Cap the eligible rent at the LHA before the Housing Benefit taper

[MaxGhenis]

Fixes #1917

Problem

housing_benefit_entitlement took the taper off the rent, capped the result at the Local Housing Allowance, and then took off non-dependant deductions: max(0, min(max(0, rent - taper), LHA_cap) - non_dep_deductions). When the rent exceeded the LHA by at least the taper, the cap absorbed the whole taper. When the excess was smaller, the cap still cut the taper by the excess.

2026, applicable income and amount set as inputs	main	this PR
Single aged 70, private renter, rent £30,000, LHA £9,467.64, taper 0.65 × (£14,948.80 − £13,312) = £1,063.92	£9,467.64	£8,403.72
Rent £12,000, LHA £9,467.64, taper £5,200	£6,800.00	£4,267.64
Rent £30,000, LHA £9,467.64, taper £13,000	£9,467.64	£0
Couple, rent £9,000, LHA £8,000, taper £2,724.93, non-dependant deductions £3,346.20 (rulespec-uk pipeline case 4)	£2,928.87	£1,928.87
Rent £8,000 below the LHA, taper £1,063.92	£6,936.08	£6,936.08 (unchanged)
Council tenant with the case 4 numbers (LHA does not apply)	£2,928.87	£2,928.87 (unchanged)

The first row is also reproduced end to end from household inputs (a single 70-year-old with State Pension £16,000 and no Guarantee Credit): housing_benefit is £9,467.64 on main and £8,403.72 here.

Law

Current revised texts, read on legislation.gov.uk (CLML data.xml) on 2026-09-30.

• SI 2006/213 reg 12D(2)(a) (same words in SI 2006/214 reg 12D(2)(a)): where a maximum rent (LHA) is determined, "the amount of a person's eligible rent shall be the maximum rent (LHA)".
• SI 2006/213 reg 13D(5) (and SI 2006/214 reg 13D(5)): "Where the applicable local housing allowance exceeds the cap rent, the maximum rent (LHA) shall be the cap rent." The cap rent is, by reg 13D(12), "the aggregate of such payments specified in regulation 12(1) (rent) which the claimant is liable to pay". So the maximum rent (LHA) is the lower of the LHA and the cap rent, which LHA_cap models as min_(benunit_rent, BRMA_LHA_rate).
• SI 2006/213 reg 70 (and SI 2006/214 reg 50): "The amount of a person's appropriate maximum housing benefit in any week shall be 100 per cent. of his eligible rent calculated on a weekly basis ... less any deductions in respect of non-dependants".
• SSCBA 1992 s.130(3)(b): "if his income exceeds the applicable amount, the amount of the housing benefit shall be what remains after the deduction from the appropriate maximum housing benefit of prescribed percentages of the excess of his income over the applicable amount". SI 2006/213 reg 71 and SI 2006/214 reg 51 set that percentage at "65 per cent".
• Northern Ireland is the same, with different numbering: SR 2006/405 reg 13C(2)(a) (eligible rent is the maximum rent (LHA)), reg 14D(5) (cap rent), reg 68 (maximum HB is eligible rent and rates less non-dependant deductions) and reg 69(b) ("in calculating the amount of a rent rebate or allowance, 65 per cent."), under SSCB(NI)A 1992 s.129(3)(b); pension age SR 2006/406 regs 13C(2)(a), 14D(5), 48 and 49(b). NI households use the same LHA path in the model (the LHA rent list includes Northern Ireland BRMAs).

So the award is max(0, eligible rent − non-dependant deductions − taper), with eligible rent min(rent, LHA) for LHA tenants: the cap comes first, then the deductions and the taper.

Change

housing_benefit_entitlement:

eligible_rent = where(lha_eligible, LHA_cap, benunit_rent)                # reg 12D(2)(a), 13D(5)
maximum_housing_benefit = eligible_rent - housing_benefit_non_dep_deductions  # reg 70
taper = max_(0, applicable_income - applicable_amount) * withdrawal_rate      # s.130(3)(b), reg 71
return max_(0, maximum_housing_benefit - taper)

Social (non-LHA) tenants get the same result as before: for them the old formula reduces to max(0, rent − taper − deductions). The variable now has a documentation string and references to all the provisions above (GB working age and pension age, and NI).

