Comparative Effectiveness of Matching Methods for Causal Inference

Matching methods for causal inference selectively prune observations from the data in order to reduce model dependence. They are successful when simultaneously maximizing balance (between the treated and control groups on the pre-treatment covariates) and the number of observations remaining in the data set. However, existing matching methods either fix the matched sample size ex ante and attempt to reduce imbalance as a result of the procedure (e.g., propensity score andMahalanobis distance matching) or fix imbalance ex ante and attempt to lose as few observations as possible ex post (e.g., coarsened exact matching and calpier-based approaches). As an alternative, we offer a simple graphical approach that addresses both criteria simultaneously and lets the user choose a matching solution from the imbalancesample size frontier. In the process of applying our approach, we also discover that propensity score matching (PSM) often approximates random matching, both in real applications and in data simulated by the processes that fit PSM theory. Moreover, contrary to conventional wisdom, random matching is not benign: it (and thus often PSM) can degrade inferences relative to not matching at all. Other methods we study do not have these or other problems we describe. However, with our easy-to-use graphical approach, users can focus on choosing a matching solution for a particular application rather than whatever method happened to be used to generate it.