IMMIGRATION POLICY AND THE AGRICULTURAL LABOR MARKET: THE EFFECT ON JOB DURATION



μi


σε


μj-1


σε


μj-1


σε

σε


Note that we can use the result of the ordered probit model in the first stage for


μj - x1α


and


σε


Also note that μ-1 = -∞, μ3 = ∞ from the assumption of normal distribution. In the
second stage of this Heckman type two-stage method, we estimate equation (2) below by ordinary

least squares with only completed spells.

(2)


ln t = z β + Pσ jλij + e = z β + βjλij + eij

We can also show that the conditional variance of the log of the duration would be

var[ln t. | ln t. is observed] = σjI1 - P ββ ],

where

I °ε J


μ1


• ʌ

- χ α

σε   J

_


' X
μ1 -1- x α


σε   J


(

2xa

σε


μj


I σε J


C • A
,. -
xlα I
Φ —
I

I σε J


μ1 -1


σε   J


. - xiα I

Φ —l- I

V σε J


Then a consistent estimator of σ2j is given by σj2


= [ei2 + /^λ δl^ ]/nj. We can obtain the
i=1

л    Λ

estimator of the asymptotic covariance matrix for [βj, βλ ] by substituting these results in the
j j

formulation in Greene (2003).



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