OLS and GLS are equivalent for the Within transformed model. (a) Using generalized inverse, show that OLS

Question:

OLS and GLS are equivalent for the Within transformed model.

(a) Using generalized inverse, show that OLS or GLS on (2.6) yields \(\widetilde{\beta}\), the Within estimator given in (2.7).

(b) Show that (2.6) satisfies the necessary and sufficient condition for OLS to be equivalent to GLS (see Baltagi (1989)).  Show that \(\operatorname{var}(Q v)=\sigma_{v}^{2} Q\) which is positive semi-definite and then use the fact that \(Q\) is idempotent and is its own generalized inverse.

image text in transcribed

image text in transcribed

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question
Question Posted: