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Matching on the Estimated Propensity Score

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  • Alberto Abadie
  • Guido W. Imbens

Abstract

Propensity score matching estimators (Rosenbaum and Rubin, 1983) are widely used in evaluation research to estimate average treatment effects. In this article, we derive the large sample distribution of propensity score matching estimators. Our derivations take into account that the propensity score is itself estimated in a first step, prior to matching. We prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators. Moreover, we derive an adjustment to the large sample variance of propensity score matching estimators that corrects for first step estimation of the propensity score. In spite of the great popularity of propensity score matching estimators, these results were previously unavailable in the literature.

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File URL: http://www.nber.org/papers/w15301.pdf
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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 15301.

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Date of creation: Aug 2009
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Handle: RePEc:nbr:nberwo:15301

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  1. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, 07.
  2. Elena Andreou & Bas J. M. Werker, 2012. "An Alternative Asymptotic Analysis of Residual-Based Statistics," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 88-99, February.
  3. Alberto Abadie & Guido W. Imbens, 2008. "On the Failure of the Bootstrap for Matching Estimators," Econometrica, Econometric Society, vol. 76(6), pages 1537-1557, November.
  4. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, 01.
  5. repec:cup:cbooks:9780521496032 is not listed on IDEAS
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Cited by:
  1. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2013. "The performance of estimators based on the propensity score," Journal of Econometrics, Elsevier, vol. 175(1), pages 1-21.
  2. Daniel L. Millimet & Rusty Tchernis, 2009. "Estimation of Treatment Effects Without an Exclusion Restriction: with an Application to the Analysis of the School Breakfast Program," NBER Working Papers 15539, National Bureau of Economic Research, Inc.
  3. David Kaplan & Jianshen Chen, 2012. "A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study," Psychometrika, Springer, vol. 77(3), pages 581-609, July.

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