Thanks Kit.
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.
Erasmo
On Mon, Jul 27, 2009 at 9:59 PM, Christopher Baum<[email protected]> wrote:
> <>
> 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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