economics letters ELSEVIER Economics Letters 48 (1995) 113-118 Bartlett-corrected tests for heteroskedastic linear models Francisco Cribari-Neto a'*, Silvia L.P. Ferrari b aDepartment of Economics, Southern Illinois University, Carbondale, IL 62901-4515, USA bDepartamento de Estatistica, Universidade de S~o Paulo, Caixa Postal 20570, $5o Paulo/SP, 01452-990, Brazil Received 6 June 1994;accepted12 August 1994 Abstract This paper uses the results in Rothenberg (Econometrica, 1984, 52, 827-842) to derive Bartlett-corrected tests for heteroskedastic linear models. The corrections are applied to three commonly used test statistics, namely: the likelihood ratio, Wald and Lagrange multiplier statistics. JEL classification: C12 1. Introduction Test statistics having an asymptotic chi-squared distribution are commonly used by applied researchers in economics and other fields. Although the chi-squared distribution is known to approximate well the null distribution function of such test statistics for large sample sizes, there is no guarantee that it provides a reliable approximation in samples of small to moderate sizes. It has even been shown that asymptotically equivalent tests can deliver conflicting inference when applied to the same data set (e.g. Berndt and Savin, 1977; Breusch, 1979; Evans and Savin, 1982; Savin, 1976). It is thus important to obtain corrected tests, i.e. modified testing procedures with better finite-sample behavior. The corrections to the likelihood ratio statistic date from 1937 (Bartlett, 1937) and were developed in full generality in 1956 (Lawley, 1956). Progress in the improvement of Lagrange multiplier and Wald tests has been much slower. Corrections to Lagrange multiplier test statistics were proposed by Cordeiro and Ferrari (1991); see also Chandra and Mukerjee (1991) and Taniguchi (1991). A correction to the Wald statistic for the test of nonlinear restrictions was derived by Ferrari and Cribari-Neto (1993). Corrections to Lagrange multiplier and Wald statistics are commonly referred to as Bartlett-type corrections. A similar literature has focused on size-corrections to critical values obtained as Cornish- * Corresponding author. 0165-1765/95/$09.50 t~) 1995 Elsevier Science B.V. All rights reserved SSDI 0165-1765(94)00597-4