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
(2)
^ . . _____ __
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 + pσu ΦYJ^
E( wm =0)=χβ - pσu 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 + pσu λ' Yγ) + ε∣ with λ the inverse of Mill’s ratio, provides
consistent estimators for β and pσu∣
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