Question: Consider the model Y X0e X 0Z u E[Ze] 0 E Zu0 0 with Y scalar and X and Z

Consider the model Y Æ X0¯Åe X Æ ¡0Z Åu E[Ze] Æ 0 E

Zu0¤

Æ 0 with Y scalar and X and Z each a k vector. You have a random sample (Yi ,Xi ,Zi : i Æ 1, ...,n). Take the control function equation e Æ u0°Åº with E[uº] Æ 0 and assume for simplicity that u is observed.

Inserting into the structural equation we find Y Æ Z0¯Åu0°Åº. The control function estimator ( b¯, b°) is OLS estimation of this equation.

(a) Show that E[Xº] Æ 0 (algebraically).

(b) Derive the asymptotic distribution of ( b¯, b°) .

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