[MaxGhenis]

WIP: please don't merge or deploy. These are public numbers, and they wait on Max's go.

Adds section 4, "Imputing in-kind benefits." BLS adds five in-kind benefits to out-of-pocket FCSUti before it estimates the thresholds: school lunch, WIC, LIHEAP, broadband subsidies and rental assistance. The section reruns the 2019–2025 replication with those benefits, using three spm-calculator receipts:

• the imputation, at 4778dfab (Add optional BLS-style in-kind benefit imputation to the CE threshold replication spm-calculator#55, merged);
• the comparison with BLS's published components and the replicate-weight standard errors, both at 708ea21d (Estimate replicate-weight standard errors for the in-kind replication spm-calculator#57, open; tags paper-inkind-components-708ea21 and paper-inkind-se-708ea21). That commit holds the same receipt bytes as 8f632e31 (#56) and a581c113 (#57); its page text corrects what it said about BLS's published covariates and standard errors and matches the paper's rental comparison and school lunch ladder.

The tags point at that commit, so a default clone of spm-calculator holds it even if #56 and #57 squash-merge.

What changes

• Section 4: imputation models, threshold levels, BLS's imputed amounts (rebuilt from its published component shares), 2022–2025 growth, and sampling and imputation uncertainty.
• Tables: inkind_levels, inkind_amounts, inkind_series, inkind_growth and inkind_accounting, generated by scripts/build_inkind_tables.py from scripts/inkind_inputs.py. \Needspace guards keep the growth and accounting tables on one page of the PDF, as the paper already does for the composite and rolling validation tables.
• Data: data/inkind/ holds the three receipts, their provenance and SHA-256 sums.
• Text elsewhere: sentences in the abstract, §3.1–3.2, §6.2 and the discussion point to the section. §3 replaces "we have not estimated the replication's sampling uncertainty" with the replication's standard errors relative to BLS's, and cites Garner (2010) and Garner and Gudrais (2018) for BLS's balanced repeated replication with the CE's 44 replicates. Appendix B, the README and the bibliography name all three receipts' commits.
• Guard: scripts/check_paper.py validates the receipts before any generator runs and regenerates the tables. It ties every in-kind estimate in the prose to a value it recomputes from the receipts, and each tie reads only the section that states the figure. Each tie also quotes the words that give the figure its meaning: its tenure label, its comparison verb, the stage or series it belongs to, and whose estimate it is. The guard also checks each receipt's SHA-256 and calculator commit against RECEIPT_PINS in scripts/inkind_inputs.py, outside the resealable data/inkind bundle.
• Method text: the WIC, school lunch, SNAP/EBT, donor-year and covariate sentences follow spm-calculator's code at 4778dfab and BLS's page, including the 2025 WIC universe (WIC_BROAD_UNIVERSE_FIRST_TARGET): for the 2025 thresholds, the WIC model also assigns participation to units that have a child under 5 but no woman aged 15 or older. The participant count follows Census's rule (every child under 5, plus the mother of a child aged 0 or 1) and states our one addition in its own sentence: we count that mother only when the unit has a woman aged 15 or older, so in the units the 2025 universe adds we count the children alone. The identities paragraph names the internet row BLS's shares balance with, the rule that picks it and the broadband subsidies we subtract from it.

Results

• With the five benefits, replicated thresholds rise 1.1 to 3.8 percent, and the replication exceeds BLS's thresholds in every tenure and year, by 0.26 to 3.53 percent.
• Under Garner and Munoz's (2021) shelter, utilities and food definitions, the out-of-pocket replication trails BLS by 1.98 to 4.20 percent. Adding the benefits brings it within −1.71 to +1.47 percent and cuts the mean absolute deviation from 3.14 to 0.72 percent. Those runs keep spending under two codes for other fuels in vacation homes, which the FMLI summaries of vacation-home utilities leave out.
• BLS's imputed benefits rose from $855 to $1,257 per unit in its band between the 2022 and 2025 thresholds, and ours from $1,027 to $1,173. Rental assistance accounts for $169 of the gap between the rises and school lunch for $94.
• The benefits change the replication's 2022–2025 growth by +0.06, +0.91 and −0.62 points by tenure, with standard errors of 0.74, 2.54 and 1.01 points (44 BRR replicates combined with the five implicates by Rubin's rules). Under either price index, every change lies within three-quarters of a standard error of zero, and the spread across implicates accounts for 17 to 46 percent of each change's variance. The standard errors leave out sampling variation in the rental model's fit, the CPS ASEC donor samples and the CE's five income imputations, and the FCSUti run holds BLS's price factors fixed. Switching to BLS's FCSUti deflator moves growth more, by 0.9 to 2.0 points.
• The replication's standard errors run 0.66 to 1.95 times BLS's published ones, by tenure and year.
• For renters in 2024–2025, BLS's imputed benefits supplied 0.62 of the 6.33 points of threshold growth, 0.57 of them from rental assistance. Ours move the replication's renter growth by −0.01 points.

