Re: st: IV probit with dummy endogenous regessors

["Brian P. Poi" <bpoi@stata.com>]

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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