One national chart can hide a thousand local exceptions. So we stopped fitting one model and fit 266 of them — the deprivation–longevity regression, estimated separately inside every sizable American metro. Every single slope came back negative.
Story № 2 showed the master gradient: across all of America's census tracts, each step up the deprivation index costs about a month of life expectancy. A skeptic has a fair objection ready. National lines can be manufactured by composition — poor Mississippi and rich Minnesota sitting at opposite ends of one chart, with no neighborhood mechanism at all.
The remedy is a habit worth stealing from applied econometrics: many small models instead of one large one. Fit the same regression separately inside every metro, where state policy, climate, health systems, and history are held roughly constant. Then look at the distribution of coefficients. If they scatter around zero, the national line was composition. If they all point the same way, you have found something closer to a law.
Before going local, tighten the screws on the national estimate. Raw, the slope is −0.83 years per 10 deprivation percentiles. Compare tracts only within the same state and it steepens to −0.91. Compare only within the same county — the strictest test, where everything from the hospital system to the weather is shared — and it steepens again, to −1.11. The gradient is not a between-region artifact. It is sharpest exactly where the skeptic said it should vanish.
Now the factory floor. Each row below is one metro's own regression — its slope and 95% interval, estimated only from its own tracts. The histogram on top shows where the 266 slopes pile up. None of them — not one — lands on the right side of zero, and 98.9 percent are significantly negative on their own. The deprivation gradient is not a national average that some lucky cities escape. It is the operating physics of every American metro we can measure.
Generalization established, the interesting question becomes the spread: why does a deprivation percentile cost 2.4 years in San Francisco–Oakland and 0.5 in Madison, Wisconsin? Here the second-stage regression delivers a finding by failing. Metro income explains essentially none of it (r ≈ 0.00 — the chart below is a cloud). Our segregation proxy — how widely deprivation is dispersed across a metro's tracts — explains almost nothing once weighted properly. Metro size, nothing. The sign of the gradient is a law; its steepness is a stubborn local fact that the obvious metro characteristics do not predict. That null is worth a chapter: whatever sets the local exchange rate between deprivation and death, it is not visible in the census — which points the search at the things censuses miss: health systems, housing stock, drug markets, history.
"Many small models" is more than a robustness check. It converts a modeling assumption — the relationship is the same everywhere — into a measured quantity with its own distribution, its own outliers, and its own second-stage questions. When the 266 coefficients agree on the sign, the finding generalizes and composition stories die. When they disagree on magnitude, the disagreement becomes data. The rest of this series will run several more findings through the same factory; the gradient is simply the first to survive intact.