An empirical process framework for covariate balance in causal inference

We propose a new perspective for the evaluation of matching procedures by considering the complexity of the function class they belong to. Under this perspective we provide theoretical guarantees on post-matching covariate balance through a finite sample concentration inequality. We apply this framework to coarsened exact matching as well as matching using the propensity score and suggest how to apply it to other algorithms. Simulation studies are used to evaluate the procedures.