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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   Mon, 28 Feb 2005 23:44:21 +0000 (GMT)

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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