Re: st: Reduced Form with biprobit

["Steven J. Carter" <sjcarter@uci.edu>]

Partha,

Yes, I only generated one data set, with 1000 observations.  I will try 
to see what happens when I generate many data sets.

You confirmed my suspicions that the reduced form was incorrect.

Thanks again for your response.

Steven

Partha Deb wrote:

> Steven,
>
> From your description it seems that you've only generated one set of 
> data. If that's the case, there is nothing in the theory that predicts 
> your point estimate will be close to the truth.  If you did your 
> experiment many times, the average of the estimates should be close to 
> the truth, esp. as the sample size gets larger.
>
> Your reduced form is not correct - unless you want y2* on the RHS of 
> the y1* equation (not y2).  The fact that the estimate you get when 
> you "back it out" is closer says nothing about its correctness.
>
> Hope this helps.
>
> Partha
>
>
> Steven J. Carter wrote:
>
> > Dear Statalist,
> >
> > I have a probit model with an endogenous dummy variable and I found 
> > some helpful hints on this thread 
> > (http://www.statacorp.com/statalist/archive/2007-05/msg00366.html.).  
> > I generated a data set to see if biprobit recovers the parameters, 
> > and it doesn't.  However, when I model the reduced form, 
> > (substituting the rhs variables in equation 2 for y2 in equation 1),  
> > and back out the structural parameters, it is pretty close.  So my 
> > question is, why does it work for the reduced form parameters, but 
> > not the recursive form?  Also, wouldn't the reduced form be similar 
> > to the forbidden regression that is discussed in Wooldridge's Cross 
> > section and Panel data text for nonlinear models?
> >
> > Here is my do file
> > *********  Confusing bivariate probit question ******
> >
> > * Note:  I generated the data in another program because I am not 
> > quite familiar with stata statistics codes yet.
> >
> > *  this is a simulated bivariate probit dataset with an endogenous 
> > regressor
> > *  model specified as
> > *  y1*=g*y2+x*b1+e1, x includes constant in both equations
> > *  y2*=x*b2+d*z+e2, where e1, e2 are normal with zero means, unit 
> > variances and correlation p
> > *  true values for parameters are g=0, b1=[-.5 .07]', b2=[0 -.1]', 
> > d=.7, p=.5
> >
> > *************
> > * do a bivariate probit as shown in greene (2003) pg 715-716
> > biprobit (y1= y2 x) (y2=x z)
> >
> > * notice that the coefficients don't match the true values
> >
> > * Now try a bivariate probit using reduced form:
> > * y1*=g*(b2*x+d*z)+b1*x
> > *    =x*(g*b2+b1)+z*(g*d)
> > *    =x*w1+z*w2
> > * y2*=b2*x+d*z+e2
> >
> > biprobit (y1=x z) (y2=x z)
> > matrix define coef2=e(b)
> >
> > * true reduced form parameters
> > matrix define rftrue=(.07, 0, -.5, -.1, .7, 0, .5)
> > matrix list coef2
> > matrix list rftrue
> > * though estimating the reduced form parameters, w1 and w2 in the 
> > first equation, solving for the structual parameters (g, b1) yields 
> > results closer * to the true parameters.
> >
> > ********* End confusing question**************
> >
> > I appreciate any input on this.
> >
> > Best
> >
> > Steven
> >
> > *
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> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
*
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