Also:

• housing_benefit_entitlement.yaml, "Reduced rent with LHA": the expectation was the capped-after-taper value. Rent 8,000, LHA_cap 1,000, taper 0.65 × (11,000 − 1,000) = 6,500: the law gives max(0, 1,000 − 6,500) = 0; main gave min(8,000 − 6,500, 1,000) = 1,000. The other three cases there are unchanged.
• The Housing Benefit docs page (stages 1 and 3 of "How PolicyEngine computes Housing Benefit") said the eligible rent is benunit_rent capped at the LHA and described the taper against the rent. It now describes the cap, the maximum benefit and the taper in the legal order.

Other places checked for the same post-taper cap, none found:

• Council Tax Reduction (simulated_council_tax_reduction_benunit, _legacy.py): max(0, liability × maximum support − taper − non-dependant deductions), no rent cap.
• Universal Credit (uc_housing_costs_element): caps the rent at uc_LHA_cap inside the housing element, before the award-level taper.
• housing_benefit_baseline_entitlement only reads the baseline simulation's housing_benefit_entitlement, so it follows this change.

Invariants

For every benefit unit, with taper = 0.65 × max(0, applicable income − applicable amount):

1. 0 ≤ HB ≤ eligible rent ≤ rent; for LHA tenants HB ≤ LHA_cap = min(rent, LHA rate).
2. HB = max(0, eligible rent − non-dependant deductions − taper).
3. HB is non-increasing in applicable income and non-dependant deductions, and non-decreasing in rent, the LHA rate and the applicable amount.
4. For an LHA tenant whose rent is at or above the LHA rate, more rent changes nothing.
5. Differential against the old order: the two agree for social tenants, where the rent is at or below the LHA, where there is no taper, and where the old award was 0. Otherwise the new award is lower, by exactly min(rent − LHA_cap, taper, old award) (derived in the test docstring; intended).
6. End to end, for pension-age renters with and without a working-age non-dependant, housing_benefit satisfies invariant 2 in the model's own applicable income, applicable amount and non-dependant deductions.

Invariants 1, 2 and 5 also hold on every one of the 61,223 benefit units in the Enhanced FRS runs below (checked in the diagnostics script).

Tests

• New housing_benefit_lha_order.yaml, 9 cases, every expectation computed by hand with the arithmetic in comments: the Bug case at unit level and end to end from household inputs; rent below the LHA; a taper between the rent excess and the LHA; a taper above the LHA; no taper; rulespec-uk pipeline case 4; a council tenant with case 4's numbers; deductions above the LHA. Applicable income and amount are inputs, so the Housing Benefit earnings disregard and the Guarantee Credit passport (both being fixed separately) cannot move any expectation. The end-to-end case also sets BRMA_LHA_rate to 9,467.64, the value the model computes for that household in 2026, so it pins the order and not the LHA table.
• New test_housing_benefit_lha_order_properties.py: Hypothesis (derandomize=True), invariants 1-6, three tests:
  • 15 generated populations of 10-40 benefit units, for the bounds, the closed form and the differential;
  • 10 populations, each with five perturbed copies, for monotonicity;
  • 10 end-to-end populations of 5-20 pension-age households, some with a working-age non-dependant.
• Each test also runs an explicit example where the orders differ, with the arithmetic worked by hand in comments:
  • for the unit-level tests, one unit for each term of the minimum in invariant 5: the taper binds (the bug case), the rent excess binds (rent 12,000), and the old award binds (the new award is 0, the old 275.07);
  • end to end: the single pensioner from the issue, alone and with a working-age non-dependant, and a pension-age couple.
• The strategies start the LHA and the applicable amount at realistic levels. Hypothesis favours small draws, and an LHA of a few pounds would leave every tapered award at 0, where the two orders agree.
• Coverage of the examples the tests actually run, counted by wrapping the real test functions:
  • unit level: 12 of 273 units in 6 of the 16 populations fall where the orders differ (5 bound by the taper, 6 by the rent excess, 1 by the old award);
  • end to end: 10 of 88 eligible households have rent above the LHA, a positive taper and HB above 0.
• The file takes about a minute of CPU (55.6 s user and 7.3 s system, including the import).
• Against main (the old formula), 6 of the 13 YAML cases in the two entitlement files fail: the five new cases where the orders differ, and the corrected old case. All three property tests fail on their explicit examples.
• Runs on this branch (local, 2026-09-30):
  • targeted YAML (every file under finance/benefit/family/housing_benefit/ and gov/dwp/pension_credit/, plus uc_legacy_mutual_exclusion.yaml): 122 passed, 0 failed, re-run on the head 02aa1eb;
  • full YAML suite (policyengine-core test policyengine_uk/tests/policy -c policyengine_uk): 1,285 passed, 0 failed, on 3a45d23. Later commits change only comments, docs, the changelog and the property tests;
  • property tests: 3 passed, re-run on 02aa1eb;
  • non-microsimulation pytest suite (-m "not microsimulation"): 318 passed, 15 skipped, 30 deselected (local, in the builder's worktree; the log does not record the commit).
• CI Test: passed on ee18b85, the head before the changelog-only commit (run 36728861200); on the head 02aa1eb it is queued (run 36739417546).
• ruff format --check . is clean.

