Caregiver-credit replication: R5 progressivity pattern on real careers

[MaxGhenis]

Caregiver-credit replication — R5 progressivity pattern on real careers

Reported, not gated. Reads no gate, changes no gate; publishes regardless of outcome. Frozen spec: #42 comment 4911453454. Anchor (#74, anchor 2): Smith, Johnson & Favreault (2020), Five Democratic Approaches to Social Security Reform (Urban Institute 103050, DYNASIM3 ID980), Table 15 (printed p. 66).

The caregiver credit is the most progressive provision the anchor scores. Table 15 reports the share of each provision's benefit increase reaching the bottom fifth of lifetime earners in 2065. Does our stack — real PSID Phase-A careers + observed births (cah85_23) + the statutory 415(a)/(b) chain transported to a common 2050 cohort — reproduce that progressivity pattern?

Four plans: bottom-quintile share of aggregate benefit gains

Plan	Credit	Child <	Year cap	Ours	Floor (½-split)	Anchor (Table 15)	In/above 52–62% band
Biden	½ avg wage	12	5	64.3%	1.16	54%	✅
Buttigieg	full avg wage	18	none	58.2%	1.75	52%	✅
Klobuchar	½ avg wage	6	none	70.7%	2.08	62%	✅
Warren	full avg wage	6	none	58.5%	2.01	55%	✅

All four land in or above the anchor's 52–62% band. Floors (the 5-seed person-disjoint half-split |A−B| noise scale) are 1–2 pp — far below the 12 pp plan-to-plan spread, so the ordering is signal.

The registered expectation held

• ½-credit designs in or above the band. Biden (64.3%) and Klobuchar (70.7%) both clear 52% — in fact both sit above 62%, exactly as pre-registered: our truncated-window observed careers expose more low-AIME person-years to the top-up, so shares run higher than the anchor's.
• Plan ordering matches (broader eligibility → larger but less concentrated gains). Concentration endpoints match the anchor — Klobuchar most concentrated (narrowest age limit + ½ credit), Buttigieg least (broadest eligibility); Spearman ρ = 0.80. Reach endpoints match too — Buttigieg most persons gaining (72.1%), Klobuchar fewest (49.4%), mirroring the anchor's 45% / 27%. (Biden and Warren swap the middle ranks; they are near-tied in the anchor at 54 vs 55.)

Conventions (reused verbatim)

• Career frame: the Phase-A pia_observed selection built exactly as replication_r7_sharing.py — coverage ≥ 0.8 of ages 22–61, age-62 eligibility 2005–2019 (born 1943–57). 1,549 careers; 1,377 are parents.
• Transport: the common 2050-eligibility transport from replication_ppi_mermin.py (build_transport) — NAWI projected to the 2048 index year, 2050 bend points per 415(a)(1)(B).
• AIME: full statutory 415(b) top-35 (the original Phase-A convention, available on full annual careers).
• PIA / gain: pre-415(g) scheduled_amount on the 2050 bends; gain = reformed − baseline PIA. Every share is invariant to the NAWI projection level (AIME, credit level, and bends all scale with NAWI[2048]). NAWI[2017] = $50,321.89 matches the paper's stated $50,322 average wage.
• Credit: in a qualifying child-year (child younger than the plan's age limit) with earnings below the credit level (fraction × NAWI[year]), earnings are topped up to the credit level; Biden's 5-year cap credits the benefit-maximising years (a chronological-selection sensitivity is reported — 64.0% vs 64.3%, so the cap convention does not drive the finding).

Named population deltas vs the DYNASIM 2065 projection (documented, not hidden)

Observed 1943–57 PSID cohorts transported to 2050 vs projected 2065 beneficiaries · individual own-record earnings vs DYNASIM's couples splitting earnings in married years · truncated observation window vs full projected careers · no mortality / benefit-receipt-years / claim-age / behavioural projection (cross-sectional PIA-gain proxy).

Artifact & tests

• runs/replication_caregiver_v1.json — one run, reported_not_gated: true, registration pointer, page-cited provenance, per-seed recomputable.
• tests/test_replication_caregiver.py — internal-consistency + pure-helper tests (always runnable) and a skipif-PSID live seed-0 reproduction pin. Full suite green; black -l 79 + ruff clean. Runtime ≈ 16 s.

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