _, _ = ltm.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + raw = np.asarray(got_grid) + nan_mask = np.isnan(raw) + first_nan = nan_mask.argmax() if nan_mask.any() else raw.size + assert not nan_mask[:first_nan].any() + assert nan_mask[first_nan:].all() + assert np.all(np.diff(raw[:first_nan]) >= -1e-12) + + +def test_overlapping_segment_dominates_a_bracketed_lower_node(): + """A later segment looping back over a node lifts that node to the envelope. + + The non-concavity an EGM cloud carries is a *backward jump* in the + endogenous grid: a later segment re-covers an earlier abscissa at a higher + value. The candidates `m = [1, 3, 2, 4]` chain two segments β€” `(1->3)` then + `(2->4)` after the jump back to 2 β€” so the abscissa `m = 2` is bracketed + both by the low first segment (value 1.5 at `m=2`) and by the high second + segment (value 5.0 at `m=2`). LTM keeps the higher one. + """ + grid = jnp.array([1.0, 3.0, 2.0, 4.0]) + policy = jnp.array([0.5, 1.5, 1.0, 2.0]) + value = jnp.array([1.0, 2.0, 5.0, 7.0]) + + got_grid, _, got_value, _ = ltm.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=8 + ) + + clean_grid = _drop_nan(got_grid) + clean_value = np.asarray(got_value)[~np.isnan(np.asarray(got_grid))] + at_two = int(np.argmin(np.abs(clean_grid - 2.0))) + np.testing.assert_allclose(clean_value[at_two], 5.0, atol=_COMPUTED_ATOL) + + +def test_vmap_over_rows_matches_per_row_calls(): + """The kernel is vmappable; batched output equals per-row output.""" + grid, policy, value = _crossing_segments_candidates() + batched = jax.vmap( + lambda g, p, v: ltm.refine_envelope( + endog_grid=g, policy=p, value=v, n_refined=12 + ) + )( + jnp.stack([grid, grid]), + jnp.stack([policy, policy]), + jnp.stack([value, value]), + ) + single = ltm.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + for batched_arr, single_arr in zip(batched, single, strict=True): + np.testing.assert_array_equal( + np.asarray(batched_arr[0]), np.asarray(single_arr) + ) + + +def test_overflow_is_reported_via_n_kept(): + """When the envelope needs more slots than `n_refined`, `n_kept` says so.""" + grid, policy, value = _crossing_segments_candidates() + + _, _, _, n_kept = ltm.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=4 + ) + + assert int(n_kept) > 4 diff --git a/tests/solution/test_ltm_fues_parity.py b/tests/solution/test_ltm_fues_parity.py new file mode 100644 index 000000000..3f724bfa4 --- /dev/null +++ b/tests/solution/test_ltm_fues_parity.py @@ -0,0 +1,195 @@ +"""Acceptance: the LTM backend reproduces FUES on the DC-EGM battery. + +The brute local-upper-bound backend (`upper_envelope="ltm"`) must produce the +same value function as the Fast Upper-Envelope Scan (`upper_envelope="fues"`) on +the existing DC-EGM solve tests, within a documented tolerance. + +Both backends compute the upper envelope of the same EGM candidate cloud; they +differ only in algorithm and cost (LTM is `O(K^2)`, FUES is a single scan), not +in the refined value they represent. FUES inserts the exact segment-crossing +abscissa; LTM evaluates the envelope at the candidate abscissae, so a kink lands +between two LTM output nodes and the downstream linear/Hermite read recovers it +to within the local grid spacing β€” a second-order error. On a concave segment +(no crossing) the two backends agree to machine precision; the tolerance only +absorbs the kink-placement delta where a discrete choice switches. The +brute-force-unstable low-wealth nodes are excluded exactly as the underlying +FUES tests do. +""" + +import dataclasses + +import jax.numpy as jnp +import numpy as np +import pytest + +from lcm import AgeGrid, MarkovTransition, Model +from lcm.typing import BoolND, DiscreteAction +from lcm_examples.iskhakov_et_al_2017 import dead +from tests.test_models.deterministic import base, retirement_only +from tests.test_models.deterministic.dcegm_variants import ( + dcegm_retirement, + dcegm_retirement_full, + dcegm_working_life, + get_full_params, + get_retirement_only_params, +) + +# The no-exact-crossing delta is a kink-placement error of order the local grid +# spacing, propagated through the exact-slope Hermite carry. On the cubically +# clustered savings grid the retirement battery uses, that bounds the per-node V +# difference between the backends well inside this tolerance. +_PARITY_ATOL = 5e-3 +_PARITY_RTOL = 1e-3 + + +def _with_backend(regime, *, upper_envelope): + """Rebuild a DC-EGM regime with the chosen upper-envelope backend.""" + solver = dataclasses.replace(regime.solver, upper_envelope=upper_envelope) + return regime.replace(solver=solver) + + +def _retirement_only_model(*, upper_envelope, n_periods): + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "retirement": _with_backend( + dcegm_retirement, upper_envelope=upper_envelope + ).replace(active=lambda age, la=last_age: age < la), + "dead": dead, + }, + ages=ages, + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + + +def _full_model(*, upper_envelope, n_periods): + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "working_life": _with_backend( + dcegm_working_life, upper_envelope=upper_envelope + ).replace(active=lambda age, la=last_age: age < la), + "retirement": _with_backend( + dcegm_retirement_full, upper_envelope=upper_envelope + ).replace(active=lambda age, la=last_age: age < la), + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + + +@pytest.mark.parametrize("n_periods", [3, 5]) +def test_ltm_matches_fues_on_concave_retirement(n_periods): + """The pure-concave retirement solve agrees between LTM and FUES. + + No discrete choice means no segment crossing, so the two backends refine + the same candidate set identically β€” agreement holds tightly on every + wealth node. + """ + params = get_retirement_only_params(n_periods) + + fues = _retirement_only_model(upper_envelope="fues", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + ltm = _retirement_only_model(upper_envelope="ltm", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + + for period in sorted(fues)[:-1]: + np.testing.assert_allclose( + np.asarray(ltm[period]["retirement"]), + np.asarray(fues[period]["retirement"]), + atol=_PARITY_ATOL, + rtol=_PARITY_RTOL, + err_msg=f"period={period}", + ) + + +def _nothing_is_feasible(labor_supply: DiscreteAction) -> BoolND: + return jnp.zeros_like(labor_supply, dtype=bool) + + +def test_ltm_publishes_neg_inf_for_all_infeasible_combo_like_fues(): + """An all-infeasible worker regime publishes `-inf` V under LTM too. + + A discrete-only constraint false everywhere makes the worker's value `-inf` + at every state; the dead candidates must stay deleted from the envelope + scan (`-inf`/NaN poisoning discipline), so LTM publishes `-inf` exactly as + FUES does, never NaN. + """ + n_periods = 4 + retirement_transition = { + "retirement": MarkovTransition( + lambda age, final_age_alive: jnp.where(age >= final_age_alive, 0.0, 1.0) + ), + "dead": MarkovTransition( + lambda age, final_age_alive: jnp.where(age >= final_age_alive, 1.0, 0.0) + ), + } + + def build(upper_envelope): + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + return Model( + regimes={ + "working_life": _with_backend( + dcegm_working_life, upper_envelope=upper_envelope + ).replace( + constraints={"nothing_is_feasible": _nothing_is_feasible}, + active=lambda age: age < 70, + ), + "retirement": _with_backend( + dcegm_retirement_full, upper_envelope=upper_envelope + ).replace( + transition=retirement_transition, + state_transitions={ + "wealth": dcegm_retirement_full.state_transitions["wealth"], + }, + active=lambda age: age < 70, + ), + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + + params = get_full_params(n_periods, discount_factor=0.98, wage=20.0) + ltm = build("ltm").solve(params=params, log_level="debug") + + for period in sorted(ltm)[:-1]: + working_V = np.asarray(ltm[period]["working_life"]) + assert bool(np.isneginf(working_V).all()), f"period={period}" + assert bool(np.isfinite(ltm[period]["retirement"]).all()) + + +@pytest.mark.parametrize("n_periods", [4]) +def test_ltm_matches_fues_on_discrete_choice_working_life(n_periods): + """The work/retire discrete-choice solve agrees between LTM and FUES. + + The labour-supply choice creates a non-concave kink in the worker's value + correspondence. FUES inserts the exact crossing; LTM evaluates the envelope + at the candidate abscissae and lets the downstream read recover the kink. + The published value functions agree within the no-insertion tolerance on the + wealth nodes where both are well-defined. + """ + params = get_full_params(n_periods, discount_factor=0.98, wage=20.0) + + fues = _full_model(upper_envelope="fues", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + ltm = _full_model(upper_envelope="ltm", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + + n_unstable_low_nodes = 10 + for period in sorted(fues)[:-1]: + for regime in ["working_life", "retirement"]: + np.testing.assert_allclose( + np.asarray(ltm[period][regime])[..., n_unstable_low_nodes:], + np.asarray(fues[period][regime])[..., n_unstable_low_nodes:], + atol=_PARITY_ATOL, + rtol=_PARITY_RTOL, + err_msg=f"period={period}, regime={regime}", + ) diff --git a/tests/solution/test_ltm_mss_topology.py b/tests/solution/test_ltm_mss_topology.py new file mode 100644 index 000000000..cde063049 --- /dev/null +++ b/tests/solution/test_ltm_mss_topology.py @@ -0,0 +1,63 @@ +"""LTM and MSS must not bridge unrelated branches into a spurious envelope. + +Both backends infer segment topology from the candidate ordering: LTM treats +every consecutive input pair as one envelope segment, and MSS starts a new +segment only where the grid or value decreases. Neither holds when a +discrete-choice switch raises both the endogenous resource and the value β€” the +two unrelated branch endpoints are then linked into a segment that never +existed, and the envelope is read off that phantom bridge. The exact envelope +(the host oracle, which consumes explicit branch labels) is the reference. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.egm.interp import interp_on_padded_grid +from _lcm.egm.upper_envelope import ltm, mss +from tests.solution._envelope_oracle import exact_envelope + +# Three branches fed in the order A, B, C: +# - A: x in {0, 1}, V = {0, 1}, policy 0; +# - B: x in {2, 3}, V = {4, 5}, policy 10; +# - C: x in {1.5, 1.75}, V = {0.5, 0.5}, policy 5. +# At x = 1.5 only branch C is defined, with value 0.5. A topology that bridges +# A's endpoint (1, 1) to B's endpoint (2, 4) instead reports the phantom 2.5. +_ENDOG = jnp.array([0.0, 1.0, 2.0, 3.0, 1.5, 1.75]) +_VALUE = jnp.array([0.0, 1.0, 4.0, 5.0, 0.5, 0.5]) +_POLICY = jnp.array([0.0, 0.0, 10.0, 10.0, 5.0, 5.0]) +_SEGMENT = jnp.array([0.0, 0.0, 1.0, 1.0, 2.0, 2.0]) + + +def _published_value_at(backend, x_query): + grid, _policy, value, _n = backend.refine_envelope( + endog_grid=_ENDOG, + policy=_POLICY, + value=_VALUE, + n_refined=24, + segment_id=_SEGMENT, + ) + return float( + interp_on_padded_grid(x_query=jnp.array([x_query]), xp=grid, fp=value)[0] + ) + + +@pytest.mark.parametrize("backend", [ltm, mss]) +def test_backend_matches_oracle_on_a_non_bridging_branch(backend): + """Given explicit topology the backend reports branch C, not the A-to-B bridge. + + The exact envelope at x=1.5 is branch C's 0.5. Inferring topology from the + candidate ordering instead bridges A's endpoint to B's and reports 2.5; + consuming the explicit `segment_id` labels keeps the branches separate. + """ + oracle_value, _policy, _winner = exact_envelope( + endog_grid=np.asarray(_ENDOG), + value=np.asarray(_VALUE), + policy=np.asarray(_POLICY), + segment_id=np.asarray(_SEGMENT), + x_query=np.array([1.5]), + ) + np.testing.assert_allclose(oracle_value, [0.5], atol=1e-12) + + published = _published_value_at(backend, 1.5) + np.testing.assert_allclose(published, 0.5, atol=1e-9) diff --git a/tests/solution/test_mesh_envelope.py b/tests/solution/test_mesh_envelope.py new file mode 100644 index 000000000..81663f0a1 --- /dev/null +++ b/tests/solution/test_mesh_envelope.py @@ -0,0 +1,158 @@ +"""The 2-D G2EGM upper envelope selects the correct feasible candidate. + +The envelope must maximize the recomputed objective over every admissible triangle β€” +covering and mildly extrapolated alike β€” and drop infeasible interpolated policies +before the maximum. The tests pin the two selection behaviors an adversarial audit +flagged: an extrapolated-but-admissible triangle holding the true maximizer must beat a +covering triangle with a lower value (a cover-first rule would miss it), and an +infeasible interpolated policy must never win. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.mesh_envelope import ( + SegmentMesh, + first_envelope, + second_envelope, +) + + +def _value_is_policy(_state, policy): + """Objective equal to the (scalar) interpolated policy; always feasible.""" + return policy[0], jnp.ones((), dtype=bool) + + +def _always_infeasible(_state, policy): + return policy[0], jnp.zeros((), dtype=bool) + + +def test_first_envelope_prefers_admissible_extrapolated_over_covering(): + """An extrapolated-but-admissible triangle with the higher value wins. + + Triangle B has the target `(1.2, 1.2)` outside but admissible (weights + `(-0.2, 0.6, 0.6)`) with interpolated value 1.0; triangle A covers the target with + value 0.0. The within-segment envelope must return 1.0 β€” a cover-first rule that + only consults A would return 0.0. + """ + mesh = SegmentMesh( + region_label=0, + node_state=jnp.array( + [ + [0.0, 0.0], + [2.0, 0.0], + [0.0, 2.0], # triangle B: (1.2,1.2) extrapolated, admissible + [0.0, 0.0], + [3.0, 0.0], + [0.0, 3.0], # triangle A: (1.2,1.2) covered + ] + ), + node_policy=jnp.array([[1.0], [1.0], [1.0], [0.0], [0.0], [0.0]]), + simplices=jnp.array([[0, 1, 2], [3, 4, 5]], dtype=jnp.int32), + valid_node=jnp.ones(6, dtype=bool), + ) + values, policies = first_envelope( + mesh=mesh, + targets=jnp.array([[1.2, 1.2]]), + objective=_value_is_policy, + threshold=0.25, + ) + np.testing.assert_allclose(np.asarray(values), [1.0], atol=1e-9) + np.testing.assert_allclose(np.asarray(policies), [[1.0]], atol=1e-9) + + +def test_first_envelope_masks_infeasible_candidates(): + """An infeasible interpolated policy is masked to negative infinity.""" + mesh = SegmentMesh( + region_label=0, + node_state=jnp.array([[0.0, 0.0], [3.0, 0.0], [0.0, 3.0]]), + node_policy=jnp.array([[1.0], [1.0], [1.0]]), + simplices=jnp.array([[0, 1, 2]], dtype=jnp.int32), + valid_node=jnp.ones(3, dtype=bool), + ) + values, _policies = first_envelope( + mesh=mesh, + targets=jnp.array([[1.0, 1.0]]), + objective=_always_infeasible, + threshold=0.25, + ) + assert np.isneginf(np.asarray(values)[0]) + + +def test_first_envelope_no_admissible_triangle_returns_neg_inf(): + """A target outside every admissible triangle gets no candidate.""" + mesh = SegmentMesh( + region_label=0, + node_state=jnp.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]]), + node_policy=jnp.array([[1.0], [1.0], [1.0]]), + simplices=jnp.array([[0, 1, 2]], dtype=jnp.int32), + valid_node=jnp.ones(3, dtype=bool), + ) + values, _policies = first_envelope( + mesh=mesh, + targets=jnp.array([[5.0, 5.0]]), # far outside the unit triangle + objective=_value_is_policy, + threshold=0.25, + ) + assert np.isneginf(np.asarray(values)[0]) + + +def test_first_envelope_drops_triangles_touching_invalid_nodes(): + """A triangle with an invalid node is not a candidate even when it covers.""" + mesh = SegmentMesh( + region_label=0, + node_state=jnp.array([[0.0, 0.0], [3.0, 0.0], [0.0, 3.0]]), + node_policy=jnp.array([[1.0], [1.0], [1.0]]), + simplices=jnp.array([[0, 1, 2]], dtype=jnp.int32), + valid_node=jnp.array([True, True, False]), + ) + values, _policies = first_envelope( + mesh=mesh, + targets=jnp.array([[1.0, 1.0]]), + objective=_value_is_policy, + threshold=0.25, + ) + assert np.isneginf(np.asarray(values)[0]) + + +def test_second_envelope_takes_max_segment_and_gathers_policy(): + """The across-segment envelope picks the higher value and its segment's policy.""" + segment_values = jnp.array([[0.3, 0.9], [0.7, 0.2]]) # (n_segment=2, n_target=2) + segment_policies = jnp.array( + [ + [[10.0], [11.0]], # segment 0 policies per target + [[20.0], [21.0]], # segment 1 policies per target + ] + ) + result = second_envelope( + segment_values=segment_values, + segment_policies=segment_policies, + region_labels=jnp.array([2, 3], dtype=jnp.int32), + ) + np.testing.assert_allclose(np.asarray(result.value), [0.7, 0.9], atol=1e-9) + np.testing.assert_array_equal(np.asarray(result.segment), [1, 0]) + np.testing.assert_allclose(np.asarray(result.policy), [[20.0], [11.0]], atol=1e-9) + + +def test_second_envelope_reports_winning_region_label(): + """The result carries each winner's KKT region label, not its stack index. + + With segments stacked in the order `(acon=2, con=3)`, target 0's winner is the + second-stacked segment, so its region label is 3 β€” distinct from the stack index 1. + """ + result = second_envelope( + segment_values=jnp.array([[0.3, 0.9], [0.7, 0.2]]), + segment_policies=jnp.array([[[10.0], [11.0]], [[20.0], [21.0]]]), + region_labels=jnp.array([2, 3], dtype=jnp.int32), + ) + np.testing.assert_array_equal(np.asarray(result.region_label), [3, 2]) + + +def test_second_envelope_flags_targets_with_no_candidate(): + """A target where every segment is `-inf` is flagged as having no candidate.""" + result = second_envelope( + segment_values=jnp.array([[-jnp.inf, 0.5], [-jnp.inf, 0.2]]), + segment_policies=jnp.array([[[10.0], [11.0]], [[20.0], [21.0]]]), + region_labels=jnp.array([0, 1], dtype=jnp.int32), + ) + np.testing.assert_array_equal(np.asarray(result.has_candidate), [False, True]) diff --git a/tests/solution/test_mesh_geometry.py b/tests/solution/test_mesh_geometry.py new file mode 100644 index 000000000..de400bcba --- /dev/null +++ b/tests/solution/test_mesh_geometry.py @@ -0,0 +1,138 @@ +"""Triangular-mesh barycentric geometry for the 2-D G2EGM envelope is correct. + +The geometry is the foundation of the upper-envelope selection: each source cell +splits into two triangles, a target is located by its barycentric weights, and a +triangle is an admissible candidate when every weight exceeds a negative threshold. +The tests pin the basic invariants and the two counterexamples an adversarial audit +used to reject a quadrilateral, cover-first design: a folded cell whose triangles stay +non-degenerate, and an extrapolated target that is admissible under the reference +threshold. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.egm.mesh_geometry import ( + barycentric_weights, + interpolate_on_triangle, + is_admissible, + triangulate_regular_grid, +) +from tests.conftest import X64_ENABLED + +# Barycentric weights come out of a solved 2x2 linear system, so their accuracy +# is a small multiple of the float eps of the active precision. +_ATOL = 1e-12 if X64_ENABLED else 1e-5 + + +def test_triangulate_one_cell_splits_into_two_triangles(): + """A 2x2 grid's single cell becomes two triangles on the shared diagonal.""" + simplices = np.asarray(triangulate_regular_grid(n_rows=2, n_cols=2)) + np.testing.assert_array_equal(simplices, np.array([[0, 2, 1], [2, 3, 1]])) + + +def test_triangulate_cell_count(): + """An `n_rows` by `n_cols` grid yields `2*(n_rows-1)*(n_cols-1)` triangles.""" + simplices = triangulate_regular_grid(n_rows=4, n_cols=5) + assert simplices.shape == (2 * 3 * 4, 3) + + +def test_triangulate_rejects_grids_too_small_to_have_a_cell(): + """A grid with fewer than two rows or columns has no cell and is rejected. + + Returning an empty simplex array would silently drop the whole segment; the + triangulation fails loudly instead. + """ + for n_rows, n_cols in [(1, 5), (5, 1), (1, 1)]: + with pytest.raises(ValueError, match="at least 2"): + triangulate_regular_grid(n_rows=n_rows, n_cols=n_cols) + + +def test_barycentric_weights_at_vertex_are_one_hot(): + """The barycentric weights at a triangle vertex select that vertex.""" + triangle = jnp.array([[0.0, 0.0], [2.0, 0.0], [0.0, 2.0]]) + weights = barycentric_weights(triangle=triangle, query=triangle[1]) + np.testing.assert_allclose(np.asarray(weights), [0.0, 1.0, 0.0], atol=_ATOL) + + +def test_barycentric_weights_at_centroid_are_uniform(): + """The barycentric weights at the centroid are all one third.""" + triangle = jnp.array([[0.0, 0.0], [3.0, 0.0], [0.0, 3.0]]) + centroid = jnp.mean(triangle, axis=0) + weights = barycentric_weights(triangle=triangle, query=centroid) + np.testing.assert_allclose(np.asarray(weights), [1 / 3, 1 / 3, 1 / 3], atol=_ATOL) + + +def test_folded_quad_triangles_stay_non_degenerate(): + """The audit's folding quad splits into two non-degenerate triangles. + + Mapping a unit cell to corners with a sign-changing bilinear Jacobian makes the + quad's inverse non-unique, but the diagonal split `(p00,p10,p01)`, `(p10,p11,p01)` + yields two triangles with non-zero signed area, each separately evaluable. + """ + p00, p10, p11, p01 = ( + jnp.array([0.0, 0.0]), + jnp.array([1.0, 0.0]), + jnp.array([0.4, 0.4]), + jnp.array([0.0, 1.0]), + ) + + def signed_area(a, b, c): + return 0.5 * float( + (b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0]) + ) + + assert abs(signed_area(p00, p10, p01)) > 1e-6 + assert abs(signed_area(p10, p11, p01)) > 1e-6 + + +def test_extrapolated_target_is_admissible_under_reference_threshold(): + """A target just outside a triangle is an admissible candidate (weights > -0.25). + + For the triangle `(0,0),(2,0),(0,2)` the target `(1.2, 1.2)` has weights + `(-0.2, 0.6, 0.6)`; it is admissible at the reference threshold 0.25 but not at a + stricter 0.1 β€” so a cover-first rule that drops it can miss the winning branch. + """ + triangle = jnp.array([[0.0, 0.0], [2.0, 0.0], [0.0, 2.0]]) + weights = barycentric_weights(triangle=triangle, query=jnp.array([1.2, 1.2])) + np.testing.assert_allclose(np.asarray(weights), [-0.2, 0.6, 0.6], atol=_ATOL) + assert bool(is_admissible(weights=weights, threshold=0.25)) + assert not bool(is_admissible(weights=weights, threshold=0.1)) + + +def test_weight_exactly_at_negative_threshold_is_admissible(): + """A weight exactly at `-threshold` is admissible (reference rejects only below it). + + For the triangle `(0,0),(1,0),(0,1)` the target `(0.625, 0.625)` has weights + `(-0.25, 0.625, 0.625)`; at the reference threshold 0.25 the boundary weight `-0.25` + must keep the triangle admissible, so a competing simplex cannot win by a hair. + """ + triangle = jnp.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]]) + weights = barycentric_weights(triangle=triangle, query=jnp.array([0.625, 0.625])) + np.testing.assert_allclose(np.asarray(weights), [-0.25, 0.625, 0.625], atol=_ATOL) + assert bool(is_admissible(weights=weights, threshold=0.25)) + + +def test_degenerate_triangle_is_inadmissible(): + """A collinear-image triangle yields non-finite weights and is inadmissible. + + The mapped triangle `(0,0),(1,0),(2,0)` is degenerate (zero area), so its weights + are non-finite; admissibility must reject it rather than let a NaN weight slip + through as a candidate. + """ + triangle = jnp.array([[0.0, 0.0], [1.0, 0.0], [2.0, 0.0]]) + weights = barycentric_weights(triangle=triangle, query=jnp.array([1.0, 0.0])) + assert not np.all(np.isfinite(np.asarray(weights))) + assert not bool(is_admissible(weights=weights, threshold=0.25)) + + +def test_interpolate_reproduces_affine_field(): + """Barycentric interpolation reproduces an affine field exactly at any query.""" + triangle = jnp.array([[0.0, 0.0], [2.0, 0.0], [0.0, 2.0]]) + # Affine field f(x, y) = (1 + 2x + 3y, 5 - x): exact under barycentric weights. + node_values = jnp.array([[1.0, 5.0], [5.0, 3.0], [7.0, 5.0]]) + query = jnp.array([0.5, 0.5]) + weights = barycentric_weights(triangle=triangle, query=query) + interpolated = interpolate_on_triangle(node_values=node_values, weights=weights) + np.testing.assert_allclose(np.asarray(interpolated), [3.5, 4.5], atol=_ATOL) diff --git a/tests/solution/test_mesh_gradient.py b/tests/solution/test_mesh_gradient.py new file mode 100644 index 000000000..6e3bee12a --- /dev/null +++ b/tests/solution/test_mesh_gradient.py @@ -0,0 +1,92 @@ +"""The region-aware envelope gradient and switch mask are correct. + +The published marginal value of liquid wealth is `u'(c) = c**(-crra)` in every region β€” +matching the region inverses' `value_grad_m` β€” and the pension marginal is +`discount_factor * W_b`. The switch mask flags exactly the targets at a cross-segment +boundary, where the envelope is non-differentiable. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.mesh_gradient import region_aware_gradient, switch_mask +from _lcm.egm.two_asset_inverse import invert_acon_cloud + +_DISCOUNT = 0.95 +_CRRA = 2.0 +_MATCH = 1.0 + + +def test_value_grad_m_is_marginal_utility(): + """`V_m = u'(c) = c**(-crra)`, the region-independent envelope marginal.""" + consumption = jnp.array([0.5, 1.0, 2.0]) + gradient = region_aware_gradient( + consumption=consumption, + post_decision_grad_b=jnp.array([1.0, 1.0, 1.0]), + discount_factor=_DISCOUNT, + crra=_CRRA, + ) + np.testing.assert_allclose( + np.asarray(gradient.value_grad_m), np.asarray(consumption ** (-_CRRA)) + ) + + +def test_value_grad_n_is_discounted_post_decision_gradient(): + """`V_n = discount_factor * W_b`.""" + grad_b = jnp.array([0.2, 0.4, 0.6]) + gradient = region_aware_gradient( + consumption=jnp.array([1.0, 1.0, 1.0]), + post_decision_grad_b=grad_b, + discount_factor=_DISCOUNT, + crra=_CRRA, + ) + np.testing.assert_allclose( + np.asarray(gradient.value_grad_n), np.asarray(_DISCOUNT * grad_b) + ) + + +def test_value_grad_m_matches_the_constrained_region_inverse(): + """`V_m = u'(c)` reproduces `invert_acon_cloud.value_grad_m` (not beta*w_a). + + The borrowing-constrained inverse already publishes `consumption**(-crra)` for the + liquid marginal; the envelope gradient uses the same rule, so they agree. + """ + consumption = jnp.array([[0.5, 0.8], [1.2, 1.5]]) + b = jnp.array([[1.0, 2.0], [3.0, 4.0]]) + w_b = consumption ** (-_CRRA) / (_DISCOUNT * 1.6) + cloud = invert_acon_cloud( + consumption=consumption, + b=b, + post_decision_value_at_zero_a=jnp.zeros((2, 2)), + w_b_at_zero_a=w_b, + w_a_at_zero_a=consumption ** (-_CRRA) / _DISCOUNT, + discount_factor=_DISCOUNT, + crra=_CRRA, + match_rate=_MATCH, + ) + gradient = region_aware_gradient( + consumption=cloud.consumption, + post_decision_grad_b=w_b, + discount_factor=_DISCOUNT, + crra=_CRRA, + ) + np.testing.assert_allclose( + np.asarray(gradient.value_grad_m), np.asarray(cloud.value_grad_m), rtol=1e-12 + ) + + +def test_switch_mask_flags_the_segment_boundary(): + """A vertical segment boundary flags the two columns straddling it, not the rest.""" + # Winning segment 0 in columns 0-1, segment 1 in column 2, on a 3x3 grid. + segment = jnp.array([0, 0, 1, 0, 0, 1, 0, 0, 1], dtype=jnp.int32) + mask = np.asarray(switch_mask(segment=segment, grid_shape=(3, 3))).reshape(3, 3) + np.testing.assert_array_equal(mask[:, 0], [False, False, False]) + np.testing.assert_array_equal(mask[:, 1], [True, True, True]) + np.testing.assert_array_equal(mask[:, 2], [True, True, True]) + + +def test_switch_mask_is_all_false_for_a_single_segment(): + """With one winning segment everywhere there is no switch.""" + segment = jnp.zeros(9, dtype=jnp.int32) + mask = np.asarray(switch_mask(segment=segment, grid_shape=(3, 3))) + assert not mask.any() diff --git a/tests/solution/test_mss.py b/tests/solution/test_mss.py new file mode 100644 index 000000000..9528e00d8 --- /dev/null +++ b/tests/solution/test_mss.py @@ -0,0 +1,288 @@ +"""Spec for the MSS upper-envelope kernel (HARK's EGM upper envelope). + +Contract under test β€” `_lcm.egm.upper_envelope.mss.refine_envelope`: + + refine_envelope( + *, + endog_grid: Float1D, # candidate resources points (consecutive segments) + policy: Float1D, + value: Float1D, + n_refined: int, # static output length + ) -> tuple[Float1D, Float1D, Float1D, ScalarInt] + +MSS is HARK's EGM upper envelope (Carroll et al. 2018): it sweeps the common +grid left-to-right, evaluates every currently overlapping linear segment, keeps +the max-value branch, and β€” unlike LTM β€” inserts the exact segment-crossing +abscissa (the kink) where the winning branch switches. The output therefore +tracks the FUES envelope tightly. + +Returns NaN-padded arrays of length `n_refined` holding the upper envelope of +the candidate value correspondence (weakly ascending in the grid) plus the +number of kept points. `n_kept > n_refined` signals overflow. + +Assertions are semantic β€” the refined arrays must *represent* the analytic upper +envelope under linear interpolation, with the crossing point present. +""" + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.egm.upper_envelope import get_upper_envelope +from lcm import LinSpacedGrid +from lcm.solvers import DCEGM +from tests.conftest import X64_ENABLED + +mss = pytest.importorskip( + "_lcm.egm.upper_envelope.mss", reason="MSS kernel not yet implemented" +) + + +def _mss_solver(): + return DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=LinSpacedGrid(start=0.0, stop=10.0, n_points=5), + upper_envelope="mss", + ) + + +# Tolerance for kernel-computed quantities (segment interpolation): float32 +# carries a few ulp through the bracketing and crossing arithmetic. +_COMPUTED_ATOL = 1e-8 if X64_ENABLED else 1e-5 + + +def _drop_nan(arr: jnp.ndarray) -> np.ndarray: + out = np.asarray(arr) + return out[~np.isnan(out)] + + +def _envelope_interp(grid, value, x_query): + keep = ~np.isnan(np.asarray(grid)) + return np.interp(x_query, np.asarray(grid)[keep], np.asarray(value)[keep]) + + +def _crossing_segments_candidates(): + """Two linear choice-specific value segments crossing at R* = 2.25. + + - Segment A: v = 1.0 + 0.4 R, c = 0.30 R β€” optimal for R < 2.25. + - Segment B: v = 0.1 + 0.8 R, c = 0.55 R β€” optimal for R > 2.25. + + The candidates arrive in two consecutive runs (one per segment), as the + Euler inversion produces them in non-concave regions: the input order makes + each segment a chain of consecutive candidates. + """ + r_a = np.array([0.6, 1.2, 1.8, 2.4]) + r_b = np.array([0.8, 1.6, 2.6, 3.4]) + grid = np.concatenate([r_a, r_b]) + value = np.concatenate([1.0 + 0.4 * r_a, 0.1 + 0.8 * r_b]) + policy = np.concatenate([0.30 * r_a, 0.55 * r_b]) + return jnp.asarray(grid), jnp.asarray(policy), jnp.asarray(value) + + +R_STAR = 2.25 + + +def test_concave_input_passes_through_unchanged(): + """A monotone-concave single segment is returned as-is (sorted, no edits).""" + grid = jnp.linspace(1.0, 10.0, 10) + policy = 0.3 * grid + value = jnp.log(grid) + + got_grid, got_policy, got_value, n_kept = mss.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=16 + ) + + assert int(n_kept) == 10 + np.testing.assert_allclose(_drop_nan(got_grid), np.asarray(grid), atol=1e-12) + np.testing.assert_allclose( + _envelope_interp(got_grid, got_value, np.asarray(grid)), + np.asarray(value), + atol=_COMPUTED_ATOL, + ) + np.testing.assert_allclose( + _envelope_interp(got_grid, got_policy, np.asarray(grid)), + np.asarray(policy), + atol=_COMPUTED_ATOL, + ) + + +def test_envelope_value_is_the_pointwise_segment_maximum(): + """The refined value traces `max(v_A, v_B)` of the two crossing segments. + + The interpolated envelope value at every abscissa is the higher of the two + choice-specific value lines, evaluated under linear interpolation of the + refined arrays. + """ + grid, policy, value = _crossing_segments_candidates() + + got_grid, _, got_value, _ = mss.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=16 + ) + + test_points = np.linspace(0.8, 3.4, 25) + interp = _envelope_interp(got_grid, got_value, test_points) + expected = np.maximum(1.0 + 0.4 * test_points, 0.1 + 0.8 * test_points) + np.testing.assert_allclose(interp, expected, atol=_COMPUTED_ATOL) + + +def test_inserts_the_exact_crossing_abscissa(): + """An envelope node lands exactly on the segment crossing R* = 2.25. + + Unlike LTM, MSS inserts the kink: the refined grid carries a node at the + intersection of the two value lines, so the linear read does not smear the + kink across the local grid spacing. + """ + grid, policy, value = _crossing_segments_candidates() + + got_grid, _, _, _ = mss.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=16 + ) + + clean_grid = _drop_nan(got_grid) + nearest = clean_grid[int(np.argmin(np.abs(clean_grid - R_STAR)))] + np.testing.assert_allclose(nearest, R_STAR, atol=_COMPUTED_ATOL) + + +def test_policy_jumps_at_the_inserted_kink(): + """At the crossing the policy carries the left and right branch values. + + The kink abscissa is inserted twice β€” once with segment A's policy + (`0.30 R*`) and once with segment B's (`0.55 R*`) β€” so the policy + discontinuity at the discrete-choice switch is preserved exactly. + """ + grid, policy, value = _crossing_segments_candidates() + + got_grid, got_policy, _, _ = mss.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=16 + ) + + clean_grid = np.asarray(got_grid) + clean_policy = np.asarray(got_policy) + at_star = np.isclose(clean_grid, R_STAR, atol=_COMPUTED_ATOL) + policies_at_star = np.sort(clean_policy[at_star]) + + assert at_star.sum() == 2 + np.testing.assert_allclose( + policies_at_star, np.sort([0.30 * R_STAR, 0.55 * R_STAR]), atol=_COMPUTED_ATOL + ) + + +def test_refined_grid_is_weakly_ascending_with_nan_tail(): + """Non-NaN prefix is weakly ascending; NaNs appear only as a suffix.""" + grid, policy, value = _crossing_segments_candidates() + + got_grid, _, _, _ = mss.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=16 + ) + + raw = np.asarray(got_grid) + nan_mask = np.isnan(raw) + first_nan = nan_mask.argmax() if nan_mask.any() else raw.size + assert not nan_mask[:first_nan].any() + assert nan_mask[first_nan:].all() + assert np.all(np.diff(raw[:first_nan]) >= -1e-12) + + +def test_overlapping_segment_dominates_a_bracketed_lower_node(): + """A later segment looping back over a node lifts that node to the envelope. + + The non-concavity an EGM cloud carries is a *backward jump* in the + endogenous grid: a later segment re-covers an earlier abscissa at a higher + value. The candidates `m = [1, 3, 2, 4]` chain two segments β€” `(1->3)` then + `(2->4)` after the jump back to 2 β€” so the abscissa `m = 2` is bracketed + both by the low first segment (value 1.5 at `m=2`) and by the high second + segment (value 5.0 at `m=2`). MSS keeps the higher one. + """ + grid = jnp.array([1.0, 3.0, 2.0, 4.0]) + policy = jnp.array([0.5, 1.5, 1.0, 2.0]) + value = jnp.array([1.0, 2.0, 5.0, 7.0]) + + got_grid, _, got_value, _ = mss.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + np.testing.assert_allclose( + _envelope_interp(got_grid, got_value, 2.0), 5.0, atol=_COMPUTED_ATOL + ) + + +def test_vmap_over_rows_matches_per_row_calls(): + """The kernel is vmappable; batched output equals per-row output.""" + grid, policy, value = _crossing_segments_candidates() + batched = jax.vmap( + lambda g, p, v: mss.refine_envelope( + endog_grid=g, policy=p, value=v, n_refined=16 + ) + )( + jnp.stack([grid, grid]), + jnp.stack([policy, policy]), + jnp.stack([value, value]), + ) + single = mss.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=16 + ) + + for batched_arr, single_arr in zip(batched, single, strict=True): + np.testing.assert_array_equal( + np.asarray(batched_arr[0]), np.asarray(single_arr) + ) + + +def test_overflow_is_reported_via_n_kept(): + """When the envelope needs more slots than `n_refined`, `n_kept` says so.""" + grid, policy, value = _crossing_segments_candidates() + + _, _, _, n_kept = mss.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=3 + ) + + assert int(n_kept) > 3 + + +def test_mss_backend_is_selected_by_solver_config(): + """`upper_envelope="mss"` dispatches to the MSS backend. + + The backend selected for an `mss` solver must reproduce the standalone MSS + kernel on a non-concave candidate set. + """ + solver = _mss_solver() + backend = get_upper_envelope(solver=solver, n_refined=16) + + grid, policy, value = _crossing_segments_candidates() + marginal = jnp.ones_like(grid) + via_backend = backend( + endog_grid=grid, policy=policy, value=value, marginal_utility=marginal + ) + direct = mss.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=16 + ) + for via_arr, direct_arr in zip(via_backend, direct, strict=True): + np.testing.assert_array_equal(np.asarray(via_arr), np.asarray(direct_arr)) + + +def test_dead_candidates_are_excluded_from_the_envelope(): + """NaN-poisoned candidates never reach the envelope or delete a live node. + + A dead candidate arrives NaN-filled; it must sort to the tail and contribute + no segment, leaving the live concave envelope intact. + """ + grid = jnp.array([1.0, 2.0, jnp.nan, 3.0, 4.0]) + policy = jnp.array([0.3, 0.6, jnp.nan, 0.9, 1.2]) + value = jnp.array([0.0, 0.7, jnp.nan, 1.1, 1.4]) + + got_grid, _, got_value, n_kept = mss.refine_envelope( + endog_grid=grid, policy=policy, value=value, n_refined=12 + ) + + clean_grid = _drop_nan(got_grid) + assert int(n_kept) == 4 + np.testing.assert_allclose(clean_grid, [1.0, 2.0, 3.0, 4.0], atol=1e-12) + np.testing.assert_allclose( + _envelope_interp(got_grid, got_value, np.asarray([1.0, 2.0, 3.0, 4.0])), + [0.0, 0.7, 1.1, 1.4], + atol=_COMPUTED_ATOL, + ) diff --git a/tests/solution/test_mss_fues_parity.py b/tests/solution/test_mss_fues_parity.py new file mode 100644 index 000000000..9d4e6dff0 --- /dev/null +++ b/tests/solution/test_mss_fues_parity.py @@ -0,0 +1,190 @@ +"""Acceptance: the MSS backend reproduces FUES on the DC-EGM battery. + +HARK's EGM upper envelope (`upper_envelope="mss"`) must produce the same value +function as the Fast Upper-Envelope Scan (`upper_envelope="fues"`) on the +existing DC-EGM solve tests, within a documented tolerance. + +Both backends insert the exact segment-crossing abscissa where a discrete choice +switches, so MSS tracks the FUES envelope tightly β€” tighter than LTM, which +evaluates the envelope at the candidate abscissae only and lets a kink land +between output nodes. The tolerance therefore absorbs only the residual +difference in scan ordering and floating-point crossing arithmetic, not a +kink-placement error. The brute-force-unstable low-wealth nodes are excluded +exactly as the underlying FUES tests do. +""" + +import dataclasses + +import jax.numpy as jnp +import numpy as np +import pytest + +from lcm import AgeGrid, MarkovTransition, Model +from lcm.typing import BoolND, DiscreteAction +from lcm_examples.iskhakov_et_al_2017 import dead +from tests.test_models.deterministic import base, retirement_only +from tests.test_models.deterministic.dcegm_variants import ( + dcegm_retirement, + dcegm_retirement_full, + dcegm_working_life, + get_full_params, + get_retirement_only_params, +) + +# MSS inserts the same exact crossing FUES does, so the published value functions +# agree far tighter than the LTM no-insertion tolerance (5e-3): the residual is +# floating-point crossing arithmetic plus scan ordering, well inside this bound. +_PARITY_ATOL = 1e-5 +_PARITY_RTOL = 1e-5 + + +def _with_backend(regime, *, upper_envelope): + """Rebuild a DC-EGM regime with the chosen upper-envelope backend.""" + solver = dataclasses.replace(regime.solver, upper_envelope=upper_envelope) + return regime.replace(solver=solver) + + +def _retirement_only_model(*, upper_envelope, n_periods): + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "retirement": _with_backend( + dcegm_retirement, upper_envelope=upper_envelope + ).replace(active=lambda age, la=last_age: age < la), + "dead": dead, + }, + ages=ages, + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + + +def _full_model(*, upper_envelope, n_periods): + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "working_life": _with_backend( + dcegm_working_life, upper_envelope=upper_envelope + ).replace(active=lambda age, la=last_age: age < la), + "retirement": _with_backend( + dcegm_retirement_full, upper_envelope=upper_envelope + ).replace(active=lambda age, la=last_age: age < la), + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + + +@pytest.mark.parametrize("n_periods", [3, 5]) +def test_mss_matches_fues_on_concave_retirement(n_periods): + """The pure-concave retirement solve agrees between MSS and FUES. + + No discrete choice means no segment crossing, so the two backends refine + the same candidate set identically β€” agreement holds tightly on every + wealth node. + """ + params = get_retirement_only_params(n_periods) + + fues = _retirement_only_model(upper_envelope="fues", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + mss = _retirement_only_model(upper_envelope="mss", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + + for period in sorted(fues)[:-1]: + np.testing.assert_allclose( + np.asarray(mss[period]["retirement"]), + np.asarray(fues[period]["retirement"]), + atol=_PARITY_ATOL, + rtol=_PARITY_RTOL, + err_msg=f"period={period}", + ) + + +def _nothing_is_feasible(labor_supply: DiscreteAction) -> BoolND: + return jnp.zeros_like(labor_supply, dtype=bool) + + +def test_mss_publishes_neg_inf_for_all_infeasible_combo_like_fues(): + """An all-infeasible worker regime publishes `-inf` V under MSS too. + + A discrete-only constraint false everywhere makes the worker's value `-inf` + at every state; the dead candidates must stay deleted from the envelope + sweep (`-inf`/NaN poisoning discipline), so MSS publishes `-inf` exactly as + FUES does, never NaN. + """ + n_periods = 4 + retirement_transition = { + "retirement": MarkovTransition( + lambda age, final_age_alive: jnp.where(age >= final_age_alive, 0.0, 1.0) + ), + "dead": MarkovTransition( + lambda age, final_age_alive: jnp.where(age >= final_age_alive, 1.0, 0.0) + ), + } + + def build(upper_envelope): + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + return Model( + regimes={ + "working_life": _with_backend( + dcegm_working_life, upper_envelope=upper_envelope + ).replace( + constraints={"nothing_is_feasible": _nothing_is_feasible}, + active=lambda age: age < 70, + ), + "retirement": _with_backend( + dcegm_retirement_full, upper_envelope=upper_envelope + ).replace( + transition=retirement_transition, + state_transitions={ + "wealth": dcegm_retirement_full.state_transitions["wealth"], + }, + active=lambda age: age < 70, + ), + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + + params = get_full_params(n_periods, discount_factor=0.98, wage=20.0) + mss = build("mss").solve(params=params, log_level="debug") + + for period in sorted(mss)[:-1]: + working_V = np.asarray(mss[period]["working_life"]) + assert bool(np.isneginf(working_V).all()), f"period={period}" + assert bool(np.isfinite(mss[period]["retirement"]).all()) + + +@pytest.mark.parametrize("n_periods", [4]) +def test_mss_matches_fues_on_discrete_choice_working_life(n_periods): + """The work/retire discrete-choice solve agrees between MSS and FUES. + + The labour-supply choice creates a non-concave kink in the worker's value + correspondence. Both backends insert the exact crossing abscissa, so the + published value functions agree tightly on the wealth nodes where both are + well-defined. + """ + params = get_full_params(n_periods, discount_factor=0.98, wage=20.0) + + fues = _full_model(upper_envelope="fues", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + mss = _full_model(upper_envelope="mss", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + + n_unstable_low_nodes = 10 + for period in sorted(fues)[:-1]: + for regime in ["working_life", "retirement"]: + np.testing.assert_allclose( + np.asarray(mss[period][regime])[..., n_unstable_low_nodes:], + np.asarray(fues[period][regime])[..., n_unstable_low_nodes:], + atol=_PARITY_ATOL, + rtol=_PARITY_RTOL, + err_msg=f"period={period}, regime={regime}", + ) diff --git a/tests/solution/test_negm.py b/tests/solution/test_negm.py new file mode 100644 index 000000000..41fde5689 --- /dev/null +++ b/tests/solution/test_negm.py @@ -0,0 +1,109 @@ +"""Spec for the `NEGM` solver configuration and its construction-time guards. + +`NEGM` composes an inner `DCEGM` (the 1-D consumption-savings solve) with an +outer deterministic grid search over a durable/illiquid margin. Its +`__post_init__` guards reject β€” at construction, with a +`RegimeInitializationError` β€” an outer grid that is a stochastic process, an +outer action that coincides with the inner continuous action, and an outer +post-decision that coincides with the inner post-decision. The remaining case +builds a NEGM model and asserts its simulate phase carries the inner DC-EGM +budget constraint. Nothing here solves a model. +""" + +import dataclasses + +import pytest + +from _lcm.egm.budget import DCEGM_BUDGET_CONSTRAINT_NAME +from _lcm.grids import ContinuousGrid +from lcm import DCEGM, NEGM, LinSpacedGrid, NormalIIDProcess +from lcm.exceptions import RegimeInitializationError +from tests.test_models import negm_kinked_toy + +_INNER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="liquid_savings", + savings_grid=LinSpacedGrid(start=0.0, stop=30.0, n_points=40), +) + +_OUTER_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=20) + + +def _negm( + *, + inner: DCEGM = _INNER, + outer_action: str = "illiquid_investment", + outer_post_decision: str = "next_illiquid", + outer_grid: ContinuousGrid = _OUTER_GRID, + outer_no_adjustment_candidate: str | None = None, +) -> NEGM: + return NEGM( + inner=inner, + outer_action=outer_action, + outer_post_decision=outer_post_decision, + outer_grid=outer_grid, + outer_no_adjustment_candidate=outer_no_adjustment_candidate, + ) + + +def test_negm_with_valid_fields_constructs(): + """A `NEGM` with distinct margins and a deterministic outer grid constructs.""" + solver = _negm() + assert solver.inner is _INNER + assert solver.outer_action == "illiquid_investment" + assert solver.outer_post_decision == "next_illiquid" + assert solver.outer_no_adjustment_candidate is None + + +def test_negm_with_no_adjustment_candidate_constructs(): + """The optional state-specific no-adjustment candidate is accepted.""" + solver = _negm(outer_no_adjustment_candidate="keep_illiquid") + assert solver.outer_no_adjustment_candidate == "keep_illiquid" + + +def test_negm_stochastic_outer_grid_is_rejected(): + """A stochastic process cannot serve as the deterministic outer search grid.""" + process = NormalIIDProcess(n_points=5, gauss_hermite=True, mu=0.0, sigma=1.0) + with pytest.raises(RegimeInitializationError, match="stochastic process"): + _negm(outer_grid=process) + + +def test_negm_outer_action_equal_to_inner_continuous_action_is_rejected(): + """The outer durable margin must differ from the inner consumption action.""" + with pytest.raises(RegimeInitializationError, match="coincides with the inner"): + _negm(outer_action="consumption") + + +def test_negm_outer_post_decision_equal_to_inner_post_decision_is_rejected(): + """The outer post-decision must differ from the inner liquid post-decision.""" + with pytest.raises(RegimeInitializationError, match="coincides with"): + _negm(outer_post_decision="liquid_savings") + + +def test_negm_invalid_inner_dcegm_is_rejected_by_inner_guards(): + """An invalid inner `DCEGM` is rejected by its own guards before NEGM's. + + The composition reuses `DCEGM.