TY - JOUR AU - Abadie,Alberto AU - Imbens,Guido W. TI - Matching on the Estimated Propensity Score JF - National Bureau of Economic Research Working Paper Series VL - No. 15301 PY - 2009 Y2 - August 2009 UR - http://www.nber.org/papers/w15301 L1 - http://www.nber.org/papers/w15301.pdf N1 - Author contact info: Alberto Abadie John F. Kennedy School of Government Harvard University 79 JFK Street Cambridge, MA 02138 Tel: 617/496-4547 Fax: 617/496-5960 E-Mail: alberto_abadie@harvard.edu Guido Imbens Department of Economics Littauer Center Harvard University 1805 Cambridge Street Cambridge, MA 02138 Tel: 617/384-7485 Fax: 617/495-7730 E-Mail: imbens@fas.harvard.edu AB - 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. ER -