Use the FRS benefit-unit capital for Pension Credit's capital test

[MaxGhenis]

Based on main, independent of #490 and #510. It needs policyengine-uk 2.107.0, the first release defining pension_credit_reported_capital (#2018), and this PR bumps the floor and lock to it. Like every uk-data merge, it lands with the batched release on Max's go (d833); the every-unit vs reporters-only choice is d800.

Why

About a third of FRS Pension Credit reporters get no modelled entitlement, and most of them fail on deemed income from imputed capital. Measured on #510's build D (2024-25 survey, FY2025-26, GB), original FRS households at survey weights, policyengine-uk main:

• 1,173k benefit units report Pension Credit; 759k are entitled in the model and 415k are not.
• 266k of the 415k fail only because of deemed income from capital.

For those 415k, the household wealth imputation and the survey's own benefit-unit capital (TOTCAPB3) disagree:

capital	under £6,000	under £16,000	over £100,000	weighted median
imputed (WAS QRF, household, pension-age share)	13%	18%	43%	£74,300
FRS TOTCAPB3	83%	96.5%	0.3%	£300

The WAS imputation predicts household wealth from income, composition, tenure and region, and knows nothing about means-tested receipt. It also carries pension wealth in corporate_wealth (#501 removes that). TOTCAPB3 is DWP's derived benefit-unit total of savings and investments, the measure its FRS-based National Statistics use. In 2023-24 DWP also assigned Pension Credit to eligible FRS non-reporters using eligibility "sourced from survey data, combined with administrative data" (FRS background information and methodology, section 8.3).

What changes

• create_frs writes pension_credit_reported_capital = FRS TOTCAPB3 for every benefit unit, or -1 where it is missing or negative (none are in 2024-25). policyengine-uk (#2018) then uses it in place of the household proxy in Pension Credit assessable capital.
• SPI-synthetic copies (impute_income) get -1, so they fall back to the household proxy. Their incomes are SPI-imputed, and the FRS donor's capital does not belong with them. In build E, 24 of the 152 SPI-synthetic PC reporters were entitled only because they carried it. Capital-gains copies keep their FRS incomes, so they keep the value.
• uprating_factors.csv and uprating_growth_factors.csv get the column with the savings row. policyengine-uk uprates it with the same per-capita GDP index, so uprate_dataset keeps the two in step.
• policyengine-uk >= 2.107.0 in pyproject.toml and uv.lock. Core 3.32.12 comes with it.
• Unchanged: savings and the other wealth columns, so wealth analyses still use the WAS imputation.

TOTCAPB3 covers financial assets only. Second homes and land, which Pension Credit also counts, are not in it.

Choice for review: every benefit unit (this PR) or reporters only.

• Filling every benefit unit gives entitled reporters and non-reporters the same capital definition.
• It matches the population DWP's take-up rate is measured against: 62% caseload take-up of 1,382k claims implies about 2.2m entitled GB benefit units.
• Filling reporters only fixes the reporter gap. Non-reporters stay on imputed capital, which understates the entitled pool.

Measured (real runs; build D plus this column, before any rebuild)

These use #510's own solver at 62% take-up, solved over GB entitled units as in #510 f09497f, original FRS households at survey weights, GB, FY2025-26. "All PRs" = policyengine-uk #2018, #2019, #1899, #1940 and #1925.

	main, build D	#2018, reporters only	#2018, every unit	all PRs, every unit
reporters not entitled	415k	159k	159k	88k (7.5%)
GB entitled benefit units	1,344k	1,600k	1,907k	2,084k
fill probability (GB solve)	0.128	0.000	0.188	0.206
claims / spending after the fill	833k / £3.57bn	1,015k / £4.69bn	1,182k / £5.16bn	1,292k / £6.00bn
scale calibration needs to reach DWP's 1,382k / £6.14bn	1.66x / 1.72x	1.36x / 1.31x	1.17x / 1.19x	1.07x / 1.02x

So with these changes calibration no longer has to inflate reporters to reach DWP's caseload. Build D took GB reporters from 1,199k (survey weights) to 1,736k.

