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Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score

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  • Keisuke Hirano
  • Guido W. Imbens
  • Geert Ridder

Abstract

We are interested in estimating the average effect of a binary treatment on a scalar outcome. If assignment to the treatment is exogenous or unconfounded, that is, independent of the potential outcomes given covariates, biases associated with simple treatment-control average comparisons can be removed by adjusting for differences in the covariates. Rosenbaum and Rubin (1983) show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates. Although adjusting for differences in the propensity score removes all the bias, this can come at the expense of efficiency, as shown by Hahn (1998), Heckman, Ichimura, and Todd (1998), and Robins, Mark, and Newey (1992). We show that weighting by the inverse of a nonparametric estimate of the propensity score, rather than the true propensity score, leads to an efficient estimate of the average treatment effect. We provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score. Copyright The Econometric Society 2003.

Suggested Citation

  • 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, July.
    • Handle: RePEc:ecm:emetrp:v:71:y:2003:i:4:p:1161-1189
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. James J. Heckman & Hidehiko Ichimura & Petra E. Todd, 1997. "Matching As An Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 605-654.
    3. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    4. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    5. Crepon, Bruno & Kramarz, Francis & Trognon, Alain, 1997. "Parameters of interest, nuisance parameters and orthogonality conditions An application to autoregressive error component models," Journal of Econometrics, Elsevier, vol. 82(1), pages 135-156.
    6. Judith K. Hellerstein & Guido W. Imbens, 1999. "Imposing Moment Restrictions From Auxiliary Data By Weighting," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 1-14, February.
    7. Joshua D. Angrist & Jinyong Hahn, 1999. "When to Control for Covariates? Panel-Asymptotic Results for Estimates of Treatment Effects," NBER Technical Working Papers 0241, National Bureau of Economic Research, Inc.
    8. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
    9. Lechner, Michael, 1999. "Earnings and Employment Effects of Continuous Off-the-Job Training in East Germany after Unification," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 74-90, January.
    10. Rajeev H. Dehejia & Sadek Wahba, 1998. "Causal Effects in Non-Experimental Studies: Re-Evaluating the Evaluation of Training Programs," NBER Working Papers 6586, National Bureau of Economic Research, Inc.
    11. V. Joseph Hotz & Guido W. Imbens & Julie H. Mortimer, 1999. "Predicting the Efficacy of Future Training Programs Using Past Experiences," NBER Technical Working Papers 0238, National Bureau of Economic Research, Inc.
    12. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267.
    13. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    14. James J. Heckman & Hidehiko Ichimura & Petra Todd, 1998. "Matching As An Econometric Evaluation Estimator," Review of Economic Studies, Oxford University Press, vol. 65(2), pages 261-294.
    15. Guido W. Imbens, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," Review of Economic Studies, Oxford University Press, vol. 64(3), pages 359-383.
    16. Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, vol. 67(6), pages 1385-1406, November.
    17. Qian, Hailong & Schmidt, Peter, 1999. "Improved instrumental variables and generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 91(1), pages 145-169, July.
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