Abstract: Matching methods are widely used for causal inference in observational studies. Of these methods, nearest neighbor matching is arguably the most popular. However, nearest neighbor matching does not, in general, yield an average treatment effect estimator that is consistent at the rate. Are matching methods not -consistent in general? In this paper, we examine a recent class of matching methods that use integer programming to directly target aggregate covariate balance, in addition to finding close neighbor matches. We show that under suitable conditions, these methods can yield simple estimators that are -consistent and asymptotically optimal.

Key words and phrases: Causal inference, integer programming, matching methods, observational studies, propensity score.