Tae Hun,
Quoting Tae Hun Kim <[email protected]>:
> 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: [email protected]
web: http://www.sml.hw.ac.uk/ecomes
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