Weaker MSE criteria and tests for linear restrictions in regression models with non-spherical disturbances

Abstract

This paper extend, in an asymptotic sense, the strong and the weaker mean square error criteria and corresponding tests to linear models with non-spherical disturbances where the error covariance matrix is unknown but a consistent estimator for it is available. The mean square error tests of Toro-Vizcorrondo and Wallace (1968) and Wallace (1972) test for the superiority of restricted over unrestricted linear estimators in a least squares context. This generalization of these tests makes them available for use with GLS, Zellner's SUR, 2SLS, 3SLS, tests of over identification, and so forth.