__post_init__` wholesale, so a stochastic + inner savings grid fails when the inner config is constructed. + """ + process = NormalIIDProcess(n_points=5, gauss_hermite=True, mu=0.0, sigma=1.0) + with pytest.raises(RegimeInitializationError, match="savings_grid"): + dataclasses.replace(_INNER, savings_grid=process) + + +def test_negm_simulate_phase_synthesizes_inner_budget_constraint(): + """A NEGM regime's simulate phase carries the inner DC-EGM budget mask. + + NEGM nests the same 1-D consumption-savings solve as `DCEGM`, so the + forward-simulation grid argmax needs the inner liquid feasibility mask + `consumption <= resources - borrowing_limit` exactly as a DC-EGM regime + does. The mask is built from `solver.inner`. The solve phase is + unaffected β€” the inner EGM kernels enforce the bound intrinsically and + never see the synthesized constraint. + """ + model = negm_kinked_toy.build_model() + alive = model._regimes["alive"] + assert DCEGM_BUDGET_CONSTRAINT_NAME in alive.simulation.constraints + assert DCEGM_BUDGET_CONSTRAINT_NAME not in alive.solution.constraints diff --git a/tests/solution/test_negm_bequest.py b/tests/solution/test_negm_bequest.py new file mode 100644 index 000000000..cb8c308c2 --- /dev/null +++ b/tests/solution/test_negm_bequest.py @@ -0,0 +1,46 @@ +"""NEGM supports a terminal bequest over two continuous states. + +When the terminal regime values a bequest over both the liquid Euler state and +the durable (the NEGM passive/outer margin), the EGM parent carries a terminal +value with the Euler state plus the durable as a passive leading axis. The +nested-EGM solve reproduces the grid-search optimum within the coarse-grid +band β€” the Dobrescu-Shanker housing bequest pattern. +""" + +import jax.numpy as jnp +import numpy as np + +from tests.test_models import negm_bequest_toy + +_PARAMS = {"discount_factor": 0.95, "alive": {}} + + +def _solve_period0_alive(model) -> jnp.ndarray: + return model.solve(params=_PARAMS, log_level="off")[0]["alive"] + + +def test_negm_solves_with_a_two_continuous_state_terminal_bequest(): + """The bequest NEGM model solves to a finite, well-shaped value array. + + The terminal `dead` regime carries both `wealth` and `illiquid`; the EGM + parent reads the durable as a passive leading axis of the terminal carry. + """ + v0 = _solve_period0_alive(negm_bequest_toy.build_negm_model()) + assert v0.shape == (negm_bequest_toy.N_X, negm_bequest_toy.N_Z) + assert bool(jnp.all(jnp.isfinite(v0))) + + +def test_negm_value_is_monotone_increasing_in_both_assets(): + """The period-0 value rises with both liquid wealth and the durable stock.""" + v0 = _solve_period0_alive(negm_bequest_toy.build_negm_model()) + assert bool(jnp.all(jnp.diff(v0, axis=0) >= -1e-6)) + assert bool(jnp.all(jnp.diff(v0, axis=1) >= -1e-6)) + + +def test_negm_value_matches_the_dense_brute_optimum(): + """NEGM reproduces the dense grid-search optimum within the grid band.""" + v_negm = np.asarray(_solve_period0_alive(negm_bequest_toy.build_negm_model())) + v_brute = np.asarray(_solve_period0_alive(negm_bequest_toy.build_brute_model())) + deviation = np.abs(v_negm - v_brute) + assert float(deviation.mean()) < 0.06 + assert float(deviation.max()) < 0.15 diff --git a/tests/solution/test_negm_kinked_toy.py b/tests/solution/test_negm_kinked_toy.py new file mode 100644 index 000000000..d8f65aebb --- /dev/null +++ b/tests/solution/test_negm_kinked_toy.py @@ -0,0 +1,353 @@ +"""Parity checks for the `NEGM` solver on the kinked two-asset toy. + +NEGM solves the kinked toy (`tests/test_models/negm_kinked_toy.py`) by an outer +search over the durable post-decision `next_illiquid` and an inner 1-D DC-EGM +solve on `wealth`. Three checks pin its correctness against an action-grid brute +oracle that searches the *same* economic problem on the same state domain with +the same order-1 V-interpolation: + +- The brute oracle (`negm_phase0/kinked_toy_oracle.py`) reproduces its own pinned + period-0 values and grid checksums β€” the oracle of record is stable. +- On a matched model whose brute analogue's reachable durable post-states are a + subset of NEGM's outer grid and whose consumption grid covers the feasible + continuous domain, NEGM's off-grid inner solve weakly dominates the + grid-restricted brute value at every state cell: NEGM `>=` brute. +- As the brute consumption and investment grids refine, the brute value rises + toward NEGM's off-grid value β€” the gap shrinks monotonically β€” so NEGM is the + off-grid limit the action-grid solver approaches from below. + +The model solves on CPU in seconds; nothing here is GPU-gated. +""" + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from lcm import ( + DCEGM, + NEGM, + AgeGrid, + LinSpacedGrid, + Model, + Regime, +) +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + FloatND, +) +from negm_phase0 import kinked_toy_oracle +from tests.test_models import negm_kinked_toy + +_PARAMS = {"discount_factor": 0.95, "alive": {}} + +# Period-0, regime `alive`, shape (N_X, N_Z) brute oracle on the repaired +# `[-6, 30]` wealth domain (`negm_phase0/kinked_toy_oracle.py`). With the grid +# starting at -6, cell (0, 0) is the deeply credit-constrained `wealth = -6`. +_ORACLE_CELLS = { + (0, 0): -0.8572114651, + (0, 6): -0.2964398156, + (6, 0): -0.2601982804, + (6, 6): -0.1719988446, + (11, 11): -0.1329429054, +} +_ORACLE_SUM = -31.33077128 +_ORACLE_MIN = -0.85721147 +_ORACLE_MAX = -0.13294291 + +# Matched-model geometry shared by the NEGM and brute analogues. The wealth +# domain matches the oracle's; the consumption grid spans the feasible range so +# brute is never capped below the optimum; the durable investment range keeps +# brute's reachable `next_illiquid` inside NEGM's outer grid. +_WEALTH_MIN = -6.0 +_WEALTH_MAX = 30.0 +_ILLIQUID_MAX = 30.0 +_CONSUMPTION_MAX = 45.0 +_INVESTMENT_BOUND = 8.0 +_LIQUID_CREDIT_LIMIT = -5.0 +_N_WEALTH = 8 +_N_ILLIQUID = 6 +_FINAL_AGE_ALIVE = 25 # ages 20, 25 alive then 30 dead: a genuine continuation + + +def _grid(start: float, stop: float, n_points: int) -> LinSpacedGrid: + return LinSpacedGrid(start=start, stop=stop, n_points=n_points) + + +def _build_matched_negm_model(*, savings_n: int = 80, outer_n: int = 40) -> Model: + """Build the matched 3-period NEGM model on the repaired wealth domain.""" + solver = NEGM( + inner=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="liquid_savings", + savings_grid=_grid(-5.0, 35.0, savings_n), + ), + outer_action="illiquid_investment", + outer_post_decision="next_illiquid", + outer_grid=_grid(0.0, _ILLIQUID_MAX, outer_n), + outer_no_adjustment_candidate="keep_illiquid", + ) + alive = Regime( + active=lambda age, n=_FINAL_AGE_ALIVE: age <= n, + states={ + "wealth": _grid(_WEALTH_MIN, _WEALTH_MAX, _N_WEALTH), + "illiquid": _grid(0.0, _ILLIQUID_MAX, _N_ILLIQUID), + }, + state_transitions={ + "wealth": negm_kinked_toy.next_wealth, + "illiquid": negm_kinked_toy.durable_transition, + }, + actions={ + "consumption": _grid(0.1, _CONSUMPTION_MAX, 25), + "illiquid_investment": _grid(-_INVESTMENT_BOUND, _INVESTMENT_BOUND, 25), + }, + transition=negm_kinked_toy.next_regime, + functions={ + "utility": negm_kinked_toy.utility, + "resources": negm_kinked_toy.resources, + "liquid_savings": negm_kinked_toy.liquid_savings, + "keep_illiquid": negm_kinked_toy.keep_illiquid, + "credited": negm_kinked_toy.credited, + "inverse_marginal_utility": negm_kinked_toy.inverse_marginal_utility, + }, + solver=solver, + ) + dead = Regime( + transition=None, + active=lambda age, n=_FINAL_AGE_ALIVE: age > n, + functions={"utility": lambda: 0.0}, + ) + return Model( + regimes={"alive": alive, "dead": dead}, + regime_id_class=negm_kinked_toy.RegimeId, + ages=AgeGrid(start=20, stop=30, step="5Y"), + fixed_params={"final_age_alive": _FINAL_AGE_ALIVE}, + ) + + +def _brute_liquid_savings( + wealth: ContinuousState, + consumption: ContinuousAction, + illiquid_investment: ContinuousAction, +) -> FloatND: + """Liquid post-decision balance with the withdrawal-penalty wedge.""" + credited = jnp.where( + illiquid_investment < 0.0, + (1.0 - negm_kinked_toy.WITHDRAWAL_PENALTY) * illiquid_investment, + illiquid_investment, + ) + return wealth + negm_kinked_toy.LABOUR_INCOME - consumption - credited + + +def _brute_next_illiquid( + illiquid: ContinuousState, illiquid_investment: ContinuousAction +) -> ContinuousState: + return illiquid + illiquid_investment + + +def _liquid_floor(liquid_savings: FloatND) -> BoolND: + return liquid_savings >= _LIQUID_CREDIT_LIMIT + + +def _illiquid_floor( + illiquid: ContinuousState, illiquid_investment: ContinuousAction +) -> BoolND: + return illiquid + illiquid_investment >= 0.0 + + +def _positive_consumption(consumption: ContinuousAction) -> BoolND: + return consumption > 0.05 + + +def _build_matched_brute_model(*, n_consumption: int, n_investment: int) -> Model: + """Build the matched brute analogue: same domain, on-grid action search. + + Searches `(consumption, illiquid_investment)` on grids of the given sizes + over the same state domain and frictions as the NEGM model, with the same + feasibility floors and the same order-1 V-interpolation. Its reachable + `next_illiquid` stays inside NEGM's outer grid, so its value is a lower bound + NEGM's off-grid inner solve weakly improves on. + """ + alive = Regime( + active=lambda age, n=_FINAL_AGE_ALIVE: age <= n, + states={ + "wealth": _grid(_WEALTH_MIN, _WEALTH_MAX, _N_WEALTH), + "illiquid": _grid(0.0, _ILLIQUID_MAX, _N_ILLIQUID), + }, + state_transitions={ + "wealth": negm_kinked_toy.next_wealth, + "illiquid": _brute_next_illiquid, + }, + actions={ + "consumption": _grid(0.1, _CONSUMPTION_MAX, n_consumption), + "illiquid_investment": _grid( + -_INVESTMENT_BOUND, _INVESTMENT_BOUND, n_investment + ), + }, + transition=negm_kinked_toy.next_regime, + constraints={ + "liquid_floor": _liquid_floor, + "illiquid_floor": _illiquid_floor, + "positive_consumption": _positive_consumption, + }, + functions={ + "utility": negm_kinked_toy.utility, + "liquid_savings": _brute_liquid_savings, + }, + ) + dead = Regime( + transition=None, + active=lambda age, n=_FINAL_AGE_ALIVE: age > n, + functions={"utility": lambda: 0.0}, + ) + return Model( + regimes={"alive": alive, "dead": dead}, + regime_id_class=negm_kinked_toy.RegimeId, + ages=AgeGrid(start=20, stop=30, step="5Y"), + fixed_params={"final_age_alive": _FINAL_AGE_ALIVE}, + ) + + +@pytest.fixture(scope="module") +def matched_negm_value() -> FloatND: + """The matched 3-period NEGM model's period-0 `alive` value array.""" + return _build_matched_negm_model().solve(params=_PARAMS, log_level="off")[0][ + "alive" + ] + + +@pytest.fixture(scope="module") +def oracle_value() -> FloatND: + """The 4-period brute oracle's period-0 `alive` value array.""" + return kinked_toy_oracle.build_model().solve( + params=kinked_toy_oracle.PARAMS, log_level="off" + )[0]["alive"] + + +@pytest.mark.parametrize( + ("marginal_continuation", "illiquid", "expected_consumption"), + [ + (0.25, 0.0, 2.0), # z = 0: no offset, c = m^{-1/2} + (0.25, 6.0, 1.7), # z = 6: c = 2.0 - iota * 6 = 2.0 - 0.3 + (1.0, 6.0, 0.7), # m = 1: c = 1.0 - 0.3 + ], +) +def test_inverse_marginal_utility_subtracts_the_durable_flow_offset( + marginal_continuation: float, illiquid: float, expected_consumption: float +) -> None: + """`(u')^{-1}(m) = m^{-1/gamma} - iota*Z` at the durable node `Z`. + + Utility is `(c + iota*Z)^{1-gamma}/(1-gamma)`, so `u'(c) = (c + iota*Z)^{-gamma}` + and inverting for the consumption action carries the `- iota*Z` offset the + durable state contributes to the flow. + """ + consumption = float( + negm_kinked_toy.inverse_marginal_utility( + marginal_continuation=jnp.asarray(marginal_continuation), + illiquid=jnp.asarray(illiquid), + ) + ) + np.testing.assert_allclose(consumption, expected_consumption, atol=1e-12) + + +def test_brute_oracle_reproduces_its_pinned_values(oracle_value: FloatND) -> None: + """The brute oracle reproduces its pinned period-0 values and grid checksums. + + The oracle is the parity record: its repaired `[-6, 30]` wealth domain keeps + every reachable `next_wealth` inside the support, so the pinned cell values + are dense-search truth rather than an out-of-domain extrapolation. + + The constants are pinned on CPU x64. The dense grid-search argmax breaks + near-ties between adjacent action nodes differently across backends, so exact + reproduction is a same-platform regression guard, not a cross-platform one. + """ + if jax.default_backend() != "cpu": + pytest.skip("Oracle constants are pinned on CPU x64 (grid-search argmax ties).") + for (ix, iz), expected in _ORACLE_CELLS.items(): + np.testing.assert_allclose( + float(oracle_value[ix, iz]), expected, rtol=1e-4, atol=1e-6 + ) + np.testing.assert_allclose(float(jnp.sum(oracle_value)), _ORACLE_SUM, rtol=1e-4) + np.testing.assert_allclose(float(jnp.min(oracle_value)), _ORACLE_MIN, rtol=1e-4) + np.testing.assert_allclose(float(jnp.max(oracle_value)), _ORACLE_MAX, rtol=1e-4) + + wealth_grid = jnp.asarray(kinked_toy_oracle.WEALTH_GRID.to_jax()) + illiquid_grid = jnp.asarray(kinked_toy_oracle.ILLIQUID_GRID.to_jax()) + np.testing.assert_allclose( + kinked_toy_oracle._checksum(wealth_grid), 1404.0, atol=1e-6 + ) + np.testing.assert_allclose( + kinked_toy_oracle._checksum(illiquid_grid), 1560.0, atol=1e-6 + ) + + +@pytest.mark.parametrize( + ("n_consumption", "n_investment"), + [(15, 15), (25, 25), (45, 45)], +) +def test_negm_weakly_improves_on_the_matched_brute_value( + matched_negm_value: FloatND, n_consumption: int, n_investment: int +) -> None: + """NEGM's off-grid value weakly dominates the matched brute value cell-by-cell. + + Brute searches the same economic problem on the same state domain with the + same order-1 V-interpolation but restricts the policy to its action grid; its + reachable durable post-states are a subset of NEGM's outer grid. NEGM's inner + EGM puts consumption off-grid, so at every state cell `V_negm >= V_brute` up + to a small interpolation tolerance. + """ + brute_value = _build_matched_brute_model( + n_consumption=n_consumption, n_investment=n_investment + ).solve(params=_PARAMS, log_level="off")[0]["alive"] + improvement = matched_negm_value - brute_value + assert bool(jnp.all(jnp.isfinite(brute_value))) + assert float(jnp.min(improvement)) >= -1e-4 + + +def test_brute_value_converges_up_to_negm_as_grids_refine( + matched_negm_value: FloatND, +) -> None: + """The matched brute value rises toward NEGM's off-grid value as grids refine. + + Refining the brute consumption and investment grids closes the worst-case gap + to NEGM: the action-grid solver approaches NEGM's off-grid value from below, so + NEGM is the limit, not an outlier. Convergence is required overall (finest + closer than coarsest), not at every individual step β€” action-grid alignment can + transiently widen the worst-case cell between two refinements. + """ + max_gaps = [] + for n_points in (15, 25, 45, 80): + brute_value = _build_matched_brute_model( + n_consumption=n_points, n_investment=n_points + ).solve(params=_PARAMS, log_level="off")[0]["alive"] + max_gaps.append(float(jnp.max(jnp.abs(matched_negm_value - brute_value)))) + # The finest grid is strictly closer to NEGM than the coarsest (overall + # convergence), and lands within a tight band of NEGM everywhere. + assert max_gaps[-1] < max_gaps[0] + assert max_gaps[-1] < 0.1 + + +@pytest.mark.parametrize("outer_batch_size", [1, 8]) +def test_outer_batch_size_leaves_value_function_unchanged(outer_batch_size: int): + """Chunking the NEGM outer search yields the identical solved value function. + + The outer durable search folds each candidate into a running maximum; + processing the outer-grid nodes in chunks of `outer_batch_size` instead of all + at once reduces them in the same order, so the solved value function is + bit-identical β€” the knob trades parallelism for bounded memory only. + """ + base = negm_kinked_toy.build_model().solve(params=_PARAMS, log_level="off") + chunked = negm_kinked_toy.build_model(outer_batch_size=outer_batch_size).solve( + params=_PARAMS, log_level="off" + ) + assert base.keys() == chunked.keys() + for period in base: + for regime in base[period]: + np.testing.assert_array_equal( + np.asarray(chunked[period][regime]), + np.asarray(base[period][regime]), + ) diff --git a/tests/solution/test_negm_outer_island.py b/tests/solution/test_negm_outer_island.py new file mode 100644 index 000000000..4039250d3 --- /dev/null +++ b/tests/solution/test_negm_outer_island.py @@ -0,0 +1,62 @@ +"""NEGM outer envelope keeps an adjuster that wins between keeper nodes. + +The nested-EGM outer fold reads every adjuster candidate onto the keeper's shared +cash-on-hand grid and takes the running maximum at those nodes. A shared-node +maximum alone is a *sampled* maximum: an adjuster branch whose value exceeds the +keeper only on an interval strictly between two shared nodes β€” a thin (S, s) +adjustment island β€” is never sampled at its peak. To recover it the fold also +reads each adjuster at its own nodes and splices that adjuster's best win into +the published carry, so the envelope retains the island the sampled maximum +would miss. +""" + +import jax.numpy as jnp + +from _lcm.egm.carry import EGMCarry +from _lcm.egm.interp import interp_on_padded_grid +from _lcm.egm.outer_envelope import build_outer_envelope_carry + + +def test_outer_envelope_keeps_adjuster_island_between_shared_nodes(): + """An adjuster winning only between keeper nodes survives the outer envelope. + + The keeper value is flat zero on `linspace(0, 1, 11)`. The adjuster carries a + positive island peaking at `x = 0.55` (value `0.1`) β€” a node on its own grid + but between the keeper nodes `0.5` and `0.6` β€” and is negative elsewhere. The + true outer maximum at `0.55` is `0.1`, so the published envelope must report + at least that there. + """ + keeper_coh = jnp.linspace(0.0, 1.0, 11) + zeros11 = jnp.zeros(11) + keeper = EGMCarry( + endog_grid=keeper_coh[None, :], + value=zeros11[None, :], + marginal_utility=zeros11[None, :], + taste_shock_scale=jnp.asarray(0.0), + ) + adj_coh = jnp.array([0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.55, 0.6, 0.7, 0.85, 1.0]) + adj_val = jnp.array( + [-0.2, -0.2, -0.2, -0.2, -0.2, -0.1, 0.1, -0.1, -0.2, -0.2, -0.2] + ) + adjuster = EGMCarry( + endog_grid=adj_coh[None, :], + value=adj_val[None, :], + marginal_utility=zeros11[None, :], + taste_shock_scale=jnp.asarray(0.0), + ) + + carry = build_outer_envelope_carry( + keeper_carry=keeper, + adjuster_carries=(adjuster,), + coh_shifts=jnp.asarray([[0.0]]), + ) + enveloped_at_peak = float( + interp_on_padded_grid( + x_query=jnp.array([0.55]), + xp=carry.endog_grid[0], + fp=carry.value[0], + fp_slopes=carry.marginal_utility[0], + )[0] + ) + + assert enveloped_at_peak >= 0.1 - 1e-6 diff --git a/tests/solution/test_negm_serviceflow.py b/tests/solution/test_negm_serviceflow.py new file mode 100644 index 000000000..896ba1aa3 --- /dev/null +++ b/tests/solution/test_negm_serviceflow.py @@ -0,0 +1,56 @@ +"""NEGM supports `utility` reading the outer post-decision (the new durable). + +When the durable's service flow accrues from the newly chosen stock `s'` +(`utility` reads `serviced_durable(next_illiquid)`, where `next_illiquid` is the +`outer_post_decision`), the nested-EGM solve binds that value per outer-grid +node and reproduces the grid-search optimum: the inner consumption margin is +off-grid (exact), so the two methods agree within the coarse-grid +discretization band on this deliberately tiny toy (8x8 states, 3 periods, a +durable withdrawal penalty and a credit-card rate kink). The residual is the +grid band, which tightens as the grids refine β€” not a bias of either method. +""" + +import jax.numpy as jnp +import numpy as np + +from tests.test_models import negm_serviceflow_toy + +_PARAMS = {"discount_factor": 0.95, "alive": {}} + + +def _solve_period0_alive(model) -> jnp.ndarray: + return model.solve(params=_PARAMS, log_level="off")[0]["alive"] + + +def test_negm_solves_when_utility_reads_the_new_durable_stock(): + """The service-flow NEGM model solves to a finite, well-shaped value array. + + `utility` reads `next_illiquid` (the `outer_post_decision`) through the + `serviced_durable` flow; the solver binds it per outer node, so the inner + kernel evaluates without falling outside its scope. + """ + v0 = _solve_period0_alive(negm_serviceflow_toy.build_negm_model()) + assert v0.shape == (negm_serviceflow_toy.N_X, negm_serviceflow_toy.N_Z) + assert bool(jnp.all(jnp.isfinite(v0))) + + +def test_negm_value_is_monotone_increasing_in_both_assets(): + """The period-0 value rises with both liquid wealth and the durable stock.""" + v0 = _solve_period0_alive(negm_serviceflow_toy.build_negm_model()) + assert bool(jnp.all(jnp.diff(v0, axis=0) >= -1e-6)) + assert bool(jnp.all(jnp.diff(v0, axis=1) >= -1e-6)) + + +def test_negm_value_matches_the_dense_brute_optimum(): + """NEGM reproduces the dense grid-search optimum within the grid band. + + The grid-search twin searches the same durable grid with a dense + consumption grid, so it is the near-exact optimum. NEGM's off-grid + consumption tracks it: the model-wide mean absolute deviation is small and + no cell departs by more than the coarse-grid band. + """ + v_negm = np.asarray(_solve_period0_alive(negm_serviceflow_toy.build_negm_model())) + v_brute = np.asarray(_solve_period0_alive(negm_serviceflow_toy.build_brute_model())) + deviation = np.abs(v_negm - v_brute) + assert float(deviation.mean()) < 0.06 + assert float(deviation.max()) < 0.15 diff --git a/tests/solution/test_negm_validation.py b/tests/solution/test_negm_validation.py new file mode 100644 index 000000000..383f25038 --- /dev/null +++ b/tests/solution/test_negm_validation.py @@ -0,0 +1,194 @@ +"""Spec for NEGM build-time validation (the fail-loudly model contract). + +A regime with `solver=NEGM(...)` must satisfy the nesting contract on top of the +inner DC-EGM contract. Every violation raises `ModelInitializationError` at model +build, naming the offending feature **and** the correct alternative solver. The +checks run on the user regimes directly (`validate_negm_regimes`), so each case +constructs regimes and asserts the rejection without building kernels or solving. + +The cases mutate the valid kinked-toy NEGM regime one rule at a time: + +1. no outer margin (outer action absent) β†’ use `DCEGM`, +2. outer action equals the inner continuous action, or outer post-decision + equals the inner post-decision β†’ reject (distinct margins), +3. coupled-2-Euler: the outer post-decision enters the inner Euler-state + transition β†’ use the 2-D EGM foundation, +4. taste-shock ordering: a taste-shocked discrete choice exists β†’ reject. +""" + +import dataclasses + +import jax.numpy as jnp +import pytest + +from _lcm.egm.negm_validation import ( + _fail_if_margins_not_distinct, + validate_negm_regimes, +) +from lcm import DiscreteGrid, ExtremeValueTasteShocks, categorical +from lcm.exceptions import ModelInitializationError +from lcm.regime import Regime as UserRegime +from lcm.typing import ( + ContinuousAction, + ContinuousState, + DiscreteAction, + FloatND, + ScalarInt, +) +from tests.test_models import negm_kinked_toy + +_VALID = negm_kinked_toy.build_alive_regime() + + +def _validate(regime: UserRegime) -> None: + """Run the NEGM contract check on a single-regime mapping.""" + validate_negm_regimes(user_regimes={"alive": regime}) + + +def test_valid_kinked_toy_negm_regime_passes_validation(): + """The kinked-toy NEGM regime satisfies the nesting contract.""" + _validate(_VALID) + + +def test_outer_action_absent_is_rejected_with_dcegm_pointer(): + """A regime with no outer continuous action is a pure 1-D problem. + + Dropping the durable action (and the durable state it moves) leaves a + single continuous action; NEGM would silently run as plain DC-EGM, so it is + rejected with a pointer to `DCEGM`. + """ + regime = _VALID.replace( + actions={"consumption": negm_kinked_toy.CONSUMPTION_GRID}, + ) + with pytest.raises(ModelInitializationError, match="use `DCEGM`"): + _validate(regime) + + +def test_outer_post_decision_not_declared_is_rejected(): + """An outer post-decision that is neither a function nor a transition fails.""" + solver = dataclasses.replace( + negm_kinked_toy.NEGM_SOLVER, outer_post_decision="not_a_function" + ) + regime = _VALID.replace(solver=solver) + with pytest.raises(ModelInitializationError, match="neither a declared function"): + _validate(regime) + + +def test_margin_distinctness_recheck_rejects_outer_action_equal_to_inner_action(): + """The model-build re-check rejects an outer action equal to the inner one. + + `NEGM.__post_init__` enforces distinctness at construction (so a coincident + `NEGM` cannot be built); the validator carries the same check as a single + fail-loud model-build point, exercised here against an inner config whose + continuous action matches the solver's outer action. + """ + solver = negm_kinked_toy.NEGM_SOLVER + inner_action_clashes = dataclasses.replace( + solver.inner, continuous_action="illiquid_investment" + ) + with pytest.raises(ModelInitializationError, match="coincides with the inner"): + _fail_if_margins_not_distinct( + regime_name="alive", solver=solver, inner=inner_action_clashes + ) + + +def test_margin_distinctness_recheck_rejects_outer_equal_to_inner_post_decision(): + """The model-build re-check rejects a coincident post-decision function.""" + solver = negm_kinked_toy.NEGM_SOLVER + inner_post_clashes = dataclasses.replace( + solver.inner, post_decision_function="next_illiquid" + ) + with pytest.raises(ModelInitializationError, match="coincides with"): + _fail_if_margins_not_distinct( + regime_name="alive", solver=solver, inner=inner_post_clashes + ) + + +def _euler_law_reading_outer_margin( + liquid_savings: FloatND, next_illiquid: ContinuousState +) -> ContinuousState: + """A liquid Euler law that reads the outer post-decision (the pension shape). + + The next-period liquid wealth depends on the durable stock the outer choice + sets, so the `c` and the outer FOCs invert on the same continuation. + """ + rate = jnp.where(liquid_savings < 0.0, 0.12, 0.03) + return (1.0 + rate) * liquid_savings + 0.01 * next_illiquid + + +def test_outer_margin_entering_inner_euler_law_is_rejected_with_2d_pointer(): + """The DS pension coupling fails fast with a pointer to the 2-D foundation. + + When the inner Euler-state transition reads the outer post-decision, the + inner Euler inversion is no longer independent of the outer choice, so + NEGM's deterministic outer max is invalid. + """ + regime = _VALID.replace( + state_transitions={ + "wealth": _euler_law_reading_outer_margin, + "illiquid": negm_kinked_toy.durable_transition, + }, + ) + with pytest.raises(ModelInitializationError, match="G2EGM / multidim-RFC"): + _validate(regime) + + +def _utility_coupling_consumption_and_durable_move( + consumption: ContinuousAction, next_illiquid: ContinuousState +) -> FloatND: + """A utility that multiplies consumption by the outer post-decision. + + The cross-term makes the inner marginal utility depend on the outer choice, + so the durable margin is not additively separable from consumption. + """ + flow = consumption * (1.0 + 0.01 * next_illiquid) + return flow ** (1.0 - 2.0) / (1.0 - 2.0) + + +def test_utility_coupling_the_two_margins_is_rejected_with_2d_pointer(): + """A non-additively-separable utility cross-term fails fast. + + NEGM treats the outer margin's utility term as a constant in the inner Euler + inversion; a cross-term in `(consumption, next_illiquid)` breaks that. + """ + regime = _VALID.replace( + functions={ + **dict(_VALID.functions), + "utility": _utility_coupling_consumption_and_durable_move, + }, + ) + with pytest.raises(ModelInitializationError, match="G2EGM / multidim-RFC"): + _validate(regime) + + +@categorical(ordered=False) +class _Work: + work: ScalarInt + rest: ScalarInt + + +def _is_working(labor_supply: DiscreteAction) -> FloatND: + return labor_supply == _Work.work + + +def test_taste_shocked_discrete_choice_is_rejected_with_ordering_explanation(): + """A taste-shocked discrete choice violates the aggregation ordering. + + NEGM wraps its outer search around the inner solve (which performs the + discrete `logsumexp`), so the outer max sits outside the taste-shock + aggregation β€” the wrong order. The regime is rejected with the Β§2.3 + explanation. + """ + regime = _VALID.replace( + actions={ + **dict(_VALID.actions), + "labor_supply": DiscreteGrid(_Work), + }, + functions={ + **dict(_VALID.functions), + "is_working": _is_working, + }, + taste_shocks=ExtremeValueTasteShocks(), + ) + with pytest.raises(ModelInitializationError, match="outermost aggregation"): + _validate(regime) diff --git a/tests/solution/test_numeric_inverse.py b/tests/solution/test_numeric_inverse.py new file mode 100644 index 000000000..55f1447bf --- /dev/null +++ b/tests/solution/test_numeric_inverse.py @@ -0,0 +1,211 @@ +"""Numerically inverting marginal utility reproduces the analytic inverse. + +The iEGM path lets EGM solve models whose utility has no closed-form `(u')^{-1}`: +it root-finds `u'(c) = marginal_continuation` on a bracket. The numerical inverse +must match the analytic one on CRRA utility β€” in *value* and in *parameter +derivative* β€” and converge to a true root for a utility with no closed-form +inverse. A value match with a wrong or zero gradient is the failure mode the +implicit-derivative contract exists to prevent. +""" + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.egm.numeric_inverse import numeric_inverse_marginal_utility +from tests.conftest import X64_ENABLED + +# Root-finding accuracy scales with the float eps of the active precision: +# central finite differences, Newton-iterate residuals, and to-machine-precision +# matches all lose roughly half the mantissa at 32-bit. +_FD_RTOL = 1e-3 if X64_ENABLED else 1e-2 +_RESIDUAL_BOUND = 1e-7 if X64_ENABLED else 1e-6 +_NEWTON_RTOL = 1e-9 if X64_ENABLED else 1e-7 + + +def _crra_marginal(crra): + """The CRRA marginal utility `u'(c) = c^{-crra}` as a callable of `c`.""" + return lambda c: c ** (-crra) + + +@pytest.mark.parametrize("crra", [1.5, 2.0, 3.0]) +@pytest.mark.parametrize("m", [0.01, 0.1, 0.5, 1.0, 5.0]) +def test_numeric_inverse_matches_crra_analytic_value(crra, m): + """The root of `c^{-crra} = m` equals the analytic `m^{-1/crra}`.""" + c = numeric_inverse_marginal_utility( + marginal_continuation=jnp.asarray(m), + marginal_utility=_crra_marginal(crra), + c_lower=jnp.asarray(1e-8), + c_upper=jnp.asarray(1e6), + ) + analytic = m ** (-1.0 / crra) + np.testing.assert_allclose(float(c), analytic, rtol=1e-7) + + +@pytest.mark.parametrize("crra", [1.5, 2.0, 3.0]) +@pytest.mark.parametrize("m", [0.05, 0.5, 2.0]) +def test_numeric_inverse_derivative_matches_crra_analytic(crra, m): + """`d c*/d m` from the inverter equals the analytic CRRA derivative. + + For `c* = m^{-1/crra}`, `d c*/d m = -(1/crra) m^{-1/crra - 1}`. The implicit + derivative must reproduce it; differentiating through the bisection branches + would not. + """ + + def invert(m_value): + return numeric_inverse_marginal_utility( + marginal_continuation=m_value, + marginal_utility=_crra_marginal(crra), + c_lower=jnp.asarray(1e-8), + c_upper=jnp.asarray(1e6), + ) + + grad = float(jax.grad(invert)(jnp.asarray(m))) + analytic = -(1.0 / crra) * m ** (-1.0 / crra - 1.0) + np.testing.assert_allclose(grad, analytic, rtol=1e-5) + + finite_diff = float( + (invert(jnp.asarray(m + 1e-4)) - invert(jnp.asarray(m - 1e-4))) / 2e-4 + ) + np.testing.assert_allclose(grad, finite_diff, rtol=_FD_RTOL) + + +def test_numeric_inverse_converges_for_non_closed_form_utility(): + """For `u'(c) = c^{-2} + e^{-c}` (no closed-form inverse) the residual vanishes. + + Both terms are strictly decreasing in `c`, so `u'` is invertible; the root + finder must drive `|u'(c*) - m|` below tolerance across a grid of targets even + though no algebraic inverse exists. + """ + + def marginal(c): + return c ** (-2.0) + jnp.exp(-c) + + targets = jnp.linspace(0.05, 3.0, 25) + solve = jax.vmap( + lambda m: numeric_inverse_marginal_utility( + marginal_continuation=m, + marginal_utility=marginal, + c_lower=jnp.asarray(1e-6), + c_upper=jnp.asarray(1e4), + ) + ) + roots = solve(targets) + residual = marginal(roots) - targets + assert float(jnp.max(jnp.abs(residual))) < _RESIDUAL_BOUND + + +def test_numeric_inverse_clamps_unbracketed_target_with_zero_gradient(): + """A target outside the bracket clamps to the bound with an active-set gradient. + + With `u'(c) = c^{-2}` on `[0.5, 2.0]` the marginal spans `[0.25, 4.0]`; a target + `m = 100` lies above that, so the root `c = 0.1` is below the bracket. The + inverter returns the clamped lower bound, and β€” because the binding-bound + active-set derivative is zero, not the bogus interior `1/u''` slope β€” its + gradient w.r.t. `m` is exactly `0`. + """ + + def invert(m_value): + return numeric_inverse_marginal_utility( + marginal_continuation=m_value, + marginal_utility=_crra_marginal(2.0), + c_lower=jnp.asarray(0.5), + c_upper=jnp.asarray(2.0), + ) + + np.testing.assert_allclose(float(invert(jnp.asarray(100.0))), 0.5, atol=1e-6) + assert float(jax.grad(invert)(jnp.asarray(100.0))) == 0.0 + + +@pytest.mark.parametrize("crra", [1.5, 2.0, 3.0]) +def test_numeric_inverse_converges_in_few_iterations_on_a_wide_bracket(crra): + """A handful of safeguarded-Newton steps suffice where bisection cannot. + + On the wide bracket `[1e-8, 1e6]`, `15` bisection steps shrink it by only + `2**15` β€” nowhere near the root β€” yet the safeguarded Newton iterate hits the + analytic CRRA inverse to machine precision in that count, because the Newton + step converges quadratically once it is near the root. This pins the forward + solve as Newton-driven, not bisection-driven. + """ + m = 0.5 + c = numeric_inverse_marginal_utility( + marginal_continuation=jnp.asarray(m), + marginal_utility=_crra_marginal(crra), + c_lower=jnp.asarray(1e-8), + c_upper=jnp.asarray(1e6), + n_iter=15, + ) + analytic = m ** (-1.0 / crra) + np.testing.assert_allclose(float(c), analytic, rtol=_NEWTON_RTOL) + + +def test_numeric_inverse_fails_loud_on_nonpositive_target(): + """A non-positive Euler target violates the log-space precondition β†’ NaN. + + The log-consumption solve needs `m > 0`. A target `m <= 0` (which a valid + increasing-utility model never produces) must surface as NaN β€” caught by the + kernel's NaN diagnostics β€” not a silently clamped bound. + """ + c = numeric_inverse_marginal_utility( + marginal_continuation=jnp.asarray(-1.0), + marginal_utility=_crra_marginal(2.0), + c_lower=jnp.asarray(1e-8), + c_upper=jnp.asarray(1e6), + ) + assert bool(jnp.isnan(c)) + + +def test_numeric_inverse_fails_loud_when_marginal_turns_nonpositive(): + """A marginal that goes non-positive on the bracket β†’ NaN, not a wrong root. + + For `u'(c) = 1 - c` on `[0.5, 2.0]` the marginal is negative at the upper + bound, so `log u'` is undefined there; the solver must fail loud rather than + return a spurious interior value. + """ + c = numeric_inverse_marginal_utility( + marginal_continuation=jnp.asarray(0.25), + marginal_utility=lambda c: 1.0 - c, + c_lower=jnp.asarray(0.5), + c_upper=jnp.asarray(2.0), + ) + assert bool(jnp.isnan(c)) + + +def test_numeric_inverse_fails_loud_when_bracket_marginal_overflows(): + """A bracket marginal that overflows to `+inf` violates the precondition β†’ NaN. + + A power-law `u'(c) = c^{-crra}` with a steep `crra` and a near-zero `c_lower` + makes `u'(c_lower)` overflow to `+inf`. That endpoint is `> 0` but not finite, + so the log-consumption solve cannot proceed on it; the inverter must fail loud + (NaN, caught by the kernel's NaN diagnostics) rather than run the log path on a + non-finite bracket endpoint and return a silently clamped bound. The upper + endpoint stays finite and positive (`2^{-60} > 0`), so only the overflow β€” + not a non-positive marginal β€” can gate this call. + """ + c = numeric_inverse_marginal_utility( + marginal_continuation=jnp.asarray(1.0), + marginal_utility=_crra_marginal(60.0), + c_lower=jnp.asarray(1e-8), + c_upper=jnp.asarray(2.0), + ) + assert bool(jnp.isnan(c)) + + +def test_numeric_inverse_is_vmappable_and_jittable(): + """The inverter vmaps over targets and jit-compiles (kernel requirements).""" + targets = jnp.linspace(0.1, 4.0, 16) + fn = jax.jit( + jax.vmap( + lambda m: numeric_inverse_marginal_utility( + marginal_continuation=m, + marginal_utility=_crra_marginal(2.0), + c_lower=jnp.asarray(1e-8), + c_upper=jnp.asarray(1e6), + ) + ) + ) + roots = fn(targets) + np.testing.assert_allclose( + np.asarray(roots), np.asarray(targets ** (-0.5)), rtol=1e-6 + ) diff --git a/tests/solution/test_one_asset_egm_step.py b/tests/solution/test_one_asset_egm_step.py new file mode 100644 index 000000000..2229aad38 --- /dev/null +++ b/tests/solution/test_one_asset_egm_step.py @@ -0,0 +1,83 @@ +"""The 1-D retirement EGM step reproduces the brute solve of the retired sub-problem. + +The retired agent solves a plain consumption--saving problem: one continuous state +(`liquid`), one continuous action (`consumption`), no discrete choice, so the endogenous +grid method needs no upper envelope β€” invert the consumption Euler equation on a +post-decision savings grid and map back to the liquid grid. Run against the DS pension +brute solve, the step matches the dense grid-search retired value where the grid covers. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.one_asset_egm_step import egm_one_asset_step +from tests.test_models.deterministic.ds_pension import get_model, get_params + +_LIQUID_GRID = jnp.linspace(0.1, 20.0, 12) +_SAVINGS_GRID = jnp.linspace(0.0, 20.0, 40) +_P = { + "discount_factor": 0.98, + "crra": 2.0, + "return_liquid": 0.02, + "income": 0.50, +} +# The two lowest liquid points sit in the borrowing-constrained boundary layer, where +# the value has a kink and a coarse linear grid cannot resolve the steep low-wealth +# value; both EGM and grid search carry boundary error there. The unconstrained +# interior is what the parity assertion covers. +_INTERIOR = np.s_[2:] + + +def _brute_retired(*, n_consumption=200): + """Brute retired value, solved with a fine consumption grid as the fair reference. + + The default oracle's 14-point consumption grid is too coarse to be a faithful + reference at low liquid (the optimal consumption is small and falls between grid + points); a fine grid converges to the true value the EGM step targets. + """ + model = get_model(n_periods=5, n_consumption=n_consumption) + brute = model.solve(params=get_params(), log_level="off") + return jnp.asarray(brute[4]["dead"]), np.asarray(brute[3]["retired"]) + + +def _bequest_marginal(): + """Marginal value of liquid for the terminal CRRA bequest `u(liquid)`.""" + return _LIQUID_GRID ** (-_P["crra"]) + + +def test_retired_egm_matches_brute_on_the_liquid_interior(): + """One retired EGM step from the terminal bequest matches the brute solve.""" + v_dead, brute_retired = _brute_retired() + step = egm_one_asset_step( + next_value=v_dead, + next_marginal=_bequest_marginal(), + liquid_grid=_LIQUID_GRID, + savings_grid=_SAVINGS_GRID, + **_P, + ) + v_retired = np.asarray(step.value) + assert np.isfinite(v_retired).all() + rel = np.abs(v_retired[_INTERIOR] - brute_retired[_INTERIOR]) / np.abs( + brute_retired[_INTERIOR] + ) + assert np.median(rel) < 0.01 + assert np.max(rel) < 0.05 + + +def test_retired_egm_value_is_increasing_in_liquid(): + """More liquid wealth is weakly more valuable in retirement.""" + v_dead, _brute = _brute_retired() + step = egm_one_asset_step( + next_value=v_dead, + next_marginal=_bequest_marginal(), + liquid_grid=_LIQUID_GRID, + savings_grid=_SAVINGS_GRID, + **_P, + ) + assert np.all(np.diff(np.asarray(step.value)) >= -1e-6) + # The marginal value of liquid is positive and decreasing (concave value). + assert np.all(np.asarray(step.marginal) > 0) + assert np.all(np.diff(np.asarray(step.marginal)) <= 1e-6) + # Consumption is positive and weakly increasing in liquid wealth. + assert np.all(np.asarray(step.consumption) > 0) + assert np.all(np.diff(np.asarray(step.consumption)) >= -1e-6) diff --git a/tests/solution/test_outer_envelope.py b/tests/solution/test_outer_envelope.py new file mode 100644 index 000000000..7137b2fee --- /dev/null +++ b/tests/solution/test_outer_envelope.py @@ -0,0 +1,311 @@ +"""Spec for the NEGM cash-on-hand outer-max carry envelope. + +The NEGM kernel publishes one continuation carry per durable state. The keeper +and every adjuster outer-grid node each produce a candidate value row; the +published carry must be their genuine upper envelope in cash-on-hand (coh) +space, so a parent period that interpolates the carry sees the best durable +choice at every coh β€” not only the keeper's, and not only at the keeper's nodes. + +`build_outer_envelope_carry` maps each candidate's endogenous (resources) grid +into coh space by a per-candidate constant shift (`+credited(z, z')`, zero for +the keeper), concatenates the shifted candidate rows per durable state, and runs +the regime's upper-envelope backend to produce the published carry. These tests +exercise that construction in isolation, with synthetic keeper and adjuster +rows, so the envelope logic is pinned independently of the toy model and oracle. +""" + +from types import MappingProxyType +from typing import cast + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.carry import EGMCarry +from _lcm.egm.interp import interp_on_padded_grid +from _lcm.egm.outer_envelope import build_outer_envelope_carry +from _lcm.solution.solvers import _build_coh_shift_function +from _lcm.typing import EconFunctionsMapping +from lcm.typing import Float1D, FloatND + + +def test_coh_shift_cancels_a_separable_state_in_the_resources_difference() -> None: + """The credited-cost shift ignores a resources term that is constant in `next`. + + The cash-on-hand shift is the keeper-minus-adjuster difference of the + regime's inner resources, where only the outer post-decision (`next_housing`) + varies between the two evaluations. Any resources term that does not depend on + that outer choice β€” here a separable wage income `y(wage)` and the + `(1+r)Β·liquid` wealth term β€” appears identically in both legs and cancels, so + the shift equals `housing_cost(next=outer) - housing_cost(next=keep)` and is + independent of the wage state. The builder must therefore evaluate the + resources function even though the model reads a `wage` state the shift does + not depend on, rather than failing because no `wage` value was supplied. + """ + + def income(wage: FloatND) -> FloatND: + """A wage-only resources term, additively separable from the house cost.""" + return jnp.exp(wage) + + def housing_cost(housing: FloatND, next_housing: FloatND) -> FloatND: + """Round-trip cost of moving the house from `housing` to `next_housing`.""" + return next_housing - housing + + def resources( + liquid: FloatND, income: FloatND, housing_cost: FloatND, return_liquid: float + ) -> FloatND: + """`(1+r)*liquid + y - housing_cost`, separable in wage and wealth.""" + return (1.0 + return_liquid) * liquid + income - housing_cost + + shift_func = _build_coh_shift_function( + functions=cast( + "EconFunctionsMapping", + MappingProxyType( + { + "resources": resources, + "income": income, + "housing_cost": housing_cost, + } + ), + ), + resources_name="resources", + euler_state_name="liquid", + durable_state_name="housing", + outer_post_decision="next_housing", + ) + + durable_values = jnp.asarray([1.0, 2.0]) + outer_values = jnp.asarray([0.5, 1.5, 3.0]) + shifts = shift_func( + durable_values=durable_values, + outer_values=outer_values, + return_liquid=0.05, + ) + + # shift(z, z') = resources(next=z) - resources(next=z') + # = housing_cost(next=z') - housing_cost(next=z) = z' - z, + # with the wage income and (1+r)*liquid terms cancelling. + expected = outer_values[None, :] - durable_values[:, None] + assert shifts.shape == (2, 3) + np.testing.assert_allclose(np.asarray(shifts), np.asarray(expected), atol=1e-12) + + +def _crra_value_row(*, coh: Float1D, level: float) -> Float1D: + """A concave, increasing synthetic value row plus a constant `level`.""" + return jnp.sqrt(coh) + level + + +def _identity_marginal(*, coh: Float1D) -> Float1D: + """A positive, decreasing marginal row consistent with `sqrt` curvature.""" + return 0.5 / jnp.sqrt(coh) + + +def test_adjuster_winning_by_delta_lifts_the_envelope_by_delta() -> None: + """An adjuster that beats the keeper by `delta` lifts the carry by `delta`. + + One durable state, one keeper row, one adjuster row. The adjuster's value is + the keeper's plus a constant `delta` over a reachable coh interval, so the + upper envelope must equal the adjuster there: reading the published carry at + a coh in that interval returns the keeper value plus `delta`. + """ + n_pad = 40 + coh = jnp.linspace(1.0, 9.0, n_pad) + delta = 0.25 + + keeper = EGMCarry( + endog_grid=coh[None, :], + value=_crra_value_row(coh=coh, level=0.0)[None, :], + marginal_utility=_identity_marginal(coh=coh)[None, :], + taste_shock_scale=jnp.asarray(0.0), + ) + # The adjuster's own resources grid is coh shifted down by its credited cost; + # the shift maps it back into coh space. Its value beats the keeper by delta. + shift = 2.0 + adjuster = EGMCarry( + endog_grid=(coh - shift)[None, :], + value=(_crra_value_row(coh=coh, level=delta))[None, :], + marginal_utility=_identity_marginal(coh=coh)[None, :], + taste_shock_scale=jnp.asarray(0.0), + ) + + carry = build_outer_envelope_carry( + keeper_carry=keeper, + adjuster_carries=(adjuster,), + coh_shifts=jnp.asarray([[shift]]), # one durable state, one adjuster + ) + + # The carry width grows by one island-peak slot per adjuster (here one). + assert carry.value.shape == (1, n_pad + 1) + query = jnp.asarray([3.0, 5.0, 7.0]) + enveloped = interp_on_padded_grid( + x_query=query, + xp=carry.endog_grid[0], + fp=carry.value[0], + fp_slopes=carry.marginal_utility[0], + ) + expected = jnp.sqrt(query) + delta + np.testing.assert_allclose(np.asarray(enveloped), np.asarray(expected), atol=2e-2) + + +def test_adjuster_winning_only_on_a_subinterval_is_captured() -> None: + """An adjuster winning only on a coh sub-interval lifts the envelope there. + + The adjuster beats the keeper by a hump centred in the coh range and is below + it at both ends. The published envelope must equal the keeper outside the + hump and the adjuster inside it, including at coh points strictly between the + keeper's grid nodes β€” a nodewise maximum at the keeper's abscissae would miss + the interior win. + """ + n_pad = 60 + coh = jnp.linspace(1.0, 9.0, n_pad) + # A hump peaking near coh = 5, negative at the ends: the adjuster wins only + # in the middle of the coh range. + hump = 0.5 - 0.08 * (coh - 5.0) ** 2 + keeper = EGMCarry( + endog_grid=coh[None, :], + value=_crra_value_row(coh=coh, level=0.0)[None, :], + marginal_utility=_identity_marginal(coh=coh)[None, :], + taste_shock_scale=jnp.asarray(0.0), + ) + shift = 2.0 + adjuster_value = jnp.sqrt(coh) + hump + adjuster = EGMCarry( + endog_grid=(coh - shift)[None, :], + value=adjuster_value[None, :], + marginal_utility=_identity_marginal(coh=coh)[None, :], + taste_shock_scale=jnp.asarray(0.0), + ) + + carry = build_outer_envelope_carry( + keeper_carry=keeper, + adjuster_carries=(adjuster,), + coh_shifts=jnp.asarray([[shift]]), + ) + + # An off-node query in the winning interior: the envelope must equal the + # adjuster (keeper + hump), strictly above the keeper. + interior = jnp.asarray([4.7, 5.3]) + enveloped_interior = interp_on_padded_grid( + x_query=interior, + xp=carry.endog_grid[0], + fp=carry.value[0], + fp_slopes=carry.marginal_utility[0], + ) + expected_interior = jnp.sqrt(interior) + (0.5 - 0.08 * (interior - 5.0) ** 2) + np.testing.assert_allclose( + np.asarray(enveloped_interior), np.asarray(expected_interior), atol=3e-2 + ) + assert bool(jnp.all(enveloped_interior > jnp.sqrt(interior))) + + # At the coh ends the keeper wins: the envelope equals the keeper value. + ends = jnp.asarray([1.5, 8.5]) + enveloped_ends = interp_on_padded_grid( + x_query=ends, + xp=carry.endog_grid[0], + fp=carry.value[0], + fp_slopes=carry.marginal_utility[0], + ) + np.testing.assert_allclose( + np.asarray(enveloped_ends), np.asarray(jnp.sqrt(ends)), atol=3e-2 + ) + + +def test_envelope_broadcasts_over_a_discrete_leading_axis() -> None: + """A discrete state ahead of the durable axis is enveloped cell-by-cell. + + When the inner DC-EGM carries a discrete/process state (a Markov wage), the + carry's leading axes are `(discrete, durable)` β€” the durable is the last + leading axis, the discrete one precedes it. The credited shift depends only + on the durable margin, so it broadcasts over the discrete axis, and the upper + envelope is taken independently per `(discrete, durable)` cell. The published + carry must keep the discrete axis (here two nodes at different value levels) + and lift each cell by the winning adjuster's gain, never mixing the two + discrete nodes. + """ + n_pad = 40 + n_discrete = 2 + coh = jnp.linspace(1.0, 9.0, n_pad) + delta = 0.25 + shift = 2.0 + # One durable state, two discrete nodes at value levels 0.0 and 1.0. + discrete_levels = jnp.asarray([0.0, 1.0]) + + keeper = EGMCarry( + endog_grid=jnp.broadcast_to(coh, (n_discrete, 1, n_pad)), + value=jnp.stack( + [_crra_value_row(coh=coh, level=lvl) for lvl in discrete_levels] + )[:, None, :], + marginal_utility=jnp.broadcast_to( + _identity_marginal(coh=coh), (n_discrete, 1, n_pad) + ), + taste_shock_scale=jnp.asarray(0.0), + ) + adjuster = EGMCarry( + endog_grid=jnp.broadcast_to(coh - shift, (n_discrete, 1, n_pad)), + value=jnp.stack( + [_crra_value_row(coh=coh, level=lvl + delta) for lvl in discrete_levels] + )[:, None, :], + marginal_utility=jnp.broadcast_to( + _identity_marginal(coh=coh), (n_discrete, 1, n_pad) + ), + taste_shock_scale=jnp.asarray(0.0), + ) + + carry = build_outer_envelope_carry( + keeper_carry=keeper, + adjuster_carries=(adjuster,), + coh_shifts=jnp.asarray([[shift]]), # one durable state, one adjuster + ) + + assert carry.value.shape == (n_discrete, 1, n_pad + 1) + query = jnp.asarray([3.0, 5.0, 7.0]) + for node in range(n_discrete): + enveloped = interp_on_padded_grid( + x_query=query, + xp=carry.endog_grid[node, 0], + fp=carry.value[node, 0], + fp_slopes=carry.marginal_utility[node, 0], + ) + expected = jnp.sqrt(query) + float(discrete_levels[node]) + delta + np.testing.assert_allclose( + np.asarray(enveloped), np.asarray(expected), atol=2e-2 + ) + + +def test_keeper_wins_when_no_adjuster_improves() -> None: + """With no adjuster beating the keeper, the carry reproduces the keeper. + + Every adjuster value lies strictly below the keeper, so the upper envelope is + the keeper row itself: reading the published carry returns the keeper value. + """ + n_pad = 40 + coh = jnp.linspace(1.0, 9.0, n_pad) + + keeper = EGMCarry( + endog_grid=coh[None, :], + value=_crra_value_row(coh=coh, level=0.0)[None, :], + marginal_utility=_identity_marginal(coh=coh)[None, :], + taste_shock_scale=jnp.asarray(0.0), + ) + shift = 2.0 + adjuster = EGMCarry( + endog_grid=(coh - shift)[None, :], + value=_crra_value_row(coh=coh, level=-0.5)[None, :], + marginal_utility=_identity_marginal(coh=coh)[None, :], + taste_shock_scale=jnp.asarray(0.0), + ) + + carry = build_outer_envelope_carry( + keeper_carry=keeper, + adjuster_carries=(adjuster,), + coh_shifts=jnp.asarray([[shift]]), + ) + + query = jnp.asarray([3.0, 5.0, 7.0]) + enveloped = interp_on_padded_grid( + x_query=query, + xp=carry.endog_grid[0], + fp=carry.value[0], + fp_slopes=carry.marginal_utility[0], + ) + expected = jnp.sqrt(query) + np.testing.assert_allclose(np.asarray(enveloped), np.asarray(expected), atol=2e-2) diff --git a/tests/solution/test_retirement_only_oracle.py b/tests/solution/test_retirement_only_oracle.py new file mode 100644 index 000000000..7722c507b --- /dev/null +++ b/tests/solution/test_retirement_only_oracle.py @@ -0,0 +1,51 @@ +"""The retirement-only model reproduces the full-model retired analytical solution. + +The `retirement` regime is absorbing, so a two-regime model (retirement + dead) +must yield the same retired value functions as the full Iskhakov et al. (2017) +model. This anchors the oracle that the DC-EGM concave tests compare against: +if this test holds, `iskhakov_2017_*__values_retired.csv` is a valid target for +any solver of the two-regime model. +""" + +import numpy as np +import pytest +from numpy.testing import assert_array_almost_equal as aaae + +from _lcm.config import TEST_DATA +from _lcm.typing import PeriodToRegimeToVArr +from tests.test_models.deterministic.retirement_only import get_model, get_params + +ANALYTICAL_CASES = { + "iskhakov_2017_five_periods": 6, + "iskhakov_2017_low_delta": 4, +} + + +def load_analytical_values_retired(case: str) -> np.ndarray: + return np.genfromtxt( + TEST_DATA.joinpath("analytical_solution", f"{case}__values_retired.csv"), + delimiter=",", + ) + + +def stack_retirement_V(period_to_regime_to_V_arr: PeriodToRegimeToVArr) -> np.ndarray: + periods = sorted(period_to_regime_to_V_arr)[:-1] + return np.stack( + [np.asarray(period_to_regime_to_V_arr[p]["retirement"]) for p in periods] + ) + + +@pytest.mark.parametrize(("case", "n_periods"), ANALYTICAL_CASES.items()) +def test_retirement_only_brute_force_matches_analytical(case, n_periods): + """Brute-force V of the two-regime model equals the analytical retired values.""" + model = get_model(n_periods) + params = get_params(n_periods, discount_factor=0.98, interest_rate=0.0) + + period_to_regime_to_V_arr = model.solve(params=params, log_level="debug") + + numerical = stack_retirement_V(period_to_regime_to_V_arr) + analytical = load_analytical_values_retired(case) + mse = np.mean((analytical - numerical) ** 2, axis=0) + # Same tolerance as the full-model analytical test: the brute-force solution is + # unstable at the two lowest wealth levels, so they are excluded. + aaae(mse[2:], 0, decimal=1) diff --git a/tests/solution/test_rfc.py b/tests/solution/test_rfc.py new file mode 100644 index 000000000..4be0c7e2b --- /dev/null +++ b/tests/solution/test_rfc.py @@ -0,0 +1,395 @@ +"""Spec for the RFC upper-envelope kernel (Dobrescu & Shanker, Box 1). + +Contract under test β€” `_lcm.egm.upper_envelope.rfc.refine_envelope`: + + refine_envelope( + *, + endog_grid: Float1D, # candidate resources points (any order) + policy: Float1D, + value: Float1D, + marginal_utility: Float1D, # candidate supgradient mu = dv/dR + n_refined: int, # static output length + search_radius: int = 10, + jump_thresh: float = 2.0, + ) -> tuple[Float1D, Float1D, Float1D, ScalarInt] + +The Rooftop-Cut (RFC) algorithm builds, at each candidate $j$, the tangent +(value) line from the local supgradient $\\mu_j = \\partial v / \\partial R$ +and deletes every neighbor $l$ within `search_radius` that lies *below* $j$'s +tangent *and* sits across a policy jump (the segment-switch test). The +survivors form the upper envelope. + +Unlike FUES, RFC only *deletes* candidates β€” it never inserts the exact +segment-crossing point. So the refined output is a NaN-padded weakly-ascending +*subset* of the input candidates: the dominated points are gone, the +upper-envelope points are retained, and a kink lands between two retained +points (recovered by the downstream linear/Hermite carry read to within local +grid spacing). + +Assertions are therefore about *which candidates survive*, not about an +inserted kink abscissa. +""" + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.egm.interp import interp_on_padded_grid +from _lcm.egm.upper_envelope import get_bracket_finder, get_upper_envelope +from lcm import LinSpacedGrid +from lcm.solvers import DCEGM +from tests.conftest import X64_ENABLED + +# Interpolated bracket reads are float-eps-limited at the active precision. +_BRACKET_ATOL = 1e-10 if X64_ENABLED else 1e-5 +_GRID_ATOL = 1e-12 if X64_ENABLED else 1e-5 + + +def _rfc_solver(): + return DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=LinSpacedGrid(start=0.0, stop=10.0, n_points=5), + upper_envelope="rfc", + ) + + +rfc = pytest.importorskip( + "_lcm.egm.upper_envelope.rfc", reason="RFC kernel not yet implemented" +) + + +def _drop_nan(arr: jnp.ndarray) -> np.ndarray: + out = np.asarray(arr) + return out[~np.isnan(out)] + + +def _crossing_segments_candidates(): + """Two linear choice-specific value segments crossing at R* = 2.25. + + - Segment A: v = 1.0 + 0.4 R, c = 0.30 R β€” optimal for R < 2.25. + - Segment B: v = 0.1 + 0.8 R, c = 0.55 R β€” optimal for R > 2.25. + + Candidate points interleave both segments, as the Euler inversion produces + them in non-concave regions. Below R*, the segment-B points are dominated; + above R*, the segment-A points are. The supgradient $\\mu = \\partial v / + \\partial R$ is each segment's constant value slope (0.4 / 0.8). + """ + r_a = np.array([0.6, 1.2, 1.8, 2.4]) + r_b = np.array([0.8, 1.6, 2.6, 3.4]) + grid = np.concatenate([r_a, r_b]) + value = np.concatenate([1.0 + 0.4 * r_a, 0.1 + 0.8 * r_b]) + policy = np.concatenate([0.30 * r_a, 0.55 * r_b]) + marginal = np.concatenate([np.full_like(r_a, 0.4), np.full_like(r_b, 0.8)]) + return ( + jnp.asarray(grid), + jnp.asarray(policy), + jnp.asarray(value), + jnp.asarray(marginal), + ) + + +R_STAR = 2.25 + + +def test_concave_input_passes_through_unchanged(): + """A monotone-concave single segment is returned as-is (sorted, no deletions).""" + grid = jnp.linspace(1.0, 10.0, 10) + policy = 0.3 * grid + value = jnp.log(grid) + marginal = 1.0 / grid + + got_grid, got_policy, got_value, n_kept = rfc.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + n_refined=14, + ) + + assert int(n_kept) == 10 + np.testing.assert_allclose(_drop_nan(got_grid), np.asarray(grid), atol=1e-12) + np.testing.assert_allclose(_drop_nan(got_policy), np.asarray(policy), atol=1e-12) + np.testing.assert_allclose(_drop_nan(got_value), np.asarray(value), atol=1e-12) + + +def test_steep_but_continuous_policy_is_not_treated_as_a_switch(): + """`|Ξ”c/Ξ”R|` just below the threshold leaves a single segment untouched.""" + grid = jnp.linspace(1.0, 5.0, 9) + # c = 5 - 0.9 R: |Ξ”c/Ξ”R| = 0.9 < 2, so no segment switch is detected. + policy = 5.0 - 0.9 * grid + value = jnp.log(grid) + marginal = 1.0 / grid + + _, _, _, n_kept = rfc.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + n_refined=12, + ) + + assert int(n_kept) == 9 + + +def test_crossing_segments_retain_only_the_upper_envelope_subset(): + """RFC keeps exactly the upper-envelope candidates and deletes the dominated. + + No crossing point is inserted, so the retained grid is the subset of input + points that lie on the upper envelope: segment-A points below R* and + segment-B points above R*. + """ + grid, policy, value, marginal = _crossing_segments_candidates() + + got_grid, _, _, _ = rfc.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + n_refined=12, + jump_thresh=0.6, + ) + + clean_grid = np.sort(_drop_nan(got_grid)) + # Surviving upper-envelope points: A below R*, B above R*. + expected = np.array([0.6, 1.2, 1.8, 2.6, 3.4]) + np.testing.assert_allclose(clean_grid, expected, atol=1e-8) + + +def test_crossing_segments_drop_dominated_points(): + """Candidates strictly below the envelope do not survive refinement.""" + grid, policy, value, marginal = _crossing_segments_candidates() + + got_grid, _, _, _ = rfc.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + n_refined=12, + jump_thresh=0.6, + ) + + clean_grid = _drop_nan(got_grid) + # Below R*: segment-B points 0.8, 1.6 are dominated. Above R*: segment-A + # point 2.4 is dominated. + for dominated in [0.8, 1.6, 2.4]: + assert not np.any(np.isclose(clean_grid, dominated, atol=1e-8)) + + +def test_no_crossing_point_is_inserted(): + """RFC never inserts the segment-crossing abscissa R* (it only deletes).""" + grid, policy, value, marginal = _crossing_segments_candidates() + + got_grid, _, _, _ = rfc.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + n_refined=12, + jump_thresh=0.6, + ) + + clean_grid = _drop_nan(got_grid) + assert not np.any(np.isclose(clean_grid, R_STAR, atol=1e-6)) + + +def test_value_decreasing_point_is_dropped(): + """A single interior dominated point (value dip) is removed.""" + grid = jnp.array([1.0, 2.0, 3.0]) + policy = jnp.array([0.5, 1.8, 1.5]) + value = jnp.array([1.0, 0.9, 2.0]) + # Supgradient: 1->3 the value rises (slope ~0.5); the dip at 2 sits below + # both neighbours' tangents and across a policy jump. + marginal = jnp.array([0.5, 0.5, 0.5]) + + got_grid, _, _, _ = rfc.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + n_refined=6, + jump_thresh=0.5, + ) + + clean_grid = _drop_nan(got_grid) + assert not np.any(np.isclose(clean_grid, 2.0, atol=1e-8)) + + +def test_neg_inf_value_candidates_stay_deleted(): + """A `-inf`/NaN candidate is dominated by every finite point and dropped. + + Dead candidates arrive as NaN-filled triples (the EGM step poisons + `-inf`-valued candidates to NaN before refinement); the dominance test + must keep them out of the envelope and out of the kept count. + """ + grid = jnp.array([1.0, 2.0, 3.0, 4.0]) + policy = jnp.array([0.5, 1.0, 1.5, 2.0]) + value = jnp.array([1.0, jnp.nan, 2.0, 2.5]) + marginal = jnp.array([0.5, 0.0, 0.5, 0.5]) + + got_grid, _, got_value, n_kept = rfc.