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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.

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Bibliographic Info

Paper provided by University of Evora, CEFAGE-UE (Portugal) in its series CEFAGE-UE Working Papers with number 2013_06.

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Length: 43 pages
Date of creation: 2013
Date of revision:
Handle: RePEc:cfe:wpcefa:2013_06

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

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References

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  1. Russell Davidson & Emmanuel Flachaire, 2000. "The Wild Bootstrap, Tamed at Last," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 1413, Econometric Society.
  2. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195060119, October.
  3. Godfrey, Leslie G., 1978. "Testing for multiplicative heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 8(2), pages 227-236, October.
  4. Godfrey, Leslie G., 1996. "Some results on the Glejser and Koenker tests for heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 72(1-2), pages 275-299.
  5. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, Elsevier, vol. 29(3), pages 305-325, September.
  6. 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, Royal Economic Society, vol. 9(1), pages 76-97, 03.
  7. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, Econometric Society, vol. 48(4), pages 817-38, May.
  8. J. A. Hausman, 1976. "Specification Tests in Econometrics," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 185, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 17(1), pages 107-112, September.
  10. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, Econometric Society, vol. 55(5), pages 1217-22, September.
  11. Machado, Jose A. F. & Silva, J. M. C. Santos, 2000. "Glejser's test revisited," Journal of Econometrics, Elsevier, Elsevier, vol. 97(1), pages 189-202, July.
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