Question: For the two SUR equations given in (10.2). Let X1 and X2 be orthogonal, i.e., X 1X2 = 0. Show that knowing the true

For the two SUR equations given in (10.2). Let X1 and X2 be orthogonal, i.e., X

1X2 = 0. Show that knowing the true Σ we get

(a) β1,GLS = β1,OLS + (σ12/σ11)(X

1X1)−1X

1y2 and β2,GLS = β2,OLS + (σ21/σ22)(X

2X2)−1 X

2y1.

(b) What are the variances of these estimates?

(c) If X1 and X2 are single regressors, what are the relative efficiencies of βi,OLS with respect to βi,GLS for i = 1, 2?

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