How Much Weak Overlap Can Doubly-Robust T-Statistics Handle?

Abstract

In the presence of weak overlap, it is known that no regular root-n-consistent estimators may exist and standard estimators may fail to be asymptotically normal. This paper shows that a thresholded version of the standard doubly robust estimator is asymptotically normal with well-calibrated Wald confidence intervals even when using nonparametric estimates of the propensity score and conditional mean outcome. The analysis implies a cost of weak overlap in terms of black-box nuisance rates and the contribution of outcome smoothness to the outcome nuisance rate. The high-level conditions yield new rules of thumb for thresholding in practice. In simulations, thresholded AIPW can exhibit moderate overrejection in small samples, but I am unable to reject a null hypothesis of exact coverage in large samples. In an empirical application, the clipped AIPW estimator that targets the standard average treatment effect yields similar precision to a heuristic 10% fixed-trimming approach that changes the target sample.