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RE: st: estimating the covariance matrix of probit two stage procedure


From   "Armelini, Guillermo" <DOCGArmelini@iese.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: estimating the covariance matrix of probit two stage procedure
Date   Mon, 24 Dec 2007 13:50:13 +0100

Thanks Maarten
 
but what about the conditional regression. As far as I know Heckman model does not consider that the conditional regression is censored, that's why I proposed doing the procedure separately.
 
Best wishes
 
Guillermo

________________________________

De: owner-statalist@hsphsun2.harvard.edu en nombre de Maarten buis
Enviado el: lun 12/24/2007 6:24
Para: statalist@hsphsun2.harvard.edu
Asunto: Re: st: estimating the covariance matrix of probit two stage procedure



--- "Armelini, Guillermo" <DOCGArmelini@iese.edu> wrote:
> I'm trying to estimate a recursive simultaneous equation using a
> probit model in the selection stage and a conditional censored
> regression in the second stage. Specifically, the model is the
> following one:
> 
> Z(i)=AV(i)+U(i) (equation 1)
>
>  Z(i)=1 if Z(i)>0
>
>  Z(i)=0 if Z(i)<=0
> 
> where A is a vector of parametes and V is a set of covariates for
> each (i)
> 
> Then I calculate Lambda which is the inverse mills of the predicted
> values of equation one for those observations in which the Dependent
> Variable is equal to 1
> 
> The second step is to calculate the tobin model:
> 
> Y(i)=bX(i)+E(i) if Z(i)=1  (second equation)
> 
> In this equation "bs" are the coefficients to be estimated and "X" is
> a vector of covariate which includes Lambda (which is the inverse
> mills of the predicted values of equation one in which the DV is = 1)
> 
> My question is how can I correct the covariance and the variance of
> the parameters since, Lee, Maddala  and Trost (1980) suggest that
> everytime a two stage model like the one I describe before is
> estimated, a procedure to correct the variance and covariance of the
> parameters should be run.
> 
> Is anybody aware about how to do this in Stata?

Yes:
heckman Y X, select(V) twostep
X should not include lambda (Stata does that for you)

Best whishes (to you and everybody else on the list),
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------


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