IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v36y2025icp81-89.html

Nearest neighbor matching: M-out-of-N bootstrapping without bias correction vs. the naive bootstrap

Author

Listed:
  • Walsh, Christopher
  • Jentsch, Carsten

Abstract

It is well known that the limiting variance of nearest neighbor matching estimators cannot be consistently estimated by a naive Efron-type bootstrap as the conditional variance of the bootstrap estimator does not generally converge to the correct limit in expectation. In essence this is caused by the fact that the bootstrap sample contains ties with positive probability even when the sample size becomes large. This negative result was originally derived in a simple setting by Abadie and Imbens (ECONOMETRICA, pp. 235–267, 76(6), 2008). A proof of concept for a direct M-out-of-N bootstrap on the data is provided in this setting. It is proven that in this setting the conditional variance of a direct M-out-of-N-type bootstrap estimator without bias-correction does converge to the correct limit in expectation. The key to the proof lies in the fact that asymptotically with probability one there are no ties in the bootstrap sample. The potential of the direct M-out-of-N-type bootstrap is investigated in simulations.

Suggested Citation

  • Walsh, Christopher & Jentsch, Carsten, 2025. "Nearest neighbor matching: M-out-of-N bootstrapping without bias correction vs. the naive bootstrap," Econometrics and Statistics, Elsevier, vol. 36(C), pages 81-89.
    • Handle: RePEc:eee:ecosta:v:36:y:2025:i:c:p:81-89
    DOI: 10.1016/j.ecosta.2023.04.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S245230622300031X
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2023.04.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Alberto Abadie & Guido W. Imbens, 2008. "On the Failure of the Bootstrap for Matching Estimators," Econometrica, Econometric Society, vol. 76(6), pages 1537-1557, November.
    3. 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.
    4. Alberto Abadie & Guido W. Imbens, 2012. "A Martingale Representation for Matching Estimators," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 833-843, June.
    5. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bodory, Hugo & Camponovo, Lorenzo & Huber, Martin & Lechner, Michael, 2024. "Nonparametric bootstrap for propensity score matching estimators," Statistics & Probability Letters, Elsevier, vol. 208(C).
    2. 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.
    3. 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.
    4. Yihui He & Fang Han, 2023. "On propensity score matching with a diverging number of matches," Papers 2310.14142, arXiv.org, revised Nov 2023.
    5. Songliang Chen & Fang Han, 2024. "On the limiting variance of matching estimators," Papers 2411.05758, arXiv.org.
    6. Roth, Jonathan & Sant’Anna, Pedro H.C. & Bilinski, Alyssa & Poe, John, 2023. "What’s trending in difference-in-differences? A synthesis of the recent econometrics literature," Journal of Econometrics, Elsevier, vol. 235(2), pages 2218-2244.
    7. Ziming Lin & Fang Han, 2024. "On the consistency of bootstrap for matching estimators," Papers 2410.23525, arXiv.org, revised Nov 2024.
    8. Taisuke Otsu & Mengshan Xu, 2022. "Isotonic propensity score matching," STICERD - Econometrics Paper Series 623, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Glazer Amanda K. & Pimentel Samuel D., 2023. "Robust inference for matching under rolling enrollment," Journal of Causal Inference, De Gruyter, vol. 11(1), pages 1-19, January.
    10. 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.
    11. Ferman, Bruno, 2021. "Matching estimators with few treated and many control observations," Journal of Econometrics, Elsevier, vol. 225(2), pages 295-307.
    12. Shu Yang & Yunshu Zhang, 2023. "Multiply robust matching estimators of average and quantile treatment effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 235-265, March.
    13. Mengshan Xu & Taisuke Otsu, 2022. "Isotonic propensity score matching," Papers 2207.08868, arXiv.org, revised Jan 2025.
    14. Matthew Blackwell & Anton Strezhnev, 2022. "Telescope matching for reducing model dependence in the estimation of the effects of time‐varying treatments: An application to negative advertising," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 377-399, January.
    15. Zhexiao Lin & Peng Ding & Fang Han, 2021. "Estimation based on nearest neighbor matching: from density ratio to average treatment effect," Papers 2112.13506, arXiv.org.
    16. Magambo, Isaiah & Dikgang, Johane & Gelo, Dambala & Tregenna, Fiona, 2021. "Gold-Mining Pollution Exposure, Health Effects and Private Healthcare Expenditure in Tanzania," MPRA Paper 108800, University Library of Munich, Germany.
    17. Francesca Baratta & Elena Folpini & Michele Ciccolella & Paola Brusa, 2023. "Patient Care in Community Pharmacies during the COVID-19 (SARS-CoV-2) Pandemic: Effectiveness of Post-Graduate Education and Further Training Courses on Revenues," IJERPH, MDPI, vol. 20(5), pages 1-8, February.
    18. Jeon, Jin Q. & Lee, Cheolwoo & Nasser, Tareque & Via, M. Tony, 2015. "Multiple lead underwriter IPOs and firm visibility," Journal of Corporate Finance, Elsevier, vol. 32(C), pages 128-149.
    19. Almer, Christian & Winkler, Ralph, 2017. "Analyzing the effectiveness of international environmental policies: The case of the Kyoto Protocol," Journal of Environmental Economics and Management, Elsevier, vol. 82(C), pages 125-151.
    20. Schlueter, Tobias & Sievers, Soenke & Hartmann-Wendels, Thomas, 2015. "Bank funding stability, pricing strategies and the guidance of depositors," Journal of Banking & Finance, Elsevier, vol. 51(C), pages 43-61.

    More about this item

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecosta:v:36:y:2025:i:c:p:81-89. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/econometrics-and-statistics .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.