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

Author

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  • 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.

Suggested Citation

  • Shaikh, Azeem M. & Simonsen, Marianne & Vytlacil, Edward J. & Yildiz, Nese, 2009. "A specification test for the propensity score using its distribution conditional on participation," Journal of Econometrics, Elsevier, vol. 151(1), pages 33-46, July.
  • Handle: RePEc:eee:econom:v:151:y:2009:i:1:p:33-46
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    References listed on IDEAS

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    3. Martin Huber, 2011. "Testing for covariate balance using quantile regression and resampling methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2881-2899, February.
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    5. Russell Davidson & Victoria Zinde-Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics, Canadian Economics Association, vol. 50(5), pages 1595-1631, December.
    6. Steven Lehrer & Gregory Kordas, 2013. "Matching using semiparametric propensity scores," Empirical Economics, Springer, vol. 44(1), pages 13-45, February.
    7. Sant’Anna, Pedro H.C. & Song, Xiaojun, 2019. "Specification tests for the propensity score," Journal of Econometrics, Elsevier, vol. 210(2), pages 379-404.
    8. Caliendo, Marco & Mahlstedt, Robert & Mitnik, Oscar A., 2017. "Unobservable, but unimportant? The relevance of usually unobserved variables for the evaluation of labor market policies," Labour Economics, Elsevier, vol. 46(C), pages 14-25.
    9. Wang-Sheng Lee, 2013. "Propensity score matching and variations on the balancing test," Empirical Economics, Springer, vol. 44(1), pages 47-80, February.
    10. Li Liang & Greene Tom, 2013. "A Weighting Analogue to Pair Matching in Propensity Score Analysis," The International Journal of Biostatistics, De Gruyter, vol. 9(2), pages 215-234, July.
    11. Pedro H. C. Sant'Anna & Xiaojun Song, 2020. "Specification tests for generalized propensity scores using double projections," Papers 2003.13803, arXiv.org.
    12. 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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