🤖 AI Summary
This study addresses the interpretational ambiguity of weighted estimators when treatment effects are heterogeneous, as their validity hinges critically on the choice of weights. To tackle this issue, the authors propose an estimator that minimizes worst-case bias and construct confidence intervals that are uniformly valid over a broad class of weighting schemes. Their approach integrates minimax bias reduction, bounds from heterogeneity-robust sensitivity analysis, and theoretical characterizations of discrepancies among weighted estimators, thereby enabling inference robust to weight uncertainty. Empirical applications illustrate the method’s utility: in Lakdawala et al.’s event study, findings remain robust across a wide range of weights, whereas in the Project STAR experiment, conclusions prove sensitive even to minor perturbations of baseline weights.
📝 Abstract
Researchers often conduct inference on weighted estimands, defined as weighted averages of group-level effects. Example settings include event studies with cohort-level effects and experiments with site-level effects. Under heterogeneous effects, different weighting schemes yield estimands with distinct empirical and policy interpretations, leading to ambiguity and disagreement over the choice of weights. I establish bounds on differences between weighted estimands and confidence bounds on effect heterogeneity, which I use to construct estimators that minimize worst-case bias and confidence intervals that are uniformly valid over classes of weighted estimands. I apply these methods to an event study in Lakdawala, Nakasone, and Kho (2023), which studies the effects of school-based internet access on test scores. I find that results are robust to broad classes of weights. I then apply the methods to Tennessee's Project STAR experiment and find that results are sensitive to small departures from baseline weights.