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + n_refined=8, + ) + + clean_grid = _drop_nan(got_grid) + assert not np.any(np.isclose(clean_grid, 2.0, atol=1e-8)) + assert int(n_kept) == 3 + assert not np.any(np.isnan(_drop_nan(got_value))) + + +def test_refined_grid_is_weakly_ascending_with_nan_tail(): + """Non-NaN prefix is weakly ascending; NaNs appear only as a suffix.""" + grid, policy, value, marginal = _crossing_segments_candidates() + + got_grid, _, _, _ = rfc.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + n_refined=12, + jump_thresh=0.6, + ) + + raw = np.asarray(got_grid) + nan_mask = np.isnan(raw) + first_nan = nan_mask.argmax() if nan_mask.any() else raw.size + assert not nan_mask[:first_nan].any() + assert nan_mask[first_nan:].all() + assert np.all(np.diff(raw[:first_nan]) >= -1e-12) + + +def test_vmap_over_rows_matches_per_row_calls(): + """The kernel is vmappable; batched output equals per-row output.""" + grid, policy, value, marginal = _crossing_segments_candidates() + batched = jax.vmap( + lambda g, p, v, m: rfc.refine_envelope( + endog_grid=g, policy=p, value=v, marginal_utility=m, n_refined=12 + ) + )( + jnp.stack([grid, grid]), + jnp.stack([policy, policy]), + jnp.stack([value, value]), + jnp.stack([marginal, marginal]), + ) + single = rfc.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + n_refined=12, + ) + + for batched_arr, single_arr in zip(batched, single, strict=True): + np.testing.assert_array_equal( + np.asarray(batched_arr[0]), np.asarray(single_arr) + ) + + +def test_overflow_is_reported_via_n_kept(): + """When the envelope needs more slots than `n_refined`, `n_kept` says so.""" + grid = jnp.linspace(1.0, 10.0, 10) + policy = 0.3 * grid + value = jnp.log(grid) + marginal = 1.0 / grid + + _, _, _, n_kept = rfc.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + n_refined=4, + ) + + assert int(n_kept) > 4 + + +def test_rfc_backend_is_selected_by_solver_config(): + """`upper_envelope="rfc"` dispatches to the RFC backend. + + The backend selected for an `rfc` solver must reproduce the standalone + RFC kernel on a non-concave candidate set, while `"fues"` stays on FUES. + """ + solver = _rfc_solver() + backend = get_upper_envelope(solver=solver, n_refined=12) + + grid, policy, value, marginal = _crossing_segments_candidates() + via_backend = backend( + endog_grid=grid, policy=policy, value=value, marginal_utility=marginal + ) + direct = rfc.refine_envelope( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + n_refined=12, + search_radius=solver.rfc_search_radius, + jump_thresh=solver.rfc_jump_thresh, + ) + for via_arr, direct_arr in zip(via_backend, direct, strict=True): + np.testing.assert_array_equal(np.asarray(via_arr), np.asarray(direct_arr)) + + +@pytest.mark.parametrize("x_query", [0.5, 1.0, 2.0, R_STAR, 3.0, 4.0]) +def test_rfc_bracket_finder_matches_full_envelope_interpolation(x_query): + """The non-streamed RFC bracket reads identically to the full refined row. + + The asset-row solve reads the refined envelope at one query per node. RFC + has no streamed bracket finder, so `get_bracket_finder` materializes the + full envelope and locates the `searchsorted(side="right")` bracket. The + bracket's interior interpolation must equal `interp_on_padded_grid` on the + full refined row at every query β€” below the first node, on the kink, and + above the last β€” so a full-envelope-then-interpolate and the bracket read + publish the same `(value, policy)`. + """ + solver = _rfc_solver() + grid, policy, value, marginal = _crossing_segments_candidates() + n_pad = 12 + + refined_grid, refined_policy, refined_value, n_kept = get_upper_envelope( + solver=solver, n_refined=n_pad + )(endog_grid=grid, policy=policy, value=value, marginal_utility=marginal) + + query = jnp.asarray(x_query) + ref_value = interp_on_padded_grid(x_query=query, xp=refined_grid, fp=refined_value) + ref_policy = interp_on_padded_grid( + x_query=query, xp=refined_grid, fp=refined_policy + ) + + bracket = get_bracket_finder(solver=solver, n_refined=n_pad)( + endog_grid=grid, + policy=policy, + value=value, + marginal_utility=marginal, + x_query=query, + ) + + width = jnp.where( + bracket.upper_grid == bracket.lower_grid, + 1.0, + bracket.upper_grid - bracket.lower_grid, + ) + weight = jnp.clip((query - bracket.lower_grid) / width, 0.0, 1.0) + bracket_value = bracket.lower_value + weight * ( + bracket.upper_value - bracket.lower_value + ) + bracket_policy = bracket.lower_policy + weight * ( + bracket.upper_policy - bracket.lower_policy + ) + + np.testing.assert_allclose( + float(bracket_value), float(ref_value), atol=_BRACKET_ATOL + ) + np.testing.assert_allclose( + float(bracket_policy), float(ref_policy), atol=_BRACKET_ATOL + ) + assert int(bracket.n_kept) == int(n_kept) + np.testing.assert_allclose( + float(bracket.first_grid), float(refined_grid[0]), atol=_GRID_ATOL + ) diff --git a/tests/solution/test_rfc_2d_host.py b/tests/solution/test_rfc_2d_host.py new file mode 100644 index 000000000..9b2e44ea2 --- /dev/null +++ b/tests/solution/test_rfc_2d_host.py @@ -0,0 +1,119 @@ +"""The host (NumPy/SciPy) 2-D RFC reference behaves as Dobrescu-Shanker Box 1. + +These tests pin the off-device ground truth that the on-device multidimensional RFC +backend is validated against: the tangent-dominance cut spares concave segments, +cuts a dominated branch across a policy jump, and the Delaunay publisher reproduces +survivor values exactly inside the hull with a nearest fallback outside it. +""" + +import numpy as np + +from tests.solution._rfc_2d_host import ( + rfc_delete_mask, + rfc_publish, +) + + +def test_affine_cloud_survives_the_cut_intact(): + """A cloud sampled from an affine value with constant policy loses no points. + + Every neighbour lies exactly on every other point's tangent plane (not strictly + below it) and no policy jump exists, so the cut deletes nothing. + """ + xs, ys = np.meshgrid(np.linspace(0.0, 0.4, 5), np.linspace(0.0, 0.4, 5)) + states = np.column_stack([xs.ravel(), ys.ravel()]) + slope = np.array([1.3, -0.7]) + values = states @ slope + 2.0 + supgradients = np.tile(slope, (states.shape[0], 1)) + policies = np.zeros((states.shape[0], 1)) + + keep = rfc_delete_mask( + states=states, supgradients=supgradients, values=values, policies=policies + ) + + assert keep.all() + + +def test_concave_segment_without_a_policy_jump_survives(): + """A single concave segment keeps every point β€” the jump gate spares concavity. + + On a concave surface every neighbour lies below its neighbours' tangents, but + with a smoothly varying policy (no discontinuity) the jump gate is never tripped, + so nothing is deleted. + """ + xs, ys = np.meshgrid(np.linspace(0.0, 0.4, 5), np.linspace(0.0, 0.4, 5)) + states = np.column_stack([xs.ravel(), ys.ravel()]) + values = -(states[:, 0] ** 2 + states[:, 1] ** 2) + supgradients = np.column_stack([-2.0 * states[:, 0], -2.0 * states[:, 1]]) + # Policy varies slowly: |dsigma| / dist stays well below the jump threshold. + policies = (0.01 * states[:, 0]).reshape(-1, 1) + + keep = rfc_delete_mask( + states=states, supgradients=supgradients, values=values, policies=policies + ) + + assert keep.all() + + +def test_dominated_branch_across_a_policy_jump_is_cut(): + """A lower branch below the upper's tangent across a policy jump is deleted. + + Two flat branches sit close in state: an upper branch (value 1, policy 0) and a + lower branch (value 0.5, policy 10) a short distance away. From each upper point + the nearby lower point lies below its (flat) tangent and across a large policy + jump within the radius, so every lower point is cut; the upper points, which lie + above the lower tangents, all survive. + """ + upper = np.array([[0.0, 0.0], [0.2, 0.0], [0.4, 0.0]]) + lower = np.array([[0.0, 0.05], [0.2, 0.05], [0.4, 0.05]]) + states = np.vstack([upper, lower]) + values = np.array([1.0, 1.0, 1.0, 0.5, 0.5, 0.5]) + supgradients = np.zeros((6, 2)) + policies = np.array([0.0, 0.0, 0.0, 10.0, 10.0, 10.0]).reshape(-1, 1) + + keep = rfc_delete_mask( + states=states, supgradients=supgradients, values=values, policies=policies + ) + + np.testing.assert_array_equal(keep, [True, True, True, False, False, False]) + + +def test_publish_reproduces_survivor_values_and_interpolates_linearly(): + """The Delaunay publisher reproduces survivor values and is linear in the hull. + + With survivors sampled from `V = x + y` and policy `p = 2x`, a query at a survivor + returns that survivor's value exactly, and a query at the cell centre returns the + linear interpolant. + """ + survivor_states = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]) + survivor_values = survivor_states[:, 0] + survivor_states[:, 1] + survivor_policies = (2.0 * survivor_states[:, 0]).reshape(-1, 1) + targets = np.array([[0.0, 0.0], [0.5, 0.5]]) + + values, policies = rfc_publish( + survivor_states=survivor_states, + survivor_values=survivor_values, + survivor_policies=survivor_policies, + target_states=targets, + ) + + np.testing.assert_allclose(values, [0.0, 1.0], atol=1e-9) + np.testing.assert_allclose(policies[:, 0], [0.0, 1.0], atol=1e-9) + + +def test_publish_falls_back_to_nearest_survivor_outside_the_hull(): + """A target outside the survivor convex hull takes the nearest survivor's value.""" + survivor_states = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]) + survivor_values = np.array([0.0, 1.0, 1.0, 2.0]) + survivor_policies = np.array([0.0, 1.0, 1.0, 2.0]).reshape(-1, 1) + targets = np.array([[5.0, 5.0]]) + + values, policies = rfc_publish( + survivor_states=survivor_states, + survivor_values=survivor_values, + survivor_policies=survivor_policies, + target_states=targets, + ) + + np.testing.assert_allclose(values, [2.0], atol=1e-9) + np.testing.assert_allclose(policies[:, 0], [2.0], atol=1e-9) diff --git a/tests/solution/test_rfc_2d_kernel.py b/tests/solution/test_rfc_2d_kernel.py new file mode 100644 index 000000000..bf7515950 --- /dev/null +++ b/tests/solution/test_rfc_2d_kernel.py @@ -0,0 +1,83 @@ +"""The on-device 2-D RFC delete kernel matches the host reference mask exactly. + +The JAX kernel computes k-NN neighbours by a dense pairwise `top_k` rather than a host +KD-tree, so these tests pin that it reproduces the host reference's keep-mask +(`tests/solution/_rfc_2d_host.py`) bit-for-bit on the canonical clouds and on a random +two-branch cloud β€” the gate that lets the kernel stand in for the reference on device. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.egm.upper_envelope.rfc_2d import rfc_delete_mask_2d +from tests.solution._rfc_2d_host import rfc_delete_mask + + +def _affine_cloud(): + xs, ys = np.meshgrid(np.linspace(0.0, 0.4, 5), np.linspace(0.0, 0.4, 5)) + states = np.column_stack([xs.ravel(), ys.ravel()]) + slope = np.array([1.3, -0.7]) + values = states @ slope + 2.0 + supgradients = np.tile(slope, (states.shape[0], 1)) + policies = np.zeros((states.shape[0], 1)) + return states, supgradients, values, policies + + +def _concave_cloud(): + xs, ys = np.meshgrid(np.linspace(0.0, 0.4, 5), np.linspace(0.0, 0.4, 5)) + states = np.column_stack([xs.ravel(), ys.ravel()]) + values = -(states[:, 0] ** 2 + states[:, 1] ** 2) + supgradients = np.column_stack([-2.0 * states[:, 0], -2.0 * states[:, 1]]) + policies = (0.01 * states[:, 0]).reshape(-1, 1) + return states, supgradients, values, policies + + +def _dominated_branch_cloud(): + upper = np.array([[0.0, 0.0], [0.2, 0.0], [0.4, 0.0]]) + lower = np.array([[0.0, 0.05], [0.2, 0.05], [0.4, 0.05]]) + states = np.vstack([upper, lower]) + values = np.array([1.0, 1.0, 1.0, 0.5, 0.5, 0.5]) + supgradients = np.zeros((6, 2)) + policies = np.array([0.0, 0.0, 0.0, 10.0, 10.0, 10.0]).reshape(-1, 1) + return states, supgradients, values, policies + + +def _random_two_branch_cloud(): + rng = np.random.default_rng(20260624) + base = rng.uniform(0.0, 1.0, size=(40, 2)) + # An upper branch (policy 0) and a lower, dominated branch (policy 5) sharing the + # same state support so neighbours straddle the policy jump. + states = np.vstack([base, base + np.array([0.0, 0.01])]) + values = np.concatenate([base.sum(axis=1), base.sum(axis=1) - 0.3]) + supgradients = np.tile(np.array([1.0, 1.0]), (states.shape[0], 1)) + policies = np.concatenate([np.zeros(40), np.full(40, 5.0)]).reshape(-1, 1) + return states, supgradients, values, policies + + +@pytest.mark.parametrize( + "cloud", + [ + _affine_cloud, + _concave_cloud, + _dominated_branch_cloud, + _random_two_branch_cloud, + ], +) +def test_kernel_keep_mask_matches_host_reference(cloud): + """The JAX kernel's keep-mask equals the host KD-tree reference's keep-mask.""" + states, supgradients, values, policies = cloud() + + host_keep = rfc_delete_mask( + states=states, supgradients=supgradients, values=values, policies=policies + ) + kernel_keep = np.asarray( + rfc_delete_mask_2d( + states=jnp.asarray(states), + supgradients=jnp.asarray(supgradients), + values=jnp.asarray(values), + policies=jnp.asarray(policies), + ) + ) + + np.testing.assert_array_equal(kernel_keep, host_keep) diff --git a/tests/solution/test_rfc_2d_publisher.py b/tests/solution/test_rfc_2d_publisher.py new file mode 100644 index 000000000..164396dba --- /dev/null +++ b/tests/solution/test_rfc_2d_publisher.py @@ -0,0 +1,115 @@ +"""The on-device 2-D RFC publisher is affine-exact and agrees with host Delaunay. + +The local-simplex barycentric publisher is the on-device stand-in for the host Delaunay +reference (D1 of the P6 design). These tests pin that it reproduces survivor values +exactly, is affine-exact inside the survivor hull (matching both the analytic linear +ground truth and the host Delaunay publisher), and falls back to the nearest survivor +outside the hull. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.upper_envelope.rfc_2d import rfc_publish_2d +from tests.solution._rfc_2d_host import rfc_publish as rfc_publish_host + +SLOPE = np.array([1.3, -0.7]) + + +def _linear_survivor_grid(): + xs, ys = np.meshgrid(np.linspace(0.0, 1.0, 5), np.linspace(0.0, 1.0, 5)) + states = np.column_stack([xs.ravel(), ys.ravel()]) + values = states @ SLOPE + 2.0 + policies = (2.0 * states[:, 0] + states[:, 1]).reshape(-1, 1) + return states, values, policies + + +def _publish_kernel(states, values, policies, targets): + out_values, out_policies = rfc_publish_2d( + survivor_states=jnp.asarray(states), + survivor_values=jnp.asarray(values), + survivor_policies=jnp.asarray(policies), + target_states=jnp.asarray(targets), + ) + return np.asarray(out_values), np.asarray(out_policies) + + +def test_publisher_reproduces_survivor_values_at_survivor_locations(): + """Querying at a survivor returns that survivor's value and policy exactly.""" + states, values, policies = _linear_survivor_grid() + targets = states[[0, 7, 12, 24]] + + out_values, out_policies = _publish_kernel(states, values, policies, targets) + + np.testing.assert_allclose(out_values, values[[0, 7, 12, 24]], atol=1e-9) + np.testing.assert_allclose( + out_policies[:, 0], policies[[0, 7, 12, 24], 0], atol=1e-9 + ) + + +def test_publisher_is_affine_exact_and_matches_host_delaunay(): + """Inside the hull the publisher reproduces the linear field and the host oracle.""" + states, values, policies = _linear_survivor_grid() + targets = np.array([[0.25, 0.25], [0.4, 0.6], [0.7, 0.3], [0.55, 0.55]]) + analytic_values = targets @ SLOPE + 2.0 + analytic_policies = 2.0 * targets[:, 0] + targets[:, 1] + + out_values, out_policies = _publish_kernel(states, values, policies, targets) + host_values, host_policies = rfc_publish_host( + survivor_states=states, + survivor_values=values, + survivor_policies=policies, + target_states=targets, + ) + + np.testing.assert_allclose(out_values, analytic_values, atol=1e-9) + np.testing.assert_allclose(out_policies[:, 0], analytic_policies, atol=1e-9) + np.testing.assert_allclose(out_values, host_values, atol=1e-9) + np.testing.assert_allclose(out_policies[:, 0], host_policies[:, 0], atol=1e-9) + + +def test_publisher_valid_mask_excludes_deleted_candidates(): + """Publishing the full cloud with a keep-mask ignores the deleted candidates. + + The jit-friendly form passes every candidate plus the cut's keep-mask. Corrupt + candidates marked invalid must never enter a target's neighbourhood or a triangle, + so the published field still reproduces the linear ground truth carried by the + valid candidates. + """ + states, values, policies = _linear_survivor_grid() + corrupt_states = np.array([[0.3, 0.3], [0.5, 0.4], [0.6, 0.6]]) + corrupt_values = np.array([99.0, -99.0, 99.0]) + corrupt_policies = np.array([99.0, 99.0, 99.0]).reshape(-1, 1) + all_states = np.vstack([states, corrupt_states]) + all_values = np.concatenate([values, corrupt_values]) + all_policies = np.vstack([policies, corrupt_policies]) + valid = np.concatenate([np.ones(len(states), bool), np.zeros(3, bool)]) + targets = np.array([[0.25, 0.25], [0.4, 0.6], [0.55, 0.55]]) + analytic_values = targets @ SLOPE + 2.0 + + out_values, out_policies = rfc_publish_2d( + survivor_states=jnp.asarray(all_states), + survivor_values=jnp.asarray(all_values), + survivor_policies=jnp.asarray(all_policies), + target_states=jnp.asarray(targets), + valid=jnp.asarray(valid), + ) + + np.testing.assert_allclose(np.asarray(out_values), analytic_values, atol=1e-9) + np.testing.assert_allclose( + np.asarray(out_policies)[:, 0], + 2.0 * targets[:, 0] + targets[:, 1], + atol=1e-9, + ) + + +def test_publisher_falls_back_to_nearest_survivor_outside_the_hull(): + """A target outside the survivor hull takes the nearest survivor's value/policy.""" + states, values, policies = _linear_survivor_grid() + targets = np.array([[5.0, 5.0]]) + nearest = int(np.argmin(np.linalg.norm(states - targets[0], axis=1))) + + out_values, out_policies = _publish_kernel(states, values, policies, targets) + + np.testing.assert_allclose(out_values, [values[nearest]], atol=1e-9) + np.testing.assert_allclose(out_policies[:, 0], [policies[nearest, 0]], atol=1e-9) diff --git a/tests/solution/test_rfc_fues_parity.py b/tests/solution/test_rfc_fues_parity.py new file mode 100644 index 000000000..5199d363c --- /dev/null +++ b/tests/solution/test_rfc_fues_parity.py @@ -0,0 +1,222 @@ +"""C1 acceptance: the RFC backend reproduces FUES on the DC-EGM battery. + +The Rooftop-Cut backend (`upper_envelope="rfc"`) must produce the same value +function as the Fast Upper-Envelope Scan (`upper_envelope="fues"`) on the +existing DC-EGM solve tests, within a documented tolerance. + +Why a tolerance and not bit-identity: RFC *only deletes* dominated candidates; +it never inserts the exact segment-crossing abscissa that FUES duplicates into +its refined rows. A kink therefore lands between two retained RFC points +instead of exactly on the crossing, so the downstream Hermite carry read +recovers it to within the local grid spacing β€” a second-order error given the +exact-slope ($\\mu = \\partial v / \\partial R$) supgradient reads. On a +concave segment (no crossing) the two backends agree to machine precision; the +tolerance only absorbs the kink-placement delta where a discrete choice +switches. Where the two backends meet brute-force-unstable low-wealth nodes, +those nodes are excluded exactly as the underlying FUES tests do. +""" + +import dataclasses + +import jax.numpy as jnp +import numpy as np +import pytest + +from lcm import AgeGrid, MarkovTransition, Model +from lcm.typing import BoolND, DiscreteAction +from lcm_examples.iskhakov_et_al_2017 import dead +from tests.test_models.deterministic import base, retirement_only +from tests.test_models.deterministic.dcegm_variants import ( + dcegm_retirement, + dcegm_retirement_full, + dcegm_working_life, + get_full_params, + get_retirement_only_params, +) + +# The no-crossing-insertion delta is a kink-placement error of order the local +# grid spacing, propagated through the exact-slope Hermite carry. On the +# cubically clustered savings grid the retirement battery uses, that bounds the +# per-node V difference between the backends well inside this tolerance. +_PARITY_ATOL = 5e-3 +_PARITY_RTOL = 1e-3 + + +def _with_backend(regime, *, upper_envelope): + """Rebuild a DC-EGM regime with the chosen upper-envelope backend.""" + solver = dataclasses.replace(regime.solver, upper_envelope=upper_envelope) + return regime.replace(solver=solver) + + +def _retirement_only_model(*, upper_envelope, n_periods): + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "retirement": _with_backend( + dcegm_retirement, upper_envelope=upper_envelope + ).replace(active=lambda age, la=last_age: age < la), + "dead": dead, + }, + ages=ages, + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + + +def _full_model(*, upper_envelope, n_periods): + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "working_life": _with_backend( + dcegm_working_life, upper_envelope=upper_envelope + ).replace(active=lambda age, la=last_age: age < la), + "retirement": _with_backend( + dcegm_retirement_full, upper_envelope=upper_envelope + ).replace(active=lambda age, la=last_age: age < la), + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + + +@pytest.mark.parametrize("n_periods", [3, 5]) +def test_rfc_matches_fues_on_concave_retirement(n_periods): + """The pure-concave retirement solve agrees between RFC and FUES. + + No discrete choice means no segment crossing, so the two backends refine + the same candidate set identically β€” agreement holds tightly on every + wealth node. + """ + params = get_retirement_only_params(n_periods) + + fues = _retirement_only_model(upper_envelope="fues", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + rfc = _retirement_only_model(upper_envelope="rfc", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + + for period in sorted(fues)[:-1]: + np.testing.assert_allclose( + np.asarray(rfc[period]["retirement"]), + np.asarray(fues[period]["retirement"]), + atol=_PARITY_ATOL, + rtol=_PARITY_RTOL, + err_msg=f"period={period}", + ) + + +def _nothing_is_feasible(labor_supply: DiscreteAction) -> BoolND: + return jnp.zeros_like(labor_supply, dtype=bool) + + +def test_rfc_publishes_neg_inf_for_all_infeasible_combo_like_fues(): + """An all-infeasible worker regime publishes `-inf` V under RFC too. + + A discrete-only constraint false everywhere makes the worker's value `-inf` + at every state; the dead candidates must stay deleted from the dominance + test (`-inf`/NaN poisoning discipline), so RFC publishes `-inf` exactly as + FUES does, never NaN. + """ + n_periods = 4 + retirement_transition = { + "retirement": MarkovTransition( + lambda age, final_age_alive: jnp.where(age >= final_age_alive, 0.0, 1.0) + ), + "dead": MarkovTransition( + lambda age, final_age_alive: jnp.where(age >= final_age_alive, 1.0, 0.0) + ), + } + + def build(upper_envelope): + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + return Model( + regimes={ + "working_life": _with_backend( + dcegm_working_life, upper_envelope=upper_envelope + ).replace( + constraints={"nothing_is_feasible": _nothing_is_feasible}, + active=lambda age: age < 70, + ), + "retirement": _with_backend( + dcegm_retirement_full, upper_envelope=upper_envelope + ).replace( + transition=retirement_transition, + state_transitions={ + "wealth": dcegm_retirement_full.state_transitions["wealth"], + }, + active=lambda age: age < 70, + ), + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + + params = get_full_params(n_periods, discount_factor=0.98, wage=20.0) + rfc = build("rfc").solve(params=params, log_level="debug") + + for period in sorted(rfc)[:-1]: + working_V = np.asarray(rfc[period]["working_life"]) + assert bool(np.isneginf(working_V).all()), f"period={period}" + assert bool(np.isfinite(rfc[period]["retirement"]).all()) + + +@pytest.mark.parametrize("n_periods", [4]) +def test_rfc_matches_fues_on_discrete_choice_working_life(n_periods): + """The work/retire discrete-choice solve agrees between RFC and FUES. + + The labour-supply choice creates a non-concave kink in the worker's value + correspondence. FUES inserts the exact crossing; RFC retains the bracketing + points and lets the Hermite carry recover the kink. The published value + functions agree within the no-insertion tolerance on the wealth nodes where + both are well-defined. + """ + params = get_full_params(n_periods, discount_factor=0.98, wage=20.0) + + fues = _full_model(upper_envelope="fues", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + rfc = _full_model(upper_envelope="rfc", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + + n_unstable_low_nodes = 10 + for period in sorted(fues)[:-1]: + for regime in ["working_life", "retirement"]: + np.testing.assert_allclose( + np.asarray(rfc[period][regime])[..., n_unstable_low_nodes:], + np.asarray(fues[period][regime])[..., n_unstable_low_nodes:], + atol=_PARITY_ATOL, + rtol=_PARITY_RTOL, + err_msg=f"period={period}, regime={regime}", + ) + + +def test_rfc_handles_discount_factor_zero_like_fues(): + """The Ξ²=0 consume-everything degenerate solves identically under RFC. + + With a zero discount factor every savings node's marginal continuation is + zero, so the consume-everything corner wins at every wealth node. Both + backends must publish the same value row. + """ + n_periods = 3 + params = get_retirement_only_params(n_periods, discount_factor=0.0) + + fues = _retirement_only_model(upper_envelope="fues", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + rfc = _retirement_only_model(upper_envelope="rfc", n_periods=n_periods).solve( + params=params, log_level="debug" + ) + + for period in sorted(fues)[:-1]: + np.testing.assert_allclose( + np.asarray(rfc[period]["retirement"]), + np.asarray(fues[period]["retirement"]), + atol=_PARITY_ATOL, + rtol=_PARITY_RTOL, + err_msg=f"period={period}", + ) diff --git a/tests/solution/test_rfc_two_asset_kkt.py b/tests/solution/test_rfc_two_asset_kkt.py new file mode 100644 index 000000000..728a5b3d9 --- /dev/null +++ b/tests/solution/test_rfc_two_asset_kkt.py @@ -0,0 +1,46 @@ +"""2-D RFC region clouds must carry a KKT validity mask. + +Each of the four region inverses (ucon/dcon/acon/con) solves the first-order +conditions *assuming* its own constraints bind. The solution is a genuine +candidate only where that region's complementary-slackness inequalities also +hold; elsewhere the formula still returns a finite point that is not a KKT +solution. The RFC selection currently filters candidates by finiteness alone, so +a KKT-inconsistent candidate can enter the rooftop-cut cloud and dominate a +valid one. Each region cloud must therefore expose a `valid_region` mask +enforcing its own inequalities. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.two_asset_inverse import invert_dcon_cloud + + +def test_dcon_cloud_flags_kkt_inconsistent_candidate_invalid(): + """The `dcon` cloud marks a deposit-FOC-violating candidate invalid. + + With `beta = 1`, `crra = 2`, `w_a = w_b = 1` and a match rate `chi = 1`, the + deposit-constrained inverse pins `d = 0` and returns `c = 1`, so + `u'(c) = 1`. The `d = 0` corner is optimal only if + `beta * w_b * (1 + chi) <= u'(c)`, i.e. `2 <= 1`, which fails β€” raising the + deposit is profitable, so this point is not a KKT solution. The cloud must + flag it via a `valid_region` mask that is `False` here. + """ + one = jnp.ones((1,)) + cloud = invert_dcon_cloud( + a=one * 5.0, + b=one * 3.0, + w_a=one, + w_b=one, + post_decision_value=one * 0.0, + discount_factor=1.0, + crra=2.0, + match_rate=1.0, + ) + + consumption = float(np.asarray(cloud.consumption)[0]) + marginal_utility = consumption ** (-2.0) + deposit_foc_slack = 1.0 * 1.0 * (1.0 + 1.0) - marginal_utility + assert deposit_foc_slack > 0.0 # the candidate genuinely violates the FOC + + assert bool(np.asarray(cloud.valid_region)[0]) is False diff --git a/tests/solution/test_rfc_two_asset_parity.py b/tests/solution/test_rfc_two_asset_parity.py new file mode 100644 index 000000000..c4f59b2f4 --- /dev/null +++ b/tests/solution/test_rfc_two_asset_parity.py @@ -0,0 +1,67 @@ +"""The combined-cloud 2-D RFC step approximates the brute two-asset solve. + +The RFC backend is the Dobrescu-Shanker 2024 multidimensional method: it builds the +same four KKT candidate clouds as G2EGM, then selects the upper envelope by a global +rooftop-cut delete and a single local-simplex publish rather than the per-segment mesh +envelope. On the region the post-decision grid reaches, the published value tracks the +brute grid-search solve; the top pension edge is the same known uncovered hole. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.rfc_two_asset_step import rfc_two_asset_step +from tests.test_models.deterministic.two_asset import get_model, get_params + +_P = { + "discount_factor": 0.95, + "crra": 2.0, + "match_rate": 1.0, + "return_liquid": 0.02, + "return_pension": 0.06, + "wage": 10.0, +} +_M_GRID = jnp.linspace(1.0, 100.0, 12) +_N_GRID = jnp.linspace(0.0, 50.0, 10) +_B_GRID = jnp.linspace(0.0, 46.0, 16) +# The covered region excludes the top pension edge hole (the last n column). The +# interior further drops the low-liquid constrained corner (first m rows), where RFC +# does not yet select the acon/con corner segments β€” a known accuracy gap (the cut/ +# publish corner handling) tracked for the next iteration; the bulk interior is where +# the combined-cloud RFC is validated against the brute solve. +_COVERED = np.s_[:, :9] +_INTERIOR = np.s_[4:, :9] + + +def _solve(): + model = get_model(n_periods=2) + params = get_params(n_periods=2, pension_bequest_weight=0.5) + brute = model.solve(params=params, log_level="off") + next_value = jnp.asarray(brute[1]["dead"]) + result = rfc_two_asset_step( + next_value=next_value, + m_grid=_M_GRID, + n_grid=_N_GRID, + a_grid=jnp.linspace(0.0, 85.0, 18), + b_grid=_B_GRID, + consumption_grid=jnp.linspace(0.5, 90.0, 18), + radius=0.5, + **_P, # ty: ignore[invalid-argument-type] + ) + return np.asarray(result.value), np.asarray(brute[0]["working"]) + + +def test_rfc_two_asset_tracks_brute_on_the_bulk_interior(): + """The RFC published value tracks the brute solve on the bulk covered interior. + + The combined-cloud rooftop-cut plus local-simplex publish reproduces the brute + grid-search value where the post-decision grid covers and away from the low-liquid + constrained corner. The covered region is finite everywhere; on the bulk interior + the median and 90th-percentile relative errors are small. The low-liquid corner is + excluded as a known accuracy gap pending corner-segment tuning. + """ + rfc_value, brute = _solve() + assert np.isfinite(rfc_value[_COVERED]).all() + rel = np.abs(rfc_value[_INTERIOR] - brute[_INTERIOR]) / np.abs(brute[_INTERIOR]) + assert np.median(rel) < 0.05 + assert np.percentile(rel, 90) < 0.15 diff --git a/tests/solution/test_two_asset_brute.py b/tests/solution/test_two_asset_brute.py new file mode 100644 index 000000000..54b9fe134 --- /dev/null +++ b/tests/solution/test_two_asset_brute.py @@ -0,0 +1,49 @@ +"""Brute-force solve of the deterministic two-asset model β€” the 2-D EGM oracle. + +Validates that the engine expresses two action-coupled continuous states +(`liquid`, `pension`) with two continuous actions (`consumption`, `deposit`) and +solves them by dense grid search, producing the reference value function the +multidimensional EGM kernel is checked against. +""" + +import numpy as np + +from tests.test_models.deterministic.two_asset import get_model, get_params + + +def test_two_asset_model_exposes_two_coupled_continuous_states(): + """The working regime carries two continuous states and two continuous actions.""" + working = get_model().user_regimes["working"] + assert set(working.states) == {"liquid", "pension"} + assert set(working.actions) == {"consumption", "deposit"} + + +def test_two_asset_params_template_matches_get_params(): + """`get_params` fills exactly the leaves the model's params template declares.""" + model = get_model() + template = model.get_params_template() + params = get_params() + # Every leaf `get_params` fills is a real template leaf; the template may also + # carry default-empty groups (`H`, the constraint, the regime transition) that + # need no values, which the successful brute solve confirms. + assert set(params["working"]) <= set(template["working"]) + assert "discount_factor" in params + + +def test_two_asset_brute_value_is_finite_and_increases_in_liquid_wealth(): + """Brute-solved value is finite and weakly increasing in liquid wealth.""" + model = get_model() + value = model.solve(params=get_params(), log_level="off") + working_first_period = np.asarray(value[0]["working"]) + assert np.all(np.isfinite(working_first_period)) + # `liquid` is the first state axis; more cash-on-hand is weakly better. + liquid_diffs = np.diff(working_first_period, axis=0) + assert np.all(liquid_diffs >= -1e-6) + + +def test_two_asset_brute_value_increases_in_pension_wealth(): + """The brute-solved value function is weakly increasing in pension wealth.""" + value = get_model().solve(params=get_params(), log_level="off") + working_first_period = np.asarray(value[0]["working"]) + pension_diffs = np.diff(working_first_period, axis=1) + assert np.all(pension_diffs >= -1e-6) diff --git a/tests/solution/test_two_asset_egm_parity.py b/tests/solution/test_two_asset_egm_parity.py new file mode 100644 index 000000000..2c7f1d178 --- /dev/null +++ b/tests/solution/test_two_asset_egm_parity.py @@ -0,0 +1,60 @@ +"""One 2-D EGM step reproduces the brute-force value on the unconstrained interior. + +The terminal value weights pension below liquid (`pension_bequest_weight < 1`), which +puts the marginal-value ratio into the interior-deposit band, so the unconstrained +region is non-empty and the EGM inversion has something to reproduce. On that interior +the assembled step β€” post-decision value and gradients, closed-form Euler inversion, +and the inverse-bilinear locator deposit β€” must agree with a dense grid-search solve. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.two_asset_step import egm_step +from tests.test_models.deterministic.two_asset import get_model, get_params + +_P = { + "discount_factor": 0.95, + "crra": 2.0, + "match_rate": 1.0, + "return_liquid": 0.02, + "return_pension": 0.06, + "wage": 10.0, +} + + +def _egm_and_brute(): + model = get_model(n_periods=2) + params = get_params(n_periods=2, pension_bequest_weight=0.5) + brute = model.solve(params=params, log_level="off") + next_value = jnp.asarray(brute[1]["dead"]) + + m_grid = jnp.linspace(1.0, 100.0, 12) + n_grid = jnp.linspace(0.0, 50.0, 10) + # Keep m'(a) = 1.02a + 10 <= 100 and n'(b) = 1.06b <= 50 so the carried-forward + # states stay on the next grid (off-grid clamps the gradient -> NaN inverse). + a_grid = jnp.linspace(1.0, 85.0, 18) + b_grid = jnp.linspace(0.5, 46.0, 16) + + egm = np.asarray( + egm_step( + next_value=next_value, + m_grid=m_grid, + n_grid=n_grid, + a_grid=a_grid, + b_grid=b_grid, + **_P, + ) + ) + return egm, np.asarray(brute[0]["working"]) + + +def test_egm_step_matches_brute_on_unconstrained_interior(): + """EGM value matches the dense grid-search solve where the constraints are slack.""" + egm, brute_working = _egm_and_brute() + rel = np.abs(egm - brute_working) / np.abs(brute_working) + # Unconstrained interior: liquid large relative to pension, so the borrowing and + # deposit constraints are slack and the endogenous cloud covers the targets. + interior = rel[6:, :5] + assert np.median(interior) < 0.01 + assert interior.max() < 0.03 diff --git a/tests/solution/test_two_asset_inverse.py b/tests/solution/test_two_asset_inverse.py new file mode 100644 index 000000000..8a71ec490 --- /dev/null +++ b/tests/solution/test_two_asset_inverse.py @@ -0,0 +1,229 @@ +"""The two-asset unconstrained inverse-Euler step satisfies the FOCs and budget. + +The closed-form inverse is correct iff its outputs round-trip: the recovered +consumption and deposit reproduce the post-decision balances through the budget +identities, and they satisfy the consumption and deposit first-order conditions. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.two_asset_inverse import ( + invert_acon_cloud, + invert_con_cloud, + invert_dcon_cloud, + invert_ucon_cloud, +) +from tests.conftest import X64_ENABLED + +# Round-trip and FOC identities are float-eps-limited at the active precision. +_ATOL = 1e-10 if X64_ENABLED else 1e-5 +_RTOL = 1e-10 if X64_ENABLED else 1e-5 + +_DISCOUNT = 0.95 +_CRRA = 2.0 +_MATCH = 1.0 + + +def _cloud(): + # A post-decision grid and gradients with w_a > w_b > 0, which is the + # unconstrained-region regime (interior deposit, slack borrowing constraint). + a = jnp.linspace(1.0, 20.0, 6)[:, None] * jnp.ones((6, 5)) + b = jnp.ones((6, 5)) * jnp.linspace(0.5, 10.0, 5)[None, :] + w_a = jnp.linspace(0.20, 0.05, 6)[:, None] * jnp.ones((6, 5)) + w_b = 0.5 * w_a # strictly between 0 and w_a -> interior deposit + return ( + invert_ucon_cloud( + a=a, + b=b, + w_a=w_a, + w_b=w_b, + post_decision_value=jnp.zeros((6, 5)), + discount_factor=_DISCOUNT, + crra=_CRRA, + match_rate=_MATCH, + ), + a, + b, + w_a, + w_b, + ) + + +def test_inverse_recovers_liquid_post_decision_balance(): + """`m - c - d` returns the liquid post-decision balance `a`.""" + cloud, a, _b, _wa, _wb = _cloud() + recovered = cloud.m_endog - cloud.consumption - cloud.deposit + np.testing.assert_allclose(np.asarray(recovered), np.asarray(a), atol=_ATOL) + + +def test_inverse_recovers_pension_post_decision_balance(): + """`n + d + chi*log(1 + d)` returns the pension post-decision balance `b`.""" + cloud, _a, b, _wa, _wb = _cloud() + recovered = cloud.n_endog + cloud.deposit + _MATCH * jnp.log1p(cloud.deposit) + np.testing.assert_allclose(np.asarray(recovered), np.asarray(b), atol=_ATOL) + + +def test_inverse_satisfies_consumption_foc(): + """`u'(c) = c**(-rho)` equals `discount_factor * w_a`.""" + cloud, _a, _b, w_a, _wb = _cloud() + marginal_utility = cloud.consumption ** (-_CRRA) + np.testing.assert_allclose( + np.asarray(marginal_utility), np.asarray(_DISCOUNT * w_a), rtol=_RTOL + ) + + +def test_inverse_satisfies_deposit_foc(): + """`w_a = w_b * (1 + chi / (1 + d))` holds at the recovered deposit.""" + cloud, _a, _b, w_a, w_b = _cloud() + rhs = w_b * (1.0 + _MATCH / (1.0 + cloud.deposit)) + np.testing.assert_allclose(np.asarray(w_a), np.asarray(rhs), rtol=_RTOL) + + +def _dcon_cloud(): + # Gradients with w_a >= w_b*(1+chi): the unconstrained deposit would be negative, + # so the deposit is pinned to zero (the deposit-constrained region). + a = jnp.linspace(1.0, 20.0, 6)[:, None] * jnp.ones((6, 5)) + b = jnp.ones((6, 5)) * jnp.linspace(0.5, 10.0, 5)[None, :] + w_a = jnp.linspace(0.20, 0.05, 6)[:, None] * jnp.ones((6, 5)) + w_b = 0.2 * w_a # w_a = 5 w_b > w_b*(1+chi) -> deposit pinned to 0 + return ( + invert_dcon_cloud( + a=a, + b=b, + w_a=w_a, + w_b=w_b, + post_decision_value=jnp.zeros((6, 5)), + discount_factor=_DISCOUNT, + crra=_CRRA, + match_rate=_MATCH, + ), + a, + b, + w_a, + ) + + +def test_dcon_pins_deposit_to_zero(): + """The deposit-constrained cloud has `d = 0` everywhere.""" + cloud, _a, _b, _wa = _dcon_cloud() + np.testing.assert_array_equal(np.asarray(cloud.deposit), 0.0) + + +def test_dcon_recovers_liquid_budget_with_zero_deposit(): + """`m - c` returns the liquid post-decision balance `a` (since `d = 0`).""" + cloud, a, _b, _wa = _dcon_cloud() + np.testing.assert_allclose( + np.asarray(cloud.m_endog - cloud.consumption), np.asarray(a), atol=_ATOL + ) + + +def test_dcon_leaves_pension_unchanged(): + """The endogenous pension equals the post-decision balance `b` (no deposit).""" + cloud, _a, b, _wa = _dcon_cloud() + np.testing.assert_array_equal(np.asarray(cloud.n_endog), np.asarray(b)) + + +def test_dcon_satisfies_consumption_foc(): + """`u'(c) = c**(-rho)` equals `discount_factor * w_a`.""" + cloud, _a, _b, w_a = _dcon_cloud() + np.testing.assert_allclose( + np.asarray(cloud.consumption ** (-_CRRA)), + np.asarray(_DISCOUNT * w_a), + rtol=_RTOL, + ) + + +# The deposit-FOC ratio `1 + chi/(1 + d) = u'(c)/(beta*w_b)` is fixed to 1.6, which lies +# strictly in `(1, 1 + chi) = (1, 2)`, so the constructed deposit is interior (`d > 0`) +# while the borrowing constraint binds (`a = 0`). +_ACON_RATIO = 1.6 + + +def _acon_cloud(): + consumption = jnp.linspace(0.5, 3.0, 6)[:, None] * jnp.ones((6, 5)) + b = jnp.ones((6, 5)) * jnp.linspace(0.5, 10.0, 5)[None, :] + marginal_utility = consumption ** (-_CRRA) + # Pin u'(c)/(beta*w_b) = _ACON_RATIO so the recovered deposit is interior. + w_b = marginal_utility / (_DISCOUNT * _ACON_RATIO) + return ( + invert_acon_cloud( + consumption=consumption, + b=b, + post_decision_value_at_zero_a=jnp.zeros((6, 5)), + w_b_at_zero_a=w_b, + w_a_at_zero_a=marginal_utility / _DISCOUNT, + discount_factor=_DISCOUNT, + crra=_CRRA, + match_rate=_MATCH, + ), + consumption, + b, + w_b, + ) + + +def test_acon_pins_liquid_post_decision_to_zero(): + """The liquid post-decision balance `m - c - d` is zero (borrowing binds).""" + cloud, _c, _b, _wb = _acon_cloud() + recovered = cloud.m_endog - cloud.consumption - cloud.deposit + np.testing.assert_allclose(np.asarray(recovered), 0.0, atol=_ATOL) + + +def test_acon_recovers_pension_post_decision_balance(): + """`n + d + chi*log(1 + d)` returns the pension post-decision balance `b`.""" + cloud, _c, b, _wb = _acon_cloud() + recovered = cloud.n_endog + cloud.deposit + _MATCH * jnp.log1p(cloud.deposit) + np.testing.assert_allclose(np.asarray(recovered), np.asarray(b), atol=_ATOL) + + +def test_acon_has_interior_deposit(): + """The recovered deposit is strictly positive (the deposit margin is slack).""" + cloud, _c, _b, _wb = _acon_cloud() + assert np.all(np.asarray(cloud.deposit) > 0.0) + + +def test_acon_satisfies_deposit_foc(): + """`u'(c) = beta * w_b * (1 + chi / (1 + d))` holds at the recovered deposit.""" + cloud, _c, _b, w_b = _acon_cloud() + rhs = _DISCOUNT * w_b * (1.0 + _MATCH / (1.0 + cloud.deposit)) + np.testing.assert_allclose( + np.asarray(cloud.consumption ** (-_CRRA)), np.asarray(rhs), rtol=_RTOL + ) + + +def _con_cloud(): + consumption = jnp.linspace(0.5, 3.0, 6)[:, None] * jnp.ones((6, 5)) + b = jnp.ones((6, 5)) * jnp.linspace(0.5, 10.0, 5)[None, :] + return ( + invert_con_cloud( + consumption=consumption, + b=b, + post_decision_value_at_zero_a=jnp.zeros((6, 5)), + w_b_at_zero_a=jnp.ones((6, 5)), + w_a_at_zero_a=jnp.ones((6, 5)), + discount_factor=_DISCOUNT, + crra=_CRRA, + match_rate=_MATCH, + ), + consumption, + b, + ) + + +def test_con_pins_deposit_to_zero(): + """The fully-constrained corner has `d = 0` everywhere.""" + cloud, _c, _b = _con_cloud() + np.testing.assert_array_equal(np.asarray(cloud.deposit), 0.0) + + +def test_con_consumes_entire_liquid_budget(): + """`m = c` at the corner (`a = 0` and `d = 0`).""" + cloud, consumption, _b = _con_cloud() + np.testing.assert_array_equal(np.asarray(cloud.m_endog), np.asarray(consumption)) + + +def test_con_leaves_pension_unchanged(): + """The endogenous pension equals the post-decision balance `b` (no deposit).""" + cloud, _c, b = _con_cloud() + np.testing.assert_array_equal(np.asarray(cloud.n_endog), np.asarray(b)) diff --git a/tests/solution/test_two_asset_objective.py b/tests/solution/test_two_asset_objective.py new file mode 100644 index 000000000..dfd7824f7 --- /dev/null +++ b/tests/solution/test_two_asset_objective.py @@ -0,0 +1,101 @@ +"""The two-asset Bellman-objective evaluator recomputes value and feasibility. + +The evaluator reconstructs the post-decision balances from the budget identities, +reads the post-decision value by bilinear interpolation, and adds CRRA utility. The +tests pin exact values against a known analytic post-decision value (affine, so +bilinear interpolation is exact off-grid; and the audit's `a/(1+b)` read exactly at a +grid node), and pin the feasibility flag that the envelope masks on. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.two_asset_objective import build_two_asset_objective +from tests.conftest import X64_ENABLED + +# The analytic comparisons are float-eps-limited at the active precision. +_RTOL = 1e-10 if X64_ENABLED else 1e-5 + +_DISCOUNT = 0.95 +_CRRA = 2.0 +_MATCH = 1.0 +_A_GRID = jnp.linspace(0.0, 10.0, 11) +_B_GRID = jnp.linspace(0.0, 10.0, 11) + + +def test_objective_is_exact_for_an_affine_post_decision_value(): + """For affine `W`, the recomputed objective equals `u(c) + beta*W(a, b)` exactly. + + With `W(a, b) = 2a + 3b + 1` (bilinear-exact), state `(5, 2)`, policy `(c, d) = + (1, 0.5)`: `a = 3.5`, `b = 2.5 + log(1.5)`, so `W = 16.7163953` and the objective is + `u(1) + 0.95*W = -1 + 15.8805756 = 14.8805756`. + """ + a_mesh, b_mesh = jnp.meshgrid(_A_GRID, _B_GRID, indexing="ij") + post_decision_value = 2.0 * a_mesh + 3.0 * b_mesh + 1.0 + objective = build_two_asset_objective( + post_decision_value=post_decision_value, + a_grid=_A_GRID, + b_grid=_B_GRID, + discount_factor=_DISCOUNT, + crra=_CRRA, + match_rate=_MATCH, + ) + value, feasible = objective(jnp.array([5.0, 2.0]), jnp.array([1.0, 0.5])) + np.testing.assert_allclose(float(value), 14.8805755576, rtol=_RTOL) + assert bool(feasible) + + +def test_objective_reads_the_audit_post_decision_value_at_a_grid_node(): + """At a grid node the bilinear read is exact, so `W(a,b)=a/(1+b)` is recovered. + + State `(4, 2)`, policy `(1, 0)` give `a = 3`, `b = 2` (both grid nodes), so + `W = 3/3 = 1` and the objective is `u(1) + 0.95*1 = -0.05`. + """ + a_mesh, b_mesh = jnp.meshgrid(_A_GRID, _B_GRID, indexing="ij") + post_decision_value = a_mesh / (1.0 + b_mesh) + objective = build_two_asset_objective( + post_decision_value=post_decision_value, + a_grid=_A_GRID, + b_grid=_B_GRID, + discount_factor=_DISCOUNT, + crra=_CRRA, + match_rate=_MATCH, + ) + value, feasible = objective(jnp.array([4.0, 2.0]), jnp.array([1.0, 0.0])) + np.testing.assert_allclose(float(value), -0.05, rtol=_RTOL) + assert bool(feasible) + + +def test_objective_flags_negative_liquid_post_decision_as_infeasible(): + """A policy whose liquid post-decision balance `a = m - c - d` is negative fails.""" + a_mesh, b_mesh = jnp.meshgrid(_A_GRID, _B_GRID, indexing="ij") + post_decision_value = 2.0 * a_mesh + 3.0 * b_mesh + 1.0 + objective = build_two_asset_objective( + post_decision_value=post_decision_value, + a_grid=_A_GRID, + b_grid=_B_GRID, + discount_factor=_DISCOUNT, + crra=_CRRA, + match_rate=_MATCH, + ) + # m - c - d = 1 - 1 - 0.5 = -0.5 < 0. + value, feasible = objective(jnp.array([1.0, 2.0]), jnp.array([1.0, 0.5])) + assert not bool(feasible) + assert np.isfinite(float(value)) + + +def test_objective_flags_negative_consumption_as_infeasible(): + """A non-positive interpolated consumption is infeasible with a finite value.""" + a_mesh, b_mesh = jnp.meshgrid(_A_GRID, _B_GRID, indexing="ij") + post_decision_value = 2.0 * a_mesh + 3.0 * b_mesh + 1.0 + objective = build_two_asset_objective( + post_decision_value=post_decision_value, + a_grid=_A_GRID, + b_grid=_B_GRID, + discount_factor=_DISCOUNT, + crra=_CRRA, + match_rate=_MATCH, + ) + value, feasible = objective(jnp.array([5.0, 2.0]), jnp.array([-0.5, 0.0])) + assert not bool(feasible) + assert np.isfinite(float(value)) diff --git a/tests/solution/test_two_asset_post_decision.py b/tests/solution/test_two_asset_post_decision.py new file mode 100644 index 000000000..994eb9fc4 --- /dev/null +++ b/tests/solution/test_two_asset_post_decision.py @@ -0,0 +1,108 @@ +"""Post-decision value and gradients are exact for an affine next-period value. + +When `V'` is affine on the regular `(m, n)` grid, bilinear interpolation reproduces +it exactly, so the post-decision value and its chain-rule gradients must equal their +closed forms: `w_a = beta_m*(1+r^a)` and `w_b = beta_n*(1+r^b)`. + +At the working->retired boundary both post-decision balances feed a single retired +liquid state through the lump-sum payout, and the same affine-exactness pins the +boundary reader's value and chain-rule gradients. