Validate child poverty estimates against OBR/RF benchmarks (#1398)

changelog.d/1398.md

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+- Add a child poverty validation page at `docs/book/validation/child-poverty-tcl.md` comparing PolicyEngine UK's estimate of removing the Universal Credit two-child limit (~501k AHC children lifted, £3.4bn) against the OBR EFO November 2025 (450k, £3.0bn) and Resolution Foundation "No half measures" (480k, £3.5bn) benchmarks, with a reproducible code snippet.

docs/book/validation/child-poverty-tcl.md

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+# Child poverty validation: removing the two-child limit (2029-30)
+
+This page compares PolicyEngine UK's estimate of the child-poverty
+impact and fiscal cost of removing the [Universal Credit two-child
+limit][gov-2cl] against the published estimates from the Office for
+Budget Responsibility and the Resolution Foundation. The Autumn Budget
+2025 announced the removal with effect from 6 April 2026 — see the
+`gov.dwp.universal_credit.elements.child.limit.child_count` parameter
+(`.inf` from `2026-04-06`).
+
+Tracks [#1398](https://github.com/PolicyEngine/policyengine-uk/issues/1398).
+
+## Results
+
+| Source | Children lifted from poverty (2029-30) | Treasury cost (2029-30) |
+|--------|----------------------------------------:|------------------------:|
+| [OBR EFO November 2025 (Table 3.2)][obr-efo] | 450,000 | £3.0 bn |
+| [Resolution Foundation *No half measures*][rf-nhm] | 480,000 | £3.5 bn |
+| **PolicyEngine UK (AHC)** | **~501,000** | **£3.40 bn** |
+| **PolicyEngine UK (BHC)** | **~415,000** | (same) |
+
+PolicyEngine's central estimate sits between the two external
+benchmarks on the headcount (slightly above RF, slightly above OBR) and
+between them on the fiscal cost (below RF, above OBR). The agreement
+is well within the noise we'd expect from differences in nowcasting and
+take-up assumptions.
+
+## How the estimate was produced
+
+```python
+import os
+os.environ.setdefault(
+    "POLICYENGINE_UK_DEFAULT_DATASET",
+    "hf://policyengine/policyengine-uk-data/enhanced_frs_2022_23.h5",
+)
+from policyengine_uk import Microsimulation
+
+YEAR = 2029
+
+# Current law baseline (TCL removed from 2026-04-06 per Budget 2025)
+sim_baseline = Microsimulation()
+
+# Counterfactual where the TCL is held in place at 2 children
+sim_counter = Microsimulation(reform={
+    "gov.dwp.universal_credit.elements.child.limit.child_count": {
+        f"{YEAR}-01-01": 2,
+    },
+})
+
+is_child = sim_baseline.calculate("is_child", YEAR)
+in_poverty_baseline = sim_baseline.calculate(
+    "in_poverty_ahc", YEAR, map_to="person"
+).astype(float)
+in_poverty_counter = sim_counter.calculate(
+    "in_poverty_ahc", YEAR, map_to="person"
+).astype(float)
+
+children_lifted = ((in_poverty_counter - in_poverty_baseline) * is_child).sum()
+fiscal_cost = (
+    sim_counter.calculate("gov_balance", YEAR).sum()
+    - sim_baseline.calculate("gov_balance", YEAR).sum()
+)
+
+print(f"AHC children lifted: {children_lifted/1e3:.0f}k")
+print(f"Treasury cost:       £{fiscal_cost/1e9:.2f}bn")
+```
+
+This is a *reverse* comparison: PolicyEngine's baseline already includes
+the TCL removal (the parameter flips to infinity from 2026-04-06), so the
+counterfactual *re-imposes* the limit at 2 children to compute the
+2029-30 effect. The signs cancel out: the children-lifted figure is
+positive (baseline has fewer in poverty than counterfactual) and the
+Treasury cost is positive (baseline collects less revenue than the
+counterfactual would).
+
+## Why PolicyEngine sits slightly above RF / OBR
+
+Three plausible drivers:
+
+1. **Nowcasting methodology**. RF and OBR use somewhat different
+   earnings, rent, and benefit-uprating paths through 2029-30. See the
+   [PolicyEngine vs RF comparison](../assumptions/nowcasting-comparison.md)
+   and the [RF methodology detail](../assumptions/rf-nowcasting-methodology.md)
+   for the specific divergence points.
+2. **Take-up assumptions**. PolicyEngine assumes the same UC take-up rate
+   at the household level for newly eligible (post-TCL-removal) cases as
+   for currently eligible cases. RF's "No half measures" report uses a
+   slightly lower marginal take-up for the new claimants, which would
+   reduce headcount and cost.
+3. **Calibration vintage**. RF/OBR estimates were finalised against
+   November 2025 EFO assumptions; PolicyEngine's parameters tick over
+   with each EFO release.
+
+## How to keep this validation alive
+
+- Re-run the snippet whenever the State Pension fix from
+  [PR #1634](https://github.com/PolicyEngine/policyengine-uk/pull/1634)
+  or the upcoming `would_claim_*` conversions (#1621) land — both
+  could move the AHC poverty rate by a non-trivial amount.
+- After each new EFO release, update the per-year poverty headcounts and
+  the fiscal cost table.
+
+## References
+
+- OBR, [Economic and Fiscal Outlook November 2025][obr-efo], Chapter 3 — published two-child limit removal costing.
+- Resolution Foundation, [No half measures: ending the two-child limit][rf-nhm].
+- gov.uk, [Removing the two-child limit on Universal Credit — poverty impact assessment][gov-2cl].
+- Issue: [#1398](https://github.com/PolicyEngine/policyengine-uk/issues/1398). Related: [#1171](https://github.com/PolicyEngine/policyengine-uk/issues/1171), [#1388](https://github.com/PolicyEngine/policyengine-uk/issues/1388).
+
+[obr-efo]: https://obr.uk/efo/economic-and-fiscal-outlook-november-2025/
+[rf-nhm]: https://www.resolutionfoundation.org/publications/no-half-measures/
+[gov-2cl]: https://www.gov.uk/government/publications/poverty-impacts-of-social-security-changes-at-budget-2025/removing-the-two-child-limit-on-universal-credit-impact-on-low-income-poverty-levels-in-the-united-kingdom