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Moving the Goalposts: Addressing Limited Overlap in the Estimation of Average Treatment Effects by Changing the Estimand

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  • Richard K. Crump
  • V. Joseph Hotz
  • Guido W. Imbens
  • Oscar A. Mitnik

Abstract

Estimation of average treatment effects under unconfoundedness or exogenous treatment assignment is often hampered by lack of overlap in the covariate distributions. This lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification. In such cases researchers have often used informal methods for trimming the sample. In this paper we develop a systematic approach to addressing such lack of overlap. We characterize optimal subsamples for which the average treatment effect can be estimated most precisely, as well as optimally weighted average treatment effects. Under some conditions the optimal selection rules depend solely on the propensity score. For a wide range of distributions a good approximation to the optimal rule is provided by the simple selection rule to drop all units with estimated propensity scores outside the range [0.1,0.9].

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0330.

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Date of creation: Oct 2006
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Handle: RePEc:nbr:nberte:0330

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  1. 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, Wiley Blackwell, vol. 64(4), pages 605-54, October.
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  4. Crump, Richard K. & Hotz, V. Joseph & Imbens, Guido W. & Mitnik, Oscar A., 2006. "Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand," IZA Discussion Papers 2347, Institute for the Study of Labor (IZA).
  5. Crump, Richard K. & Hotz, V. Joseph & Imbens, Guido W. & Mitnik, Oscar A., 2006. "Nonparametric Tests for Treatment Effect Heterogeneity," IZA Discussion Papers 2091, Institute for the Study of Labor (IZA).
  6. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, Econometric Society, vol. 74(1), pages 235-267, 01.
  7. Joshua D. Angrist & Guido W. Imbens, 1995. "Identification and Estimation of Local Average Treatment Effects," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0118, National Bureau of Economic Research, Inc.
  8. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, American Economic Association, vol. 93(2), pages 126-132, May.
  9. Joshua D. Angrist, 1998. "Estimating the Labor Market Impact of Voluntary Military Service Using Social Security Data on Military Applicants," Econometrica, Econometric Society, Econometric Society, vol. 66(2), pages 249-288, March.
  10. Jeffrey Smith & Petra Todd, 2003. "Does Matching Overcome Lalonde's Critique of Nonexperimental Estimators?," University of Western Ontario, CIBC Centre for Human Capital and Productivity Working Papers, University of Western Ontario, CIBC Centre for Human Capital and Productivity 20035, University of Western Ontario, CIBC Centre for Human Capital and Productivity.
  11. Guido W. Imbens & Whitney Newey & Geert Ridder, 2006. "Mean-squared-error Calculations for Average Treatment Effects," IEPR Working Papers, Institute of Economic Policy Research (IEPR) 06.57, Institute of Economic Policy Research (IEPR).
  12. Guido W. Imbens, 2003. "Nonparametric Estimation of Average Treatment Effects under Exogeneity: A Review," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0294, National Bureau of Economic Research, Inc.
  13. Guido Imbens, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 1166, Econometric Society.
  14. Xiaohong Chen & Han Hong & Alessandro Tarozzi, 2008. "Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1644, Cowles Foundation for Research in Economics, Yale University.
  15. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, American Economic Association, vol. 76(4), pages 604-20, September.
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  20. 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.
  21. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," Econometrica, Econometric Society, Econometric Society, vol. 66(5), pages 1017-1098, September.
  22. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, Econometric Society, vol. 66(2), pages 315-332, March.
  23. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(2), pages 261-94, April.
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