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Bootstrap Inference of Matching Estimators for Average Treatment Effects

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  • Taisuke Otsu
  • Yoshiyasu Rai

Abstract

It is known that the naive bootstrap is not asymptotically valid for a matching estimator of the average treatment effect with a fixed number of matches. In this article, we propose asymptotically valid inference methods for matching estimators based on the weighted bootstrap. The key is to construct bootstrap counterparts by resampling based on certain linear forms of the estimators. Our weighted bootstrap is applicable for the matching estimators of both the average treatment effect and its counterpart for the treated population. Also, by incorporating a bias correction method in Abadie and Imbens (2011), our method can be asymptotically valid even for matching based on a vector of covariates. A simulation study indicates that the weighted bootstrap method is favorably comparable with the asymptotic normal approximation. As an empirical illustration, we apply the proposed method to the National Supported Work data. Supplementary materials for this article are available online.

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  • Taisuke Otsu & Yoshiyasu Rai, 2017. "Bootstrap Inference of Matching Estimators for Average Treatment Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1720-1732, October.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:520:p:1720-1732
    DOI: 10.1080/01621459.2016.1231613
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    9. Andr'es Ram'irez-Hassan & Raquel Vargas-Correa & Gustavo Garc'ia & Daniel Londo~no, 2020. "Optimal selection of the number of control units in kNN algorithm to estimate average treatment effects," Papers 2008.06564, arXiv.org.
    10. Hugo Bodory & Lorenzo Camponovo & Martin Huber & Michael Lechner, 2020. "The Finite Sample Performance of Inference Methods for Propensity Score Matching and Weighting Estimators," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(1), pages 183-200, January.
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    14. D’Arcangelo, Filippo Maria & Pavan, Giulia & Calligaris, Sara, 2022. "The Impact of the European Carbon Market on Firm Productivity: Evidence from Italian Manufacturing Firms," FEEM Working Papers 324170, Fondazione Eni Enrico Mattei (FEEM).
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    18. Huber, Martin & Camponovo, Lorenzo & Bodory, Hugo & Lechner, Michael, 2016. "A wild bootstrap algorithm for propensity score matching estimators," FSES Working Papers 470, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
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    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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