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Heteroskedasticity Testing Through a Comparison of Wald Statistics

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  • José M.R. Murteira

    () (Faculdade de Economia, Universidade de Coimbra, and CEMAPRE)

  • Esmeralda A. Ramalho

    () (Departamento de Economia and CEFAGE-UE, Universidade de Évora)

  • Joaquim J.S. Ramalho

    () (Departamento de Economia and CEFAGE-UE, Universidade de Évora)

Abstract

This paper shows that a test for heteroskedasticity within the context of classical linear regression can be based on the difference between Wald statistics in heteroskedasticity-robust and nonrobust forms. The test is asymptotically distributed under the null hypothesis of homoskedasticity as chi-squared with one degree of freedom. The power of the test is sensitive to the choice of parametric restriction used by the Wald statistics, so the supremum of a range of individual test statistics is proposed. Two versions of a supremum-based test are considered: the first version does not have a known asymptotic null distribution, so the bootstrap is employed to approximate its empirical distribution. The second version has a known asymptotic distribution and, in some cases, is asymptotically pivotal under the null. A simulation study illustrates the use and .nite-sample performance of both versions of the test. In this study, the bootstrap is found to provide better size control than asymptotic critical values, namely with heavy-tailed, asymmetric distributions of the covariates. In addition, the use of well-known modifications of the heteroskedasticity consistent covariance matrix estimator of OLS coefficients is also found to benefit the tests'overall behaviour.

Suggested Citation

  • José M.R. Murteira & Esmeralda A. Ramalho & Joaquim J.S. Ramalho, 2013. "Heteroskedasticity Testing Through a Comparison of Wald Statistics," CEFAGE-UE Working Papers 2013_06, University of Evora, CEFAGE-UE (Portugal).
  • Handle: RePEc:cfe:wpcefa:2013_06
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    References listed on IDEAS

    as
    1. L. G. Godfrey & C. D. Orme & J. M. C. Santos Silva, 2006. "Simulation-based tests for heteroskedasticity in linear regression models: Some further results," Econometrics Journal, Royal Economic Society, vol. 9(1), pages 76-97, March.
    2. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, pages 162-169.
    3. Machado, Jose A. F. & Silva, J. M. C. Santos, 2000. "Glejser's test revisited," Journal of Econometrics, Elsevier, vol. 97(1), pages 189-202, July.
    4. 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.
    5. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    6. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
    7. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 112-134.
    8. 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.
    9. Godfrey, Leslie G., 1996. "Some results on the Glejser and Koenker tests for heteroskedasticity," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 275-299.
    10. Godfrey, Leslie G., 1978. "Testing for multiplicative heteroskedasticity," Journal of Econometrics, Elsevier, vol. 8(2), pages 227-236, October.
    11. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, vol. 17(1), pages 107-112, September.
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    More about this item

    Keywords

    Heteroskedasticity testing; White test; Wald test; Supremum.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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