Large Sample Properties of Matching for Balance

TL;DR

This paper investigates a class of matching methods that optimize covariate balance directly, demonstrating they can achieve $\

Contribution

It introduces integer programming-based matching methods that directly target covariate balance, achieving $\

Findings

Matching methods can be $\

Under certain conditions, these methods are $\

They can produce $\

Abstract

Matching methods are widely used for causal inference in observational studies. Among them, nearest neighbor matching is arguably the most popular. However, nearest neighbor matching does not generally yield an average treatment effect estimator that is $\sqrt{n}$-consistent (Abadie and Imbens, 2006). Are matching methods not $\sqrt{n}$-consistent in general? In this paper, we study a recent class of matching methods that use integer programming to directly target aggregate covariate balance as opposed to finding close neighbor matches. We show that under suitable conditions these methods can yield simple estimators that are $\sqrt{n}$-consistent and asymptotically optimal.