Add Cold Weather Payment planning doc (#435)

changelog.d/435.md

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+- Add a Cold Weather Payment planning docs page at `docs/book/programs/gov/dwp/cold-weather-payment-plan.md` covering the SI 1988/1724 qualifying-benefit-and-weather-event eligibility, a three-phase implementation route (expected-value -> regional weather mixing -> back-cast lookups), and the Scotland Winter Heating Payment equivalent under SSI 2023/8.

docs/book/programs/gov/dwp/cold-weather-payment-plan.md

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+# Cold Weather Payment (planned)
+
+```{warning}
+**Not yet modelled.** The Cold Weather Payment (CWP) is a DWP payment
+of **£25 per 7-day period of recorded cold weather** to qualifying
+households in England, Wales and (historically) Northern Ireland.
+PolicyEngine UK doesn't currently model it. This page captures the
+proposed scope, tracked under
+[#435](https://github.com/PolicyEngine/policyengine-uk/issues/435).
+
+In Scotland the equivalent benefit is the **Winter Heating Payment**
+(£59.75 per qualifying household per winter, replacing CWP from
+February 2023) — also not modelled.
+```
+
+## What CWP is
+
+Defined in [The Social Fund Cold Weather Payments (General)
+Regulations 1988][cwp-1988] (SI 1988/1724). A household qualifies if
+**all** of the following hold:
+
+- The address is in a postcode covered by a weather station that
+  recorded **7 consecutive days** at or below 0°C (forecast or
+  observed) in the qualifying period (1 November – 31 March).
+- A member of the benunit receives one of the **qualifying benefits**:
+  Pension Credit; Income Support, JSA-IB, or ESA-IR (in either case
+  with a disability-related premium, a child under 5, or in a few
+  other circumstances); Universal Credit (with limited capability for
+  work, a disability addition, or a child under 5).
+
+The payment is £25 per 7-day cold period; multiple cold periods
+trigger multiple payments. Outturn averages ~£100m to ~£200m/year
+nationally depending on winter severity.
+
+## Why this is harder than other DWP benefits
+
+The eligibility test combines an administrative benefit check (clean
+for PolicyEngine) with a **geographic weather event** (no FRS
+analogue). Modelling the weather side has three plausible approaches:
+
+1. **Expected-value parameterisation**: a single national
+   `cold_weather_payments_expected_periods` parameter capturing the
+   long-run-average number of 7-day cold periods triggered per winter.
+   Multiply by `£25 × qualifying_household` to produce the expected
+   annual payment. Easy to implement, accurate in aggregate, wrong in
+   any specific winter.
+2. **Regional weather mixing**: a per-region weather-event
+   distribution (e.g. North East has more cold periods than London on
+   average), parameterised from Met Office historic data. Captures the
+   distributional skew without forecasting any particular winter.
+3. **Year-specific lookups**: tabulate the DWP-published *Cold Weather
+   Payment statistics* by region by year and use those as historical
+   inputs. Most accurate for back-cast simulations; needs ongoing
+   updating.
+
+Recommendation: **option 2 (regional mixing)** for prospective analysis
+and option 3 for back-casts where the data is available.
+
+## Proposed scope
+
+### Phase 1 — qualifying-benefit gate + expected-value payment
+
+- New parameter `gov.dwp.cold_weather_payment.amount` = £25 (since
+  the scheme's inception).
+- New parameter
+  `gov.dwp.cold_weather_payment.expected_periods_per_year` =
+  long-run national average from DWP CWP statistics.
+- New variable `cold_weather_payment_eligible` (BenUnit, YEAR) that
+  fires if any benunit member receives one of the qualifying benefits
+  with the relevant addition / age trigger.
+- New variable `cold_weather_payment` (BenUnit, YEAR) = `amount` ×
+  `expected_periods_per_year` × `eligible`.
+
+This delivers a model that gets the policy-relevant slice right
+(*who* qualifies for CWP and how it interacts with their other
+benefits) at the cost of smoothing year-to-year weather variance.
+
+### Phase 2 — regional weather mixing
+
+Add a `gov.dwp.cold_weather_payment.expected_periods_by_region` table
+parameterised from Met Office observation data, and a household-side
+lookup by `region`.
+
+### Phase 3 — Scotland Winter Heating Payment
+
+Different rules and a different administration — modelled as a
+separate variable:
+
+- `winter_heating_payment_scotland_eligible`: any benunit member on
+  Pension Credit + Scotland residence (the WHP qualifying-benefit
+  list is broader than CWP).
+- `winter_heating_payment_scotland` = `amount` × `eligible` where
+  `amount` is the flat per-household winter payment (£59.75 in
+  2023-24, uprated subsequently).
+
+## Data needs
+
+- DWP, [Cold Weather Payment statistics](https://www.gov.uk/government/collections/cold-weather-payments-statistics) — caseload and expenditure by region by winter, primary calibration source.
+- DWP-published WHP statistics (Scotland) — Phase 3 calibration.
+- Met Office, [UK climate historic stations](https://www.metoffice.gov.uk/research/climate/maps-and-data/historic-station-data) — Phase 2 regional expected-period parameterisation.
+
+The FRS gives `region` cleanly, so the geographic gate is no extra
+data work for Phase 1/2.
+
+## Open questions
+
+- The qualifying-benefit list for CWP is narrower than for WHD —
+  specifically the disability/child-under-5 triggers within UC and the
+  legacy benefits. Should the eligibility be modelled as a single
+  composite condition variable, or as separate `_via_uc` /
+  `_via_legacy` / `_via_pc` flags?
+- CWP averages ~£100m/year — well below most modelled benefits, but
+  the marginal household-level impact is meaningful for the low-income
+  pensioners and disabled households it targets. Worth modelling
+  Phase 1 even if Phase 2 doesn't follow.
+- Welsh Government has occasionally topped up CWP from devolved funds.
+  Should the model expose a `wales_top_up` parameter for reform
+  analyses?
+
+## References
+
+- [The Social Fund Cold Weather Payments (General) Regulations 1988 (SI 1988/1724)][cwp-1988].
+- gov.uk, [Cold Weather Payment](https://www.gov.uk/cold-weather-payment).
+- DWP, [Cold Weather Payment statistics](https://www.gov.uk/government/collections/cold-weather-payments-statistics).
+- Scottish equivalent: [Winter Heating Payment (Scotland) Regulations 2023 (SSI 2023/8)](https://www.legislation.gov.uk/ssi/2023/8/contents).
+- Issue: [#435](https://github.com/PolicyEngine/policyengine-uk/issues/435).
+
+[cwp-1988]: https://www.legislation.gov.uk/uksi/1988/1724