Add Warm Home Discount planning doc (#502)

changelog.d/502.md

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+- Add a Warm Home Discount planning docs page at `docs/book/programs/gov/ofgem/warm-home-discount-plan.md` covering the two-group structure (auto Core Group 1 keyed on Pension Credit Guarantee Credit, EPC-based Core Group 2 in England, application-based Core 2 in Scotland/Wales), the devolved variants, and a three-phase implementation route that recommends modelling only Core Group 1 in v1 as the cleanest defensible scope.

docs/book/programs/gov/ofgem/warm-home-discount-plan.md

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+# Warm Home Discount (planned)
+
+```{warning}
+**Not yet modelled.** The Warm Home Discount (WHD) is an Ofgem-administered
+scheme that pays a one-off rebate of £150 per qualifying household per
+winter, off their domestic electricity bill. PolicyEngine UK doesn't
+currently model it. This page captures the proposed scope, tracked
+under [#502](https://github.com/PolicyEngine/policyengine-uk/issues/502).
+```
+
+## Why modelling WHD is harder than it looks
+
+The Warm Home Discount has two components, with different eligibility
+rules:
+
+- **Core Group 1**: people in receipt of the **Guarantee Credit element
+  of Pension Credit**. This group is identified automatically by DWP
+  data-matching and the rebate is applied to their electricity bill
+  without an application. Eligibility for this group is a clean,
+  centrally-defined rule and is straightforwardly modellable from the
+  existing PolicyEngine variables (`pension_credit`).
+- **Core Group 2** ("Broader Group" until 2022-23): people whose home is
+  **assessed as having a high energy cost** and who are on certain
+  qualifying means-tested benefits (UC, IS, JSA-IB, ESA-IR, HB, CTC, WTC
+  in particular bands). The high-energy-cost assessment uses an
+  Energy Performance Certificate (EPC) plus VOA property data; the
+  qualifying-benefit list shifted in England in 2022-23 ([source][gov-2022]).
+
+The combination of (a) the EPC-based property assessment, (b) different
+schemes in England, Scotland, and Wales, and (c) the absence of a
+public point-in-time eligibility register makes this harder to model
+than typical means-tested benefits.
+
+## Devolved variants
+
+| Nation | Core 1 (PC Guarantee Credit) | Core 2 ("Broader Group") |
+|--------|-------------------------------|---------------------------|
+| England | yes — auto, £150 | yes — EPC-based property assessment + qualifying benefits |
+| Scotland | yes — auto, £150 | by **application** through energy suppliers; criteria vary year to year |
+| Wales | yes — auto, £150 | by **application** through energy suppliers; criteria vary year to year |
+
+Scotland and Wales did not adopt the 2022 England reform that swapped
+the application-based Broader Group for the EPC-based Core 2; instead
+both retain the application model.
+
+## Proposed scope
+
+### Phase 1 — Core Group 1 only
+
+The single cleanest WHD modelling target: payment to any household
+with positive `pension_credit_guarantee_credit` in the winter season.
+~1 million households per year by DWP outturn (out of ~3 million WHD
+recipients).
+
+- New parameter `gov.ofgem.warm_home_discount.core_group_1.amount`
+  (£150 since winter 2022-23, £140 before).
+- New variable `warm_home_discount_core_1` (Household, YEAR) =
+  `amount` if any benunit member has positive Pension Credit Guarantee
+  Credit, else 0.
+- Roll into a `warm_home_discount` umbrella variable; Phase 2 adds the
+  Core Group 2 leg.
+
+### Phase 2 — Core Group 2 (England)
+
+Requires:
+
+- Adding EPC band as a household input variable (or imputing it from
+  property age/type via a `policyengine-uk-data` second-stage QRF).
+- Encoding the qualifying-benefit list per scheme year (the list
+  changed in winter 2022-23).
+- Property-cost-score parameters from Ofgem's annual scheme rules.
+
+This is the bulk of the work.
+
+### Phase 3 — Scotland and Wales
+
+Application-based Core 2 isn't modellable from administrative
+eligibility rules alone. The reasonable approximation is a take-up rate
+applied to the same qualifying-benefit set:
+
+- A `would_claim_warm_home_discount_scotland` / `_wales` stochastic
+  flag in `policyengine-uk-data` calibrated against Ofgem-published
+  Scottish/Welsh recipient counts.
+
+## Alternative: model as a Core 1-only umbrella
+
+Given the complexity of Phase 2 and the relatively modest fiscal
+weight of WHD (~£400m/year on Core 1 across the UK), a defensible v1
+is to model **only** Core Group 1 and document Core Group 2 as
+under-imputed. That captures the most policy-relevant slice (Pension
+Credit interaction, eligibility through the means-tested-benefit
+ladder) at minimal modelling cost.
+
+Reform analysis using PolicyEngine to "expand WHD to all UC
+households" or similar would still work with Phase 1 alone by setting
+a Core-1-equivalent uplift on the WHD parameter.
+
+## Data needs
+
+- **Ofgem WHD statistics**:
+  [Warm Home Discount Scheme: annual reports](https://www.ofgem.gov.uk/publications/warm-home-discount-annual-reports)
+  give per-scheme-year recipient counts and total spend by group.
+- **DWP Pension Credit caseload** — already used for Pension Credit
+  calibration; no new data work needed for Phase 1.
+- **EPC distribution by property type** for Phase 2 — VOA + ONS data
+  exist but need cross-walking to FRS rows.
+
+## Open questions
+
+- The WHD scheme year runs October to March; PolicyEngine UK
+  variables are year-level. Should the variable represent the rebate
+  paid during the simulation year (Oct-Mar payments), or the rebate
+  accrued during the simulation year (Mar-Oct accrual window)? UC and
+  Pension Credit conventions suggest the former.
+- The auto-payment for Core Group 1 means the rebate is functionally
+  irreversible — it doesn't depend on the household applying. Does the
+  model need a `would_claim_warm_home_discount` flag at all for Core 1,
+  or should it just be `defined_for = "has_pension_credit_guarantee_credit"`?
+  Recommendation: skip the take-up gate for Core 1.
+
+## References
+
+- [Warm Home Discount Scheme: official guidance](https://www.gov.uk/the-warm-home-discount-scheme).
+- [Warm Home Discount (England and Wales) Regulations 2022 (SI 2022/687)](https://www.legislation.gov.uk/uksi/2022/687/contents) — the 2022-23 reform that introduced the EPC-based England Core Group 2.
+- [Warm Home Discount (Scotland) Regulations 2022 (SI 2022/690)](https://www.legislation.gov.uk/uksi/2022/690/contents) — devolved variant.
+- Ofgem, [Warm Home Discount Scheme: annual reports][gov-2022].
+- Issue: [#502](https://github.com/PolicyEngine/policyengine-uk/issues/502).
+
+[gov-2022]: https://www.ofgem.gov.uk/publications/warm-home-discount-annual-reports