[Limdep Nlogit List] Selection model

[Jadwiga Kostrzewska]

Dear all,
I am estimating the selection model with commands (in LimDep 9.0):
PROBIT; Lhs=SELEKCJA; Rhs=W; Hold$
SELECT; Lhs=ZAL; Rhs=XW; MLE$
In the manual it is written:
E30-14: “b and varb contain beta, sigma and rho”. (The beta is a vector 
of parameters in the second equation.)
E30-12 in the frame: “Although this model computes an estimate of alpha, 
it does not replace the estimates that have been retained with the ;Hold 
instruction in the preceding PROBIT command”. (The alpha is a vector of 
parameters in the first equation.)
But in the LimDep program: b=(est.alpha, est.beta, sigma, rho), not 
(est.beta, sigma, rho). Moreover est.alpha in b is not equal to the 
estimators of alpha in PROBIT model.

I have some questions:
Which estimates of alpha for the selection model are correct? That is 
which set of alpha, these from b in the selection model or these from 
the probit model, are better? One more question is: Which set of alpha 
does varb in the selection model is related to?

The similar question is about the parameter vector of alpha in the 
selection model with heteroscedasticity. In this model b=(beta, gamma in 
the heterosc. equation, sigma, rho). I do not know which set of alpha 
should I take: the limited information MLE estimator of alpha from the 
model:    PROBIT; Lhs=SELEKCJA; Rhs=W$    or the estimator from the 
homoscedastic selection model:
PROBIT; Lhs=SELEKCJA; Rhs=W; Hold$
SELECT; Lhs=ZAL; Rhs=XW; MLE$  ?

Thank you for the answers.
Best regards,
Jadwiga Kostrzewska

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