UK spine: condition SPI UC receipt on benefit-unit composition and add a UC-specific child count

[juaristi22]

Problem

PR #829 removes the two measured blockers affecting reported Universal Credit support: it carries FRS benefit-unit capital into uc_reported_capital, redraws capital coherently for SPI-channel reporters, and refreshes would_claim_uc after the last universal_credit_reported writer.

The rebuilt uk-publication-stack-829 candidate confirms that this repair works, but four UC with-children targets remain outside the 25% target-fit bound. The remaining deficit comes primarily from the joint distribution of SPI-imputed UC receipt, benefit-unit composition, and income rather than from capital or calibration grain.

This issue succeeds #828 for the residual after its capital-coherence fix. It also carries a smaller target-definition correction: the DWP child-count cells should use a UC-specific count that includes qualifying young people rather than the generic under-18 num_children variable.

Evidence

Applying #829 to the spine-k support raises initial positive-UC support from 4.264 million to 5.123 million benefit units, a gain of 0.859 million. Across the four deferred with-children cells, support rises by approximately 0.330 million. The final calibrated errors improve by 1–3 percentage points but remain between -26.6% and -33.6%.

Cell	DWP target	Support before #829	Support after #829	Gain	After / target
Single with children	2,213,760	893,072	997,023	+103,951	45.0%
Couple with children	911,392	698,834	862,655	+163,822	94.7%
One child	1,269,512	649,491	764,701	+115,210	60.2%
Two children	1,103,880	580,941	681,216	+100,276	61.7%
Five or more children	77,894	41,585	48,258	+6,673	62.0%

This identifies the family-shape residual more precisely: initial support for couples with children reaches 94.7% of the target, while support for lone parents reaches 45.0%. The numbered-child failures largely reflect the missing lone-parent mass.

The #829 blocker measurements also isolate the remaining mechanism:

• the union of reported-UC support blocked by false would_claim_uc or capital above £16,000 falls from 1.497 million to 0.019 million;
• approximately 1.249 million weighted SPI reporter benefit units still receive zero modeled UC because uc_income_reduction exhausts their pre-cap award; and
• capital, the benefit cap, and deductions do not explain that remaining reporter-zero mass.

Reporter-to-positive-award conversion differs sharply by source channel:

Family type	Base FRS	SPI support channel
Lone parent	632k / 665k = 95%	99k / 171k = 58%
Couple with children	459k / 533k = 86%	145k / 706k = 20%

These are aggregate, disclosure-safe measurements; no source records are disclosed.

Why this happens

The SPI income stage currently operates at person grain:

1. Stage 1 draws the SPI income vector using age, gender, and region.
2. Stage 2 draws universal_credit_reported with the other FRS-only outputs using age, gender, region, and six individual income predictors.

Neither stage conditions UC receipt on benefit-unit child count, lone-parent/couple status, partner income, or combined benefit-unit income. The stage can therefore draw a person as a UC reporter while independently drawing enough income for that person or their partner to eliminate the benefit unit's modeled UC award.

PR #829 correctly stratifies the later capital redraw by dependent-child band and couple status. That protects the receipt-capital relationship, but it cannot repair the earlier receipt-income relationship.

Proposed fix 1: impute UC receipt with benefit-unit predictors

Run a focused comparison between two implementations:

1. Add mapped benefit-unit predictors to the existing FRS-only stage-2 draw, including family type, UC child-count band, partner status, and combined benefit-unit income.
2. Split universal_credit_reported from the general person-level output vector and impute it at benefit-unit grain after SPI incomes exist.

The second approach has a narrower production blast radius because changing the current joint stage-2 model can also move pension contributions and every other benefit-reported output. A dedicated UC draw should condition on:

• lone parent, couple with children, single without children, or couple without children;
• UC-specific child count or 0/1/2/3+ band;
• summed benefit-unit employment and self-employment income;
• partner and investment income;
• region and claimant age; and
• positive modeled UC before take-up, so a reporter draw does not select a benefit unit whose income already eliminates its award.

The existing #829 capital-coherence stage should remain after the final reporter writer so it can redraw reporter capital and refresh would_claim_uc.

Proposed fix 2: add num_uc_children

The numbered-child target bindings currently use num_children, which counts benefit-unit members aged under 18. DWP counts children on the UC claim, including qualifying young people aged 16–19 in non-advanced education.

PolicyEngine-UK already exposes is_child_or_qualifying_young_person_for_universal_credit. Add a benefit-unit num_uc_children variable that sums this flag and bind the five DWP numbered-child targets to it.

This corrects the target semantics but does not explain most of the current deficit. On spine-k, approximately 78,000 weighted positive-UC benefit units change child count under the UC-specific definition. The one-child cell gains about 1,000 support, while the two-child and five-plus cells lose about 5,000 and 3,000 respectively.

Explicitly out of scope

• Do not raise the general would_claim_uc probability. The 0.55/0.70/0.85 probes primarily add childless claimants and reduce housing-benefit support.
• Do not force universal_credit > 0 solely because a source row reports UC.
• Do not add or renew target-fit exclusions as a substitute for changing the support distribution.
• Do not remove or suppress the SPI income or WAS wealth tails.

Acceptance criteria

• The UC reporter model conditions on benefit-unit family composition and combined income, not only person-level income.
• A before/after receipt reports weighted universal_credit_reported > 0 to universal_credit > 0 conversion by FRS/SPI channel and family type.
• Initial support increases for single_with_children and the failing numbered-child cells without relying on a general take-up increase.
• num_uc_children sums the existing UC child-or-qualifying-young-person flag at benefit-unit grain.
• The five DWP numbered-child target bindings use num_uc_children; the family-type cells remain at benefit-unit grain.
• The UK spine: preserve FRS benefit-unit capital for UC, re-anchor take-up after SPI (#828) #829 capital and would_claim_uc coherence stage remains after the final reported-UC writer, with its blocker receipt still green.
• A rebuilt candidate reruns calibration and the T0–T6 battery before retiring the four UC exclusions.
• The rebuild reports housing benefit, HMRC income-band, private-pension, and state-pension target movement so solver-pressure claims can be reassessed.

References

• UK spine: preserve FRS benefit-unit capital for UC while retaining WAS household wealth #828 — FRS capital and UC take-up coherence
• PR UK spine: preserve FRS benefit-unit capital for UC, re-anchor take-up after SPI (#828) #829 — implementation of UK spine: preserve FRS benefit-unit capital for UC while retaining WAS household wealth #828
• UC residual after the pension-wealth split: support 4.24m vs 6.76m — re-draw undershoot, the 0.55 take-up freeze, and composition shape #809 — prior UC support and take-up probes
• PR Re-bind the DWP UC composition and TCL disability-children targets to the publisher's grain (#808, #809) #813 — benefit-unit re-binding of the DWP UC composition targets
• Port UK compact source stages and 2024-25 refresh from uk-data #145 — draw-quality workstream
• WS-E spine deferrals: known bugs and signed inconsistencies awaiting their increment #796 — WS-E spine-deferrals tracker