Question: Consider an i.i.d. sample {Yi ,Xi } i 1, ...,n where X is k1. Assume the linear conditional expectation model Y X0e with

Consider an i.i.d. sample {Yi ,Xi } i Æ 1, ...,n where X is k£1. Assume the linear conditional expectation model Y Æ X0¯Åe with E[e j X] Æ 0. Assume that n¡1X 0X Æ I k (orthonormal regressors).

Consider the OLS estimator b¯.

(a) Find V b¯

Æ var

£ b¯

(b) In general, are b¯j and b¯` for j 6Æ ` correlated or uncorrelated?

(c) Find a sufficient condition so that b¯j and b¯` for j 6Æ ` are uncorrelated.

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