On Estimating Regression Coefficients in Seemingly Unrelated Regression System

In the system of m (m >= 2) seemingly unrelated regressions, we show that the Gauss-Markov estimator (GME) of any regression coefficients has unique simplified form, which exactly equals to the one-step covariance-adjusted estimator of the regression coefficients, and hence we conclude that for any finite k >= 2 the k-step covariance-adjusted estimator degenerates to the one-step covariance-adjusted estimator and the corresponding two-stage Aitken estimator has exactly one simplified form. Also, the unique simplified expression of the GME is just the estimator presented in the Theorem 1 of Wang' work [1988]. A new estimate of regression coefficients in seemingly unrelated regression system, Science in China, Series A 10, 1033-1040].