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

Published online by Cambridge University Press:  04 January 2017

Jens Hainmueller*
Department of Political Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139. e-mail:


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.

Research Article
Copyright © The Author 2011. Published by Oxford University Press on behalf of the Society for Political Methodology 

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