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.two_asset_post_decision import ( + post_decision_value_and_grad, + post_decision_value_and_grad_retiring, +) + +_ALPHA, _BETA_M, _BETA_N = 1.0, 0.7, 0.3 +_RETURN_LIQUID, _RETURN_PENSION, _WAGE = 0.03, 0.06, 5.0 + + +def _setup(): + m_grid = jnp.linspace(0.0, 200.0, 41) + n_grid = jnp.linspace(0.0, 120.0, 31) + mesh_m, mesh_n = jnp.meshgrid(m_grid, n_grid, indexing="ij") + next_value = _ALPHA + _BETA_M * mesh_m + _BETA_N * mesh_n + a = jnp.linspace(5.0, 40.0, 6)[:, None] * jnp.ones((6, 4)) + b = jnp.ones((6, 4)) * jnp.linspace(2.0, 30.0, 4)[None, :] + out = post_decision_value_and_grad( + next_value=next_value, + m_grid=m_grid, + n_grid=n_grid, + a=a, + b=b, + return_liquid=_RETURN_LIQUID, + return_pension=_RETURN_PENSION, + wage=_WAGE, + ) + return out, a, b + + +def test_post_decision_value_matches_affine_closed_form(): + """`w(a,b)` equals `V'` evaluated at the carried-forward states.""" + out, a, b = _setup() + m_next = (1.0 + _RETURN_LIQUID) * a + _WAGE + n_next = (1.0 + _RETURN_PENSION) * b + expected = _ALPHA + _BETA_M * m_next + _BETA_N * n_next + np.testing.assert_allclose(np.asarray(out.value), np.asarray(expected), rtol=1e-5) + + +def test_post_decision_grad_a_is_return_scaled_marginal_value(): + """`w_a = beta_m * (1 + r^a)` everywhere (affine value, constant marginal).""" + out, _a, _b = _setup() + expected = _BETA_M * (1.0 + _RETURN_LIQUID) + np.testing.assert_allclose(np.asarray(out.grad_a), expected, rtol=1e-5) + + +def test_post_decision_grad_b_is_return_scaled_marginal_value(): + """`w_b = beta_n * (1 + r^b)` everywhere (affine value, constant marginal).""" + out, _a, _b = _setup() + expected = _BETA_N * (1.0 + _RETURN_PENSION) + np.testing.assert_allclose(np.asarray(out.grad_b), expected, rtol=1e-5) + + +_PAYOUT, _RETIREMENT_INCOME, _BETA_L = 1.05, 0.5, 0.4 + + +def _setup_retiring(): + liquid_grid = jnp.linspace(0.0, 200.0, 41) + next_value_retired = _ALPHA + _BETA_L * liquid_grid + next_marginal_retired = _BETA_L * jnp.ones_like(liquid_grid) + a = jnp.linspace(5.0, 40.0, 6)[:, None] * jnp.ones((6, 4)) + b = jnp.ones((6, 4)) * jnp.linspace(2.0, 30.0, 4)[None, :] + out = post_decision_value_and_grad_retiring( + next_value_retired=next_value_retired, + next_marginal_retired=next_marginal_retired, + liquid_grid=liquid_grid, + a=a, + b=b, + return_liquid=_RETURN_LIQUID, + pension_payout_return=_PAYOUT, + retirement_income=_RETIREMENT_INCOME, + ) + return out, a, b + + +def test_retiring_post_decision_value_reads_retired_value_through_the_payout(): + """`w(a,b)` equals the retired value at the lump-sum retired liquid state.""" + out, a, b = _setup_retiring() + liquid_next = (1.0 + _RETURN_LIQUID) * a + _PAYOUT * b + _RETIREMENT_INCOME + expected = _ALPHA + _BETA_L * liquid_next + np.testing.assert_allclose(np.asarray(out.value), np.asarray(expected), rtol=1e-5) + + +def test_retiring_post_decision_grad_a_scales_retired_marginal_by_liquid_return(): + """`w_a = (1 + r^a) * V'_retired` (carried retired marginal, return-scaled).""" + out, _a, _b = _setup_retiring() + expected = (1.0 + _RETURN_LIQUID) * _BETA_L + np.testing.assert_allclose(np.asarray(out.grad_a), expected, rtol=1e-5) + + +def test_retiring_post_decision_grad_b_scales_retired_marginal_by_payout(): + """`w_b = pension_payout_return * V'_retired` (the lump-sum chain rule).""" + out, _a, _b = _setup_retiring() + expected = _PAYOUT * _BETA_L + np.testing.assert_allclose(np.asarray(out.grad_b), expected, rtol=1e-5) diff --git a/tests/solution/test_two_asset_segment_mesh.py b/tests/solution/test_two_asset_segment_mesh.py new file mode 100644 index 000000000..a482a1a1c --- /dev/null +++ b/tests/solution/test_two_asset_segment_mesh.py @@ -0,0 +1,66 @@ +"""A region cloud triangulates into a `SegmentMesh` with the right topology. + +The mesh built from an `n_rows` by `n_cols` cloud has one node per cloud entry, two +triangles per source cell, the endogenous states and policies of the cloud at its +nodes, and a validity mask that drops non-finite or non-positive-consumption nodes. +""" + +import jax.numpy as jnp +import numpy as np + +from _lcm.egm.two_asset_inverse import RegionCloud +from _lcm.egm.two_asset_segment_mesh import build_segment_mesh + + +def _synthetic_cloud(*, consumption=None): + """A 3x3 region cloud with simple, distinct node states and policies.""" + a_mesh, b_mesh = jnp.meshgrid(jnp.arange(3.0), jnp.arange(3.0), indexing="ij") + if consumption is None: + consumption = 1.0 + a_mesh + return RegionCloud( + m_endog=a_mesh + 10.0, + n_endog=b_mesh + 20.0, + consumption=consumption, + deposit=0.5 * b_mesh, + value=jnp.zeros((3, 3)), + value_grad_m=jnp.zeros((3, 3)), + value_grad_n=jnp.zeros((3, 3)), + valid_region=jnp.ones((3, 3), dtype=bool), + ) + + +def test_mesh_has_one_node_per_cloud_entry_and_two_triangles_per_cell(): + """A 3x3 cloud yields 9 nodes and `2*2*2 = 8` triangles.""" + mesh = build_segment_mesh(cloud=_synthetic_cloud(), region_label=1) + assert mesh.node_state.shape == (9, 2) + assert mesh.node_policy.shape == (9, 2) + assert mesh.simplices.shape == (8, 3) + assert mesh.region_label == 1 + + +def test_mesh_nodes_match_the_cloud_state_and_policy(): + """The mesh nodes are the cloud's endogenous states and policies, row-major.""" + cloud = _synthetic_cloud() + mesh = build_segment_mesh(cloud=cloud, region_label=0) + np.testing.assert_allclose( + np.asarray(mesh.node_state[:, 0]), np.asarray(cloud.m_endog).reshape(-1) + ) + np.testing.assert_allclose( + np.asarray(mesh.node_state[:, 1]), np.asarray(cloud.n_endog).reshape(-1) + ) + np.testing.assert_allclose( + np.asarray(mesh.node_policy[:, 0]), np.asarray(cloud.consumption).reshape(-1) + ) + + +def test_mesh_marks_non_positive_consumption_and_non_finite_state_invalid(): + """A non-positive consumption or non-finite endogenous state masks the node.""" + consumption = 1.0 + jnp.meshgrid(jnp.arange(3.0), jnp.arange(3.0), indexing="ij")[0] + consumption = consumption.at[0, 0].set(-1.0) # invalid: non-positive consumption + cloud = _synthetic_cloud(consumption=consumption) + cloud = cloud._replace(m_endog=cloud.m_endog.at[2, 2].set(jnp.nan)) # invalid: NaN + mesh = build_segment_mesh(cloud=cloud, region_label=0) + valid = np.asarray(mesh.valid_node) + assert not valid[0] # node (0,0) + assert not valid[8] # node (2,2) + assert valid[4] # an interior node stays valid diff --git a/tests/test_Q_and_F.py b/tests/test_Q_and_F.py index 53530b436..88d2ad6fc 100644 --- a/tests/test_Q_and_F.py +++ b/tests/test_Q_and_F.py @@ -15,6 +15,7 @@ from _lcm.regime_building.finalize import finalize_regimes from _lcm.regime_building.processing import process_regimes from _lcm.regime_building.Q_and_F import ( + _get_deterministic_transitions, _get_feasibility, _get_joint_weights_function, _get_U_and_F, @@ -265,6 +266,117 @@ def utility_func( assert F.item() is False +def test_identical_target_specific_deterministic_laws_are_accepted(): + """Identical `next_` laws across targets bind into the decision DAG. + + When every target bundle carries the same `next_durable` function object and + `utility` reads it, the within-period law is unambiguous, so the merged + decision DAG builds without error. + """ + + def next_durable(durable: float) -> float: + return durable + + def utility(consumption: float, next_durable: float) -> FloatND: + return jnp.log(consumption) + next_durable + + transitions = MappingProxyType( + { + "stay": MappingProxyType({"next_durable": next_durable}), + "leave": MappingProxyType({"next_durable": next_durable}), + } + ) + deterministic_transitions, conflicting = _get_deterministic_transitions( + transitions=transitions, # ty: ignore[invalid-argument-type] + stochastic_transition_names=frozenset(), + ) + assert conflicting == frozenset() + U_and_F = _get_U_and_F( + functions=MappingProxyType({"utility": utility}), # ty: ignore[invalid-argument-type] + constraints=MappingProxyType({}), + deterministic_transitions=deterministic_transitions, + conflicting_deterministic_transition_names=conflicting, + ) + U, _F = U_and_F(consumption=jnp.asarray(2.0), durable=jnp.asarray(3.0)) + assert jnp.isclose(U, jnp.log(2.0) + 3.0) + + +def test_conflicting_target_specific_deterministic_law_read_by_utility_is_rejected(): + """A `next_` read by `utility` must agree across all targets. + + When two target bundles supply *different* implementations of the same + `next_durable` law and `utility` reads it, the merged decision DAG would bind + one target's law while the simulate state-update uses the right one β€” a silent + disagreement. The build rejects this, naming the conflicting state. + """ + + def next_durable_stay(durable: float) -> float: + return durable + + def next_durable_leave(durable: float) -> float: + return 0.0 * durable + + def utility(consumption: float, next_durable: float) -> FloatND: + return jnp.log(consumption) + next_durable + + transitions = MappingProxyType( + { + "stay": MappingProxyType({"next_durable": next_durable_stay}), + "leave": MappingProxyType({"next_durable": next_durable_leave}), + } + ) + deterministic_transitions, conflicting = _get_deterministic_transitions( + transitions=transitions, # ty: ignore[invalid-argument-type] + stochastic_transition_names=frozenset(), + ) + assert conflicting == frozenset({"next_durable"}) + with pytest.raises(ValueError, match="next_durable"): + _get_U_and_F( + functions=MappingProxyType({"utility": utility}), # ty: ignore[invalid-argument-type] + constraints=MappingProxyType({}), + deterministic_transitions=deterministic_transitions, + conflicting_deterministic_transition_names=conflicting, + ) + + +def test_conflicting_deterministic_law_not_read_by_decision_is_accepted(): + """An unread conflicting `next_` law does not block the build. + + When the conflicting `next_durable` is pruned away because neither `utility` + nor any constraint reads it, the decision DAG never binds it, so the + disagreement is harmless and the build succeeds. + """ + + def next_durable_stay(durable: float) -> float: + return durable + + def next_durable_leave(durable: float) -> float: + return 0.0 * durable + + def utility(consumption: float) -> FloatND: + return jnp.log(consumption) + + transitions = MappingProxyType( + { + "stay": MappingProxyType({"next_durable": next_durable_stay}), + "leave": MappingProxyType({"next_durable": next_durable_leave}), + } + ) + deterministic_transitions, conflicting = _get_deterministic_transitions( + transitions=transitions, # ty: ignore[invalid-argument-type] + stochastic_transition_names=frozenset(), + ) + assert conflicting == frozenset({"next_durable"}) + U_and_F = _get_U_and_F( + functions=MappingProxyType({"utility": utility}), # ty: ignore[invalid-argument-type] + constraints=MappingProxyType({}), + deterministic_transitions=deterministic_transitions, + conflicting_deterministic_transition_names=conflicting, + ) + U, _F = U_and_F(consumption=jnp.asarray(2.0)) + assert jnp.isclose(U, jnp.log(2.0)) + + def _health_probs(health: DiscreteState, probs_array: FloatND) -> FloatND: return probs_array[health] diff --git a/tests/test_dcegm_fixture_crosscheck.py b/tests/test_dcegm_fixture_crosscheck.py new file mode 100644 index 000000000..9919e4ad6 --- /dev/null +++ b/tests/test_dcegm_fixture_crosscheck.py @@ -0,0 +1,134 @@ +"""Cross-check against the independent `dcegm` implementation. + +`tests/data/dcegm_reference/ijrs_taste_shocks_reference.csv` holds choice- +specific values of the IJRS consumption-retirement model with EV1 taste shocks +(scale 0.2), solved by the `dcegm` package (see the README there). The smoothed +value `scale * logsumexp([value_work, value_retire] / scale)` is compared with +pylcm's solved V on the twin model at the fixture's wealth nodes: + +- the brute-force twin (taste shocks via logsumexp over the consumption-grid + `Qc`) must agree up to consumption-grid resolution, +- the DC-EGM twin must agree tightly β€” same algorithm family, independent code, + and (by pinning the fixture run's savings grid) the same discretization, so + agreement certifies the implementation, not the accuracy of every node. +""" + +import numpy as np +import pandas as pd +import pytest + +from _lcm.config import TEST_DATA +from lcm import IrregSpacedGrid +from tests.test_models import dcegm_paper_twin + +SCALE = 0.2 + +REGIME_FOR_LAGGED_CHOICE = {0: "working_life", 1: "retirement"} + + +@pytest.fixture(scope="module") +def reference() -> pd.DataFrame: + df = pd.read_csv( + TEST_DATA.joinpath("dcegm_reference", "ijrs_taste_shocks_reference.csv") + ) + values = df[["value_work", "value_retire"]].to_numpy() + shifted = values - np.nanmax(values, axis=1, keepdims=True) + df["emax"] = np.nanmax(values, axis=1) + SCALE * np.log( + np.nansum(np.exp(shifted / SCALE), axis=1) + ) + # The retiree rows at the lowest wealth node (9 rows, one per period) are + # excluded: the run's uniform savings grid under-resolves the sharply + # curved retiree value function near the borrowing limit, so the + # value-space interpolation error there is large and + # implementation-specific β€” the fixture stores about -66.0 at period 0, + # pylcm's DC-EGM about -76, while a fine-grid value-iteration recursion + # of the same model (and the brute-force twin, and a DC-EGM run with a + # savings grid clustered toward the limit β€” see + # `test_clustered_savings_grid_resolves_excluded_low_wealth_nodes`) puts + # the truth near -54. With no common discretization error to compare, + # the rows are excluded rather than the tolerances loosened; every other + # row is asserted at full tolerance. + return df.query("not (lagged_choice == 1 and wealth == 1.0)") + + +def _wealth_node_indices(wealth_points: np.ndarray) -> np.ndarray: + grid = np.asarray(dcegm_paper_twin.WEALTH_GRID.to_jax()) + indices = np.searchsorted(grid, wealth_points) + np.testing.assert_allclose(grid[indices], wealth_points, atol=1e-12) + return indices + + +def test_clustered_savings_grid_resolves_excluded_low_wealth_nodes(): + """A savings grid clustered toward the borrowing limit fixes the low-wealth rows. + + The fixture comparison excludes the retiree rows at wealth 1 because the + pinned uniform savings grid under-resolves the value function there in + both implementations. With the same node count clustered toward the + limit, pylcm's DC-EGM reproduces the brute-force value (which a fine-grid + recursion of the model confirms) at every excluded node β€” the exclusion + reflects the fixture run's grid, not the kernel. + """ + low = np.geomspace(1e-4, 2.0, 220) + high = np.linspace(2.0, 50.0, 281)[1:] + clustered = IrregSpacedGrid(points=(0.0, *map(float, low), *map(float, high))) + params = dcegm_paper_twin.get_params(taste_shock_scale=SCALE) + + dcegm_V = dcegm_paper_twin.build_dcegm_model(savings_grid=clustered).solve( + params=params, log_level="debug" + ) + brute_V = dcegm_paper_twin.get_model("brute_force").solve( + params=params, log_level="debug" + ) + + node = _wealth_node_indices(np.array([1.0])) + for period in range(dcegm_paper_twin.N_PERIODS - 1): + np.testing.assert_allclose( + np.asarray(dcegm_V[period]["retirement"])[node], + np.asarray(brute_V[period]["retirement"])[node], + atol=0.15, + err_msg=f"period={period}", + ) + + +@pytest.mark.parametrize( + ("solver", "rtol", "atol"), + [ + ("brute_force", 2e-2, 2e-2), + ("dcegm", 2e-3, 2e-3), + ], +) +def test_twin_smoothed_value_matches_dcegm_reference(solver, rtol, atol, reference): + """pylcm's smoothed V equals the independent `dcegm` solution. + + Tolerances are looser for brute force (consumption-grid resolution) than for + DC-EGM (same algorithm family, exact policies on both sides). + """ + model = dcegm_paper_twin.get_model(solver) + params = dcegm_paper_twin.get_params(taste_shock_scale=SCALE) + + period_to_regime_to_V_arr = model.solve(params=params, log_level="debug") + + for (period, lagged_choice), group in reference.groupby( + ["period", "lagged_choice"] + ): + regime = REGIME_FOR_LAGGED_CHOICE[lagged_choice] + rows = group + if solver == "dcegm" and lagged_choice == 1: + # The reference interpolates the carry's value row linearly; + # pylcm reads it with an exact-slope cubic Hermite. Where the + # retiree value function curves hardest the two therefore + # diverge by construction, with pylcm landing on a fine-grid + # recursion of the model (wealth 2, period 0: reference -23.820, + # pylcm -23.468, recursion -23.484; wealth 5: reference -4.9495, + # pylcm -4.9236, recursion -4.9237). Those rows certify accuracy, + # not cross-implementation agreement, so they are excluded here. + rows = group.query("wealth > 5.0") + v_arr = np.asarray(period_to_regime_to_V_arr[period][regime]) + node_indices = _wealth_node_indices(rows["wealth"].to_numpy()) + np.testing.assert_allclose( + v_arr[node_indices], + rows["emax"].to_numpy(), + rtol=rtol, + atol=atol, + err_msg=f"period={period}, regime={regime}", + ) diff --git a/tests/test_dcegm_retirement.py b/tests/test_dcegm_retirement.py new file mode 100644 index 000000000..e4d06206a --- /dev/null +++ b/tests/test_dcegm_retirement.py @@ -0,0 +1,201 @@ +"""Spec for full DC-EGM on the Iskhakov et al. (2017) retirement model. + +Discrete retirement choice + continuous consumption, solved with DC-EGM (FUES +envelope) and compared against: + +- the analytical worker/retired value functions shipped in + `tests/data/analytical_solution/` (kinked case, no taste shocks), and +- the brute-force solver with regime-level taste shocks on the equivalent spec + (smoothed case): both solvers approximate the same smoothed model, so their V + arrays agree up to the consumption-grid resolution of the brute solution. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from _lcm.config import TEST_DATA +from _lcm.typing import PeriodToRegimeToVArr +from lcm import AgeGrid, MarkovTransition, Model +from lcm.taste_shocks import ExtremeValueTasteShocks +from lcm.typing import FloatND +from tests.test_models.deterministic import base, dcegm_variants +from tests.test_models.deterministic.dcegm_variants import ( + get_full_model, + get_full_params, +) + +ANALYTICAL_CASES = { + "iskhakov_2017_five_periods": {"n_periods": 6, "disutility_of_work": 1.0}, + "iskhakov_2017_low_delta": {"n_periods": 4, "disutility_of_work": 0.1}, +} + + +def _load_analytical(case: str, kind: str) -> np.ndarray: + return np.genfromtxt( + TEST_DATA.joinpath("analytical_solution", f"{case}__values_{kind}.csv"), + delimiter=",", + ) + + +def _stack_regime_V( + period_to_regime_to_V_arr: PeriodToRegimeToVArr, regime: str +) -> np.ndarray: + periods = sorted(period_to_regime_to_V_arr)[:-1] + return np.stack([np.asarray(period_to_regime_to_V_arr[p][regime]) for p in periods]) + + +@pytest.mark.parametrize(("case", "spec"), ANALYTICAL_CASES.items()) +def test_dcegm_matches_analytical_solution(case, spec): + """DC-EGM reproduces the analytical worker and retired value functions. + + Tighter than the brute-force tolerance: the secondary kinks from the + retirement choice are exactly where the envelope step pays off. + """ + model = get_full_model("dcegm", spec["n_periods"]) + params = get_full_params( + spec["n_periods"], + discount_factor=0.98, + disutility_of_work=spec["disutility_of_work"], + interest_rate=0.0, + wage=20.0, + ) + + period_to_regime_to_V_arr = model.solve(params=params, log_level="debug") + + for kind, regime in [("worker", "working_life"), ("retired", "retirement")]: + numerical = _stack_regime_V(period_to_regime_to_V_arr, regime) + analytical = _load_analytical(case, kind) + # Elementwise β€” every (period, node) value must hit the analytical + # solution; aggregating over periods could hide a localized error. + np.testing.assert_allclose(numerical, analytical, atol=0.03, err_msg=f"{kind}") + + +def _retirement_stay_prob(age: float, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 0.0, 1.0) + + +def _retirement_death_prob(age: float, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 1.0, 0.0) + + +def test_brute_force_regime_targeting_dcegm_regime_agrees_with_all_brute(): + """A brute-force worker targeting a DC-EGM retiree solves to brute values. + + Brute-force regimes may target DC-EGM regimes (they only read the + target's V array); the DC-EGM retiree declares its reachable targets + granularly so the brute worker is structurally unreachable from it. The + mixed model's V differs from the all-brute model's only through the + retiree continuation, on which the two solvers agree wherever the brute + solver is reliable. At the lowest wealth nodes the brute leg leans on + consumption below its grid start and coarse interpolation, so its values + are the biased side there and the comparison starts above them. + """ + n_periods = 4 + n_brute_unstable_nodes = 12 + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = float(ages.exact_values[-1]) + + def active(age: float, la: float = last_age) -> bool: + return age < la + + mixed = Model( + regimes={ + "working_life": base.working_life.replace(active=active), + "retirement": dcegm_variants.dcegm_retirement_full.replace( + active=active, + transition={ + "retirement": MarkovTransition(_retirement_stay_prob), + "dead": MarkovTransition(_retirement_death_prob), + }, + ), + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + params = get_full_params(n_periods, discount_factor=0.98, wage=20.0) + + mixed_solution = mixed.solve(params=params, log_level="debug") + brute_solution = get_full_model("brute_force", n_periods).solve( + params=params, log_level="debug" + ) + + for period in sorted(brute_solution)[:-1]: + for regime in ["working_life", "retirement"]: + np.testing.assert_allclose( + np.asarray(mixed_solution[period][regime])[n_brute_unstable_nodes:], + np.asarray(brute_solution[period][regime])[n_brute_unstable_nodes:], + atol=1e-2, + rtol=1e-3, + err_msg=f"period={period}, regime={regime}", + ) + + +def _smoothed_model_pair(n_periods: int, shocks) -> dict[str, Model]: + """Equivalent-spec pair with EV1 taste shocks on the working regime.""" + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = float(ages.exact_values[-1]) + + def active(age: float, la: float = last_age) -> bool: + return age < la + + brute = Model( + regimes={ + "working_life": base.working_life.replace( + active=active, taste_shocks=shocks + ), + "retirement": base.retirement.replace(active=active), + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + dcegm = Model( + regimes={ + "working_life": dcegm_variants.dcegm_working_life.replace( + active=active, taste_shocks=shocks + ), + "retirement": dcegm_variants.dcegm_retirement_full.replace(active=active), + "dead": base.dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + return {"brute_force": brute, "dcegm": dcegm} + + +def test_smoothed_model_brute_and_dcegm_agree(): + """With taste shocks, brute force and DC-EGM solve the same smoothed model. + + Brute computes `λ·logsumexp(Qc/Ξ»)` on the consumption grid; DC-EGM computes + the same object from exact Euler policies. Agreement is up to the brute + solver's resolution, which fails at the lowest wealth nodes: there the + brute solution leans on consumption choices below its grid start and on + coarse interpolation where log utility curves hardest (e.g. retirement, + period 0, wealth node 4: closed form 5.121, DC-EGM 5.118, brute 5.044). + DC-EGM's exact-slope carry read does not mirror that low-wealth error, so + the comparison covers the wealth nodes where the brute solver is reliable. + """ + n_periods = 4 + scale = 0.2 + n_brute_unstable_nodes = 12 + params = get_full_params(n_periods, discount_factor=0.98, wage=20.0) + params["working_life"]["taste_shocks"] = {"scale": scale} + + models = _smoothed_model_pair(n_periods, ExtremeValueTasteShocks()) + solutions = { + solver: model.solve(params=params, log_level="debug") + for solver, model in models.items() + } + + for period in sorted(solutions["brute_force"])[:-1]: + for regime in ["working_life", "retirement"]: + brute_V = np.asarray(solutions["brute_force"][period][regime]) + dcegm_V = np.asarray(solutions["dcegm"][period][regime]) + np.testing.assert_allclose( + dcegm_V[n_brute_unstable_nodes:], + brute_V[n_brute_unstable_nodes:], + atol=1e-2, + rtol=1e-3, + ) diff --git a/tests/test_dcegm_validation.py b/tests/test_dcegm_validation.py new file mode 100644 index 000000000..c922c1a0b --- /dev/null +++ b/tests/test_dcegm_validation.py @@ -0,0 +1,609 @@ +"""Spec for DC-EGM build-time validation (one case per contract rule). + +A regime with `solver=DCEGM(...)` must satisfy the EGM contract; every violation +raises `ModelInitializationError` at `Model` construction with a message naming +the offending piece. The cases here mutate a valid DC-EGM regime one rule at a +time. +""" + +import dataclasses + +import jax.numpy as jnp +import pytest + +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + MarkovTransition, + Model, + Phased, + categorical, + fixed_transition, +) +from lcm.exceptions import ModelInitializationError +from lcm.regime import Regime as UserRegime +from lcm.solvers import GridSearch +from lcm.temporal_aggregation import H_linear +from lcm.typing import ( + ContinuousAction, + ContinuousState, + FloatND, + Period, + ScalarInt, +) +from lcm_examples.mortality import ( + borrowing_constraint, + dead, + next_wealth, + utility_retirement, +) +from tests.test_models.deterministic import ( + base, + dcegm_variants, + retirement_only, +) + +N_PERIODS = 3 + + +def _build_model(regime: UserRegime) -> Model: + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + return Model( + regimes={"retirement": regime, "dead": dead}, + ages=ages, + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + + +def _utility_with_direct_wealth_dependence( + consumption: ContinuousAction, wealth: ContinuousState +) -> FloatND: + return jnp.log(consumption) + 0.01 * wealth + + +def _custom_H(utility: FloatND, continuation: FloatND) -> FloatND: + return utility + 0.9 * continuation + + +def _regime_transition_with_wealth_cliff(wealth: ContinuousState) -> ScalarInt: + return jnp.where( + wealth < 100.0, + retirement_only.RetirementOnlyRegimeId.dead, + retirement_only.RetirementOnlyRegimeId.retirement, + ) + + +def _stochastic_next_wealth( + savings: FloatND, + interest_rate: float, + period: Period, # noqa: ARG001 +) -> FloatND: + probs = jnp.where(interest_rate > 0, 0.5, 0.5) * jnp.ones_like(savings) + return jnp.stack([probs, probs]) + + +def _stochastic_next_aime( + aime: ContinuousState, + interest_rate: float, +) -> FloatND: + probs = jnp.where(interest_rate > 0, 0.5, 0.5) * jnp.ones_like(aime) + return jnp.stack([probs, probs]) + + +def _next_aime_depending_on_consumption( + aime: ContinuousState, consumption: ContinuousAction +) -> ContinuousState: + return aime + 0.1 * consumption + + +def _next_aime_decaying(aime: ContinuousState) -> ContinuousState: + return 0.95 * aime + + +def _impute_wealth_memo(wealth: ContinuousState) -> ContinuousState: + return wealth + + +def _next_wealth_memo(wealth_memo: ContinuousState) -> ContinuousState: + return wealth_memo + + +def _utility_reading_carried_state( + consumption: ContinuousAction, wealth_memo: ContinuousState +) -> FloatND: + return jnp.log(consumption) + 0.01 * wealth_memo + + +def _without_function(regime: UserRegime, name: str) -> UserRegime: + functions = {k: v for k, v in regime.functions.items() if k != name} + return regime.replace(functions=functions) + + +@categorical(ordered=False) +class _ShardedKind: + a: ScalarInt + b: ScalarInt + + +def _utility_reading_kind(consumption: ContinuousAction, kind: ScalarInt) -> FloatND: + return jnp.log(consumption) + 0.0 * kind + + +def _build_with_model_level_sharded_pruned() -> Model: + """The DCEGM regime never reads the sharded state, so it is pruned there.""" + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + return Model( + regimes={"retirement": VALID, "dead": dead}, + states={"kind": DiscreteGrid(_ShardedKind, distributed=True)}, + ages=ages, + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + + +def _build_with_model_level_sharded_used() -> Model: + """The DCEGM regime reads the sharded state, so it survives onto the regime.""" + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + retirement = VALID.replace( + functions={**dict(VALID.functions), "utility": _utility_reading_kind}, + state_transitions={ + **dict(VALID.state_transitions), + "kind": fixed_transition("kind"), + }, + ) + return Model( + regimes={"retirement": retirement, "dead": dead}, + states={"kind": DiscreteGrid(_ShardedKind, distributed=True)}, + ages=ages, + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + + +def _build_with_regime_level_sharded_terminal() -> Model: + """A distributed state is declared regime-level on the terminal target.""" + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + return Model( + regimes={ + "retirement": VALID, + "dead": dead.replace( + states={"kind": DiscreteGrid(_ShardedKind, distributed=True)} + ), + }, + ages=ages, + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + + +@pytest.mark.parametrize( + ("build", "match"), + [ + (_build_with_model_level_sharded_pruned, "pruned from non-terminal"), + (_build_with_model_level_sharded_used, "must not be distributed in a DCEGM"), + ( + _build_with_regime_level_sharded_terminal, + "sharding is declared at the model level", + ), + ], +) +def test_sharded_state_cannot_feed_a_dcegm_carry(build, match): + """No sharded state can reach a carry consumed by a DCEGM parent. + + A DCEGM parent reads its carry rows by integer indexing along whole discrete + axes; a device-sharded axis would break that index, and the carry channel is + not co-mapped device-local the way the continuation value array is. Three + independent rules already make every route to such a configuration + unconstructible β€” a model-level sharded state pruned from a non-terminal + regime, a sharded discrete state surviving onto a DCEGM regime, and a + regime-level `distributed` declaration are each rejected β€” so no dedicated + carry guard is needed. Relaxing any one rule must keep the carry case + rejected (or add carry co-mapping). + """ + with pytest.raises(ModelInitializationError, match=match): + build() + + +# A regime satisfying the full DC-EGM contract; every case below breaks one rule. +VALID = dcegm_variants.dcegm_retirement + + +CASES = { + "missing_resources_function": ( + lambda: _without_function(VALID, "resources"), + "resources", + ), + "missing_post_decision_function": ( + lambda: _without_function(VALID, "savings"), + "savings", + ), + "transition_bypasses_post_decision_state": ( + lambda: VALID.replace(state_transitions={"wealth": next_wealth}), + "post", + ), + "utility_depends_on_wealth_directly": ( + lambda: VALID.replace( + functions={ + **dict(VALID.functions), + "utility": _utility_with_direct_wealth_dependence, + } + ), + "utility", + ), + "constraint_touches_continuous_variables": ( + lambda: VALID.replace( + constraints={"borrowing_constraint": borrowing_constraint} + ), + "constraint", + ), + "utility_reads_continuous_state_through_carried_state": ( + lambda: VALID.replace( + states={ + **dict(VALID.states), + "wealth_memo": Phased( + solve=_impute_wealth_memo, + simulate=LinSpacedGrid(start=1.0, stop=400.0, n_points=4), + ), + }, + state_transitions={ + **dict(VALID.state_transitions), + "wealth_memo": _next_wealth_memo, + }, + functions={ + **dict(VALID.functions), + "utility": _utility_reading_carried_state, + }, + ), + "utility", + ), + "custom_bellman_aggregator": ( + lambda: VALID.replace(functions={**dict(VALID.functions), "H": _custom_H}), + "H", + ), + "second_continuous_action": ( + lambda: VALID.replace( + actions={ + **dict(VALID.actions), + "leisure": LinSpacedGrid(start=0.1, stop=1.0, n_points=5), + } + ), + "continuous action", + ), + "stochastic_passive_state_transition": ( + lambda: VALID.replace( + states={ + **dict(VALID.states), + "aime": LinSpacedGrid(start=0.0, stop=5.0, n_points=4), + }, + state_transitions={ + **dict(VALID.state_transitions), + "aime": MarkovTransition(_stochastic_next_aime), + }, + ), + "'aime'.*is stochastic", + ), + "passive_state_transition_depends_on_consumption": ( + lambda: VALID.replace( + states={ + **dict(VALID.states), + "aime": LinSpacedGrid(start=0.0, stop=5.0, n_points=4), + }, + state_transitions={ + **dict(VALID.state_transitions), + "aime": _next_aime_depending_on_consumption, + }, + ), + "not passive", + ), + "regime_transition_cliff_in_wealth": ( + lambda: VALID.replace(transition=_regime_transition_with_wealth_cliff), + "regime transition function.*discontinuous", + ), + "stochastic_euler_state_transition": ( + lambda: VALID.replace( + state_transitions={"wealth": MarkovTransition(_stochastic_next_wealth)} + ), + "stochastic", + ), + # `batch_size` on the Euler / discrete / passive grids is no longer a + # contract violation β€” it is the supported memory knob that splays the + # solve (Euler grid β†’ `lax.map` over asset nodes; combo grids β†’ per-axis + # `productmap`). Construction is covered below; numerical correctness in + # `tests/solution/test_egm_batch_size_euler.py` and `_combos.py`. + "runtime_savings_grid": ( + lambda: VALID.replace( + solver=dataclasses.replace( + dcegm_variants.DCEGM_SOLVER, + savings_grid=IrregSpacedGrid(n_points=8), + ) + ), + "runtime", + ), + "runtime_euler_state_grid": ( + lambda: VALID.replace(states={"wealth": IrregSpacedGrid(n_points=100)}), + "runtime", + ), + "runtime_continuous_action_grid": ( + lambda: VALID.replace(actions={"consumption": IrregSpacedGrid(n_points=50)}), + "runtime", + ), +} + + +@pytest.mark.parametrize(("build", "match"), CASES.values(), ids=CASES.keys()) +def test_dcegm_contract_violation_raises(build, match): + """Each contract violation fails fast at Model construction.""" + with pytest.raises(ModelInitializationError, match=match): + _build_model(build()) + + +def test_passive_continuous_state_constructs(): + """A passive continuous state (deterministic, decision-independent) is valid.""" + regime = VALID.replace( + states={ + **dict(VALID.states), + "aime": LinSpacedGrid(start=0.0, stop=5.0, n_points=4), + }, + state_transitions={ + **dict(VALID.state_transitions), + "aime": _next_aime_decaying, + }, + ) + model = _build_model(regime) + assert model.n_periods == N_PERIODS + + +def test_dcegm_phased_H_with_default_solve_variant_constructs(): + """A `Phased` H whose solve variant is the default aggregator is admitted. + + DC-EGM reads only the solve-phase `H`; the simulate variant is free. A naive + present-bias regime declares `H = Phased(solve=H_linear, simulate=...)`, so + the solve runs the exact Euler inversion and present bias enters only the + simulate-phase re-optimization. + """ + regime = VALID.replace( + functions={ + **dict(VALID.functions), + "H": Phased(solve=H_linear, simulate=_custom_H), + } + ) + model = _build_model(regime) + assert model.n_periods == N_PERIODS + + +def test_dcegm_phased_H_with_custom_solve_variant_raises(): + """A `Phased` H whose *solve* variant is custom still violates the contract.""" + regime = VALID.replace( + functions={ + **dict(VALID.functions), + "H": Phased(solve=_custom_H, simulate=H_linear), + } + ) + with pytest.raises(ModelInitializationError, match="solve-phase Bellman"): + _build_model(regime) + + +def test_batched_euler_state_grid_constructs(): + """`batch_size` on the Euler grid is a valid memory knob, not a violation. + + It splays the per-asset-node solve into `lax.map` blocks; the solver still + builds. Numerical invariance across block sizes is covered in + `tests/solution/test_egm_batch_size_euler.py`. + """ + regime = VALID.replace( + states={"wealth": LinSpacedGrid(start=1, stop=400, n_points=100, batch_size=50)} + ) + model = _build_model(regime) + assert model.n_periods == N_PERIODS + + +def _impute_pension(age: int) -> ContinuousState: + return jnp.asarray(0.1 * age) + + +def _next_pension(pension: ContinuousState) -> ContinuousState: + return pension + + +def test_carried_state_with_decision_free_imputation_constructs(): + """A carried state imputed independently of the decision variables is valid. + + Carried states are derived functions in the solve phase β€” no grid axis β€” + so they are invisible to the DC-EGM state classification, and a + decision-free imputation keeps every consumer evaluable at the savings + stage. + """ + regime = VALID.replace( + states={ + **dict(VALID.states), + "pension": Phased( + solve=_impute_pension, + simulate=LinSpacedGrid(start=0.0, stop=10.0, n_points=4), + ), + }, + state_transitions={ + **dict(VALID.state_transitions), + "pension": _next_pension, + }, + ) + model = _build_model(regime) + assert model.n_periods == N_PERIODS + + +def _cliff_supplement(wealth: ContinuousState) -> FloatND: + return jnp.where(wealth <= 100.0, 5.0, 0.0) + + +def _kinked_supplement(wealth: ContinuousState) -> FloatND: + return 5.0 * jnp.clip((150.0 - wealth) / 50.0, 0.0, 1.0) + + +def _next_wealth_with_cliff( + savings: FloatND, cliff_supplement: FloatND +) -> ContinuousState: + return savings + cliff_supplement + + +def _next_wealth_with_kink( + savings: FloatND, kinked_supplement: FloatND +) -> ContinuousState: + return savings + kinked_supplement + + +def test_euler_law_with_cliff_in_euler_state_raises(): + """A law whose residual jumps in the Euler state fails at model build. + + A jump makes the child's value function discontinuous, so the true + policy bunches next-period wealth at the discontinuity β€” a corner where + the Euler equation does not hold and which EGM's candidate set cannot + represent. Kinked (continuous) residuals are solvable per asset node. + """ + regime = VALID.replace( + state_transitions={"wealth": _next_wealth_with_cliff}, + functions={**dict(VALID.functions), "cliff_supplement": _cliff_supplement}, + ) + with pytest.raises(ModelInitializationError, match=r"discontinuous.*bunches"): + _build_model(regime) + + +def test_euler_law_with_kinked_phase_out_constructs(): + """A law reading the Euler state through a continuous kink is valid.""" + regime = VALID.replace( + state_transitions={"wealth": _next_wealth_with_kink}, + functions={**dict(VALID.functions), "kinked_supplement": _kinked_supplement}, + ) + model = _build_model(regime) + assert model.n_periods == N_PERIODS + + +def _retirement_stay_prob(age: int, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 0.0, 1.0) + + +def _retirement_death_prob(age: int, final_age_alive: float) -> FloatND: + return jnp.where(age >= final_age_alive, 1.0, 0.0) + + +def _three_regime_model_with_brute_worker(retirement_transition) -> Model: + """Model with a brute-force worker regime next to a DC-EGM retirement regime.""" + ages = AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "working_life": base.working_life.replace( + active=lambda age, la=last_age: age < la + ), + "retirement": dcegm_variants.dcegm_retirement_full.replace( + transition=retirement_transition, + active=lambda age, la=last_age: age < la, + ), + "dead": dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + + +def test_granular_transition_excluding_brute_regime_passes(): + """Declared reachability narrows the target-compatibility check. + + A granular regime transition declares its key set as the reachable + targets; regimes outside it are structurally unreachable. A DC-EGM + regime whose declared targets are itself and a terminal regime may + therefore coexist with a brute-force non-terminal regime it never + transitions into (the brute regime targeting the DC-EGM regime is + allowed in that direction). + """ + model = _three_regime_model_with_brute_worker( + { + "retirement": MarkovTransition(_retirement_stay_prob), + "dead": MarkovTransition(_retirement_death_prob), + } + ) + assert model.n_periods == N_PERIODS + + +def test_coarse_transition_reaching_brute_regime_raises(): + """A coarse regime transition declares every regime reachable. + + The same model fails the target-compatibility check once the DC-EGM + regime's transition is a bare callable: the brute-force non-terminal + regime becomes a declared target. + """ + with pytest.raises(ModelInitializationError, match="GridSearch"): + _three_regime_model_with_brute_worker(base.next_regime_from_retirement) + + +def test_non_dcegm_non_terminal_target_raises(): + """A DC-EGM regime may not target a brute-force non-terminal regime.""" + brute_target = dcegm_variants.dcegm_retirement.replace( + solver=GridSearch(), + state_transitions={"wealth": next_wealth}, + constraints={"borrowing_constraint": borrowing_constraint}, + functions={"utility": utility_retirement}, + ) + dcegm_source = dcegm_variants.dcegm_working_life.replace( + active=lambda age: age < 60, + ) + ages = AgeGrid(start=40, stop=60, step="10Y") + with pytest.raises( + ModelInitializationError, + match="non-terminal target of a DCEGM regime must itself use the DCEGM", + ): + Model( + regimes={ + "working_life": dcegm_source, + "retirement": brute_target.replace(active=lambda age: age < 60), + "dead": dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + + +def _ordinary_inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + return 1.0 / marginal_continuation + + +def test_brute_force_inverse_marginal_utility_keeps_its_params(): + """`marginal_continuation` stays a user param outside DC-EGM regimes. + + Only the DC-EGM kernel supplies `marginal_continuation` at solve time. In + a brute-force regime, a function named `inverse_marginal_utility` is an + ordinary regime function, so its argument must surface in the params + template like any other. + """ + regime = retirement_only.retirement.replace( + functions={ + **dict(retirement_only.retirement.functions), + "inverse_marginal_utility": _ordinary_inverse_marginal_utility, + }, + active=lambda age: age < 60, + ) + model = _build_model(regime) + + template = model.get_params_template() + + assert "marginal_continuation" in template["retirement"]["inverse_marginal_utility"] + + +def test_brute_force_solver_explicit_equals_default(): + """`solver=GridSearch()` is the default: identical solution either way.""" + params = retirement_only.get_params(N_PERIODS) + + default_model = retirement_only.get_model(N_PERIODS) + explicit = retirement_only.retirement.replace( + solver=GridSearch(), + active=lambda age: age < 60, + ) + explicit_model = _build_model(explicit) + + got_default = default_model.solve(params=params, log_level="debug") + got_explicit = explicit_model.solve(params=params, log_level="debug") + + for period in got_default: + for regime in got_default[period]: + assert bool( + jnp.array_equal( + got_default[period][regime], got_explicit[period][regime] + ) + ) diff --git a/tests/test_distributed.py b/tests/test_distributed.py index e29a4b081..cf05186a6 100644 --- a/tests/test_distributed.py +++ b/tests/test_distributed.py @@ -221,20 +221,29 @@ def _compiled_solve_kernel_hlo(model: Model, *, regime_name: str, period: int) - {name: _build_zero_V_arr(topology=topo) for name, topo in topology.items()} ) regime = regimes[regime_name] - state_action_space = regime.solution.state_action_space( - regime_params=flat_params[regime_name] - ) - lower_args = { - **dict(state_action_space.states), - **dict(state_action_space.actions), - "next_regime_to_V_arr": next_regime_to_V_arr, - **dict(flat_params[regime_name]), - "period": jnp.int32(period), - "age": model.ages.values[period], # noqa: PD011 - } - kernel = regime.solution.max_Q_over_a[period] - hlo = jax.jit(kernel).lower(**lower_args).compile().as_text() - assert hlo is not None + period_kernel = regime.solution.period_kernels[period] + # Lower every shared core the period kernel carries exactly as backward + # induction does (a brute regime carries the single `"main"` core); the + # continuation V enters through `build_lower_args`, so the optimized HLO + # reflects the real sharded read. + texts: list[str] = [] + for core_key, core in period_kernel.cores().items(): + lower_args = period_kernel.build_lower_args( + core_key=core_key, + state_action_space=regime.solution.state_action_space( + regime_params=flat_params[regime_name] + ), + next_regime_to_V_arr=next_regime_to_V_arr, + next_regime_to_egm_carry=MappingProxyType({}), + flat_params=flat_params, + period=period, + ages=model.ages, + ) + text = jax.jit(core).lower(**lower_args).compile().as_text() + assert text is not None + texts.append(text) + hlo = "\n".join(texts) + assert hlo return hlo diff --git a/tests/test_ds_app1_euler_accuracy.py b/tests/test_ds_app1_euler_accuracy.py new file mode 100644 index 000000000..96b86ffb8 --- /dev/null +++ b/tests/test_ds_app1_euler_accuracy.py @@ -0,0 +1,191 @@ +"""DS-2026 Application 1 FUES Euler-error accuracy harness. + +Application 1 of Dobrescu & Shanker (2026) is the deterministic discrete-retirement +model: log utility with a per-period work cost `tau`, a deterministic wage while +working, an absorbing retirement choice, and a constant gross return. The paper's +Table 2 reports the FUES accuracy column as the mean `log10` consumption Euler +error along a simulated sample path (Judd 1992). FUES is pylcm's default DC-EGM +upper envelope, so the harness solves the model with DC-EGM, simulates, and scores +the Euler equation along the working-regime path. The same harness scores the RFC +column (the paper's fourth method) by passing `upper_envelope="rfc"`. + +These tests run a single small solve at a time (asset grid <= 1000, shortened +horizon) so they stay local-safe; the full paper grids {1000..10000} at T=50 are a +GPU/CI sweep. +""" + +import numpy as np +import pandas as pd +import pytest + +from benchmarks.ds_replication.app1_retirement_accuracy import ( + app1_accuracy_table, + app1_euler_error, + app1_timing, + sample_path_euler_error, +) + +# Local-safe horizon: shorter than the paper's T=50 so a single solve+simulate is +# fast, but long enough that workers retire mid-path and the working-regime Euler +# equation has interior, non-switch points to score. +_LOCAL_N_PERIODS = 20 +_LOCAL_N_SUBJECTS = 300 + + +def test_app1_euler_error_is_finite_and_in_paper_ballpark(): + """The FUES Euler error at tau=1, n_grid=1000 is finite, negative, and sane. + + The mean log10 consumption Euler error is a negative number (more negative = + more accurate); the paper reports roughly -1.6 for tau=1 at the full grids, + so at a coarser local grid the metric sits in the -1.0 to -4.0 band. + """ + error = app1_euler_error( + tau=1.0, + n_grid=1000, + n_periods=_LOCAL_N_PERIODS, + n_subjects=_LOCAL_N_SUBJECTS, + seed=0, + ) + assert np.isfinite(error) + assert -4.0 < error < -1.0 + + +def test_app1_euler_error_improves_under_grid_refinement(): + """A finer asset grid yields a more accurate (more negative) FUES Euler error. + + The endogenous grid method nulls the Euler residual at the endogenous nodes; + interpolating the policy back onto the coarse exogenous grid reintroduces it, + so refining the grid drives the residual down. Going from 300 to 1000 asset + points must shrink the mean log10 error by a clear margin. + """ + coarse = app1_euler_error( + tau=1.0, + n_grid=300, + n_periods=_LOCAL_N_PERIODS, + n_subjects=_LOCAL_N_SUBJECTS, + seed=0, + ) + fine = app1_euler_error( + tau=1.0, + n_grid=1000, + n_periods=_LOCAL_N_PERIODS, + n_subjects=_LOCAL_N_SUBJECTS, + seed=0, + ) + assert -4.0 < coarse < -1.0 + assert -4.0 < fine < -1.0 + assert fine < coarse - 0.5 + + +def test_app1_accuracy_table_has_one_row_per_cell(): + """The sweep returns one FUES Euler-error row per `(tau, n_grid)` cell.""" + table = app1_accuracy_table( + taus=(1.0,), + n_grids=(300, 1000), + n_periods=_LOCAL_N_PERIODS, + n_subjects=_LOCAL_N_SUBJECTS, + seed=0, + ) + assert list(table.columns) == ["tau", "n_grid", "fues_euler_error"] + assert len(table) == 2 + assert table["fues_euler_error"].between(-4.0, -1.0).all() + + +def test_sample_path_euler_error_recovers_a_planted_residual(): + """A hand-built two-period working path reproduces its analytic Euler error. + + With `c_t` chosen so that `c_euler_t = c_{t+1} / (beta*(1+r))` overshoots `c_t` + by exactly 10%, the relative deviation is 0.1 and the metric is `log10(0.1)`. + The retirement-switch and constrained points are dropped, leaving only the + single interior working-to-working transition. + """ + beta, r = 0.96, 0.02 + c_next = 8.0 + c_euler = c_next / (beta * (1.0 + r)) + c_t = c_euler / 1.1 # so c_euler / c_t - 1 = 0.1 + panel = pd.DataFrame( + { + "subject_id": [0, 0, 0], + "period": [0, 1, 2], + "regime_name": ["working_life", "working_life", "retirement"], + "labor_supply": ["work", "work", "retire"], + "consumption": [c_t, c_next, 5.0], + # Interior: consumption leaves strictly positive savings. + "wealth": [c_t + 50.0, c_next + 50.0, 30.0], + } + ) + error = sample_path_euler_error(panel=panel, interest_rate=r, discount_factor=beta) + assert error == pytest.approx(np.log10(0.1), abs=1e-9) + + +def test_app1_rfc_euler_error_is_in_the_same_regime_as_fues(): + """RFC-1D reproduces the FUES accuracy regime on Application 1. + + The rooftop-cut (`upper_envelope="rfc"`) and the FUES scan are both exact at + the endogenous nodes and reintroduce the residual only through the policy + interpolation onto the coarse grid, so on this retirement model they land in + the same mean log10 Euler-error band. + """ + config = { + "tau": 1.0, + "n_grid": 1000, + "n_periods": _LOCAL_N_PERIODS, + "n_subjects": _LOCAL_N_SUBJECTS, + "seed": 0, + } + fues = app1_euler_error(upper_envelope="fues", **config) + rfc = app1_euler_error(upper_envelope="rfc", **config) + assert np.isfinite(rfc) + assert -4.0 < rfc < -1.0 + assert abs(rfc - fues) < 1.0 + + +def test_app1_timing_separates_compile_from_runtime(): + """The first solve times compile-plus-run; later solves time pure execution. + + JAX caches the compiled solve, so the compile cost (first-call time minus the + steady-state runtime) is strictly positive, and the steady-state runtime is a + finite, positive number. + """ + timing = app1_timing(tau=1.0, n_grid=300, n_periods=_LOCAL_N_PERIODS, n_runs=2) + assert np.isfinite(timing["compile_time"]) + assert np.isfinite(timing["runtime"]) + assert timing["runtime"] > 0.0 + assert timing["compile_time"] > 0.0 + + +def test_app1_timing_measures_compile_after_a_warm_cache(): + """Compile time stays positive even if the same config was solved earlier. + + `app1_timing` clears the JAX compilation cache before its first solve, so a + prior solve of the same `(method, shape)` does not warm-start the compile + measurement into noise. + """ + app1_euler_error( + tau=1.0, + n_grid=300, + n_periods=_LOCAL_N_PERIODS, + n_subjects=_LOCAL_N_SUBJECTS, + seed=0, + ) + timing = app1_timing(tau=1.0, n_grid=300, n_periods=_LOCAL_N_PERIODS, n_runs=2) + assert timing["compile_time"] > 0.0 + + +def test_app1_taste_shock_variant_is_in_paper_ballpark(): + """The taste-shock retirement variant (Table 6, scale 0.05) scores a sane error. + + EV1 taste shocks smooth the work/retire margin but leave the continuous + consumption Euler equation intact, so the mean log10 error stays in the same + band as the deterministic Table 2 baseline. + """ + error = app1_euler_error( + tau=1.0, + n_grid=1000, + n_periods=_LOCAL_N_PERIODS, + n_subjects=_LOCAL_N_SUBJECTS, + seed=0, + taste_shock_scale=0.05, + ) + assert np.isfinite(error) + assert -4.0 < error < -1.0 diff --git a/tests/test_ds_app3_euler_accuracy.py b/tests/test_ds_app3_euler_accuracy.py new file mode 100644 index 000000000..8a19d717f --- /dev/null +++ b/tests/test_ds_app3_euler_accuracy.py @@ -0,0 +1,303 @@ +"""DS-2026 Application 3 VFI Euler-error accuracy harness. + +Application 3 of Dobrescu & Shanker (2026) is the discrete-housing model +(extended Fella 2014): log Cobb-Douglas utility over consumption and housing +services, a discrete housing stock with an own-vs-rent choice, a proportional +housing-adjustment cost, and a **Markov wage**. The paper's no-tax tables +(Table 4 / Table 7) report the VFI accuracy column as the mean `log10` +consumption Euler error along a simulated sample path. The brute/VFI (GridSearch) +solver solves this model locally, so the harness solves, simulates, and scores +the stochastic Euler equation along the working-regime path β€” the wage being +Markov, the Euler expectation is a transition-probability-weighted sum over +next-period wage nodes. + +These tests run a single small solve at a time (asset grid <= 80, wage nodes +<= 5, shortened horizon) so they stay local-safe; the full paper grids at T=20 +are a GPU/CI sweep. +""" + +import numpy as np +import pandas as pd +import pytest + +from benchmarks.ds_replication.app3_discrete_housing_accuracy import ( + _wage_nodes_and_transition, + app3_vfi_accuracy_table, + app3_vfi_euler_error, + sample_path_euler_error, +) + +# Local-safe horizon: shorter than the paper's T=20 so a single solve+simulate is +# fast, but long enough that the working-regime Euler equation has interior, +# non-switch points to score. +_LOCAL_N_PERIODS = 10 +_LOCAL_N_SUBJECTS = 200 + + +def test_app3_vfi_euler_error_is_finite_negative_and_in_vfi_band(): + """The VFI Euler error at a small grid is finite, negative, and VFI-plausible. + + The mean log10 consumption Euler error is a negative number (more negative = + more accurate). The brute/VFI solver searches consumption on a discrete grid, + so at these small grids the metric sits in a coarse-VFI band, roughly -3.0 to + -0.5. + """ + error = app3_vfi_euler_error( + n_assets=40, + n_wage_nodes=3, + n_periods=_LOCAL_N_PERIODS, + n_consumption=60, + n_subjects=_LOCAL_N_SUBJECTS, + seed=0, + ) + assert np.isfinite(error) + assert -3.0 < error < -0.5 + + +def test_app3_vfi_euler_error_stays_in_band_across_consumption_grids(): + """The VFI error stays in the coarse-VFI band across consumption-grid sizes. + + The grid-search solver chooses consumption on a discrete grid, so the + consumption-grid resolution drives its accuracy. Both a coarse and a finer + consumption grid land in the same plausible VFI band β€” the metric is a finite, + negative number throughout (the monotone full-horizon refinement is a T=20 + GPU/CI-scale property, noisy at the short local horizon). + """ + coarse = app3_vfi_euler_error( + n_assets=40, + n_wage_nodes=3, + n_periods=_LOCAL_N_PERIODS, + n_consumption=40, + n_subjects=_LOCAL_N_SUBJECTS, + seed=0, + ) + fine = app3_vfi_euler_error( + n_assets=40, + n_wage_nodes=3, + n_periods=_LOCAL_N_PERIODS, + n_consumption=120, + n_subjects=_LOCAL_N_SUBJECTS, + seed=0, + ) + assert -3.0 < coarse < -0.5 + assert -3.0 < fine < -0.5 + + +def test_app3_vfi_accuracy_table_has_one_row_per_asset_grid(): + """The sweep returns one VFI Euler-error row per asset-grid size.""" + table = app3_vfi_accuracy_table( + n_assets_grid=(30, 40), + n_wage_nodes=3, + n_periods=_LOCAL_N_PERIODS, + n_consumption=60, + n_subjects=_LOCAL_N_SUBJECTS, + seed=0, + ) + assert list(table.columns) == ["n_assets", "n_wage_nodes", "vfi_euler_error"] + assert len(table) == 2 + assert table["vfi_euler_error"].between(-3.0, -0.5).all() + + +def test_sample_path_euler_error_weights_the_markov_wage_expectation(): + """A hand-built path reproduces its analytic transition-weighted Euler error. + + With two wage nodes whose transition row `P[wage_t] = (0.25, 0.75)` mixes a + next-period consumption of 4 (at wage node 0) and 8 (at wage node 1) for the + held housing level, the expected marginal utility is + `0.25*alpha/4 + 0.75*alpha/8`, so + `c_euler = alpha / (beta*(1+r) * E[u'])`. The single interior, + non-housing-switch working-to-working transition reproduces + `log10(|c_euler/c_t - 1|)` exactly. + """ + alpha, beta, r = 0.77, 0.93, 0.06 + wage_nodes = np.array([-0.4, 0.4]) + # Source wage node 0; its transition row mixes the two next-period nodes. + wage_transition = np.array([[0.25, 0.75], [0.5, 0.5]]) + c_next_node0, c_next_node1 = 4.0, 8.0 + expected_marginal = 0.25 * alpha / c_next_node0 + 0.75 * alpha / c_next_node1 + c_euler = alpha / (beta * (1.0 + r) * expected_marginal) + c_t = c_euler / 1.1 # so |c_euler / c_t - 1| = 0.1 + + sample_panel = pd.DataFrame( + { + "subject_id": [0, 0], + "period": [0, 1], + "regime_name": ["working", "working"], + "assets": [10.0, 5.0], # next assets > 0: interior, unconstrained + "wage": [wage_nodes[0], wage_nodes[0]], + "consumption": [c_t, 6.0], + "housing": ["own_h2", "own_h2"], + "housing_choice": ["own_h2", "own_h2"], # no switch this period or next + } + ) + # The policy panel supplies `c_{t+1}(a'=5, own_h2, wage_j)` for each next node. + policy_panel = pd.DataFrame( + { + "subject_id": [0, 1], + "period": [1, 1], + "regime_name": ["working", "working"], + "assets": [5.0, 5.0], + "wage": [wage_nodes[0], wage_nodes[1]], + "consumption": [c_next_node0, c_next_node1], + "housing": ["own_h2", "own_h2"], + "housing_choice": ["own_h2", "own_h2"], + } + ) + error = sample_path_euler_error( + sample_panel=sample_panel, + policy_panel=policy_panel, + wage_nodes=wage_nodes, + wage_transition=wage_transition, + interest_rate=r, + discount_factor=beta, + alpha=alpha, + ) + assert error == pytest.approx(np.log10(0.1), abs=1e-9) + + +def test_sample_path_euler_error_drops_housing_switch_points(): + """A working-to-working transition that switches housing is not scored. + + The discrete housing-adjustment margin is a value-function kink, so a point + where the held housing differs from the chosen housing is excluded β€” exactly + as Application 1 excludes the work/retire switch. With every transition a + switch, no point survives and the scorer raises. + """ + wage_nodes = np.array([-0.4, 0.4]) + wage_transition = np.array([[0.5, 0.5], [0.5, 0.5]]) + sample_panel = pd.DataFrame( + { + "subject_id": [0, 0], + "period": [0, 1], + "regime_name": ["working", "working"], + "assets": [10.0, 5.0], + "wage": [wage_nodes[0], wage_nodes[0]], + "consumption": [3.0, 6.0], + "housing": ["rent", "rent"], + "housing_choice": ["own_h1", "own_h1"], # switches both periods + } + ) + policy_panel = pd.DataFrame( + { + "subject_id": [0], + "period": [1], + "regime_name": ["working"], + "assets": [5.0], + "wage": [wage_nodes[0]], + "consumption": [6.0], + "housing": ["own_h1"], + "housing_choice": ["own_h1"], + } + ) + with pytest.raises(ValueError, match="No valid interior"): + sample_path_euler_error( + sample_panel=sample_panel, + policy_panel=policy_panel, + wage_nodes=wage_nodes, + wage_transition=wage_transition, + ) + + +def test_sample_path_euler_error_with_taxes_uses_after_tax_marginal_return(): + """With taxes the scorer discounts by `1 + r - T'(a')`, not the gross `1 + r`. + + The with-tax budget is `R = (1 + r) a - T(a) + y + h`, so a unit of saving earns + `1 + r - T'(a')` and the interior consumption Euler equation reads + `u'(c_t) = beta (1 + r - tau_k) E[u'(c_{t+1})]`, with `tau_k` the marginal rate + of the bracket holding `a'`. At `a' = 5.0` the bracket `[3.87, 6.97)` has + `tau_k = 0.024`, so the implied consumption uses the return `1.06 - 0.024`. + """ + alpha, beta, r = 0.77, 0.93, 0.06 + after_tax_return = 1.0 + r - 0.024 # bracket [3.87, 6.97) marginal rate + wage_nodes = np.array([-0.4, 0.4]) + wage_transition = np.array([[0.25, 0.75], [0.5, 0.5]]) + c_next_node0, c_next_node1 = 4.0, 8.0 + expected_marginal = 0.25 * alpha / c_next_node0 + 0.75 * alpha / c_next_node1 + c_euler = alpha / (beta * after_tax_return * expected_marginal) + c_t = c_euler / 1.1 # so |c_euler / c_t - 1| = 0.1 + + sample_panel = pd.DataFrame( + { + "subject_id": [0, 0], + "period": [0, 1], + "regime_name": ["working", "working"], + "assets": [10.0, 5.0], # a' = 5.0 sits in bracket [3.87, 6.97) + "wage": [wage_nodes[0], wage_nodes[0]], + "consumption": [c_t, 6.0], + "housing": ["own_h2", "own_h2"], + "housing_choice": ["own_h2", "own_h2"], + } + ) + policy_panel = pd.DataFrame( + { + "subject_id": [0, 1], + "period": [1, 1], + "regime_name": ["working", "working"], + "assets": [5.0, 5.0], + "wage": [wage_nodes[0], wage_nodes[1]], + "consumption": [c_next_node0, c_next_node1], + "housing": ["own_h2", "own_h2"], + "housing_choice": ["own_h2", "own_h2"], + } + ) + error = sample_path_euler_error( + sample_panel=sample_panel, + policy_panel=policy_panel, + wage_nodes=wage_nodes, + wage_transition=wage_transition, + interest_rate=r, + discount_factor=beta, + alpha=alpha, + use_taxes=True, + ) + assert error == pytest.approx(np.log10(0.1), abs=1e-9) + + +def test_sample_path_euler_error_with_taxes_excludes_tax_notch_points(): + """A point whose next assets sit on a tax-bracket boundary is not scored. + + At a bracket boundary the capital-income tax's level jump makes `T'` one-sided + or undefined, so the smooth Euler equality does not hold there. With the single + transition landing exactly on the boundary `a' = 6.97`, no point survives the + with-tax filter and the scorer raises. + """ + wage_nodes = np.array([-0.4, 0.4]) + wage_transition = np.array([[0.5, 0.5], [0.5, 0.5]]) + sample_panel = pd.DataFrame( + { + "subject_id": [0, 0], + "period": [0, 1], + "regime_name": ["working", "working"], + "assets": [10.0, 6.97], # a' = 6.97 is the bracket boundary + "wage": [wage_nodes[0], wage_nodes[0]], + "consumption": [3.0, 6.0], + "housing": ["own_h2", "own_h2"], + "housing_choice": ["own_h2", "own_h2"], + } + ) + policy_panel = pd.DataFrame( + { + "subject_id": [0], + "period": [1], + "regime_name": ["working"], + "assets": [6.97], + "wage": [wage_nodes[0]], + "consumption": [6.0], + "housing": ["own_h2"], + "housing_choice": ["own_h2"], + } + ) + with pytest.raises(ValueError, match="No valid interior"): + sample_path_euler_error( + sample_panel=sample_panel, + policy_panel=policy_panel, + wage_nodes=wage_nodes, + wage_transition=wage_transition, + use_taxes=True, + ) + + +def test_wage_transition_rows_are_probabilities(): + """The Rouwenhorst wage transition matrix has rows summing to one.""" + _nodes, transition = _wage_nodes_and_transition(n_wage_nodes=5) + np.testing.assert_allclose(transition.sum(axis=1), 1.0, atol=1e-10) diff --git a/tests/test_models/dcegm_paper_twin.py b/tests/test_models/dcegm_paper_twin.py new file mode 100644 index 000000000..1fd967c50 --- /dev/null +++ b/tests/test_models/dcegm_paper_twin.py @@ -0,0 +1,328 @@ +"""pylcm twin of the `dcegm` package's IJRS consumption-retirement toy model. + +Mirrors the model documented in `tests/data/dcegm_reference/generate_fixtures.py` +so its solution is comparable to the fixture CSV generated by the independent +`dcegm` implementation: + +- CRRA utility `(c**(1 - rho) - 1) / (1 - rho)` minus work disutility `delta`; + EV1 taste shocks on the work/retire choice (scale is a runtime param). +- Income is earned one period after working and indexed by the receiving + period's age: the wealth transition uses the *current* work choice, which is + exactly the `dcegm` lagged-choice timing. +- Retirement is absorbing (separate regime without the work action). +- The `dcegm` final period consumes everything but still draws the taste shock + on the (income-less) work/retire choice. Its smoothed value has the closed + form `crra(wealth) + scale * log(1 + exp(-delta / scale))` for an agent who + was working, and `crra(wealth)` for a retiree β€” encoded as two terminal + regimes. + +Builders return the brute-force and DC-EGM spec variants of the same model. +""" + +import dataclasses +import functools +from typing import Literal + +import jax.numpy as jnp + +from _lcm.grids import ContinuousGrid +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + LogSpacedGrid, + Model, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.taste_shocks import ExtremeValueTasteShocks +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteAction, + FloatND, + ScalarInt, +) + +MIN_AGE = 20 +N_PERIODS = 10 +LAST_ALIVE_AGE = MIN_AGE + N_PERIODS - 2 # 28; the final period is terminal + +# The wealth grid must reach down to the consumption floor (0.001): the floor +# makes near-zero wealth reachable, and a grid that starts above it lets the +# brute solver's edge clamp make consuming down to the floor look good. CRRA +# value is sharply curved at low wealth, so the grid is geometric below 0.5, +# fine-stepped through the low fixture nodes (1, 2, 5), and 0.5-stepped above +# β€” every fixture wealth point (1, 2, 5, 10, 20, 35) sits exactly on a node. +_FLOOR_WEALTH_POINTS = tuple(0.001 * (0.5 / 0.001) ** (i / 120) for i in range(120)) +_MID_WEALTH_POINTS = tuple(0.5 + 0.05 * i for i in range(90)) +_TOP_WEALTH_POINTS = tuple(5.0 + 0.25 * i for i in range(181)) +WEALTH_GRID = IrregSpacedGrid( + points=_FLOOR_WEALTH_POINTS + _MID_WEALTH_POINTS + _TOP_WEALTH_POINTS +) +# Log spacing resolves the small optimal consumption of poor retirees; the +# lower end matches the consumption floor so the lowest wealth node keeps a +# feasible consumption choice. +CONSUMPTION_GRID = LogSpacedGrid(start=0.001, stop=50.0, n_points=400) +# Matches the `dcegm` run's exogenous savings grid exactly. Its uniform +# spacing under-resolves the sharply curved retiree value function near the +# borrowing limit (in the reference implementation and in pylcm alike); the +# fixture comparison keeps it for comparability, and +# `build_dcegm_model(savings_grid=...)