Some Exact Finite Sample Properties of Zellner’s Seemingly Unrelated Regression Equations Estimates

This paper considers Zellner’s "Aitken" estimator \hat\beta_Z 1 of β₁ based on the unrestricted estimate S of Σ =（σ_ij） in the system of m seemingly unrelated regressions: Y_i = X_iβ_i +ε_i（i = 1, …, m）,and derive finite sample variance matrix of the \hat\beta_Z 1 under the condition X'₁X_i（i=2,…,m）. This condition is weaker than the condition X'_iX_j = 0（i≠j,i,j = 1, …,m） considered by Zellner （1963）,Kataota （1967） and Revanker （1974）.