UK CGT: impute BADR gains, bind the Table 3 gains-by-income joint, and condition gain carriers on wealth (post-#979 level and income-interaction findings) #1014

Why

The #979 national candidate (c5f107ab…, staged 2026-09-23) fits 74 of its 77 CGT rows within 10% and 60 within 1%, yet the CGT it carries is unstable against the income targets and does not look like real households. Measured on that file, its spine, the #1006 control calibration (spine-assessment-v23-ctl, 1,062 targets on the same 33-stage spine plus the income-anchor stages) and the eFRS 1.57.3 file:

1. The engine cannot tax BADR gains, so the calibration is fitting a tax function it cannot match. HMRC 2024-25: 61,000 individuals claimed BADR or Investors' Relief on £18.4bn of gains, taxed £1.8bn at 10% (Table 4.1). Neither dataset carries a BADR column, so the engine charges those gains at the main rates (the 2024 fiscal-year blend, 21.7% higher). That is the whole of the hmrc.cgt.liability_total miss: gains land at −1.3%, liability at +10.3% (£24.8bn on £117.7bn against HMRC's £22.5bn on £119.3bn), and the tax-by-age rows sit at +10.0% (45–54), +13.0% (55–64) and +14.6% (65–74) while the gains-by-age rows fit within 1%. The same rows sit at +12.8% and +18.8% in the UK income anchors at the calibration year and reserved top-tail income rows (income-anchor lane, PolicyEngine/chronicle#280) #1006 control run. At 2026-27 it is about £1.2bn of the dashboard's £30.0bn baseline (24% instead of 18% on ~£20bn). PolicyEngine/policyengine-uk#1861 (merged, 2.99.x; microcosm-build already requires ≥2.100.0) added the capital_gains_badr input and schedule, so the engine side is done.

2. Gains by taxable income is not a target, and the calibration moves it freely. HMRC Table 3 (2024-25) is the surface the amounts are drawn from, so the prior spine reproduces its all-gains margin: taxpayers 292k / 51k / 94k / 23k / 35k / 62k across the six bands against published 292k / 49k / 93k / 21k / 34k / 62k, gains within 3–22% per band. HMRC's own summary: 55% of gains come from the 17% of CGT-liable individuals with taxable income above £125,140. After the UK CGT: interpolate the sub-exempt remainder, anchor the clone incidence, and fence projected entrants (#970) #979 solve the £50,000–99,999 band holds £34.7bn of gains against £17.2bn published, the £200,000+ band £42.5bn against £55.1bn, the £125,140–199,999 band 23k taxpayers against 34k, and the share of gains above £125,140 of income is 41%. Under the UK income anchors at the calibration year and reserved top-tail income rows (income-anchor lane, PolicyEngine/chronicle#280) #1006 control's target set the same rows land elsewhere again (£0–37,699 band £32.1bn against £24.6bn; above-£125k share 47%). The 76 Table 3 band facts have stayed fenced since UK capital gains: imputed distribution has no top tail, missing 55% of CGT #552 (UK: banded CGT gains targets (by size of gain) to constrain the distribution, not just count + total #467, UK CGT top-tail age and geography joints inherit from incidence and look off — benchmark against HMRC marginals #725).

3. The gain carriers are drawn on income alone, and their wealth does not fit their gains. cgt_incidence_clone and cgt_band_donors use the Advani–Summers percent_with_gains by total-income band; the redraw ranks by prior amount within income band; the asset-type stage assigns a type afterwards. Among liable gainers on the UK CGT: interpolate the sub-exempt remainder, anchor the clone incidence, and fence projected entrants (#970) #979 file, the Spearman correlation of gains with gross financial wealth is 0.04, with corporate wealth 0.03, with property wealth 0.07. Of the 74 rows with £1m+ gains, 62% have zero corporate wealth and 66% under £100k of financial wealth (median £52k). The £1m–5m gainers' median financial wealth is £65k; the £5m+ gainers are 23% owner-occupiers. On main the SPI copies' and band donors' WAS columns are additionally the FRS parent's (UK spine: make SPI support households internally consistent (SPI-first order, housing shell) #1012).

