Labour supply dynamics - PolicyEngine UK documentation

The dynamics module enables modelling of behavioural responses to tax and benefit policy changes. When you change income tax rates or benefit amounts, people may respond by adjusting their work patterns - either changing hours worked (intensive margin) or deciding whether to work at all (extensive margin). This guide shows how to incorporate these dynamic effects into your analysis.

Understanding labour supply responses¶

PolicyEngine UK implements the Office for Budget Responsibility’s labour supply elasticity framework. The model captures two key behavioural responses:

Intensive margin (progression) - How people adjust their working hours in response to changes in take-home pay. Someone facing a higher marginal tax rate might reduce their hours, while someone benefiting from a tax cut might work more.

Extensive margin (participation) - Whether people choose to work at all. Changes in the financial reward from working affect decisions to enter or leave employment.

Both responses depend on elasticities that vary by demographic group. The current apply_dynamics coordinator runs progression only: it leaves participation disabled and returns participation=None. The separate participation function remains available for controlled development work; the coordinator does not combine its response with progression.

Basic dynamics calculation¶

To apply dynamics to any microsimulation, create baseline and reformed simulations, then call apply_dynamics:

from policyengine_uk import Microsimulation
from policyengine_uk.model_api import Scenario

# Define baseline and reform scenarios
baseline_scenario = Scenario(
    parameter_changes={
        "gov.hmrc.national_insurance.class_1.rates.employee.main": 0.12,
    }
)

reform_scenario = Scenario(
    parameter_changes={
        "gov.hmrc.national_insurance.class_1.rates.employee.main": 0.10,
    }
)

# Create microsimulations
baseline = Microsimulation(scenario=baseline_scenario)
reformed = Microsimulation(scenario=reform_scenario)

# Set up baseline link and apply dynamics
reformed.baseline.apply_parameter_changes(baseline_scenario.parameter_changes)
dynamics = reformed.apply_dynamics(2025)

# View FTE impacts
print(
    f"Substitution effect FTEs: {dynamics.fte_impacts.substitution_response_ftes:,.0f}"
)
print(f"Income effect FTEs: {dynamics.fte_impacts.income_response_ftes:,.0f}")
if dynamics.fte_impacts.participation_response_ftes is not None:
    print(
        f"Participation FTEs: {dynamics.fte_impacts.participation_response_ftes:,.0f}"
    )
print(f"Total FTE change: {dynamics.fte_impacts.ftes:,.0f}")

This example models a 2 percentage point cut in National Insurance contributions and calculates the resulting change in full-time equivalent employment.

Working with dynamics results¶

The apply_dynamics method returns a LabourSupplyResponseData object containing detailed results:

# Access progression responses (intensive margin)
progression = dynamics.progression
print(f"Workers affected: {len(progression):,}")
print(f"Average hours change: {progression['total_response_ftes'].mean():.3f} FTEs")

# Access participation responses (extensive margin)
participation = dynamics.participation
if participation is not None:
    print(f"Employment change: {participation['participation_change'].sum():,.0f}")

# FTE impacts provide summary statistics
fte = dynamics.fte_impacts
print(f"Total labour supply response: {fte.ftes:,.0f} FTEs")

The progression DataFrame contains individual-level responses including wage changes, elasticities applied and resulting employment income adjustments. Participation results are absent from the current coordinator.

Separate participation calls¶

policyengine_uk.dynamics.participation.apply_participation_responses accepts an explicit year for demographics, gain-to-work counterfactuals and earnings/hours writeback. calculate_participation_elasticities also accepts a year; omitting it uses the simulation default. These calls use the weighted Microsimulation interface, including situations supplied without a population dataset.

Partnership groups include cohabiting couples, as corrected in PR #2445. Spillover bins use eligible response candidates only. The existing coefficients, 20 bins, unweighted within-bin averages and spillover assumptions remain unchanged.

A local numpy.random.RandomState preserves the seeded MT19937 draw order: ascending worker rows, then ascending non-worker rows, including zero-probability and nonpositive-wage candidates. It leaves NumPy’s global random state unchanged. Entrants’ weekly hours use WEEKS_IN_YEAR to produce annual hours. The current coordinator still returns no participation results; cost and performance work remains open in issue #1836.

Analysing distributional effects¶

Combine dynamics with standard microsimulation analysis to understand how behavioural responses vary across the population:

# Get individual responses
progression = dynamics.progression

# Add demographic information
progression["decile"] = reformed.calculate(
    "household_income_decile", 2025, map_to="person"
)
progression["age_group"] = pd.cut(
    reformed.calculate("age", 2025),
    bins=[0, 30, 50, 65, 100],
    labels=["Under 30", "30-49", "50-64", "65+"],
)

# Analyse by income decile
by_decile = progression.groupby("decile").agg(
    {
        "total_response_ftes": "sum",
        "substitution_response_ftes": "sum",
        "income_response_ftes": "sum",
    }
)

print("FTE changes by income decile:")
print(by_decile.round(0))

Understanding the elasticity framework¶

The model uses different elasticities for different groups based on empirical evidence:

# Examine elasticities applied
elasticities = progression[["substitution_elasticity", "income_elasticity"]].describe()
print("Elasticity distribution:")
print(elasticities)

# See which groups have different elasticities
progression["has_children"] = reformed.calculate("is_parent", 2025)
by_parent = progression.groupby("has_children")[
    ["substitution_elasticity", "income_elasticity"]
].mean()
print("\nElasticities by parental status:")
print(by_parent)

Substitution elasticities range from 0.094 to 0.439 depending on demographics, while income elasticities range from -0.185 to 0. Lone fathers and lone mothers use the same youngest-child age groups and coefficients from OBR Table A2. The participation coefficient helper also assigns both sexes to the lone-parent rows in OBR Table A1; apply_dynamics currently applies only progression responses. The model excludes certain groups from responses: self-employed workers, students, those aged 60+, and adults beyond the two oldest in each household. Their employment income is left unchanged.

