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On the consistency of bootstrap for matching estimators

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  • Ziming Lin
  • Fang Han

Abstract

In a landmark paper, Abadie and Imbens (2008) showed that the naive bootstrap is inconsistent when applied to nearest neighbor matching estimators of the average treatment effect with a fixed number of matches. Since then, this finding has inspired numerous efforts to address the inconsistency issue, typically by employing alternative bootstrap methods. In contrast, this paper shows that the naive bootstrap is provably consistent for the original matching estimator, provided that the number of matches, $M$, diverges. The bootstrap inconsistency identified by Abadie and Imbens (2008) thus arises solely from the use of a fixed $M$.

Suggested Citation

  • Ziming Lin & Fang Han, 2024. "On the consistency of bootstrap for matching estimators," Papers 2410.23525, arXiv.org, revised Nov 2024.
    • Handle: RePEc:arx:papers:2410.23525
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    References listed on IDEAS

    as
    1. Zhexiao Lin & Fang Han, 2024. "On the failure of the bootstrap for Chatterjee’s rank correlation," Biometrika, Biometrika Trust, vol. 111(3), pages 1063-1070.
    2. James J. Heckman & Hidehiko Ichimura & Petra E. Todd, 1997. "Matching As An Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 605-654.
    3. Zhexiao Lin & Peng Ding & Fang Han, 2023. "Estimation Based on Nearest Neighbor Matching: From Density Ratio to Average Treatment Effect," Econometrica, Econometric Society, vol. 91(6), pages 2187-2217, November.
    4. Bodory, Hugo & Camponovo, Lorenzo & Huber, Martin & Lechner, Michael, 2024. "Nonparametric bootstrap for propensity score matching estimators," Statistics & Probability Letters, Elsevier, vol. 208(C).
    5. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    6. Alberto Abadie & Guido W. Imbens, 2011. "Bias-Corrected Matching Estimators for Average Treatment Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 1-11, January.
    7. Sourav Chatterjee, 2021. "A New Coefficient of Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 2009-2022, October.
    8. Alberto Abadie & Jann Spiess, 2022. "Robust Post-Matching Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 983-995, April.
    9. 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.
    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.
    11. 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.
    12. James J. Heckman & Hidehiko Ichimura & Petra Todd, 1998. "Matching As An Econometric Evaluation Estimator," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(2), pages 261-294.
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