Add the Child Tax Credit qualifying young person period after leaving education

[MaxGhenis]

Fixes #2290

Stacked on #2299, #2387 and #2279. Do not merge before them. This PR builds on #2299's Child Benefit routes (which carry #2387) and #2279's date fact. Until they merge, the diff here also shows their commits. This PR's own change:

git diff origin/cb-qyp-school-leaver-routes origin/ctc-qyp-school-leaver-routes

Summary

is_qualifying_young_person_for_child_tax_credit modelled only the education and training condition (Child Tax Credit Regulations 2002 reg. 5(3)(a) and (ab)). Two rules for a young person who has left education were missing:

Rule	Who	How the model reads it
Reg. 4	from the 16th birthday until the 31 August that next follows, with no education condition	is_before_first_september_following_16th_birthday (from #2279)
Reg. 5(3)(b)	under 18, for 20 weeks after leaving, while registered for work or training with a qualifying body	new input is_in_child_tax_credit_extension_period, false by default

The second condition (reg. 5(4)) applies to both. A young person who has left education or training and works 24 hours a week or more qualifies through neither.

Against its base (the item 1 branch at 2575e9e, which carries main 4d80b29 and #2279), 2024-25, YAML cases run as plain simulations on both (scratch/probe_C_base_vs_branch.txt):

Case	Variable	Base	This PR
1: parent 40, 16-year-old who has left school	young person's is_qualifying_young_person_for_child_tax_credit	false	true
	CTC_child_element	£0	£3,455
2: as 1, working 24 hours	young person's CTC QYP status	false	false (reg. 5(4)(a))
	young person's Child Benefit QYP status	true	true
11: 17-year-old in the 20 weeks	CTC_child_element	£0	£3,455

It changes years up to 2024-25: tax credits ended on 5 April 2025. This is a follow-up from #2279. It needs #2285, which stops a young person who heads their own benefit unit being their own qualifying young person (QYP).

The law

Child Tax Credit Regulations 2002:

• Reg. 4: "(1) Subject to paragraph (1A), a person who attains the age of sixteen is a qualifying young person from the date on which that person attained that age until 31st August which next follows that date. (1A) A person who attains the age of sixteen on 31st August is a qualifying young person from the date on which that person attained that age. (2) Paragraph (1) is subject to regulation 5 but as if there were no requirement to satisfy the first condition specified in paragraph (3) of that regulation. (2A) Paragraph (1A) is subject to regulation 5."
• Reg. 5(3)(b): the first condition is also met by a person "under the age of eighteen years and— (i) he ceased to receive full-time education or to undertake approved training (the date of that event being referred to as “the relevant leaving date”); (ii) within 3 months of the relevant leaving date, he has notified the Board [...] that he is registered for work or training with a qualifying body, and (iii) not more than 20 weeks has elapsed since the relevant leaving date."
• Reg. 5(4): "The second condition is that the period in question is not (and does not include)— (a) a week in which he (having ceased to receive full-time education or approved training) becomes engaged in remunerative work [...] (c) a period in respect of which that person receives income support, income-related employment and support allowance [...], income-based jobseeker's allowance [...] or universal credit".
• Reg. 2(1): "“remunerative work” means work which is— (a) done for payment or in expectation of payment, (b) undertaken for not less than 24 hours a week [...]".

HMRC's TCTM02220, which the entry-condition variable already cites, says: "There is no requirement for the qualifying young person to satisfy the condition of being in full-time non-advanced education or approved training up to and including 31 August following their 16th birthday. However, during this period, they have to satisfy the other conditions relating to qualifying young people."

Change

is_qualifying_young_person_for_child_tax_credit is now: aged 16 to 19, not receiving benefits in their own right (reg. 5(4)(c)), and any of

• in education or training begun before 19 (reg. 5(3)(a), (ab), (3A); unchanged);
• before the 31 August after the 16th birthday (reg. 4), unless the person has ceased full-time education or approved training and is in remunerative work (reg. 4(2) lifts the first condition only; reg. 5(4)(a));
• under 18, having ceased, not in remunerative work, in the 20 weeks (reg. 5(3)(b), 5(4)(a)).

New: is_in_child_tax_credit_extension_period (input), is_in_remunerative_work_for_child_tax_credit (average weekly hours of 24 or more), and the parameters remunerative_work_hours and extension_period_age_limit.

Having ceased. Reg. 5(4)(a) applies to a person "having ceased to receive full-time education or approved training", so a student's hours do not matter (YAML Case 4). Full-time education at a school or college counts at any level (reg. 5(5)): a 16-year-old in full-time advanced education has not ceased it, so works 24 hours and keeps the reg. 4 period (YAML Case 15), although advanced education fails the first condition. An apprentice's education is received by virtue of their employment and is treated as having ceased (Case 5). The review of this PR found that a first version took failing the non-advanced test as having ceased; the property oracle had the same mistake, and both are fixed.

Not modelled: interruptions (reg. 5(7)); the Working Tax Credit rules reg. 2(1) points to for counting hours.

The annual approximation, and a 16th birthday on 31 August

Reg. 4 reads #2279's date fact: a year counts if it starts (6 April) before the end of the period. That is every 16-year-old (age on 6 October) and a 17-year-old born from 1 September to 6 October.

Reg. 4(1A) gives a 16th birthday on 31 August no period without education. Its effect is to stop the period running to the next year's 31 August. The date fact already ends that person's period in the year of the birthday, so no separate exclusion is needed. That year still counts, as the one in which they are a child until 30 August (YAML Case 8), and the year after does not (Case 7). An exclusion for 31 August birthdays was written and removed: it would have dropped a year in which the person is a child for nearly five months.

