st: re: overidentifying restrictions

[Christopher Baum <baum@bc.edu>]

<>
Erasmo said

"The Sargan-Hansen test is a test of overidentifying restrictions. The  
joint null hypothesis is that the instruments are valid instruments,  
i.e., uncorrelated with the error term, and that the excluded  
instruments are correctly excluded from the estimated equation. "
My question is about the meaning of the joint null hypothesis. To me  
is difficult to envision how the instrument being "uncorrelated with  
the error term" is different from the "excluded instruments are  
correctly excluded from the estimated equation".

You could have a model in which both y1 and y2 respond to epsilon, but  
do not interact with one another. In that case y2 would not be a valid  
instrument for y1 as it would be correlated with epsilon. Nevertheless  
it would not enter the y1 equation as significant. The 'correctly  
excluded from the estimated equation' clause can be tested with a  
simple regression: see whether each of the excluded instruments would  
have a significant coefficient if removed from the 'excluded' list and  
placed in the equation. But instruments must satisfy three conditions:
1) orthogonal to epsilon
2) only indirectly influence y
3) correlated with that for which they are instruments (that is, they  
must not be 'weak')
and the Sargan-Hansen test can consider 1) and 2) together. If the z's  
are incorrectly excluded from the y equation, they will be in the  
error term, and thus 1) will be violated.

Kit Baum   |   Boston College Economics and 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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