Re: st: -endog-test under xtivreg2: Jansen's J-stats

[Ari Dothan <ari.dothan@gmail.com>]

Thanks a lot, Professor Baum. I have not seen these considerations elsewhere
Best regards

On 2/23/11, Christopher Baum <kit.baum@bc.edu> wrote:
> <>
> "
>  "If it's overidentified, i.e., you're using all the plausible
> instruments (see my comment above), then the J stat is a specification
> test.  If the stat is large, then you *fail* the test, because the
> null is that all the instruments are valid, and a large J stat means
> you reject the null."
>
> can someone explain why a large J means rejection of the null in this case?
>
>
> The Hansen (not Jansen!) J statistic is the GMM optimization criterion. In
> an exactly ID model, you can always make it zero because you have as
> many equations as unknowns (parameters) and in general that can be solved
> exactly. In an overID model, you have more equations (moment conditions)
> than parameters, so for any choice of parameters, it is likely that you will
> fail to satisfy some (or all) of the moment conditions exactly. But remember
> that
> the moment conditions are of the form E[Z'u] = 0, so that they are asserting
> that each column of the instrument matrix is orthogonal to the error term.
> If the data
> disagree violently with one or more of those conditions, you have evidence
> that at least some of the instruments are not properly exogenous. That
> disagreement manifests itself in a large J, that is, you tried to minimize
> something and it ended up pretty big.
>
> The (joint) null is that the model is specified properly (y = X b+ u in the
> case of IV-GMM) AND E[Z'u] = 0. If you get a large J, there is evidence
> against that
> null, so you reject the hypothesis that your instruments are exogenous
> AND/OR that the equation is properly specified.
>
> We have an example somewhere (perhaps in one of the B-S-S papers) where you
> get a huge J, which goes away if you move an excluded instrument
> into the equation. That is a case where the J is challenging specification
> rather than exogeneity (the instrument in question cannot be correlated with
> error by construction, as it is something like age).
>
> 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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-- 
Ari Dothan
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