st: re: overidentifying restrictions

[Kit Baum <baum@bc.edu>]

<>
Erasmo said

I hope you don't mind if I ask for an additional clarification. I  
thought that if instruments are orthogonal to epsilon (1), then it  
must be that they (the instruments) only inderectly influence y (2).  
That is, it seems to me that (2) is absorbed by (1), but it is very  
likely that I am missing the point.

Well, in the classical (OLS) regression model y = X b + u, the X  
variables are orthogonal to u, but they certainly influence y  
directly... so I don't see how a statement of orthogonality conditions  
on [(X Z) vs u] tells me that X belongs in the equation but Z does  
not. That is the problem of specification of the model. What we do  
know is that if some of the Zs are really Xs, and we leave them out of  
the estimated model, then their presence in the error term will likely  
show up in an overid test. (There is a somewhat implausible textbook  
case relating to omitted variables being orthogonal to omitted  
regressors, but that is unlikely to occur in real data).
Kit

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



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