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Specification tests for the propensity score

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  • Sant’Anna, Pedro H.C.
  • Song, Xiaojun

Abstract

This paper proposes new nonparametric diagnostic tools to assess the asymptotic validity of different treatment effects estimators that rely on the correct specification of the propensity score. We derive a particular restriction relating the propensity score distribution of treated and control groups, and develop specification tests based upon it. The resulting tests do not suffer from the “curse of dimensionality” when the vector of covariates is high-dimensional, are fully data-driven, do not require tuning parameters such as bandwidths, and are able to detect a broad class of local alternatives converging to the null at the parametric rate n−1∕2, with n the sample size. We show that the use of an orthogonal projection on the tangent space of nuisance parameters facilitates the simulation of critical values by means of a multiplier bootstrap procedure, and can lead to power gains. The finite sample performance of the tests is examined by means of a Monte Carlo experiment and an empirical application. Open-source software is available for implementing the proposed tests.

Suggested Citation

  • Sant’Anna, Pedro H.C. & Song, Xiaojun, 2019. "Specification tests for the propensity score," Journal of Econometrics, Elsevier, vol. 210(2), pages 379-404.
  • Handle: RePEc:eee:econom:v:210:y:2019:i:2:p:379-404
    DOI: 10.1016/j.jeconom.2019.02.002
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    Cited by:

    1. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    2. Pedro H. C. Sant'Anna & Xiaojun Song & Qi Xu, 2022. "Covariate distribution balance via propensity scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1093-1120, September.
    3. Hans Fricke & Markus Frölich & Martin Huber & Michael Lechner, 2020. "Endogeneity and non‐response bias in treatment evaluation – nonparametric identification of causal effects by instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(5), pages 481-504, August.
    4. Pedro H. C. Sant'Anna & Xiaojun Song, 2020. "Specification tests for generalized propensity scores using double projections," Papers 2003.13803, arXiv.org.
    5. Frazier, David T. & Oka, Tatsushi & Zhu, Dan, 2019. "Indirect inference with a non-smooth criterion function," Journal of Econometrics, Elsevier, vol. 212(2), pages 623-645.

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    More about this item

    Keywords

    Empirical processes; Integrated moments; Multiplier bootstrap; Projection; Treatment effects;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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