Pre-existing defects in dynamics/participation.py that surface when the participation model is enabled

Summary

Four defects in policyengine_uk/dynamics/participation.py that predate #1828/#1829 and are dormant only because apply_participation_responses is commented out of its coordinator (dynamics/labour_supply.py:157). They should be resolved before the extensive margin is switched on.

Found across three adversarial reviews of #1828 and #1829. None is caused by those PRs, and I have deliberately not fixed them there — bundling them would have made both harder to review.

1. Demographic reads have no period argument

calculate_participation_elasticities calls sim.calculate("gender"), "is_married", "benunit_count_children", "youngest_child_age", "employment_income", "adult_index" and others without a period, while the quintiles handed to it were computed for an explicit year. Same at the adult_index read in apply_participation_responses.

So at year=2027 the model combines 2027 quintiles with default-period demographics and earnings. Silent, and wrong in a way that grows with the gap between the default period and the requested year.

2. Children set the bin edges for the spillover calculation

Every child is assigned quintile 1 — the highest-elasticity row of OBR Table A1 — giving them a mean elasticity of 0.492 against 0.217 for adults. They are correctly excluded from responses, but they are not excluded from pd.cut(elasticities, bins=20), which defines the elasticity groups used for the surplus/spillover loop. On enhanced_frs_2024_25 that is 23,265 children shifting how adults are grouped.

3. np.random.seed mutates global NumPy state

apply_participation_responses calls np.random.seed(random_seed), which reseeds the process-wide generator rather than a local Generator. Anything else drawing random numbers later in the same process is silently affected. policyengine-uk-data has already moved its own stochastic assignments to seeded generators for this reason.

4. Cost

Per call, impute_wages_for_nonworkers is recomputed four times, and calculate_gain_to_work triggers 2 x count_adults full household_net_income recomputes — eight complete model runs at the default count_adults=2. The two for i in np.where(...) loops iterate about 90,000 times in Python. A single invocation takes about 6.5 seconds on the Enhanced FRS; the stochastic loops are the obvious thing to vectorise.

Also worth knowing

The exit path (left_work, and the hours writeback for people leaving employment) has never been exercised: a tax cut produces entrants and no exits, and no test constructs a reform that pushes anyone out. It may be fine; it is simply unverified.

Start in policyengine_uk/dynamics/participation.py and inspect its calls from dynamics/labour_supply.py:157, including calculate_participation_elasticities and apply_participation_responses. Review existing participation tests and the untested exit path, then verify the four reported defects and the Enhanced FRS runtime behavior are addressed before enabling the coordinator.