4. Why it is unstable. 1,003 person rows carry every liable gain; 15 carry half; one band-donor row (weight 100, a £172m gain, the Pareto top stratum of the £5m+ × £200k+ cell) carries 13% of the national total at prior and is halved by calibration; the effective sample size of weighted gains is 29 at prior and 23 after. Those rows also carry the income and region targets: each liable row has non-zero loadings on 21–97 targets (median 46); the 1,061 liable rows carry 52% of the private-pension £500k–1m amount row, 34% of the North East 200k+ total-income row and 23% of the SPI savings-interest 200k+ row. The 120 demoted (sub-exempt) band donors, blind to every CGT row, carry 23–35% of several 200k+ region and ITL rows, which is why the entrants fence reads 68.5k on the UK CGT: interpolate the sub-exempt remainder, anchor the clone incidence, and fence projected entrants (#970) #979 target set and 146.9k on UK income anchors at the calibration year and reserved top-tail income rows (income-anchor lane, PolicyEngine/chronicle#280) #1006's (see the diagnosis in UK income anchors at the calibration year and reserved top-tail income rows (income-anchor lane, PolicyEngine/chronicle#280) #1006 (comment)). With no income joint in the loss, the solver fits the size-band, age and region rows by re-weighting whichever heavy rows the income side leaves it.

The level and its projection profile (2024-25 is the forestalling year; our GDP-per-capita uprating carries the spike flat while the OBR path dips and then grows) are a separate question: PolicyEngine/uk-cgt-reform#2 and the #875 deliverable deferred to the next vintage. This issue is about the three structural fixes that hold the joints.

WP1: impute BADR-qualifying gains (main-based)

• Chronicle first. HMRC CGT Table 4 is not on the feed. Package Tables 4.1–4.4 (2021-22 to 2024-25; individuals by eight bands of BADR/IR-qualifying gain, trusts total, all total; taxpayers, qualifying gains, tax at the 10% rate). 2024-25 individuals: 61k / £18,443m / £1,821m. By band (lower limit, taxpayers k, gains £m): 0: 5 / 32; 10k: 8 / 129; 25k: 6 / 224; 50k: 8 / 575; 100k: 11 / 1,866; 250k: 8 / 2,901; 500k: 8 / 5,929; 1m+: 7 / 6,787. Gains are before losses and the exempt amount. Source: Table_4_2026_Business_asset_disposal_and_investors_reliefs.ods in the 2026 release.
• Spine. Write capital_gains_badr (the engine's merged BADR/IR input) in hmrc_cgt_asset_type_spine or a sibling stage right after it: among liable gainers not flagged residential, with a main asset type in the business-asset and unlisted-share types, flag claimants and set the qualifying amount so the household-weighted count and gains by Table 4.1 band match, with the same solve pattern as the residential flag (declared propensity, weighted systematic walk, reported Bernoulli envelope). Qualifying gain ≤ min(net gain, the £1m lifetime limit); the 1m+ band's mean of £970k says the limit binds. Add person.capital_gains_badr to the export allow-list (terminal_gates.py and gates.json), the coverage manifest, the H2 parity fixture and the certification digests.
• Calibration. cgt_2024_tax then carries the BADR schedule. Expect hmrc.cgt.liability_total from +10.3% to within a few percent with gains_total unchanged, and the tax-by-age rows inside tolerance. Whether the Table 4 totals become fitted rows or diagnostics is a ruling (below).
• Dashboard. capital_gains_badr flows through uk-cgt-reform unchanged; the 2026-27 baseline should drop by about £1.2bn and the reckoner's BADR rows become runnable.
• Acceptance. Table 4.1 bands within publication rounding on the spine; residential flags, targets and every non-CGT column byte-identical; liability within 3% at 2024 with gains within 1%; the age rows fit.

WP2: bind the Table 3 gains-by-income joint (stacked on #1006)

• Rows. The all-gains margin of Table 3: six taxable-income bands (£0–37,699; 37,700–49,999; 50,000–99,999; 100,000–125,139; 125,140–199,999; 200,000+) × taxpayers and gains, 12 rows, from hmrc_cgt_conditioning_facts.json (dimension cgt_taxable_income_band, record set hmrc.cgt_table3_2026.ty2024.all_gains). Family hmrc_cgt or a new hmrc_cgt_income family under family_equal (ruling).
• Measurement. The shape of hmrc.cgt.taxpayers_by_gain_band: parameter_gated_threshold on cgt_2024_gains, groupby_variable plus band_filter_dimension, with a new dated measure cgt_2024_taxable_income in measure_simulation._CGT_CALIBRATION_VARIABLES (engine adjusted_net_income less allowances at 2024, HMRC's taxable-income concept). The redraw's component-sum proxy is the fallback; report both side by side once.
• Why stacked on UK income anchors at the calibration year and reserved top-tail income rows (income-anchor lane, PolicyEngine/chronicle#280) #1006. The contract, registry pins and frozen scoring register are where UK income anchors at the calibration year and reserved top-tail income rows (income-anchor lane, PolicyEngine/chronicle#280) #1006 lives (1,124 references, uprating appliers, two new families), and the distortion is largest under its target set, so it has to be measured there. Stacked PRs get no CI: local funnel plus the targeted shard.
• Measurement plan. Twin calibration on the UK income anchors at the calibration year and reserved top-tail income rows (income-anchor lane, PolicyEngine/chronicle#280) #1006 spine with and without the 12 rows: the Table 3 joint, the fence entrants, the 15 heaviest rows' weight ratios, the effective sample size of weighted gains, and the income-tax and SPI 200k+ band fits. The conflict becomes explicit in the loss; some SPI or ITL rows may worsen, and that is the point. Independently of the rows, add a Table 3 drift check to the terminal battery so a solve that moves an income band's gains by more than a declared share is visible.

