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Wild Cluster Bootstrap Confidence Intervals

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  • James G. MacKinnon

    (Queen's University)

Abstract

Confidence intervals based on cluster-robust covariance matrices can be constructed in many ways. In addition to conventional intervalsobtained by inverting Wald (t) tests, the paper studies intervals obtained by inverting LM tests, studentized bootstrap intervals basedon the wild cluster bootstrap, and restricted bootstrap intervals obtained by inverting bootstrap Wald and LM tests. It also studies the choice of an auxiliary distribution for the wild bootstrap, a modified covariance matrix based on transforming the residuals, which was proposed previously, and modified wild bootstrap procedures based onthe same idea, which are new. Some procedures perform extraordinarily well even with the number of clusters is small.

Suggested Citation

  • James G. MacKinnon, 2014. "Wild Cluster Bootstrap Confidence Intervals," Working Paper 1329, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1329
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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1329.pdf
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    References listed on IDEAS

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    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. 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.
    3. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    4. Breusch, T S, 1979. "Conflict among Criteria for Testing Hypotheses: Extensions and Comments," Econometrica, Econometric Society, vol. 47(1), pages 203-207, January.
    5. James G. MacKinnon, 2012. "Thirty Years Of Heteroskedasticity-robust Inference," Working Paper 1268, Economics Department, Queen's University.
    6. 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.
    7. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    8. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    9. 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.
    10. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(1), pages 249-275.
    11. Russell Davidson & James G. MacKinnon, 2014. "Bootstrap Confidence Sets with Weak Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 651-675, August.
    12. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    13. Davidson, James & Monticini, Andrea & Peel, David, 2007. "Implementing the wild bootstrap using a two-point distribution," Economics Letters, Elsevier, vol. 96(3), pages 309-315, September.
    14. repec:clg:wpaper:2013-17 is not listed on IDEAS
    15. 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.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Podstawski, Maximilian & Velinov, Anton, 2018. "The state dependent impact of bank exposure on sovereign risk," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 88, pages 63-75.
    2. MacKinnon, James G., 2023. "Fast cluster bootstrap methods for linear regression models," Econometrics and Statistics, Elsevier, vol. 26(C), pages 52-71.
    3. 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.
    4. 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.
    5. 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.
    6. James G. MacKinnon, 2019. "How cluster-robust inference is changing applied econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 52(3), pages 851-881, August.
    7. François Gardes, 2021. "Biases on variances estimated on large data-sets," Documents de travail du Centre d'Economie de la Sorbonne 21022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    8. Podstawski, Maximilian & Velinov, Anton, 2018. "The state dependent impact of bank exposure on sovereign risk," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 63-75.
    9. 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.
    10. François Gardes, 2021. "Biases on variances estimated on large data-sets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03325118, HAL.
    11. 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.
    12. Bartlett, Robert P. & McCrary, Justin, 2019. "How rigged are stock markets? Evidence from microsecond timestamps," Journal of Financial Markets, Elsevier, vol. 45(C), pages 37-60.
    13. Ritter, Joseph A., 2018. "Incentive effects of SNAP work requirements," Staff Papers 281156, University of Minnesota, Department of Applied Economics.
    14. François Gardes, 2021. "Biases on variances estimated on large data-sets," Post-Print halshs-03325118, HAL.

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    More about this item

    Keywords

    wild bootstrap; auxiliary distribution; CRVE; cluster-robust inference; studentized bootstrap;
    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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