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Specification tests for generalized propensity scores using double projections

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  • Pedro H. C. Sant'Anna
  • Xiaojun Song

Abstract

This paper proposes a new class of nonparametric tests for the correct specification of generalized propensity score models. The test procedure is based on two different projection arguments, which lead to test statistics with several appealing properties. They accommodate high-dimensional covariates; are asymptotically invariant to the estimation method used to estimate the nuisance parameters and do not requite estimators to be root-n asymptotically linear; are fully data-driven and do not require tuning parameters, can be written in closed-form, facilitating the implementation of an easy-to-use multiplier bootstrap procedure. We show that our proposed tests are able to detect a broad class of local alternatives converging to the null at the parametric rate. Monte Carlo simulation studies indicate that our double projected tests have much higher power than other tests available in the literature, highlighting their practical appeal.

Suggested Citation

  • Pedro H. C. Sant'Anna & Xiaojun Song, 2020. "Specification tests for generalized propensity scores using double projections," Papers 2003.13803, arXiv.org.
  • Handle: RePEc:arx:papers:2003.13803
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    References listed on IDEAS

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    1. Escanciano, J. Carlos, 2006. "A Consistent Diagnostic Test For Regression Models Using Projections," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1030-1051, December.
    2. Sokbae Lee & Ryo Okui & Yoon†Jae Whang, 2017. "Doubly robust uniform confidence band for the conditional average treatment effect function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(7), pages 1207-1225, November.
    3. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    4. Cattaneo, Matias D., 2010. "Efficient semiparametric estimation of multi-valued treatment effects under ignorability," Journal of Econometrics, Elsevier, vol. 155(2), pages 138-154, April.
    5. Mora, Juan & Moro-Egido, Ana I., 2008. "On specification testing of ordered discrete choice models," Journal of Econometrics, Elsevier, vol. 143(1), pages 191-205, March.
    6. Shu Yang & Guido W. Imbens & Zhanglin Cui & Douglas E. Faries & Zbigniew Kadziola, 2016. "Propensity score matching and subclassification in observational studies with multi‐level treatments," Biometrics, The International Biometric Society, vol. 72(4), pages 1055-1065, December.
    7. 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.
    8. S. Derya Uysal, 2015. "Doubly Robust Estimation of Causal Effects with Multivalued Treatments: An Application to the Returns to Schooling," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 763-786, August.
    9. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, December.
    10. Sun, Zhihua & Chen, Feifei & Zhou, Xiaohua & Zhang, Qingzhao, 2017. "Improved model checking methods for parametric models with responses missing at random," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 147-161.
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