396 PART TWO: RELAXING THE ASSUMPTIONS OF THE CLASSICAL MODEL
which is a constant. That is, the variance of the transformed disturbance term u* is now homoscedastic. Since we are still retaining the other assumptions of the classical model, the finding that it is u that is homoscedastic suggests that if we apply OLS to the transformed model (11.3.3) it will produce estimators that are BLUE. In short, the estimated ¡1 and ¡* are now BLUE and not the OLS estimators ¡31 and fc.
This procedure of transforming the original variables in such a way that the transformed variables satisfy the assumptions of the classical model and then applying OLS to them is known as the method of generalized least squares (GLS). In short, GLS is OLS on the transformed variables that satisfy the standard least-squares assumptions. The estimators thus obtained are known as GLS estimators, and it is these estimators that are BLUE.
The actual mechanics of estimating ¡* and ¡* are as follows. First, we write down the SRF of (11.3.3)
Now, to obtain the GLS estimators, we minimize
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