` accepts a clustered grid where the +# low-wealth region matters. +SAVINGS_GRID = LinSpacedGrid(start=0.0, stop=50.0, n_points=500) + + +@categorical(ordered=False) +class TwinRegimeId: + working_life: ScalarInt + retirement: ScalarInt + done_from_working: ScalarInt + done_retired: ScalarInt + + +@categorical(ordered=True) +class WorkChoice: + work: ScalarInt + retire: ScalarInt + + +def crra(consumption: FloatND, rho: float) -> FloatND: + return (consumption ** (1.0 - rho) - 1.0) / (1.0 - rho) + + +def is_working(work_choice: DiscreteAction) -> BoolND: + return work_choice == WorkChoice.work + + +def utility_working( + consumption: ContinuousAction, is_working: BoolND, rho: float, delta: float +) -> FloatND: + return crra(consumption, rho) - jnp.where(is_working, delta, 0.0) + + +def utility_retired(consumption: ContinuousAction, rho: float) -> FloatND: + return crra(consumption, rho) + + +def utility_done_from_working( + wealth: ContinuousState, rho: float, delta: float, taste_scale: float +) -> FloatND: + """Smoothed consume-all value incl. the final-period choice taste shock.""" + return crra(wealth, rho) + taste_scale * jnp.log( + 1.0 + jnp.exp(-delta / taste_scale) + ) + + +def utility_done_retired(wealth: ContinuousState, rho: float) -> FloatND: + return crra(wealth, rho) + + +def labor_income( + is_working: BoolND, + age: float, + constant: float, + exp_coeff: float, + exp_squared: float, +) -> FloatND: + """Income from working this period, paid next period at next period's age.""" + next_age = age + 1.0 + log_income = constant + exp_coeff * next_age + exp_squared * next_age**2 + return jnp.where(is_working, jnp.exp(log_income), 0.0) + + +def next_wealth( + wealth: ContinuousState, + consumption: ContinuousAction, + labor_income: FloatND, + interest_rate: float, + floor: float, +) -> ContinuousState: + return jnp.maximum( + (1.0 + interest_rate) * (wealth - consumption) + labor_income, floor + ) + + +def resources(wealth: ContinuousState) -> FloatND: + return wealth + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + return resources - consumption + + +def next_wealth_from_savings( + savings: FloatND, + labor_income: FloatND, + interest_rate: float, + floor: float, +) -> ContinuousState: + return jnp.maximum((1.0 + interest_rate) * savings + labor_income, floor) + + +def inverse_marginal_utility(marginal_continuation: FloatND, rho: float) -> FloatND: + """Inverse of `u'(c) = c**(-rho)`.""" + return marginal_continuation ** (-1.0 / rho) + + +def borrowing_constraint( + consumption: ContinuousAction, wealth: ContinuousState +) -> BoolND: + return consumption <= wealth + + +def next_regime_from_working(work_choice: DiscreteAction, age: float) -> ScalarInt: + last = age >= LAST_ALIVE_AGE + retire = work_choice == WorkChoice.retire + return jnp.where( + last, + jnp.where(retire, TwinRegimeId.done_retired, TwinRegimeId.done_from_working), + jnp.where(retire, TwinRegimeId.retirement, TwinRegimeId.working_life), + ) + + +def next_regime_from_retirement(age: float) -> ScalarInt: + return jnp.where( + age >= LAST_ALIVE_AGE, TwinRegimeId.done_retired, TwinRegimeId.retirement + ) + + +done_from_working = UserRegime( + transition=None, + states={"wealth": WEALTH_GRID}, + functions={"utility": utility_done_from_working}, +) + +done_retired = UserRegime( + transition=None, + states={"wealth": WEALTH_GRID}, + functions={"utility": utility_done_retired}, +) + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, +) + + +def _working_life(solver: Literal["brute_force", "dcegm"]) -> UserRegime: + brute = UserRegime( + transition=next_regime_from_working, + states={"wealth": WEALTH_GRID}, + actions={ + "work_choice": DiscreteGrid(WorkChoice), + "consumption": CONSUMPTION_GRID, + }, + taste_shocks=ExtremeValueTasteShocks(), + active=lambda age: age <= LAST_ALIVE_AGE, + state_transitions={"wealth": next_wealth}, + constraints={"borrowing_constraint": borrowing_constraint}, + functions={ + "utility": utility_working, + "is_working": is_working, + "labor_income": labor_income, + }, + ) + if solver == "brute_force": + return brute + return brute.replace( + state_transitions={"wealth": next_wealth_from_savings}, + constraints={}, + functions={ + "utility": utility_working, + "is_working": is_working, + "labor_income": labor_income, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, + ) + + +def _retirement(solver: Literal["brute_force", "dcegm"]) -> UserRegime: + brute = UserRegime( + transition=next_regime_from_retirement, + states={"wealth": WEALTH_GRID}, + actions={"consumption": CONSUMPTION_GRID}, + active=lambda age: age <= LAST_ALIVE_AGE, + state_transitions={"wealth": next_wealth}, + constraints={"borrowing_constraint": borrowing_constraint}, + functions={"utility": utility_retired}, + ) + if solver == "brute_force": + return brute + return brute.replace( + state_transitions={"wealth": next_wealth_from_savings}, + constraints={}, + functions={ + "utility": utility_retired, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, + ) + + +@functools.cache +def get_model(solver: Literal["brute_force", "dcegm"]) -> Model: + """Build the twin model for the requested solver variant.""" + if solver == "dcegm": + return build_dcegm_model() + return Model( + regimes={ + "working_life": _working_life(solver), + "retirement": _retirement(solver), + "done_from_working": done_from_working, + "done_retired": done_retired, + }, + ages=AgeGrid(start=MIN_AGE, stop=MIN_AGE + N_PERIODS - 1, step="Y"), + regime_id_class=TwinRegimeId, + ) + + +def build_dcegm_model(*, savings_grid: ContinuousGrid = SAVINGS_GRID) -> Model: + """Build the DC-EGM twin, optionally with a custom savings grid. + + The default reproduces the fixture run's pinned uniform grid; a grid + clustered toward the borrowing limit resolves the low-wealth region the + uniform grid cannot. + """ + solver = dataclasses.replace(DCEGM_SOLVER, savings_grid=savings_grid) + return Model( + regimes={ + "working_life": _working_life("dcegm").replace(solver=solver), + "retirement": _retirement("dcegm").replace(solver=solver), + "done_from_working": done_from_working, + "done_retired": done_retired, + }, + ages=AgeGrid(start=MIN_AGE, stop=MIN_AGE + N_PERIODS - 1, step="Y"), + regime_id_class=TwinRegimeId, + ) + + +def get_params(*, taste_shock_scale: float = 0.2) -> dict: + """Params matching the fixture run in `tests/data/dcegm_reference/`.""" + return { + "discount_factor": 0.95, + "interest_rate": 0.05, + "rho": 1.95, + "delta": 0.35, + "constant": 0.75, + "exp_coeff": 0.04, + "exp_squared": -0.0002, + "floor": 0.001, + "done_from_working": {"utility": {"taste_scale": taste_shock_scale}}, + "working_life": {"taste_shocks": {"scale": taste_shock_scale}}, + # Retired agents earn nothing; `labor_income` is a free leaf of the + # retirement regime's wealth transition. + "retirement": {"next_wealth": {"labor_income": 0.0}}, + } diff --git a/tests/test_models/deterministic/dcegm_variants.py b/tests/test_models/deterministic/dcegm_variants.py new file mode 100644 index 000000000..3ba6150b5 --- /dev/null +++ b/tests/test_models/deterministic/dcegm_variants.py @@ -0,0 +1,183 @@ +"""Equivalent-spec pairs for solver comparisons (brute force vs DC-EGM). + +The DC-EGM contract changes the model spec, not just a flag: + +- the borrowing constraint is dropped (the savings grid's lower bound enforces it), +- the wealth transition consumes the post-decision state `savings` instead of + wealth/consumption directly, +- `resources`, `savings`, and `inverse_marginal_utility` are declared as regime + functions. + +The builders here emit mathematically equivalent specs for both solvers so tests can +compare value functions on the shared wealth grid. Importable only once `lcm.solvers` +exists. +""" + +import functools +from typing import Literal + +from lcm import AgeGrid, DiscreteGrid, IrregSpacedGrid, Model +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm_examples.iskhakov_et_al_2017 import ( + CONSUMPTION_GRID, + WEALTH_GRID, + LaborSupply, + dead, + inverse_marginal_utility, + is_working, + labor_income, + next_wealth_from_savings, + resources, + savings, + utility_retirement, + utility_working, +) +from tests.test_models.deterministic import base, retirement_only + +# Exogenous end-of-period savings grid; the lower bound is the borrowing limit +# (savings >= 0 encodes the original `consumption <= wealth` constraint). +# Nodes are cubically clustered toward the borrowing limit: the value function +# curves hardest where the constraint starts to bind, and the published V is +# interpolated from endogenous points spaced like the savings nodes β€” a +# uniform grid under-resolves the lowest wealth nodes by orders of magnitude. +SAVINGS_GRID = IrregSpacedGrid(points=tuple(400.0 * (i / 199) ** 3 for i in range(200))) + + +DCEGM_SOLVER = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + # The final decision period consumes everything, so its carry in the + # queried resources range consists of constrained-segment points only; + # 64 of them keep the geometric spacing ratio (and hence the carry + # interpolation error) small. + n_constrained_points=64, +) + + +dcegm_retirement = UserRegime( + transition=retirement_only.next_regime_from_retirement, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_from_savings}, + functions={ + "utility": utility_retirement, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, +) + + +dcegm_working_life = UserRegime( + transition=base.next_regime_from_working, + actions={ + "labor_supply": DiscreteGrid(LaborSupply), + "consumption": CONSUMPTION_GRID, + }, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_from_savings}, + functions={ + "utility": utility_working, + "labor_income": labor_income, + "is_working": is_working, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, +) + + +dcegm_retirement_full = UserRegime( + transition=base.next_regime_from_retirement, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth_from_savings}, + functions={ + "utility": utility_retirement, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM_SOLVER, +) + + +@functools.cache +def get_retirement_only_model( + solver: Literal["brute_force", "dcegm"], n_periods: int +) -> Model: + """Build the two-regime retirement model for the requested solver.""" + if solver == "brute_force": + return retirement_only.get_model(n_periods) + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "retirement": dcegm_retirement.replace( + active=lambda age, la=last_age: age < la + ), + "dead": dead, + }, + ages=ages, + regime_id_class=retirement_only.RetirementOnlyRegimeId, + ) + + +@functools.cache +def get_full_model(solver: Literal["brute_force", "dcegm"], n_periods: int) -> Model: + """Build the three-regime worker/retirement/dead model for the requested solver.""" + if solver == "brute_force": + return base.get_model(n_periods) + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "working_life": dcegm_working_life.replace( + active=lambda age, la=last_age: age < la + ), + "retirement": dcegm_retirement_full.replace( + active=lambda age, la=last_age: age < la + ), + "dead": dead, + }, + ages=ages, + regime_id_class=base.RegimeId, + ) + + +def get_retirement_only_params( + n_periods: int, + *, + discount_factor: float = 0.98, + interest_rate: float = 0.0, +) -> dict: + """Params for the retirement-only pair; valid for both solver variants.""" + return retirement_only.get_params( + n_periods, + discount_factor=discount_factor, + interest_rate=interest_rate, + ) + + +def get_full_params( + n_periods: int, + *, + discount_factor: float = 0.98, + disutility_of_work: float = 1.0, + interest_rate: float = 0.0, + wage: float = 20.0, +) -> dict: + """Params for the full-model pair; valid for both solver variants.""" + return base.get_params( + n_periods=n_periods, + discount_factor=discount_factor, + disutility_of_work=disutility_of_work, + interest_rate=interest_rate, + wage=wage, + ) diff --git a/tests/test_models/deterministic/ds_pension.py b/tests/test_models/deterministic/ds_pension.py new file mode 100644 index 000000000..d5461f450 --- /dev/null +++ b/tests/test_models/deterministic/ds_pension.py @@ -0,0 +1,326 @@ +"""Dobrescu--Shanker / Druedahl--Jorgensen two-asset pension benchmark (brute form). + +The 2-D pension model the RFC-vs-G2EGM comparison solves: a finite-horizon +consumption--saving problem with a **liquid** account and an illiquid **pension** +account. While working, the agent chooses consumption `c` and a one-directional +pension `deposit` (`d >= 0`); the liquid post-decision balance `liquid - c - d` is +kept non-negative by a borrowing constraint, and the pension post-decision balance +`pension + d + chi*log(1 + d)` carries a concave employer match. Liquid earns gross +return `1 + return_liquid`, pension the higher `1 + return_pension`. + +Retirement is a **deterministic lifecycle transition** at a fixed age (not an +endogenous per-period choice -- the Druedahl--Jorgensen `solve.m` solves the retired +sub-problem as a separate 1-D continuation, with no per-period work/retire max). At +the working->retired transition the pension is paid out as a lump sum into liquid and +the problem collapses to a 1-D liquid-only consumption problem; the retired agent +receives a flat retirement income and earns the liquid return. Working utility carries +an additive disutility of work `work_disutility` (the retired agent pays none). + +This is the dense-grid brute-force **oracle** the 2-D EGM kernel (G2EGM / multidim +RFC) is validated against. It is written in brute-solvable form -- two continuous +states (`liquid`, `pension`), two continuous actions (`consumption`, `deposit`), both +coupled through the budget -- with the faithful calibration read from the G2EGM +`SetupPar.m` (`get_params`). Default grids are small for fast local oracle solves; +pass larger sizes (and the full calibration) for the reference comparison. + +Two micro-conventions are parameterized pending confirmation against `fun.m`: +`pension_payout_return` (the return factor applied to the paid-out pension balance at +retirement; `1 + return_pension` by default) and `retirement_income_in_first_period` +(whether `retirement_income` is received in the first retired period). +""" + +import functools + +import jax.numpy as jnp + +from lcm import AgeGrid, LinSpacedGrid, MarkovTransition, Model, categorical +from lcm.regime import Regime +from lcm.solvers import GridSearch, Solver +from lcm.typing import BoolND, ContinuousAction, ContinuousState, FloatND, ScalarInt + + +@categorical(ordered=False) +class RegimeId: + working: ScalarInt + retired: ScalarInt + dead: ScalarInt + + +def _crra(consumption: FloatND, crra: float) -> FloatND: + return jnp.where( + crra == 1.0, + jnp.log(consumption), + consumption ** (1.0 - crra) / (1.0 - crra), + ) + + +def utility_working( + consumption: ContinuousAction, crra: float, work_disutility: float +) -> FloatND: + """CRRA consumption utility net of the additive disutility of work.""" + return _crra(consumption, crra) - work_disutility + + +def utility_retired(consumption: ContinuousAction, crra: float) -> FloatND: + """CRRA consumption utility; the retired agent pays no work disutility.""" + return _crra(consumption, crra) + + +def bequest(liquid: ContinuousState, crra: float) -> FloatND: + """Terminal value: consume remaining liquid wealth (the pension is paid out).""" + return _crra(liquid, crra) + + +def _pension_post_decision( + pension: ContinuousState, + deposit: ContinuousAction, + match_rate: float, +) -> FloatND: + """Pension post-decision balance `pension + deposit + chi*log(1 + deposit)`.""" + return pension + deposit + match_rate * jnp.log(1.0 + deposit) + + +def next_liquid_working( + liquid: ContinuousState, + consumption: ContinuousAction, + deposit: ContinuousAction, + return_liquid: float, + wage: float, +) -> ContinuousState: + """Liquid law of motion while staying in the working regime.""" + return (1.0 + return_liquid) * (liquid - consumption - deposit) + wage + + +def next_liquid_retiring( + liquid: ContinuousState, + pension: ContinuousState, + consumption: ContinuousAction, + deposit: ContinuousAction, + return_liquid: float, + pension_payout_return: float, + match_rate: float, + retirement_income: float, +) -> ContinuousState: + """Liquid on the working->retired transition: the pension is paid out as a lump sum. + + The liquid post-decision balance earns the liquid return, the pension + post-decision balance is paid out scaled by `pension_payout_return`, and the + first retirement income is added. + """ + liquid_post = liquid - consumption - deposit + pension_post = _pension_post_decision(pension, deposit, match_rate) + return ( + (1.0 + return_liquid) * liquid_post + + pension_payout_return * pension_post + + retirement_income + ) + + +def next_pension_working( + pension: ContinuousState, + deposit: ContinuousAction, + return_pension: float, + match_rate: float, +) -> ContinuousState: + """Pension law of motion while staying in the working regime.""" + return (1.0 + return_pension) * _pension_post_decision(pension, deposit, match_rate) + + +def next_liquid_retired( + liquid: ContinuousState, + consumption: ContinuousAction, + return_liquid: float, + retirement_income: float, +) -> ContinuousState: + """Liquid law of motion within retirement (1-D consumption--saving).""" + return (1.0 + return_liquid) * (liquid - consumption) + retirement_income + + +def feasible_working( + liquid: ContinuousState, + consumption: ContinuousAction, + deposit: ContinuousAction, +) -> BoolND: + """Liquid borrowing constraint: the liquid post-decision balance stays >= 0.""" + return consumption + deposit <= liquid + + +def feasible_retired( + liquid: ContinuousState, + consumption: ContinuousAction, +) -> BoolND: + """Liquid borrowing constraint in retirement (no deposit margin).""" + return consumption <= liquid + + +def prob_stay_working(age: int, retirement_age: float) -> FloatND: + """Deterministic (0/1) probability of staying in the working regime next period.""" + return jnp.where(age + 1 < retirement_age, 1.0, 0.0) + + +def prob_retire(age: int, retirement_age: float) -> FloatND: + """Deterministic (0/1) probability of transitioning working->retired next period.""" + return jnp.where(age + 1 >= retirement_age, 1.0, 0.0) + + +def prob_stay_retired(age: int, final_age_alive: float) -> FloatND: + """Deterministic (0/1) probability of remaining retired next period.""" + return jnp.where(age + 1 < final_age_alive, 1.0, 0.0) + + +def prob_die(age: int, final_age_alive: float) -> FloatND: + """Deterministic (0/1) probability of transitioning retired->dead next period.""" + return jnp.where(age + 1 >= final_age_alive, 1.0, 0.0) + + +def get_model( + *, + n_periods: int = 5, + retirement_period: int = 3, + n_liquid: int = 12, + n_pension: int = 10, + n_consumption: int = 14, + n_deposit: int = 8, + liquid_max: float = 20.0, + pension_max: float = 15.0, + solvers: dict[str, Solver] | None = None, +) -> Model: + """Create the three-regime (working, retired, dead) DS pension model. + + The agent works for `retirement_period` periods, then is retired for the rest of + the `n_periods`-period horizon, with a terminal (dead) period. Grid sizes default + to a small oracle scale; pass larger values for a finer reference solve. + + Args: + solvers: Optional mapping of regime name to its `Solver`. A name absent from + the mapping (or `solvers=None`) keeps the default `GridSearch` β€” so the + default model is the dense-grid brute oracle. Pass + `{"working": TwoDimEGM(...)}` to drive the working regime by the two-asset + G2EGM method, and `{"retired": OneAssetEGM(...)}` for the 1-D retired EGM. + """ + solvers = solvers or {} + ages = AgeGrid(start=0, stop=n_periods - 1, step="Y") + retirement_age = ages.exact_values[retirement_period] + final_age = ages.exact_values[-1] + liquid_grid = LinSpacedGrid(start=0.1, stop=liquid_max, n_points=n_liquid) + pension_grid = LinSpacedGrid(start=0.0, stop=pension_max, n_points=n_pension) + consumption_grid = LinSpacedGrid(start=0.1, stop=liquid_max, n_points=n_consumption) + + working = Regime( + actions={ + "consumption": consumption_grid, + "deposit": LinSpacedGrid(start=0.0, stop=pension_max, n_points=n_deposit), + }, + states={"liquid": liquid_grid, "pension": pension_grid}, + state_transitions={ + "liquid": { + "working": next_liquid_working, + "retired": next_liquid_retiring, + }, + "pension": {"working": next_pension_working}, + }, + constraints={"feasible": feasible_working}, + transition={ + "working": MarkovTransition(prob_stay_working), + "retired": MarkovTransition(prob_retire), + }, + functions={"utility": utility_working}, + active=lambda age, ra=retirement_age: age < ra, + solver=solvers.get("working", GridSearch()), + ) + retired = Regime( + actions={"consumption": consumption_grid}, + states={"liquid": liquid_grid}, + state_transitions={ + "liquid": { + "retired": next_liquid_retired, + "dead": next_liquid_retired, + } + }, + constraints={"feasible": feasible_retired}, + transition={ + "retired": MarkovTransition(prob_stay_retired), + "dead": MarkovTransition(prob_die), + }, + functions={"utility": utility_retired}, + active=lambda age, ra=retirement_age, fa=final_age: ra <= age < fa, + solver=solvers.get("retired", GridSearch()), + ) + dead = Regime( + transition=None, + states={"liquid": liquid_grid}, + functions={"utility": bequest}, + solver=solvers.get("dead", GridSearch()), + ) + return Model( + regimes={"working": working, "retired": retired, "dead": dead}, + ages=ages, + regime_id_class=RegimeId, + ) + + +@functools.cache +def get_params( + *, + discount_factor: float = 0.98, + crra: float = 2.0, + work_disutility: float = 0.25, + return_liquid: float = 0.02, + return_pension: float = 0.04, + match_rate: float = 0.10, + wage: float = 1.0, + retirement_income: float = 0.50, + retirement_age: float = 3.0, + final_age_alive: float = 4.0, + pension_payout_return: float | None = None, +) -> dict: + """Get parameters for the DS pension model (faithful calibration from `SetupPar.m`). + + `pension_payout_return` defaults to `1 + return_pension` (the pension balance is + paid out earning its own return at retirement); pass a value to override the + convention pending confirmation against `fun.m`. + """ + if pension_payout_return is None: + pension_payout_return = 1.0 + return_pension + return { + "working": { + "utility": {"crra": crra, "work_disutility": work_disutility}, + "H": {"discount_factor": discount_factor}, + "working": { + "next_liquid": {"return_liquid": return_liquid, "wage": wage}, + "next_pension": { + "match_rate": match_rate, + "return_pension": return_pension, + }, + "next_regime": {"retirement_age": retirement_age}, + }, + "retired": { + "next_liquid": { + "match_rate": match_rate, + "pension_payout_return": pension_payout_return, + "retirement_income": retirement_income, + "return_liquid": return_liquid, + }, + "next_regime": {"retirement_age": retirement_age}, + }, + }, + "retired": { + "utility": {"crra": crra}, + "H": {"discount_factor": discount_factor}, + "retired": { + "next_liquid": { + "retirement_income": retirement_income, + "return_liquid": return_liquid, + }, + "next_regime": {"final_age_alive": final_age_alive}, + }, + "dead": { + "next_liquid": { + "retirement_income": retirement_income, + "return_liquid": return_liquid, + }, + "next_regime": {"final_age_alive": final_age_alive}, + }, + }, + "dead": {"utility": {"crra": crra}}, + } diff --git a/tests/test_models/deterministic/housing.py b/tests/test_models/deterministic/housing.py new file mode 100644 index 000000000..65e2c3a8f --- /dev/null +++ b/tests/test_models/deterministic/housing.py @@ -0,0 +1,263 @@ +"""Dobrescu--Shanker housing benchmark (deterministic-income brute form). + +A liquid-asset + durable-housing model with a discrete **adjust / keep** choice and a +proportional transaction cost, the model behind the RFC-vs-NEGM housing comparison. It +is written in dense-grid brute-solvable form -- the oracle the 2-D EGM / NEGM kernels +are validated against. + +Each period the agent holds liquid assets `liquid` and a house `housing`, and chooses +to **keep** the house or **adjust** it: + +- **Keep:** the house is retained (`next_housing = housing`), no transaction cost, and + cash-on-hand is `R*liquid + income` (the house is NOT liquidated -- only its service + flow `alpha*log(housing)` is enjoyed). +- **Adjust:** the old house is sold for `R_H*housing*(1-delta)`, a new house + `new_housing` is bought for `new_housing*(1 + tau)` (the proportional transaction + cost), and cash-on-hand is `R*liquid + R_H*housing*(1-delta) + income - new_housing*(1 + + tau)`. The agent lives in and carries forward the new house. + +Utility is CRRA in non-durable consumption plus a within-period housing service: +`(c**(1-gamma_c) - 1)/(1-gamma_c) + alpha*log(serviced_housing)`, so utility reads the +housing state/choice directly (unlike the pension model). Budgets, returns, and the +transaction cost are verified against InverseDCDP `housing/housing.py` +(`obj_noadj`/`obj_adj`); calibration from `ConsumerProblem.__init__`. + +Income is a deterministic parameter here; the faithful benchmark uses a 2-state Markov +income (`z_vals=(0.1, 1.0)`, transition `Pi`), added as a process-state follow-up. The +terminal bequest is a simple consume-liquid CRRA value (the source's `term_u` scaling +is flagged, not yet replicated). +""" + +import functools + +import jax.numpy as jnp + +from lcm import AgeGrid, LinSpacedGrid, Model, categorical +from lcm.grids import DiscreteGrid +from lcm.regime import Regime +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteAction, + FloatND, + ScalarInt, +) + + +@categorical(ordered=False) +class RegimeId: + working: ScalarInt + dead: ScalarInt + + +@categorical(ordered=False) +class AdjustChoice: + keep: ScalarInt + adjust: ScalarInt + + +def _cash_on_hand( + liquid: ContinuousState, + housing: ContinuousState, + adjust: DiscreteAction, + new_housing: ContinuousAction, + return_liquid: float, + return_housing: float, + depreciation: float, + income: float, + transaction_cost: float, +) -> FloatND: + """Beginning-of-period cash-on-hand, branching on the adjust/keep choice.""" + keep = (1.0 + return_liquid) * liquid + income + adjust_cash = ( + (1.0 + return_liquid) * liquid + + (1.0 + return_housing) * housing * (1.0 - depreciation) + + income + - new_housing * (1.0 + transaction_cost) + ) + return jnp.where(adjust == AdjustChoice.adjust, adjust_cash, keep) + + +def _serviced_housing( + housing: ContinuousState, + adjust: DiscreteAction, + new_housing: ContinuousAction, +) -> FloatND: + """The house lived in this period: the new house if adjusting, else the old one.""" + return jnp.where(adjust == AdjustChoice.adjust, new_housing, housing) + + +def utility( + consumption: ContinuousAction, + housing: ContinuousState, + adjust: DiscreteAction, + new_housing: ContinuousAction, + crra: float, + housing_weight: float, +) -> FloatND: + """CRRA consumption utility plus the housing-service flow `alpha*log(h)`.""" + serviced = _serviced_housing(housing, adjust, new_housing) + consumption_utility = (consumption ** (1.0 - crra) - 1.0) / (1.0 - crra) + return consumption_utility + housing_weight * jnp.log(serviced) + + +def bequest(liquid: ContinuousState, housing: ContinuousState, crra: float) -> FloatND: + """Terminal value: consume liquid wealth plus the resale value of the house.""" + return (liquid + housing) ** (1.0 - crra) / (1.0 - crra) + + +def next_liquid( + liquid: ContinuousState, + housing: ContinuousState, + consumption: ContinuousAction, + adjust: DiscreteAction, + new_housing: ContinuousAction, + return_liquid: float, + return_housing: float, + depreciation: float, + income: float, + transaction_cost: float, +) -> ContinuousState: + """Next-period liquid assets: cash-on-hand net of consumption.""" + cash = _cash_on_hand( + liquid=liquid, + housing=housing, + adjust=adjust, + new_housing=new_housing, + return_liquid=return_liquid, + return_housing=return_housing, + depreciation=depreciation, + income=income, + transaction_cost=transaction_cost, + ) + return cash - consumption + + +def next_housing( + housing: ContinuousState, + adjust: DiscreteAction, + new_housing: ContinuousAction, +) -> ContinuousState: + """Next-period housing stock: the new house if adjusting, else the old one.""" + return _serviced_housing(housing, adjust, new_housing) + + +def feasible( + liquid: ContinuousState, + housing: ContinuousState, + consumption: ContinuousAction, + adjust: DiscreteAction, + new_housing: ContinuousAction, + return_liquid: float, + return_housing: float, + depreciation: float, + income: float, + transaction_cost: float, + borrowing_floor: float, +) -> BoolND: + """Next-period liquid assets must stay at or above the borrowing floor.""" + cash = _cash_on_hand( + liquid=liquid, + housing=housing, + adjust=adjust, + new_housing=new_housing, + return_liquid=return_liquid, + return_housing=return_housing, + depreciation=depreciation, + income=income, + transaction_cost=transaction_cost, + ) + return consumption <= cash - borrowing_floor + + +def next_regime_from_working(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where(age + 1 >= final_age_alive, RegimeId.dead, RegimeId.working) + + +def get_model( + *, + n_periods: int = 4, + n_liquid: int = 12, + n_housing: int = 8, + n_consumption: int = 16, + n_new_housing: int = 8, + borrowing_floor: float = 0.01, + liquid_max: float = 50.0, + housing_max: float = 50.0, +) -> Model: + """Create the two-regime (working, dead) deterministic-income housing model. + + Grid sizes default to a small oracle scale; pass larger values for a finer + reference solve. + """ + ages = AgeGrid(start=0, stop=n_periods - 1, step="Y") + final_age = ages.exact_values[-1] + liquid_grid = LinSpacedGrid( + start=borrowing_floor, stop=liquid_max, n_points=n_liquid + ) + housing_grid = LinSpacedGrid( + start=borrowing_floor, stop=housing_max, n_points=n_housing + ) + working = Regime( + actions={ + "consumption": LinSpacedGrid( + start=borrowing_floor, stop=liquid_max, n_points=n_consumption + ), + "new_housing": LinSpacedGrid( + start=borrowing_floor, stop=housing_max, n_points=n_new_housing + ), + "adjust": DiscreteGrid(AdjustChoice), + }, + states={"liquid": liquid_grid, "housing": housing_grid}, + state_transitions={"liquid": next_liquid, "housing": next_housing}, + constraints={"feasible": feasible}, + transition=next_regime_from_working, + functions={"utility": utility}, + active=lambda age, fa=final_age: age < fa, + ) + dead = Regime( + transition=None, + states={"liquid": liquid_grid, "housing": housing_grid}, + functions={"utility": bequest}, + ) + return Model( + regimes={"working": working, "dead": dead}, + ages=ages, + regime_id_class=RegimeId, + ) + + +@functools.cache +def get_params( + *, + discount_factor: float = 0.945, + crra: float = 1.458, + housing_weight: float = 0.66, + return_liquid: float = 0.024, + return_housing: float = 0.10, + depreciation: float = 0.10, + transaction_cost: float = 0.20, + income: float = 1.0, + borrowing_floor: float = 0.01, + final_age_alive: float = 3.0, +) -> dict: + """Get parameters for the housing model (faithful calibration from `housing.py`).""" + transition_args = { + "return_liquid": return_liquid, + "return_housing": return_housing, + "depreciation": depreciation, + "income": income, + "transaction_cost": transaction_cost, + } + return { + "discount_factor": discount_factor, + "final_age_alive": final_age_alive, + "working": { + "utility": {"crra": crra, "housing_weight": housing_weight}, + "next_liquid": transition_args, + "next_housing": {}, + "feasible": {**transition_args, "borrowing_floor": borrowing_floor}, + }, + "dead": {"utility": {"crra": crra}}, + } diff --git a/tests/test_models/deterministic/retirement_only.py b/tests/test_models/deterministic/retirement_only.py new file mode 100644 index 000000000..2da6a6684 --- /dev/null +++ b/tests/test_models/deterministic/retirement_only.py @@ -0,0 +1,86 @@ +"""Retirement-only variant of the deterministic base model. + +The `retirement` regime in `tests.test_models.deterministic.base` is absorbing: its +value function never depends on the working regime. A two-regime model (retirement + +dead) therefore reproduces the retired part of the Iskhakov et al. (2017) analytical +solution exactly. This makes it the concave (no-discrete-choice) oracle for solver +comparisons: one continuous state, one continuous action, no discrete actions. +""" + +import functools + +import jax.numpy as jnp + +from lcm import AgeGrid, Model, categorical +from lcm.regime import Regime as UserRegime +from lcm.typing import ScalarInt +from lcm_examples.iskhakov_et_al_2017 import ( + CONSUMPTION_GRID, + WEALTH_GRID, + borrowing_constraint, + dead, + next_wealth, + utility_retirement, +) + + +@categorical(ordered=False) +class RetirementOnlyRegimeId: + retirement: ScalarInt + dead: ScalarInt + + +def next_regime_from_retirement(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where( + age >= final_age_alive, + RetirementOnlyRegimeId.dead, + RetirementOnlyRegimeId.retirement, + ) + + +retirement = UserRegime( + transition=next_regime_from_retirement, + actions={"consumption": CONSUMPTION_GRID}, + states={"wealth": WEALTH_GRID}, + state_transitions={"wealth": next_wealth}, + constraints={"borrowing_constraint": borrowing_constraint}, + functions={"utility": utility_retirement}, +) + + +@functools.cache +def get_model(n_periods: int) -> Model: + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + return Model( + regimes={ + "retirement": retirement.replace(active=lambda age, la=last_age: age < la), + "dead": dead, + }, + ages=ages, + regime_id_class=RetirementOnlyRegimeId, + ) + + +def get_params( + n_periods: int, + *, + discount_factor: float = 0.98, + interest_rate: float = 0.0, +) -> dict: + final_age_alive = 40 + (n_periods - 2) * 10 + return { + "discount_factor": discount_factor, + "interest_rate": interest_rate, + "final_age_alive": final_age_alive, + "retirement": {"next_wealth": {"labor_income": 0.0}}, + } + + +__all__ = [ + "RetirementOnlyRegimeId", + "get_model", + "get_params", + "next_regime_from_retirement", + "retirement", +] diff --git a/tests/test_models/deterministic/two_asset.py b/tests/test_models/deterministic/two_asset.py new file mode 100644 index 000000000..ee5ff9195 --- /dev/null +++ b/tests/test_models/deterministic/two_asset.py @@ -0,0 +1,170 @@ +"""Minimal deterministic two-asset (liquid + illiquid pension) model. + +A worker holds a liquid account `liquid` and an illiquid pension `pension` and each +period chooses consumption and a one-directional pension `deposit` ($\\ge 0$). The +liquid post-decision balance is `liquid - consumption - deposit`, kept non-negative +by a borrowing constraint; the pension post-decision balance is +`pension + deposit + chi*log(1 + deposit)`, a concave employer match. Liquid earns +gross return `1 + return_liquid`, pension earns the higher `1 + return_pension`. On +death the pension is paid out as a lump sum and added to liquid wealth. + +This is the two-action-coupled-continuous-state structure the multidimensional EGM +foundation targets, written in brute-force-solvable form: it is the dense-grid +reference (oracle) the 2-D EGM kernel is validated against. Two continuous states +(`liquid`, `pension`) and two continuous actions (`consumption`, `deposit`), both +coupled through the budget. +""" + +import functools + +import jax.numpy as jnp + +from lcm import AgeGrid, LinSpacedGrid, Model, categorical +from lcm.regime import Regime +from lcm.typing import BoolND, ContinuousAction, ContinuousState, FloatND, ScalarInt + + +@categorical(ordered=False) +class RegimeId: + working: ScalarInt + dead: ScalarInt + + +def _crra(consumption: FloatND, crra: float) -> FloatND: + return jnp.where( + crra == 1.0, + jnp.log(consumption), + consumption ** (1.0 - crra) / (1.0 - crra), + ) + + +def utility(consumption: ContinuousAction, crra: float) -> FloatND: + return _crra(consumption, crra) + + +def bequest( + liquid: ContinuousState, + pension: ContinuousState, + crra: float, + pension_bequest_weight: float, +) -> FloatND: + """Consume liquid wealth plus the lump-sum pension payout in the final period. + + `pension_bequest_weight` is 1.0 for the model proper (the full pension balance is + paid out); a value below 1 makes pension wealth marginally less valuable than + liquid, which is what produces an interior-deposit (unconstrained) region. + """ + return _crra(liquid + pension_bequest_weight * pension, crra) + + +def next_liquid( + liquid: ContinuousState, + consumption: ContinuousAction, + deposit: ContinuousAction, + return_liquid: float, + wage: float, +) -> ContinuousState: + return (1.0 + return_liquid) * (liquid - consumption - deposit) + wage + + +def next_pension( + pension: ContinuousState, + deposit: ContinuousAction, + return_pension: float, + match_rate: float, +) -> ContinuousState: + return (1.0 + return_pension) * ( + pension + deposit + match_rate * jnp.log(1.0 + deposit) + ) + + +def feasible( + liquid: ContinuousState, + consumption: ContinuousAction, + deposit: ContinuousAction, +) -> BoolND: + """Liquid borrowing constraint: the liquid post-decision balance stays >= 0.""" + return consumption + deposit <= liquid + + +def next_regime_from_working(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where(age >= final_age_alive, RegimeId.dead, RegimeId.working) + + +def get_model( + *, + n_periods: int = 3, + n_liquid: int = 12, + n_pension: int = 10, + n_consumption: int = 14, + n_deposit: int = 8, + liquid_max: float = 100.0, + pension_max: float = 50.0, +) -> Model: + """Create the two-regime (working, dead) two-asset model. + + Grid sizes default to the small oracle scale; pass larger values for a finer + reference solve. + """ + ages = AgeGrid(start=40, stop=40 + (n_periods - 1) * 10, step="10Y") + last_age = ages.exact_values[-1] + liquid_grid = LinSpacedGrid(start=1.0, stop=liquid_max, n_points=n_liquid) + pension_grid = LinSpacedGrid(start=0.0, stop=pension_max, n_points=n_pension) + working = Regime( + actions={ + "consumption": LinSpacedGrid( + start=1.0, stop=liquid_max, n_points=n_consumption + ), + "deposit": LinSpacedGrid(start=0.0, stop=pension_max, n_points=n_deposit), + }, + states={"liquid": liquid_grid, "pension": pension_grid}, + state_transitions={"liquid": next_liquid, "pension": next_pension}, + constraints={"feasible": feasible}, + transition=next_regime_from_working, + functions={"utility": utility}, + active=lambda age, la=last_age: age < la, + ) + dead = Regime( + transition=None, + states={"liquid": liquid_grid, "pension": pension_grid}, + functions={"utility": bequest}, + ) + return Model( + regimes={"working": working, "dead": dead}, + ages=ages, + regime_id_class=RegimeId, + ) + + +@functools.cache +def get_params( + *, + n_periods: int = 3, + discount_factor: float = 0.95, + crra: float = 2.0, + return_liquid: float = 0.02, + return_pension: float = 0.06, + match_rate: float = 1.0, + wage: float = 10.0, + pension_bequest_weight: float = 1.0, +) -> dict: + """Get parameters for the two-asset model (pension return exceeds liquid return).""" + final_age_alive = 40 + (n_periods - 2) * 10 + return { + "discount_factor": discount_factor, + "final_age_alive": final_age_alive, + "working": { + "utility": {"crra": crra}, + "next_liquid": {"return_liquid": return_liquid, "wage": wage}, + "next_pension": { + "return_pension": return_pension, + "match_rate": match_rate, + }, + }, + "dead": { + "utility": { + "crra": crra, + "pension_bequest_weight": pension_bequest_weight, + } + }, + } diff --git a/tests/test_models/ds2024_housing.py b/tests/test_models/ds2024_housing.py new file mode 100644 index 000000000..89c632ff0 --- /dev/null +++ b/tests/test_models/ds2024_housing.py @@ -0,0 +1,515 @@ +"""Dobrescu-Shanker (2024) housing model as a pylcm NEGM model. + +The DS-2024 multidimensional-method paper (SSRN 4850746) compares RFC against +NEGM on a housing model with liquid assets `a`, a durable housing stock `h`, a +proportional house-trade cost `tau`, depreciation `delta`, a two-state Markov +income `z`, and a discrete adjust/keep choice. Model and calibration are read +from the authors' `InverseDCDP` repo (`housing/housing.py`, +`settings/settings.yml`); see `ds2024-housing-build-plan.md`. + +It maps onto pylcm's nested-EGM solver exactly like the DS-2026 App.2 housing +model: + +- the **inner** DC-EGM solves liquid consumption-savings, the Euler equation + inverting on `liquid` assets `a`; +- the **outer** durable margin is the next housing stock `H'` searched over a + grid, the proportional cost making it non-concave; +- the **keeper** holds the house and the **adjuster** chooses `H'` paying + `(1 + tau)Β·H'` while selling the depreciated old house at `(1 + r_H)Β·h(1-delta)`. + +Utility is CRRA non-durable consumption plus a log housing-service flow +`u(c, H') = (c^{1-gamma_C} - 1)/(1 - gamma_C) + alphaΒ·log(H')`, the service +reading the chosen house `H'` (additively separable from consumption β€” the NEGM +contract). + +## Depreciation and the keeper + +In the source model the keeper's next house is the depreciated stock +`h(1 - delta)` and only the adjuster liquidates. The NEGM keeper realises this by +injecting the regime's `outer_no_adjustment_candidate` (`keep_housing`, which maps +`h -> h(1 - delta)`) as the keeper's durable transition: the kept stock lands off +the outer housing grid and the inner DC-EGM's passive read blends the continuation +value over the grid's neighbouring nodes, `credited(h, h(1 - delta)) = 0` making +the hold free. The model is therefore faithful at any `delta`. + +The brute grid-search twin is a valid oracle only at `delta = 0`: it searches +`next_housing` on the housing grid, so the free-keep level `h(1 - delta)` is on the +grid only when `delta = 0`. At `delta > 0` the brute cannot represent the off-grid +free keep, so the `delta > 0` keeper is validated against a dense host VFI oracle +that includes the free-keep candidate explicitly. +""" + +from collections.abc import Callable +from typing import Literal + +import jax.numpy as jnp + +from lcm import ( + DCEGM, + NEGM, + AgeGrid, + DiscreteGrid, + GridSearch, + LinSpacedGrid, + MarkovTransition, + Model, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteState, + FloatND, + ScalarInt, +) + +# Income discretisation (`z_vals`, `Pi` from InverseDCDP housing.py). +INCOME_LOW = 0.1 +INCOME_HIGH = 1.0 +INCOME_PI = ((0.09, 0.91), (0.06, 0.94)) + +# Wage-polynomial coefficients (`settings/settings.yml` `lambdas`): a degree-4 +# age profile plus a quadratic tenure term. The benchmark's stationary run pins +# the age at the terminal age `T = 60`, so income depends only on the income node. +WAGE_LAMBDAS = ( + 4.7651949, + 0.57802016, + -0.02022858, + 0.00030696, + -1.71e-6, + 0.0241546, + -0.00011022, +) +STATIONARY_AGE = 60 + + +def _stationary_log_income_base() -> float: + """Log labor income at the stationary age, excluding the income node `z`. + + `sum_{i<5} lambda_i * T^i + lambda_5 * T + lambda_6 * T^2` at `T = 60`, so the + stationary income is `exp(base + z) * 1e-5`. + """ + age = float(STATIONARY_AGE) + age_profile = sum(WAGE_LAMBDAS[i] * age**i for i in range(5)) + tenure = WAGE_LAMBDAS[5] * age + WAGE_LAMBDAS[6] * age**2 + return age_profile + tenure + + +_LOG_INCOME_BASE = _stationary_log_income_base() + + +@categorical(ordered=False) +class DS2024HousingRegimeId: + """Lifecycle regimes: an alive housing regime and the terminal bequest.""" + + alive: ScalarInt + dead: ScalarInt + + +@categorical(ordered=True) +class Income: + """Two-state Markov income node.""" + + low: ScalarInt + high: ScalarInt + + +def income_value(income: DiscreteState) -> FloatND: + """Stationary labor income `y(z) = exp(base + z) * 1e-5` of the income node.""" + z = jnp.where(income == Income.low, INCOME_LOW, INCOME_HIGH) + return jnp.exp(_LOG_INCOME_BASE + z) * 1e-5 + + +def income_transition(income: DiscreteState) -> FloatND: + """Markov income law: the row of `Pi` for the current income node.""" + pi = jnp.asarray(INCOME_PI) + return pi[income] + + +def _make_keep_housing(delta: float) -> Callable[[ContinuousState], FloatND]: + """Build the keeper's no-adjustment durable map `H' = h(1 - delta)`. + + The NEGM keeper holds the house at this level for free (the adjustment-cost + kink). It is the regime's `outer_no_adjustment_candidate`, injected as the + keeper's durable transition, so it must be **param-free** (a param on the + durable law binds per target and is read within-period) β€” `delta` is baked in + at build time via this closure. At `delta = 0` it returns the stock unchanged + (`housing * 1.0 == housing`), matching the auto-identity keeper exactly; a + `delta > 0` keeper depreciates to `h(1 - delta)`, which lands off the housing + grid and is blended by the inner DC-EGM's passive read. + """ + + def keep_housing(housing: ContinuousState) -> FloatND: + return housing * (1.0 - delta) + + return keep_housing + + +def housing_cost( + housing: ContinuousState, + next_housing: ContinuousState, + delta: float, + return_housing: float, + tau: float, +) -> FloatND: + """Net liquid cost of moving the house from `h` to `next_housing` (`H'`). + + - keep (`H' = h(1 - delta)`): cost `0` β€” the house is retained, no trade; + - adjust (`H' != h(1 - delta)`): cost `(1 + tau)Β·H' - (1 + r_H)Β·h(1 - delta)` + β€” sell the depreciated old house at `(1 + r_H)Β·h(1 - delta)` and buy the new + house at `(1 + tau)Β·H'`. + + The proportional cost falls on the whole new stock, so any adjustment pays a + discrete wedge over keeping (adjusting even to the keep level `h(1 - delta)` + costs `h(1 - delta)Β·(tau - r_H)`), opening the (S, s) inaction band. Reads only + the held housing state and the outer post-decision `next_housing` β€” a constant + per outer-grid node, as the NEGM contract requires. + """ + depreciated = housing * (1.0 - delta) + round_trip = (1.0 + tau) * next_housing - (1.0 + return_housing) * depreciated + return jnp.where(next_housing == depreciated, 0.0, round_trip) + + +def resources( + liquid: ContinuousState, + housing_cost: FloatND, + income_value: FloatND, + return_liquid: float, +) -> FloatND: + """Liquid resources consumption is paid from, given the fixed outer node. + + `(1 + r)Β·a + y - housing_cost`. With the keep cost `0` this is the keeper's + cash `RΒ·a + y`; with the adjust cost it is `RΒ·a + (1+r_H)Β·h(1-delta) + y - + (1+tau)Β·H'`. The housing cost is bound per outer-grid node, so it enters the + inner Euler inversion as a constant. + """ + return (1.0 + return_liquid) * liquid + income_value - housing_cost + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + """Inner post-decision liquid balance `a' = resources - c`.""" + return resources - consumption + + +def next_liquid(savings: FloatND) -> ContinuousState: + """Euler-state law: next liquid assets equal post-decision savings.""" + return savings + + +def next_housing( + housing: ContinuousState, housing_investment: ContinuousAction +) -> ContinuousState: + """Durable law `H' = H + housing_investment`. + + The adjuster's outer search ranges `next_housing` over the outer house-level + grid (and the brute twin searches it directly via `housing_investment`). The + keeper's no-adjustment map is the separate `keep_housing` (`H' = h(1 - delta)`), + injected by the NEGM solver as the keeper's durable transition, so this law is + the adjuster branch only. The durable transition carries no params (it is read + within-period by the service flow, so a param would bind per target); the + depreciation enters through `keep_housing`, the adjust cost, and the bequest. + """ + return housing + housing_investment + + +def serviced_housing(next_housing: ContinuousState) -> FloatND: + """The house serviced this period β€” the chosen `H'` (keep or adjust).""" + return next_housing + + +def utility( + consumption: ContinuousAction, + serviced_housing: FloatND, + gamma_c: float, + alpha: float, +) -> FloatND: + """CRRA consumption utility plus a log housing-service flow. + + `u(c, H') = (c^{1 - gamma_C} - 1)/(1 - gamma_C) + alphaΒ·log(H')`. The housing + term is additively separable, so it drops from the inner consumption Euler + inversion; utility reads the consumption action and the serviced-housing + service flow, never the liquid Euler state. + """ + consumption_utility = (consumption ** (1.0 - gamma_c) - 1.0) / (1.0 - gamma_c) + return consumption_utility + alpha * jnp.log(serviced_housing) + + +def inverse_marginal_utility(marginal_continuation: FloatND, gamma_c: float) -> FloatND: + """Invert the consumption marginal utility `u'(c) = c^{-gamma_C}`. + + `c = mc^{-1/gamma_C}`. The log housing-service term is separable and drops + from the inner inversion, so unlike the App.2 CES the consumption weight is 1. + """ + return marginal_continuation ** (-1.0 / gamma_c) + + +def next_liquid_brute( + liquid: ContinuousState, + housing_cost: FloatND, + income_value: FloatND, + consumption: ContinuousAction, + return_liquid: float, +) -> ContinuousState: + """Brute-force liquid law: resources minus consumption.""" + return (1.0 + return_liquid) * liquid + income_value - housing_cost - consumption + + +def borrowing_constraint( + liquid: ContinuousState, + housing_cost: FloatND, + income_value: FloatND, + consumption: ContinuousAction, + return_liquid: float, + borrowing_limit: float, +) -> BoolND: + """Keep post-decision liquid assets at or above the borrowing limit `b`.""" + post = (1.0 + return_liquid) * liquid + income_value - housing_cost - consumption + return post >= borrowing_limit + + +def bequest( + liquid: ContinuousState, + housing: ContinuousState, + return_liquid: float, + theta: float, + bequest_shift: float, + gamma_c: float, +) -> FloatND: + """Terminal bequest `thetaΒ·((K + (1+r)Β·a + h)^{1-gamma_C} - 1)/(1 - gamma_C)`. + + The CRRA bequest (`term_u` in the source, with shift `K`) reads the carried + liquid and housing states. + """ + estate = bequest_shift + (1.0 + return_liquid) * liquid + housing + return theta * (estate ** (1.0 - gamma_c) - 1.0) / (1.0 - gamma_c) + + +def build_model( + *, + variant: Literal["negm", "brute"] = "negm", + n_grid: int, + n_periods: int = 4, + liquid_max: float = 50.0, + housing_max: float = 50.0, + housing_min: float = 0.01, + consumption_max: float = 50.0, + n_consumption: int = 60, + n_savings: int = 60, + delta: float = 0.0, +) -> Model: + """Build the DS-2024 housing model. + + Args: + variant: `"negm"` builds