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Add bereavement support plan: BSP formula + historical WPA (#466 #465)#1737

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Add bereavement support plan: BSP formula + historical WPA (#466 #465)#1737
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Summary

  • Formula for Bereavement Support Payment #466 asks for a rule-based Bereavement Support Payment formula (the current bsp.py is just adds = [\"bsp_reported\"] — no derived eligibility). Widowed Parent's Allowance #465 asks for historical Widowed Parent's Allowance for back-cast analysis.
  • These are the same pair of questions, so persist them in one combined plan at docs/book/programs/gov/dwp/bereavement-support-plan.md.
  • Covers:
    • the current reported-only state and what it can't do (reform analysis, post-FRS-reference bereavement, historical WPA);
    • BSP rule structure: lump sum + 18 monthly instalments at higher (with dependent child) or standard rate; cohabiting-partner extension from 9 Feb 2023 via SI 2023/134;
    • Phase 1: BSP rule-based formula with three new input variables (is_bereaved_recently, bsp_higher_rate_eligible, bsp_months_remaining);
    • Phase 2: WPA (historical) with the same formula shape but per-year uprated rate and the 2001-04 to 2017-04 bereavement-date window;
    • Phase 3: data-side is_bereaved_recently flag imputation in policyengine-uk-data from FRS marital-status transitions and DWP bereavement statistics;
    • open questions on BSP uprating (currently flat since 2017), a reform-side "treat WPA as BSP" toggle, and the cohabiting-partner effective-date logic.
  • Closes both Formula for Bereavement Support Payment #466 and Widowed Parent's Allowance #465 in the planning sense.
  • Pure documentation; no code changes.

Test plan

  • Markdown lints cleanly.
  • Docs build job picks up the new page under programs/gov/dwp/.

🤖 Generated with Claude Code

#466 asks for a rule-based Bereavement Support Payment formula
(current bsp.py is just adds = ["bsp_reported"], no derived
eligibility). #465 asks for historical Widowed Parent's Allowance for
back-cast analysis.

These are the same pair of questions ("model bereavement benefits
beyond the reported amount") so persist them in a single combined
plan.

The page covers:

- the current reported-only state and what it can't do (reform
  analysis, post-FRS-reference bereavement, historical WPA),
- BSP rule structure: lump sum + 18 monthly instalments at higher
  (with dependent child) or standard rate; cohabiting-partner
  extension from 9 Feb 2023 via SI 2023/134,
- Phase 1: BSP rule-based formula with three new input variables
  (is_bereaved_recently, bsp_higher_rate_eligible,
  bsp_months_remaining),
- Phase 2: WPA (historical) with the same formula shape but
  per-year uprated rate and the 2001-04 to 2017-04 bereavement-date
  window,
- Phase 3: data-side bereavement flag imputation in
  policyengine-uk-data from FRS marital-status transitions and DWP
  bereavement statistics,
- open questions on BSP uprating (currently flat since 2017), a
  reform-side "treat WPA as BSP" toggle, and the cohabiting-partner
  effective-date logic.
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