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st: estimating the covariance matrix of probit two stage procedure


From   "Armelini, Guillermo" <DOCGArmelini@iese.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: estimating the covariance matrix of probit two stage procedure
Date   Mon, 24 Dec 2007 00:57:04 +0100

Hello everybody,
 
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?
 
Guillermo
 
 


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