Capital gains realisation response

People choose when to realise capital gains, so a change in the tax on gains changes the gains realised. PolicyEngine UK models this realisation response for every reform: by default, realised gains respond at a retention-rate elasticity of 1.

How the response works¶

A reform scales each person’s realised gains by

where $G_0$ is their gains before the response (capital_gains_before_response), $t_0$ and $t_1$ their marginal rates on gains under the baseline’s and the reform’s rules, and $e$ the elasticity. $1 - t$ is the retention rate, the share of a marginal pound of gains kept after tax.

• The rates. Each rate is marginal_tax_rate_on_capital_gains, a share-weighted marginal rate across the person’s schedules (main rates, Business Asset Disposal Relief, residential property, carried interest). Both are measured at the person’s gains before the response, with every behavioural response switched off, so their difference reflects the reform alone.

• The schedules. Gains qualifying for Business Asset Disposal Relief or Investors’ Relief respond at capital_gains_badr_elasticity, and the rest at capital_gains_elasticity, both to the same change in the person’s rate.

• The result. capital_gains is the gains before the response plus capital_gains_behavioural_response, and capital_gains_tax charges the realised gains.

The default assumption¶

gov.simulation.capital_gains_responses.elasticity is 1.0, and gains qualifying for the relief take the same 1.0. This is PolicyEngine’s central assumption: the value Advani, Lonsdale and Summers (2024, pp. 36–37) use for the medium-term (five-year) effect of their reform package, with the range they consider, 0.5 to 2.0, as sensitivities.

The assumption has limits:

• For rate changes alone it is low. Their starting point is about 1.5, Agersnap and Zidar’s five-year estimate. They bring it down to 1.0 for their package’s base changes, removing the uplift at death and charging gains on emigration, and because taxing gains and income alike moves income back from gains into income tax, which they count as revenue kept. They expect a reform without those base changes to have a higher elasticity, and so lower revenue (p. 37). PolicyEngine adds no income tax back, so for a reform to rates alone their reasoning points to a higher value, such as their unadjusted 1.5. The default then overstates what a rate rise raises. Adopting 1.0 does not reproduce their revenue estimates.

• It is a medium-term value. The studies behind it find larger responses soon after a reform: about 1.6 at three to five years (Agersnap and Zidar) and 1.8 in the first year for large gainers in Canada (Lavecchia and Tazhitdinova), much of it retiming (pp. 34–35). Forestalling before a reform isn’t modelled either. A score for the first year after a reform is likely to understate the response.

• No income tax is added back. Shifting between gains and income is separate work (#1982, #1805), and the central value already includes a cross-base adjustment.

• The start date is a convention. The value applies in every period. Its start date is the start of the model’s timeline, not a change in law.

For a marginal rate on gains rising from 24% to 45%, the default scales realised gains by $0.55 / 0.76 \approx 0.7237$. A marginal tax rate elasticity of -0.7, a different convention, gives $(0.45 / 0.24)^{-0.7} \approx 0.6440$: the two are not interchangeable.

from policyengine_uk import Simulation

situation = {
    "people": {
        "person": {
            "age": {2026: 45},
            "employment_income": {2026: 100_000},
            "capital_gains": {2026: 200_000},
        }
    },
    "benunits": {"benunit": {"members": ["person"]}},
    "households": {"household": {"members": ["person"]}},
}
rates = {
    "gov.hmrc.cgt.higher_rate": {"2026": 0.45},
    "gov.hmrc.cgt.additional_rate": {"2026": 0.45},
}
reformed = Simulation(situation=situation, reform=rates)
# The marginal rate on the gains rises from 24% to 45%, so realised gains
# fall to 0.55 / 0.76 of £200,000, about £144,737.
print(reformed.calculate("capital_gains", 2026))

Large rate rises¶

With this response, the revenue from a single rate on gains peaks where the rate is $1 / (1 + e)$: 50% at the default, 40% at 1.5, 33% at 2.0 and about 22% at the 3.6 of the OBR comparison below. So for a large rate rise the elasticity can decide whether revenue rises or falls. In the example above, the person’s capital gains tax rises by £16,502 at the default and by £6,777 at 1.5, and falls by £20,536 at 3.6. Official costings can have the other sign. As of 2024, HMRC’s ready reckoner had a 10 percentage point rise in the top rates raising over £5bn before behaviour, and losing £2bn a year by the third year once behaviour is counted (Advani, Lonsdale and Summers 2024, p. 33).

What the response moves¶

• Household incomes. Realised gains are part of household market income. So the response moves household net income as well as the tax.

  • For a capital gains tax rise, net income falls by the tax plus the gains no longer realised. Those gains are deferred, not lost: the assets are still held.

  • In the example above, the person’s net income falls by £71,765 with the response and £41,370 without it. Revenue rises by £16,502, not £41,370.

  • Per-household impacts, income deciles, and winners and losers all count the gains not realised as income lost.

  This was already true for anyone who set an elasticity; the default makes it the published figure. For revenue, use gov_balance or the tax variables, not the change in household net income. Whether distributional measures should use gains before the response is an open methodology question.

• Reforms to other taxes. Income tax bands and allowances decide which capital gains tax rate gains fall in. So a reform to them changes the rate on some people’s gains, and their realisations respond.

  • With earnings of £30,000 and gains of £20,000, cutting the basic rate band to £20,000, or the personal allowance to £5,000, lowers realised gains by £1,463 (7.3%).

