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From |
DE SOUZA Eric <eric.de_souza@coleurope.eu> |

To |
"statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |

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

Date |
Wed, 23 Feb 2011 16:29:59 +0100 |

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 > > > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > -- Ari Dothan * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**re: st: -endog-test under xtivreg2: Jansen's J-stats***From:*Christopher Baum <kit.baum@bc.edu>

**Re: st: -endog-test under xtivreg2: Jansen's J-stats***From:*Ari Dothan <ari.dothan@gmail.com>

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