Abstract
Abstract For a system of two seemingly unrelated regression equations, a necessary and sufficient condition is obtained for a general linear estimator of the regression coefficients to be better than the OLS estimator in terms of the mean-square error-matrix (MSEM) criterion. According to this condition a concise biased estimator is proposed, and a two-stage estimator based on a generalized unrestricted estimate of the dispersion matrix is suggested. The exact MSEM of the two-stage estimator is derived, its superiorities over the OLS estimator and even over the Aitken estimator introduced by Zellner (1963. J. Amer. Statist. Assoc. 58, 977–992) are examined. An F-distribution statistic for testing MSEM-dominance is provided.
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