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Bootstrap and Asymptotic Inference with Multiway Clustering

Listed author(s):
  • James G. MacKinnon

    ()

    (Queen's University)

  • Morten Ørregaard Nielsen

    ()

    (Queen's University)

  • Matthew D. Webb

    ()

    (Carleton University)

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.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1386.pdf
File Function: First version 2017
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Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1386.

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Length: 25 pages
Date of creation: Aug 2017
Handle: RePEc:qed:wpaper:1386
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  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. 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.
  9. 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.
  10. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
  11. 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.
  12. 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.
  13. 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.
  14. Matthew D. Webb, 2014. "Reworking Wild Bootstrap Based Inference for Clustered Errors," Working Papers 1315, Queen's University, Department of Economics.
  15. 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.
  16. 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.
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