Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T18:25:56.407Z Has data issue: false hasContentIssue false
  • English
  • Français

HOW RELIABLE ARE BOOTSTRAP-BASED HETEROSKEDASTICITY ROBUST TESTS?

Published online by Cambridge University Press:  27 April 2022

Benedikt M. Pötscher  and
David Preinerstorfer
Benedikt M. Pötscher*
Affiliation:
Department of Statistics, University of Vienna
David Preinerstorfer
Affiliation:
SEPS-SEW, University of St. Gallen
*
Address correspondence to Benedikt Pötscher, Department of Statistics, University of Vienna, A-1090 Oskar-Morgenstern Platz 1, Vienna, Austria; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We develop theoretical finite-sample results concerning the size of wild bootstrap-based heteroskedasticity robust tests in linear regression models. In particular, these results provide an efficient diagnostic check, which can be used to weed out tests that are unreliable for a given testing problem in the sense that they overreject substantially. This allows us to assess the reliability of a large variety of wild bootstrap-based tests in an extensive numerical study.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 4 , August 2023 , pp. 789 - 847
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

Financial support of the second author by the Program of Concerted Research Actions (ARC) of the Université libre de Bruxelles is gratefully acknowledged. We thank two referees, the Co-Editor, and the Editor for helpful comments.

References

REFERENCES

Bates, D. & Eddelbuettel, D. (2013) Fast and elegant numerical linear algebra using the RcppEigen package. Journal of Statistical Software 52, 1–24.CrossRefGoogle Scholar
Beran, R. (1986). Discussion: Jackknife, bootstrap and other resampling methods in regression analysis. Annals of Statistics 14, 1295–1298.CrossRefGoogle Scholar
Chesher, A. & Jewitt, I. (1987) The bias of a heteroskedasticity consistent covariance matrix estimator. Econometrica 55, 1217–1222.CrossRefGoogle Scholar
Chesher, A.D. (1989) Hájek inequalities, measures of leverage, and the size of heteroskedasticity robust Wald tests. Econometrica 57, 971–977.CrossRefGoogle Scholar
Chesher, A.D. & Austin, G. (1991) The finite-sample distributions of heteroskedasticity robust Wald statistics. Journal of Econometrics 47, 153–173.CrossRefGoogle Scholar
Cragg, J.G. (1983) More efficient estimation in the presence of heteroscedasticity of unknown form. Econometrica 51, 751–763.CrossRefGoogle Scholar
Cragg, J.G. (1992) Quasi-Aitken estimation for heteroscedasticity of unknown form. Journal of Econometrics 54, 179–201.CrossRefGoogle Scholar
Cribari-Neto, F. (2004) Asymptotic inference under heteroskedasticity of unknown form. Computational Statistics & Data Analysis 45, 215–233.CrossRefGoogle Scholar
Cribari-Neto, F. & Lima, M.d.G.A. (2009) Heteroskedasticity-consistent interval estimators. Journal of Statistical Computation and Simulation 79, 787–803.CrossRefGoogle Scholar
Davidson, R. & Flachaire, E. (2008) The wild bootstrap, tamed at last. Journal of Econometrics 146, 162–169.CrossRefGoogle Scholar
Davidson, R. & MacKinnon, J.G. (1985) Heteroskedasticity-robust tests in regressions directions. Annales de l’INSÉÉ 59/60, 183–218.Google Scholar
DiCiccio, C.J., Romano, J.P., & Wolf, M. (2019) Improving weighted least squares inference. Econometrics and Statistics 10, 96–119.CrossRefGoogle Scholar
Eicker, F. (1963) Asymptotic normality and consistency of the least squares estimators for families of linear regressions. Annals of Mathematical Statistics 34, 447–456.CrossRefGoogle Scholar
Eicker, F. (1967). Limit theorems for regressions with unequal and dependent errors. In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66) , vol. I: Statistics, pp. 59–82. University of California Press.Google Scholar
Flachaire, E. (1999) A better way to bootstrap pairs. Economics Letters 64, 257–262.CrossRefGoogle Scholar
