Add Benefits-in-Kind planning docs page (#1654)

changelog.d/1654.md

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+- Add a "Benefits in Kind (planned)" docs page at `docs/book/programs/gov/hmrc/benefits-in-kind.md` capturing the agreed scope (Phase 1 MVP categories), the FRS coverage gap, the proposed imputation approach, knock-on effects through ANI/HICBC, and open questions, so future BiK work has a stable reference in the repo.

docs/book/programs/gov/hmrc/benefits-in-kind.md

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+# Benefits in Kind (planned)
+
+```{warning}
+**Not yet modelled.** This page captures the planned scope and roadmap for
+adding benefits-in-kind (BiK) modelling to PolicyEngine UK. Tracked under
+[#1654](https://github.com/PolicyEngine/policyengine-uk/issues/1654);
+remove the warning and the "Planned" sections below once the MVP lands.
+```
+
+## Current state in the model
+
+There is no BiK modelling in the repo today. The *integration hook*
+already exists:
+
+- `policyengine_uk/variables/gov/hmrc/income_tax/bases/taxable_employment_income.py`
+  adds an `employment_benefits` term to taxable earnings.
+- `policyengine_uk/variables/household/benefits/employment_benefits.py`
+  currently only sums `statutory_sick_pay` and `statutory_maternity_pay` —
+  i.e. statutory cash payments, not P11D-style benefits-in-kind.
+
+So the slot exists, but nothing fills it.
+
+## Planned scope
+
+UK BiK has a long tail. Roughly 80% of the aggregate taxable BiK base is
+captured by five categories — we will MVP these and defer the rest.
+
+### Phase 1 — MVP
+
+| Category | P11D section | Notes |
+|----------|--------------|-------|
+| Company cars | F | Biggest single category by value |
+| Car fuel benefit | F | |
+| Private medical and dental insurance | I | |
+| Living accommodation | D | |
+| Beneficial loans | H | Interest below the HMRC official rate |
+
+### Phase 2 — moderate prevalence
+
+Vans and van fuel (G); vouchers and credit cards (C); mileage allowances
+above HMRC approved rates (E); relocation expenses above £8k (J); assets
+transferred or placed at disposal (A, L).
+
+### Phase 3 — long tail / niche
+
+Services supplied (K); payments on employee's behalf (B); entertainment;
+non-qualifying travel and subsistence; employer-paid income tax;
+educational assistance.
+
+### Exempt — out of scope
+
+Trivial benefits under £50; one mobile phone; workplace parking and
+nurseries; employer pension contributions; cycle-to-work; eye tests for
+VDU users; pensions advice up to £500.
+
+## Implementation plan
+
+### Variables
+
+- A new `benefit_in_kind` variable on `Person`, summing typed
+  sub-components.
+- One sub-variable per BiK category in
+  `variables/gov/hmrc/income_tax/bik/` (`company_car_benefit`,
+  `car_fuel_benefit`, `private_medical_benefit`,
+  `living_accommodation_benefit`, `beneficial_loan_benefit`).
+- Add `benefit_in_kind` to `employment_benefits` so it flows into
+  `taxable_employment_income` through the existing hook.
+
+### Parameters
+
+New tree under `parameters/gov/hmrc/income_tax/bik/`:
+
+- `company_car/appropriate_percentage_by_co2.yaml` (year-by-year CO2 bands)
+- `company_car/fuel_charge_multiplier.yaml`
+- `company_car/electric_vehicle_rates.yaml`
+- `car_fuel/multiplier.yaml`
+- `living_accommodation/cost_threshold.yaml` (currently £75k)
+- `beneficial_loan/official_rate.yaml`
+- `beneficial_loan/de_minimis.yaml` (currently £10k)
+- `vouchers/...` (Phase 2)
+
+### Knock-on effects
+
+BiK feeds into adjusted net income, which means it touches:
+
+- the personal allowance taper at £100k,
+- the High Income Child Benefit Charge,
+- the tapered annual allowance for pensions,
+- **Class 1A NICs (employer side)** — not currently modelled in the repo;
+  treated as a separate workstream.
+
+### Tests
+
+- Unit tests per BiK category against worked HMRC examples.
+- Integration tests asserting BiK flows through to taxable employment
+  income, ANI, and HICBC where applicable.
+
+## Data needs and FRS coverage
+
+| Component | FRS has flag? | FRS has value? | Calibration source |
+|-----------|---------------|----------------|--------------------|
+| Company car | Yes | No (no list price / CO2 / fuel) | HMRC *Benefits in Kind statistics*, *Company Car Tax statistics* |
+| Car fuel | Partially (fuel-provided flag) | No | HMRC BiK statistics |
+| Private medical insurance | Yes (employer-paid flag) | No | HMRC BiK statistics |
+| Living accommodation | Yes (job-tied accommodation flag) | No | HMRC BiK statistics; SPI (restricted) |
+| Beneficial loans | No reliable flag | No | HMRC BiK statistics; SPI (restricted) |
+
+### Public sources
+
+- **HMRC Benefits in Kind statistics** — annual P11D-based release;
+  recipient counts and total taxable values by category and income band.
+  Primary calibration target.
+- **HMRC Company Car Tax statistics** — CO2 and fuel-type distributions.
+- **HMRC Personal Incomes Statistics (SPI tables)** — published totals.
+- **DVLA / SMMT** — new-car registrations for company-car list-price/CO2
+  distributions.
+
+### Restricted-access (HMRC Datalab)
+
+- **SPI microdata** — actual P11D values per individual; gold standard
+  but requires accreditation and stays in the secure environment.
+- **RTI / PAYE** — payrolled BiK (growing share since 2016 mandatory
+  payrolling reforms).
+
+### Imputation approach (proposed)
+
+1. Use FRS flags to decide *who* receives each BiK type.
+2. For each type, draw a value from a distribution calibrated so the
+   population total and income-band breakdown match HMRC's published BiK
+   statistics — mirrors the second-stage imputation pattern flagged in
+   [#1621](https://github.com/PolicyEngine/policyengine-uk/issues/1621).
+3. For company cars: either (a) skip the list-price/CO2 mechanics and
+   assign a calibrated taxable value directly, or (b) layer a simplified
+   CO2-band model over an imputed list-price distribution. Recommend (a)
+   for MVP and (b) as a Phase-1.5 refinement.
+
+## Effort estimate
+
+- Framework wiring + a flat-value `benefit_in_kind` variable feeding the
+  existing hook: ~1–2 days.
+- Phase 1 MVP (five categories, calibrated imputation, knock-on effects
+  through ANI/HICBC, tests): ~2 weeks.
+- Trustworthy distributional version (CO2 bands modelled, beneficial-loan
+  amounts, sensitivity-checked imputation): closer to a month, with most
+  time on the data side rather than the rules.
+- Class 1A NICs (employer side): separate workstream.
+
+## Open questions
+
+- Do we model Class 1A NICs (employer side) in the same effort, or split
+  it out?
+- Should BiK enter Universal Credit and legacy means tests as earned
+  income? HMRC treats most BiK as taxable but UC reads earned income from
+  RTI: payrolled BiK flows through, non-payrolled BiK does not — needs a
+  decision.
+- Pursue HMRC Datalab access for SPI/RTI microdata, or stick to
+  public-aggregate calibration for now?