st: Reduced Form with biprobit

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

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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