Question: Take the linear model Y X0e. Let the OLS estimator for be b with OLS residual bei . Let the IV estimator for

Take the linear model Y Æ X0¯Åe. Let the OLS estimator for ¯ be b¯ with OLS residual bei .

Let the IV estimator for ¯ using some instrument Z be e¯ with IV residual eei Æ Yi ¡ X0 i

e¯. If X is indeed endogenous, will IV “fit” better than OLS in the sense that Pni

Æ1 ee2 i

Ç

Pni

Æ1 be2 i , at least in large samples?

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