Re: st: Reduced Form with biprobit

[Partha Deb <partha.deb@hunter.cuny.edu>]

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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--
Partha Deb
Department of Economics
Hunter College
ph:  (212) 772-5435
fax: (212) 772-5398
http://urban.hunter.cuny.edu/~deb/

Emancipate yourselves from mental slavery
None but ourselves can free our minds.
	- Bob Marley

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