IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2603.18870.html

Inference in Regression Discontinuity Designs with Clustered Data

Author

Listed:
  • Claudia Noack
  • Tomasz Olma
  • Christoph Rothe

Abstract

Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and derive high-level conditions under which the standard local linear RD estimator is asymptotically normal. We verify that our high-level assumptions hold across a wide range of empirical designs, including settings of growing cluster sizes. We further show that clustered standard errors that are currently used in practice can be either inconsistent or overly conservative in finite samples. To address these issues, we propose a novel nearest-neighbor-type variance estimator and illustrate its properties in a diverse set of empirical applications.

Suggested Citation

  • Claudia Noack & Tomasz Olma & Christoph Rothe, 2026. "Inference in Regression Discontinuity Designs with Clustered Data," Papers 2603.18870, arXiv.org.
    • Handle: RePEc:arx:papers:2603.18870
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2603.18870
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bhattacharya, Debopam, 2005. "Asymptotic inference from multi-stage samples," Journal of Econometrics, Elsevier, vol. 126(1), pages 145-171, May.
    2. Djogbenou, Antoine A. & MacKinnon, James G. & Nielsen, Morten Ørregaard, 2019. "Asymptotic theory and wild bootstrap inference with clustered errors," Journal of Econometrics, Elsevier, vol. 212(2), pages 393-412.
    3. Claudia Noack & Christoph Rothe, 2024. "Bias‐Aware Inference in Fuzzy Regression Discontinuity Designs," Econometrica, Econometric Society, vol. 92(3), pages 687-711, May.
    4. A. Colin Cameron & Douglas L. Miller, 2015. "A Practitioner’s Guide to Cluster-Robust Inference," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 317-372.
    5. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    6. Melanie Wasserman, 2021. "Up the Political Ladder: Gender Parity in the Effects of Electoral Defeats," AEA Papers and Proceedings, American Economic Association, vol. 111, pages 169-173, May.
    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. Shimizu, Yuya, 2025. "Nonparametric regression under cluster sampling," Journal of Econometrics, Elsevier, vol. 252(PA).
    2. Jean-Marie Dufour & Tianyu He, 2025. "Nonparametric methods for comparing distribution functionals for dependent samples with application to inequality measures," Papers 2512.21862, arXiv.org.
    3. Wenjie Wang & Yichong Zhang, 2021. "Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters," Papers 2108.13707, arXiv.org, revised Jan 2024.
    4. Yuya Sasaki & Yulong Wang, 2022. "Non-Robustness of the Cluster-Robust Inference: with a Proposal of a New Robust Method," Papers 2210.16991, arXiv.org, revised Jan 2025.
    5. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    6. Guillermo Cruces & Dario Tortarolo & Gonzalo Vazquez-Bare, 2023. "Design of partial population experiments with an application to spillovers in tax compliance," IFS Working Papers W23/17, Institute for Fiscal Studies.
    7. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Testing for the appropriate level of clustering in linear regression models," Journal of Econometrics, Elsevier, vol. 235(2), pages 2027-2056.
    8. Doko Tchatoka, Firmin & Wang, Wenjie, 2021. "Size-corrected Bootstrap Test after Pretesting for Exogeneity with Heteroskedastic or Clustered Data," MPRA Paper 110899, University Library of Munich, Germany.
    9. Guillermo Cruces & Dario Tortarolo & Gonzalo Vazquez-Bare, 2022. "Design of two-stage experiments with an application to spillovers in tax compliance," IFS Working Papers W22/32, Institute for Fiscal Studies.
    10. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2023. "Leverage, influence, and the jackknife in clustered regression models: Reliable inference using summclust," Stata Journal, StataCorp LLC, vol. 23(4), pages 942-982, December.
    11. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2021. "Wild Bootstrap and Asymptotic Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 505-519, March.
    12. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2024. "Cluster-Robust Jackknife and Bootstrap Inference for Binary Response Models," Working Paper 1515, Economics Department, Queen's University.
    13. Tom Boot & Gianmaria Niccodemi & Tom Wansbeek, 2023. "Unbiased estimation of the OLS covariance matrix when the errors are clustered," Empirical Economics, Springer, vol. 64(6), pages 2511-2533, June.
    14. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Cluster-robust inference: A guide to empirical practice," Journal of Econometrics, Elsevier, vol. 232(2), pages 272-299.
    15. James G. MacKinnon & Morten {O}rregaard Nielsen & Matthew D. Webb, 2024. "Cluster-robust jackknife and bootstrap inference for logistic regression models," Papers 2406.00650, arXiv.org, revised May 2025.
    16. Hwang, Jungbin, 2021. "Simple and trustworthy cluster-robust GMM inference," Journal of Econometrics, Elsevier, vol. 222(2), pages 993-1023.
    17. Djogbenou, Antoine A. & MacKinnon, James G. & Nielsen, Morten Ørregaard, 2019. "Asymptotic theory and wild bootstrap inference with clustered errors," Journal of Econometrics, Elsevier, vol. 212(2), pages 393-412.
    18. James G. MacKinnon & Matthew D. Webb, 2020. "When and How to Deal with Clustered Errors in Regression Models," Working Paper 1421, Economics Department, Queen's University.
    19. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2023. "Fast and reliable jackknife and bootstrap methods for cluster‐robust inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(5), pages 671-694, August.
    20. Peter Z. Schochet, 2025. "Power Analyses for Estimation of Complier Average Causal Effects Under Random Encouragement Designs in Education Research: Theory and Guidance," Journal of Educational and Behavioral Statistics, , vol. 50(1), pages 44-71, February.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2603.18870. 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.