Question: Take the linear homoskedastic CEF Y X0e (4.63) E[e j X] 0 E e2 j X 2 and suppose

Take the linear homoskedastic CEF Y ¤

Æ X0¯Åe (4.63)

E[e j X] Æ 0 E

e2 j X

Æ ¾2 and suppose that Y ¤ is measured with error. Instead of Y ¤, we observe Y Æ Y ¤ Åu where u is measurement error. Suppose that e and u are independent and E[u j X] Æ 0 E £
u2 j X ¤
Æ ¾2 u(X)

(a) Derive an equation for Y as a function of X. Be explicit to write the error term as a function of the structural errors e and u. What is the effect of this measurement error on the model (4.63)?

(b) Describe the effect of this measurement error on OLS estimation of ¯ in the feasible regression of the observed Y on X.

(c) Describe the effect (if any) of this measurement error on standard error calculation for b¯.

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