Is the Hayashi proof valid for unbalanced-panel?
R
----- Original Message -----
From: "Jian Zhang" <[email protected]>
To: "Schaffer, Mark E" <[email protected]>;
<[email protected]>; <[email protected]>
Sent: Monday, July 17, 2006 8:44 PM
Subject: RE: st: RE: a question on testing for random effect model against
fixed effect model
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: [email protected]
> > [mailto:[email protected]] On Behalf Of Jian Zhang
> > Sent: 16 July 2006 08:36
> > To: [email protected]
> > 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: [email protected]
> 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" <[email protected]>
> > > To: <[email protected]>
> > > 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: [email protected]
> > > 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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