I am reading Greene, Econometric Analysis, 7th Addition,

I am seeking a point of clarrification.

"The case of identical regressors is quite common [think a VAR mode].... In this special case, generalized least squares is equivalent to equation by equation ordinary least sqaures".

Can somebody explain why?

Is this because the covaraince matrix is the same when I estimate the first equation of a VAR versus the second equation? Or any other reasons?

  • $\begingroup$ Thanks @Cowboy Trader, so you're confimring, from the slides, .... "But, no gains if identical regressors –for example, in the CAPM.  GLS is the same as OLS. " period, no exceptions. $\endgroup$ – Jack Salah Apr 17 '19 at 12:42
  • $\begingroup$ Many econometrics textbooks, e.g. Davidson & McKinnon "Econometric Theory and Methods", p. 500, include proofs showing how the GLS estimator simply collapses to the equation-by-equation OLS estimator in the case you are interested in. $\endgroup$ – Richard Hardy Apr 19 '19 at 12:00
  • $\begingroup$ I think your title might be improved by asking "why" or "how" instead of "whether", otherwise it does not seem to match closely to your post. $\endgroup$ – Richard Hardy Apr 19 '19 at 12:02

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