Table 6—
Best Linear Prediction of the Conditional Average Treatment Effect
| Parameter | (1) | (2) | (3) | (4) |
|---|---|---|---|---|
| β1 (average treatment effect) | 1.15 | 1.06 | 1.08 | 1.11 |
| (0.221) | (0.200) | (0.263) | (0.247) | |
| β2 (heterogeneity) | 0.0148 | 0.0133 | 0.0137 | 0.0126 |
| (0.003) | (0.00268) | (0.00346) | (0.00317) | |
| Horvitz-Thompson transformation | X | X | ||
| Trimming threshold | 5% | 5% | 1% | 1% |
| Observations (millions) | 21,724 | 21,724 | 23,075 | 23,075 |
Notes: Columns 1 and 3 present regression estimates of equation (5) from the main text. Columns 2 and 4 present estimates of equation (A6) from the online Appendix. The dependent variable is the one-day mortality rate per million beneficiaries. The parameter β1 measures the average mortality effect of being exposed to one day of air when the wind that day is blowing from a direction associated with high air pollution. Rejecting the null hypothesis that β2 = 0 implies that heterogeneity is present and that the proxy predictor, Ŝ(Zit), captures a component of this heterogeneity. These regressions omit observations with estimated propensity scores less than the trimming threshold or greater than 1 minus the threshold. Standard errors, clustered by county, are reported in parentheses.