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

[DE SOUZA Eric <eric.de_souza@coleurope.eu>]

The J test as a test for over-identification is standard to econometric textbooks dealing with instrumental variables.

It is also a general principle of statistics that a specific null hypothesis is always formulated in the context of a (general) maintained hypothesis, i.e;, the assumptions underlying the model. A rejection of the null could proceed either from a rejection of the specific hypothesis or a more general rejection of the general maintained hypothesis.

Example: a static time-series regression model will often be plagued by problems of autocorrelation in the residuals. This problem can arise from a lack of dynamics in the model


Eric de Souza
College of Europe
Brugge (Bruges), Belgium
http://www.coleurope.eu



-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Ari Dothan
Sent: 23 February 2011 15:24
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: -endog-test under xtivreg2: Jansen's J-stats

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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