Economics of Migration: Problem Set 4
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Economics of Migration: Problem Set 4
March 14, 2023
1. Suppose you use cross sectional data to estimate the wage profiles of immigrants. Use a diagram to show the possible bias for the wage growth if the cohort quality rises over time.
2. Suppose the quality of cohorts remains the same over time, can the wage growth of immigrants be overestimated?
3. [optional] Consider wage regressions where we control for cohort and year effects:
lnwit(I) = b1(I)Xit+b2(I)EXit+b3(I)YSMit+Σmbm(I)Cim+Σtγt(I)Tit + eit(I) lnwit(N) = b1(N)Xit+b2(N)EXit+Σtγt(N)Tit + eit(N) (1)
• t is an index for the cross section year of data in which the individual i is observed.
• Xit is a vector of individual characteristics, e.g. gender, marital status and education level.
• EXit is potential work experience.
• Tit is a dummy variable, being equal to 1 if individual i is drawn from cross section year t ,
• γt(I) and γt(N) are period effects on log wages of immigrants and natives,
• Cim is an indicator function, being equal to the calendar year m in which the immi- grant i arrived otherwise zero,
• Years since migration YSMit = Tit(t − Cim).
Explain why we cannot identify b3(I) . What assumptions do we need in order to identify b3(I)? Suppose we could obtain an estimate of bm(I) from other studies, would we be able to identify b3(I)?
2023-05-20