一类SUR模型参数两步估计的有限样本结果

Some Exact Finite Results of Zellner's Estimators in m Seemingly Unrelated Regressions

对于m（3）SUR模型（1），其设计矩阵满足条件（4），本文得到了回归系数βi（i＝1，…，m）的两步Aitken估计的精确协方差表达式，从而获得了两步估计优于LS估计的有限样本性质．特别是，当m＝3时本文结果可以与Revankar（1974）给出的一类两方程SUR模型结果相比较.

For m(3) seemingly unrleated regression equations: yi = Xiβi+εi,(i=1,…, m), with P1 =… = Pk, Pk+1 =… = Ps, Ps+1 =… = Pm and P1 =Ps+Pm, where Pi = Xi(Xi'Xi)-1Xi',the exact finite sample covariance matrix of Zellner's two-step Aitken estimator βi of βi(i =1…，m), based on the unrestricted estimate S of ∑ = (σij ) are obtained.When m = 3, all the three βi (i = 1, 2, 3) are shown to be more efficient then the OLS estimators of βi, for moderate departures of from zero, and the efficiencies are shown to be increased with the sample size n. These results can be compared with those obtained by Revankar(1974)for a system of 2SUR with X1 = (X2, L)