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

Political Analysis (2012) 20: 25-46

22 Pages Posted: 4 Aug 2011 Last revised: 3 Jun 2012

See all articles by Jens Hainmueller

Jens Hainmueller

Stanford University - Department of Political Science; Stanford Graduate School of Business; Stanford Immigration Policy Lab

Date Written: August 4, 2011

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.

Keywords: reweighting, matching, propensity score, causal inference

JEL Classification: C21

Suggested Citation

Hainmueller, Jens, Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies (August 4, 2011). Political Analysis (2012) 20: 25-46. Available at SSRN: https://ssrn.com/abstract=1904869 or http://dx.doi.org/10.2139/ssrn.1904869

Jens Hainmueller (Contact Author)

Stanford University - Department of Political Science ( email )

Stanford, CA 94305
United States

HOME PAGE: http://www.stanford.edu/~jhain/

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Stanford Immigration Policy Lab

30 Alta Road
Stanford, CA 94305
United States

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