  • Costings that include capital gains tax, such as gov_balance, move with that response.

When there is no response¶

• No baseline. A simulation built directly in policyengine-core (as the YAML tests are) has no baseline to compare with.

• No elasticity. The static settings below switch the response off.

• The baseline’s rules. A simulation built without a reform, every branch of it, a reform’s own baseline, and a reform that changes only the behavioural response settings all apply their baseline’s rules. Their rates would be equal, so nothing is measured.

• No gains. Where no one has gains or losses, nothing is measured.

• No change at the margin. The response answers the rate on a person’s last pound of gains. A reform to one band’s rate does nothing for someone whose last pound falls in another band. Raising only the higher rate to 45% raises the example person’s tax from £47,280 to £65,642 with no response, as their last pound of gains is taxed at the unchanged additional rate.

The response answers changes in the rules. A simulation whose inputs change while its rules don’t has no response. Marginal tax rates on earnings hold realised gains at the simulation’s own values: a pay rise is not a reform for the response to answer.

Rules changed after a simulation is built count too. A simulation built without a reform keeps a copy of itself, taken when it was built, as its baseline. If a modifier then edits its parameters, it responds against that copy.

Other assumptions¶

Every setting is an ordinary parameter, so a reform or scenario can change it for the years it covers. A reform dict’s year key, such as "2026", covers that fiscal year only; "2000-01-01.2100-12-31" covers every year.

RESPONSES = "gov.simulation.capital_gains_responses"
EVERY_YEAR = "2000-01-01.2100-12-31"

# Static: no response.
static = {
    f"{RESPONSES}.elasticity": {EVERY_YEAR: 0},
    f"{RESPONSES}.mtr_elasticity": {EVERY_YEAR: 0},
    f"{RESPONSES}.separate_badr_elasticity": {EVERY_YEAR: False},
}
# CenTax's sensitivities, or any other value.
lower = {f"{RESPONSES}.elasticity": {"2026": 0.5}}
upper = {f"{RESPONSES}.elasticity": {"2026": 2.0}}
# The OBR's elasticities: 3.6 for main-rate gains and badr_elasticity's 1.4
# for qualifying gains. This compares elasticities, not the OBR's full
# costing, which includes further effects.
obr = {
    f"{RESPONSES}.elasticity": {"2026": 3.6},
    f"{RESPONSES}.separate_badr_elasticity": {"2026": True},
}
static_costing = Simulation(situation=situation, reform={**rates, **static})

The response scales the gains already in the data, so it can’t change their level. A comparison in pounds with the OBR’s costing therefore mixes the gap between the elasticities with any gap in the level of gains and capital gains tax.

The marginal tax rate convention¶

gov.simulation.capital_gains_responses.mtr_elasticity scales gains by $(t_1 / t_0)^{e}$ instead, and can’t be combined with a retention-rate elasticity in the same period.

• The default gives way. Where the retention-rate settings keep their defaults, an MTR elasticity applies alone in its periods and the retention-rate elasticities count as zero. A CapitalGainsResponseWarning says so, once per tax-benefit system and period.

• Silencing the warning. Setting the retention-rate elasticity to 0 for the same periods gives the same results without the warning.

• Conflicts raise. A retention-rate elasticity changed to a nonzero value raises a ValueError alongside an MTR elasticity, as does a separate relief elasticity.

• An explicit 1. A retention-rate elasticity set to its default of 1 can’t be told apart from the default, so it resolves in the same way.

legacy = {f"{RESPONSES}.mtr_elasticity": {"2026": -0.7}}
# Warns: the retention-rate default counts as zero in 2026.
with_warning = Simulation(situation=situation, reform={**rates, **legacy})
# The same results, without the warning.
explicit = {**legacy, f"{RESPONSES}.elasticity": {"2026": 0}}
without_warning = Simulation(situation=situation, reform={**rates, **explicit})

The assumption a simulation applies¶

capital_gains_response_assumption resolves a simulation’s settings for a year as the response does, after every reform and modifier applied so far. Its to_dict() gives the convention, the elasticities for main-rate and qualifying gains, the MTR elasticity, the separate relief switch, and whether each is the default, an override or set to zero for an MTR elasticity. It is there to record with a run’s results.

from policyengine_uk.utils.capital_gains import capital_gains_response_assumption

print(capital_gains_response_assumption(reformed, 2026).to_dict())

Moving from the static default¶

The elasticity used to default to 0, so CGT reforms were costed statically unless a caller set an elasticity.

• Static results. Set the static settings above for the years you run.

• MTR elasticity alone. Results are unchanged, with a warning. Set the retention-rate elasticity to 0 to silence it.

• Revenue. Realised gains are part of household income. With a response, the change in household net income no longer equals the change in revenue, so use gov_balance for reforms that move the tax on gains.

• Household and distributional results. They now count gains no longer realised as income lost, and reforms to income tax bands and allowances move realised gains too (see What the response moves).

Runtime¶

A reform that changes the rules measures two marginal rates on gains per simulation and year: one for the reform and one for its baseline. Each recalculates capital gains tax, and what it depends on, in branches of the simulation; on the enhanced FRS that adds about two seconds per reformed simulation and year. Simulations without a reform, baselines, reforms to the behavioural settings alone, and populations without gains skip the measurement.

The marginal rate on gains is the rise in capital gains tax per pound of marginal gains. Realised gains reach household net income only as market income and through that tax, so it is also the share of marginal gains net income does not keep; a test checks that no other variable reads realised gains.