An empirical process framework for covariate balance in causal inference

TL;DR

This paper introduces an empirical process framework to evaluate covariate balance in matching procedures for causal inference, providing theoretical guarantees and practical applications to various matching algorithms.

Contribution

It offers a novel empirical process perspective with finite sample guarantees for covariate balance, applicable to multiple matching methods.

Findings

The framework provides theoretical bounds on covariate imbalance.

Simulation studies validate the effectiveness of the approach.

Applicable to coarsened exact matching and propensity score matching.

Abstract

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.