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The Wild Bootstrap, Tamed at Last

Author Info

Listed author(s):
  • Russell Davidson

    ()

    (Department of Economics, Queen's University and GREQAM)

  • Emmanuel Flachaire

    ()

    (STICERD, London School of Economics)

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.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1000.pdf
File Function: First version 2001
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Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1000.

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Length: 34 pages
Date of creation: Oct 2001
Handle: RePEc:qed:wpaper:1000
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Keywords: Wild Bootstrap; Heteroskedasticity Consistent Covariance Matrix Estimators; Size distortion;

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Find related papers by JEL classification:
  • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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  1. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
  2. Flachaire, Emmanuel, 1999. "A better way to bootstrap pairs," Economics Letters, Elsevier, vol. 64(3), pages 257-262, September.
  3. 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.
  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.
  6. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, 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.
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