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Re: st: IV probit with dummy endogenous regessors


From   "Brian P. Poi" <bpoi@stata.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: IV probit with dummy endogenous regessors
Date   Thu, 10 May 2007 11:05:27 -0500 (CDT)

On Thu, 10 May 2007 margherita.comola@upf.edu wrote:

Dear Statalister,

I have a few basic questions about IV probit.

My model is a probit with dummy endogenous regressors (for every dummy endogenous regressor I have 3 dummy instruments).

Can I use ivprobit, or it can be only used with continuous endogenous regressors?

As Wooldridge (2002, p. 472) emphasizes, both the two-step and maximum-likelihood estimators implemented by -ivprobit- (and -ivtobit-) require that the endogenous regressors be continuous.

The model fitted by -ivprobit- can be written as

y1* = x'beta + delta*y2 + u1
y2 = x'gamma + z'eta + v2

with y1 = 1 if y1* > 0 and 0 otherwise, where y2 is endogenous, x represents the included exogenous variables, and z are the additional instruments. Both estimators assume that u1 and v2 are bivariate normal. Thus, since v2 is normal, y2 given x and z must also be normal, and that rules out discrete variables (of which a dummy is a special case).

-- Brian Poi
-- bpoi@stata.com


Reference
----------
Wooldridge, J. M. (2002). Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press.
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