Pötscher, Benedikt M. and Preinerstorfer, David (2020): How Reliable are Bootstrapbased Heteroskedasticity Robust Tests?

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Abstract
We develop theoretical finitesample results concerning the size of wild bootstrapbased 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 bootstrapbased tests in an extensive numerical study.
Item Type:  MPRA Paper 

Original Title:  How Reliable are Bootstrapbased Heteroskedasticity Robust Tests? 
Language:  English 
Keywords:  wild bootstrapbased heteroskedasticity robust tests, size distortions 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables 
Item ID:  100234 
Depositing User:  Benedikt Poetscher 
Date Deposited:  10 May 2020 15:38 
Last Modified:  10 May 2020 15:38 
References:  Bates, D. and Eddelbuettel, D. (2013). Fast and elegant numerical linear algebra using the RcppEigen package. Journal of Statistical Software, 52 1–24. Beran, R. (1986). Discussion: Jackknife, bootstrap and other resampling methods in regression analysis. Annals of Statistics, 14 1295–1298. Chesher, A. and Jewitt, I. (1987). The bias of a heteroskedasticity consistent covariance matrix estimator. Econometrica, 55 1217–1222. Chesher, A. D. (1989). Hájek inequalities, measures of leverage, and the size of heteroskedasticity robust wald tests. Econometrica, 57 971–977. Chesher, A. D. and Austin, G. (1991). The ﬁnitesample distributions of heteroskedasticity robust wald statistics. Journal of Econometrics, 47 153–173. Cragg, J. G. (1983). More efficient estimation in the presence of heteroscedasticity of unknown form. Econometrica, 51 751–763. Cragg, J. G. (1992). QuasiAitken estimation for heteroscedasticity of unknown form. Journal of Econometrics, 54 179–201. CribariNeto, F. (2004). Asymptotic inference under heteroskedasticity of unknown form. Computational Statistics & Data Analysis, 45 215 – 233. CribariNeto, F. and Lima, M. d. G. A. (2009). Heteroskedasticityconsistent interval estimators. Journal of Statistical Computation and Simulation, 79 787–803. Davidson, R. and Flachaire, E. (2008). The wild bootstrap, tamed at last. Journal of Econometrics, 146 162–169. Davidson, R. and MacKinnon, J. G. (1985). Heteroskedasticityrobust tests in regressions directions. Ann. I.N.S.É.É. 183–218. DiCiccio, C. J., Romano, J. P. and Wolf, M. (2019). Improving weighted least squares inference. Econometrics and Statistics, 10 96–119. Eicker, F. (1963). Asymptotic normality and consistency of the least squares estimators for families of linear regressions. Annals of Mathematical Statistics, 34 447–456. 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). Univ. California Press, Berkeley, Calif., Vol. I: Statistics, pp. 59–82. Flachaire, E. (1999). A better way to bootstrap pairs. Economics Letters, 64 257–262. Flachaire, E. (2005a). Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap. Computational Statistics & Data Analysis, 49 361–376. Flachaire, E. (2005b). More efficient tests robust to heteroskedasticity of unknown form. Econometric Reviews, 24 219–241. Godfrey, L. G. (2006). Tests for regression models with heteroskedasticity of unknown form. Computational Statistics & Data Analysis, 50 2715–2733. Godfrey, L. G. and Orme, C. D. (2004). Controlling the ﬁnite sample signiﬁcance levels of heteroskedasticityrobust tests of several linear restrictions on regression coeﬃcients. Economics Letters, 82 281–287. Hinkley, D. V. (1977). Jackkniﬁng in unbalanced situations. Technometrics, 19 285–292. Horowitz, J. L. (1997). Bootstrap methods in econometrics: theory and numerical performance. In Advances in Economics and Econometrics: Theory and Applications: Seventh World Congress (D. M. Kreps and K. F. Wallis, eds.), vol. 3 of Econometric Society Monographs. Cambridge University Press, 188–222. Imbens, G. W. and Kolesár, M. (2016). Robust standard errors in small samples: Some practical advice. The Review of Economics and Statistics, 98 701–712. Lin, E. S. and Chou, T.S. (2018). Finitesample reﬁnement of GMM approach to nonlinear models under heteroskedasticity of unknown form. Econometric Reviews, 37 1–28. Liu, R. Y. (1988). Bootstrap procedures under some noni.i.d. models. Annals of Statistics, 16 1696–1708. Long, J. S. and Ervin, L. H. (2000). Using heteroscedasticity consistent standard errors in the linear regression model. The American Statistician, 54 217–224. MacKinnon, J. G. (2013). Thirty years of heteroskedasticityrobust inference. In Recent Advances and Future Directions in Causality, Prediction, and Speciﬁcation Analysis (X. Chen and N. R. E. Swanson, eds.). Springer, 437–462. MacKinnon, J. G. and White, H. (1985). Some heteroskedasticityconsistent covariance matrix estimators with improved ﬁnite sample properties. Journal of Econometrics, 29 305325. Mammen, E. (1993). Bootstrap and wild bootstrap for highdimensional linear models. Annals of Statistics, 21 255–285. Pötscher, B. M. and Preinerstorfer, D. (2018). Controlling the size of autocorrelation robust tests. Journal of Econometrics, 207 406–431. Pötscher, B. M. and Preinerstorfer, D. (2020). Controlling the size of heteroskedasticity robust tests. In preparation. Preinerstorfer, D. (2020). wbsd: wild bootstrap size diagnostics, version 1.0.0. Preinerstorfer, D. and Pötscher, B. M. (2016). On size and power of heteroskedasticity and autocorrelation robust tests. Econometric Theory, 32 261–358. R Core Team (2020). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.Rproject.org/. Richard, P. (2017). Robust heteroskedasticityrobust tests. Economics Letters, 159 28–32. Robinson, G. (1979). Conditional properties of statistical procedures. Annals of Statistics, 7 742–755. Romano, J. P. and Wolf, M. (2017). Resurrecting weighted least squares. Journal of Econometrics, 197 1–19. Rothenberg, T. J. (1988). Approximate power functions for some robust tests of regression coefficients. Econometrica, 56 997–1019. van Giersbergen, N. P. A. and 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. White, H. (1980). A heteroskedasticityconsistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48 817–838. 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. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/100234 