Add bereavement support plan: BSP formula + historical WPA (#466 #465)

changelog.d/466.md

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+- Add a bereavement support planning docs page at `docs/book/programs/gov/dwp/bereavement-support-plan.md` covering the proposed rule-based BSP formula (Pensions Act 2014 Part 5, SI 2017/410, 18-month payment window from SI 2023/134) and a Phase 2 extension covering historical Widowed Parent's Allowance under SSCBA 1992 s.39A; combined plan closes #466 and #465.

docs/book/programs/gov/dwp/bereavement-support-plan.md

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+# Bereavement support: BSP formula and historical WPA (planned)
+
+```{warning}
+**Currently reported-only.** PolicyEngine UK models the Bereavement
+Support Payment (BSP) as `adds = ["bsp_reported"]` — i.e. the value
+flows through from the dataset, with no derived eligibility or
+rule-based amount. This page captures the proposed formula-based
+extension covering both BSP and the legacy Widowed Parent's Allowance
+(WPA) for historical analysis. Tracks
+[#466](https://github.com/PolicyEngine/policyengine-uk/issues/466) and
+the related historical-WPA ask in
+[#465](https://github.com/PolicyEngine/policyengine-uk/issues/465).
+```
+
+## What's currently modelled
+
+Just the FRS-reported amount:
+
+```python
+class bsp(Variable):
+    label = "Bereavement Support Payment"
+    entity = Person
+    definition_period = YEAR
+    value_type = float
+    unit = GBP
+    adds = ["bsp_reported"]
+```
+
+That means:
+
+- Reform analyses changing BSP rates have no household-level surface.
+- Anyone bereaved after the FRS reference week never appears as a BSP
+  recipient even if eligible.
+- The legacy WPA is not modelled at all — anyone reporting it in
+  historical FRS waves drops into the residue.
+
+## Proposed scope
+
+### Phase 1 — BSP rule-based formula
+
+The BSP under the [Pensions Act 2014, Part 5][pa-2014-5] and the
+[Bereavement Support Payment Regulations 2017][bsp-regs] (SI 2017/410)
+pays:
+
+- A **lump-sum** of either £2,500 (Standard Rate) or £3,500 (Higher
+  Rate, with a dependent child).
+- A **monthly payment** of £100 (Standard) or £350 (Higher) for up to
+  **18 monthly instalments** after a death on or after 6 April 2017
+  (extended from 12 months by the Bereavement Benefits
+  (Remedial) Order 2023, SI 2023/134, after the McLaughlin / Jackson
+  ECHR rulings).
+
+To model this we need:
+
+- `is_bereaved_recently` (Person, YEAR) — a new input flagging
+  whether the person has been bereaved in the last 18 months.
+- `bsp_higher_rate_eligible` (Person, YEAR) — whether they have a
+  dependent child.
+- `bsp_months_remaining` (Person, YEAR) — how many of the 18 monthly
+  instalments fall within the simulation year.
+
+The BSP formula then becomes:
+
+```
+bsp = (
+    lump_sum_amount * is_bereaved_recently
+    + monthly_amount * bsp_months_remaining
+)
+```
+
+Both `lump_sum_amount` and `monthly_amount` parameter trees split on
+`bsp_higher_rate_eligible` (£3,500 / £350 vs £2,500 / £100).
+
+### Phase 2 — WPA (historical) under the same formula
+
+Widowed Parent's Allowance (under [Social Security Contributions and
+Benefits Act 1992 s. 39A][sscba-39a]) was paid for deaths between
+April 2001 and 5 April 2017. The benefit:
+
+- Continued for as long as the surviving spouse had a dependent child.
+- Was uprated annually.
+- Was replaced by BSP for deaths from 6 April 2017.
+
+For historical analyses the model should:
+
+- Add `wpa_eligible` (Person, YEAR) — bereavement date 2001-04 to
+  2017-04 inclusive, with a dependent child.
+- Add `widowed_parents_allowance` (Person, YEAR) as a derived
+  formula reading the WPA rate parameter (which would need
+  backfilling under `gov/dwp/wpa/rate.yaml`).
+
+WPA receipts are now a closing tail of the recipient pool (no new
+awards) but still appear in current FRS waves; the present model
+treats those as a generic `maintenance_income`-class residue. Closing
+this gap improves the alignment of HBAI net income for the few
+thousand remaining recipients.
+
+### Phase 3 — data-side bereavement flag
+
+`is_bereaved_recently` doesn't exist in the FRS as a clean field; it
+would need imputing in `policyengine-uk-data` from:
+
+- the FRS marital-status code transitions between waves (widowed in
+  current wave but not in the previous wave),
+- DWP BSP/WPA caseload by region by year as the calibration target.
+
+This is the heaviest of the three phases; without it the new
+variables work for the household-calculator (which can input the flag
+directly) but not for microsim aggregates.
+
+## Open questions
+
+- BSP is currently uprated discretionarily rather than by statute. The
+  monthly rate has been £100/£350 since 2017 with no annual uprating.
+  Should the parameter tree carry an explicit
+  `uprating: gov.economic_assumptions.indices.obr.consumer_price_index`
+  to mirror what other DWP rates do, or hold flat to match the
+  historical reality?
+- WPA recipients who would have been on BSP under the new rules: do we
+  want a reform-side parameter "treat all WPA receipts as if they were
+  BSP" for counterfactual analysis?
+- The McLaughlin / Jackson ECHR rulings extended BSP to cohabiting
+  partners with children from 9 February 2023. The current
+  `bsp_higher_rate_eligible` rule should encode this in its
+  effective-date logic.
+
+## References
+
+- [Pensions Act 2014, Part 5](https://www.legislation.gov.uk/ukpga/2014/19/part/5) — primary statute for BSP.
+- [Bereavement Support Payment Regulations 2017 (SI 2017/410)][bsp-regs].
+- [Bereavement Benefits (Remedial) Order 2023 (SI 2023/134)](https://www.legislation.gov.uk/uksi/2023/134/contents) — cohabiting-parent extension and 18-month limit.
+- [SSCBA 1992 s. 39A][sscba-39a] — legacy WPA basis.
+- gov.uk, [Bereavement Support Payment](https://www.gov.uk/bereavement-support-payment) and [Widowed Parent's Allowance](https://www.gov.uk/widowed-parents-allowance).
+- DWP, [Bereavement support statistics](https://www.gov.uk/government/collections/dwp-statistical-summaries-on-bereavement-payments).
+- Issues: [#466](https://github.com/PolicyEngine/policyengine-uk/issues/466) (BSP formula), [#465](https://github.com/PolicyEngine/policyengine-uk/issues/465) (historical WPA).
+
+[pa-2014-5]: https://www.legislation.gov.uk/ukpga/2014/19/part/5
+[bsp-regs]: https://www.legislation.gov.uk/uksi/2017/410/contents
+[sscba-39a]: https://www.legislation.gov.uk/ukpga/1992/4/section/39A