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Wild Bootstrap and Asymptotic Inference with Multiway Clustering

Author

Listed:
  • James G. MacKinnon

    () (Queen's University)

  • Morten Ø. Nielsen

    () (Queen's University and CREATES)

  • Matthew D. Webb

    () (Carleton University)

Abstract

We study two cluster-robust variance estimators (CRVEs) for regression models with clustering in two dimensions and give conditions under which t-statistics based on each of them yield asymptotically valid inferences. In particular, one of the CRVEs requires stronger assumptions about the nature of the intra-cluster correlations. We then propose several wild bootstrap procedures and state conditions under which they are asymptotically valid for each type of t-statistic. Extensive simulations suggest that using certain bootstrap procedures with one of the t-statistics generally performs very well. An empirical example confirms that bootstrap inferences can differ substantially from conventional ones

Suggested Citation

  • James G. MacKinnon & Morten Ø. Nielsen & Matthew D. Webb, 2019. "Wild Bootstrap and Asymptotic Inference with Multiway Clustering," Working Paper 1415, Economics Department, Queen's University.
  • Handle: RePEc:qed:wpaper:1415
    as

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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1415.pdf
    File Function: First version 2019
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    References listed on IDEAS

    as
    1. Nathan Nunn, 2008. "The Long-term Effects of Africa's Slave Trades," The Quarterly Journal of Economics, Oxford University Press, vol. 123(1), pages 139-176.
    2. 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.
    3. repec:clg:wpaper:2013-20 is not listed on IDEAS
    4. James G. MacKinnon & Matthew D. Webb, 2018. "The wild bootstrap for few (treated) clusters," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 114-135, June.
    5. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    6. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    7. Thompson, Samuel B., 2011. "Simple formulas for standard errors that cluster by both firm and time," Journal of Financial Economics, Elsevier, vol. 99(1), pages 1-10, January.
    8. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November.
    9. 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.
    10. 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.
    11. Andrew V. Carter & Kevin T. Schnepel & Douglas G. Steigerwald, 2017. "Asymptotic Behavior of a t -Test Robust to Cluster Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 99(4), pages 698-709, July.
    12. Hansen, Christian B., 2007. "Asymptotic properties of a robust variance matrix estimator for panel data when T is large," Journal of Econometrics, Elsevier, vol. 141(2), pages 597-620, December.
    13. Nathan Nunn & Leonard Wantchekon, 2011. "The Slave Trade and the Origins of Mistrust in Africa," American Economic Review, American Economic Association, vol. 101(7), pages 3221-3252, December.
    14. Gonçalves, Sílvia & Vogelsang, Timothy J., 2011. "Block Bootstrap Hac Robust Tests: The Sophistication Of The Naive Bootstrap," Econometric Theory, Cambridge University Press, vol. 27(4), pages 745-791, August.
    15. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    16. David Roodman & James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2019. "Fast and wild: Bootstrap inference in Stata using boottest," Stata Journal, StataCorp LP, vol. 19(1), pages 4-60, March.
    17. 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.
    18. James G. MacKinnon & Matthew D. Webb, 2017. "Wild Bootstrap Inference for Wildly Different Cluster Sizes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 233-254, March.
    19. MacKinnon , James G., 2015. "Wild Cluster Bootstrap Confidence Intervals," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 11-33, Mars-Juin.
    20. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    21. Matthew D. Webb, 2014. "Reworking Wild Bootstrap Based Inference For Clustered Errors," Working Paper 1315, Economics Department, Queen's University.
    22. James G. MacKinnon & Matthew D. Webb, 2018. "Wild Bootstrap Randomization Inference For Few Treated Clusters," Working Paper 1404, Economics Department, Queen's University.
    23. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2018. "Asymptotic results under multiway clustering," Papers 1807.07925, arXiv.org, revised Aug 2018.
    24. 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.
    25. Bester, C. Alan & Conley, Timothy G. & Hansen, Christian B., 2011. "Inference with dependent data using cluster covariance estimators," Journal of Econometrics, Elsevier, vol. 165(2), pages 137-151.
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    Citations

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    Cited by:

    1. Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2018. "The wild bootstrap with a "small" number of "large" clusters," CeMMAP working papers CWP27/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Ferman, Bruno, 2019. "Inference in Differences-in-Differences: How Much Should We Trust in Independent Clusters?," MPRA Paper 93746, University Library of Munich, Germany.
    3. James G. MacKinnon & Matthew D. Webb, 2019. "When and How to Deal with Clustered Errors in Regression Models," Working Paper 1421, Economics Department, Queen's University.

    More about this item

    Keywords

    CRVE; grouped data; clustered data; cluster-robust variance estimator; two-way clustering; wild cluster bootstrap; robust inference;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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