Question: Take themodel Y X0e E[e j X] 0 Z X0u E[u j X] 0 where X is a k vector and

Take themodel Y Æ X0¯Åe E[e j X] Æ 0 Z Æ X0¯°Åu E[u j X] Æ 0 where X is a k vector and Z is scalar. Your goal is to estimate the scalar parameter °. You use a two-step estimator:

• Estimate b¯ by least squares of Y on X.
• Estimate b° by least squares of Z on X0 b¯.

(a) Show that b° is consistent for °.

(b) Find the asymptotic distribution of b° when ° Æ 0.

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