Generalized Optimal Matching Methods for Causal Inference

TL;DR

This paper introduces generalized optimal matching (GOM), a comprehensive framework for causal inference that unifies and extends existing methods, including kernel optimal matching (KOM), offering improved balance, efficiency, and robustness.

Contribution

The paper develops a unified theoretical framework for GOM, encompassing many existing methods and introducing KOM, which combines interpretability, consistency, and efficiency in causal inference.

Findings

KOM achieves $\,\sqrt{n}$-consistency and robustness.

GOM framework unifies and extends existing matching methods.

KOM provides transparent interval estimation in limited overlap settings.

Abstract

We develop an encompassing framework for matching, covariate balancing, and doubly-robust methods for causal inference from observational data called generalized optimal matching (GOM). The framework is given by generalizing a new functional-analytical formulation of optimal matching, giving rise to the class of GOM methods, for which we provide a single unified theory to analyze tractability, consistency, and efficiency. Many commonly used existing methods are included in GOM and, using their GOM interpretation, can be extended to optimally and automatically trade off balance for variance and outperform their standard counterparts. As a subclass, GOM gives rise to kernel optimal matching (KOM), which, as supported by new theoretical and empirical results, is notable for combining many of the positive properties of other methods in one. KOM, which is solved as a linearly-constrained convex-quadratic optimization problem, inherits both the interpretability and model-free consistency of matching but can also achieve the $\sqrt{n}$-consistency of well-specified regression and the efficiency and robustness of doubly robust methods. In settings of limited overlap, KOM enables a very transparent method for interval estimation for partial identification and robust coverage. We demonstrate these benefits in examples with both synthetic and real data