Validating against OBR estimates¶

For policies analysed by the OBR, compare your results with their published estimates:

# Example: National Insurance cut from Autumn Statement 2023
# OBR estimated ~94,000 FTE increase

baseline_scenario = Scenario(
    parameter_changes={
        "gov.hmrc.national_insurance.class_1.rates.employee.main": 0.12,
    }
)

reform_scenario = Scenario(
    parameter_changes={
        "gov.hmrc.national_insurance.class_1.rates.employee.main": 0.10,
    }
)

baseline = Microsimulation(scenario=baseline_scenario)
reformed = Microsimulation(scenario=reform_scenario)
reformed.baseline.apply_parameter_changes(baseline_scenario.parameter_changes)

dynamics = reformed.apply_dynamics(2025)
print(f"Modelled FTE increase: {dynamics.fte_impacts.ftes:,.0f}")
print(f"OBR estimate: 94,000")
print(f"Difference: {(dynamics.fte_impacts.ftes - 94_000):+,.0f}")

This example runs the current progression-only coordinator. It is not a validation of the disabled participation route or a promise of agreement with the OBR total. Data, grouping, imputation and calibration choices also affect the comparison.

Elasticity-based responses¶

Separately from apply_dynamics, a reform can set gov.simulation.labour_supply_responses.substitution_elasticity and gov.simulation.labour_supply_responses.income_elasticity. Each person’s employment_income_behavioral_response is then their employment income before responses times the substitution elasticity times relative_wage_change, plus the income elasticity times relative_income_change. Both changes compare the reform with its baseline (simulation.baseline), each measured with every behavioural response switched off and at the reform’s earnings and capital gains before responses: relative_wage_change is the relative change in one minus the marginal tax rate, and relative_income_change the relative change in household net income. The changes are capped at gov.simulation.labour_supply_responses.bounds. The response is part of employment_income, so it feeds into every result that depends on it.

Two things follow from measuring against simulation.baseline:

The baseline is current law. simulation.baseline is built without the reform, whatever policy a comparison treats as its baseline. When two simulations are compared and the elasticities are set on the reform side only, the reform’s response also answers the comparison’s baseline policy. For a single earner on £30,000 in 2026, the response to a 22% basic rate is about -£187, and to that rate plus a £13,000 personal allowance about -£193. Compared with the 22% rate costed without responses, the second reform shows the whole -£193, not the -£6 or so the allowance adds. Setting the elasticities on both sides of the comparison isolates the reform’s own response.
Only earnings and gains are held. Both measurements take the reform’s earnings and capital gains before responses. Any other input the reform’s scenario changes (a data modifier, say, or removing economic assumptions) keeps each simulation’s own value, so the difference counts as policy in relative_income_change.

from policyengine_uk import Simulation

situation = {
    "people": {"person": {"age": {2025: 30}, "employment_income": {2025: 40_000}}},
    "benunits": {"benunit": {"members": ["person"]}},
    "households": {"household": {"members": ["person"]}},
}
reformed = Simulation(
    situation=situation,
    reform={
        "gov.hmrc.income_tax.rates.uk[0].rate": {"2025": 0.30},
        "gov.simulation.labour_supply_responses.substitution_elasticity": {
            "2025": 0.25
        },
        "gov.simulation.labour_supply_responses.income_elasticity": {"2025": -0.05},
    },
)
# The marginal rate rises from 28% to 38%, so the wage after tax falls by 5/36,
# and net income falls by £2,743 of £32,145: a response of about -£1,218.
print(reformed.calculate("employment_income_behavioral_response", 2025))

Unlike these labour supply elasticities, which are zero unless a reform sets them, capital gains respond to reforms by default: see the capital gains realisation response.

Technical implementation details¶

The dynamics calculation proceeds through several steps:

Marginal rate calculation - Computes effective marginal tax rates by simulating small income changes
Elasticity application - Applies group-specific elasticities to wage and income changes
Response calculation - Determines employment income adjustments based on elasticities
FTE conversion - Translates income changes to full-time equivalent employment

The model follows OBR methodology when the gov.dynamic.obr_labour_supply_assumptions parameter is true (default for 2024 onwards).

Limitations and considerations¶

When using dynamics, be aware of these limitations:

The model assumes no general equilibrium effects (wages don’t adjust)
Elasticities are based on historical evidence and may not apply to very large reforms
Self-employed workers are excluded as their labour supply is harder to model
The model doesn’t capture long-term effects like human capital accumulation

The size of these limitations has not been established for every reform. Participation calibration and broader performance work remain outside these implementation corrections.