Abstract:
Consider a system of two seemingly unrelated regression equautions
yi=
XiBi+
ui(
i=1,2), Where
Xi(
i=1,2) is the repression matrices for which
P1P2=
P2P1(
Pi=
Xi(
X'iXi)
-1X'i,
i=1,2). This system includes some special special models considered in some paperes 1-4.Let
βiand
∧βi(
i= l,2) be the
β-estimatiors based,respectively, on the restricted estimate
S of Σ and on tile unrestricted estimate
S of Σ. This paper derives the finite sample variances of the
βi(
i = 1, 2), and examines their efficiency with respect to the
∧βiand with respect tile OLS estimator
bi obtained directly from the ith equation.It is shown that for large values of the sample size
n or the correlation coefficient|ρ|the estimator
βimay be more efficient than
bi,and for samll values of|ρ|the restricted estimator
βi can work better than the unrestricted estimator
∧βi(
i = 1, 2).