Revision for the r4 review (c7398da, 99c567b, f28157c, ac6b591, a07bcba)

Applies every blocking and major finding of the r4 review (~/reviews/spm-creamer-email-2026-11-05/paper-inkind-review-r4-fable/REVISION-SPEC.md, changes A–R); the minor and nit findings it leaves are listed with reasons in that folder's DEFERRED.md.

• BLS's methods: §2.1 names the July 2026 correction and the 0.82 share; §4 describes BLS's imputation from its methods page and Garner and Gudrais (2018, BLS WP 510), and says where our covariates, pooling and rent model differ. The calculator page (spm-calculator 708ea21) no longer says BLS hasn't published covariates or its standard-error method.
• Census's school lunch values: P-EBT in 2020 and 2021; from reference year 2023, Census's fall 2022 method; BLS's traditional method before and after the COVID-19 period; F_MV_SL, the 2014–2017 research values and the 2018 CPS ASEC Bridge File's 2017 values named and not read.
• Growth accounting (new Table 8): BLS's 2022–2025 growth beyond CPI-U splits into its FCSUti index on the out-of-pocket terms (33 to 39 percent), its imputed benefits (5 to 13 percent) and out-of-pocket spending beyond the index (54 to 60 percent), with re-ranking reported separately (−0.01, +0.82, −0.34 points). With the index's lead on the benefits' terms too, the benefits supply 4.3, 6.8 and 11.7 percent.
• Year table (new Table 6): BLS's and our in-band amounts and rental assistance per renter for 2019–2025, with standard errors; from the 2019 to the 2022 thresholds BLS's rental assistance per renter rose 17 percent and ours 20 percent, and ours exceeds BLS's by 71 to 80 percent for the 2019–2023 thresholds.
• Standard errors: for the 2022–2025 rises in band amounts ($191, $444, $50) and for the benefits' lifts (0.31 to 0.61 points for owners with mortgages and renters; 1.04 to 2.00 for owners without).
• CPI vintage: §4.4 and §6.3 state BLS's interpolated October 2025 CPI-U (138.289 against the official 138.198).
• Abstract and discussion: carry the accounting's shares and qualify the growth result to the CE's spending summaries; with the written definitions and the composite CPI, the benefits change growth by +0.09, −1.51 and −0.05 points.
• Independent check (Opus 5.5, in session) of 99c567b: f28157c, ac6b591 and a07bcba replace "differ more in level than in growth" (false for 2022–2025) with the 2019–2022 growth figures, name the deflator on the lift standard errors, describe BLS's band as each year's band in §6.2, add the alternative split, relabel Table 8's index row and widen its label column, and fix four read-twice sentences and the CPI vintage citation's placement.
• Rendering: report numbers move into each bibliography entry's type field so citeproc prints "Working Paper 2021-17", not "Nos."; a \Needspace keeps Table 8 on one page.
• Known follow-up: the replication receipt's limitations strings predate this revision (they say BLS has not published its imputation code or covariates and date P-EBT to 2020–2023). The receipts are byte-pinned, so correcting them needs a regenerated receipt in spm-calculator and a repin; the paper's text and the calculator page carry the corrected statements.

