IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2206.09644.html
   My bibliography  Save this paper

Unbiased estimation of the OLS covariance matrix when the errors are clustered

Author

Listed:
  • Tom Boot
  • Gianmaria Niccodemi
  • Tom Wansbeek

Abstract

When data are clustered, common practice has become to do OLS and use an estimator of the covariance matrix of the OLS estimator that comes close to unbiasedness. In this paper we derive an estimator that is unbiased when the random-effects model holds. We do the same for two more general structures. We study the usefulness of these estimators against others by simulation, the size of the $t$-test being the criterion. Our findings suggest that the choice of estimator hardly matters when the regressor has the same distribution over the clusters. But when the regressor is a cluster-specific treatment variable, the choice does matter and the unbiased estimator we propose for the random-effects model shows excellent performance, even when the clusters are highly unbalanced.

Suggested Citation

  • Tom Boot & Gianmaria Niccodemi & Tom Wansbeek, 2022. "Unbiased estimation of the OLS covariance matrix when the errors are clustered," Papers 2206.09644, arXiv.org.
    • Handle: RePEc:arx:papers:2206.09644
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2206.09644
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Guido W. Imbens & Michal Kolesár, 2016. "Robust Standard Errors in Small Samples: Some Practical Advice," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 701-712, October.
    2. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    3. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    4. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 239-253.
    5. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    6. 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.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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 LP, vol. 23(4), pages 942-982, December.
    7. Antoine A. Djogbenou & James G. MacKinnon & Morten Ø. Nielsen, 2017. "Validity Of Wild Bootstrap Inference With Clustered Errors," Working Paper 1383, Economics Department, Queen's University.
    8. 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.
    9. Jeffrey D. Michler & Anna Josephson, 2022. "Recent developments in inference: practicalities for applied economics," Chapters, in: A Modern Guide to Food Economics, chapter 11, pages 235-268, Edward Elgar Publishing.
    10. 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.
    11. Wenjie Wang & Yichong Zhang, 2021. "Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters," Papers 2108.13707, arXiv.org, revised Jan 2024.
    12. James G. MacKinnon, 2019. "How cluster‐robust inference is changing applied econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 52(3), pages 851-881, August.
    13. Pötscher, Benedikt M. & Preinerstorfer, David, 2021. "Valid Heteroskedasticity Robust Testing," MPRA Paper 107420, University Library of Munich, Germany.
    14. Pötscher, Benedikt M. & Preinerstorfer, David, 2023. "How Reliable Are Bootstrap-Based Heteroskedasticity Robust Tests?," Econometric Theory, Cambridge University Press, vol. 39(4), pages 789-847, August.
    15. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    16. Thomas, Duncan & Lavy, Victor & Strauss, John, 1996. "Public policy and anthropometric outcomes in the Cote d'Ivoire," Journal of Public Economics, Elsevier, vol. 61(2), pages 155-192, August.
    17. Bruno Ferman & Cristine Pinto, 2019. "Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 452-467, July.
    18. 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.
    19. James G. MacKinnon & Morten {O}rregaard Nielsen & Matthew D. Webb, 2024. "Cluster-robust jackknife and bootstrap inference for binary response models," Papers 2406.00650, arXiv.org.
    20. Kurt Wurthmann, 2017. "Implicit Theories and Issue Characteristics as Determinants of Moral Awareness and Intentions," Journal of Business Ethics, Springer, vol. 142(1), pages 93-116, April.

    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:2206.09644. 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.