Skip to main content
×
Home
    • Aa
    • Aa

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

  • Jens Hainmueller (a1)
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.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

M. Brookhart , S. Schneeweiss , K. Rothman , R. Glynn , J. Avorn , and T. Sturmer 2006. Variable selection for propensity score models. American Journal of Epidemiology 163: 1149–56.

S. DellaVigna , and E. Kaplan 2007. The Fox News effect: Media bias and voting. Quarterly Journal of Economics 122: 1187–34.

W. Deming , and F. Stephan 1940. On the least squares adjustment of a sampled frequency table when the expected marginal totals are known. The Annals of Mathematical Statistics 11: 427–44.

C. Drake 1993. Effects of misspecification of the propensity score on estimators of treatment effect. Biometrics 49: 1231–36.

M. Frölich 2007. Propensity score matching without conditional independence assumption with an application to the gender wage gap in the United Kingdom. The Econometrics Journal 10: 359407.

B. B. Hansen , and J. Bowers 2008. Covariate balance in simple, stratified and clustered comparative studies. Statistical Science 23: 219–36.

K. Imai , G. King , and E. Stuart 2008. Misunderstandings among experimentalists and observationalists: Balance test fallacies in causal inference. Journal of the Royal Statistical Society, Series A 171: 481502.

G. Imbens 2004. Nonparametric estimation of average treatment effects under exogeneity: A review. Review of Economics and Statistics 86: 429.

G. Imbens , R. Spady , and P. Johnson 1998. Information theoretic approaches to inference in moment condition models. Econometrica 66: 333–57.

J. Ladd , and G. Lenz 2009. Exploiting a rare communication shift to document the persuasive power of the news media. American Journal of Political Science 53: 394–10.

J. Ladd , and G. Lenz 2009. Exploiting a rare communication shift to document the persuasive power of the news media. American Journal of Political Science 53: 394–10.

D. McCaffrey , G. Ridgeway , and A. Morral 2004. Propensity score estimation with boosted regression for evaluating adolescent substance abuse treatment. Psychological Methods 9: 403–25.

J. Qin , B. Zhang , and D. Leung 2009. Empirical likelihood in missing data problems. Journal of the American Statistical Association 104: 1492–503.

T. Read , and N. Cressie 1988. Goodness-of-fit statistics for discrete multivariate data. New York: Springer.

P. R. Rosenbaum , and D. B. Rubin 1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70: 4155.

J. S. Sekhon 2009. Opiates for the matches: Matching methods for causal inference. Annual Review of Political Science 12: 487–08.

J. Smith , and P. Todd 2001. Reconciling conflicting evidence on the performance of propensity-score matching methods. American Economic Review 91: 112–18.

Z. Zhao 2004. Using matching to estimate treatment effects: Data requirements, matching metrics, and Monte Carlo evidence. Review of Economics and Statistics 86: 91107.

Z. Zhao 2004. Using matching to estimate treatment effects: Data requirements, matching metrics, and Monte Carlo evidence. Review of Economics and Statistics 86: 91107.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax
Type Description Title
PDF
Supplementary Materials

Hainmueller supplementary material
Appendix

 PDF (665 KB)
665 KB

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 9 *
Loading metrics...

Abstract views

Total abstract views: 71 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 30th March 2017. This data will be updated every 24 hours.