Add the Child Benefit qualifying young person routes for young people who have left education

[MaxGhenis]

Fixes #2287

Stacked on #2387 and #2279. Do not merge before them. This PR reads #2279's date fact (is_before_first_september_following_16th_birthday), and #2279 waits on d1345. It needs #2387, which stops a young person's own income counting in the parent's Housing Benefit, Income Support, tax credit and Council Tax Reduction means tests: without it, a working school-leaver this PR makes a young person would bring their earnings into those tests. Until both merge, the diff here also shows their commits. This PR's own change, against main with both merged:

git diff $(git merge-tree --write-tree $(git merge-tree --write-tree origin/main origin/uc-pc-qyp-sixteen-route) origin/means-tests-dependants-income) origin/cb-qyp-school-leaver-routes

Summary

is_qualifying_young_person_for_child_benefit modelled only the education and training condition (Child Benefit (General) Regulations 2006 reg. 3). A young person who had left education was never a Child Benefit qualifying young person (QYP), and so never a "young person" for Housing Benefit, Income Support, income-based JSA, income-related ESA or Council Tax Reduction in England and Wales, which all take the Child Benefit definition (SSCBA 1992 s.142).

This PR adds the three conditions for young people who have left:

Regulation	Who	How the model reads it
4	under 17, left education, until the 31 August after the 16th birthday	is_before_first_september_following_16th_birthday (from #2279)
5	under 18, registered with the careers service, not in remunerative work, for a 20-week extension period the responsible person asked for	new input is_in_child_benefit_extension_period, false by default
7	under 20, from leaving until the terminal date (end of February, May, August or November)	new input is_before_child_benefit_terminal_date, false by default

Reg. 7(3) pays no Child Benefit "by virtue of this regulation" in a week of remunerative work. The model applies it to the Child Benefit amount only, so the young person stays a QYP for the legacy schemes.

Against its base (main 4d80b29 with #2279 merged), 2026-27, the YAML cases below run as plain simulations on both (scratch/probe_B_main_vs_branch.txt; the base has no input for the reg. 5 and reg. 7 routes, so the probe drops them there):

Case	Variable	Base	This PR
1: parent 40, 16-year-old who has left school	young person's is_qualifying_young_person_for_child_benefit	false	true
	child_benefit_entitlement	£0	£1,406.60
	is_lone_parent	false	true
7: 17-year-old in an extension period	child_benefit_entitlement	£0	£1,406.60
10: 18-year-old before the terminal date, 23 hours	child_benefit_entitlement	£0	£1,406.60
11: as 10, 24 hours	young person's QYP status	false	true
	child_benefit_entitlement	£0	£0 (reg. 7(3))

This is a follow-up from #2279. It needs #2285, which stops a young person who heads their own benefit unit being paid Child Benefit for themselves.

The law

Child Benefit (General) Regulations 2006:

• Reg. 2(2): "Where more than one of those regulations apply to a person, he is a qualifying young person until the last of them ceases to be satisfied."
• Reg. 4: "(1) This regulation applies in the case of a person who has not attained the age of 17 and who has left relevant education or training. (2) Subject to paragraph (3), the condition is that the 31st August next following the person's 16th birthday has not passed. (3) In the case of a person who attains the age of 16 on 31 August in any year, the condition is that the 1st September immediately following has not passed."
• Reg. 5: "(1) This regulation applies in the case of a person who has not attained the age of 18. (2) The condition is that— (a) the person has ceased to be in education or training; (b) the person is registered for work, education or for training with a qualifying body; (c) the person is not engaged in remunerative work; (d) the extension period which applies in the case of that person has not expired; (e) immediately before the extension period begins, the person who is responsible for him is entitled to child benefit in respect of him without regard to this regulation; and (f) the individual who is responsible for that person, within three months of that person's ceasing education or training, has made a request for the payment of child benefit during the extension period [...]". The period "ends 20 weeks after it started" (reg. 5(3)).
• Reg. 7: "(1) This regulation applies in the case of a person who has not attained the age of 20. (2) The condition is that the period found in accordance with Cases 1 and 2 has not expired in that person's case". Case 1 runs "from the date on which he ceases to receive relevant education or approved training, up to and including— (a) the week including the terminal date", which is "(a) the last day in February, (b) the last day in May, (c) the last day in August, (d) the last day in November, whichever first occurs after the date on which the person's relevant education or approved training ceased". "(3) Child benefit is not payable in respect of a qualifying young person by virtue of this regulation for any week in which he is engaged in remunerative work."
• Reg. 1(3): "“remunerative work” means work of not less than 24 hours a week— (a) in respect of which payment is made; or (b) which is done in expectation of payment".
• Reg. 8: the person must not be receiving income support, income-based JSA, incapacity benefit, a tax credit, ESA or universal credit.
• HB Regs 2006 reg. 19(1): a young person is "a person who falls within the definition of qualifying young person in section 142 of the Act". IS Regs 1987 reg. 14(1) says the same of "section 142 of the Contributions and Benefits Act".

