Some Finite Sample Results in the Context of Two Seemingly Unrelated Regression Equations

In this article, we consider a system of two "seemingly unrelated regression" equations (y i = X i β i + u i , i = 1, 2) with , and examine some finite sample properties of β-estimators based on the unrestricted estimate S of Σ = (σ ij ). The estimator of β 2 is shown to be identical with the direct OLS estimator b 2 obtained from Equation 2. The estimator of β 1 is shown to be more efficient than b 1 , the direct OLS estimator of β 1 obtained from Equation 1, for moderate departures of from zero; the efficiency, moreover, is shown to increase rapidly with the sample size for any given ρ.