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

Abstract

I study inference on the average causal effect under weak overlap. It is known that when the propensity score density is large near zero, no regular root-n-consistent estimators exist and standard estimators may fail to be asymptotically normal. As a result, previous approaches to causal inference under weak overlap have relied on nonstandard estimators, nonstandard confidence intervals, or have settled for targeting nonstandard causal estimands. I show that statistical inference in this setting need not be so difficult: standard Wald confidence intervals for the standard doubly robust estimator are valid for the standard causal estimand, provided the estimator uses an appropriate trimming or clipping strategy to control extreme estimated propensities. The key is to clip at a rate decaying slowly enough to obtain asymptotic normality, but quickly enough that the bias introduced by clipping is second-order. Wald confidence interval validity for clipped AIPW requires unusually stringent nuisance error conditions, so I propose rules of thumb for the choice of trimming or clipping threshold. In simulations, clipped AIPW achieves near-nominal inference in large samples, but the difficulty of outcome regression can lead to moderate over-rejection in small and moderate samples. In an empirical application, the clipped AIPW estimator that targets the standard average treatment effect yields similar precision to the heuristic 10% fixed-trimming approach that changes the target sample.