Journal of Econometrics 97 (2000) 189}202 Glejser's test revisited Jose H A.F. Machado, J.M.C. Santos Silva* Faculdade de Economia, Universidade Nova de Lisboa, Portugal ISEG, Universidade Te & cnica de Lisboa, R. do Quelhas 6, 1200 Lisboa, Portugal Abstract Godfrey (1996, Journal of Econometrics 72, 275}299) has shown that the Glejser test for heteroskedasticity is valid only under conditional symmetry. Here, modi"cations of the Glejser test are suggested. The proposed test statistics are asymptotically valid even when the disturbances are not symmetrically distributed and can be used to test for hetero- skedasticity when conditional location functions other than the conditional mean are estimated. 2000 Elsevier Science S.A. All rights reserved. JEL classixcation: C52 Keywords: Conditional symmetry; Glejser test; Heteroskedasticity; Regression quantiles 1. Introduction Godfrey (1996) showed that the well-known Glejser (1969) test for hetero- skedasticity is not valid when the disturbances of the model are not symmetric- ally distributed around zero. In this paper, modi"cations of the Glejser test are suggested. The proposed test statistics do not require assumptions about the symmetry of the distribution of the disturbances and are asymptotically equiva- lent to the Glejser test in certain circumstances. Given the limitations of the Glejser test and the availability of simple and well-established alternative tests for heteroskedasticity (see Breusch and Pagan, * Corresponding author. Fax: 351-213922781. E-mail address: jmcss@iseg.utl.pt (J.M.C. Santos Silva). 0304-4076/00/$ - see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 0 4 - 4 0 7 6 ( 0 0 ) 0 0 0 1 6 - 6