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The Wild Bootstrap, Tamed at Last

Author

Listed:
  • Russell Davidson

    (GREQAM and Queen's University)

  • Emmanuel Flachaire

    (GREQAM)

Abstract

In this paper we are interested in inference based on heteroskedasticity consistent covariance matrix estimators, for which the appropriate bootstrap is a version of the wild bootstrap. Simulation results, obtained by a new very efficient method, show that all wild bootstrap tests exhibit substantial size distortion if the error terms are skewed and strongly heteroskedastic. The distortion is however less, sometimes much less, if one uses a version of the wild bootstrap, belonging to a class we call ``tamed'', which benefit from an asymptotic refinement related to the asymptotic independence of the bootstrapped test statistic and the bootstrap DGP. This version always gives better results than the version usually recommended in the literature, and gives exact results for some specific cases. However, when exact results are not available, we find that the rate of convergence to zero of the size distortion of wild bootstrap tests is not very rapid: in some cases, significant size distortion still remains for samples of size~100.

Suggested Citation

  • Russell Davidson & Emmanuel Flachaire, 2000. "The Wild Bootstrap, Tamed at Last," Econometric Society World Congress 2000 Contributed Papers 1413, Econometric Society.
    • Handle: RePEc:ecm:wc2000:1413
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    References listed on IDEAS

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    1. repec:cup:cbooks:9780521589833 is not listed on IDEAS
    2. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    3. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, Decembrie.
    4. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    5. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
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    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. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, University Library of Munich, Germany, revised 05 Mar 1996.
    9. Flachaire, Emmanuel, 1999. "A better way to bootstrap pairs," Economics Letters, Elsevier, vol. 64(3), pages 257-262, September.
    10. 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.
    11. repec:cup:cbooks:9780521589826 is not listed on IDEAS
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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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