IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2602.16376.html

Two-way Clustering Robust Variance Estimator in Quantile Regression Models

Author

Listed:
  • Ulrich Hounyo
  • Jiahao Lin

Abstract

We study inference for linear quantile regression with two-way clustered data. Using a separately exchangeable array framework and a projection decomposition of the quantile score, we characterize regime-dependent convergence rates and establish a self-normalized Gaussian approximation. We propose a two-way cluster-robust sandwich variance estimator with a kernel-based density ``bread'' and a projection-matched ``meat'', and prove consistency and validity of inference in Gaussian regimes. We also show an impossibility result for uniform inference in a non-Gaussian interaction regime.

Suggested Citation

  • Ulrich Hounyo & Jiahao Lin, 2026. "Two-way Clustering Robust Variance Estimator in Quantile Regression Models," Papers 2602.16376, arXiv.org.
    • Handle: RePEc:arx:papers:2602.16376
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2602.16376
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bryan S. Graham, 2024. "Sparse Network Asymptotics for Logistic Regression Under Possible Misspecification," Econometrica, Econometric Society, vol. 92(6), pages 1837-1868, November.
    2. 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.
    3. Bradley Larsen & Ziao Ju & Adam Kapor & Chuan Yu, 2020. "The Effect of Occupational Licensing Stringency on the Teacher Quality Distribution," NBER Working Papers 28158, National Bureau of Economic Research, Inc.
    4. Andreas Hagemann, 2017. "Cluster-Robust Bootstrap Inference in Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 446-456, January.
    5. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    6. Kallenberg, Olav, 1989. "On the representation theorem for exchangeable arrays," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 137-154, July.
    7. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2019. "Empirical Process Results for Exchangeable Arrays," Papers 1906.11293, arXiv.org, revised May 2020.
    8. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2011. "Robust Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(2), pages 238-249, April.
    9. Parente Paulo M.D.C. & Santos Silva João M.C., 2016. "Quantile Regression with Clustered Data," Journal of Econometric Methods, De Gruyter, vol. 5(1), pages 1-15, January.
    10. Antonio F. Galvao & Jungmo Yoon, 2024. "HAC Covariance Matrix Estimation in Quantile Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(547), pages 2305-2316, July.
    11. Kraft, Matthew A. & Brunner, Eric J. & Dougherty, Shaun M. & Schwegman, David J., 2020. "Teacher accountability reforms and the supply and quality of new teachers," Journal of Public Economics, Elsevier, vol. 188(C).
    12. Kengo Kato, 2012. "Asymptotic normality of Powell’s kernel estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 255-273, April.
    13. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2018. "Asymptotic results under multiway clustering," Papers 1807.07925, arXiv.org, revised Aug 2018.
    14. Konrad Menzel, 2021. "Bootstrap With Cluster‐Dependence in Two or More Dimensions," Econometrica, Econometric Society, vol. 89(5), pages 2143-2188, September.
    15. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
    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. Chen, Kaicheng & Vogelsang, Timothy J., 2024. "Fixed-b asymptotics for panel models with two-way clustering," Journal of Econometrics, Elsevier, vol. 244(1).
    2. Laurent Davezies & Xavier D'Haultf{oe}uille & Yannick Guyonvarch, 2025. "Analytic inference with two-way clustering," Papers 2506.20749, arXiv.org, revised Feb 2026.
    3. Chiang, Harold D. & Matsushita, Yukitoshi & Otsu, Taisuke, 2025. "Multiway empirical likelihood," Journal of Econometrics, Elsevier, vol. 249(PA).
    4. Kaicheng Chen & Harold D. Chiang, 2026. "Cross-Fitting-Free Debiased Machine Learning with Multiway Dependence," Papers 2602.11333, arXiv.org, revised Apr 2026.
    5. Liu, Nan & Liu, Yanbo & Sasaki, Yuya, 2026. "Estimation and inference for causal functions with multi-way clustered data," Journal of Econometrics, Elsevier, vol. 253(C).
    6. Harold D Chiang & Yukun Ma & Joel Rodrigue & Yuya Sasaki, 2021. "Dyadic double/debiased machine learning for analyzing determinants of free trade agreements," Papers 2110.04365, arXiv.org, revised Dec 2022.
    7. James G. MacKinnon & Morten {O}rregaard Nielsen & Matthew D. Webb, 2024. "Jackknife inference with two-way clustering," Papers 2406.08880, arXiv.org, revised Mar 2026.
    8. Koen Jochmans, 2026. "Two-Way Clustering with Non-Exchangeable Data," Working Papers hal-05471067, HAL.
    9. Yap, Luther, 2025. "Asymptotic theory for two-way clustering," Journal of Econometrics, Elsevier, vol. 249(PB).
    10. Ruonan Xu & Luther Yap, 2024. "Clustering with Potential Multidimensionality: Inference and Practice," Papers 2411.13372, arXiv.org.
    11. Harold D. Chiang & Kengo Kato & Yuya Sasaki, 2023. "Inference for High-Dimensional Exchangeable Arrays," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 1595-1605, July.
    12. Richard K. Crump & Nikolay Gospodinov & Ignacio Lopez Gaffney, 2024. "A New Jackknife Variance Estimator for Time-Series and Panel Regressions," Staff Reports 1133, Federal Reserve Bank of New York.
    13. Harold D. Chiang & Kengo Kato & Yukun Ma & Yuya Sasaki, 2022. "Multiway Cluster Robust Double/Debiased Machine Learning," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1046-1056, June.
    14. 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.
    15. Wang, Wenjie & Zhang, Yichong, 2024. "Wild bootstrap inference for instrumental variables regressions with weak and few clusters," Journal of Econometrics, Elsevier, vol. 241(1).
    16. Bruno Ferman, 2023. "Inference in difference‐in‐differences: How much should we trust in independent clusters?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 358-369, April.
    17. Daniel Gaigall & Stefan Weber, 2025. "Jointly Exchangeable Collective Risk Models: Interaction, Structure, and Limit Theorems," Papers 2504.06287, arXiv.org, revised Feb 2026.
    18. 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.
    19. 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.
    20. Lu, Xun & Su, Liangjun, 2023. "Uniform inference in linear panel data models with two-dimensional heterogeneity," Journal of Econometrics, Elsevier, vol. 235(2), pages 694-719.

    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:2602.16376. 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: http://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.