Question

a) Suppose that wage is determined by the following true population model that satisfies the assumptions for the MLR model. wage=βo +β1edu+β2abil+u

where β2 > 0 and abil = γ0 +γ1edu+w, γ1 > 0. As abil is not observed, the following model is estimated instead

wage=αo +α1edu+v whereu,v,andwareerrorterms. ShowthatE[αˆ]>β andE[αˆ]>β .

(b) Consider the model:
log(wage) = β0 + β1female + β2exper + β3female ∗ exper + u

where exper is the years of work experience, and female is a dummy vari- able (1 if the person is female, and 0 otherwise). How would you calculate the difference in the return of experience between males and females in this model?

(c) Consider the model:
yt =α0 +β0xt +β1xt−1 +β2xt−2 +β3xt−3 +ut

Given a permanent increase in x, how would you measure the long run effect on y?

Answer 1