st: orthogonal regression

[Kit Baum <baum@bc.edu>]

If this is your model then you would use

ivreg2 y1 (y2=iv1 iv2) x1 x2  ,liml
ivreg2 y2 (y1=iv1 iv2) x1 x2 ,liml

to estimate it with LIML.

In any instrumental variables approach you do not 'define the  
instruments for each endogenous variable'. That is a common fallacy  
in thinking about IV and IV-like estimators. IV projects each  
endogenous variable on all the instruments---included and excluded--- 
in the course of estimation.

Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


On Dec 13, 2006, at 2:33 AM, Alvaro wrote:


> I have two endogenous variables y1 and y2, and exogenous ones, x.
> With these variables the following models would find theoretical  
> support:
> y1=beta0+beta1*y2+beta2*x1+beta3*x2+epsilon1
> y2=alpha0+alpha1*y1+alpha2*x1+alpha3*x2+epsilon2
>
>   I also have to iv variables for each of the endogenous variables
> (ie: the ranks of each endogenous variable: iv1, for y1 and iv2 for  
> y2).
>
> In order to apply orthogonal regressions using the option liml, I
> imagine I should define the instruments for each endogenous variable.
>
> My question is how to define these? I'm expecting alpha1=beta1 in
> orthogonal regressions. For this to happen I should use the same ivs
> in both models but this doesn't make much sense with my current  
> instruments?
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