New invariants, checked before every render:

18. For each tenure, the three parts (prices (φ−π)(B22−I22)/B22, benefits (I25−πI22)/B22, out-of-pocket ((B25−I25)−φ(B22−I22))/B22) sum to (B25−πB22)/B22, BLS's growth beyond CPI-U, and each share the prose states recomputes from BLS's receipt. With the index's lead on the benefits' terms too (prices φ−π, benefits (I25−φI22)/B22), the parts still sum to it, the out-of-pocket part is unchanged, and exactly (φ−π)I22/B22 moves from benefits to prices.
19. The re-ranking, home internet share, year table, rise and lift standard errors, and CPI vintage the prose states recompute from the receipts; rises pair replicate r of 2022 with replicate r of 2025.

New tests: GrowthAccountingProperties (the identity on random inputs, the alternative split's conservation, invariance to the dollar unit, a misstated share and a negative part rejected, and a differential check against the receipts) and ReceiptTieProperties (re-ranking, internet share, rise pairing under rotation, positive standard errors, CPI vintage) in tests/test_inkind_inputs.py; 110 prose mutations in tests/test_paper_guard.py, including a new price-validation region.

Invariants (checked before every render)

1. The out-of-pocket run reproduces data/current's replication artifact: the archived hash matches, and the thresholds are identical in every year and tenure.
2. BLS's published shares, thresholds and tenure shares satisfy T_h = 0.82 (C + SU_h + 0.2 F), with F = C + Σ_h P_h SU_h, within $0.00001 in every year from 2019 to 2025.
3. The paper's rebuild of BLS's imputed terms (nslp, wic and broadband in C; liheap and rental assistance in SU_h) equals the receipt's recorded terms in 2022 and 2025 for every tenure.
4. Each year's implicates average to the reported threshold with benefits. Lifts, gaps and growth rates recompute from the thresholds, and the per-benefit rises sum to the total rise.
5. The component receipt names the replication receipt's hash, and its package run reproduces the replication receipt's thresholds.
6. The uncertainty receipt names both other receipts' hashes and reads the replication receipt's CE bundles, CPS ASEC files, CPI file and imputation seed. Its full-sample thresholds (replicate 0) equal the replication receipt's (package run) and the component receipt's (FCSUti run) in every year, tenure and implicate, and its BLS standard errors equal the paper's own records of BLS's published ones.
7. Every source file that two receipts both fingerprint carries the same SHA-256 in each.
8. Every standard error recomputes from the stored replicate thresholds: standard BRR, V = Σ_r (θ_r − θ)² / 44; Rubin's rules across implicates; Barnard–Rubin degrees of freedom on 43. Growth replicates pair replicate r of one window with replicate r of the other.
9. The regenerated tables match the committed tables byte for byte.
10. The share formula the section prints, evaluated against BLS's receipt, reproduces BLS's imputed shares of growth beyond CPI-U for every tenure.
11. The method constants the section quotes from the calculator (179 school days, the 150 percent cutoff for free lunch and for the cells, the WIC participant count, the woman test on the mother of a child aged 0 or 1 and the units where it binds, the 2025 WIC universe, twelve months of WIC, the midpoint of the reference period, twelve times the rent difference, the mean of the five income imputations) come from spm_calculator/ce_inkind.py at the SHA-256 the replication receipt records (c23e6f26…). The 47th–53rd percentile band comes from spm_calculator/ce_threshold.py at the SHA-256 the same receipt records (4efbe2b0…). Garner and Munoz's utilities rule, the vacation-home mortgage principal the written-definition runs remove, the rule that picks BLS's internet row and the broadband subtraction come from spm_calculator/ce_bls_shares.py at the SHA-256 the component receipt records (c6ef2d75…).
12. Each receipt's SHA-256 and provenance commit equal RECEIPT_PINS, whose digests equal git show <commit>:spm_calculator/data/current/<receipt> in spm-calculator. A resealed receipt can keep every other invariant: mirroring a year's replicates around the full sample keeps every squared deviation. Only this pin rejects it, and the guard checks it last, so a resealed edit that an earlier invariant catches fails with that invariant's label.
13. Section 4.5's growth period, the half-sample quarter pairs and the thresholds they affect come from the receipts and the replication's 20-quarter windows; Appendix B and the README count the receipts from their provenance and name each commit, and the README names both tags.
14. The written-definition runs remove vacation-home utilities and the vacation-home mortgage principal in every year from 2019 to 2025, with no negative amount removed and no unit's utilities below zero afterwards. The number of vacation-home fuel codes §4.5 says they keep equals the number the component receipt's stated limitation names, and that limitation gives the same reason the paper does (the FMLI summaries leave them out).
15. The bibliography's two spm-calculator entries match the provenance commits field for field: the in-kind note names the imputation commit, then the components commit, and its link opens PolicyEngine's docs/ce-inkind-imputation.md at the components commit; the standard-error note and link carry the standard-error commit.
16. The first reference year with Census school lunch values and the survey whose files carry them, the internet row BLS's shares use in each threshold year, the programs the participation models cover (by name and count), the number of benefits and the amounts caption's implicate count all come from the receipts.
17. The uncertainty receipt's method record lists the CPI series and BLS's FCSUti index among the inputs its replicates hold fixed, as §4.5 says.

