Simple and Bias-Corrected Matching Estimators for Average Treatment Effects

Matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases. In this article, we develop a new framework to analyze the properties of matching estimators and establish a number of new results. First, we show that matching estimators include a conditional bias term which may not vanish at a rate faster than root-N when more than one continuous variable is used for matching. As a result, matching estimators may not be root-N-consistent. Second, we show that even after removing the conditional bias, matching estimators with a fixed number of matches do not reach the semiparametric efficiency bound for average treatment effects, although the efficiency loss may be small. Third, we propose a bias-correction that removes the conditional bias asymptotically, making matching estimators root-N-consistent. Fourth, we provide a new estimator for the conditional variance that does not require consistent nonparametric estimation of unknown functions. We apply the bias-corrected matching estimators to the study of the effects of a labor market program previously analyzed by La