Matching estimators with few treated and many control observations

Abstract

We analyze the properties of matching estimators when there are few treated, but many control observations. We show that, under standard assumptions, the nearest neighbor matching estimator for the average treatment effect on the treated is asymptotically unbiased in this framework. However, when the number of treated observations is fixed, the estimator is not consistent, and it is generally not asymptotically normal. Since standard inferential techniques are inadequate in this setting, we propose alternative inferential procedures based on the theory of randomization tests under approximate symmetry.