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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