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Re: st: overidentification test


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu, Tae Hun Kim <thkim91@gmail.com>
Subject   Re: st: overidentification test
Date   Tue, 15 Mar 2005 22:48:10 +0000 (GMT)

TaeHun,

The two tests are testing different things.

The benchmark estimation in Case (1) takes treats smom as exogenous, i.e.,
it includes it as part of the orthogonality conditions.  The J test asks
whether the excluded instruments (dratio dfarm dfuel) provide valid
orthogonality conditions.  The orthog(smom) option then asks whether smom
should be treated as endogenous, i.e., removed from the list of
orthogonality conditions.  It does this by comparing the benchmark
estimation with another, unreported estimation in which smom is endogenous.

What is odd about the results reported for Case (1) is that the benchmark
estimation has 3 excluded instruments and no endogenous variables, and so
the J test should have 3 degrees of freedom ... but it is reported below as
having 2 dofs.

The estimation in Case (2) treats smom as endogenous, and the J test asks
whether the excluded instruments (dratio dfarm dfuel) provide valid
orthogonality conditions in this case.

The difference between the unreported estimation with smom endogenous that
is used for the orthog option in Case (1), and the estimation in Case (2),
is that they use different estimates of the GMM weighting matrix.  Both
estimates are valid under the null.

The big problem with these results is that there is no specification that
passes the basic J test of orthogonality conditions.  Even when smom is
treated as endogenous (Case 2), the J test is failed/the orthogonality
conditions are invalid.  Adding smom to the list of orthogonality conditions
(Case 1), not surprising, doesn't make things any better - the J test is
still failed.

What you need is a specification in which, say, smom is endogenous and the J
test is passed.  Then you have a valid specification and you can do an
endogeneity test, i.e., ask whether you can add smom to the orthogonality
conditions.

Hope this helps.

--Mark

Quoting Tae Hun Kim <thkim91@gmail.com>:

> Hello Statalist.
> I want to test overidentification test with ivreg2.
> I think we can obtain Hansen J statistic with and without 'orthog'
> option.
> Actually, I used orthog option to test endogeneity.
> 
> Here is the code and results.(smom : endogenous variable)
> -case(1) :  with orthog option
> ivreg2 fmom y87 y88 y89 y90 y91 y92 y93 y94 y95 y96 y97 y98 y99
> y00
> y01 y02  s87 s88 s89 s90 s91 s92 s93 s94 s95 s96 s97 s98 s99 s00
> s01
> s02 smom ( = dratio dfarm dfuel ), gmm orthog(smom);
> Hansen J statistic (unconstrained) : 11.111-> Chi-sq(2)
> P-val=0.00387
> C statistic : 25.748-> Chi-sq(1) P-val=0.0000
> 
> -case (2) : without orthog option
> ivreg2 fmom y87 y88 y89 y90 y91 y92 y93 y94 y95 y96 y97 y98 y99
> y00
> y01 y02   s87 s88 s89 s90 s91 s92 s93 s94 s95 s96 s97 s98 s99 s00
> s01
> s02 (smom=dratio dfarm dfuel ), gmm;
> Hansen J statistic (overidentification test of all instruments) :
> 5.822-> Chi-sq(2) P-val=0.05442
> 
> ==> so, case(1) rejects the null but case (2) doesn't
> 
> My question is which one I have to choose as a overidentification
> test.
> Thanks,
> TaeHun Kim
> *
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> 



Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3294
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes

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