Invariants

1. Reg. 4 against calendar arithmetic that shares no code with the model: a person outside education, not working, is a QYP for a year exactly when they are 16 to 19 on 6 October and some of the year falls on or before the last day they are a child or in the reg. 4 period (30 August for a 16th birthday on 31 August).
2. Over every combination of age, education, training, apprenticeship, own-right benefits, the age the course began, the two leaver facts and hours: the status is the education condition; or the reg. 4 period, unless the person has ceased education or training and is in remunerative work; or the 20 weeks for a person under 18 who has ceased and is not in remunerative work; within ages 16 to 19 and without own-right benefits. So remunerative work ends both routes for a person who has ceased and never a student's status, an advanced student keeps the reg. 4 period whatever their hours, the 20 weeks end at 18 and never reach a student whose course began at 19, and with the leaver facts off the status is the education condition's alone, as before.
3. Switching a leaver fact on never removes the status.
4. The benefit unit's child or QYP is a child or QYP who is not its claimant or partner and not looked after.

Tests

• Properties, new test_child_tax_credit_school_leaver_routes_properties.py:
  • invariant 1 for every date of birth from 2004 to 2009 (2,192 people, ages 14 to 20 on 6 October 2024), 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 12,288 combinations (the age the course began is drawn too: 17, or a course begun at 19);
  • invariants 2 and 4 on generated benefit units, where a claimant can be a QYP by status.
• Oracle, test_child_and_adult_definitions_properties.py: Child Tax Credit joins the other three programmes in the 16-year-old route, for a person who has left education.
• YAML, new child_tax_credit_school_leaver_routes.yaml, 16 cases hand-computed (2024-25; child element £3,455):

Case	Facts	Expected
1	parent 40, 16-year-old who has left school	QYP; one child element, £3,455
2	as 1, working 24 hours	not a QYP (reg. 5(4)(a)); Child Benefit still counts them
3	as 1, working 23 hours	QYP
4	16 at school, working 24 hours	QYP: the bar is for a person "having ceased"
5	16-year-old apprentice, 30 hours	not a QYP
6	born 15 September 2007 (17 on 6 October)	the period runs to 31 August 2024: QYP
7	born 31 August 2007	no period to the next 31 August: not a QYP
8	born 31 August 2008	a child until 30 August 2024: the year counts
9	16, receiving a benefit in own right	not a QYP (reg. 5(4)(c))
10	17, left school	not a QYP by default
11	17, in the 20 weeks	QYP (reg. 5(3)(b))
12	as 11, working 24 hours	not a QYP
13	18, extension input set	not a QYP
14	lone 16-year-old who has left school	a QYP by status, not their own
15	16, full-time advanced education, 24 hours	QYP: reg. 4(2) lifts the first condition, and they have not ceased education (reg. 5(5)); £3,455
16	17, the same student, outside the reg. 4 period	not a QYP; £0

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, 3, 6, 8, 14	all four
Reg. 5(3)(b) dropped	11	the grid; the generated units
No remunerative work bar for a leaver	2, 5, 12	the grid; the generated units
Remunerative work bars a student too	4	the grid; the generated units
The 20 weeks without the under-18 limit	13	the grid
Leaver routes open to a student whose course began at 19	none	the grid

Round 2 mutations at 33fa9ee (mutation/prC_r2.txt):

Mutation	YAML cases	Property tests
Failing the non-advanced test counts as having ceased (the round 1 bug)	15	the grid; the generated units
The 20 weeks open to a person who has not ceased	none	the grid
Remunerative work bars the reg. 4 period for everyone	15	the grid; the generated units

The rows above them were run at earlier heads, before the formula was restructured. The last of those first passed every test. The grid fixed the age the course began at 17, so it never drew a student who fails reg. 5(3A); it now draws a course begun at 19 as well. No YAML case can catch it without setting the 16th-birthday fact by hand for a 19-year-old: with the fact computed from the date of birth, a student who fails the entry condition is 19, the fact is false and the 20 weeks have ended, so the mutated and the real formula agree.

Run locally at 33fa9ee:

• policyengine-core test on the 8 YAML files the branch changes against main (the PRs below it included): 87 passed.
• pytest on the 7 Python test files it changes against main: 47 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: the item 1 branch at e626d3f (main e01f2f5, #2279, #2387 and #2299), so the figures are this PR's alone. Branch: 33fa9ee. Outputs: impact/prC_r2/.

No household's income changes in any year, and no tax credit award changes. Tax credits ended in April 2025; the model still computes the elements for later years, so they are shown, but no award follows from them.

• In 2024-25, 81 records (103,117 weighted people) become CTC qualifying young persons by status. 22 records (4,875 weighted) are in a family whose claimant now counts them, all aged 16 or 17 and outside education. As for Child Benefit, most are alone in their own benefit unit (FRS benefit units keep some qualifying young persons apart from the adults responsible for them policyengine-uk-data#562).
• CTC_child_element rises for those 22 benefit units: +£16.8m in 2024-25. None of them claims tax credits (is_CTC_eligible false and child_tax_credit £0 before and after; impact/prC_r1/context.txt on the earlier base), so child_tax_credit, tax_credits, net income and poverty are identical in every record and year.
• tax_credits_applicable_income is identical too. On the earlier base, without Count only the claimant's and partner's income in the legacy means tests #2387, it rose by £17,171.75 in 4 of those units, the newly counted young person's own miscellaneous_income (impact/prC_r1/income_probe.txt); Count only the claimant's and partner's income in the legacy means tests #2387 stops a young person's own income counting.

Reproducer: policyengine_uk/tests/test_child_tax_credit_school_leaver_routes_properties.py::test_status_is_the_first_condition_or_a_leaver_fact_under_the_second

axiom: CTC Regs 2002 reg 4, reg 5(3)(b) and reg 5(4)(a) TheAxiomFoundation/rulespec-uk#361 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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