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The Wild Bootstrap, Tamed At Last

Author

Listed:
  • Emmanuel Flachaire

    (STICERD, London School of Economics)

  • Russell Davidson

    (McGill University)

Abstract

Various versions of the wild bootstrap are studied as applied to regression models with heteroskedastic errors. We develop formal Edgeworth expansions for the error in the rejection probability (ERP) of wild bootstrap tests based on asymptotic t statistics computed with a heteroskedasticity consistent covariance matrix estimator. Particular interest centers on the choice of the auxiliary distribution used by the wild bootstrap in order to generate bootstrap error terms. We find that the Rademacher distribution usually gives smaller ERPs, in small samples, than the version of the wild bootstrap that seems most popular in the literature, even though it does not benefit from the latter's skewness correction. This conclusion, based on Edgeworth expansions, is confirmed by a series of simulation experiments. We conclude that a particular version of the wild bootstrap is to be preferred in almost all practical situations, and we show analytically that it, and no other version, gives perfect inference in a special case.

Suggested Citation

  • Emmanuel Flachaire & Russell Davidson, 2001. "The Wild Bootstrap, Tamed At Last," Working Paper 1000, Economics Department, Queen's University.
  • Handle: RePEc:qed:wpaper:1000
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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1000.pdf
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    References listed on IDEAS

    as
    1. Flachaire, Emmanuel, 1999. "A better way to bootstrap pairs," Economics Letters, Elsevier, vol. 64(3), pages 257-262, September.
    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. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
    4. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819, November.
    5. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    6. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, University Library of Munich, Germany, revised 05 Mar 1996.
    7. 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.
    8. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826, November.
    9. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833, November.
    10. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, Decembrie.
    11. 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.
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    More about this item

    Keywords

    Wild Bootstrap; Heteroskedasticity Consistent Covariance Matrix Estimators; Size distortion;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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