HMRC CGT aggregate and size-of-gain band targets are mutually infeasible (aggregate includes trusts) #607

What is wrong

The HMRC CGT calibration targets in policyengine_uk_data/targets/sources/hmrc_cgt.py can't all be met at once, so calibration with non-negative weights has to trade them off. An independent review of PR #557 found this, and the problem already affects main's 2024+ targets.

• The aggregate targets require 378,000 taxpayers and £65.900bn of gains.
• The nine size-of-gain bands require 275,000 taxpayers and £62.207bn above £12,300 (hmrc_cgt.py:65–68, 163–179, 201–229 on Calibrate SPI income bands to their projected values, and map the 2023-24 outturn to 2023 #557's head c9229ee).
• The contradiction: the band compute functions put every above-AEA gain at £12,300 or more into those bands. So the other 103,000 people must have gains below £12,300, and can contribute at most about £1.267bn. The targets require £3.693bn, so the bound is broken by about £2.43bn.
• The likely cause: HMRC's headline CGT taxpayer count includes individuals and trusts (https://www.gov.uk/government/statistics/quality-report-taxpayers-and-traders/quality-report-numbers-of-taxpayers-and-registered-traders), while the size-of-gain bands describe individuals.

The review checked this by running the real compute closures on 24 synthetic boundary cases in 2023 and 2024. Its evidence is in the hub's review folder for #557.

Related

• Calibrate SPI income bands to their projected values, and map the 2023-24 outturn to 2023 #557 first tried to also move the CGT base year to 2023, which would have switched this infeasible set on for 2023. That part is deferred: Calibrate SPI income bands to their projected values, and map the 2023-24 outturn to 2023 #557 is now narrowed to the SPI fix.
• Start capital gains on HMRC's 2024-25 size-of-gain table #571 (capital gains on HMRC's 2024-25 size-of-gain table) changes the band source. Re-check the feasibility against Start capital gains on HMRC's 2024-25 size-of-gain table #571's bands before fixing.

Fix

On top of #571:

1. Make the aggregate and band targets consistent: individuals only. Either exclude trusts from the aggregate, or drop the aggregate where the bands cover the same population. Cite the source split.
2. Move the CGT base year to the PE convention: 2023-24 is PE year 2023.
3. Add a feasibility regression test. For every year, the aggregate taxpayers and gains must be reachable given the band partition, the AEA and the below-band ceiling.