The migration of unskilled youth: Is there any wage gain?

where W is the log-wage, X the set of explanatory variables and M a dummy variable indicating
whether or not the individual migrated after leaving school;_u is the stochastic error term, assumed to
be normally distributed with zero mean and variance M* = Yγ + e ∣.

Treatment of the selection bias.

The question is: does a measure the impact of migration? If the decision to migrate and the level of
wage are correlated, the least square estimates of a will overestimate the migration effect (Greene,
1993). We therefore model migration decision as:

'M = 1 if M* = Yγ+e > 0

^ . . _____ __

M = 0 if M* = Yγ + e ≤ 0

and M* = Yγ + e∣                             (3)

where M is equal to 1 if the individual migrates and 0 otherwise and Y is a set of explanatory variables
for the migration benefit M*, which is latent.

Assuming that u and e are bivariate normally distributed with p the correlation,
E ( W/M = 1) = Xβ + a + E ( u∣M = 1)

E ( W/M = 1) = Xβ + a + E ( u∣e > - Yγ) = Xβ + a + pσ_u ΦYJ^

E^{( wm} =⁰⁾=^{χβ -} p^σu 1^Y)

where (!) and Φ ∣ are, respectively, the density and the distribution function.

We use the Heckman two-step estimation procedure (Heckman, 1979) which is as follows:

- the probit estimation of (3) provides estimations for γ and ψ( Yγ) and Φ( Yγ)∣ can therefore be
computed.

-the OLS estimation of W = Xβ + oM + pσ_u λ' Yγ) + ε∣ with λ the inverse of Mill’s ratio, provides
consistent estimators for β and pσ_u∣

As the estimated standard errors for the coefficients are not consistent estimates, we compute
heteroscedastic consistent standard errors using the formulas suggested by White (1980).

By estimating a common wage equation, we implicitly constrain the coefficients to be equal for
migrants and non-migrants alike. We have therefore estimated two wage equations, taking into account
the selection bias: one for migrants and one for non-migrants.

The data and estimated models

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