The Balancing Act in Causal Inference

TL;DR

This paper reviews methods for estimating inverse propensity weights in causal inference, emphasizing covariate balance as key for robust treatment effect estimation, and compares traditional propensity score modeling with balancing approaches.

Contribution

It provides a comprehensive comparison of propensity score-based and balancing methods for inverse weighting, highlighting their theoretical foundations and practical implications.

Findings

Balancing approaches estimate weights by achieving covariate balance.

Inverse propensity weighting is central for causal effect estimation under strong ignorability.

The paper discusses generalizations to policy evaluation and individualized treatment effects.

Abstract

The idea of covariate balance is at the core of causal inference. Inverse propensity weights play a central role because they are the unique set of weights that balance the covariate distributions of different treatment groups. We discuss two broad approaches to estimating these weights: the more traditional one, which fits a propensity score model and then uses the reciprocal of the estimated propensity score to construct weights, and the balancing approach, which estimates the inverse propensity weights essentially by the method of moments, finding weights that achieve balance in the sample. We review ideas from the causal inference, sample surveys, and semiparametric estimation literatures, with particular attention to the role of balance as a sufficient condition for robust inference. We focus on the inverse propensity weighting and augmented inverse propensity weighting estimators for the average treatment effect given strong ignorability and consider generalizations for a broader class of problems including policy evaluation and the estimation of individualized treatment effects.