Tests

• tests/test_inkind_inputs.py: seeded property tests, 2,000 draws each, standard library only.
  • The tests declare the benefit classification themselves (school lunch, WIC and broadband shared; LIHEAP and rental assistance in shelter and utilities) and check the module against it.
  • The imputed-term rebuild equals the threshold change from adding the benefits under a direct evaluation of the identity (a differential test).
  • It adds over disjoint benefit sets.
  • Shared benefits add the same dollars to every tenure, and so does broadband alone.
  • Mix-weighted terms equal 0.82 × 1.2 × the pooled benefits.
  • A tenure's own rental assistance moves its term by 0.82 (1 + 0.2 P_h).
  • Plus growth round trips, and _close rejecting non-finite values.
  • Replicate variance: nonnegative, unchanged by shifting every estimate or permuting the replicates, zero when every replicate equals the full sample, and refuses fewer than 44 replicates.
  • Mirroring every replicate around its full-sample value keeps each replicate variance and every Rubin quantity, so no variance check can see it; a mirrored, resealed receipt passes load_inkind and uncertainty_figures and fails check_receipt_pins. The committed receipts match their pins.
  • Rubin's rules match a direct evaluation of their definitions (a differential test, 2,000 draws). Total variance bounds both components, the missing-information fraction lies in [0, 1] and the degrees of freedom in [0, 43], and identical implicates leave only sampling variance.
  • The committed uncertainty receipt recomputes; one moved replicate fails; rotating the 2025 replicates against 2022's fails the stage-change check.
  • A deliberately broken rebuild (no 0.2 F term) fails 4 of the 7 identity tests.
• tests/test_paper_guard.py: each of these fails without repairing anything:
  • a corrupt receipt, before any generator runs;
  • an extra file under data/inkind;
  • a resealed receipt with its hashes updated (first on the cross-receipt hash link, then on data/current);
  • an internally consistent edit to one threshold, against the component receipt;
  • table drift and a missing include;
  • nine prose drifts across the section, abstract, §6.2 and Appendix B, plus twelve more in the standard-error sentences of §3, §4.4, §4.5 and Appendix B (among them the growth period, the half-sample thresholds and Appendix B's receipt count), and the §4.4 stage-change sentence moved into §4.5;
  • a README that miscounts the receipts, shortens a commit or names a stale tag;
  • fourteen edits that keep every figure and change its meaning: swapped tenure labels on the growth changes and on the shares, BLS's and our shares swapped, four flipped comparison verbs in the section and one in the discussion, a changed operator or year in the share formula, 180 school days, and a WIC mother aged 18 or older;
  • a resealed uncertainty receipt whose replicates no longer match its stored standard errors, one that names the wrong receipts, one whose full-sample thresholds drift from the replication, one with altered BLS standard errors, receipts whose shared code fingerprints differ, one with a zeroed CE bundle hash, and one with a changed imputation seed;
  • a resealed uncertainty receipt with its 2019 replicates mirrored, which fails only on the pinned digest, and a provenance record naming another calculator commit;
  • two figures restated in another section;
  • two drifts in the written-definition sentences of §4.2 and §4.5: the vacation-home utilities the runs remove, and the number of fuel codes they keep;
  • five resealed component receipts, repinned so they reach the drift checks: one whose runs keep 2022's vacation-home utilities, one whose runs keep its vacation-home mortgage principal, one that leaves 57 units' 2022 utilities below zero, one that reads 2024's internet row from the total row, and one whose stated limitation names a third kept fuel code. An unchanged reseal passes the whole guard as their control;
  • a resealed, repinned uncertainty receipt whose held-fixed inputs no longer list the price indexes;
  • twenty-seven more edits that keep every figure and change its meaning or a method fact: the lift's direction in the section, abstract and discussion; swapped stages in the 2024–2025 renter growth and the written-definition ranges; swapped benefits in the difference by benefit; swapped owners of the imputed totals and of the 2024–2025 rental assistance per renter; swapped price series; the deflator the share formula names; the implicate rise's price index; the growth window in the caption; the renters' half of the utilities rule and the reason the runs keep two fuel codes; the 2025 WIC universe's year and rule, the infant age and the pregnant-woman count; the five income imputations; the percentile band; the first Census school lunch year; the internet row years; and the program, benefit and caption implicate counts;
  • nine more of the same kind: a mother counted in the units the 2025 universe adds, the years of the imputed totals, the tenure of BLS's 2024–2025 split, the survey whose files carry Census's lunch values, a program in the participation list, the vacation-home principal kept, the internet-row rule, broadband added instead of subtracted, and FCSUti price factors that vary;
  • a bibliography citing either stale commit, a stale components link alone, the two entries' commits swapped, the commits swapped inside the in-kind note, or a link to a fork.
• Mutation audit (at d2e94a0): a script perturbed each of the 127 numbers in the in-kind passages and reran the guard, which caught 69. The 58 it missed were years; method constants (ages 5, 18 and 65, 150 percent of poverty, 179 school days, the 0.2 in the identity, the 80 percent food allocation); and the abstract's 1.17, 2.58 and 0.75, which the gap below covers. The guard now pins the constants listed in invariant 11.