Change

• is_qualifying_young_person_for_child_benefit: aged 16 to 19, not receiving benefits in their own right (reg. 8), and any of: education or training begun before 19 (reg. 3, unchanged); the reg. 4 date fact; the reg. 5 extension condition; the reg. 7 input.
• New meets_qualifying_young_person_extension_period_condition_for_child_benefit: under 18, the extension input, and not in remunerative work (reg. 5(1), (2)(c)).
• New is_in_remunerative_work_for_child_benefit: average weekly hours of 24 or more, with a new parameter remunerative_work_hours.
• New is_child_benefit_payable_for_person: the unit's child or QYP, unless they qualify through reg. 7 alone and are in remunerative work (reg. 7(3) with reg. 2(2)). child_benefit_child_index and child_benefit_respective_amount read it, so a barred young person does not take the eldest-child rate.
• The legacy flag is_child_or_young_person_for_legacy_benefits is not edited. It follows the Child Benefit QYP, so Housing Benefit, the legacy benefits, lone-parent status and Council Tax Reduction pick the routes up.

Not modelled: reg. 6 (interruptions), reg. 7 Case 2 beyond the input, and the Income Support, incapacity benefit and tax credit limbs of reg. 8. The Income Support limb is #2302, stacked on this PR; the own-right input here covers Universal Credit, ESA and JSA.

The annual approximation for reg. 4

Reg. 4 ends on 31 August (1 September for a 16th birthday on 31 August). Universal Credit's route in #2279 ends "up to, but not including" 1 September. Both dates fall in the same fiscal year, so a year that starts (6 April) before one starts before the other, and reg. 4 reads #2279's fact unchanged. As there, a year counts if any of it falls in the period: every 16-year-old (age on 6 October), and a 17-year-old born from 1 September to 6 October. #2279 sets out the bias of that rule; this PR follows it so that Child Benefit, Universal Credit and Pension Credit agree on a 16-year-old.

Invariants

1. Reg. 4 against calendar arithmetic that shares no code with the model: a person outside education is a QYP for a year exactly when they are 16 to 19 on 6 October and the year starts on or before the reg. 4 end date, for every date of birth.
2. Over every combination of age, education, training, own-right benefits, the three leaver facts and hours, the status is the union of the four conditions within ages 16 to 19 and without own-right benefits. So each condition ends at its age limit, own-right benefits exclude every condition, and with the leaver facts off the status is reg. 3's alone, as before.
3. Switching a leaver fact on never removes the status.
4. Child Benefit is payable for the unit's child or QYP unless they qualify through reg. 7 alone and are in remunerative work; they stay a QYP and a legacy young person.
5. Child Benefit entitlement is the eldest payable member at the eldest rate and each other at the additional rate, for 52 weeks.

Tests

• Properties, new test_child_benefit_school_leaver_routes_properties.py:
  • invariant 1 for every date of birth from 2006 to 2011 (2,191 people, ages 14 to 20 on 6 October 2026), with the 31 August, 1 September and 6/7 October edges asserted, and again on Hypothesis-drawn dates of birth and years;
  • invariants 2 to 4 over 6,144 combinations (8 ages, every education value, training, own-right benefits, hours of 0, 23 and 24, and the 8 combinations of the three facts);
  • invariant 5 on generated benefit units, from the inputs and the weekly rates alone.
• Oracle, test_child_and_adult_definitions_properties.py: Child Benefit joins Universal Credit and Pension Credit in the 16-year-old route.
• YAML, new child_benefit_school_leaver_routes.yaml, 16 cases hand-computed (2026-27; eldest rate £27.05 × 52 = £1,406.60):

Case	Facts	Expected
1	parent 40, 16-year-old who has left school	QYP; Child Benefit £1,406.60; legacy young person; lone parent
2	16-year-old apprentice, 30 hours	QYP and paid: reg. 4 has no education or work condition
3	born 15 September 2009 (17 on 6 October)	the period runs to 31 August 2026: QYP
4	born 31 August 2009	the period ended on 1 September 2025: not a QYP
5	17 and 18, left school	neither is a QYP by default
6	16, receiving a benefit in own right	not a QYP (reg. 8)
7	17, in an extension period	QYP (reg. 5)
8	as 7, working 24 hours	not a QYP (reg. 5(2)(c))
9	18, extension input set	not a QYP (reg. 5(1))
10	18, before the terminal date, 23 hours	QYP and paid (reg. 7)
11	as 10, 24 hours, earning £20,000	still a QYP and a legacy young person; Child Benefit £0 (reg. 7(3)); the parent's HB, IS and CTR applicable income £0: the young person's earnings are not the parent's (#2387)
12	16, before the terminal date, 40 hours	paid: reg. 4 also applies (reg. 2(2))
13	parent, working 18-year-old before the terminal date, child of 10	the child of 10 is the eldest paid child: £1,406.60
14	20, terminal input set	not a QYP
15	two 16-year-olds, one at school, one left	(£27.05 + £17.90) × 52 = £2,337.40
16	lone 16-year-old who has left school	a QYP by status, not their own

• Changed expectation. housing_benefit_applicable_income_childcare_element.yaml asserted that a disabled 16-year-old outside education "is not a relevant young person". Reg. 4 makes them a young person until 31 August, so HB reg. 28(6) counts them (1 relevant child, £9,000). The case is split in two: the default, and the same person with the reg. 4 period ended, which keeps the original point that the disability age extension does not itself create the status.

