Tests for the Independence Between Two Seemingly Unrelated Regression Equations

Abstract

When the error terms in two different regression equations are correlated, Zellner proposed an alternative estimator for the coefficients of each equation based on an estimated covariance matrix between the two error terms. However, since an estimated covariance matrix is used, the OLSE seems better than Zellner's estimator when the correlation of the two equations is close enough to zero. This paper considers the problem of testing the independence between two regression equations and derives a locally best invariant test for a one-sided alternative hypothesis and a locally best unbiased and invariant test for a two-sided alternative.