Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score
We are interested in estimating the average effect of a binary treatment on a scalar outcome. If assignment to the treatment is independent of the potential outcomes given pre-treatment variables, biases associated with simple treatment-control average comparisons can be removed by adjusting for differences in the pre-treatment variables. Rosenbaum and Rubin (1983, 1984) show that adjusting solely for differences between treated and control units in a scalar function of the pre-treatment variables, the propensity score, also removes the entire bias associated with differences in pre-treatment variables. Thus it is possible to obtain unbiased estimates of the treatment effect without conditioning on a possibly high-dimensional vector of pre-treatment variables. Although adjusting for the propensity score removes all the bias, this can come at the expense of efficiency. We show that weighting with the inverse of a nonparametric estimate of the propensity score, rather than the true propensity score, leads to an efficient estimate of the population average treatment effect. This result holds whether the pre-treatment variables have discrete or continuous distributions. We provide intuition for this result in a number of ways. First we show that with discrete covariates exact adjustment for the estimated propensity score is identical to adjustment for the pre-treatment variables. Second, we show that weighting by the inverse of the estimated propensity score can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score. Finally we connect our results to other results on efficient estimation through weighting.
|Date of creation:||01 Aug 2000|
|Date of revision:|
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/pastmeetings.asp
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
- 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.
- Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998.
"Information Theoretic Approaches to Inference in Moment Condition Models,"
Econometric Society, vol. 66(2), pages 333-358, March.
- Imbens, G.W. & Johnson, P. & Spady, R.H., 1995. "Information Theoretic Approaches to Inference in Movement Condition Models," Economics Papers 99, Economics Group, Nuffield College, University of Oxford.
- Guido W. Imbens & Phillip Johnson & Richard H. Spady, 1995. "Information Theoretic Approaches to Inference in Moment Condition Models," NBER Technical Working Papers 0186, National Bureau of Economic Research, Inc.
- Guido W. Imbens & Phillip Johnson & Richard H. Spady, 1995. "Information Theoretic Approaches to Inference in Moment Condition Models," Harvard Institute of Economic Research Working Papers 1736, Harvard - Institute of Economic Research.
- Guido W Imbens, Phillip Johnson & Richard H Spady, . "Information theoretic approaches to inference in moment condition model," Economics Papers W12., Economics Group, Nuffield College, University of Oxford.
- 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.
- 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.
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
- Heckman, James J & Ichimura, Hidehiko & Todd, Petra E, 1997. "Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 605-54, October.
- Imbens, Guido W, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," Review of Economic Studies, Wiley Blackwell, vol. 64(3), pages 359-83, July.
- Newey, W.K., 1991.
"The Asymptotic Variance of Semiparametric Estimators,"
583, Massachusetts Institute of Technology (MIT), Department of Economics.
- Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November.
- Newey, W.K., 1989. "The Asymptotic Variance Of Semiparametric Estimotors," Papers 346, Princeton, Department of Economics - Econometric Research Program.
- Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, vol. 67(6), pages 1385-1406, November.
- 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.
- 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.
- 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.
- 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.
- 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.
- Guido W. Imbens & Judith K. Hellerstein, 1996.
"Imposing Moment Restrictions from Auxiliary Data by Weighting,"
NBER Technical Working Papers
0202, National Bureau of Economic Research, Inc.
- 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.
- Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 261-94, April.
When requesting a correction, please mention this item's handle: RePEc:ecm:wc2000:1166. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.