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Bootstrap And Asymptotic Inference With Multiway Clustering

Author

Listed:
  • James G. MacKinnon

    (Queen's University)

  • Matthew D. Webb

    (Carleton University)

  • Morten Ø. Nielsen

    (Queen's University and CREATES)

Abstract

We study a cluster-robust variance estimator (CRVE) for regression models with clustering in two dimensions that was proposed in Cameron, Gelback, 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 & Matthew D. Webb & Morten Ø. Nielsen, 2017. "Bootstrap And Asymptotic Inference With Multiway Clustering," Working Paper 1386, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1386
    as

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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1386.pdf
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    References listed on IDEAS

    as
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    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. Matthew D. Webb, 2023. "Reworking wild bootstrap‐based inference for clustered errors," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 56(3), pages 839-858, August.
    7. 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.
    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. MacKinnon, James G., 2020. "Wild cluster bootstrap confidence intervals," L'Actualité Economique, Société Canadienne de Science Economique, vol. 96(4), pages 721-743, Décembre.
    10. 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.
    11. 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.
    12. 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.
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    14. James E. Pustejovsky & Elizabeth Tipton, 2018. "Small-Sample Methods for Cluster-Robust Variance Estimation and Hypothesis Testing in Fixed Effects Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 672-683, October.
    15. 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.
    16. 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.
    17. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Tumen, Semih, 2021. "The effect of refugees on native adolescents’ test scores: Quasi-experimental evidence from PISA," Journal of Development Economics, Elsevier, vol. 150(C).
    2. 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.
    3. 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.
    4. Yusuf Emre Akgunduz & Emine Meltem Bastan & Ufuk Demiroglu & Semih Tumen, 2021. "Product‐level estimates of exchange rate pass‐through: Evidence from Turkey☆," The World Economy, Wiley Blackwell, vol. 44(7), pages 2203-2226, July.
    5. Tumen, Semih & Ulucan, Hakan, 2019. "Empowered or Impoverished: The Impact of Panic Buttons on Domestic Violence," IZA Discussion Papers 12847, Institute of Labor Economics (IZA).
    6. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2018. "Asymptotic results under multiway clustering," Papers 1807.07925, arXiv.org, revised Aug 2018.
    7. 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.
    8. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    9. Harold D. Chiang & Yuya Sasaki, 2019. "Lasso under Multi-way Clustering: Estimation and Post-selection Inference," Papers 1905.02107, arXiv.org, revised Aug 2019.
    10. James G. MacKinnon & Matthew D. Webb, 2017. "Pitfalls When Estimating Treatment Effects Using Clustered Data," Working Paper 1387, Economics Department, Queen's University.

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    More about this item

    Keywords

    clustered data; cluster-robust variance estimator; CRVE; wild bootstrap; wild cluster bootstrap; two-way clustering;
    All these keywords.

    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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