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A specification test for the propensity score using its distribution conditional on participation

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Author Info

  • Shaikh, Azeem M.
  • Simonsen, Marianne
  • Vytlacil, Edward J.
  • Yildiz, Nese

Abstract

Propensity score matching has become a popular method for the estimation of average treatment effects. In empirical applications, researchers almost always impose a parametric model for the propensity score. This practice raises the possibility that the model for the propensity score is misspecified and therefore the propensity score matching estimator of the average treatment effect may be inconsistent. We show that the common practice of calculating estimates of the densities of the propensity score conditional on the participation decision provides a means for examining whether the propensity score is misspecified. In particular, we derive a restriction between the density of the propensity score among participants and the density among nonparticipants. We show that this restriction between the two conditional densities is equivalent to a particular orthogonality restriction and derive a formal test based upon it. The resulting test is shown via a simulation study to have dramatically greater power than competing tests for many alternatives. The principal disadvantage of this approach is loss of power against some alternatives.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 151 (2009)
Issue (Month): 1 (July)
Pages: 33-46

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Handle: RePEc:eee:econom:v:151:y:2009:i:1:p:33-46

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Propensity score matching Specification test Nonparametric alternative;

References

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  1. 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.
  2. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
  3. Dehejia, R.H. & Wahba, S., 1998. "Propensity Score Matching Methods for Non-Experimental Causal Studies," Discussion Papers 1998_02, Columbia University, Department of Economics.
  4. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
  5. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
  6. Michael Lechner, 2000. "An Evaluation of Public-Sector-Sponsored Continuous Vocational Training Programs in East Germany," Journal of Human Resources, University of Wisconsin Press, vol. 35(2), pages 347-375.
  7. 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.
  8. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," Econometrica, Econometric Society, vol. 66(5), pages 1017-1098, September.
  9. Lars Skipper & Marianne Simonsen, 2006. "The costs of motherhood: an analysis using matching estimators," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(7), pages 919-934.
  10. Heckman, James J. & Lalonde, Robert J. & Smith, Jeffrey A., 1999. "The economics and econometrics of active labor market programs," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 31, pages 1865-2097 Elsevier.
  11. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
  12. Michael Lechner, 2002. "Program Heterogeneity And Propensity Score Matching: An Application To The Evaluation Of Active Labor Market Policies," The Review of Economics and Statistics, MIT Press, vol. 84(2), pages 205-220, May.
  13. Barbara Sianesi, 2004. "An Evaluation of the Swedish System of Active Labor Market Programs in the 1990s," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 133-155, February.
  14. 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.
  15. Smith, Jeffrey & Todd, Petra, 2005. "Rejoinder," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 365-375.
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Citations

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Cited by:
  1. Steven Lehrer & Gregory Kordas, 2013. "Matching using semiparametric propensity scores," Empirical Economics, Springer, vol. 44(1), pages 13-45, February.
  2. Wang-Sheng Lee, 2013. "Propensity score matching and variations on the balancing test," Empirical Economics, Springer, vol. 44(1), pages 47-80, February.
  3. Martin Huber, 2010. "Testing for covariate balance using quantile regression and resampling methods," University of St. Gallen Department of Economics working paper series 2010 2010-18, Department of Economics, University of St. Gallen.
  4. Dehejia, Rajeev, 2013. "The porous dialectic: Experimental and non-experimental methods in development economics," Working Paper Series UNU-WIDER Research Paper , World Institute for Development Economic Research (UNU-WIDER).
  5. Huber, Martin, 2012. "Identifying causal mechanisms in experiments (primarily) based on inverse probability weighting," Economics Working Paper Series 1213, University of St. Gallen, School of Economics and Political Science, revised May 2013.

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