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


From   jean ries <ries@ires.ucl.ac.be>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: IV est. /w binary endogenous and binary dependent var
Date   Thu, 09 Dec 2004 14:07:56 +0100

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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