Question: Take themodel in vector notation Y X e E[e j X ] 0 E ee0 j X . Assume for

Take themodel in vector notation Y Æ X ¯Åe E[e j X ] Æ 0 E

ee0 j X

Æ §.

Assume for simplicity that § is known. Consider the OLS and GLS estimators b¯ Æ
¡
X 0X ¢¡1 ¡
X 0Y ¢
and e¯ Æ
¡
X 0§¡1X ¢¡1 ¡
X 0§¡1Y ¢
. Compute the (conditional) covariance between b¯ and e¯ :
E h¡ b¯¡¯
¢ ¡ e¯¡¯
¢0 j X i Find the (conditional) covariancematrix for b¯¡ e¯ :
E h¡ b¯¡ e¯
¢ ¡ b¯¡¯
¢0 j X i .

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