ECON0041 Migration and Job Search Problem Set 2 UCL

Economics of Migration and Job Search: Problem Set 2
Suphanit Piyapromdee


1. Assume that firms produce output using high and low skill labor
 ρ ρ 1/ρ
Yt = At θht Lht + L`t

where Let with e ∈ {h, `} is the aggregate labor input of workers of skill e in time t;
σE = 1/(1 − ρ) is the elasticity of substitution between skill groups;θet is the relative
productivity level of skilled to unskilled labor.
Within each skill group, workers differ by age (or experience)
η η
1/η
Let = αeY LeY t + LeOt

where a ∈ {Y, O} denotes young and old, and one of the αea is normalized to one;
σA = 1/(1 − η) is the elasticity of substitution between age groups.
Within each age group, workers differ by immigration status
 1/δ
δ M δ
Leat = Neat + βeat Meat

N is normalized to one.
where N denotes natives and M denotes immigrants, and βeat

(a) (optional) Assume perfect competition, verify that labor demand takes the fol-
lowing form

s 1 s
lnWeat = lnAt + lnLt + lnθet + lnαea + lnβeat
σE
   
1 1 1 1 1
+ − lnLet + − lnLeat − lnSeat
σA σE σI σA σI

where S ∈ {N, M} is an immigrant status.
Solution: to be shown in tutorial.
M?
(b) How would you estimate σE , σA , σI and θht , αeY , βeat
M by subtracting lnwN from lnwM ,
Solution: Step 1: Estimate σI and βeat eat eat
 M   
weat 1 Meat
ln = de + da + dt − ln
wNeat σI Neat

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