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Matching on the Estimated Propensity Score

  • Alberto Abadie
  • Guido W. Imbens

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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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
Note: LS
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  1. repec:dgr:kubcen:200456 is not listed on IDEAS
  2. Imbens, Guido & Abadie, Alberto, 2008. "On the Failure of the Bootstrap for Matching Estimators," Scholarly Articles 3043415, Harvard University Department of Economics.
  3. 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.
  4. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  5. 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.
  6. Andreou, E. & Werker, B.J.M., 2004. "An Alternative Asymptotic Analysis of Residual-Based Statistics," Discussion Paper 2004-56, Tilburg University, Center for Economic Research.
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