Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies

2011/10/17 by Jens Hainmueller · 90 citations
Mathematics · #Advanced Causal Inference Techniques #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · doi:10.1093/pan/mpr025

openalex publication_date 2011/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

This paper proposes entropy balancing, a data preprocessing method to achieve covariate balance in observational studies with binary treatments. Entropy balancing relies on a maximum entropy reweighting scheme that calibrates unit weights so that the reweighted treatment and control group satisfy a potentially large set of prespecified balance conditions that incorporate information about known sample moments. Entropy balancing thereby exactly adjusts inequalities in representation with respect to the first, second, and possibly higher moments of the covariate distributions. These balance improvements can reduce model dependence for the subsequent estimation of treatment effects. The method assures that balance improves on all covariate moments included in the reweighting. It also obviates the need for continual balance checking and iterative searching over propensity score models that may stochastically balance the covariate moments. We demonstrate the use of entropy balancing with Monte Carlo simulations and empirical applications.

Citations

• Large Sample Properties of Generalized Method of Moments Estimators
• The central role of the propensity score in observational studies for causal effects
• Variable Selection for Propensity Score Models
• Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score

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