Totals on build D's calibrated weights overshoot, because those weights already inflate reporters (GB Pension Credit is £6.24bn on main and £8.17bn with #2018 and every unit filled, without recalibration). On the same static basis (2025-26, calibrated weights, main against #2018 with every unit filled), other outputs that read the Pension Credit assessment also move:

• UK Housing Benefit £8.33bn → £8.59bn (guarantee credit passport);
• UK Council Tax Reduction £1.84bn → £1.98bn (pension-age CTR takes PC capital and the GC passport);
• pensioner relative poverty BHC 21.78% → 21.62%.

Build E, below, gives the rebuilt figures.

Rebuild: build E vs D′ (real production builds, 1 OA clone, 512 epochs; GB, FY2025-26)

The #510 session ran both builds:

• E: Solve Pension Credit take-up over entitled benefit units #510 at f09497f (GB-only take-up solve) plus this change's TOTCAPB3 column, on policyengine-uk ef45fc1b (main + #2018 + #2019 + #1899 + #1940 + #1925).
• D′: Solve Pension Credit take-up over entitled benefit units #510 at f09497f alone, on the locked policyengine-uk 2.102.5.

	E	D′	DWP
Before calibration (survey weights)
GB reporters / of whom entitled	1,192k / 1,105k (93%)	1,196k / 771k (64%)
GB entitled benefit units	2,129k	1,368k	~2.2m implied
fill probability	0.209	0.129
GB claims / spending after the fill	1,341k / £6.17bn	859k / £3.64bn	1,382k / £6.14bn
After calibration
GB claims / spending	1,403k / £6.27bn	1,428k / £6.22bn	1,382k / £6.14bn
survey reporters (excluding SPI-synthetic copies), calibrated vs survey weights	1,251k vs 1,192k (+5%)	1,687k vs 1,196k (+41%)
SPI-synthetic reporters' calibrated weight (not anchored in #510)	58.6k	48.9k
take-up among entitled	60.2%	73.4%	62%
national fit: median abs(ratio-1) / share within 10%	4.0% / 83.9%	4.0% / 84.5%
Minimum guarantee +10% (same seeded flags)
newly entitled / share claiming	529k / 25.2%	214k / 20.4%
added spending (to the newly entitled)	£1.89bn (£0.081bn)	£1.89bn (£0.028bn)

Pensioner poverty rises in E. Relative AHC goes from 17.5% to 18.4% (all-person AHC 23.6% to 23.7%). I split it by running both datasets under both policyengine-uk trees (2025, calibrated weights):

pensioner relative poverty AHC	main code	combined code
D′ data and weights	17.39%	17.30%
E data and weights	19.76%	18.43%

• Code alone (D′ weights): −0.09pp.
• E's data and weights (combined code): +1.13pp.

The rise comes from calibration no longer inflating reporters. In D′ the +41% reporter upweight stood in for entitlement the model missed, and it crowded out entitled pensioners who don't claim. In E those people get their weight back. Pensioners in entitled, non-claiming benefit units rise from 0.70m to 1.29m, and those of them in AHC poverty from 0.16m to 0.32m. Take-up among the entitled falls to 60%, against DWP's 62%. The poverty figure moves away from HBAI, so it is called out here for review.

Remaining gap (all PRs, every unit filled; survey weights, 88k)

class	k
income more than 10% above the appropriate amount (misreporting or income measurement)	43.5
income within 10% of the appropriate amount	21.3
capital (FRS capital itself over the disregard)	8.6
mixed-age couples	5.7
Savings Credit age test at birthday boundaries	4.6
earnings	4.1

Most of this is survey reporting that the model should not chase.

Tests

tests/test_pension_credit_reported_capital.py checks four invariants:

1. Finite, non-negative TOTCAPB3 is carried over unchanged.
2. Missing, non-numeric or negative values become -1.
3. A table with no TOTCAPB3 column gives -1 throughout.
4. Over randomised inputs, the output is always -1 or non-negative, one per benefit unit.

Before merge

1. policyengine-uk#2018 merged and released; bump the lock here.
2. Integration build E: done; see the section above.
3. Decide whether to accept the pensioner-poverty move (+0.9pp relative AHC, from correct take-up weighting). This is part of d800.
4. Build E predates the SPI -1 change. That change only stops 24 SPI copies being entitled through their donor's FRS capital, and Solve Pension Credit take-up over entitled benefit units #510 already draws those copies rather than anchoring them, so the next batch build will show any effect.

axiom: n/a: data change

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