Seemingly Unrelated Regressions
10.1 When Is OLS as Efficient as Zellner’s SUR?
a. From (10.2), OLS on this system gives
p /Р 1,ols I
p ols = "
P2,ols I

This is OLS on each equation taken separately. For (10.2), the estimated var("ols) is given by
where s2 = RSS/(2T — (K1 + K2)) and RSS denotes the residual sum of squares of this system. In fact, the RSS = e,1e1 + e2e2 = RSS1 + RSS2 where
ei = yi — Xi P i, ols fori = 1,2.
If OLS was applied on each equation separately, then
var (p 1,ol^ = s2 (X1X1)1 with s2 = RSS1/(T — K1)
and
var (p2,ol^ = s2 (X2X2)1 with s2 = RSS2/(T — K2).
Therefore, the estimates of the variancecovariance matrix of OLS from the system of two equations differs from OLS on each equation s...
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