Dataset impact (Enhanced FRS 2024-25, current weights, real runs of main vs this branch)

2026	main	this PR	change
Housing Benefit	£14.227bn	£14.225bn	−£2.0m
HB caseload (benefit units)	1,711.7k	1,711.7k	0
of which wholly pension-age	£13.843bn	£13.841bn	−£1.6m
mixed-age	£0.200bn	£0.200bn	0
working-age	£0.184bn	£0.184bn	−£0.3m
UC / Pension Credit / Council Tax Reduction / benefit cap reduction	£79.32bn / £6.99bn / £2.35bn / £1.18bn	unchanged	0
Household net income			−£2.0m (= HB change)
AHC poverty, pensioners	10.814%	10.818%	+0.004pp
AHC poverty, all / BHC poverty, all	18.664% / 14.357%	18.665% / 14.357%	+0.001pp / 0

Who moves (benefit units receiving HB on main, weighted):

	all	pension-age	mixed-age	working-age
HB recipients	1,711.7k (1,279 records)	1,664.4k	19.3k	28.0k
LHA tenants	564.3k (178)	547.8k	13.0k	3.6k
rent above the LHA	370.4k (92)	367.4k	1.1k	1.8k
… with a positive taper: lose HB	1.8k (12)	1.4k (8)	0	0.4k (4)
… with no taper: unchanged	368.6k (80)	366.0k	1.1k	1.4k

Only those who have the LHA applied, pay rent above it and have income above the applicable amount can lose, and all 12 of those records do. They are six pairs of records with identical inputs and different weights. Nobody gains, and nobody loses all their HB. The loss is the taper for 10 records (1.6k weighted) and the excess of rent over the LHA for 2 (0.2k). The effect is small because most HB recipients who pay rent above the LHA have no taper. For 334.1k of the 368.6k (52 records) the model computes Guarantee Credit above zero and housing_benefit_applicable_income is 0, which is what the current Guarantee Credit passport, unchanged here, gives (it sets applicable income to 0 when someone in the unit is over State Pension age and guarantee_credit > 0). Of those, 48 records (332.9k) receive Pension Credit and 4 (1.2k) do not (see "Not in this PR"). The rest have applicable income at or below the applicable amount.

housing_benefit_entitlement also changes for 655 records (654k weighted, 593 of them working-age) that do not receive HB (not eligible or not claiming), so housing_benefit does not change for them.

Caveat: the Enhanced FRS weights were calibrated to an HB total under the old code. The figures are from impact/dataset_impact.py and impact/compare_impact.py on a read-only copy of enhanced_frs_2024_25.h5; the breakdown is from impact/diag_lha.py, which also checks that main's entitlement equals the old formula, this branch's equals the new one, and old − new = min(rent − LHA_cap, taper, old) on every benefit unit.