WP3: condition the gain carriers on wealth as well as income (stacked on #1012; investigate first)

• Why after UK spine: make SPI support households internally consistent (SPI-first order, housing shell) #1012. On main every SPI copy and band donor carries its FRS parent's WAS wealth. UK spine: make SPI support households internally consistent (SPI-first order, housing shell) #1012 runs the SPI block before was_wealth, so the SPI half's wealth follows its income (investment income against financial wealth 0.14 → 0.63; band donors' median financial wealth £48k–67k → £209k–1.57m by band). Conditioning the CGT draw on wealth before that would bake the inheritance in. The CGT stages already run after WAS in every tree.
• Candidate designs, decided after measuring. (a) Propensity = Advani–Summers(income band) × a wealth tilt in the household's gross financial, corporate and non-main-residence property wealth, normalised within income band so the Table 3 margins are untouched. (b) Asset type first: draw the Table 7 type, then require the matching stock (financial wealth for shares, other residential property for residential gains, corporate wealth for business assets and BADR), ranking within type by the stock. (c) Both.
• Anchors. No published joint of gains with wealth exists, so this is a declared modelling assumption checked against what does exist: Table 7 composition by gain band (already a diagnostic), Table 8's residential gainers against second-property ownership, WAS shares of unlisted-share and business-asset holders among top-income households, and CenTax's remuneration-including-gains profiles where usable.
• Measurement. Joint of gains with each stock; the share of £1m+ gainers with zero relevant stock; the Table 3, age and region margins unchanged; downstream, the SPI savings-interest and dividend band fits and any wealth-conditioned reform on the dashboard.

Stacking and order

• WP1 on main now, after the Chronicle Table 4 package; whichever of WP1 and UK income anchors at the calibration year and reserved top-tail income rows (income-anchor lane, PolicyEngine/chronicle#280) #1006 lands second re-pins the stage roster, coverage manifest, parity fixture and digests (mechanical).
• WP2 stacked on UK income anchors at the calibration year and reserved top-tail income rows (income-anchor lane, PolicyEngine/chronicle#280) #1006, measured on its spine before UK income anchors at the calibration year and reserved top-tail income rows (income-anchor lane, PolicyEngine/chronicle#280) #1006's own licensed rebuild so the two effects are not confounded.
• WP3 stacked on UK spine: make SPI support households internally consistent (SPI-first order, housing shell) #1012 once its measurement is in; an investigation memo before any implementation.
• None of it should predate UK income anchors at the calibration year and reserved top-tail income rows (income-anchor lane, PolicyEngine/chronicle#280) #1006 or UK spine: make SPI support households internally consistent (SPI-first order, housing shell) #1012: the derived surfaces would be regenerated twice and the measurement basis would move underneath.

Related, not in scope

• Demoted band donors and lighter rows (120 donors per band, more carriers in the top Table 3 cells): UK CGT: sub-exempt gains capped at exactly the annual exempt amount become 10.8m taxpayers under uprating; interpolate the remainder below the threshold and anchor incidence #970's open ruling.
• Level and projection profile: PolicyEngine/uk-cgt-reform#2, UK CGT: translate the 2024-25 gains outturn to the 2025 calibration year (forestalling year; OBR CGT +44.2% signed on the stack register) #875.
• UK CGT top-tail age and geography joints inherit from incidence and look off — benchmark against HMRC marginals #725 (age and region joints), Capital gains as primitives: asset-class positions + accrued gains + realization model, with dual-mode provenance #320 (gains as primitives, long-run).

Decisions needed

1. WP2 family and grain: rows in hmrc_cgt or a new family; the 12 margin rows or also the 6 × 10 cells.
2. WP2 grouping concept: engine taxable income at 2024 or the redraw's proxy.
3. WP1: Table 4 totals as fitted rows or diagnostics; IR folded into BADR (the engine's input already merges them).
4. WP3 design after the investigation.

🤖 Generated with Claude Code