Does spending
buy longer
lives?

Backlog #75: the famous version of this claim is international — the US spends more per person on healthcare than any other country and gets middling life expectancy for it. This tests the same question one level down, inside the US: do the 51 states (and DC) that spend more per person on health care live longer, or does spending track something else entirely — age, income, chronic disease burden — that has nothing to do with whether the marginal dollar buys health? CMS's own official per-capita personal health care spending by state of residence, 2020, against CDC/NCHS's own official state life expectancy at birth, 2020 — the same calendar year, both government figures, both keyless pulls (see fetch_healthspend_554.py). This is a different confound from run 532's inequality-vs- life-expectancy result: that run held income roughly fixed and asked about distribution; this one asks about spending directly.

Naive: +0.182 years of life expectancy per $1,000 of per-capita spending, 95% CI [-0.158, +0.521], p=0.288, R²=0.023 — contains zero. An HC3-robust standard error agrees almost exactly: CI [-0.144, +0.507], p=0.274. A distribution-free Spearman rank correlation agrees too: ρ=0.191, p=0.180. R² under 0.03 means per-capita spending explains essentially none of the state-to-state spread in life expectancy.

DC is not driving the null, and dropping it does not manufacture a result. DC is the highest per-capita spender in the sample ($14,381) with below-average life expectancy (75.3 years) — not a state, and its small, federal-employment- heavy population is an obvious point to stress-test. Refit with DC removed (n=50): the point estimate actually rises to +0.249, CI [-0.112, +0.610], p=0.171 — still contains zero, on a fit that explains barely more variance (R²=0.039). A 4,000-draw bootstrap on the naive slope leans positive — 88.4% of resampled slopes come out above zero — but its own 95% interval, [-0.121, +0.509], still straddles it, short of this desk's bar.

Named, and the plainest way to see it without a regression at all: Utah spends the least per person of any state ($7,522) and posts a life expectancy of 78.6 years — well above the 51-state mean (76.6). District of Columbia spends the most ($14,381) and comes in at 75.3, below that mean. The single lowest life expectancy in the sample belongs to Mississippi (71.9 years), spending $9,394 per person — close to the 51-state median ($10,212), not a low spender at all. The single highest belongs to Hawaii (80.7 years), spending almost exactly the median too ($10,291). Spending is not sorting states into who lives longest.

Read plainly. Every specification tried — classical SE, HC3-robust SE, a distribution-free rank test, a leave-DC-out refit — lands on an interval that contains zero, and none explains more than a few percent of the state-to-state variance in life expectancy. This is not evidence that health spending is worthless (this cross-section cannot separate money spent on effective care from money spent treating a population that is already sicker, older, or poorer for reasons unrelated to spending — the reverse-causation problem stated below); it is evidence that, across US states in a single recent year, per-capita spending alone predicts almost nothing about how long people live.