Universal hours and the 2-year-old offer start on the age at 6 October, not the term after the birthday #2588

Since 2.147.2 (#2570), working-parent hours start with the first 1 January, 1 April or 1 September after a child reaches the minimum age (extended_childcare_entitlement_term_share, SI 2022/1134 reg 27). The universal 15 hours and the 2-year-old offer still use the whole age on 6 October, the date the engine places birthdays around. #2570 lists this under "Not in this PR".

The rule

• Universal hours start with the term after the third birthday: 1 April for a birthday from 1 January to 31 March, 1 September for 1 April to 31 August, and 1 January for 1 September to 31 December (SI 2014/2147 reg 3; DfE statutory guidance, A1.6).
• The 2-year-old offer starts the same way after the second birthday (DfE guidance A1.4).

What the model does

universal_childcare_entitlement_eligible and targeted_childcare_entitlement test the whole age on 6 October of the model year. In model year Y:

• Missed. A child born from 7 October to 31 December of Y−3 is 2 on 6 October, so it gets no universal hours. Under the rule it is funded from 1 January of Y+1, the spring term.
• Over-credited. A child born from 1 April to 6 October of Y−3 is 3 on 6 October, so it gets the whole year. Under the rule it is funded only from 1 September or 1 January.
• The 2-year-old offer has the same pattern one year down.

The two errors offset in a year's total hours only roughly. They disagree on who is funded in which term, which matters wherever a term is counted: DfE's January census and a reform's cost by term.

Proposed change

Give universal and targeted hours their own term share, as extended_childcare_entitlement_term_share does:

• the share of the year's three terms that start after the third (or second) birthday;
• read from the date of birth through utils.dates.term_starts;
• multiplied into the universal base and the targeted amount, beside early_years_term_share_before_school;
• eligibility needs a share above 0.

A household simulation that gives only a whole age is unchanged in the same way as #2570: the child is taken to be born on 6 April.

Context

Microcosm (PolicyEngine/microcosm#1338) now measures DfE's January registrations at the spring term. Its universal and 2-year-old rows count every child of the DfE age, mirroring the term-after-birthday start that the engine does not yet apply, so it can fit take-up against DfE without the engine's gap. Once this lands, the mirror can read the engine instead.

Related: #2570, #2567.