Estimating causal effects with optimization-based methods: A review and empirical comparison

TL;DR

This paper reviews and empirically compares optimization-based causal inference methods, highlighting their strengths, limitations, and potential for further development in balancing covariates and estimating causal effects.

Contribution

It provides a comprehensive overview and comparison of optimization-based causal inference methods, identifying gaps and opportunities for operational research contributions.

Findings

Optimization methods improve covariate balance over traditional approaches

Empirical comparison reveals strengths and weaknesses of different methods

Opportunities for new optimization-based causal inference techniques are discussed

Abstract

In the absence of randomized controlled and natural experiments, it is necessary to balance the distributions of (observable) covariates of the treated and control groups in order to obtain an unbiased estimate of a causal effect of interest; otherwise, a different effect size may be estimated, and incorrect recommendations may be given. To achieve this balance, there exist a wide variety of methods. In particular, several methods based on optimization models have been recently proposed in the causal inference literature. While these optimization-based methods empirically showed an improvement over a limited number of other causal inference methods in their relative ability to balance the distributions of covariates and to estimate causal effects, they have not been thoroughly compared to each other and to other noteworthy causal inference methods. In addition, we believe that there exist several unaddressed opportunities that operational researchers could contribute with their advanced knowledge of optimization, for the benefits of the applied researchers that use causal inference tools. In this review paper, we present an overview of the causal inference literature and describe in more detail the optimization-based causal inference methods, provide a comparative analysis of the prevailing optimization-based methods, and discuss opportunities for new methods.