Add DLA and SDA documentation page (#771) (#1709)

* Add DLA and SDA documentation page (#771)

Ticks off the DLA and SDA entries in #771's docs-pages todo list.

Combined into one page because both are closed-to-new-claims legacy DWP
disability benefits with very small modelling surface area:

- DLA: two component variables (dla_m, dla_sc), each taking a
  categorical band from the dataset input and multiplying the weekly
  rate by WEEKS_IN_YEAR. The eligibility-by-activity scoring is not
  re-derived because the dataset records bands directly; the relevant
  population (under-16s and unmigrated working-age recipients) is set
  by the calibration step in policyengine-uk-data.
- SDA: single weekly flat-rate payment, binary eligibility taken from
  sda_reported, maximum age-related addition assumed (justified because
  the remaining 2001-frozen caseload skews old).

References cover SSCBA 1992 s.68/s.71, the Welfare Reform Acts that
closed both schemes to new claims, and the DWP caseload statistics page
used for calibration.

* Fix household_benefits aggregation claim in DLA/SDA docs

There is no personal_benefits variable; dla and sda are added directly
to the household_benefits adds list.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

Author: vahid-ahmadi

changelog.d/771-disability-legacy-docs.md

@@ -0,0 +1 @@
+- Add a documentation page covering Disability Living Allowance (mobility + self-care components, both DLA bands taken from dataset categoricals) and Severe Disablement Allowance (binary read from `sda_reported`, maximum age-related addition assumed); ticks off two more #771 docs-pages entries.

docs/book/programs/gov/dwp/disability-legacy-benefits.md

@@ -0,0 +1,75 @@
+# DLA and Severe Disablement Allowance
+
+PolicyEngine UK models two **legacy** DWP disability benefits alongside
+the current PIP (covered in [its own page](./PIP.ipynb)):
+
+- **Disability Living Allowance (DLA)** — closed to new working-age
+  claims in April 2013 but still paid to existing recipients and to
+  children under 16.
+- **Severe Disablement Allowance (SDA)** — closed to new claims in
+  April 2001 and replaced by Incapacity Benefit / ESA / Universal Credit;
+  legacy recipients continue to receive it.
+
+Both are non-means-tested and are added directly into the
+`household_benefits` aggregate (via the `dla` and `sda` variables in its
+`adds` list).
+
+## Disability Living Allowance
+
+DLA has two independent components, each with its own band structure:
+
+| Component | Bands | Variable | Parameter file |
+|-----------|-------|----------|----------------|
+| Mobility (`dla_m`) | Higher / Lower / None | `dla_m` | `gov/dwp/dla/mobility/{higher,lower}.yaml` |
+| Self-care (`dla_sc`) | Higher / Middle / Lower / None | `dla_sc` | `gov/dwp/dla/self_care/{higher,middle,lower}.yaml` |
+
+A claimant's band on each component is taken from the dataset inputs
+`dla_m_category` and `dla_sc_category` (each an enum on `Person`). For
+each band the formula multiplies the published **weekly** rate by
+`WEEKS_IN_YEAR` to produce an annual amount; the combined award is
+
+```python
+dla = dla_sc + dla_m
+```
+
+i.e. a recipient on the higher mobility rate and the higher self-care
+rate stacks both, producing the maximum DLA award.
+
+### Eligibility (informational)
+
+PolicyEngine doesn't re-derive eligibility for DLA because the dataset
+records categorical band assignments rather than the underlying
+self-care / mobility activity scores. New claims have been routed to
+PIP for working-age claimants since April 2013, so the population that
+remains on DLA is overwhelmingly:
+
+- children under 16 (DLA continues to be available),
+- adults who were on DLA on 8 April 2013 and have not yet been migrated
+  to PIP at reassessment.
+
+Migration to PIP is handled by the calibration step in
+`policyengine-uk-data`, not by a re-derivation here.
+
+## Severe Disablement Allowance
+
+SDA is a single weekly flat-rate payment, exposed as the variable `sda`.
+Eligibility is treated as binary and read straight from the dataset
+input `sda_reported`:
+
+```python
+sda = (sda_reported > 0) * gov.dwp.sda.maximum * WEEKS_IN_YEAR
+```
+
+The model assumes recipients are entitled to the **maximum** age-related
+addition. This is a deliberate simplification: SDA was closed to new
+claims in 2001 and the remaining caseload is small and old enough that
+nearly all recipients qualify for the highest age-related addition.
+
+## References
+
+- DLA primary statute: [Social Security Contributions and Benefits Act 1992 s. 71](https://www.legislation.gov.uk/ukpga/1992/4/section/71).
+- DLA closure to new working-age claims: [Welfare Reform Act 2012 Part 4](https://www.legislation.gov.uk/ukpga/2012/5/part/4) and [The Personal Independence Payment (Transitional Provisions) Regulations 2013 (SI 2013/387)](https://www.legislation.gov.uk/uksi/2013/387/contents).
+- DWP, [Disability Living Allowance: detailed information](https://www.gov.uk/disability-living-allowance).
+- SDA primary statute: [Social Security Contributions and Benefits Act 1992 s. 68](https://www.legislation.gov.uk/ukpga/1992/4/section/68) (since repealed for new claims).
+- SDA closure to new claims: [The Welfare Reform and Pensions Act 1999 s. 65](https://www.legislation.gov.uk/ukpga/1999/30/section/65).
+- DWP, [DLA and SDA caseload statistics](https://www.gov.uk/government/collections/disability-living-allowance-statistics) used by `policyengine-uk-data` for calibration.