Mutation checks, each applied alone in a copy of the branch (YAML cases and property tests that fail):

Mutation	YAML cases	Property tests
Reg. 4 dropped	1, 2, 3, 15, 16	both calendar tests; the union grid
Reg. 5 dropped	7	the union grid
Reg. 7 dropped	10, 11	the union grid
Reg. 5 without the remunerative work bar	8	the union grid
Reg. 5 without the under-18 limit	9	the union grid
Reg. 7(3) ignored (always payable)	11, 13	the union grid
Reg. 7(3) bars every working young person	2, 12	the union grid; the entitlement count
Remunerative work from 25 hours	8, 11	the union grid

Run locally at e626d3f (logs in the session folder):

• policyengine-core test on the 7 YAML files the branch changes against main (Count 16-year-olds outside education as UC and Pension Credit qualifying young persons until the 1 September after their 16th birthday #2279's and Count only the claimant's and partner's income in the legacy means tests #2387's included): 71 passed.
• pytest on the 6 Python test files it changes against main: 43 passed.
• The whole stack at c6c46e6 (this PR's line with Count 16-year-olds outside education as UC and Pension Credit qualifying young persons until the 1 September after their 16th birthday #2279, Count only the claimant's and partner's income in the legacy means tests #2387 and the Child Benefit, CTC, terminal-date and Income Support follow-ups): policyengine-core test on the 198 YAML files that mention these programmes, 2,000 passed; pytest on the 76 Python test files that mention them is still running and will be added here.
• ruff format --check and ruff check on policyengine_uk: clean.

The full suites run in CI.

Microsimulation impact

Real runs on Enhanced FRS 2024-25 (uk-data 1.58.0, sha256 5ba399ea5ab9a6c7), one run each for 2024-25 to 2030-31, exact comparison of every record. Base: main e01f2f5 with #2279 (9d2fadb) and #2387 merged (a local merge, eeabc65e3), so the figures are this PR's alone. Branch: e626d3f. Outputs: impact/prB_r2/ in the session folder.

Who changes. In 2026-27, 102 records (203,321 weighted people) become Child Benefit qualifying young persons by status. Only 22 records (4,929 weighted) are in a family whose claimant now counts them: in the microdata most 16-year-olds outside education are the only member of their own benefit unit, apart from their parents (PolicyEngine/policyengine-uk-data#562), and since #2285 nobody is their own QYP.

Aggregates (£ million a year):

Variable	Records that differ	2024-25	2026-27	2030-31
child_benefit	22	+4.6	+4.9	+5.5
household_tax	4 (8 in 2030-31)	+1.5	+1.6	+1.8
household_net_income	22	+3.1	+3.3	+3.6
housing_benefit_applicable_income	22	+3.1	+3.3	+3.6
council_tax_reduction_applicable_income	22	+3.1	+3.3	+3.6

The tax is the High Income Child Benefit Charge: in 2026-27 the change in household_tax equals the change in CB_HITC exactly (impact/prB_r2/hitc_check.txt).

Per benefit unit in 2026-27 (impact/prB_r2/context.txt): in 16 units the new Child Benefit (£930.80, the additional rate, or £1,406.60) is added to both applicable incomes in full. In 4 units the charge takes back all or nearly all of it, so the applicable incomes move by under £1 either way. In the 2 units whose parent becomes a lone parent, Council Tax Reduction income rises by the £1,406.60, and Housing Benefit income by £1,040 less, because the lone parent earnings disregard is £25 a week where a single claimant's is £5. No Housing Benefit, Income Support, Council Tax Reduction, Universal Credit, tax credit or Pension Credit award changes in any year: these families are not on those benefits. is_lone_parent changes for those 2 records (35 weighted).

Winners and losers (household_net_income, changes over 50p):

Year	Gaining (records / weighted households)	Mean gain	Losing
2024-25	18 / 3,530	£886	0
2026-27	20 / 4,274	£781	0
2030-31	18 / 3,628	£1,001	0

In 2026-27 the gaining households by decile of base household income: 1 (529 weighted), 2 (863), 3 (1,419), 4 (283), 6 (475) and 9 (706, each gaining £0.59 after the charge). People in poverty after housing costs fall by 3,899 and before housing costs by 196.

Reproducer: policyengine_uk/tests/test_child_benefit_school_leaver_routes_properties.py::test_status_is_the_union_of_the_four_conditions

axiom: Child Benefit (General) Regulations 2006 regs 2, 4, 5, 7 and 8 TheAxiomFoundation/rulespec-uk#356 queued (addendum; blocker stated there: the rows are in an unreleased ingest, axiom-corpus#765, and a billed encoder run needs approval)

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