[Limdep Nlogit List] Selection model

William Greene wgreene at stern.nyu.edu
Fri May 8 20:40:12 EST 2009


Jadwiga:
(1) Both estimates are correct. The probit estimates reported with
the PROBIT command are limited information MLEs.  LIML because they
are estimated aside from rho, sigma and beta.  The MLE computed with
SELECT is a FIML estimator, for the same reason. Both are consistent
and asymptotically normally distributed. In theory, the FIML estimator
is more efficient. In a finite sample, however, the difference will
often be small because rho is usually estimated with a fair amount of
sampling variation, and this is transmitted to the estimator of
alpha.
(2) B and VARB in the SELECTION model contain the FIML results from
the selection estimator, not the original PROBIT estimates.
(3) You can use either estimator. The only difference between them
is efficiency, and this is likely to be a small difference in
practice.
Regards,
Bill Greene

----- Original Message -----
From: "Jadwiga Kostrzewska" <dwakotki at wp.pl>
To: "Limdep and Nlogit Mailing List" <limdep at limdep.itls.usyd.edu.au>
Sent: Friday, May 8, 2009 4:33:57 AM GMT -05:00 Columbia
Subject: [Limdep Nlogit List] Selection model

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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