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Approximate Power Functions for Some Robust Tests of Regression Coefficients

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  • Rothenberg, Thomas J

Abstract

Edgeworth approximations are developed for the distribution functio ns of some statistics for testing a linear hypothesis on the coefficient s in a regression model with an unknown error covariance matrix. Adjust ments to the asymptotic critical values are found to insure that the tests have correct size to second order of approximation. The power loss due to the estimation of the error covariance matrix is calculated. Some examples involving heteroskedasticity and autocorrelation suggest that the null rejection probabilities of common robust regression tests are often considerably greater than their nominal level. Moreover, the cost of not knowing the error covariance matrix can be substantial. Copyright 1988 by The Econometric Society.

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  • Rothenberg, Thomas J, 1988. "Approximate Power Functions for Some Robust Tests of Regression Coefficients," Econometrica, Econometric Society, vol. 56(5), pages 997-1019, September.
    • Handle: RePEc:ecm:emetrp:v:56:y:1988:i:5:p:997-1019
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    Cited by:

    1. Hausman, Jerry & Kuersteiner, Guido, 2008. "Difference in difference meets generalized least squares: Higher order properties of hypotheses tests," Journal of Econometrics, Elsevier, vol. 144(2), pages 371-391, June.
    2. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    3. Symeonides Spyridon D. & Karavias Yiannis & Tzavalis Elias, 2017. "Size corrected Significance Tests in Seemingly Unrelated Regressions with Autocorrelated Errors," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-41, January.
    4. Magdalinos, Michael A. & Symeonides, Spyridon D., 1995. "Alternative size corrections for some GLS test statistics the case of the AR(1) model," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 35-59.
    5. Linton, Oliver, 1997. "An Asymptotic Expansion in the GARCH(l, 1) Model," Econometric Theory, Cambridge University Press, vol. 13(4), pages 558-581, February.
    6. Banerjee, Anurag N. & Magnus, Jan R., 2000. "On the sensitivity of the usual t- and F-tests to covariance misspecification," Journal of Econometrics, Elsevier, vol. 95(1), pages 157-176, March.
    7. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    8. Richard, Patrick, 2017. "Robust heteroskedasticity-robust tests," Economics Letters, Elsevier, vol. 159(C), pages 28-32.
    9. Banerjee, A.N., 1997. "The sensitivity of estimates, inferences and forecasts of linear models," Other publications TiSEM 3238733e-f996-4fd9-95ec-0, Tilburg University, School of Economics and Management.
    10. Pötscher, Benedikt M. & Preinerstorfer, David, 2021. "Valid Heteroskedasticity Robust Testing," MPRA Paper 117855, University Library of Munich, Germany, revised Jul 2023.
    11. Matsushita, Yukitoshi & Otsu, Taisuke, 2023. "Second-order refinements for t-ratios with many instruments," Journal of Econometrics, Elsevier, vol. 232(2), pages 346-366.
    12. Hidehiko Ichimura & Oliver Linton, 2001. "Asymptotic expansions for some semiparametric program evaluation estimators," CeMMAP working papers 04/01, Institute for Fiscal Studies.
    13. Hausman, Jerry & Palmer, Christopher, 2012. "Heteroskedasticity-robust inference in finite samples," Economics Letters, Elsevier, vol. 116(2), pages 232-235.
    14. Rayner, Robert K., 1991. "Resampling methods for tests in regression models with autocorrelated errors," Economics Letters, Elsevier, vol. 36(3), pages 281-284, July.
    15. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    16. Johansen, Soren, 2002. "A small sample correction for tests of hypotheses on the cointegrating vectors," Journal of Econometrics, Elsevier, vol. 111(2), pages 195-221, December.
    17. Pötscher, Benedikt M. & Preinerstorfer, David, 2023. "How Reliable Are Bootstrap-Based Heteroskedasticity Robust Tests?," Econometric Theory, Cambridge University Press, vol. 39(4), pages 789-847, August.
    18. Yukitoshi Matsushita & Taisuke Otsu, 2020. "Second-order refinements for t-ratios with many instruments," STICERD - Econometrics Paper Series 612, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    19. Saraswata Chaudhuri & Eric Renault, 2015. "Shrinkage of Variance for Minimum Distance Based Tests," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 328-351, March.
    20. 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.
    21. Moreira, Marcelo J. & Porter, Jack R. & Suarez, Gustavo A., 2009. "Bootstrap validity for the score test when instruments may be weak," Journal of Econometrics, Elsevier, vol. 149(1), pages 52-64, April.
    22. Steigerwald, Douglas G & Erb, Jack, 2007. "Accurately Sized Test Statistics with Misspecified Conditional Homoskedasticity," University of California at Santa Barbara, Economics Working Paper Series qt5rv0z5dz, Department of Economics, UC Santa Barbara.
    23. Oliver Linton, 1997. "Second Order Approximation in a Linear Regression with Heteroskedasticity for Unknown Form," Cowles Foundation Discussion Papers 1151, Cowles Foundation for Research in Economics, Yale University.
    24. Swamy Paravastu & Peter Muehlen & Jatinder Singh Mehta & I-Lok Chang, 2022. "The State Of Econometrics After John W. Pratt, Robert Schlaifer, Brian Skyrms, And Robert L. Basmann," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 627-654, November.
    25. Matsushita, Yukitoshi & Otsu, Taisuke, 2023. "Second-order refinements for t-ratios with many instruments," LSE Research Online Documents on Economics 111065, London School of Economics and Political Science, LSE Library.

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