Heteroskedasticity Testing Through a Comparison of Wald Statistics
AbstractThis 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 InfoPaper provided by University of Evora, CEFAGE-UE (Portugal) in its series CEFAGE-UE Working Papers with number 2013_06.
Length: 43 pages
Date of creation: 2013
Date of revision:
Heteroskedasticity testing; White test; Wald test; Supremum.;
Other versions of this item:
- José Murteira & Esmeralda Ramalho & Joaquim Ramalho, 2013. "Heteroskedasticity testing through a comparison of Wald statistics," Portuguese Economic Journal, Springer, Springer, vol. 12(2), pages 131-160, August.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-03-09 (All new papers)
- NEP-ECM-2013-03-09 (Econometrics)
- NEP-ORE-2013-03-09 (Operations Research)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Russell Davidson & Emmanuel Flachaire, 2000.
"The Wild Bootstrap, Tamed at Last,"
Econometric Society World Congress 2000 Contributed Papers, Econometric Society
1413, Econometric Society.
- Emmanuel Flachaire, 2001. "The Wild Bootstrap, Tamed at Last," STICERD - Distributional Analysis Research Programme Papers, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE 58, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Davidson, R. & Flachaire, E., 1999. "The Wild Bootstrap, Tamed at Last," G.R.E.Q.A.M., Universite Aix-Marseille III 99a32, Universite Aix-Marseille III.
- Russell Davidson & Emmanuel Flachaire, 2001. "The Wild Bootstrap, Tamed at Last," Working Papers, Queen's University, Department of Economics 1000, Queen's University, Department of Economics.
- Russell Davidson & Emmanuel Flachaire, 2001. "The wild bootstrap, tamed at last," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 6560, London School of Economics and Political Science, LSE Library.
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195060119, October.
- Godfrey, Leslie G., 1978. "Testing for multiplicative heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 8(2), pages 227-236, October.
- 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.
- 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.
- James G. MacKinnon & Halbert White, 1983. "Some Heteroskedasticity Consistent Covariance Matrix Estimators with Improved Finite Sample Properties," Working Papers, Queen's University, Department of Economics 537, Queen's University, Department of Economics.
- 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.
- 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.
- 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.
- Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 17(1), pages 107-112, September.
- 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.
- 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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