Weighted bootstrap consistency for matching estimators: The role of bias-correction

Abstract

We show that the purpose of consistent bias-correction for matching estimators of treatment effects is two-fold. Firstly, it is known to improve point estimation to get rid of asymptotically non-negligible bias terms. Secondly, point estimates, it will also distort inference leading e.g. to invalid confidence intervals. In simulations, we show that the choice of the bias-correction estimator that practitioners still have to make, can severely affect the weighted bootstrap’s performance when estimating the asymptotic variance in finite samples. In particular, simple rules such as estimating the bias based on linear regressions in the treatment arms can lead to very poor weighted bootstrap based variance estimates.