At the end of Section 8 7, it is suggested that the OLS estimator could have a smaller mean squared error than the 2SLS estimator Using (8 4), the results of Exercise 1, and Theorem 8 1, show that the result will be true if How can you verify that this is at least possible The right hand side is a rank one, nonnegative definite matrix What can be said about the left hand side 1 Qxx QxzQzQzx yy' (o2 n) y'Qz r

Question: At the end of Section 8.7, it is suggested that the OLS estimator could have a smaller mean squared error than the 2SLS estimator. Using

At the end of Section 8.7, it is suggested that the OLS estimator could have a smaller mean squared error than the 2SLS estimator. Using (8-4), the results of Exercise 1, and Theorem 8.1, show that the result will be true if

1 Qxx QxzQzQzx>> -yy'. (o2/n) + y'Qz&r

How can you verify that this is at least possible? The right-hand-side is a rank one, nonnegative definite matrix.What can be said about the left-hand side?

1 Qxx QxzQzQzx>> -yy'. (o2/n) + y'Qz&r

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