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

[Christopher Baum <kit.baum@bc.edu>]

<>
"
 "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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