Not in this PR

• The protections in reg 12D(3) (on a death) and 12D(5) (13 weeks where the claimant could afford the rent when taken on), and the reg 12M transitional protection, are not modelled, before or after this change.
• How the eligible rent itself is derived (benunit_rent, LHA_cap, BRMA_LHA_rate) is unchanged.
• Interaction with the Guarantee Credit passport fix: 4 records (1.2k weighted; 2 pension-age, 2 mixed-age) are HB recipients with rent above the LHA whose applicable income is 0 through the passport although they receive no Pension Credit. If the passport comes to key on receipt, any of them with income above the applicable amount would start to pay a taper, and this change would then apply to them.
• Combined effect of the three HB means-test fixes: a real run with all three merged on 1c5b4d0 (Key the Housing Benefit Guarantee Credit passport on receipt #1927 at 58ee875, Take Housing Benefit earnings disregards from net earnings only #1908 at 8bed988 and this PR at ee18b85, which differs from the head only in the changelog; research files impact/combined.json and impact/combined_vs_main.json) gives Housing Benefit £14.227bn → £13.780bn in 2026 (−£0.447bn), with 170.2k benefit units losing, none gaining, and 80.4k of the losers losing all their HB. That run does not include Abolish working-age Housing Benefit from 1 July 2026 (NI 1 October 2026) #1910 or Split pension-age Housing Benefit allowances by when State Pension age was attained #1913, and has not been repeated with them.
• The working-age −£0.3m above will change once Abolish working-age Housing Benefit from 1 July 2026 (NI 1 October 2026) #1910 lands. Abolish working-age Housing Benefit from 1 July 2026 (NI 1 October 2026) #1910 multiplies housing_benefit_entitlement by housing_benefit_payable_share in housing_benefit_pre_benefit_cap, and that share is the part of the year before the abolition date (1 July 2026 in Great Britain, 1 October 2026 in Northern Ireland) for a unit with no one over State Pension age. None of the 4 working-age records that lose here has a member over State Pension age, so their loss would be scaled down by that share. Not run.
• LHA_eligible is "renting and no member in social housing". SI 2006/213 reg 13C(5) (same words in SI 2006/214 reg 13C(5)) says the maximum rent (LHA) rules do "not apply in a case where" the landlord is a registered social landlord or registered provider of social housing, "paragraph 4(1)(b) of Schedule 3 to the Consequential Provisions Regulations (savings provision) applies", "the tenancy is an excluded tenancy of a type mentioned in any of paragraphs 4 to 11 of Schedule 2", the claim relates to "a houseboat, caravan or mobile home" or "rent payable in relation to a hostel", or the rent officer has found "a substantial part of the rent" attributable to board and attendance. LHA_eligible does not test any of the cases after the first. The model's accommodation_type has a MOBILE category ("Caravan/Mobile home or houseboat"), but LHA_eligible does not read it, so it treats those cases as LHA cases too, and the new order reaches them. Unchanged by this PR.
• SI 2006/213 reg 75 and SI 2006/214 reg 56: Housing Benefit "shall not be payable where the amount to which a person would otherwise be entitled is less than 50 pence per benefit week". Not modelled, before or after this change, so an award the new order cuts below 50p a week stays positive.
• The Northern Ireland rates side: SR 2006/405 reg 68(b) adds "100 per cent. of his eligible rates" to the maximum, and reg 69(a) sets the taper "in calculating the amount of a rate rebate, 20 per cent.". No Housing Benefit variable models a rate rebate (domestic_rates enters household tax and net income only), so NI households get the rent side only, before and after this change.
• Overlap with open PRs: no other open PR edits the variable or the tests this PR changes. git merge-tree of this head with each of Replace generic child and adult flags with each programme's legal definitions #1896 (16940d8), Take Housing Benefit earnings disregards from net earnings only #1908 (8bed988), Abolish working-age Housing Benefit from 1 July 2026 (NI 1 October 2026) #1910 (bd9272a), Split pension-age Housing Benefit allowances by when State Pension age was attained #1913 (f159ff4) and Key the Housing Benefit Guarantee Credit passport on receipt #1927 (d8c24d9) is clean.
  • Replace generic child and adult flags with each programme's legal definitions #1896 edits Housing Benefit files including housing_benefit_assessable_capital.py, housing_benefit_applicable_income_disregard.py and LHA_category.py, none of which this PR touches. The end-to-end YAML case sets BRMA_LHA_rate as an input, so a change in the LHA category cannot move it.
  • Take Housing Benefit earnings disregards from net earnings only #1908 (earnings disregards) does not touch these files.
  • Abolish working-age Housing Benefit from 1 July 2026 (NI 1 October 2026) #1910 (working-age abolition) edits housing_benefit_pre_benefit_cap.py, the direct consumer of housing_benefit_entitlement: it multiplies the entitlement by housing_benefit_payable_share. That scales whatever this PR's formula returns and does not depend on the order inside it.
  • Abolish working-age Housing Benefit from 1 July 2026 (NI 1 October 2026) #1910, Split pension-age Housing Benefit allowances by when State Pension age was attained #1913 and Key the Housing Benefit Guarantee Credit passport on receipt #1927 edit other parts of the Housing Benefit docs notebook: the introduction and abolition section (Abolish working-age Housing Benefit from 1 July 2026 (NI 1 October 2026) #1910), the applicable amount section (Split pension-age Housing Benefit allowances by when State Pension age was attained #1913), and a new Guarantee Credit passport paragraph in the eligibility section (Key the Housing Benefit Guarantee Credit passport on receipt #1927). This PR edits stages 1 and 3 of the computation list.