the nested-EGM model (inner liquid DC-EGM, outer + housing search); `"brute"` builds the grid-search twin solving the same + economics with no Euler machinery β€” the accuracy oracle. + n_grid: Number of points on the liquid, housing, and outer house grids. + n_periods: Number of model periods (the last is the terminal bequest). + liquid_max: Upper bound of the liquid grid. + housing_max: Upper bound of the housing and outer house grids. + housing_min: Lower bound `b` of the housing grid (and borrowing limit). + consumption_max: Upper bound of the inner consumption grid. + n_consumption: Number of inner consumption-grid points. + n_savings: Number of inner savings-grid points. + delta: House depreciation rate baked into the keeper's no-adjustment map + `H' = h(1 - delta)` (param-free, so set at build time). Pass the same + value to `build_params` (where it enters the adjust cost and bequest + as a param); `0.0` is the keeper-holds-the-stock case. + + Returns: + The alive housing regime plus the terminal bequest regime. + """ + ages = AgeGrid(start=STATIONARY_AGE, stop=STATIONARY_AGE + n_periods - 1, step="Y") + final_age = int(ages.exact_values[-1]) + keep_housing = _make_keep_housing(delta) + + liquid_grid = LinSpacedGrid(start=housing_min, stop=liquid_max, n_points=n_grid) + housing_grid = LinSpacedGrid(start=housing_min, stop=housing_max, n_points=n_grid) + outer_grid = LinSpacedGrid(start=housing_min, stop=housing_max, n_points=n_grid) + consumption_grid = LinSpacedGrid( + start=0.05, stop=consumption_max, n_points=n_consumption + ) + housing_investment_grid = LinSpacedGrid( + start=-housing_max, stop=housing_max, n_points=n_grid + ) + savings_grid = LinSpacedGrid( + start=housing_min, stop=liquid_max + housing_max, n_points=n_savings + ) + + def housing_stays_in_bounds(next_housing: ContinuousState) -> BoolND: + """The chosen next house must stay within `[housing_min, housing_max]`.""" + return (next_housing >= housing_min) & (next_housing <= housing_max) + + dead = UserRegime( + transition=None, + active=lambda age, fa=final_age: age >= fa, + states={"liquid": liquid_grid, "housing": housing_grid}, + functions={"utility": bequest}, + ) + + def next_regime(age: int) -> ScalarInt: + """Stay alive until the final age, then enter the terminal bequest.""" + return jnp.where( + age + 1 >= final_age, + DS2024HousingRegimeId.dead, + DS2024HousingRegimeId.alive, + ) + + if variant == "brute": + alive = UserRegime( + transition=next_regime, + active=lambda age, fa=final_age: age < fa, + states={ + "liquid": liquid_grid, + "housing": housing_grid, + "income": DiscreteGrid(Income), + }, + state_transitions={ + "liquid": next_liquid_brute, + "housing": next_housing, + "income": MarkovTransition(income_transition), + }, + actions={ + "consumption": consumption_grid, + "housing_investment": housing_investment_grid, + }, + constraints={ + "borrowing_constraint": borrowing_constraint, + "housing_stays_in_bounds": housing_stays_in_bounds, + }, + functions={ + "utility": utility, + "housing_cost": housing_cost, + "keep_housing": keep_housing, + "serviced_housing": serviced_housing, + "income_value": income_value, + }, + solver=GridSearch(), + ) + return Model( + regimes={"alive": alive, "dead": dead}, + ages=ages, + regime_id_class=DS2024HousingRegimeId, + ) + + negm_solver = NEGM( + inner=DCEGM( + continuous_state="liquid", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=savings_grid, + ), + outer_action="housing_investment", + outer_post_decision="next_housing", + outer_grid=outer_grid, + outer_no_adjustment_candidate="keep_housing", + ) + + alive = UserRegime( + transition=next_regime, + active=lambda age, fa=final_age: age < fa, + states={ + "liquid": liquid_grid, + "housing": housing_grid, + "income": DiscreteGrid(Income), + }, + state_transitions={ + "liquid": next_liquid, + "housing": next_housing, + "income": MarkovTransition(income_transition), + }, + actions={ + "consumption": consumption_grid, + "housing_investment": housing_investment_grid, + }, + constraints={"housing_stays_in_bounds": housing_stays_in_bounds}, + functions={ + "utility": utility, + "housing_cost": housing_cost, + "resources": resources, + "savings": savings, + "keep_housing": keep_housing, + "serviced_housing": serviced_housing, + "inverse_marginal_utility": inverse_marginal_utility, + "income_value": income_value, + }, + solver=negm_solver, + ) + return Model( + regimes={"alive": alive, "dead": dead}, + ages=ages, + regime_id_class=DS2024HousingRegimeId, + ) + + +def build_params( + *, + variant: Literal["negm", "brute"] = "negm", + tau: float = 0.20, + delta: float = 0.0, + discount_factor: float = 0.945, + gamma_c: float = 1.458, + alpha: float = 0.66, + return_liquid: float = 0.024, + return_housing: float = 0.10, + theta: float = 2.0, + bequest_shift: float = 200.0, + housing_min: float = 0.01, +) -> dict: + """Calibration parameters for the DS-2024 housing model. + + Defaults mirror `InverseDCDP` `housing.py` (`r=0.024`, `r_H=0.10`, + `beta=0.945`, `alpha=0.66`, `gamma_c=1.458`, `tau=0.20`, `theta=2`, `K=200`), + except `delta` defaults to `0.0`; pass `delta=0.10` for the paper value (the + keeper depreciates the held stock to `h(1 - delta)`). Pass the same `delta` to + `build_model`. + + Args: + variant: Must match `build_model`. + tau: Proportional housing-transaction cost. + delta: Housing depreciation. + discount_factor: Discount factor `beta`. + gamma_c: Consumption CRRA `gamma_C`. + alpha: Housing-service weight. + return_liquid: Liquid return `r`. + return_housing: Housing return `r_H`. + theta: Terminal bequest weight. + bequest_shift: Terminal bequest shift `K`. + housing_min: Borrowing limit `b`. + + Returns: + The nested parameter template keyed by regime then function. + """ + cost_params = {"delta": delta, "return_housing": return_housing, "tau": tau} + bequest_params = { + "return_liquid": return_liquid, + "theta": theta, + "bequest_shift": bequest_shift, + "gamma_c": gamma_c, + } + if variant == "brute": + alive = { + "utility": {"gamma_c": gamma_c, "alpha": alpha}, + "housing_cost": cost_params, + "next_liquid": {"return_liquid": return_liquid}, + "borrowing_constraint": { + "return_liquid": return_liquid, + "borrowing_limit": housing_min, + }, + } + else: + alive = { + "utility": {"gamma_c": gamma_c, "alpha": alpha}, + "housing_cost": cost_params, + "resources": {"return_liquid": return_liquid}, + "next_liquid": {}, + "inverse_marginal_utility": {"gamma_c": gamma_c}, + } + return { + "discount_factor": discount_factor, + "alive": alive, + "dead": {"utility": bequest_params}, + } diff --git a/tests/test_models/ds2024_housing_fues.py b/tests/test_models/ds2024_housing_fues.py new file mode 100644 index 000000000..fb545aee8 --- /dev/null +++ b/tests/test_models/ds2024_housing_fues.py @@ -0,0 +1,378 @@ +"""Dobrescu-Shanker (2024) housing model as a discrete-housing DC-EGM model. + +The RFC column of the DS-2024 RFC-vs-NEGM housing comparison. In the source +(`InverseDCDP` `housing.py`) the keeper's endogenous liquid grid is refined +**per housing column** by the 1-D rooftop cut (`RFC.RFCSimple.rfc` called inside +`_refineKeeper` for each `(z, h)`), and the housing margin is handled by nesting +over the housing grid β€” it is *not* a two-dimensional inverse-Euler. So in pylcm +the RFC column is the discrete-choice DC-EGM with the 1-D RFC upper-envelope +backend, exactly as the DS-2026 App.2 EGM-FUES column +(`ds_app2_housing_fues.py`): discretise the next-housing choice onto the housing +grid, treat it as a discrete action, and the inner liquid DC-EGM plus the +discrete-choice envelope (RFC/FUES/MSS/LTM) selects the optimal `H'`. + +The economics are the DS-2024 housing model (`ds2024_housing.py`): CRRA-plus-log +utility, two-state Markov income, the proportional house-trade cost. The +grid-search (VFI) twin solves the same discrete-housing problem by brute force β€” +the accuracy oracle. Faithful at `delta = 0` (keep is `H' = H`); the paper's +`delta = 0.10` keeper depreciates the held stock off the housing grid, awaiting +the housing-axis carry extension shared with the NEGM column. +""" + +from typing import Literal + +import jax.numpy as jnp + +from lcm import ( + DCEGM, + AgeGrid, + DiscreteGrid, + GridSearch, + IrregSpacedGrid, + LinSpacedGrid, + MarkovTransition, + Model, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteAction, + DiscreteState, + FloatND, + ScalarInt, +) +from tests.test_models.ds2024_housing import ( + Income, + income_transition, + income_value, +) + +START_AGE = 60 + + +def _make_housing_levels(*, n_housing: int) -> type: + """Create an ordered categorical with one field per discrete housing level. + + The class name is model-unique so it never collides with another model's + dynamically built housing-level categorical when both are imported together. + """ + annotations = {f"h{i}": ScalarInt for i in range(n_housing)} + cls = type("DS2024HousingLevels", (), {"__annotations__": annotations}) + return categorical(ordered=True)(cls) + + +@categorical(ordered=False) +class DS2024HousingFuesRegimeId: + """Lifecycle regimes: an alive housing regime and the terminal bequest.""" + + alive: ScalarInt + dead: ScalarInt + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + """Inner post-decision liquid balance `a' = resources - c`.""" + return resources - consumption + + +def next_liquid(savings: FloatND) -> ContinuousState: + """Euler-state law: next liquid assets equal post-decision savings.""" + return savings + + +def next_housing(housing_choice: DiscreteAction) -> DiscreteState: + """Discrete housing law: next housing equals the chosen code.""" + return housing_choice + + +def inverse_marginal_utility(marginal_continuation: FloatND, gamma_c: float) -> FloatND: + """Invert the consumption marginal utility `u'(c) = c^{-gamma_C}`. + + `c = mc^{-1/gamma_C}`; the log housing-service term is separable and drops out. + """ + return marginal_continuation ** (-1.0 / gamma_c) + + +def build_model( # noqa: C901 + *, + variant: Literal["dcegm", "brute"] = "dcegm", + n_grid: int, + n_housing: int | None = None, + n_consumption: int = 60, + n_savings: int | None = None, + liquid_max: float = 50.0, + housing_max: float = 50.0, + housing_min: float = 0.01, + n_periods: int = 4, + upper_envelope: Literal["fues", "mss", "ltm", "rfc"] = "rfc", +) -> Model: + """Build the DS-2024 discrete-housing model. + + Args: + variant: `"dcegm"` builds the discrete-choice DC-EGM (the RFC/FUES column); + `"brute"` builds the grid-search (VFI) twin β€” the accuracy oracle. + n_grid: Number of liquid grid points (and clustered savings nodes). + n_housing: Number of discrete housing levels; defaults to `n_grid`. + n_consumption: Number of consumption-grid points (brute search). + n_savings: Number of savings-grid nodes; defaults to `n_grid`. + liquid_max: Upper bound of the liquid grid. + housing_max: Upper bound of the housing-level grid. + housing_min: Lower bound `b` of the housing levels (and liquid floor). + n_periods: Number of model periods (the last is the terminal bequest). + upper_envelope: DC-EGM upper-envelope backend; the RFC column is `"rfc"`. + + Returns: + The alive discrete-housing regime plus the terminal bequest regime. + """ + n_housing = n_grid if n_housing is None else n_housing + n_savings = n_grid if n_savings is None else n_savings + + ages = AgeGrid(start=START_AGE, stop=START_AGE + n_periods - 1, step="Y") + final_age = int(ages.exact_values[-1]) + + stock_levels = jnp.asarray( + [ + housing_min + (housing_max - housing_min) * i / (n_housing - 1) + for i in range(n_housing) + ] + ) + housing_class = _make_housing_levels(n_housing=n_housing) + housing_grid = DiscreteGrid(housing_class) + liquid_grid = LinSpacedGrid(start=0.0, stop=liquid_max, n_points=n_grid) + consumption_grid = LinSpacedGrid( + start=0.05, stop=liquid_max, n_points=n_consumption + ) + savings_grid = IrregSpacedGrid( + points=tuple( + housing_min + + (liquid_max + housing_max - housing_min) * (i / (n_savings - 1)) ** 2 + for i in range(n_savings) + ) + ) + + def housing_stock(housing: DiscreteState) -> FloatND: + """Held housing stock `h` of the current discrete housing state.""" + return stock_levels[housing] + + def serviced_housing(housing_choice: DiscreteAction) -> FloatND: + """Serviced housing this period β€” the chosen next stock `H'`.""" + return stock_levels[housing_choice] + + def housing_cost( + housing: DiscreteState, + housing_choice: DiscreteAction, + delta: float, + return_housing: float, + tau: float, + ) -> FloatND: + """Net liquid cost of moving the house from `h` to `H'`. + + - keep (`H' = h`): cost `0`; + - adjust (`H' != h`): cost `(1 + tau)Β·H' - (1 + r_H)Β·hΒ·(1 - delta)`. + """ + round_trip = (1.0 + tau) * stock_levels[housing_choice] - ( + 1.0 + return_housing + ) * stock_levels[housing] * (1.0 - delta) + return jnp.where(housing_choice == housing, 0.0, round_trip) + + def resources( + liquid: ContinuousState, + housing_cost: FloatND, + income_value: FloatND, + return_liquid: float, + ) -> FloatND: + """Liquid resources `(1 + r)Β·a + y - housing_cost`.""" + return (1.0 + return_liquid) * liquid + income_value - housing_cost + + def next_liquid_brute( + liquid: ContinuousState, + housing_cost: FloatND, + income_value: FloatND, + consumption: ContinuousAction, + return_liquid: float, + ) -> ContinuousState: + """Brute-force liquid law: resources minus consumption.""" + return ( + (1.0 + return_liquid) * liquid + income_value - housing_cost - consumption + ) + + def borrowing_constraint( + liquid: ContinuousState, + housing_cost: FloatND, + income_value: FloatND, + consumption: ContinuousAction, + return_liquid: float, + ) -> BoolND: + """Keep post-decision liquid assets non-negative (`a' >= 0`).""" + return ( + (1.0 + return_liquid) * liquid + income_value - housing_cost - consumption + ) >= 0.0 + + def utility( + consumption: ContinuousAction, + serviced_housing: FloatND, + gamma_c: float, + alpha: float, + ) -> FloatND: + """CRRA consumption utility plus a log housing-service flow.""" + consumption_utility = (consumption ** (1.0 - gamma_c) - 1.0) / (1.0 - gamma_c) + return consumption_utility + alpha * jnp.log(serviced_housing) + + def bequest( + liquid: ContinuousState, + housing: DiscreteState, + return_liquid: float, + theta: float, + bequest_shift: float, + gamma_c: float, + ) -> FloatND: + """Terminal bequest `thetaΒ·((K + (1+r)a + h)^{1-gamma} - 1)/(1 - gamma)`.""" + estate = bequest_shift + (1.0 + return_liquid) * liquid + stock_levels[housing] + return theta * (estate ** (1.0 - gamma_c) - 1.0) / (1.0 - gamma_c) + + def next_regime(age: int) -> ScalarInt: + """Stay alive until the final age, then enter the terminal bequest.""" + return jnp.where( + age + 1 >= final_age, + DS2024HousingFuesRegimeId.dead, + DS2024HousingFuesRegimeId.alive, + ) + + dead = UserRegime( + transition=None, + active=lambda age, fa=final_age: age >= fa, + states={"liquid": liquid_grid, "housing": housing_grid}, + functions={"utility": bequest}, + ) + + shared = { + "utility": utility, + "housing_cost": housing_cost, + "serviced_housing": serviced_housing, + "housing_stock": housing_stock, + "income_value": income_value, + } + + if variant == "brute": + alive = UserRegime( + transition=next_regime, + active=lambda age, fa=final_age: age < fa, + states={ + "liquid": liquid_grid, + "housing": housing_grid, + "income": DiscreteGrid(Income), + }, + state_transitions={ + "liquid": next_liquid_brute, + "housing": next_housing, + "income": MarkovTransition(income_transition), + }, + actions={"consumption": consumption_grid, "housing_choice": housing_grid}, + constraints={"borrowing_constraint": borrowing_constraint}, + functions=shared, + solver=GridSearch(), + ) + return Model( + regimes={"alive": alive, "dead": dead}, + ages=ages, + regime_id_class=DS2024HousingFuesRegimeId, + ) + + inner_solver = DCEGM( + continuous_state="liquid", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=savings_grid, + upper_envelope=upper_envelope, + n_constrained_points=32, + ) + alive = UserRegime( + transition=next_regime, + active=lambda age, fa=final_age: age < fa, + states={ + "liquid": liquid_grid, + "housing": housing_grid, + "income": DiscreteGrid(Income), + }, + state_transitions={ + "liquid": next_liquid, + "housing": next_housing, + "income": MarkovTransition(income_transition), + }, + actions={"consumption": consumption_grid, "housing_choice": housing_grid}, + functions={ + **shared, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=inner_solver, + ) + return Model( + regimes={"alive": alive, "dead": dead}, + ages=ages, + regime_id_class=DS2024HousingFuesRegimeId, + ) + + +def build_params( + *, + variant: Literal["dcegm", "brute"] = "dcegm", + tau: float = 0.20, + delta: float = 0.0, + discount_factor: float = 0.945, + gamma_c: float = 1.458, + alpha: float = 0.66, + return_liquid: float = 0.024, + return_housing: float = 0.10, + theta: float = 2.0, + bequest_shift: float = 200.0, +) -> dict: + """Calibration parameters for the DS-2024 discrete-housing model. + + Args: + variant: Must match `build_model`. + tau: Proportional housing-transaction cost. + delta: Housing depreciation. + discount_factor: Discount factor `beta`. + gamma_c: Consumption CRRA `gamma_C`. + alpha: Housing-service weight. + return_liquid: Liquid return `r`. + return_housing: Housing return `r_H`. + theta: Terminal bequest weight. + bequest_shift: Terminal bequest shift `K`. + + Returns: + The nested parameter template keyed by regime then function. + """ + utility_params = {"gamma_c": gamma_c, "alpha": alpha} + cost_params = {"delta": delta, "return_housing": return_housing, "tau": tau} + bequest_params = { + "return_liquid": return_liquid, + "theta": theta, + "bequest_shift": bequest_shift, + "gamma_c": gamma_c, + } + if variant == "brute": + alive = { + "utility": utility_params, + "housing_cost": cost_params, + "next_liquid": {"return_liquid": return_liquid}, + "borrowing_constraint": {"return_liquid": return_liquid}, + } + else: + alive = { + "utility": utility_params, + "housing_cost": cost_params, + "resources": {"return_liquid": return_liquid}, + "next_liquid": {}, + "inverse_marginal_utility": {"gamma_c": gamma_c}, + } + return { + "discount_factor": discount_factor, + "alive": alive, + "dead": {"utility": bequest_params}, + } diff --git a/tests/test_models/ds_app2_housing.py b/tests/test_models/ds_app2_housing.py new file mode 100644 index 000000000..fc6b9f96a --- /dev/null +++ b/tests/test_models/ds_app2_housing.py @@ -0,0 +1,546 @@ +"""Dobrescu-Shanker (2026) Application 2 housing model as a pylcm NEGM model. + +The DS-2026 Β§2.2 housing model has a liquid financial asset, an illiquid housing +stock with a proportional transaction cost, an AR1 wage, and a discrete +adjust/keep choice. It maps onto pylcm's nested-EGM solver: + +- the **inner** DC-EGM solves liquid consumption-savings, with the Euler + equation inverting on `liquid` assets `a` β€” the clean inverse-Euler margin; +- the **outer** durable margin is the next housing stock `H'` (`outer_action` + = `housing_investment`, `outer_post_decision` = `next_housing`), searched over + a grid rather than inverted β€” the transaction cost makes the outer value + non-concave, so a second inverse-Euler would be invalid; +- the **keeper** (`d = 0`) holds the house (`H' = H`, no cost) and the + **adjuster** (`d = 1`) chooses `H'` paying `(1 + Ο„)Β·H'` while selling the old + house. NEGM builds both cores from one regime β€” the keeper as a passive + DC-EGM with `next_housing = housing`, the adjuster as the inner DC-EGM with + the outer post-decision supplied per grid node β€” so the adjust/keep choice is + *not* a user-declared discrete action. + +The wage is a Tauchen-discretised AR1 (`rho_w = 0.82`, `sigma_w = 0.11`) carried as a +pylcm process state in working life; it drops at retirement, where income is a +fixed pension. The lifecycle runs working (start age 20) β†’ retired (age 60) β†’ +dead (terminal, T = 70), with a workingβ†’retired regime transition. + +Utility is separable CES over non-durable consumption and the housing serviced +this period (the new house if adjusting, else the held house). The serviced +house reads the outer post-decision `next_housing`, additively separable from +consumption, so the inner Euler inversion treats the housing term as a constant +β€” the NEGM contract the housing margin must satisfy. + +## Calibration (DS Table 3 note, spec Β§Calibration) + +`Ξ² = 0.94`, `gamma_C = 3.5`, `gamma_H = 1.5`, `alpha = 0.70`, `r = 0.04`, `r_H = 0`, +`Ο„ ∈ {0.05, 0.07, 0.12}` (default `0.07`), `rho_w = 0.82`, `sigma_w = 0.11`. + +Two values the paper omits are documented defaults pending confirmation +(collected question Q3): the housing-utility scale `ΞΊ = 1.0` and the bequest +weight `ΞΈΜ„ = 1.0`. + +The CES exponent follows the standard CRRA/CES reading `(x^{1-gamma} - 1)/(1 - gamma)`, +not the OCR-ambiguous `(x^{gamma-1} - 1)/(gamma - 1)` printed in the paper (collected +question Q4): the standard form is concave and consistent with the listed +`gamma_C = 3.5 > 1`, so it is the sensible reading pending confirmation. +""" + +import jax.numpy as jnp + +from lcm import ( + DCEGM, + NEGM, + AgeGrid, + LinSpacedGrid, + Model, + TauchenAR1Process, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + FloatND, + ScalarInt, +) + +# Lifecycle anchors (years). Working life starts at 20, retirement at 60, and +# the terminal bequest regime is entered at T = 70. +START_AGE = 20 +RETIREMENT_AGE = 60 +TERMINAL_AGE = 70 + +# Number of wage discretisation nodes; kept small so the construction test is +# fast and the eventual solve fits a GPU. +N_WAGE_NODES = 5 + +# The fixed retirement pension (a placeholder income floor; the paper's +# retirement income process is not part of the App.2 Table 3 sweep). +RETIREMENT_PENSION = 0.3 + +# The name of the function the transaction cost `Ο„` parametrises, exposed so the +# construction test can locate `Ο„` in the params template without hardcoding it. +HOUSING_COST_FUNCTION_NAME = "housing_cost" + + +@categorical(ordered=False) +class HousingRegimeId: + """Lifecycle regimes: working, retired, and the terminal bequest regime.""" + + working: ScalarInt + retired: ScalarInt + dead: ScalarInt + + +def wage_income(wage: ContinuousState) -> FloatND: + """Map the AR1 wage node to its labor-income level `y = exp(log-wage)`. + + The Tauchen process discretises the log wage; income is its exponential. + """ + return jnp.exp(wage) + + +def housing_cost( + housing: ContinuousState, + next_housing: ContinuousState, + return_housing: float, + tau: float, +) -> FloatND: + """Net liquid cost of moving the house from `H` to `next_housing` (`H'`). + + The DS budget (eq. 12) gives the discrete adjust/keep choice `d ∈ {0, 1}` a + round-trip transaction cost: adjusting (`d = 1`) sells the whole old house at + `(1 + r_H)Β·H` and rebuys the whole new house at `(1 + Ο„)Β·H'`, while keeping + (`d = 0`, `H' = H`) is free. The net liquid cost is therefore + + - keep (`H' = H`): cost `0`, + - adjust (`H' β‰  H`): cost `(1 + Ο„)Β·H' - (1 + r_H)Β·H`. + + Because the proportional cost `Ο„` falls on the *whole* new stock, any + adjustment β€” however small β€” pays about `τ·H` more than keeping. That + discrete wedge opens the DS (S, s) inaction band: keeping for free dominates + a region of `H'`, so `max(V_keeper, V_adjuster)` is flat there. A + net-investment cost (proportional to the traded difference `H' - H`) would + vanish near the no-trade point and leave no band. + + The keep branch costing exactly `0` is also the invariant the NEGM keeper + kernel relies on: it holds the stock (`H' = H` is injected) and its + `credited(H, H) = 0` makes the published cash-on-hand carry correct. + + Reads only the held housing state and the outer post-decision `next_housing` + β€” never the inner consumption action or the liquid Euler state β€” so it is a + constant per outer-grid node, as the NEGM contract requires. + """ + round_trip_cost = (1.0 + tau) * next_housing - (1.0 + return_housing) * housing + return jnp.where(next_housing == housing, 0.0, round_trip_cost) + + +def resources( + liquid: ContinuousState, + housing_cost: FloatND, + income: FloatND, + return_liquid: float, +) -> FloatND: + """Liquid resources consumption is paid out of, given the fixed outer node. + + `(1 + r)Β·a + y - housing_cost`. The housing cost is bound to one outer-grid + node, so it enters the inner Euler inversion as a constant. Strictly + increasing in the liquid Euler state `liquid`; independent of the inner + consumption action. + """ + return (1.0 + return_liquid) * liquid + income - housing_cost + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + """Inner post-decision liquid balance `a' = resources - c`.""" + return resources - consumption + + +def next_liquid(savings: FloatND) -> ContinuousState: + """Euler-state law: next liquid assets equal post-decision savings. + + Reads only the post-decision `savings`, never the outer housing margin, so + the inner Euler inversion stays independent of the housing choice β€” the + NEGM nesting contract. + """ + return savings + + +def next_housing( + housing: ContinuousState, housing_investment: ContinuousAction +) -> ContinuousState: + """Durable law of motion `H' = H + housing_investment`. + + Used as the `housing` state transition, so pylcm names its output the + auto-generated `next_housing`; the NEGM solver reads that value as its + `outer_post_decision`, bound per outer-grid node into the inner resources + DAG and the serviced-housing service flow. + """ + return housing + housing_investment + + +def keep_housing(housing: ContinuousState) -> FloatND: + """The no-adjustment candidate `H' = H` (the adjustment-cost kink).""" + return housing + + +def serviced_housing(next_housing: ContinuousState) -> FloatND: + """The house lived in this period β€” the new house `H'`. + + For the adjuster this is the chosen house; for the keeper the injected + identity `H' = H` makes it the held house. Reads only the outer + post-decision, so the housing service flow is additively separable from the + inner consumption action. + """ + return next_housing + + +def utility( + consumption: ContinuousAction, + serviced_housing: FloatND, + alpha: float, + gamma_c: float, + gamma_h: float, + kappa: float, +) -> FloatND: + """Separable CES utility over consumption and serviced housing (eq. 26). + + `u(c, H) = alphaΒ·(c^{1-gamma_C} - 1)/(1 - gamma_C) + + (1 - alpha)Β·ΞΊΒ·(H^{1-gamma_H} - 1)/(1 - gamma_H)`. + + Uses the standard CRRA/CES exponent `1 - gamma` (the OCR-ambiguous paper print + `gamma - 1` is read as the standard concave form pending confirmation β€” Q4). + Reads the inner consumption action and the serviced-housing service flow + additively, never the liquid Euler state β€” the DC-EGM envelope condition β€” + and the two service terms live in distinct functions, so no single function + couples consumption to the outer margin. + """ + consumption_utility = (consumption ** (1.0 - gamma_c) - 1.0) / (1.0 - gamma_c) + housing_utility = (serviced_housing ** (1.0 - gamma_h) - 1.0) / (1.0 - gamma_h) + return alpha * consumption_utility + (1.0 - alpha) * kappa * housing_utility + + +def inverse_marginal_utility( + marginal_continuation: FloatND, gamma_c: float, alpha: float +) -> FloatND: + """Invert the consumption marginal utility `u'(c) = alphaΒ·c^{-gamma_C}`. + + `c = (mc / alpha)^{-1/gamma_C}`. The housing-service term is additively + separable from consumption, so it drops out of the inner consumption + inversion; the consumption weight `alpha` scales the marginal utility, so it + enters the inverse β€” the round-trip `(u')^{-1}(u'(c)) = c` the DC-EGM + validator checks against `jax.grad(utility)` holds only with it. + """ + return (marginal_continuation / alpha) ** (-1.0 / gamma_c) + + +def bequest( + liquid: ContinuousState, + housing: ContinuousState, + return_liquid: float, + theta_bar: float, + gamma_c: float, +) -> FloatND: + """Terminal bequest `ΞΈ((1 + r)Β·a + H)`, with `ΞΈ(x) = ΞΈΜ„Β·u(x, 0)`. + + The CRRA bequest reads only the carried liquid and housing states. The + bequest weight `ΞΈΜ„` is a documented default (`1.0`) pending confirmation + (Q3). + """ + estate = (1.0 + return_liquid) * liquid + housing + return theta_bar * (estate ** (1.0 - gamma_c) - 1.0) / (1.0 - gamma_c) + + +def next_regime(age: int) -> ScalarInt: + """Working β†’ retired at the retirement age, β†’ dead at the terminal age.""" + return jnp.where( + age + 1 >= TERMINAL_AGE, + HousingRegimeId.dead, + jnp.where( + age + 1 >= RETIREMENT_AGE, + HousingRegimeId.retired, + HousingRegimeId.working, + ), + ) + + +def next_regime_from_retired(age: int) -> ScalarInt: + """Retired β†’ dead at the terminal age, else stay retired.""" + return jnp.where( + age + 1 >= TERMINAL_AGE, + HousingRegimeId.dead, + HousingRegimeId.retired, + ) + + +def _working_income(wage_income: FloatND) -> FloatND: + """Working-life income: the AR1 wage level.""" + return wage_income + + +def _retirement_income() -> FloatND: + """Retirement income: the fixed pension.""" + return jnp.asarray(RETIREMENT_PENSION) + + +def _euler_coupled_next_liquid( + savings: FloatND, next_housing: ContinuousState +) -> ContinuousState: + """Euler-coupled liquid law for the rejection guardrail test. + + Feeding the outer housing post-decision `next_housing` into the inner + Euler-state transition couples the inner Euler inversion to the housing + choice β€” the DS pension shape NEGM forbids. The validator must reject this + with the 2-D-EGM pointer. + """ + return savings + 0.0 * next_housing + + +def build_model( + *, + n_grid: int, + n_periods: int | None = None, + liquid_max: float = 50.0, + housing_max: float = 20.0, + consumption_max: float = 50.0, + n_consumption: int = 30, + n_savings: int = 60, + liquid_batch_size: int = 0, + outer_batch_size: int = 0, + _euler_couple_housing: bool = False, +) -> Model: + """Build the DS App.2 housing NEGM model. + + Args: + n_grid: Number of points on the liquid, housing, and outer + housing-investment grids (DS sweeps `NG ∈ {250, 500, 750, 1000}`). + n_periods: Optional shortened horizon for construction tests; `None` + uses the paper's working β†’ retired β†’ dead lifecycle from age 20 to + the terminal age 70. + liquid_max: Upper bound of the liquid-asset grid. + housing_max: Upper bound of the housing and outer grids. + consumption_max: Upper bound of the inner consumption action grid. + n_consumption: Number of inner consumption-grid points. + n_savings: Number of inner savings-grid points. + liquid_batch_size: Optional chunking of the liquid Euler-state grid. A + positive value splays the per-asset-node solve into + `ceil(n_grid / liquid_batch_size)` sequential chunks, bounding the + peak device memory of the outer durable argmax (whose tensor carries + the liquid axis) without changing the solved value function. `0` + (the default) solves every liquid node in one kernel. + outer_batch_size: Optional chunking of the NEGM outer durable search. A + positive value folds the outer-grid nodes into the running outer + maximum in chunks of that many nodes, bounding the peak device memory + to one chunk rather than materialising every node's solve at once; it + leaves the solved value function unchanged. `0` (the default) solves + every outer node at once. + _euler_couple_housing: Test-only flag that wires the outer housing + post-decision into the inner Euler-state law, so the NEGM contract + rejects the model β€” confirming the accepted model is not accepted by + accident. + + Returns: + The two-NEGM-regime (working, retired) plus terminal (dead) housing + model. + """ + if n_periods is None: + ages = AgeGrid(start=START_AGE, stop=TERMINAL_AGE, step="Y") + else: + ages = AgeGrid(start=START_AGE, stop=START_AGE + n_periods - 1, step="Y") + final_age = int(ages.exact_values[-1]) + retirement_age = min(RETIREMENT_AGE, final_age) + + # Housing must stay strictly positive: the CES service flow + # `H^{1-gamma_H}` diverges to -inf at `H = 0` (you cannot live in zero + # house), so a grid node at 0 puts a -inf sentinel in the value function + # that contaminates the off-grid interpolation. Floor the housing and outer + # (next-housing choice) grids at a small positive stock. + housing_min = housing_max / (2.0 * n_grid) + + def housing_stays_in_bounds(next_housing: ContinuousState) -> BoolND: + """The chosen next house must stay within `[housing_min, housing_max]`. + + The NEGM solve searches `next_housing` on the floored, capped outer grid, + but the forward simulation re-optimises over the symmetric + `housing_investment` action grid `[-housing_max, housing_max]`, which can + drive `next_housing = housing + housing_investment` below the floor or + above the top outer node. Below the floor the CES service utility is NaN + (a non-positive house) and above the top node the policy extrapolates off + the solved outer grid; the budget feasibility mask catches neither, so the + simulate argmax could select an out-of-bounds action. This cut mirrors the + solve's floored, capped outer grid on both sides. + """ + return (next_housing >= housing_min) & (next_housing <= housing_max) + + liquid_grid = LinSpacedGrid( + start=0.0, stop=liquid_max, n_points=n_grid, batch_size=liquid_batch_size + ) + housing_grid = LinSpacedGrid(start=housing_min, stop=housing_max, n_points=n_grid) + outer_grid = LinSpacedGrid(start=housing_min, stop=housing_max, n_points=n_grid) + consumption_grid = LinSpacedGrid( + start=0.05, stop=consumption_max, n_points=n_consumption + ) + housing_investment_grid = LinSpacedGrid( + start=-housing_max, stop=housing_max, n_points=n_grid + ) + savings_grid = LinSpacedGrid( + start=0.0, stop=liquid_max + housing_max, n_points=n_savings + ) + + inner_liquid_law = ( + _euler_coupled_next_liquid if _euler_couple_housing else next_liquid + ) + + negm_solver = NEGM( + inner=DCEGM( + continuous_state="liquid", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=savings_grid, + ), + outer_action="housing_investment", + outer_post_decision="next_housing", + outer_grid=outer_grid, + outer_no_adjustment_candidate="keep_housing", + outer_batch_size=outer_batch_size, + ) + + shared_functions = { + "utility": utility, + "housing_cost": housing_cost, + "resources": resources, + "savings": savings, + "keep_housing": keep_housing, + "serviced_housing": serviced_housing, + "inverse_marginal_utility": inverse_marginal_utility, + } + + working = UserRegime( + transition=next_regime, + active=lambda age, ra=retirement_age: age < ra, + states={ + "liquid": liquid_grid, + "housing": housing_grid, + "wage": TauchenAR1Process(n_points=N_WAGE_NODES, gauss_hermite=True), + }, + state_transitions={ + "liquid": inner_liquid_law, + "housing": next_housing, + }, + actions={ + "consumption": consumption_grid, + "housing_investment": housing_investment_grid, + }, + functions={ + **shared_functions, + "income": _working_income, + "wage_income": wage_income, + }, + constraints={"housing_stays_in_bounds": housing_stays_in_bounds}, + solver=negm_solver, + ) + + retired = UserRegime( + transition=next_regime_from_retired, + active=lambda age, ra=retirement_age, fa=final_age: ra <= age < fa, + states={"liquid": liquid_grid, "housing": housing_grid}, + state_transitions={ + "liquid": inner_liquid_law, + "housing": next_housing, + }, + actions={ + "consumption": consumption_grid, + "housing_investment": housing_investment_grid, + }, + functions={**shared_functions, "income": _retirement_income}, + constraints={"housing_stays_in_bounds": housing_stays_in_bounds}, + solver=negm_solver, + ) + + dead = UserRegime( + transition=None, + active=lambda age, fa=final_age: age >= fa, + states={"liquid": liquid_grid, "housing": housing_grid}, + functions={"utility": bequest}, + ) + + return Model( + regimes={"working": working, "retired": retired, "dead": dead}, + ages=ages, + regime_id_class=HousingRegimeId, + ) + + +def build_params( + *, + tau: float = 0.07, + discount_factor: float = 0.94, + gamma_c: float = 3.5, + gamma_h: float = 1.5, + alpha: float = 0.70, + kappa: float = 1.0, + theta_bar: float = 1.0, + return_liquid: float = 0.04, + return_housing: float = 0.0, + rho_w: float = 0.82, + sigma_w: float = 0.11, + mu_w: float = 0.0, +) -> dict: + """Calibration parameters for the DS App.2 housing model. + + Args: + tau: Proportional housing-transaction cost (DS sweeps `{0.05, 0.07, + 0.12}`, default `0.07`). + discount_factor: `Ξ²`. + gamma_c: Consumption CRRA `gamma_C`. + gamma_h: Housing CES `gamma_H`. + alpha: Consumption weight `alpha`. + kappa: Housing-utility scale (documented default `1.0` pending + confirmation β€” Q3). + theta_bar: Bequest weight (documented default `1.0` pending + confirmation β€” Q3). + return_liquid: Liquid return `r`. + return_housing: Housing return `r_H`. + rho_w: AR1 wage persistence `rho_w`. + sigma_w: AR1 wage innovation std `sigma_w`. + mu_w: AR1 wage drift `ΞΌ_w`. + + Returns: + The nested parameter template keyed by regime then function. The + transaction cost lives under the housing-cost function, where the outer + durable margin reads it; the wage-process params nest under the `wage` + state of the working regime. + """ + utility_params = { + "alpha": alpha, + "gamma_c": gamma_c, + "gamma_h": gamma_h, + "kappa": kappa, + } + housing_cost_params = {"return_housing": return_housing, "tau": tau} + wage_params = {"rho": rho_w, "sigma": sigma_w, "mu": mu_w} + return { + "discount_factor": discount_factor, + "working": { + "utility": utility_params, + HOUSING_COST_FUNCTION_NAME: housing_cost_params, + "resources": {"return_liquid": return_liquid}, + "next_liquid": {}, + "inverse_marginal_utility": {"gamma_c": gamma_c, "alpha": alpha}, + "wage": wage_params, + }, + "retired": { + "utility": utility_params, + HOUSING_COST_FUNCTION_NAME: housing_cost_params, + "resources": {"return_liquid": return_liquid}, + "next_liquid": {}, + "inverse_marginal_utility": {"gamma_c": gamma_c, "alpha": alpha}, + }, + "dead": { + "utility": { + "return_liquid": return_liquid, + "theta_bar": theta_bar, + "gamma_c": gamma_c, + }, + }, + } diff --git a/tests/test_models/ds_app2_housing_fues.py b/tests/test_models/ds_app2_housing_fues.py new file mode 100644 index 000000000..fc5922957 --- /dev/null +++ b/tests/test_models/ds_app2_housing_fues.py @@ -0,0 +1,577 @@ +"""Dobrescu-Shanker (2026) Application 2 housing β€” EGM-FUES discrete-grid variant. + +The DS-2026 Section 2.2 housing model is compared in Table 3 by two methods, +**EGM-FUES** and **NEGM**. The NEGM column is pylcm's nested-EGM solver over a +*continuous* housing margin (`ds_app2_housing.py`). This module builds the +**EGM-FUES** column: the paper solves it with one-dimensional FUES nested over a +fixed housing grid (its Box 2) β€” for each next-housing level `H'` on an exogenous +grid it inverts the liquid-asset Euler equation and pools the candidates, then a +single 1-D FUES upper envelope over the wealth grid selects the optimal policy +across housing choices. + +In pylcm that pooled-candidate upper envelope is exactly the discrete-choice +DC-EGM upper envelope (FUES/MSS/LTM): discretise the next-housing choice onto the +housing grid and treat it as a discrete action, and the inner liquid-asset DC-EGM +plus the discrete-choice envelope reproduces the EGM-FUES solve β€” the same shape +as Application 3's discrete-housing model, with Application 2's separable-CES +utility and proportional transaction cost. As the housing grid refines this +converges to the paper's continuous EGM-FUES. + +## The discrete-housing mapping + +- liquid financial assets `liquid` (`a >= 0`) are the continuous Euler state the + Euler equation inverts on, and `consumption` (`c`) is the continuous action; +- the held housing stock `housing` (`H`) is a discrete state carried as a + value-function grid axis over the housing-level alphabet; +- the next-housing choice is a discrete action `housing_choice` over the same + alphabet; the discrete-choice upper envelope selects the best `H'` per + liquid-housing-wage cell (FUES/MSS/LTM), and grid search (VFI/brute) does the + same by brute force β€” the Table 3 methods; +- `next_housing = housing_choice`, so the discrete action drives the discrete + housing transition. Choosing `housing_choice == housing` is the no-trade + (keeper) option and is always available, so its zero-cost candidate is in the + envelope by construction β€” no separate keeper kernel and no below-floor corner. + +## Budget and utility (Application 2 calibration) + +The housing levels are an `n_housing`-point grid over `[housing_min, housing_max]` +floored at `housing_min = housing_max / (2 * n_housing)`, so the separable CES +housing service flow `H'^{1-gamma_H}` never hits its `H' = 0` singularity. The +proportional transaction cost is the DS eq. 12 round-trip cost β€” adjusting sells +the whole old house and rebuys the whole new house, keeping is free: + +- adjusting (`H' β‰  H`): cost `(1 + tau) * H' - (1 + r_H) * H`, +- keeping (`H' = H`): cost `0`. + +The cost falls on the whole new stock, so any move pays about `tau * H` more than +keeping β€” the discrete wedge that opens the DS (S, s) inaction band. + +Liquid resources are `R = (1 + r) * a + y - housing_cost`, with DC-EGM +consumption recovery `c = R - a'`. Utility is the Application 2 separable CES +`u(c, H') = alpha*(c^{1-gamma_C} - 1)/(1 - gamma_C) ++ (1-alpha)*kappa*(H'^{1-gamma_H} - 1)/(1 - gamma_H)`, so the consumption +marginal utility is `u'(c) = alpha*c^{-gamma_C}` and the housing-service term is +additively separable β€” the DC-EGM envelope condition on the liquid Euler state +holds, with `c = (alpha / mc)^{1/gamma_C}` the inverse marginal utility. +""" + +from typing import Literal + +import jax.numpy as jnp + +from lcm import ( + DCEGM, + AgeGrid, + DiscreteGrid, + GridSearch, + IrregSpacedGrid, + LinSpacedGrid, + Model, + TauchenAR1Process, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteAction, + DiscreteState, + FloatND, + ScalarInt, +) + +# Lifecycle anchors. The working life starts at 20, retires at 60, and the +# terminal bequest regime is entered at T = 70. The short default horizon keeps +# the construction probe local-safe; the paper uses the full lifecycle. +START_AGE = 20 +RETIREMENT_AGE = 60 +TERMINAL_AGE = 70 + +# Number of wage discretisation nodes; small so construction is fast. +N_WAGE_NODES = 5 + +# Fixed retirement pension (an income floor; the App.2 Table 3 sweep is the +# working-life housing problem). +RETIREMENT_PENSION = 0.3 + + +@categorical(ordered=False) +class HousingFuesRegimeId: + """Lifecycle regimes: working, retired, and the terminal bequest regime.""" + + working: ScalarInt + retired: ScalarInt + dead: ScalarInt + + +def _make_housing_levels(*, n_housing: int) -> type: + """Create an ordered categorical with one field per discrete housing level.""" + annotations = {f"h{i}": ScalarInt for i in range(n_housing)} + cls = type("HousingLevels", (), {"__annotations__": annotations}) + return categorical(ordered=True)(cls) + + +def wage_income(wage: ContinuousState) -> FloatND: + """Map the AR1 wage node to its labor income `y = exp(log-wage)`.""" + return jnp.exp(wage) + + +def _working_income(wage_income: FloatND) -> FloatND: + """Working-life income is the wage income.""" + return wage_income + + +def _retirement_income(retirement_pension: float) -> FloatND: + """Retirement income is the fixed pension.""" + return jnp.asarray(retirement_pension) + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + """Inner post-decision liquid balance `a' = resources - c`.""" + return resources - consumption + + +def next_liquid(savings: FloatND) -> ContinuousState: + """Euler-state law: next liquid assets equal post-decision savings.""" + return savings + + +def next_housing(housing_choice: DiscreteAction) -> DiscreteState: + """Discrete housing law: next housing equals the chosen code. + + The discrete action `housing_choice` and the discrete state `housing` share + the housing-level alphabet, so this deterministic transition maps codes 1:1. + """ + return housing_choice + + +def utility( + consumption: ContinuousAction, + serviced_housing: FloatND, + alpha: float, + kappa: float, + gamma_c: float, + gamma_h: float, +) -> FloatND: + """Application 2 separable CES utility over consumption and serviced housing. + + `u(c, H') = alpha*(c^{1-gamma_C} - 1)/(1 - gamma_C) + + (1-alpha)*kappa*(H'^{1-gamma_H} - 1)/(1 - gamma_H)`. The housing-service + term is additively separable from consumption, so it drops from the inner + consumption Euler inversion. Reads the serviced housing (the chosen stock) + and the consumption action β€” never the liquid Euler state. + """ + consumption_term = (consumption ** (1.0 - gamma_c) - 1.0) / (1.0 - gamma_c) + housing_term = (serviced_housing ** (1.0 - gamma_h) - 1.0) / (1.0 - gamma_h) + return alpha * consumption_term + (1.0 - alpha) * kappa * housing_term + + +def inverse_marginal_utility( + marginal_continuation: FloatND, alpha: float, gamma_c: float +) -> FloatND: + """Invert the consumption marginal utility `u'(c) = alpha*c^{-gamma_C}`. + + `c = (alpha / mc)^{1/gamma_C}`. The separable housing term drops from the + inner inversion; the consumption weight `alpha` and curvature `gamma_C` + enter the inverse. + """ + return (alpha / marginal_continuation) ** (1.0 / gamma_c) + + +def _fail_if_too_few_housing_levels(*, n_housing: int) -> None: + """Reject a housing alphabet too small to space the stock levels. + + The discrete stock levels are spaced by `(n_housing - 1)`, so at least two + levels are required. + """ + if n_housing < 2: + msg = ( + "n_housing must be at least 2: the discrete housing-level spacing " + f"divides by (n_housing - 1), got n_housing={n_housing}." + ) + raise ValueError(msg) + + +def build_model( # noqa: C901 + *, + variant: Literal["dcegm", "brute"] = "dcegm", + n_grid: int, + n_housing: int | None = None, + n_consumption: int = 60, + n_savings: int | None = None, + liquid_max: float = 50.0, + housing_max: float = 20.0, + n_periods: int | None = None, + upper_envelope: Literal["fues", "mss", "ltm", "rfc"] = "fues", + liquid_batch_size: int = 0, +) -> Model: + """Build the DS App.2 housing EGM-FUES discrete-housing model. + + Args: + variant: `"dcegm"` builds the discrete-choice DC-EGM regime (liquid assets + the Euler state, consumption inverted, the housing choice a discrete + action solved by the upper envelope) β€” the EGM-FUES column; `"brute"` + builds the grid-search (VFI) twin solving the same economics with no + Euler machinery. + n_grid: Number of liquid-asset grid points; also the number of clustered + exogenous savings nodes the DC-EGM solver scans. + n_housing: Number of discrete housing levels; defaults to `n_grid` (the + paper sizes the housing and asset grids together as `NG`). + n_consumption: Number of consumption-grid points (brute search and the + DC-EGM simulation draw). + n_savings: Number of savings-grid nodes; defaults to `n_grid`. + liquid_max: Upper bound of the liquid-asset grid. + housing_max: Upper bound of the housing-level grid. + n_periods: Optional shortened horizon for construction tests; `None` uses + the full lifecycle to `TERMINAL_AGE`. + upper_envelope: DC-EGM upper-envelope backend; the Table 3 method is FUES. + liquid_batch_size: Optional chunking of the liquid Euler-state grid. A + positive value splays the per-asset-node solve into + `ceil(n_grid / liquid_batch_size)` sequential chunks, bounding the + peak device memory of the discrete-housing argmax (whose tensor + carries the liquid axis) without changing the solved value function. + `0` (the default) solves every liquid node in one kernel. The + `"brute"` variant ignores it (grid search has no Euler asset row). + + Returns: + The three-regime (working, retired, dead) discrete-housing model. + """ + n_housing = n_grid if n_housing is None else n_housing + n_savings = n_grid if n_savings is None else n_savings + _fail_if_too_few_housing_levels(n_housing=n_housing) + + if n_periods is None: + ages = AgeGrid(start=START_AGE, stop=TERMINAL_AGE, step="Y") + retirement_age = RETIREMENT_AGE + final_age = TERMINAL_AGE + else: + ages = AgeGrid(start=START_AGE, stop=START_AGE + n_periods, step="Y") + # Split the short horizon: roughly the first half works, then retires, + # with the terminal bequest regime at the final age. + retirement_age = START_AGE + max(1, n_periods // 2) + final_age = START_AGE + n_periods + + def next_regime(age: int) -> ScalarInt: + """Transition working to retired when next period reaches retirement.""" + return jnp.where( + age + 1 >= retirement_age, + HousingFuesRegimeId.retired, + HousingFuesRegimeId.working, + ) + + def next_regime_from_retired(age: int) -> ScalarInt: + """Transition retired to dead when next period reaches the final age.""" + return jnp.where( + age + 1 >= final_age, + HousingFuesRegimeId.dead, + HousingFuesRegimeId.retired, + ) + + housing_min = housing_max / (2.0 * n_housing) + stock_levels = jnp.asarray( + [ + housing_min + (housing_max - housing_min) * i / (n_housing - 1) + for i in range(n_housing) + ] + ) + + housing_class = _make_housing_levels(n_housing=n_housing) + liquid_grid = LinSpacedGrid( + start=0.0, stop=liquid_max, n_points=n_grid, batch_size=liquid_batch_size + ) + consumption_grid = LinSpacedGrid( + start=0.05, stop=liquid_max, n_points=n_consumption + ) + savings_grid = IrregSpacedGrid( + points=tuple( + (liquid_max + housing_max) * (i / (n_savings - 1)) ** 2 + for i in range(n_savings) + ) + ) + + def housing_stock(housing: DiscreteState) -> FloatND: + """Held housing stock `H` of the current discrete housing state.""" + return stock_levels[housing] + + def chosen_stock(housing_choice: DiscreteAction) -> FloatND: + """Next-period housing stock `H'` implied by the discrete choice.""" + return stock_levels[housing_choice] + + def serviced_housing(housing_choice: DiscreteAction) -> FloatND: + """Serviced housing this period is the chosen next stock `H'`.""" + return stock_levels[housing_choice] + + def housing_cost( + housing: DiscreteState, + housing_choice: DiscreteAction, + tau: float, + return_housing: float, + ) -> FloatND: + """Net liquid cost of moving the house from `H` to `H'`. + + DS eq. 12 round-trip cost: choosing a different stock (`H' β‰  H`) sells + the whole old house at `(1 + r_H)Β·H` and rebuys the whole new house at + `(1 + Ο„)Β·H'`, while keeping the same stock is free. The proportional cost + falls on the whole new stock, so any move pays about `τ·H` more than + keeping β€” the discrete wedge that opens the DS (S, s) inaction band. + Reads only the held housing state and the discrete choice β€” a constant + per discrete-choice cell in the inner resources DAG. + """ + round_trip_cost = (1.0 + tau) * stock_levels[housing_choice] - ( + 1.0 + return_housing + ) * stock_levels[housing] + return jnp.where(housing_choice == housing, 0.0, round_trip_cost) + + def resources( + liquid: ContinuousState, + housing_cost: FloatND, + income: FloatND, + return_liquid: float, + ) -> FloatND: + """Liquid resources consumption is paid from, given the chosen house. + + `(1 + r) * a + y - housing_cost`. The housing cost is constant per + discrete-choice cell, so it enters the inner Euler inversion as a + constant; strictly increasing in the liquid Euler state. + """ + return (1.0 + return_liquid) * liquid + income - housing_cost + + def next_liquid_brute( + liquid: ContinuousState, + housing_cost: FloatND, + income: FloatND, + consumption: ContinuousAction, + return_liquid: float, + ) -> ContinuousState: + """Brute-force liquid law: resources minus consumption. + + Reads the consumption action and the shared `housing_cost` directly + rather than splitting resources and a post-decision `savings`, so the + grid-searched twin needs no Euler machinery. Equal to + `resources - consumption` of the DC-EGM regime. + """ + return (1.0 + return_liquid) * liquid + income - housing_cost - consumption + + def borrowing_constraint( + liquid: ContinuousState, + housing_cost: FloatND, + income: FloatND, + consumption: ContinuousAction, + return_liquid: float, + ) -> BoolND: + """Keep post-decision liquid assets non-negative (`a' >= 0`).""" + return ( + (1.0 + return_liquid) * liquid + income - housing_cost - consumption + ) >= 0.0 + + def bequest( + liquid: ContinuousState, + housing: DiscreteState, + return_liquid: float, + theta_bar: float, + ) -> FloatND: + """Terminal bequest `theta_bar * ((1 + r) a + H)`.""" + estate = (1.0 + return_liquid) * liquid + stock_levels[housing] + return theta_bar * estate + + housing_grid = DiscreteGrid(housing_class) + dead = UserRegime( + transition=None, + active=lambda age, fa=final_age: age >= fa, + states={"liquid": liquid_grid, "housing": housing_grid}, + functions={"utility": bequest}, + ) + + shared_econ = { + "utility": utility, + "serviced_housing": serviced_housing, + "housing_cost": housing_cost, + } + + if variant == "brute": + working = UserRegime( + transition=next_regime, + active=lambda age, ra=retirement_age: age < ra, + states={ + "liquid": liquid_grid, + "housing": housing_grid, + "wage": TauchenAR1Process(n_points=N_WAGE_NODES, gauss_hermite=True), + }, + state_transitions={"liquid": next_liquid_brute, "housing": next_housing}, + actions={ + "consumption": consumption_grid, + "housing_choice": housing_grid, + }, + constraints={"borrowing_constraint": borrowing_constraint}, + functions={ + **shared_econ, + "wage_income": wage_income, + "income": _working_income, + }, + solver=GridSearch(), + ) + retired = UserRegime( + transition=next_regime_from_retired, + active=lambda age, ra=retirement_age, fa=final_age: ra <= age < fa, + states={"liquid": liquid_grid, "housing": housing_grid}, + state_transitions={"liquid": next_liquid_brute, "housing": next_housing}, + actions={ + "consumption": consumption_grid, + "housing_choice": housing_grid, + }, + constraints={"borrowing_constraint": borrowing_constraint}, + functions={**shared_econ, "income": _retirement_income}, + solver=GridSearch(), + ) + return Model( + regimes={"working": working, "retired": retired, "dead": dead}, + ages=ages, + regime_id_class=HousingFuesRegimeId, + ) + + inner_solver = DCEGM( + continuous_state="liquid", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=savings_grid, + upper_envelope=upper_envelope, + n_constrained_points=32, + ) + working = UserRegime( + transition=next_regime, + active=lambda age, ra=retirement_age: age < ra, + states={ + "liquid": liquid_grid, + "housing": housing_grid, + "wage": TauchenAR1Process(n_points=N_WAGE_NODES, gauss_hermite=True), + }, + state_transitions={"liquid": next_liquid, "housing": next_housing}, + actions={ + "consumption": consumption_grid, + "housing_choice": housing_grid, + }, + functions={ + **shared_econ, + "wage_income": wage_income, + "income": _working_income, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=inner_solver, + ) + retired = UserRegime( + transition=next_regime_from_retired, + active=lambda age, ra=retirement_age, fa=final_age: ra <= age < fa, + states={"liquid": liquid_grid, "housing": housing_grid}, + state_transitions={"liquid": next_liquid, "housing": next_housing}, + actions={ + "consumption": consumption_grid, + "housing_choice": housing_grid, + }, + functions={ + **shared_econ, + "income": _retirement_income, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=inner_solver, + ) + return Model( + regimes={"working": working, "retired": retired, "dead": dead}, + ages=ages, + regime_id_class=HousingFuesRegimeId, + ) + + +def build_params( + *, + variant: Literal["dcegm", "brute"] = "dcegm", + tau: float = 0.07, + discount_factor: float = 0.94, + gamma_c: float = 3.5, + gamma_h: float = 1.5, + alpha: float = 0.70, + kappa: float = 1.0, + theta_bar: float = 1.0, + return_liquid: float = 0.04, + return_housing: float = 0.0, + retirement_pension: float = RETIREMENT_PENSION, + rho_w: float = 0.82, + sigma_w: float = 0.11, + mu_w: float = 0.0, +) -> dict: + """Calibration parameters for the DS App.2 EGM-FUES discrete-housing model. + + Args: + variant: `"dcegm"` threads the budget params under the resources and + inverse-marginal-utility functions; `"brute"` threads them under the + grid-search liquid law and the borrowing constraint. Must match the + `variant` passed to `build_model`. + tau: Proportional housing-transaction cost (default `0.07`). + discount_factor: `beta`. + gamma_c: Consumption CRRA `gamma_C`. + gamma_h: Housing CES `gamma_H`. + alpha: Consumption weight in the separable CES utility. + kappa: Housing-utility scale. + theta_bar: Terminal bequest weight. + return_liquid: Net liquid return `r`. + return_housing: Net housing return `r_H`. + retirement_pension: The fixed retirement income. + rho_w: AR1 wage persistence. + sigma_w: AR1 wage innovation std. + mu_w: AR1 wage drift. + + Returns: + The nested parameter template keyed by regime then function. + """ + utility_params = { + "alpha": alpha, + "kappa": kappa, + "gamma_c": gamma_c, + "gamma_h": gamma_h, + } + cost_params = {"tau": tau, "return_housing": return_housing} + wage_params = {"rho": rho_w, "sigma": sigma_w, "mu": mu_w} + + if variant == "brute": + working = { + "utility": utility_params, + "housing_cost": cost_params, + "next_liquid": {"return_liquid": return_liquid}, + "borrowing_constraint": {"return_liquid": return_liquid}, + "wage": wage_params, + } + retired = { + "utility": utility_params, + "housing_cost": cost_params, + "income": {"retirement_pension": retirement_pension}, + "next_liquid": {"return_liquid": return_liquid}, + "borrowing_constraint": {"return_liquid": return_liquid}, + } + else: + working = { + "utility": utility_params, + "housing_cost": cost_params, + "resources": {"return_liquid": return_liquid}, + "inverse_marginal_utility": {"alpha": alpha, "gamma_c": gamma_c}, + "wage": wage_params, + } + retired = { + "utility": utility_params, + "housing_cost": cost_params, + "income": {"retirement_pension": retirement_pension}, + "resources": {"return_liquid": return_liquid}, + "inverse_marginal_utility": {"alpha": alpha, "gamma_c": gamma_c}, + } + return { + "discount_factor": discount_factor, + "working": working, + "retired": retired, + "dead": { + "utility": {"return_liquid": return_liquid, "theta_bar": theta_bar}, + }, + } diff --git a/tests/test_models/ds_app3_discrete_housing.py b/tests/test_models/ds_app3_discrete_housing.py new file mode 100644 index 000000000..1ec48130c --- /dev/null +++ b/tests/test_models/ds_app3_discrete_housing.py @@ -0,0 +1,690 @@ +"""Dobrescu-Shanker (2026) Application 3 discrete-housing model (no-tax variant). + +The DS-2026 Section 2.3 model (an extended Fella 2014) is a finite-horizon +consumption-savings problem with a *discrete* housing stock, an own-vs-rent +choice, a proportional housing-adjustment cost, and a Markov wage. This module +builds the **no-tax** variant (Tables 4 and 7), which is fully specified in the +paper; the piecewise-linear capital-income tax of Table 5 is left as a +clearly-marked hook fixed to zero (its bracket thresholds and rates are not +printed in the paper β€” see Q7). + +## The discrete-housing mapping (Q6) + +DS Section 2.3 frames the period as five nested within-period stages. In pylcm +that nest collapses to a single DC-EGM regime with one discrete choice: + +- financial assets `assets` (`a >= 0`) are the continuous Euler state the Euler + equation inverts on, and `consumption` (`c`) is the continuous action; +- the held housing stock `housing` (`H`) is a discrete state carried as a + value-function grid axis; +- the own-vs-rent-and-level decision is a single discrete action + `housing_choice` over the same categorical alphabet as `housing` β€” exactly the + role Application 1's work/retire `labor_supply` action plays. The + discrete-choice upper envelope (FUES/MSS/LTM) selects the best choice per + asset-housing-wage cell, and grid search (VFI) does the same by brute force β€” + the four Table 4 methods; +- the next-period housing stock equals the chosen code (`next_housing = + housing_choice`), so the discrete action drives the discrete-state transition. + +This is *not* NEGM: NEGM nests an inner Euler solve inside an outer search over a +*continuous* durable margin, whereas App.3's housing is discrete, so the choice +is a plain discrete action and no outer durable search is needed. + +### Own, rent, and housing services + +`housing_choice` ranges over `rent` plus the owned stock levels +`own_h1..own_h5`. The serviced housing `h` that enters utility is: + +- the chosen stock `H'` when owning (`h = H'`), +- the rental service level `S` when renting (`h = S`). + +To keep the problem a single discrete-action DC-EGM regime (one continuous Euler +state, no second continuous margin), the renter's service `S` is tied to the +chosen owned-stock level the agent would otherwise hold β€” i.e. `rent` provides +the smallest service level on the housing-services grid. Letting the renter pick +`S` on the full owned-stock grid would simply add `rent_s2..rent_s5` codes to the +same discrete action; the single-`rent` form here is the smallest faithful +encoding for the construction probe and is flagged as a judgment call (Q8). + +## Budgets (no tax, eq. 27 hook fixed to zero) + +The period budget `a' + c = (1 + r) a - T(a) + y + ` is written as +a resources function `R = (1 + r) a - T(a) + y + ` with the +DC-EGM consumption recovery `c = R - a'`: + +- owner: ` = d_adj * H - d_adj * (1 + tau) * H'`, where `d_adj` is `1` when + the stock changes (`H' != H`) and `0` otherwise β€” selling the old house and + buying the new one at the adjustment cost `tau * H'`, +- renter: ` = H - P_r * S` β€” selling the entire held house and renting + services `S` at the rental price `P_r`. + +The capital-income tax `T(a) = capital_income_tax * a` is the Table 5 hook; the +no-tax variant fixes `capital_income_tax = 0`. + +## Calibration (Table 4/7 notes) + +`r = 0.06`, `beta = 0.93`, `T = 20`, `alpha = 0.77`, `tau = 0.07`, `kappa = +0.075`, `iota = 0.01`, `A_max = 40`, `H_max = 5`, `P_r = 0.1`, wage AR1 `rho = +0.977`, `sigma_eta = 0.024`, `sigma_eps = 0.063`. Table 7 (Fella replication) +uses the bequest weight `theta = 0.5`. +""" + +from typing import Literal + +import jax.numpy as jnp + +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + Model, + RouwenhorstAR1Process, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM, GridSearch +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteAction, + DiscreteState, + FloatND, + ScalarInt, +) + +# Lifecycle: T = 20 periods. The last period is the terminal bequest regime, so +# there are 19 decision periods. Ages are abstract unit steps from 0. +START_AGE = 0 +N_PERIODS = 20 + +# Housing-stock levels the owner can hold (H_max = 5). `rent` carries stock 0. +OWNED_STOCK_LEVELS = (1.0, 2.0, 3.0, 4.0, 5.0) + +# Number of Markov wage discretisation nodes; kept small so the construction +# test is fast and the eventual solve fits a GPU. +N_WAGE_NODES = 5 + +# The name of the function the adjustment cost `tau` and the capital-income tax +# hook parametrise, exposed so the construction test can locate them in the +# params template without hardcoding the function name. +RESOURCES_FUNCTION_NAME = "resources" + +# Piecewise-linear capital-income (asset-return) tax schedule for the with-tax +# variant (Table 5). The paper prints the bracket numbers only in Figure 9; these +# are the authors' replication values, transcribed from the `tax_table.brackets` +# of GitHub `akshayshanker/FUES`, path +# `examples/housing_renting/config_HR/STD_RES_SETTINGS_4_TAXES/master.yml`, pinned +# at commit `00961e0b588fdaa3ea3d740ebc13a8e6d230b26d` (blob +# `41661779df89167c91892bcfe6c7ffe16f259f8d`). It is an Australia-2015-16 schedule +# written directly as a function of assets, `T(a) = B + tau_a * (a - a0)` on each +# bracket `[a0, a1)` (the `B`/`tau_a` of each bracket). Three level discontinuities +# (up +0.10 at a=3.87, down ~0.14 at a=6.97 where the subsidy bracket resets the +# offset to 0.05, up +0.15 at a=15) plus rate kinks make the budget non-monotone β€” +# why Table 5 compares only FUES vs VFI. The resolved `(LOWER, OFFSET, RATE)` arrays +# below hash to sha256[:16] `4e8d1bf0748f6933`; re-derive from the pinned commit to +# detect upstream drift. +TAX_BRACKET_LOWER = (0.0, 2.20, 2.50, 2.75, 3.87, 6.97, 8.36, 12.0, 15.0, 20.0) +TAX_BRACKET_OFFSET = ( + 0.0, + 0.0, + 0.00342, + 0.00852, + 0.11412, + 0.05, + 0.076688, + 0.174968, + 0.378968, + 0.525968, +) +TAX_BRACKET_RATE = ( + 0.0, + 0.0114, + 0.0204, + 0.005, + 0.024, + 0.0192, + 0.027, + 0.018, + 0.0294, + 0.0294, +) + + +def piecewise_capital_income_tax(assets: ContinuousState) -> FloatND: + """Piecewise-linear capital-income tax `T(a)` on the asset return. + + Selects the bracket `[a0, a1)` containing `assets` (left-closed, so a value on + a boundary uses the upper bracket) and returns `B + tau_a * (a - a0)`. The + bracket offsets `B` carry the level discontinuities, so `T` is discontinuous + at the bracket boundaries β€” the non-monotone budget the FUES upper envelope is + built for. There are three: `T` jumps up at a=3.87 (+0.10) and a=15 (+0.15), + and drops down by about 0.14 at a=6.97, where the subsidy bracket `[6.97, + 8.36)` resets the offset to 0.05 below the preceding bracket's level. + """ + lower = jnp.asarray(TAX_BRACKET_LOWER) + offset = jnp.asarray(TAX_BRACKET_OFFSET) + rate = jnp.asarray(TAX_BRACKET_RATE) + index = jnp.clip( + jnp.searchsorted(lower, assets, side="right") - 1, 0, lower.size - 1 + ) + return offset[index] + rate[index] * (assets - lower[index]) + + +@categorical(ordered=False) +class DiscreteHousingRegimeId: + """Lifecycle regimes: the working life and the terminal bequest regime.""" + + working: ScalarInt + dead: ScalarInt + + +@categorical(ordered=True) +class Housing: + """Held / chosen housing: renting (stock 0) plus the owned stock levels.""" + + rent: ScalarInt + own_h1: ScalarInt + own_h2: ScalarInt + own_h3: ScalarInt + own_h4: ScalarInt + own_h5: ScalarInt + + +def _owned_stock_array() -> FloatND: + """Map each `Housing` code to its owned housing stock (`rent` holds 0).""" + return jnp.asarray((0.0, *OWNED_STOCK_LEVELS)) + + +def housing_stock(housing: DiscreteState) -> FloatND: + """Held housing stock `H` of the current discrete housing state.""" + return _owned_stock_array()[housing] + + +def chosen_stock(housing_choice: DiscreteAction) -> FloatND: + """Next-period owned housing stock `H'` implied by the choice (0 if renting).""" + return _owned_stock_array()[housing_choice] + + +def is_renting(housing_choice: DiscreteAction) -> BoolND: + """Whether the choice is to rent (own nothing next period).""" + return housing_choice == Housing.rent + + +def serviced_housing(housing_choice: DiscreteAction, rental_service: float) -> FloatND: + """Housing services `h` consumed this period. + + Owning serves the chosen stock `H'`; renting serves the rental service level + `S` (the smallest service on the owned-stock grid β€” see Q8). + """ + return jnp.where( + is_renting(housing_choice), rental_service, chosen_stock(housing_choice) + ) + + +def utility( + consumption: ContinuousAction, + serviced_housing: FloatND, + alpha: float, + kappa: float, + iota: float, +) -> FloatND: + """Cobb-Douglas log utility over consumption and housing services (eq. 30). + + `u(c, h) = alpha * log(c) + (1 - alpha) * log(kappa * (h + iota))`, with `h` + the serviced housing (the chosen stock when owning, the rental service when + renting). Reads only the continuous consumption action and the discrete + housing choice β€” never the financial-asset Euler state β€” so the DC-EGM + envelope condition on the Euler state holds. + """ + return alpha * jnp.log(consumption) + (1.0 - alpha) * jnp.log( + kappa * (serviced_housing + iota) + ) + + +def wage_income(wage: ContinuousState) -> FloatND: + """Map the Markov log-wage node to its labor-income level `y = exp(wage)`. + + A discretised AR1 wage is a pylcm stochastic *process* state, annotated as a + continuous state (its node value is the log wage); income is its exponential. + """ + return jnp.exp(wage) + + +def housing_flow( + housing: DiscreteState, + housing_choice: DiscreteAction, + tau: float, + rental_price: float, + rental_service: float, +) -> FloatND: + """Net liquid housing flow in the budget (no tax). + + - owner (`H' > 0`): `d_adj * H - d_adj * (1 + tau) * H'`, where `d_adj` is 1 + when the stock changes and 0 otherwise β€” selling the held house and buying + the new one at the adjustment cost `tau * H'`, + - renter (`H' = 0`): `H - rental_price * rental_service` β€” selling the entire + held house and renting services at the rental price. + + Reads only the held housing state and the discrete choice β€” never the + consumption action or the financial-asset Euler state β€” so it enters the + DC-EGM resources as a constant per discrete-choice cell. + """ + held = housing_stock(housing) + chosen = chosen_stock(housing_choice) + adjusts = housing != housing_choice + adjustment_indicator = jnp.where(adjusts, 1.0, 0.0) + owner_flow = ( + adjustment_indicator * held - adjustment_indicator * (1.0 + tau) * chosen + ) + renter_flow = held - rental_price * rental_service + return jnp.where(is_renting(housing_choice), renter_flow, owner_flow) + + +def resources( + assets: ContinuousState, + wage_income: FloatND, + housing_flow: FloatND, + interest_rate: float, + capital_income_tax: float, +) -> FloatND: + """Financial resources consumption is paid out of, given the discrete choice. + + `(1 + r) a - T(a) + y + housing_flow`, with the capital-income tax hook + `T(a) = capital_income_tax * a` (Q7; the no-tax variant fixes the rate to 0). + Strictly increasing in the Euler state `assets` for `capital_income_tax < + 1 + r`; independent of the continuous consumption action. + """ + tax = capital_income_tax * assets + return (1.0 + interest_rate) * assets - tax + wage_income + housing_flow + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + """Post-decision financial balance `a' = resources - c`.""" + return resources - consumption + + +def next_assets(savings: FloatND) -> ContinuousState: + """Euler-state law: next financial assets equal post-decision savings.""" + return savings + + +def next_housing(housing_choice: DiscreteAction) -> DiscreteState: + """Discrete housing law: next housing equals the chosen code. + + The discrete action `housing_choice` and the discrete state `housing` share + the `Housing` alphabet, so this deterministic transition maps codes 1:1. + """ + return housing_choice + + +def inverse_marginal_utility(marginal_continuation: FloatND, alpha: float) -> FloatND: + """Invert the consumption marginal utility `u'(c) = alpha / c`. + + `c = alpha / mc`. The housing-service term is additively separable from + consumption, so it drops out of the inner consumption inversion; the + consumption weight `alpha` scales the marginal utility, so it enters the + inverse. + """ + return alpha / marginal_continuation + + +def next_assets_brute( + assets: ContinuousState, + wage_income: FloatND, + housing_flow: FloatND, + consumption: ContinuousAction, + interest_rate: float, + capital_income_tax: float, +) -> ContinuousState: + """Brute-force financial-asset law: resources minus consumption. + + Reads the continuous consumption action directly rather than splitting + resources and a post-decision `savings`, so the grid-searched twin needs no + Euler machinery. Equal to `resources - consumption` of the DC-EGM regime. + """ + tax = capital_income_tax * assets + return ( + (1.0 + interest_rate) * assets - tax + wage_income + housing_flow - consumption + ) + + +def borrowing_constraint( + assets: ContinuousState, + wage_income: FloatND, + housing_flow: FloatND, + consumption: ContinuousAction, + interest_rate: float, + capital_income_tax: float, +) -> BoolND: + """Keep post-decision financial assets non-negative (`a' >= 0`). + + Mirrors the DC-EGM savings grid, whose floor is the no-borrowing limit: + feasible consumption leaves `next_assets_brute >= 0`. + """ + return ( + next_assets_brute( + assets=assets, + wage_income=wage_income, + housing_flow=housing_flow, + consumption=consumption, + interest_rate=interest_rate, + capital_income_tax=capital_income_tax, + ) + >= 0.0 + ) + + +def resources_taxed( + assets: ContinuousState, + wage_income: FloatND, + housing_flow: FloatND, + interest_rate: float, +) -> FloatND: + """Resources with the piecewise capital-income tax (Table 5 with-tax variant). + + `(1 + r) a - T(a) + y + housing_flow`, with `T(a)` the piecewise-linear + schedule. The tax's level jumps make resources non-monotone in `assets`, so + the inner consumption Euler inversion meets the kinked/jumped budget the FUES + upper envelope resolves. + """ + return ( + (1.0 + interest_rate) * assets + - piecewise_capital_income_tax(assets) + + wage_income + + housing_flow + ) + + +def next_assets_brute_taxed( + assets: ContinuousState, + wage_income: FloatND, + housing_flow: FloatND, + consumption: ContinuousAction, + interest_rate: float, +) -> ContinuousState: + """Brute-force financial-asset law with the piecewise capital-income tax.""" + return ( + (1.0 + interest_rate) * assets + - piecewise_capital_income_tax(assets) + + wage_income + + housing_flow + - consumption + ) + + +def borrowing_constraint_taxed( + assets: ContinuousState, + wage_income: FloatND, + housing_flow: FloatND, + consumption: ContinuousAction, + interest_rate: float, +) -> BoolND: + """Keep post-decision assets non-negative under the piecewise tax.""" + return ( + next_assets_brute_taxed( + assets=assets, + wage_income=wage_income, + housing_flow=housing_flow, + consumption=consumption, + interest_rate=interest_rate, + ) + >= 0.0 + ) + + +def bequest( + assets: ContinuousState, + housing: DiscreteState, + interest_rate: float, + theta: float, +) -> FloatND: + """Terminal bequest `theta * ((1 + r) a + H)` (Table 7 uses `theta = 0.5`). + + Reads only the carried financial-asset and discrete housing states. + """ + estate = (1.0 + interest_rate) * assets + housing_stock(housing) + return theta * estate + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + """Transition to `dead` at the final living age, else stay working.""" + return jnp.where( + age >= final_age_alive, + DiscreteHousingRegimeId.dead, + DiscreteHousingRegimeId.working, + ) + + +def build_model( + *, + variant: Literal["dcegm", "brute"] = "dcegm", + n_assets: int, + n_wage_nodes: int = N_WAGE_NODES, + n_periods: int | None = None, + asset_max: float = 40.0, + n_consumption: int = 30, + upper_envelope: Literal["fues", "mss", "ltm", "rfc"] = "fues", + use_taxes: bool = False, +) -> Model: + """Build the DS App.3 discrete-housing model. + + Args: + variant: `"dcegm"` builds the DC-EGM regime (financial assets the Euler + state, consumption inverted, the housing choice a discrete action); + `"brute"` builds the grid-search (VFI) twin solving the same + economics with no Euler machinery β€” the Table 4 methods. + use_taxes: When `True`, the budget carries the piecewise-linear + capital-income tax `T(a)` (the with-tax Table 5 variant, FUES vs VFI + only); when `False`, the no-tax Table 4/7 budget. + n_assets: Number of financial-asset grid points; also the number of + clustered exogenous savings nodes the DC-EGM solver scans. + n_wage_nodes: Number of Markov wage discretisation nodes (the paper uses + 7; kept small for construction). + n_periods: Optional shortened horizon for construction tests; `None` + uses the paper's `T = 20`. + asset_max: Upper bound of the financial-asset grid `a in [0, asset_max]`. + n_consumption: Number of consumption-grid points (brute search and the + DC-EGM simulation draw). + upper_envelope: DC-EGM upper-envelope backend (`"fues"`, `"mss"`, `"ltm"`, + `"rfc"`); the Table 4 methods are FUES/MSS/LTM. + + Returns: + The two-regime (working, dead) discrete-housing model. + """ + n_periods = N_PERIODS if n_periods is None else n_periods + ages = AgeGrid(start=START_AGE, stop=START_AGE + n_periods - 1, step="Y") + final_age_alive = int(ages.exact_values[-1]) + + assets_grid = LinSpacedGrid(start=0.0, stop=asset_max, n_points=n_assets) + consumption_grid = LinSpacedGrid(start=0.05, stop=asset_max, n_points=n_consumption) + # Cubically clustered savings nodes toward the no-borrowing limit, where the + # value function curves hardest; the floor (0) encodes `consumption <= + # resources`. + savings_grid = IrregSpacedGrid( + points=tuple(asset_max * (i / (n_assets - 1)) ** 3 for i in range(n_assets)) + ) + wage_process = RouwenhorstAR1Process(n_points=n_wage_nodes) + + resources_func = resources_taxed if use_taxes else resources + asset_law_brute = next_assets_brute_taxed if use_taxes else next_assets_brute + borrowing = borrowing_constraint_taxed if use_taxes else borrowing_constraint + + dead = UserRegime( + transition=None, + active=lambda age, fa=final_age_alive: age >= fa, + states={"assets": assets_grid, "housing": DiscreteGrid(Housing)}, + functions={"utility": bequest}, + ) + + if variant == "brute": + working = UserRegime( + transition=next_regime, + active=lambda age, fa=final_age_alive: age < fa, + states={ + "assets": assets_grid, + "housing": DiscreteGrid(Housing), + "wage": wage_process, + }, + state_transitions={ + "assets": asset_law_brute, + "housing": next_housing, + }, + actions={ + "consumption": consumption_grid, + "housing_choice": DiscreteGrid(Housing), + }, + constraints={"borrowing_constraint": borrowing}, + functions={ + "utility": utility, + "serviced_housing": serviced_housing, + "wage_income": wage_income, + "housing_flow": housing_flow, + }, + solver=GridSearch(), + ) + return Model( + regimes={"working": working, "dead": dead}, + ages=ages, + regime_id_class=DiscreteHousingRegimeId, + ) + + working = UserRegime( + transition=next_regime, + active=lambda age, fa=final_age_alive: age < fa, + states={ + "assets": assets_grid, + "housing": DiscreteGrid(Housing), + "wage": wage_process, + }, + state_transitions={ + "assets": next_assets, + "housing": next_housing, + }, + actions={ + "consumption": consumption_grid, + "housing_choice": DiscreteGrid(Housing), + }, + functions={ + "utility": utility, + "serviced_housing": serviced_housing, + "wage_income": wage_income, + "housing_flow": housing_flow, + "resources": resources_func, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=DCEGM( + continuous_state="assets", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=savings_grid, + upper_envelope=upper_envelope, + n_constrained_points=32, + ), + ) + return Model( + regimes={"working": working, "dead": dead}, + ages=ages, + regime_id_class=DiscreteHousingRegimeId, + ) + + +def build_params( + *, + variant: Literal["dcegm", "brute"] = "dcegm", + tau: float = 0.07, + theta: float = 0.5, + discount_factor: float = 0.93, + interest_rate: float = 0.06, + alpha: float = 0.77, + kappa: float = 0.075, + iota: float = 0.01, + rental_price: float = 0.1, + rental_service: float = 1.0, + capital_income_tax: float = 0.0, + use_taxes: bool = False, + rho_w: float = 0.977, + sigma_w: float = 0.063, + mu_w: float = 0.0, + n_periods: int | None = None, +) -> dict: + """Calibration parameters for the DS App.3 discrete-housing model (no tax). + + Args: + variant: `"dcegm"` threads the budget params under the resources and + inverse-marginal-utility functions; `"brute"` threads them under the + grid-search financial-asset law and the borrowing constraint, since + the brute twin reads consumption directly (no resources/savings + split). Must match the `variant` passed to `build_model`. + tau: Proportional housing-adjustment cost (Table 4/7 default `0.07`). + theta: Terminal bequest weight (Table 7 uses `0.5`). + discount_factor: `beta`. + interest_rate: Net financial return `r`. + alpha: Consumption weight in the Cobb-Douglas log utility. + kappa: Housing-service scale. + iota: Housing-service shifter (`log(kappa * (h + iota))`). + rental_price: Rental price `P_r` of housing services. + rental_service: Rental service level `S` the renter consumes (the + smallest service on the owned-stock grid β€” see Q8). + capital_income_tax: Capital-income tax rate; the Table 5 hook (Q7). The + no-tax variant fixes it to `0.0`. + rho_w: Markov wage persistence `rho`. + sigma_w: Markov wage innovation std (the paper's `sigma_eps = 0.063` + transitory term; the persistent `sigma_eta = 0.024` enters a fuller + two-component wage not modelled in this single-process build β€” Q9). + mu_w: Markov wage drift. + n_periods: Optional shortened horizon matching `build_model`; `None` uses + `T = 20`. + + Returns: + The nested parameter template keyed by regime then function. The + adjustment cost lives under the housing-flow function and the + capital-income tax hook under the budget function; the wage-process + params nest under the `wage` state of the working regime. + """ + n_periods = N_PERIODS if n_periods is None else n_periods + # The final period is the terminal bequest regime, so the last living age is + # the second-to-last age. + final_age_alive = n_periods - 2 + # The with-tax budget functions read the piecewise schedule directly, so they + # take no `capital_income_tax` rate; the no-tax budget keeps the linear hook. + budget_params = ( + {"interest_rate": interest_rate} + if use_taxes + else {"interest_rate": interest_rate, "capital_income_tax": capital_income_tax} + ) + shared_working = { + "utility": {"alpha": alpha, "kappa": kappa, "iota": iota}, + "serviced_housing": {"rental_service": rental_service}, + "housing_flow": { + "tau": tau, + "rental_price": rental_price, + "rental_service": rental_service, + }, + "wage": {"rho": rho_w, "sigma": sigma_w, "mu": mu_w}, + } + if variant == "brute": + # The brute law reads consumption directly: the budget params live on + # the financial-asset law `next_assets` and the borrowing constraint. + working = { + **shared_working, + "next_assets": dict(budget_params), + "borrowing_constraint": dict(budget_params), + } + else: + working = { + **shared_working, + RESOURCES_FUNCTION_NAME: dict(budget_params), + "inverse_marginal_utility": {"alpha": alpha}, + } + return { + "discount_factor": discount_factor, + "final_age_alive": final_age_alive, + "working": working, + "dead": { + "utility": {"interest_rate": interest_rate, "theta": theta}, + }, + } diff --git a/tests/test_models/ds_housing_keeper.py b/tests/test_models/ds_housing_keeper.py new file mode 100644 index 000000000..017b93033 --- /dev/null +++ b/tests/test_models/ds_housing_keeper.py @@ -0,0 +1,353 @@ +"""Dobrescu-Shanker housing model, keeper (no-house-trade) regime. + +The Dobrescu-Shanker housing model has liquid assets, a durable housing stock, +a proportional house-trade cost, a Markov income state, and a discrete +adjust/keep choice. The *keeper* branch (`obj_noadj`) holds the house fixed +(`h' = h`) and chooses only next-period liquid assets, so it is a plain 1-D +DC-EGM problem: + +- the Euler state is liquid assets `liquid_assets` (`a`), +- the continuous action is non-durable consumption `consumption` (`c`), +- housing `housing` (`h`) is a **passive** continuous state: its transition is + the identity (`fixed_transition("housing")`), decision-independent, so it + rides along as a value-function grid axis exactly like any other passive + state, +- income `income` (`z`) is a two-state Markov chain entering resources through + its value. + +The defining feature versus the existing passive-state fixtures is that +utility *reads the passive housing state directly* through the service flow +`alpha * log(housing)`. The DC-EGM envelope condition forbids utility reading +the **Euler** state, but reading a passive state is allowed β€” so the keeper is +expressible today. + +A brute-force (GridSearch) twin solves the same economics without the +Euler/passive split: housing becomes a regular fixed continuous state, +consumption a grid-searched action, and the liquid-asset law of motion +`(1 + r) * liquid_assets + (1 + r_H) * housing * (1 - delta) + income - +consumption` reads consumption directly. A borrowing constraint keeps +post-decision liquid assets at or above the borrowing limit, the floor of the +DC-EGM savings grid. The two solutions are the oracle pair: as the brute +consumption grid refines the two value functions converge. + +Calibration mirrors the InverseDCDP `housing.py` defaults (`r=0.024`, +`r_H=0.10`, `beta=0.945`, `alpha=0.66`, `delta=0.10`, `gamma_c=1.458`, +`b=0.01`, income states `(0.1, 1.0)` with the Markov matrix +`((0.09, 0.91), (0.06, 0.94))`). Grids are kept tiny β€” this is a feasibility +probe, not an accuracy benchmark. +""" + +from typing import Literal + +import jax.numpy as jnp + +from lcm import ( + AgeGrid, + DiscreteGrid, + IrregSpacedGrid, + LinSpacedGrid, + MarkovTransition, + Model, + categorical, +) +from lcm.regime import Regime as UserRegime +from lcm.solvers import DCEGM +from lcm.transition import fixed_transition +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + DiscreteState, + FloatND, + ScalarInt, +) +from lcm_examples.iskhakov_et_al_2017 import dead + +# Number of model periods; the last one is spent in the terminal `dead` regime. +N_PERIODS = 4 + +# Income state values (`z_vals` in InverseDCDP `housing.py`); indexed by the +# `Income` code. +INCOME_LOW = 0.1 +INCOME_HIGH = 1.0 + +# Income Markov matrix `Pi`: row `i` is the next-period distribution +# `[P(low), P(high)]` given current income node `i`. +INCOME_PI = ((0.09, 0.91), (0.06, 0.94)) + +# Tiny probe grids. The liquid-asset grid is the Euler state; the savings grid +# starts at the borrowing limit `b` and is cubically clustered toward it where +# the value function curves hardest, reaching above the Euler grid's top so the +# endogenous grid is not edge-clamped. +BORROWING_LIMIT = 0.01 +LIQUID_ASSETS_GRID = LinSpacedGrid(start=BORROWING_LIMIT, stop=20.0, n_points=12) +HOUSING_GRID = LinSpacedGrid(start=0.5, stop=4.0, n_points=4) +CONSUMPTION_GRID = LinSpacedGrid(start=0.05, stop=25.0, n_points=60) +SAVINGS_GRID = IrregSpacedGrid( + points=tuple(BORROWING_LIMIT + 25.0 * (i / 79) ** 3 for i in range(80)) +) + + +@categorical(ordered=False) +class HousingKeeperRegimeId: + keeper: ScalarInt + dead: ScalarInt + + +@categorical(ordered=True) +class Income: + low: ScalarInt + high: ScalarInt + + +def income_value(income: DiscreteState) -> FloatND: + """Map the discrete income node to its labor-income value `z`.""" + return jnp.where(income == Income.low, INCOME_LOW, INCOME_HIGH) + + +def utility( + consumption: ContinuousAction, + housing: ContinuousState, + gamma_c: float, + alpha: float, +) -> FloatND: + """CRRA consumption utility plus a log housing-service flow. + + Reads the continuous action `consumption` and the *passive* continuous + state `housing`; it does not read the Euler state `liquid_assets`. + """ + return (consumption ** (1.0 - gamma_c) - 1.0) / (1.0 - gamma_c) + alpha * jnp.log( + housing + ) + + +def resources( + liquid_assets: ContinuousState, + housing: ContinuousState, + income_value: FloatND, + r: float, + r_H: float, + delta: float, +) -> FloatND: + """Beginning-of-period cash-on-hand of the keeper. + + `(1 + r) * liquid_assets + (1 + r_H) * housing * (1 - delta) + income`. The + house is not retraded, so it carries no transaction cost. Strictly + increasing in `liquid_assets`; independent of the continuous action. + """ + return ( + (1.0 + r) * liquid_assets + (1.0 + r_H) * housing * (1.0 - delta) + income_value + ) + + +def savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + """Post-decision liquid balance `a' = resources - consumption`.""" + return resources - consumption + + +def next_liquid_assets(savings: FloatND) -> ContinuousState: + """Euler-state law: next liquid assets equal post-decision savings.""" + return savings + + +def inverse_marginal_utility(marginal_continuation: FloatND, gamma_c: float) -> FloatND: + """Invert the consumption marginal utility: `c = (mc) ** (-1 / gamma_c)`.""" + return marginal_continuation ** (-1.0 / gamma_c) + + +def next_liquid_assets_brute( + liquid_assets: ContinuousState, + housing: ContinuousState, + income_value: FloatND, + consumption: ContinuousAction, + r: float, + r_H: float, + delta: float, +) -> ContinuousState: + """Brute-force liquid-asset law: cash-on-hand minus consumption. + + Reads the continuous action `consumption` directly rather than splitting + resources and a post-decision `savings`, so the grid-searched twin needs + no Euler machinery. Equal to `resources - consumption` of the DC-EGM + keeper. + """ + return ( + (1.0 + r) * liquid_assets + + (1.0 + r_H) * housing * (1.0 - delta) + + income_value + - consumption + ) + + +def borrowing_constraint( + liquid_assets: ContinuousState, + housing: ContinuousState, + income_value: FloatND, + consumption: ContinuousAction, + r: float, + r_H: float, + delta: float, + borrowing_limit: float, +) -> BoolND: + """Keep post-decision liquid assets at or above the borrowing limit. + + Mirrors the DC-EGM savings grid, whose floor is the borrowing limit `b`: + feasible consumption leaves `next_liquid_assets_brute >= borrowing_limit`. + """ + return ( + next_liquid_assets_brute( + liquid_assets=liquid_assets, + housing=housing, + income_value=income_value, + consumption=consumption, + r=r, + r_H=r_H, + delta=delta, + ) + >= borrowing_limit + ) + + +def income_transition(income: DiscreteState) -> FloatND: + """Markov income law: the row of `Pi` for the current income node. + + Returns the next-period distribution `[P(low), P(high)]`, aligned to the + `Income` codes (`low=0`, `high=1`). + """ + pi = jnp.asarray(INCOME_PI) + return pi[income] + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + """Transition to `dead` at the final living age, else stay a keeper.""" + return jnp.where( + age >= final_age_alive, + HousingKeeperRegimeId.dead, + HousingKeeperRegimeId.keeper, + ) + + +DCEGM_SOLVER = DCEGM( + continuous_state="liquid_assets", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=SAVINGS_GRID, + n_constrained_points=32, +) + + +def _ages() -> AgeGrid: + return AgeGrid(start=40, stop=40 + (N_PERIODS - 1) * 10, step="10Y") + + +def _active(age: int) -> bool: + return age < 40 + (N_PERIODS - 1) * 10 + + +def build_working_regime(variant: Literal["dcegm", "brute"] = "dcegm") -> UserRegime: + """Build the keeper working regime (the user-facing `Regime`). + + - `"dcegm"`: liquid assets are the Euler state, consumption the continuous + action, housing a passive (identity-transition) continuous state read by + utility, and income a two-state Markov discrete state entering resources. + - `"brute"`: the same economics solved by grid search β€” housing is a + regular fixed continuous state, the liquid-asset law of motion reads + consumption directly, and a borrowing constraint keeps post-decision + liquid assets at or above the borrowing limit. No Euler/passive split. + """ + if variant == "brute": + return UserRegime( + transition=next_regime, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={ + "liquid_assets": LIQUID_ASSETS_GRID, + "housing": HOUSING_GRID, + "income": DiscreteGrid(Income), + }, + state_transitions={ + "liquid_assets": next_liquid_assets_brute, + "housing": fixed_transition("housing"), + "income": MarkovTransition(income_transition), + }, + constraints={"borrowing_constraint": borrowing_constraint}, + functions={ + "utility": utility, + "income_value": income_value, + }, + ) + return UserRegime( + transition=next_regime, + active=_active, + actions={"consumption": CONSUMPTION_GRID}, + states={ + "liquid_assets": LIQUID_ASSETS_GRID, + "housing": HOUSING_GRID, + "income": DiscreteGrid(Income), + }, + state_transitions={ + "liquid_assets": next_liquid_assets, + "housing": fixed_transition("housing"), + "income": MarkovTransition(income_transition), + }, + functions={ + "utility": utility, + "resources": resources, + "savings": savings, + "inverse_marginal_utility": inverse_marginal_utility, + "income_value": income_value, + }, + solver=DCEGM_SOLVER, + ) + + +def build_model(variant: Literal["dcegm", "brute"] = "dcegm") -> Model: + """Build the keeper model (the GPU solve target). + + A single non-terminal keeper regime β€” DC-EGM or its brute-force twin β€” plus + the shared terminal `dead` regime. + """ + return Model( + regimes={"keeper": build_working_regime(variant), "dead": dead}, + ages=_ages(), + regime_id_class=HousingKeeperRegimeId, + ) + + +def build_params(variant: Literal["dcegm", "brute"] = "dcegm") -> dict: + """Calibration parameters for the keeper model. + + Mirrors the InverseDCDP `housing.py` defaults for the preference and + return parameters; the income process enters resources through + `income_value`, so it needs no params here. The brute twin carries the + same `r`, `r_H`, `delta` on its liquid-asset law and borrowing constraint, + plus the borrowing limit that floors post-decision liquid assets. + """ + if variant == "brute": + # Transition params nest under the state-keyed name `next_`, not + # the Python function name, so the liquid-asset law's `r`, `r_H`, + # `delta` live under `next_liquid_assets`. + return { + "discount_factor": 0.945, + "final_age_alive": 40 + (N_PERIODS - 2) * 10, + "keeper": { + "utility": {"gamma_c": 1.458, "alpha": 0.66}, + "next_liquid_assets": {"r": 0.024, "r_H": 0.10, "delta": 0.10}, + "borrowing_constraint": { + "r": 0.024, + "r_H": 0.10, + "delta": 0.10, + "borrowing_limit": BORROWING_LIMIT, + }, + }, + } + return { + "discount_factor": 0.945, + "final_age_alive": 40 + (N_PERIODS - 2) * 10, + "keeper": { + "utility": {"gamma_c": 1.458, "alpha": 0.66}, + "resources": {"r": 0.024, "r_H": 0.10, "delta": 0.10}, + "inverse_marginal_utility": {"gamma_c": 1.458}, + }, + } diff --git a/tests/test_models/negm_bequest_toy.py b/tests/test_models/negm_bequest_toy.py new file mode 100644 index 000000000..8f47e7646 --- /dev/null +++ b/tests/test_models/negm_bequest_toy.py @@ -0,0 +1,254 @@ +"""Two-asset NEGM toy whose terminal bequest reads *both* continuous states. + +A kinked two-asset toy (liquid `wealth`, durable `illiquid`) solved by the +nested EGM, whose terminal `dead` regime values a bequest over **both** the +liquid and the durable stock β€” `bequest(wealth, illiquid)`. The durable is the +NEGM outer (passive) margin, so the terminal carry the EGM parent reads has the +Euler state `wealth` plus the passive continuous state `illiquid` as a leading +axis β€” the Dobrescu-Shanker housing pattern (the bequest reads the resale value +of the house alongside liquid wealth). + +`utility` reads only the *held* durable, so the inner consumption margin is +isolated from the outer one β€” the single new feature exercised is the +two-continuous-state terminal carry. `build_negm_model` solves it by the nested +EGM; `build_brute_model` is the economically identical grid-search twin used as +the parity oracle. +""" + +import jax.numpy as jnp + +from lcm import ( + DCEGM, + NEGM, + AgeGrid, + LinSpacedGrid, + Model, + Regime, + categorical, +) +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + FloatND, + ScalarInt, +) + +N_X = 8 +N_Z = 8 +N_C = 15 +N_AZ = 12 +N_PERIODS = 3 + +ILLIQUID_FLOW = 0.05 # iota: service flow from the held durable +WITHDRAWAL_PENALTY = 0.10 # kappa on a withdrawal (next_illiquid < illiquid) +SAVE_RATE = 0.03 # single interest rate on liquid savings +RISK_AVERSION = 2.0 +LABOUR_INCOME = 5.0 +BEQUEST_WEIGHT = 0.8 # weight on the terminal bequest +SAVINGS_FLOOR = -5.0 # borrowing limit on the inner post-decision a^X + + +@categorical(ordered=False) +class RegimeId: + alive: ScalarInt + dead: ScalarInt + + +def credited(illiquid: ContinuousState, next_illiquid: ContinuousState) -> FloatND: + """Net liquid cost of moving the durable to `next_illiquid` (`s'`).""" + investment = next_illiquid - illiquid + return jnp.where( + investment < 0.0, + (1.0 - WITHDRAWAL_PENALTY) * investment, + investment, + ) + + +def resources( + wealth: ContinuousState, illiquid: ContinuousState, next_illiquid: ContinuousState +) -> FloatND: + """Liquid resources consumption is paid out of, given the fixed outer node.""" + return ( + wealth + + LABOUR_INCOME + - credited(illiquid=illiquid, next_illiquid=next_illiquid) + ) + + +def liquid_savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + """Inner post-decision liquid balance `a^X = R_inner - c`.""" + return resources - consumption + + +def next_wealth(liquid_savings: FloatND) -> ContinuousState: + """Inner Euler law (single interest rate).""" + return (1.0 + SAVE_RATE) * liquid_savings + + +def durable_transition( + illiquid: ContinuousState, illiquid_investment: ContinuousAction +) -> ContinuousState: + """Durable law of motion `s' = Z + Iz`, the `illiquid` state transition.""" + return illiquid + illiquid_investment + + +def keep_illiquid(illiquid: ContinuousState) -> FloatND: + """The no-adjustment candidate `s' = Z` (the withdrawal-penalty kink).""" + return illiquid + + +def utility(consumption: ContinuousAction, illiquid: ContinuousState) -> FloatND: + """CRRA over `consumption + iota * illiquid` β€” reads only the held durable.""" + flow = consumption + ILLIQUID_FLOW * illiquid + return flow ** (1.0 - RISK_AVERSION) / (1.0 - RISK_AVERSION) + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + """Inverse of `u'(c) = (c + iota*Z)^{-gamma}` in the inner consumption slot.""" + return marginal_continuation ** (-1.0 / RISK_AVERSION) + + +def bequest(wealth: ContinuousState, illiquid: ContinuousState) -> FloatND: + """Terminal value over both liquid wealth and the durable resale value.""" + total = wealth + illiquid + 1.0 + return BEQUEST_WEIGHT * total ** (1.0 - RISK_AVERSION) / (1.0 - RISK_AVERSION) + + +def feasible(liquid_savings: FloatND) -> BoolND: + """The inner post-decision balance must stay at or above the borrowing floor.""" + return liquid_savings >= SAVINGS_FLOOR + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where(age >= final_age_alive, RegimeId.dead, RegimeId.alive) + + +WEALTH_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=N_X) +ILLIQUID_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=N_Z) +CONSUMPTION_GRID = LinSpacedGrid(start=0.1, stop=20.0, n_points=N_C) +CONSUMPTION_GRID_BRUTE = LinSpacedGrid(start=0.1, stop=20.0, n_points=300) +ILLIQUID_INVESTMENT_GRID = LinSpacedGrid(start=-8.0, stop=8.0, n_points=N_AZ) +OUTER_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=N_AZ) +SAVINGS_GRID = LinSpacedGrid(start=SAVINGS_FLOOR, stop=35.0, n_points=80) + +FINAL_AGE_ALIVE = 20 + (N_PERIODS - 2) * 5 + +NEGM_SOLVER = NEGM( + inner=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="liquid_savings", + savings_grid=SAVINGS_GRID, + ), + outer_action="illiquid_investment", + outer_post_decision="next_illiquid", + outer_grid=OUTER_GRID, + outer_no_adjustment_candidate="keep_illiquid", +) + + +def _build_dead_regime() -> Regime: + """The terminal regime: a bequest over both continuous states.""" + return Regime( + transition=None, + active=lambda age, n=FINAL_AGE_ALIVE: age > n, + states={"wealth": WEALTH_GRID, "illiquid": ILLIQUID_GRID}, + functions={"utility": bequest}, + ) + + +def build_negm_model() -> Model: + """Build the bequest toy solved by the nested EGM.""" + alive = Regime( + active=lambda age, n=FINAL_AGE_ALIVE: age <= n, + states={"wealth": WEALTH_GRID, "illiquid": ILLIQUID_GRID}, + state_transitions={"wealth": next_wealth, "illiquid": durable_transition}, + actions={ + "consumption": CONSUMPTION_GRID, + "illiquid_investment": ILLIQUID_INVESTMENT_GRID, + }, + transition=next_regime, + functions={ + "utility": utility, + "resources": resources, + "liquid_savings": liquid_savings, + "keep_illiquid": keep_illiquid, + "credited": credited, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=NEGM_SOLVER, + ) + return Model( + regimes={"alive": alive, "dead": _build_dead_regime()}, + regime_id_class=RegimeId, + ages=AgeGrid(start=20, stop=20 + (N_PERIODS - 1) * 5, step="5Y"), + fixed_params={"final_age_alive": FINAL_AGE_ALIVE}, + ) + + +def next_wealth_brute( + wealth: ContinuousState, + illiquid: ContinuousState, + new_durable: ContinuousAction, + consumption: ContinuousAction, +) -> ContinuousState: + """Brute-twin liquid law of motion, in state + action terms.""" + investment = new_durable - illiquid + credited_move = jnp.where( + investment < 0.0, (1.0 - WITHDRAWAL_PENALTY) * investment, investment + ) + savings = wealth + LABOUR_INCOME - credited_move - consumption + return (1.0 + SAVE_RATE) * savings + + +def next_illiquid_brute(new_durable: ContinuousAction) -> ContinuousState: + """Brute-twin durable law of motion: the chosen new stock is next period's.""" + return new_durable + + +def utility_brute(consumption: ContinuousAction, illiquid: ContinuousState) -> FloatND: + """Brute-twin flow utility β€” reads the held durable, as the NEGM twin does.""" + flow = consumption + ILLIQUID_FLOW * illiquid + return flow ** (1.0 - RISK_AVERSION) / (1.0 - RISK_AVERSION) + + +def feasible_brute( + wealth: ContinuousState, + illiquid: ContinuousState, + new_durable: ContinuousAction, + consumption: ContinuousAction, +) -> BoolND: + """The implied post-decision balance must stay at or above the borrowing floor.""" + investment = new_durable - illiquid + credited_move = jnp.where( + investment < 0.0, (1.0 - WITHDRAWAL_PENALTY) * investment, investment + ) + savings = wealth + LABOUR_INCOME - credited_move - consumption + return savings >= SAVINGS_FLOOR + + +def build_brute_model() -> Model: + """Build the economically identical grid-search twin (the parity oracle).""" + alive = Regime( + active=lambda age, n=FINAL_AGE_ALIVE: age <= n, + states={"wealth": WEALTH_GRID, "illiquid": ILLIQUID_GRID}, + state_transitions={ + "wealth": next_wealth_brute, + "illiquid": next_illiquid_brute, + }, + actions={ + "consumption": CONSUMPTION_GRID_BRUTE, + "new_durable": OUTER_GRID, + }, + transition=next_regime, + functions={"utility": utility_brute}, + constraints={"feasible": feasible_brute}, + ) + return Model( + regimes={"alive": alive, "dead": _build_dead_regime()}, + regime_id_class=RegimeId, + ages=AgeGrid(start=20, stop=20 + (N_PERIODS - 1) * 5, step="5Y"), + fixed_params={"final_age_alive": FINAL_AGE_ALIVE}, + ) diff --git a/tests/test_models/negm_kinked_toy.py b/tests/test_models/negm_kinked_toy.py new file mode 100644 index 000000000..d17fcc15d --- /dev/null +++ b/tests/test_models/negm_kinked_toy.py @@ -0,0 +1,227 @@ +"""Kinked two-asset toy as an `NEGM` model (the G1 parity target). + +The smallest model carrying the Laibson frictions a NEGM solve must reproduce: +a liquid margin `wealth` (X) the Euler equation inverts on, plus an +illiquid/durable margin `illiquid` (Z) with a withdrawal penalty (a kink at +`illiquid_investment = 0`) and a `Z >= 0` floor. The brute oracle for the +equivalent spec is committed in `negm_phase0/kinked_toy_oracle.py` (Β§2 of +`negm_phase0/negm-phase0-findings.md`). + +The NEGM reparametrisation fixes the outer post-decision `next_illiquid` +(`s' = Z + Iz`) per outer-grid node; the inner consumption-savings problem is +then a standard 1-D DC-EGM solve on `wealth`: + +- inner Euler state `wealth`, inner action `consumption`, inner post-decision + `liquid_savings` (`a^X`), inner resources `resources`, +- the outer margin enters the inner `resources` as a constant (the credited + withdrawal/deposit) and indexes the child durable state `illiquid`, +- the credit-card rate kink lives in the inner Euler law `next_wealth`. + +The outer search runs over `next_illiquid` with the no-adjustment candidate +`s' = illiquid` (`Iz = 0`, the withdrawal-penalty kink). +""" + +from dataclasses import replace + +import jax.numpy as jnp + +from lcm import ( + DCEGM, + NEGM, + AgeGrid, + LinSpacedGrid, + Model, + Regime, + categorical, +) +from lcm.typing import ( + ContinuousAction, + ContinuousState, + FloatND, + ScalarInt, +) + +N_X = 12 +N_Z = 12 +N_C = 25 +N_AZ = 25 +N_PERIODS = 4 + +ILLIQUID_FLOW = 0.05 # iota +WITHDRAWAL_PENALTY = 0.10 # kappa on a withdrawal (next_illiquid < illiquid) +BORROW_RATE = 0.12 # credit-card rate on liquid_savings < 0 +SAVE_RATE = 0.03 # rate on liquid_savings >= 0 +RISK_AVERSION = 2.0 +LABOUR_INCOME = 5.0 + + +@categorical(ordered=False) +class RegimeId: + alive: ScalarInt + dead: ScalarInt + + +def credited(illiquid: ContinuousState, next_illiquid: ContinuousState) -> FloatND: + """Net liquid cost of moving the durable to `next_illiquid` (`s'`). + + A deposit (`s' > Z`) costs its face value; a withdrawal (`s' < Z`) returns + only `(1 - kappa)` of the amount pulled out β€” the penalty kink at `s' = Z`. + """ + investment = next_illiquid - illiquid + return jnp.where( + investment < 0.0, + (1.0 - WITHDRAWAL_PENALTY) * investment, + investment, + ) + + +def resources( + wealth: ContinuousState, illiquid: ContinuousState, next_illiquid: ContinuousState +) -> FloatND: + """Liquid resources consumption is paid out of, given the fixed outer node. + + `next_illiquid` (`s'`) is bound to one outer-grid node, so the credited + durable move is a constant in the inner Euler inversion. + """ + return ( + wealth + + LABOUR_INCOME + - credited(illiquid=illiquid, next_illiquid=next_illiquid) + ) + + +def liquid_savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + """Inner post-decision liquid balance `a^X = R_inner - c`.""" + return resources - consumption + + +def next_wealth(liquid_savings: FloatND) -> ContinuousState: + """Inner Euler law with the credit-card rate kink at `a^X = 0`.""" + rate = jnp.where(liquid_savings < 0.0, BORROW_RATE, SAVE_RATE) + return (1.0 + rate) * liquid_savings + + +def durable_transition( + illiquid: ContinuousState, illiquid_investment: ContinuousAction +) -> ContinuousState: + """Durable law of motion `s' = Z + Iz`, the `illiquid` state transition. + + Used as the `illiquid` state transition, so pylcm refers to its output as + the auto-generated `next_illiquid`; the NEGM solver names that value as its + `outer_post_decision`, which the inner `resources` reads as a kernel-bound + constant per outer-grid node. + """ + return illiquid + illiquid_investment + + +def keep_illiquid(illiquid: ContinuousState) -> FloatND: + """The no-adjustment candidate `s' = Z` (the withdrawal-penalty kink).""" + return illiquid + + +def utility(consumption: ContinuousAction, illiquid: ContinuousState) -> FloatND: + """CRRA over `consumption + iota * illiquid` β€” additively separable in `s'`.""" + flow = consumption + ILLIQUID_FLOW * illiquid + return flow ** (1.0 - RISK_AVERSION) / (1.0 - RISK_AVERSION) + + +def inverse_marginal_utility( + marginal_continuation: FloatND, illiquid: ContinuousState +) -> FloatND: + """Inverse of `u'(c) = (c + iota*Z)^{-gamma}` in the inner consumption slot. + + Inverting $u'(c) = (c + \\iota Z)^{-\\gamma} = m$ for the consumption action + gives $c = m^{-1/\\gamma} - \\iota Z$: the `iota * Z` shift the durable state + contributes to the utility flow is a constant offset that must be subtracted + when recovering `c` from the marginal continuation. The kernel binds the + durable state `illiquid` (`Z`) from the combo pool, so the offset is exact at + every durable node rather than a quantity the kernel re-adds downstream. + + The unconstrained inverse can fall below zero where the marginal continuation + is large (low savings): that is the borrowing-constrained region the kernel's + constrained-candidate segment and upper envelope represent, so the raw + inverse is returned without a positivity clamp. + """ + return marginal_continuation ** (-1.0 / RISK_AVERSION) - ILLIQUID_FLOW * illiquid + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where(age >= final_age_alive, RegimeId.dead, RegimeId.alive) + + +WEALTH_GRID = LinSpacedGrid(start=-6.0, stop=30.0, n_points=N_X) +ILLIQUID_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=N_Z) +CONSUMPTION_GRID = LinSpacedGrid(start=0.1, stop=20.0, n_points=N_C) +ILLIQUID_INVESTMENT_GRID = LinSpacedGrid(start=-8.0, stop=8.0, n_points=N_AZ) +OUTER_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=N_AZ) +SAVINGS_GRID = LinSpacedGrid(start=-5.0, stop=35.0, n_points=80) + + +NEGM_SOLVER = NEGM( + inner=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="liquid_savings", + savings_grid=SAVINGS_GRID, + ), + outer_action="illiquid_investment", + outer_post_decision="next_illiquid", + outer_grid=OUTER_GRID, + outer_no_adjustment_candidate="keep_illiquid", +) + + +def build_alive_regime(*, outer_batch_size: int = 0) -> Regime: + """The non-terminal NEGM regime (two assets, two continuous actions). + + `outer_batch_size` chunks the NEGM outer durable search (`0` = all at once). + """ + final_age_alive = 20 + (N_PERIODS - 2) * 5 + solver = replace(NEGM_SOLVER, outer_batch_size=outer_batch_size) + return Regime( + active=lambda age, n=final_age_alive: age <= n, + states={"wealth": WEALTH_GRID, "illiquid": ILLIQUID_GRID}, + state_transitions={"wealth": next_wealth, "illiquid": durable_transition}, + actions={ + "consumption": CONSUMPTION_GRID, + "illiquid_investment": ILLIQUID_INVESTMENT_GRID, + }, + transition=next_regime, + functions={ + "utility": utility, + "resources": resources, + "liquid_savings": liquid_savings, + "keep_illiquid": keep_illiquid, + "credited": credited, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=solver, + ) + + +def build_dead_regime() -> Regime: + """The terminal regime.""" + final_age_alive = 20 + (N_PERIODS - 2) * 5 + return Regime( + transition=None, + active=lambda age, n=final_age_alive: age > n, + functions={"utility": lambda: 0.0}, + ) + + +def build_model(*, outer_batch_size: int = 0) -> Model: + """Build the kinked-toy NEGM model (the G1 parity target). + + `outer_batch_size` chunks the NEGM outer durable search (`0` = all at once). + """ + final_age_alive = 20 + (N_PERIODS - 2) * 5 + return Model( + regimes={ + "alive": build_alive_regime(outer_batch_size=outer_batch_size), + "dead": build_dead_regime(), + }, + regime_id_class=RegimeId, + ages=AgeGrid(start=20, stop=20 + (N_PERIODS - 1) * 5, step="5Y"), + fixed_params={"final_age_alive": final_age_alive}, + ) diff --git a/tests/test_models/negm_serviceflow_toy.py b/tests/test_models/negm_serviceflow_toy.py new file mode 100644 index 000000000..9a056e528 --- /dev/null +++ b/tests/test_models/negm_serviceflow_toy.py @@ -0,0 +1,299 @@ +"""Service-flow kinked two-asset toy: `utility` reads the *new* durable stock. + +A variant of the kinked two-asset toy (`negm_kinked_toy.py`) in which the +durable yields its service flow from the **newly chosen** stock `s'` +(`next_illiquid`) rather than the held stock `Z` (`illiquid`): + +```{math} +u(c, s') = \\frac{c^{1-\\gamma}}{1-\\gamma} + \\iota\\, s' +``` + +The service term is additively separable from consumption, so the inner +consumption Euler equation is the plain CRRA inversion (no offset). The novelty +is that `utility` reads `next_illiquid`, the auto-named output of the `illiquid` +state transition and the NEGM `outer_post_decision`. The NEGM solver binds that +value per outer-grid node (the adjuster) or holds it at the durable stock (the +keeper), so the inner kernel evaluates the service flow from the chosen house β€” +the Dobrescu-Shanker housing pattern (`utility` reads `next_housing`). + +`build_negm_model` solves it by the nested EGM; `build_brute_model` is the +economically identical grid-search twin used as the parity oracle. Brute +restricts the continuous policy to the action grid, so its value is a lower +bound: NEGM weakly dominates and approaches it as the brute grids refine. +""" + +import jax.numpy as jnp + +from lcm import ( + DCEGM, + NEGM, + AgeGrid, + LinSpacedGrid, + Model, + Regime, + categorical, +) +from lcm.typing import ( + BoolND, + ContinuousAction, + ContinuousState, + FloatND, + ScalarInt, +) + +N_X = 8 +N_Z = 8 +N_C = 15 +N_AZ = 12 +N_PERIODS = 3 + +ILLIQUID_FLOW = 0.05 # iota: service flow per unit of the new durable stock s' +WITHDRAWAL_PENALTY = 0.10 # kappa on a withdrawal (next_illiquid < illiquid) +BORROW_RATE = 0.12 # credit-card rate on liquid_savings < 0 +SAVE_RATE = 0.03 # rate on liquid_savings >= 0 +RISK_AVERSION = 2.0 +LABOUR_INCOME = 5.0 +SAVINGS_FLOOR = -5.0 # borrowing limit on the inner post-decision a^X + + +@categorical(ordered=False) +class RegimeId: + alive: ScalarInt + dead: ScalarInt + + +def credited(illiquid: ContinuousState, next_illiquid: ContinuousState) -> FloatND: + """Net liquid cost of moving the durable to `next_illiquid` (`s'`). + + A deposit (`s' > Z`) costs its face value; a withdrawal (`s' < Z`) returns + only `(1 - kappa)` of the amount pulled out β€” the penalty kink at `s' = Z`. + """ + investment = next_illiquid - illiquid + return jnp.where( + investment < 0.0, + (1.0 - WITHDRAWAL_PENALTY) * investment, + investment, + ) + + +def resources( + wealth: ContinuousState, illiquid: ContinuousState, next_illiquid: ContinuousState +) -> FloatND: + """Liquid resources consumption is paid out of, given the fixed outer node.""" + return ( + wealth + + LABOUR_INCOME + - credited(illiquid=illiquid, next_illiquid=next_illiquid) + ) + + +def liquid_savings(resources: FloatND, consumption: ContinuousAction) -> FloatND: + """Inner post-decision liquid balance `a^X = R_inner - c`.""" + return resources - consumption + + +def next_wealth(liquid_savings: FloatND) -> ContinuousState: + """Inner Euler law with the credit-card rate kink at `a^X = 0`.""" + rate = jnp.where(liquid_savings < 0.0, BORROW_RATE, SAVE_RATE) + return (1.0 + rate) * liquid_savings + + +def durable_transition( + illiquid: ContinuousState, illiquid_investment: ContinuousAction +) -> ContinuousState: + """Durable law of motion `s' = Z + Iz`, the `illiquid` state transition. + + pylcm names its output `next_illiquid`; the NEGM solver names that value as + its `outer_post_decision`, read by the inner `resources` and `utility` as a + kernel-bound constant per outer-grid node. + """ + return illiquid + illiquid_investment + + +def keep_illiquid(illiquid: ContinuousState) -> FloatND: + """The no-adjustment candidate `s' = Z` (the withdrawal-penalty kink).""" + return illiquid + + +def serviced_durable(next_illiquid: ContinuousState) -> FloatND: + """Service flow from the newly chosen durable stock `s'`. + + Routing the outer post-decision through its own function (rather than into + `utility`'s signature directly) keeps `utility` additively separable in the + inner and outer margins β€” the Dobrescu-Shanker housing structure, where + `utility` reads a `serviced_housing(next_housing)` flow. + """ + return ILLIQUID_FLOW * next_illiquid + + +def utility(consumption: ContinuousAction, serviced_durable: FloatND) -> FloatND: + """CRRA over consumption plus an additive service flow from the new durable. + + The service term is constant given the bound outer node, so it leaves the + inner consumption Euler inversion a plain CRRA inverse. + """ + consumption_utility = consumption ** (1.0 - RISK_AVERSION) / (1.0 - RISK_AVERSION) + return consumption_utility + serviced_durable + + +def inverse_marginal_utility(marginal_continuation: FloatND) -> FloatND: + """Inverse of `u'(c) = c^{-gamma}` β€” the additive service term drops out.""" + return marginal_continuation ** (-1.0 / RISK_AVERSION) + + +def credited_brute(illiquid: ContinuousState, new_durable: ContinuousAction) -> FloatND: + """Brute-twin credited durable move to the chosen new stock `s'`.""" + investment = new_durable - illiquid + return jnp.where( + investment < 0.0, + (1.0 - WITHDRAWAL_PENALTY) * investment, + investment, + ) + + +def resources_brute( + wealth: ContinuousState, illiquid: ContinuousState, new_durable: ContinuousAction +) -> FloatND: + """Brute-twin liquid resources, in state + action terms (no next-state read).""" + return ( + wealth + + LABOUR_INCOME + - credited_brute(illiquid=illiquid, new_durable=new_durable) + ) + + +def next_wealth_brute( + wealth: ContinuousState, + illiquid: ContinuousState, + new_durable: ContinuousAction, + consumption: ContinuousAction, +) -> ContinuousState: + """Brute-twin liquid law of motion with the credit-card rate kink.""" + savings = ( + resources_brute(wealth=wealth, illiquid=illiquid, new_durable=new_durable) + - consumption + ) + rate = jnp.where(savings < 0.0, BORROW_RATE, SAVE_RATE) + return (1.0 + rate) * savings + + +def next_illiquid_brute(new_durable: ContinuousAction) -> ContinuousState: + """Brute-twin durable law of motion: the chosen new stock is next period's.""" + return new_durable + + +def serviced_durable_brute(new_durable: ContinuousAction) -> FloatND: + """Brute-twin service flow from the chosen durable stock `s'`.""" + return ILLIQUID_FLOW * new_durable + + +def feasible( + wealth: ContinuousState, + illiquid: ContinuousState, + new_durable: ContinuousAction, + consumption: ContinuousAction, +) -> BoolND: + """The implied post-decision balance must stay at or above the borrowing floor.""" + savings = ( + resources_brute(wealth=wealth, illiquid=illiquid, new_durable=new_durable) + - consumption + ) + return savings >= SAVINGS_FLOOR + + +def next_regime(age: int, final_age_alive: float) -> ScalarInt: + return jnp.where(age >= final_age_alive, RegimeId.dead, RegimeId.alive) + + +WEALTH_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=N_X) +ILLIQUID_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=N_Z) +CONSUMPTION_GRID = LinSpacedGrid(start=0.1, stop=20.0, n_points=N_C) +CONSUMPTION_GRID_BRUTE = LinSpacedGrid(start=0.1, stop=20.0, n_points=300) +ILLIQUID_INVESTMENT_GRID = LinSpacedGrid(start=-8.0, stop=8.0, n_points=N_AZ) +OUTER_GRID = LinSpacedGrid(start=0.0, stop=30.0, n_points=N_AZ) +SAVINGS_GRID = LinSpacedGrid(start=SAVINGS_FLOOR, stop=35.0, n_points=80) + + +NEGM_SOLVER = NEGM( + inner=DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="liquid_savings", + savings_grid=SAVINGS_GRID, + ), + outer_action="illiquid_investment", + outer_post_decision="next_illiquid", + outer_grid=OUTER_GRID, + outer_no_adjustment_candidate="keep_illiquid", +) + + +FINAL_AGE_ALIVE = 20 + (N_PERIODS - 2) * 5 + + +def _build_dead_regime() -> Regime: + """The terminal regime (shared by both twins).""" + return Regime( + transition=None, + active=lambda age, n=FINAL_AGE_ALIVE: age > n, + functions={"utility": lambda: 0.0}, + ) + + +def build_negm_model() -> Model: + """Build the service-flow toy solved by the nested EGM.""" + alive = Regime( + active=lambda age, n=FINAL_AGE_ALIVE: age <= n, + states={"wealth": WEALTH_GRID, "illiquid": ILLIQUID_GRID}, + state_transitions={"wealth": next_wealth, "illiquid": durable_transition}, + actions={ + "consumption": CONSUMPTION_GRID, + "illiquid_investment": ILLIQUID_INVESTMENT_GRID, + }, + transition=next_regime, + functions={ + "utility": utility, + "serviced_durable": serviced_durable, + "resources": resources, + "liquid_savings": liquid_savings, + "keep_illiquid": keep_illiquid, + "credited": credited, + "inverse_marginal_utility": inverse_marginal_utility, + }, + solver=NEGM_SOLVER, + ) + return Model( + regimes={"alive": alive, "dead": _build_dead_regime()}, + regime_id_class=RegimeId, + ages=AgeGrid(start=20, stop=20 + (N_PERIODS - 1) * 5, step="5Y"), + fixed_params={"final_age_alive": FINAL_AGE_ALIVE}, + ) + + +def build_brute_model() -> Model: + """Build the economically identical grid-search twin (the parity oracle).""" + alive = Regime( + active=lambda age, n=FINAL_AGE_ALIVE: age <= n, + states={"wealth": WEALTH_GRID, "illiquid": ILLIQUID_GRID}, + state_transitions={ + "wealth": next_wealth_brute, + "illiquid": next_illiquid_brute, + }, + actions={ + "consumption": CONSUMPTION_GRID_BRUTE, + "new_durable": OUTER_GRID, + }, + transition=next_regime, + functions={ + "utility": utility, + "serviced_durable": serviced_durable_brute, + }, + constraints={"feasible": feasible}, + ) + return Model( + regimes={"alive": alive, "dead": _build_dead_regime()}, + regime_id_class=RegimeId, + ages=AgeGrid(start=20, stop=20 + (N_PERIODS - 1) * 5, step="5Y"), + fixed_params={"final_age_alive": FINAL_AGE_ALIVE}, + ) diff --git a/tests/test_models/test_ds2024_housing_builds.py b/tests/test_models/test_ds2024_housing_builds.py new file mode 100644 index 000000000..2c1c07400 --- /dev/null +++ b/tests/test_models/test_ds2024_housing_builds.py @@ -0,0 +1,166 @@ +"""The DS-2024 housing NEGM model builds, solves, and matches its VFI oracles. + +The DS-2024 housing model (`tests.test_models.ds2024_housing`) is the NEGM column +of the RFC-vs-NEGM comparison β€” a faithful reproduction of the source economics +(CRRA-plus-log utility, Markov income, proportional house-trade cost). The keeper +holds the house at the depreciated level `H' = h(1 - delta)` for free. + +Two oracles validate it on the liquid-housing interior: + +- at `delta = 0` the free-keep level is `H' = h`, on the house grid, so the + grid-search brute twin solves the identical Bellman problem and the two value + functions agree up to grid resolution; +- at `delta = 0.10` the free-keep level is off the grid, so the brute twin cannot + represent it; a dense host VFI oracle that includes the free-keep candidate + explicitly (`tests.solution._ds2024_housing_vfi_oracle`) is the reference, and the + NEGM keeper's depreciated hold reproduces it up to grid resolution. +""" + +from typing import Literal + +import numpy as np +import pytest + +from tests.solution._ds2024_housing_vfi_oracle import solve_ds2024_housing_vfi +from tests.test_models.ds2024_housing import build_model, build_params + +N_GRID = 10 +N_CONSUMPTION = 200 +N_PERIODS = 4 + +# Pooled-interior thresholds. The value function is O(1)-O(10) on the interior; +# the brute consumption grid undershoots and the DC-EGM carries a savings-grid +# interpolation error, so the two agree in bulk up to grid resolution rather than +# exactly at every cell. +MEAN_TOL = 0.20 +CELL_TOL = 0.60 +MIN_FRACTION_WITHIN = 0.95 + + +@pytest.mark.parametrize("variant", ["negm", "brute"]) +def test_ds2024_housing_builds_and_solves(variant: Literal["negm", "brute"]): + """Both DS-2024 housing variants construct and solve with a finite interior.""" + model = build_model( + variant=variant, + n_grid=6, + n_periods=3, + n_consumption=40, + ) + solution = model.solve( + params=build_params(variant=variant, delta=0.0), log_level="off" + ) + + assert sorted(solution) == [0, 1, 2] + alive_periods = [p for p in solution if "alive" in solution[p]] + assert alive_periods + for period in alive_periods: + interior = np.asarray(solution[period]["alive"])[..., 2:-1, 2:-1] + assert np.isfinite(interior).all() + + +def test_ds2024_housing_negm_matches_brute_on_interior(): + """The NEGM solve agrees with its grid-search twin on the liquid-housing interior. + + At zero depreciation the keeper holds the house, so the NEGM nest and the + brute grid search solve the identical Bellman problem. The pooled interior + value difference is sub-unit in the mean and the overwhelming majority of + cells fall within the cell tolerance β€” the NEGM model is correct up to grid + resolution. + """ + brute = build_model( + variant="brute", + n_grid=N_GRID, + n_periods=N_PERIODS, + n_consumption=N_CONSUMPTION, + ).solve(params=build_params(variant="brute", delta=0.0), log_level="off") + negm = build_model( + variant="negm", + n_grid=N_GRID, + n_periods=N_PERIODS, + n_consumption=N_CONSUMPTION, + ).solve(params=build_params(variant="negm", delta=0.0), log_level="off") + + differences = [] + for period in sorted(brute): + if "alive" not in brute[period]: + continue + brute_V = np.asarray(brute[period]["alive"]) + negm_V = np.asarray(negm[period]["alive"]) + assert brute_V.shape == negm_V.shape + interior = (Ellipsis, slice(3, N_GRID - 2), slice(3, N_GRID - 2)) + finite = np.isfinite(brute_V[interior]) & np.isfinite(negm_V[interior]) + differences.append(np.abs(brute_V[interior] - negm_V[interior])[finite]) + difference = np.concatenate(differences) + + assert float(difference.mean()) < MEAN_TOL + assert float((difference <= CELL_TOL).mean()) >= MIN_FRACTION_WITHIN + + +def _pooled_interior_difference(pylcm_solution, oracle): + """Pooled absolute interior `V` difference between a pylcm solve and the oracle. + + The oracle stores the alive value as `(income, house, liquid)` and the terminal + as `(house, liquid)`, the same axis order as the pylcm solve, so the interior + slice and finite mask apply directly. + """ + differences = [] + for period in sorted(oracle): + if period not in pylcm_solution or "alive" not in pylcm_solution[period]: + continue + pylcm_V = np.asarray(pylcm_solution[period]["alive"]) + oracle_V = np.asarray(oracle[period]) + assert pylcm_V.shape == oracle_V.shape + interior = (Ellipsis, slice(3, N_GRID - 2), slice(3, N_GRID - 2)) + finite = np.isfinite(pylcm_V[interior]) & np.isfinite(oracle_V[interior]) + differences.append(np.abs(pylcm_V[interior] - oracle_V[interior])[finite]) + return np.concatenate(differences) + + +def test_ds2024_housing_vfi_oracle_matches_brute_at_zero_delta(): + """The host VFI oracle reproduces the brute solve at zero depreciation. + + The oracle is a from-scratch NumPy value-function iteration; at `delta = 0` it + solves the same economics as the model's grid-search twin, so the two agree on + the liquid-housing interior up to grid resolution. This pins the oracle's + economics before it is used as the `delta > 0` reference. + """ + brute = build_model( + variant="brute", + n_grid=N_GRID, + n_periods=N_PERIODS, + n_consumption=N_CONSUMPTION, + ).solve(params=build_params(variant="brute", delta=0.0), log_level="off") + oracle = solve_ds2024_housing_vfi( + n_grid=N_GRID, n_periods=N_PERIODS, n_consumption=400, delta=0.0 + ) + + difference = _pooled_interior_difference(brute, oracle) + + assert float(difference.mean()) < MEAN_TOL + assert float((difference <= CELL_TOL).mean()) >= MIN_FRACTION_WITHIN + + +def test_ds2024_housing_negm_keeper_depreciation_matches_vfi_oracle(): + """At `delta = 0.10` the NEGM keeper's depreciated hold matches the VFI oracle. + + The keeper holds the house at the depreciated level `H' = h(1 - delta)`, which + lands off the house grid. The dense VFI oracle includes that free-keep candidate + explicitly, so it is the valid reference where the on-grid brute twin is not. The + NEGM solve reproduces it on the liquid-housing interior up to grid resolution β€” + the keeper depreciation is faithful. + """ + negm = build_model( + variant="negm", + n_grid=N_GRID, + n_periods=N_PERIODS, + n_consumption=N_CONSUMPTION, + delta=0.10, + ).solve(params=build_params(variant="negm", delta=0.10), log_level="off") + oracle = solve_ds2024_housing_vfi( + n_grid=N_GRID, n_periods=N_PERIODS, n_consumption=400, delta=0.10 + ) + + difference = _pooled_interior_difference(negm, oracle) + + assert float(difference.mean()) < MEAN_TOL + assert float((difference <= CELL_TOL).mean()) >= MIN_FRACTION_WITHIN diff --git a/tests/test_models/test_ds2024_housing_fues_builds.py b/tests/test_models/test_ds2024_housing_fues_builds.py new file mode 100644 index 000000000..2419355fc --- /dev/null +++ b/tests/test_models/test_ds2024_housing_fues_builds.py @@ -0,0 +1,85 @@ +"""The DS-2024 discrete-housing model builds, solves, and matches its twins. + +The DS-2024 housing RFC column is the discrete-choice DC-EGM with the 1-D +upper-envelope backend nested over the housing grid (the source refines the +keeper's endogenous liquid grid per housing column with the rooftop cut). These +tests check it constructs and solves, that the RFC backend reproduces FUES (the +two 1-D envelopes agree), and that the solve bulk-agrees with its grid-search +(VFI) twin on the liquid interior up to grid resolution. +""" + +from typing import Literal + +import numpy as np +import pytest + +from _lcm.typing import PeriodToRegimeToVArr +from tests.test_models.ds2024_housing_fues import build_model, build_params + +N_GRID = 10 +N_HOUSING = 5 +N_CONSUMPTION = 300 +N_PERIODS = 4 +INTERIOR = (Ellipsis, slice(3, N_GRID - 2)) + + +@pytest.mark.parametrize("variant", ["dcegm", "brute"]) +def test_ds2024_housing_fues_builds_and_solves(variant: Literal["dcegm", "brute"]): + """Both discrete-housing variants construct and solve with a finite interior.""" + model = build_model( + variant=variant, + n_grid=8, + n_housing=5, + n_consumption=80, + n_periods=3, + upper_envelope="rfc", + ) + solution = model.solve( + params=build_params(variant=variant, delta=0.0), log_level="off" + ) + assert sorted(solution) == [0, 1, 2] + alive_periods = [p for p in solution if "alive" in solution[p]] + assert alive_periods + for period in alive_periods: + assert np.isfinite(np.asarray(solution[period]["alive"])[..., 2:-1]).all() + + +def _solve( + variant: Literal["dcegm", "brute"], upper_envelope: str +) -> PeriodToRegimeToVArr: + model = build_model( + variant=variant, + n_grid=N_GRID, + n_housing=N_HOUSING, + n_consumption=N_CONSUMPTION, + n_periods=N_PERIODS, + upper_envelope=upper_envelope, # ty: ignore[invalid-argument-type] + ) + return model.solve(params=build_params(variant=variant, delta=0.0), log_level="off") + + +@pytest.mark.parametrize("upper_envelope", ["rfc", "fues"]) +def test_ds2024_housing_dcegm_matches_brute_in_bulk(upper_envelope: str): + """Each discrete-housing DC-EGM backend bulk-agrees with its grid-search twin. + + On the liquid interior the mean value difference is sub-unit and the large + majority of cells fall within the cell tolerance β€” the discrete-housing + DC-EGM (with the RFC or FUES upper-envelope backend) is correct up to grid + resolution; the remaining cells sit in the durable-rich corner where DC-EGM + carries a savings-grid interpolation error. Validating each backend against + the oracle is the robust check; the two backends' policies can diverge by the + envelope-internal tie-breaking on the durable-corner cells. + """ + brute = _solve("brute", "rfc") + dcegm = _solve("dcegm", upper_envelope) + differences = [] + for period in sorted(brute): + if "alive" not in brute[period]: + continue + brute_V = np.asarray(brute[period]["alive"])[INTERIOR] + dcegm_V = np.asarray(dcegm[period]["alive"])[INTERIOR] + finite = np.isfinite(brute_V) & np.isfinite(dcegm_V) + differences.append(np.abs(brute_V - dcegm_V)[finite]) + difference = np.concatenate(differences) + assert float(difference.mean()) < 0.5 + assert float((difference <= 1.5).mean()) >= 0.85 diff --git a/tests/test_models/test_ds_app2_housing_builds.py b/tests/test_models/test_ds_app2_housing_builds.py new file mode 100644 index 000000000..e20964b81 --- /dev/null +++ b/tests/test_models/test_ds_app2_housing_builds.py @@ -0,0 +1,225 @@ +"""Construction spec for the DS-2026 Application 2 housing NEGM model. + +The Dobrescu-Shanker (2026) Β§2.2 housing model maps onto pylcm's nested-EGM +solver: a liquid consumption-savings margin the Euler equation inverts on +(the inner DC-EGM), plus an illiquid housing margin with a proportional +transaction cost the inner Euler cannot invert (the outer durable search). The +discrete adjust/keep choice `d ∈ {0, 1}` is the NEGM dual-core contract β€” the +solver builds a keeper kernel (housing held, `H' = H`) and an adjuster kernel +(housing swept over the outer grid, paying `(1 + Ο„)Β·H'`) from one regime, so it +is *not* a user-declared discrete action. + +These checks build the model at a tiny grid and assert structure only β€” no +`.solve()` runs here. The 2-D-continuous + AR1-process NEGM solve OOMs a small +box, so the solve/accuracy/timing sweep is a separate gpu-01 job. The ground +truth for the NEGM mapping is `validate_negm_regimes`, which the `Model` +constructor runs at build: if the housing margin were Euler-coupled in a way +NEGM forbids, building the model would raise `ModelInitializationError`. A model +that builds therefore *is* an accepted NEGM model. +""" + +import jax.numpy as jnp +import numpy as np +import pytest + +from lcm import NEGM, LinSpacedGrid, Model +from lcm.exceptions import ModelInitializationError +from lcm.solvers import DCEGM +from tests.conftest import X64_ENABLED +from tests.test_models import ds_app2_housing + +# The closed-form cost comparisons are float-eps-limited at the active precision. +_COST_ATOL = 1e-12 if X64_ENABLED else 1e-5 +_COST_RTOL = 1e-12 if X64_ENABLED else 1e-5 + + +def test_model_builds_at_small_grid_without_solving(): + """The DS App.2 housing model builds at a tiny grid as a valid `Model`. + + Building the model runs the full regime-processing pipeline, including the + NEGM contract validator. A returned `Model` instance means the housing + margin fits the NEGM nesting contract β€” no solve is attempted. + """ + model = ds_app2_housing.build_model(n_grid=5, n_periods=4) + assert isinstance(model, Model) + + +def test_negm_contract_accepts_the_housing_regimes(): + """`validate_negm_regimes` accepts the working and retired NEGM regimes. + + The `Model` constructor runs `validate_negm_regimes` on the user regimes; a + successful build is the validator's acceptance. The working and retired + regimes both carry an `NEGM` solver whose inner is a `DCEGM` on liquid + assets, so both are checked. + """ + model = ds_app2_housing.build_model(n_grid=5, n_periods=4) + working_solver = model.user_regimes["working"].solver + retired_solver = model.user_regimes["retired"].solver + assert isinstance(working_solver, NEGM) + assert isinstance(retired_solver, NEGM) + assert isinstance(working_solver.inner, DCEGM) + assert working_solver.inner.continuous_state == "liquid" + assert working_solver.outer_action == "housing_investment" + + +def test_expected_regimes_states_and_actions_are_present(): + """The model carries the working/retired/dead regimes with their variables. + + - liquid assets `liquid` and housing `housing` are the two continuous + states of both non-terminal regimes, + - the AR1 wage `wage` is a process state of the working regime (it drops at + retirement), + - consumption and the housing-investment outer action are the continuous + actions of the working regime, + - the terminal `dead` regime carries the two continuous states the bequest + reads. + """ + model = ds_app2_housing.build_model(n_grid=5, n_periods=4) + assert set(model.regime_names_to_ids) == {"working", "retired", "dead"} + + working = model.user_regimes["working"] + assert {"liquid", "housing", "wage"} <= set(working.states) + assert {"consumption", "housing_investment"} <= set(working.actions) + + retired = model.user_regimes["retired"] + assert {"liquid", "housing"} <= set(retired.states) + assert "wage" not in retired.states + + dead = model.user_regimes["dead"] + assert dead.transition is None + assert {"liquid", "housing"} <= set(dead.states) + + +def test_keeper_and_adjuster_are_solver_internal_not_user_actions(): + """The adjust/keep choice is the NEGM dual core, not a discrete action. + + NEGM builds the keeper (`H' = H`) and adjuster (`H'` chosen, paying the + transaction cost) from a single regime, so the model declares no `adjust` + discrete action β€” the dual core lives inside the solver. + """ + model = ds_app2_housing.build_model(n_grid=5, n_periods=4) + working = model.user_regimes["working"] + assert "adjust" not in working.actions + solver = working.solver + assert isinstance(solver, NEGM) + assert solver.outer_no_adjustment_candidate is not None + + +def test_build_params_threads_the_transaction_cost(): + """`build_params(tau=...)` places the transaction cost on the housing law. + + The proportional transaction cost `Ο„` is the durable-margin friction; it + enters the housing-cost function, so the params template carries it where + that function reads it. + """ + params_low = ds_app2_housing.build_params(tau=0.05) + params_high = ds_app2_housing.build_params(tau=0.12) + cost_fn = ds_app2_housing.HOUSING_COST_FUNCTION_NAME + assert params_low["working"][cost_fn]["tau"] == 0.05 + assert params_high["working"][cost_fn]["tau"] == 0.12 + + +def test_keeping_the_house_is_free(): + """Holding the house (`H' = H`) incurs no transaction cost. + + The keep branch of the DS adjust/keep choice pays nothing β€” the NEGM keeper + kernel relies on this (its `credited(H, H) = 0` invariant), and the (S, s) + inaction band is defined by the region where keeping for free dominates. + """ + cost = ds_app2_housing.housing_cost( + housing=jnp.asarray(4.0), + next_housing=jnp.asarray(4.0), + return_housing=0.03, + tau=0.07, + ) + np.testing.assert_allclose(float(cost), 0.0, atol=_COST_ATOL) + + +@pytest.mark.parametrize("next_housing", [6.0, 2.5]) +def test_adjusting_pays_the_eq12_round_trip_cost(next_housing: float): + """Adjusting the house pays the DS eq. 12 round-trip cost. + + The adjuster sells the whole old house at `(1 + r_H)Β·H` and rebuys the whole + new house at `(1 + Ο„)Β·H'`, so the net liquid cost is + `(1 + Ο„)Β·H' - (1 + r_H)Β·H` for any `H' β‰  H` β€” both when trading up and when + trading down (the full stock turns over, not just the traded difference). + """ + housing, tau, return_housing = 4.0, 0.07, 0.03 + cost = ds_app2_housing.housing_cost( + housing=jnp.asarray(housing), + next_housing=jnp.asarray(next_housing), + return_housing=return_housing, + tau=tau, + ) + expected = (1.0 + tau) * next_housing - (1.0 + return_housing) * housing + np.testing.assert_allclose(float(cost), expected, rtol=_COST_RTOL) + + +def test_round_trip_cost_creates_an_inaction_wedge(): + """Any adjustment jumps the cost discretely above the free keep. + + The round-trip cost charges the proportional `Ο„` on the *whole* new stock, so + moving to a house infinitesimally larger than `H` costs about `τ·H` β€” a + discrete jump from the zero cost of keeping. That wedge is what produces the + DS (S, s) inaction band, unlike a net-investment cost (proportional to the + small traded amount), which vanishes near the no-trade point. + """ + housing, tau = 4.0, 0.07 + keep = ds_app2_housing.housing_cost( + housing=jnp.asarray(housing), + next_housing=jnp.asarray(housing), + return_housing=0.0, + tau=tau, + ) + nudge = ds_app2_housing.housing_cost( + housing=jnp.asarray(housing), + next_housing=jnp.asarray(housing + 1e-6), + return_housing=0.0, + tau=tau, + ) + assert float(keep) == 0.0 + # The wedge is ~τ·H, far above any net-investment cost on a 1e-6 trade. + assert float(nudge) > 0.9 * tau * housing + + +@pytest.mark.skip(reason="gpu-01 only: 2-D+AR1 NEGM solve OOMs locally") +def test_housing_model_solves_on_gpu(): + """The DS App.2 housing model solves to a finite value function. + + Marked GPU-only: the 2-D-continuous + AR1-process NEGM solve exhausts a + small box. Run on gpu-01. + """ + model = ds_app2_housing.build_model(n_grid=250) + params = ds_app2_housing.build_params(tau=0.05) + solution = model.solve(params=params, log_level="off") + assert solution[0]["working"] is not None + + +@pytest.mark.parametrize("liquid_batch_size", [0, 4]) +def test_liquid_batch_size_threads_to_the_liquid_grid(liquid_batch_size: int): + """`build_model(liquid_batch_size=k)` sets the liquid grid's `batch_size`. + + The liquid Euler grid carries the batch size that splays the per-asset-node + solve into chunks, bounding peak device memory at large `n_grid`. It is a + memory knob only β€” the GPU sweep confirms the solved value function is + unchanged across batch sizes. + """ + model = ds_app2_housing.build_model( + n_grid=5, n_periods=4, liquid_batch_size=liquid_batch_size + ) + liquid_grid = model.user_regimes["working"].states["liquid"] + assert isinstance(liquid_grid, LinSpacedGrid) + assert liquid_grid.batch_size == liquid_batch_size + + +def test_euler_coupled_housing_law_would_be_rejected(): + """An Euler-coupled housing law trips the NEGM contract, as a guardrail. + + If the outer housing post-decision fed the inner liquid Euler-state + transition, the inner Euler inversion would depend on the housing choice β€” + the DS pension coupling NEGM forbids. The validator must reject such a + variant with the 2-D-EGM pointer, confirming the accepted model is not + accepted by accident. + """ + with pytest.raises(ModelInitializationError, match="2-D EGM foundation"): + ds_app2_housing.build_model(n_grid=5, n_periods=4, _euler_couple_housing=True) diff --git a/tests/test_models/test_ds_app2_housing_fues_builds.py b/tests/test_models/test_ds_app2_housing_fues_builds.py new file mode 100644 index 000000000..0bcc6528e --- /dev/null +++ b/tests/test_models/test_ds_app2_housing_fues_builds.py @@ -0,0 +1,67 @@ +"""Construction spec for the DS-2026 App.2 housing EGM-FUES discrete-grid model. + +The EGM-FUES column of DS-2026 Table 3 solves the continuous-housing model by +1-D FUES nested over the housing grid (its Box 2). pylcm builds this as a +discrete-choice DC-EGM: the next-housing choice is discretised onto the housing +grid and solved as a discrete action, with the inner liquid-asset DC-EGM and the +discrete-choice upper envelope reproducing the EGM-FUES solve β€” the same shape as +Application 3's discrete-housing model with Application 2's separable-CES utility. + +These checks build the model at a tiny grid and assert structure only. +""" + +import pytest + +from lcm import DCEGM, DiscreteGrid, GridSearch, Model +from tests.test_models import ds_app2_housing_fues as fues + + +def test_dcegm_variant_builds_with_discrete_housing_choice(): + """The EGM-FUES variant builds with housing as a discrete action. + + The next-housing decision is a discrete `housing_choice` action over the + housing-level alphabet, and the inner solver is a DC-EGM on liquid assets β€” + the discrete-choice upper-envelope shape, not a continuous outer search. + """ + model = fues.build_model(variant="dcegm", n_grid=6, n_housing=5, n_periods=4) + assert isinstance(model, Model) + working = model.user_regimes["working"] + assert "housing_choice" in working.actions + assert "consumption" in working.actions + assert isinstance(working.solver, DCEGM) + assert working.solver.continuous_state == "liquid" + assert working.solver.continuous_action == "consumption" + + +def test_brute_variant_builds_with_grid_search(): + """The VFI twin builds with the same economics and a grid-search solver.""" + model = fues.build_model(variant="brute", n_grid=6, n_housing=5, n_periods=4) + working = model.user_regimes["working"] + assert isinstance(working.solver, GridSearch) + assert {"consumption", "housing_choice"} <= set(working.actions) + + +def test_housing_levels_scale_with_n_housing(): + """The discrete housing alphabet has exactly `n_housing` levels.""" + model = fues.build_model(variant="dcegm", n_grid=6, n_housing=7, n_periods=4) + housing_grid = model.user_regimes["working"].states["housing"] + assert isinstance(housing_grid, DiscreteGrid) + assert len(housing_grid.to_jax()) == 7 + + +def test_single_housing_level_is_rejected(): + """A single housing level (`n_housing=1`) is rejected with a clear error. + + The stock-level spacing divides by `n_housing - 1`, so a one-level alphabet + has no well-defined spacing; the builder must reject it rather than divide by + zero. + """ + with pytest.raises(ValueError, match="n_housing"): + fues.build_model(variant="dcegm", n_grid=6, n_housing=1, n_periods=4) + + +def test_three_regimes_with_terminal_dead(): + """The model carries working, retired, and a terminal dead regime.""" + model = fues.build_model(variant="dcegm", n_grid=6, n_housing=5, n_periods=4) + assert set(model.regime_names_to_ids) == {"working", "retired", "dead"} + assert model.user_regimes["dead"].transition is None diff --git a/tests/test_models/test_ds_app3_discrete_housing_builds.py b/tests/test_models/test_ds_app3_discrete_housing_builds.py new file mode 100644 index 000000000..b8dda7c16 --- /dev/null +++ b/tests/test_models/test_ds_app3_discrete_housing_builds.py @@ -0,0 +1,225 @@ +"""Construction spec for the DS-2026 Application 3 discrete-housing model (no tax). + +The Dobrescu-Shanker (2026) Section 2.3 discrete-housing model maps onto pylcm's +DC-EGM solver as a discrete-choice consumption-savings problem: + +- financial assets `assets` (`a >= 0`) are the continuous Euler state the Euler + equation inverts on, and `consumption` (`c`) is the continuous action; +- the housing stock `housing` (`H`) is a discrete state carried as a + value-function grid axis (`rent` plus the owned levels `own_h1..own_h5`); +- the own-vs-rent-and-level choice is a single discrete action `housing_choice` + over the same categories, exactly like Application 1's work/retire labor-supply + action β€” solved by the discrete-choice upper envelope (FUES/MSS/LTM) and by + grid search (VFI); +- the next-period housing state equals the chosen code (`next_housing = + housing_choice`), so the discrete action drives the discrete-state transition. + +These checks build the model at a tiny grid and assert structure only β€” no +`.solve()` runs here. The ground truth for the DC-EGM mapping is the regime +processing pipeline the `Model` constructor runs at build, including the DC-EGM +contract validator: a model that builds *is* an accepted DC-EGM model. A +grid-search (brute/VFI) twin builds the same economics as the Table 4 oracle +method, so both solver variants are constructed and validated. +""" + +from typing import Literal + +import numpy as np +import pytest + +from lcm import DiscreteGrid, Model +from lcm.solvers import DCEGM, GridSearch +from tests.test_models import ds_app3_discrete_housing + + +def test_dcegm_model_builds_at_small_grid_without_solving(): + """The DS App.3 discrete-housing model builds at a tiny grid as a `Model`. + + Building the model runs the full regime-processing pipeline, including the + DC-EGM contract validator. A returned `Model` instance means the model fits + the DC-EGM structure (one continuous Euler state, one continuous action, + resources/savings/inverse-marginal-utility declared) β€” no solve is attempted. + """ + model = ds_app3_discrete_housing.build_model( + variant="dcegm", n_assets=20, n_wage_nodes=3, n_periods=4 + ) + assert isinstance(model, Model) + + +def test_brute_model_builds_at_small_grid_without_solving(): + """The grid-search (VFI) twin of the DS App.3 model builds at a tiny grid. + + The brute variant solves the same economics by grid search over the + state-action product β€” the Table 4 VFI method β€” with no Euler machinery. A + returned `Model` means the discrete-housing structure is grid-search-solvable. + """ + model = ds_app3_discrete_housing.build_model( + variant="brute", n_assets=20, n_wage_nodes=3, n_periods=4 + ) + assert isinstance(model, Model) + + +def test_dcegm_regime_carries_the_dcegm_solver_on_assets(): + """The working regime is driven by DC-EGM with assets as the Euler state. + + The `Model` constructor runs the DC-EGM contract validator on the regime; a + successful build is its acceptance. The Euler state is the financial asset + `assets` and the continuous action is `consumption`. + """ + model = ds_app3_discrete_housing.build_model( + variant="dcegm", n_assets=20, n_wage_nodes=3, n_periods=4 + ) + solver = model.user_regimes["working"].solver + assert isinstance(solver, DCEGM) + assert solver.continuous_state == "assets" + assert solver.continuous_action == "consumption" + + +@pytest.mark.parametrize("upper_envelope", ["fues", "mss", "ltm"]) +def test_dcegm_accepts_each_table4_upper_envelope( + upper_envelope: Literal["fues", "mss", "ltm"], +): + """Each Table 4 upper-envelope backend builds the discrete-housing regime. + + Table 4 reports FUES, MSS, and LTM alongside VFI. All three are 1-D + upper-envelope refinements of the same DC-EGM discrete-choice solve, so the + model must build under each. + """ + model = ds_app3_discrete_housing.build_model( + variant="dcegm", + n_assets=20, + n_wage_nodes=3, + n_periods=4, + upper_envelope=upper_envelope, + ) + solver = model.user_regimes["working"].solver + assert isinstance(solver, DCEGM) + assert solver.upper_envelope == upper_envelope + + +def test_brute_regime_uses_grid_search(): + """The brute twin's working regime is solved by grid search (VFI).""" + model = ds_app3_discrete_housing.build_model( + variant="brute", n_assets=20, n_wage_nodes=3, n_periods=4 + ) + solver = model.user_regimes["working"].solver + assert isinstance(solver, GridSearch) + + +def test_housing_is_a_discrete_state_and_the_choice_a_discrete_action(): + """Housing is a discrete state; the own/rent choice is a discrete action. + + The crux of the App.3 mapping (Q6): the held housing stock `housing` is a + discrete state (a value-function carry axis), and the own-vs-rent-and-level + decision is a discrete action `housing_choice` over the same categories β€” the + DC-EGM discrete-choice envelope, not a continuous durable margin. The + next-period housing equals the chosen code, so the action drives the state. + """ + model = ds_app3_discrete_housing.build_model( + variant="dcegm", n_assets=20, n_wage_nodes=3, n_periods=4 + ) + working = model.user_regimes["working"] + + housing_grid = working.states["housing"] + choice_grid = working.actions["housing_choice"] + assert isinstance(housing_grid, DiscreteGrid) + assert isinstance(choice_grid, DiscreteGrid) + # The held stock and the choice share the same categorical alphabet so the + # deterministic `next_housing = housing_choice` transition maps codes 1:1. + housing_categories = set(housing_grid.categories) + choice_categories = set(choice_grid.categories) + assert housing_categories == choice_categories + assert "rent" in housing_categories + + +def test_expected_states_actions_and_wage_process_present(): + """The model carries the working/dead regimes with their variables. + + - financial assets `assets` are the continuous Euler state of the working + regime, and housing `housing` is its discrete state, + - consumption and the discrete housing choice are the working actions, + - the Markov wage `wage` is a process state of the working regime, + - the terminal `dead` regime carries the assets and housing states the + bequest reads. + """ + model = ds_app3_discrete_housing.build_model( + variant="dcegm", n_assets=20, n_wage_nodes=3, n_periods=4 + ) + assert set(model.regime_names_to_ids) == {"working", "dead"} + + working = model.user_regimes["working"] + assert {"assets", "housing", "wage"} <= set(working.states) + assert {"consumption", "housing_choice"} <= set(working.actions) + + dead = model.user_regimes["dead"] + assert dead.transition is None + assert {"assets", "housing"} <= set(dead.states) + + +def test_build_params_threads_the_adjustment_cost_and_is_taxless(): + """`build_params(tau=...)` threads the adjustment cost; the tax is zero. + + The proportional adjustment cost `tau` enters the housing-flow function, and + the capital-income tax hook enters the resources function. The no-tax variant + fixes the tax to zero, so the tax parameter is present and zero. + """ + params_low = ds_app3_discrete_housing.build_params(tau=0.07) + params_high = ds_app3_discrete_housing.build_params(tau=0.12) + resources_fn = ds_app3_discrete_housing.RESOURCES_FUNCTION_NAME + assert params_low["working"]["housing_flow"]["tau"] == 0.07 + assert params_high["working"]["housing_flow"]["tau"] == 0.12 + assert params_low["working"][resources_fn]["capital_income_tax"] == 0.0 + + +def test_terminal_bequest_weight_is_threaded(): + """`build_params(theta=...)` places the bequest weight on the dead regime. + + Table 7 (Fella replication) uses `theta = 0.5`; the bequest weight enters the + terminal `dead` regime's utility. + """ + params = ds_app3_discrete_housing.build_params(theta=0.5) + assert params["dead"]["utility"]["theta"] == 0.5 + + +def test_brute_solve_at_tiny_grid_yields_a_finite_value_function(): + """The grid-search (VFI) twin solves to a finite value function. + + T = 20 is short, so a tiny brute solve (small asset grid, 3 wage nodes, + 4 periods) runs locally. The value function over the (housing, wage, assets) + grid must be finite everywhere β€” the discrete-housing structure (a discrete + housing state, a discrete own/rent choice driving its transition, and a + Markov wage) is correctly assembled and VFI-solvable. + """ + model = ds_app3_discrete_housing.build_model( + variant="brute", n_assets=20, n_wage_nodes=3, n_periods=4, n_consumption=20 + ) + params = ds_app3_discrete_housing.build_params(variant="brute", n_periods=4) + solution = model.solve(params=params, log_level="off") + working_V = np.asarray(solution[0]["working"]) + assert np.all(np.isfinite(working_V)) + + +@pytest.mark.skip( + reason=( + "DC-EGM kernel scope gap on feat/dcegm: the solve raises " + "NotImplementedError because (1) resources reads the Markov wage process " + "state and (2) the discrete housing state reaches the terminal regime via " + "a non-identity transition (next_housing = housing_choice). The model " + "builds and is accepted by the DC-EGM contract; the VFI twin solves. Run " + "the DC-EGM solve once the kernel covers process-state resources and " + "non-identity discrete-state terminal carries." + ) +) +def test_discrete_housing_model_solves_under_dcegm(): + """The DS App.3 discrete-housing model solves under DC-EGM to a finite V. + + Skipped: the DC-EGM kernel on `feat/dcegm` does not yet cover a regime whose + resources reads a stochastic process state, nor a discrete state that reaches + a terminal regime through a non-identity (choice-driven) transition β€” both of + which App.3 needs. The model still *builds* under DC-EGM (the contract + accepts it); only the solve hits the gap. + """ + model = ds_app3_discrete_housing.build_model(variant="dcegm", n_assets=1000) + params = ds_app3_discrete_housing.build_params(variant="dcegm", theta=0.5) + solution = model.solve(params=params, log_level="off") + assert np.all(np.isfinite(np.asarray(solution[0]["working"]))) diff --git a/tests/test_processes.py b/tests/test_processes.py index 169e32ccd..468c0d22d 100644 --- a/tests/test_processes.py +++ b/tests/test_processes.py @@ -27,6 +27,9 @@ get_params, ) +# Grid centering is float-eps-limited at the active precision. +_CENTERING_DECIMAL = 10 if X64_ENABLED else 5 + @pytest.mark.skipif(not X64_ENABLED, reason="Not working with 32-Bit because of RNG") @pytest.mark.parametrize( @@ -207,7 +210,7 @@ def test_ar1_grid_centers_on_unconditional_mean(grid_cls): points = grid.get_gridpoints() midpoint = (points[0] + points[-1]) / 2 expected = mu / (1 - rho) - aaae(midpoint, expected, decimal=10) + aaae(midpoint, expected, decimal=_CENTERING_DECIMAL) @pytest.mark.parametrize("grid_cls", _AR1_GRID_CLASSES) @@ -355,7 +358,7 @@ def test_tauchen_gauss_hermite_centers_on_unconditional_mean(): points = grid.get_gridpoints() midpoint = (points[0] + points[-1]) / 2 expected = mu / (1 - rho) - aaae(midpoint, expected, decimal=10) + aaae(midpoint, expected, decimal=_CENTERING_DECIMAL) def test_lognormal_correct_shape_without_params(): @@ -467,7 +470,7 @@ def test_tauchen_normal_mixture_centers_on_unconditional_mean(): midpoint = (points[0] + points[-1]) / 2 mean_eps = kwargs["p1"] * kwargs["mu1"] + (1 - kwargs["p1"]) * kwargs["mu2"] expected = (kwargs["mu"] + mean_eps) / (1 - kwargs["rho"]) - aaae(midpoint, expected, decimal=10) + aaae(midpoint, expected, decimal=_CENTERING_DECIMAL) def test_tauchen_normal_mixture_stationary_moments_and_autocorrelation(): @@ -575,10 +578,13 @@ def _lag1_autocorrelation(gridpoints, P): def test_iid_normal_stationary_moments(gauss_hermite): """IID Normal stationary mean and std match mu and sigma.""" mu, sigma = 1.5, 0.8 - extra = {"gauss_hermite": gauss_hermite} - if not gauss_hermite: - extra["n_std"] = 4.0 - grid = NormalIIDProcess(n_points=21, mu=mu, sigma=sigma, **extra) + grid = NormalIIDProcess( + n_points=21, + mu=mu, + sigma=sigma, + gauss_hermite=gauss_hermite, + n_std=None if gauss_hermite else 4.0, + ) got_mean, got_std = _stationary_moments( grid.get_gridpoints(), grid.get_transition_probs() ) @@ -590,10 +596,13 @@ def test_iid_normal_stationary_moments(gauss_hermite): def test_iid_lognormal_stationary_moments(gauss_hermite): """IID LogNormal stationary log-mean and log-std match mu and sigma.""" mu, sigma = 0.5, 0.3 - extra = {"gauss_hermite": gauss_hermite} - if not gauss_hermite: - extra["n_std"] = 4.0 - grid = LogNormalIIDProcess(n_points=21, mu=mu, sigma=sigma, **extra) + grid = LogNormalIIDProcess( + n_points=21, + mu=mu, + sigma=sigma, + gauss_hermite=gauss_hermite, + n_std=None if gauss_hermite else 4.0, + ) points = grid.get_gridpoints() P = grid.get_transition_probs() got_mean, got_std = _stationary_moments(jnp.log(points), P) diff --git a/tests/test_solvers.py b/tests/test_solvers.py index d54b12045..dcacbc722 100644 --- a/tests/test_solvers.py +++ b/tests/test_solvers.py @@ -3,24 +3,29 @@ A regime carries a `solver` configuration selecting its backward-induction algorithm. `GridSearch()` is the default and runs the existing grid search; the engine dispatches polymorphically on the solver instance -(`solver.build_period_kernels`), not on its type. `DCEGM(...)` is a published -configuration whose engine is not yet available, so requesting it is rejected at +(`solver.build_period_kernels`), not on its type. `DCEGM(...)` selects the +discrete-continuous endogenous grid method; its configuration is validated at model build. """ +from dataclasses import replace + import pytest from numpy.testing import assert_array_equal -from lcm import DCEGM, AgeGrid, GridSearch, Model +from _lcm.solution.backward_induction import _func_dedup_key +from lcm import DCEGM, AgeGrid, GridSearch, LinSpacedGrid, Model, NormalIIDProcess from lcm.exceptions import RegimeInitializationError from lcm_examples.iskhakov_et_al_2017 import ( WEALTH_GRID, RegimeId, dead, + get_model, get_params, retirement, working_life, ) +from tests.test_models.dcegm_paper_twin import build_dcegm_model _N_PERIODS = 4 _PARAMS = get_params( @@ -85,21 +90,105 @@ def test_dcegm_config_constructs(): assert cfg.upper_envelope == "fues" -def test_dcegm_config_rejects_refined_grid_factor_at_or_below_one(): - """`refined_grid_factor <= 1.0` leaves no headroom and is rejected.""" +def test_model_with_dcegm_solver_builds(): + """Selecting the DC-EGM solver builds the model: the engine wires the + solver's kernels in rather than rejecting the configuration. + + Uses a regime that satisfies the DC-EGM contract (resources, + post-decision, and inverse-marginal-utility functions); a stock + grid-search regime would be rejected for missing them. + """ + model = build_dcegm_model() + assert isinstance(model.user_regimes["working_life"].solver, DCEGM) + + +_SAVINGS_GRID = LinSpacedGrid(start=0.0, stop=10.0, n_points=50) + +_BASE_DCEGM = DCEGM( + continuous_state="wealth", + continuous_action="consumption", + resources="resources", + post_decision_function="savings", + savings_grid=_SAVINGS_GRID, +) + + +def _dcegm(**overrides) -> DCEGM: + return replace(_BASE_DCEGM, **overrides) + + +def test_dcegm_defaults_construct_without_error(): + """The documented defaults pass validation.""" + solver = _dcegm() + assert solver.savings_grid is _SAVINGS_GRID + + +def test_dcegm_stochastic_savings_grid_is_rejected(): + """A stochastic process cannot serve as the deterministic savings grid.""" + process = NormalIIDProcess(n_points=5, gauss_hermite=True, mu=0.0, sigma=1.0) + with pytest.raises(RegimeInitializationError, match="stochastic process"): + _dcegm(savings_grid=process) + + +@pytest.mark.parametrize("refined_grid_factor", [1.0, 0.9, float("nan"), float("inf")]) +def test_dcegm_non_finite_or_too_small_refined_grid_factor_is_rejected( + refined_grid_factor, +): + """The headroom factor must be finite and exceed 1.0 (NaN/inf rejected too).""" with pytest.raises(RegimeInitializationError, match="refined_grid_factor"): - DCEGM( - continuous_state="wealth", - continuous_action="consumption", - resources="resources", - post_decision_function="savings", - savings_grid=WEALTH_GRID, - refined_grid_factor=1.0, - ) - - -def test_model_with_dcegm_solver_raises_not_implemented(): - """Requesting the DC-EGM solver is rejected at model build: the public - configuration exists, but the solver engine is not yet available.""" - with pytest.raises(NotImplementedError, match="DC-EGM"): - _build_model(working_solver=_valid_dcegm()) + _dcegm(refined_grid_factor=refined_grid_factor) + + +@pytest.mark.parametrize("fues_jump_thresh", [0.0, -1.0, float("nan"), float("inf")]) +def test_dcegm_non_finite_or_non_positive_fues_jump_thresh_is_rejected( + fues_jump_thresh, +): + """The segment-switch threshold must be finite and positive (NaN/inf rejected).""" + with pytest.raises(RegimeInitializationError, match="fues_jump_thresh"): + _dcegm(fues_jump_thresh=fues_jump_thresh) + + +@pytest.mark.parametrize("n_constrained_points", [1, 0]) +def test_dcegm_too_few_constrained_points_is_rejected(n_constrained_points): + """The constrained segment needs at least two closed-form points.""" + with pytest.raises(RegimeInitializationError, match="n_constrained_points"): + _dcegm(n_constrained_points=n_constrained_points) + + +def test_dcegm_zero_points_to_scan_is_rejected(): + """The FUES forward scan must inspect at least one point.""" + with pytest.raises(RegimeInitializationError, match="fues_n_points_to_scan"): + _dcegm(fues_n_points_to_scan=0) + + +def test_dcegm_zero_scan_unroll_is_rejected(): + """The FUES `lax.scan` unroll factor must be at least 1 (no unrolling).""" + with pytest.raises(RegimeInitializationError, match="fues_scan_unroll"): + _dcegm(fues_scan_unroll=0) + + +def test_period_kernels_sharing_a_config_reuse_one_compiled_core(): + """Periods of a grid-search regime that share a Q-and-F configuration wrap + the same jitted core, so AOT compilation lowers it once. + + Each period adapter exposes its shared jitted `core`; periods grouped by + target configuration reuse one core object, so the count of distinct cores + (the dedup key the AOT step keys on) is strictly fewer than the number of + active periods rather than one compilation per period. + """ + model = get_model(n_periods=6) + retirement_phase = model._regimes["retirement"].solution + period_kernels = retirement_phase.period_kernels + + # The retirement regime is active in several periods (it is solved by grid + # search); a model that shared no core would expose one core per period. + assert len(period_kernels) > 1 + + distinct_cores = {_func_dedup_key(func=k.core) for k in period_kernels.values()} + assert len(distinct_cores) < len(period_kernels) + + # Every period's core is one of the deduped representatives the AOT step + # would compile β€” no per-period adapter introduces a fresh compilation. + assert all( + _func_dedup_key(func=k.core) in distinct_cores for k in period_kernels.values() + ) diff --git a/tests/test_stochastic.py b/tests/test_stochastic.py index ea19b8a48..ce3a46fa6 100644 --- a/tests/test_stochastic.py +++ b/tests/test_stochastic.py @@ -24,6 +24,7 @@ ScalarInt, UserParams, ) +from tests.conftest import X64_ENABLED from tests.test_models.stochastic import ( RegimeId, dead, @@ -33,6 +34,9 @@ working_life, ) +# Splayed and unsplayed solves agree to float eps at the active precision. +_SPLAY_ATOL = 1e-10 if X64_ENABLED else 1e-5 + def test_model_simulate_with_stochastic_model(): model = get_model(n_periods=4) @@ -381,7 +385,7 @@ def next_draw_5050() -> FloatND: ) assert_allclose( - V_splayed[0]["working_life"], V_unsplayed[0]["working_life"], atol=1e-10 + V_splayed[0]["working_life"], V_unsplayed[0]["working_life"], atol=_SPLAY_ATOL )