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st: simultaneous bivariate probit with mutual endogeneity


From   Michele Mancini <mmancini.stata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: simultaneous bivariate probit with mutual endogeneity
Date   Fri, 25 Feb 2011 14:05:11 +0000

Hi Statalisters,

I have to estimate the following bivariate probit:

Y1=a*Y2+b1X1
Y2=c*Y1+b2X2

where X1 and X2 are two sets of different variables (some of them are
the same) and Y1 and Y2 are two [0,1] endogenous variables.
I don't have any problem using -biprobit- but there is a problem
indeed: coherency conditions. The literature says that a coherency
condition is a*c=0.
With this condition you force the system to be recursive, setting for
example c=0.
Imposing c=0 and using -biprobit- is fine: high significance and rho
is different from zero (p=0.0000).
But I'd like to try another way. I've read this paper (Hajivassiliou
2008, pag.15: http://www.nuffield.ox.ac.uk/General/Seminars/Papers/969.pdf):
imposing a>0 and c<0 you have solved the problem, using conditional
MLE in a way that the observed LDVs to lay outside the empy region
(see pag. 20-21 of the paper).
How can I perform this using -biprobt- or other Stata commands?

Thank you.

Michele Mancini
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