axiom: SI 2006/213 regs 12D(2)(a), 70 and 71 (and SI 2006/214 regs 50-51) — TheAxiomFoundation/rulespec-uk#370 queued

🤖 Generated with Claude Code

[vahid-ahmadi]

Reviewed: approve with nits. The new order is max(0, where(LHA, min(rent, LHA), rent) − non-dependant deductions − 0.65 × excess). It matches regs 12D(2)(a) and 13D(5) (SI 2006/213 and 2006/214), reg 70 and SI 2006/214 reg 50, and regs 71 and 51 under SSCBA s.130(3)(b).

The council-tenant result is unchanged (I checked the algebra), and zero rent, rent below the LHA and non-dependant deductions above the rent all floor at 0. I hand-checked all 9 YAML cases. Locally the HB and Pension Credit YAML tests pass (120) and the property tests pass (3). Merged with #1927, 136 pass.

1. Nit: the label in LHA_cap.py:12, "Applicable amount for LHA", is now wrong for what the variable holds. Rename it "Maximum rent (LHA)".
2. Nit: the end-to-end case in housing_benefit_lha_order.yaml:39 sets state_pension_reported: 16_000 and also inputs applicable income. Add a comment that the input overrides the computed income.
3. Nit: the description still says the pytest counts "will be added".
4. Pre-existing: the separate taper on rates in Northern Ireland (SR 2006/405 reg 69(a)) isn't modelled.

The aggregate is small, about −£2m.

[MaxGhenis]

Thanks, Vahid. All four points are handled:

1. LHA_cap label: now "Maximum rent (LHA)". Its documentation cites reg 13D(5).
2. End-to-end case: commented that the applicable-income input overrides the income computed from the State Pension.
3. Pytest placeholder: the description now has the counts.
4. NI rates taper: listed under "Not in this PR".

Head 066cb2d. There is no change in behaviour since your review.

[juaristi22]

Codex review — ready to merge

Reviewed commit 066cb2dd6a3781d2af142ab54c6b7dee6c9a4aa7. COMPLETE; 0 confirmed blocking finding(s). Independent code/test and policy/source reviews were consolidated for the changed behavior and affected dependencies.

No actionable code/test defect found. housing_benefit_entitlement.py:45–66 now chooses eligible rent before subtracting non-dependant deductions and the means-test taper, and floors the result at zero. Private renters use min(rent,LHA); social renters use rent. The lower-rent, zero-taper and zero-award cases continue to agree with the old formula.

The property suite includes explicit examples at all three distinct bounds of the intended difference, monotonicity checks, and final Housing Benefit for pensioner households with and without non-dependants. These exercise the change beyond a copied formula oracle. Confidence: high.

No confirmed policy defect in the changed rent-cap/taper order.

The current formula first determines eligible rent (LHA_cap for an LHA case), subtracts nondependant deductions, then subtracts65% of positive excess income and floors the result at zero. HB regs13D(5),70 and71 and the pension-age regs12D(2),50 and51 require that ordering. NI regs14D(5),48 and49(b) make the equivalent distinction for rent. In particular, high rent must not absorb the income taper: the cap applies to maximum eligible rent before the taper. Non-LHA rent behavior remains algebraically unchanged.

Sources: GB LHA cap, GB maximum/taper, 65%, pension-age eligible rent, NI rent taper.

The LHA-cap label and explanatory test/body nits are addressed at066cb2dd. The separate NI rates rebate20% taper is outside this changed rent calculation and is pre-existing; do not count it as a regression introduced here. LHA transitional-protection/category rules are likewise not newly implemented by this ordering fix. Coordinate subsequent shared-file changes without dropping this order.

Validation: 16 passed, 1 warning. Changed implementation and relevant final-award/dependency tests were checked at this exact commit. 9 official source originals were inspected and their cached bytes verified. No material review gaps remain within this scope; private population-impact claims were not independently rerun.

Focused tests used an existing cached Python 3.13 environment (Core 3.32.9, NumPy 2.1.3, pandas 2.3.1, microdf-python 1.2.1, Hypothesis 6.168.2, pytest 8.4.2) with this PR’s isolated source snapshot. No dependencies were installed; this was not a freshly synced lock environment or a full-suite/population run. This is a review comment, not a formal GitHub review vote.

Live check before posting (2026-10-02T10:41:05.635577+00:00): same commit, CLEAN; all reported CI checks pass.