Flachaire, E. (2005a) Bootstrapping heteroskedastic regression models: Wild bootstrap vs. pairs bootstrap. Computational Statistics & Data Analysis 49, 361–376.CrossRefGoogle Scholar
Flachaire, E. (2005b) More efficient tests robust to heteroskedasticity of unknown form. Econometric Reviews 24, 219–241.CrossRefGoogle Scholar
Godfrey, L.G. (2006) Tests for regression models with heteroskedasticity of unknown form. Computational Statistics & Data Analysis 50, 2715–2733.CrossRefGoogle Scholar
Godfrey, L.G. & Orme, C.D. (2004) Controlling the finite sample significance levels of heteroskedasticity-robust tests of several linear restrictions on regression coefficients. Economics Letters 82, 281–287.CrossRefGoogle Scholar
Hinkley, D.V. (1977). Jackknifing in unbalanced situations. Technometrics 19, 285–292.CrossRefGoogle Scholar
Horowitz, J.L. (1997). Bootstrap methods in econometrics: Theory and numerical performance. In Kreps, D.M. & Wallis, K.F. (eds.), Advances in Economics and Econometrics: Theory and Applications: Seventh World Congress , Econometric Society Monographs, 3, pp. 188–222. Cambridge University Press.CrossRefGoogle Scholar
Imbens, G.W. & Kolesár, M. (2016) Robust standard errors in small samples: Some practical advice. Review of Economics and Statistics 98, 701–712.CrossRefGoogle Scholar
Lin, E.S. & Chou, T.-S. (2018) Finite-sample refinement of GMM approach to nonlinear models under heteroskedasticity of unknown form. Econometric Reviews 37, 1–28.CrossRefGoogle Scholar
Liu, R.Y. (1988) Bootstrap procedures under some non-i.i.d. models. Annals of Statistics 16, 1696–1708.CrossRefGoogle Scholar
Long, J.S. & Ervin, L.H. (2000) Using heteroscedasticity consistent standard errors in the linear regression model. American Statistician 54, 217–224.Google Scholar
MacKinnon, J.G. (2013) Thirty years of heteroskedasticity-robust inference. In Chen, X. & Swanson, N.R.E. (eds.), Recent Advances and Future Directions in Causality, Prediction, and Specification Analysis , pp. 437–462. Springer.CrossRefGoogle Scholar
MacKinnon, J.G. & White, H. (1985) Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties. Journal of Econometrics 29, 305–325.CrossRefGoogle Scholar
Mammen, E. (1993) Bootstrap and wild bootstrap for high-dimensional linear models. Annals of Statistics 21, 255–285.CrossRefGoogle Scholar
Pötscher, B.M. & Preinerstorfer, D. (2018) Controlling the size of autocorrelation robust tests. Journal of Econometrics 207, 406–431.CrossRefGoogle Scholar
Pötscher, B.M. & Preinerstorfer, D. (2021) Valid Heteroskedasticity Robust Testing. Working Paper.Google Scholar
Preinerstorfer, D. (2020) wbsd: Wild Bootstrap Size Diagnostics, version 1.0.0.Google Scholar
Preinerstorfer, D. & Pötscher, B.M. (2016) On size and power of heteroskedasticity and autocorrelation robust tests. Econometric Theory 32, 261–358.CrossRefGoogle Scholar
R Core Team (2020) R: A Language and Environment for Statistical Computing . R Foundation for Statistical Computing. https://www.R-project.org/.Google Scholar
Richard, P. (2017) Robust heteroskedasticity-robust tests. Economics Letters 159, 28–32.CrossRefGoogle Scholar
Robinson, G. (1979) Conditional properties of statistical procedures. Annals of Statistics 7, 742–755.Google Scholar
Romano, J.P. & Wolf, M. (2017) Resurrecting weighted least squares. Journal of Econometrics 197, 1–19.CrossRefGoogle Scholar
Rothenberg, T.J. (1988) Approximate power functions for some robust tests of regression coefficients. Econometrica 56, 997–1019.CrossRefGoogle Scholar
van Giersbergen, N.P.A. & Kiviet, J.F. (2002) How to implement the bootstrap in static or stable dynamic regression models: Test statistic versus confidence region approach. Journal of Econometrics 108, 133–156.CrossRefGoogle Scholar
White, H. (1980) A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48, 817–838.CrossRefGoogle Scholar
Wu, C.-F.J. (1986) Jackknife, bootstrap and other resampling methods in regression analysis. Annals of Statistics 14, 1261–1350. With discussion and a rejoinder by the author.Google Scholar