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Re: st: Heteroskedastic robust version of endogeneity test


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu, Tae Hun Kim <thkim91@gmail.com>
Subject   Re: st: Heteroskedastic robust version of endogeneity test
Date   Tue, 01 Mar 2005 17:15:53 +0000 (GMT)

Tae Hun,

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

> 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?

I think your interpretation is correct.

--Mark
  
> 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
> > > *
> > > *   For searches and help try:
> > > *   http://www.stata.com/support/faqs/res/findit.html
> > > *   http://www.stata.com/support/statalist/faq
> > > *   http://www.ats.ucla.edu/stat/stata/
> > >
> > 
> > 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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> > 
> > This message is subject to http://www.hw.ac.uk/disclaim.htm
> > 
> >
> -------------------------------------------------------------------
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> >
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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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