Abstract:
This paper extends, 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,
ZSLS, 3SLS, tests of over identification, and so forth.
