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5、covariance matrix: V( ) = z (X- er)z - . (4.12) In general, b is superior to LS applied to each of the L equations separately, but there are two special cases in which these estimation procedures are identical. The first case is that in which X, . . . , X, are all identical. We can then write X for
6、each of these matrices so that the observation matrix on the exogenous variables in (4.8) and (4.9) takes the form x o.o 0 x.o z=. . . I : =18X. . . . 0 0:-x (4.13) Ch. I: Linear Algebra and Matrix Methods This implies Z (PCM)Z = (1X)(z- z)(zx) =x- XX and 19 z (z- z)z- z (x- z) = z(xx)- (zex)(8- ez) =zo(x x)- X . It is now readily verified from (4.11) that fi
