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Bootstrap and Asymptotic Inference with Multiway Clustering

Author

Listed:
  • James G. MacKinnon

    () (Queen's University)

  • Morten Ørregaard Nielsen

    () (Queen's University)

  • Matthew D. Webb

    () (Carleton University)

Abstract

We study a cluster-robust variance estimator (CRVE) for regression models with clustering in two dimensions that was proposed in Cameron, Gelbach, and Miller (2011). We prove that this CRVE is consistent and yields valid inferences under precisely stated assumptions about moments and cluster sizes. We then propose several wild bootstrap procedures and prove that they are asymptotically valid. Simulations suggest that bootstrap inference tends to be much more accurate than inference based on the t distribution, especially when there are few clusters in at least one dimension. An empirical example confirms that bootstrap inferences can differ substantially from conventional ones.

Suggested Citation

  • James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2017. "Bootstrap and Asymptotic Inference with Multiway Clustering," Working Papers 1386, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:1386
    as

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    File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1386.pdf
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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. 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.
    5. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    6. 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.
    7. 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.
    8. Antoine Djogbenou & James G. MacKinnon & Morten Ørregaard Nielsen, 2017. "Validity of Wild Bootstrap Inference with Clustered Errors," Working Papers 1383, Queen's University, Department of Economics.
    9. repec:tpr:restat:v:99:y:2017:i:4:p:698-709 is not listed on IDEAS
    10. 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.
    11. 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.
    12. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
    13. 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.
    14. repec:wly:japmet:v:32:y:2017:i:2:p:233-254 is not listed on IDEAS
    15. Romano, Joseph P. & Wolf, Michael, 2000. "A more general central limit theorem for m-dependent random variables with unbounded m," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 115-124, April.
    16. 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.
    17. Matthew D. Webb, 2014. "Reworking Wild Bootstrap Based Inference for Clustered Errors," Working Papers 1315, Queen's University, Department of Economics.
    18. 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.
    19. 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.
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    Citations

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    Cited by:

    1. David Roodman & James G. MacKinnon & Morten Orregard Nielsen & Matthew D. Webb, 2018. "Fast and Wild: Bootstrap Inference in Stata Using boottest," Working Papers 1406, Queen's University, Department of Economics.
    2. 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.
    3. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2018. "Asymptotic results under multiway clustering," Papers 1807.07925, arXiv.org, revised Aug 2018.
    4. James G. MacKinnon & Matthew D. Webb, 2017. "Pitfalls when Estimating Treatment Effects Using Clustered Data," Working Papers 1387, Queen's University, Department of Economics.
    5. James G. MacKinnon & Matthew D. Webb, 2017. "Pitfalls when Estimating Treatment Effects Using Clustered Data," Working Papers 1387, Queen's University, Department of Economics.

    More about this item

    Keywords

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

    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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