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, 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)
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