Thanks, Mark! It seems that the CALCULATED standard hausman test statistic is always positive
even in FINITE samples (i.e., calculated V(b)-v(B) is positive definite) as long as one uses same
variance estimates (mathematically this is proved by Hayashi, 2000, as you mentioned:
"This appendix proves that the Avar(q_hat) in (5.2.21) is positive definite and the Hausman
statistic (5.2.22) is guaranteed to be nonnegative in any finite samples."
(Hayashi, Econometrics (2000), Appendix 5.A, pp. 346-349 and 334-335.)
So by adding option -sigmamore- or -sigmaless-, I did get a positive standard hausman test
(Chi square).
However, confusing to me is that at the end of the results of implementing hausman test in stata
there is one line saying (V(b)-V(B) is not positive definite) despite that I added option
–sigmamore- and got a positive Chi square. Any thoughts why stata said that? From what I
understand, calculated V(b)-V(B) should be ALWAYS positive definite as long as one uses option
–sigmamore- or -sigmaless-. The statement made by stata results seems to contradict the
mathematical argument made by Hayoshi.
Best regards,
Jian Zhang
> Jian,
>
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jian Zhang
> > Sent: 16 July 2006 08:36
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: a question on testing for random effect model
> > against fixed effect model
> >
> > Thanks, Clive and Rodrigo!
> >
> > I wonder if there is an alternative test for random effect
> > against fixed effect or a robust form of hausman test if the
> > assumptions made for Hausman test do not hold (one of the
> > assumptions for hausman test is the homoskedasticity and
> > uncorrelation of the idiosyncratic errors.
> > But this is often invalid.)
>
> Sorry to come in late on this, but I have three suggestions relating to
> your original question.
>
> First, in a standard (i.e., non-robust) Hausman test, you can guarantee
> a positive test statistic by using the -sigmamore- or -sigmaless-
> options; the former is more traditional. Second, including the constant
> isn't traditional in a fixed vs. random effects hausman test. Third, if
> you want to do a heteroskedastic- or cluster-robust version of the test,
> you can use the artificial regression version of the test described in
> Wooldridge's 2002 book (and I believe discussed in Statalist last year
> by Vince Wiggins, if I'm not mistaken) and use robust or cluster-robust
> standard errors in the artificial regression. The artificial regression
> version will also guarantee a positive test statistic (of course!).
>
> Cheers,
> Mark
>
> Prof. Mark Schaffer
> Director, CERT
> Department of Economics
> School of Management & Languages
> Heriot-Watt University, Edinburgh EH14 4AS
> tel +44-131-451-3494 / fax +44-131-451-3296
> email: m.e.schaffer@hw.ac.uk
> web: http://www.sml.hw.ac.uk/ecomes
>
>
> >
> > Jian
> >
> >
> > On Sat, 15 Jul 2006, Rodrigo A. Alfaro wrote:
> >
> > > Jian,
> > >
> > > Try -xtreg, re sa- instead of -xtreg, re- the additional
> > option takes
> > > care "more carefully" the unbalanced issue using Swamy-Arora method.
> > >
> > > Read Method and Formulas in the manual, for version 8:
> > > http://www.stata-press.com/manuals/stata8/xtreg.pdf and version 9:
> > > http://www.stata.com/bookstore/pdf/xtreg.pdf
> > >
> > > Rodrigo.
> > >
> > >
> > > ----- Original Message -----
> > > From: "Clive Nicholas" <Clive.Nicholas@newcastle.ac.uk>
> > > To: <statalist@hsphsun2.harvard.edu>
> > > Sent: Saturday, July 15, 2006 4:19 AM
> > > Subject: Re: st: a question on testing for random effect
> > model against
> > > fixed effect model
> > >
> > >
> > > Jian Zhang wrote:
> > >
> > > > I have a question on testing random effect model against fixed
> > > > effect model. Hope that you can help me out. Here is the question;
> > > >
> > > > I am applying random effect model and fixed effect model to an
> > > > unbanlanced panel data (use xtreg, re and xtreg, fe). To
> > test which
> > > > model is more appropriate, I run a hausman test.
> > However, the test
> > > > statistics (the chi square) is negative. This makes
> > hausman testing
> > > > impossible, since chi square cann't be negative. The reason that
> > > > hausman test doesn't work is that the model's error
> > structure does
> > > > not meet the assumptions made for the hausman test.
> > >
> > > [...]
> > >
> > > Did you run the following:
> > >
> > > xtreg ..., fe
> > >
> > > est store fixed
> > >
> > > xtreg ..., re
> > >
> > > hausman fixed ., alleqs constant
> > >
> > > If not, see if that works. Works for me every time I have to use it.
> > >
> > > CLIVE NICHOLAS |t: 0(044)7903 397793
> > > Politics |e: clive.nicholas@ncl.ac.uk
> > > Newcastle University |http://www.ncl.ac.uk/geps
> > >
> > > Whereever you go and whatever you do, just remember this. No matter
> > > how many like you, admire you, love you or adore you, the number of
> > > people turning up to your funeral will be largely
> > determined by local
> > > weather conditions.
> > >
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> > >
> > *
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> >
> >
>
> *
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>
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