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Antoine said
If you are ready to assume joint normality, then -biprobit- should do
the trick:
/*------------------------------*/
clear
set obs 10000
set seed 987654321
drawnorm e1 e2, cov(1,0.5\0.5,1)
drawnorm x1 x2 z1 z2
g endog=(1+z1+z2+e1>0)
g y=(1+endog+x1+x2+e2>0)
probit y endog x1 x2 /*biased*/
biprobit (y= endog x1 x2) (endog=z1 z2)
I'm not so sure. Stata will allow you to estimate that model, but it
calls it the "seemingly unrelated bivariate probit" model. That model
is described in Greene, Econometric Analysis 6ed (p. 817), as
analogous to SUR ("in the same spirit as the seemingly unrelated
regression model"): that is, two equations in which there are nothing
but exogenous explanatory variables. The way in which Antoine has
written the model is one in which you surely could use cmp, as it is
recursive (y depends on endog, but endog does not depend on y). But
I'm not sure that the assumptions of the SUBP model are satisfied here.
Greene (p. 817) describes a model in which an endogenous regressor is
binary as a 'treatment effects' model and suggests that it should be
treated as a selection problem.
Kit Baum | Boston College Economics & DIW Berlin | http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming
| http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata | http://www.stata-press.com/books/imeus.html
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