Re: st: IV estimation for probit models with binary endogenous variable...?

[Antoine Terracol <Antoine.Terracol@univ-paris1.fr>]

Kit, I miht have misunderstood your comment, but I read in -cmp-'s help 
file that:

As a matter of algorithm, cmp is an SUR (seemingly unrelated 
regressions) estimator. It treats the
    equations as independent from each other except for modeling their 
underlying errors as jointly normally
    distributed. Mathematically, the likelihood it computes is 
conditioned on observing all right-side
    variables, including those that also appear on the left side of 
equations.  However, it can actually fit
    a much larger class of models. Maximum likelihood (ML) SUR 
estimators, including cmp, are appropriate
    for an important class of simultaneous equation models, in which 
endogenous variables appear on the
    right side of structural equations as well as the left. Models of 
this kind for which ML SUR is
    nevertheless consistent must satisfy two criteria:

        1) They are recursive. In other words, the equations can be 
arranged so that the matrix of
        coefficients of the dependent variables in each others' 
equations is triangular. As emphasized
        above, this means the models have clearly defined stages, 
though there can be more than one equation
        per stage.

        2) Dependent variables in one stage enter subsequent stages 
only as observed. Returning to the
        example in the first paragraph, if C is a categorical variable 
modeled as ordered probit, then C,
        not the latent variable underlying it, call it C*, must figure 
in the model for D.



In the following example, -cmp- and -biprobit- give the same results

/*---------------------------*/
clear
set obs 1000
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)
cmp (y = endog x1 x2) (endog  = z1 z2), ind(4 4)
biprobit (y = endog x1 x2) (endog  = z1 z2)
/*---------------------------*/

Antoine


Kit Baum wrote:
> <>   
> 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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