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

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

I forgot to include this part of -cmp-'s help file in my previous message:


    So some Stata estimation commands have wider applicability than 
many realize. sureg (X=Y) (Y=Z), isure
    typically matches ivreg X (Y=Z) exactly even though the 
documentation does not describe sureg as an
    instrumental variables (IV) estimator.  (Iterated SUR is not a true 
ML estimator, but it converges to
    the same solution as ML-based SUR, as implemented, for example, in 
the demonstration command mysureg.
    See Pagan (1979) on the LIML-iterated SUR connection.) And biprobit 
(X=Y) (Y=Z) will consistently
    estimate an IV model in which X and Y are binary.


Antoine



Antoine Terracol wrote:
> 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
> >
> >
> >
> >
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/help.cgi?search
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/


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