Known gap, older than this PR

The abstract's evaluation figures (1.17, 2.58 and 0.75 percent) still pass the guard when changed alone, because their ties read the whole document and the body states the same figures. #13, stacked on this PR, scopes those ties to the abstract, and #14 does the same for every section. Both rebase onto this PR once its review settles the guard.

Plan

• Section, tables, guard ties and tests
• GPT-6.1 Sol review of the section at 0a03075: 642c108 addresses findings 1–9
• GPT-6.1 Sol review of the standard errors at 46f18f5: 9ba8f61 addresses findings 1–5
• Round 2 review of both sets of fixes at 6e8d449 (Opus 5.5 in session while every Codex lane sat held): c924d7a addresses findings 1–9
• Round 3 review of c924d7a (Opus 5.5 in session while every Codex and Claude lane sat held): it approved, with six optional findings. d296dcf addresses findings 1–5; finding 6 (a calendar line in the cover email) is Max's call
• Keep the in-kind growth table on one page (dfbf478): d296dcf's longer WIC passage had pushed its last row onto the next page
• Full suite at dfbf478: 91 tests pass
• Delta check of d296dcf and dfbf478 (Subfleet review job 20261110-104708-spm-paper-delta-dfbf478, queued while every lane sits held)
• Replace "we have not estimated sampling uncertainty" with replicate-weight standard errors (receipt from open Estimate replicate-weight standard errors for the in-kind replication spm-calculator#57)
• Repoint both receipts to the vacation-home utilities fix (Compare the in-kind replication with BLS's published threshold components spm-calculator#56 at 8f632e31, #57 at a581c113) in 6e8d449
• Repoint again if Estimate replicate-weight standard errors for the in-kind replication spm-calculator#57 changes before it merges; after a squash merge, repinning to the main commit stays optional because the tags keep 708ea21
• r4 review (Fable 5.2, 2026-11-10) fixes: c7398da (text, figures, tables, guard, tests, calculator re-pin) and 99c567b (citations, Table 8 layout)
• Independent check of the r4 revision at 99c567b (Opus 5.5 in session; Subfleet lanes held): f28157c, ac6b591 and a07bcba address its findings, with the calculator page repinned to 708ea21
• Full suite at a07bcba
• Tag inkind-section-2026-11 on the final commit (Appendix B links to it)
• Max's go before merge and deploy

axiom: n/a: paper text, tables and receipts; no policy rule changes

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