Robust Confidence Intervals for Average Treatment Effects under Limited Overlap *Estimators of average treatment effects under unconfounded treatment assignment are known to become rather imprecise if there is limited overlap in the covariate distributions between the treatment groups.But such limited overlap can also have a detrimental effect on inference, and lead for example to highly distorted confidence intervals.This paper shows that this is because the coverage error of traditional confidence intervals is not so much driven by the total sample size, but by the number of observations in the areas of limited overlap.At least some of these "local sample sizes" are often very small in applications, up to the point where distributional approximation derived from the Central Limit Theorem become unreliable.Building on this observation, the paper proposes two new robust confidence intervals that are extensions of classical approaches to small sample inference.It shows that these approaches are easy to implement, and have superior theoretical and practical properties relative to standard methods in empirically relevant settings.They should thus be useful for practitioners.

In this paper, we propose a method to evaluate the effect of a counterfactual change in the unconditional distribution of a single covariate on the unconditional distribution of an outcome variable of interest. Both fixed and infinitesimal changes are considered. We show that such effects are point identified under general conditions if the covariate affected by the counterfactual change is continuously distributed, but are typically only partially identified if its distribution is discrete. For the latter case, we derive informative bounds, making use of the available information. We also discuss estimation and inference.