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Re: st: Heteroskedastic robust version of endogeneity test


From   Tae Hun Kim <thkim91@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Heteroskedastic robust version of endogeneity test
Date   Tue, 1 Mar 2005 11:10:19 -0600

Thank you very much for the help.

As you suggested, I updated -ivreg2- and got two J
statistics(constrained and unconstrained)
The result is 
Hansen J statistic (constrained) : 27.609-> Chi-sq(2) P-val=0.0000
Hansen J statistic (unconstrained) : 6.618-> Chi-sq(1) P-val=0.01009
C statistic : 20.990-> Chi-sq(1) P-val=0.0000
==> so, I concluded instruments aren't orthgonal

But I changed the set of excluded instruments and estimated it again
The result is 
Hansen J statistic (constrained) : 30.141-> Chi-sq(2) P-val=0.0000
Hansen J statistic (unconstrained) : 1.279-> Chi-sq(1) P-val=0.25816
C statistic : 28.862-> Chi-sq(1) P-val=0.0000
==> so, it indicates that instruments are orthgonal to the error term
and 'smom' variable is endogenous.

Could you confirm whether my interpretation is right or not?
 
Thanks,
T.H Kim




On Mon, 28 Feb 2005 23:44:21 +0000 (GMT), Mark Schaffer
<M.E.Schaffer@hw.ac.uk> wrote:
> Tae Hun,
> 
> Quoting Tae Hun Kim <thkim91@gmail.com>:
> 
> > Hello Statalist.
> > I would appreciate some help on the following problem.
> > I want to conduct heteroskedastic robust endogeneity test. Most
> > previous postings related to endogeneity test assume conditional
> > homoskedasticity. As long as I know, if error term is
> > heteroskedastic,
> > p-value is wrong. so, we might obtain wrong conclusion.
> >
> > To test endogeneity (heteroskedastic robust version)
> > --------- equation----
> > . 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 ( = dgovern dratio ), gmm orthog(smom);
> > **Smom : suspected engogenous variable
> > ----test result---------
> > Hansen J statistic (Lagrange mulitplier test of excluded
> > instruments):
> > 27.609
> >                                   Chi-sq(2) P-val =   0.00000
> > C statistic (exogeneity/orthogonality of specified instruments):
> >
> >  20.990
> >                                  Chi-sq(1) P-val =   0.00000
> > Instruments tested: smom
> > ------------------------------------------------------------------------------
> > Instruments:   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 dgovern dratio
> > ------------------------------------------------------------------------------
> >
> > I think the result says 'smom' is endogenous(C-ststistic:20.990) and
> > two excluded instruments are not orthogonal to the error term(Hansen J
> > statistic :27.609)
> > Q1. My code and My interpretation are right?
> 
> Mostly yes.  I think you should update your version of -ivreg2-, because the
> latest version will display the J statistics for both the constrained (smom
> exogenous) and unconstrained (smom endogenous) specifications.  You'll
> probably find that both have J statistics that suggest that the
> orthogonality conditions aren't met (one will be 27.609 and the other will
> be about 7).  This implies that the C-statistic doesn't mean much, because
> you are comparing two misspecified equations.  But see below.
> 
> > But I just tried to test overidentification as the following
> > equation
> > 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=dgovern dratio), gmm;
> > ----------test result------------
> > Hansen J statistic (overidentification test of all instruments):
> >
> >   3.633
> >                          Chi-sq(1) P-val =   0.05665
> > ------------------------------------------------------------------------------
> > Instrumented: smom
> > Instruments:   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   dgovern dratio
> > ------------------------------------------------------------------------------
> >
> > the result indicates that instruments are orthogonal under 5%
> > significance level
> >
> > Q2 : why two results are different? Did i miss something?
> 
> This one is equivalent to the unconstrained version mentioned above (smom
> endogenous).  The difference is, I think, because the first version uses an
> estimate of the covariance matrix of orthogonality conditions that
> guarantees a positive C statistic, which is different from the one used
> here.  In my experience, the difference is usually small, but yours is a bit
> larger than usual.
> 
> That said, the conclusions don't differ that much - a p-value of 6% is
> basically just as much a concern as a p-value of 5%!
> 
> Hope this helps.
> 
> Mark
> 
> > Thanks in advance,
> >
> > T.H 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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