Re: st: IV est. /w binary endogenous and binary dependent var

[jean ries <ries@ires.ucl.ac.be>]

Mark Schaffer wrote:

> I had a look at biprobit, too.  The syntax seems compatible with what 
> Guido wants to do, e.g.,
>
> biprobit (y = w x1-xn) (w = z x1-xn)
>
> but it wasn't clear to me from a quick perusal of the manual entry 
> that biprobit will properly handle the fact that the w that appears 
> in the first eqn is the dependent variable in the second.  The help 
> file refers to this as a "Seemingly unrelated bivariate probit 
> model", which makes me think that it won't do what Guido wants.
>
> Any biprobit experts out there who can clarify this?
You are right: the "seemingly unrelated bivariate probit model" is 
different from Guido's problem. However, Greene (2000, pp.852-855) shows 
that in a case where you have a variable that appears on the right hand 
side of one and on the left hand side of the other equation, the 
log-likelihood will be the same as in a seemingly unrelated bivariate 
probit model. Thus, Guido could do:
. biprobit (y = w x1-xn) (w = z x1-xn)
A "seemingly unrelated" point: Abadie (2003) presents a semiparametric 
estimator for the binary outcome - binary instrument case. This 
estimator is not (yet) implemented in Stata, but Abadie provides some 
Matlab code: http://ksghome.harvard.edu/~aabadie/larf.html .

Alberto ABADIE, 2003, Semiparametric Instrumental Variable Estimation of 
Treatment Response Models,  Journal of Econometrics, vol. 113(2), 231-263.
William GREENE, 2000, Econometric Analysis, 4th edition, Prentice Hall, 
Upper Saddle River.

jean

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