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RE: st: RE: a question on testing for random effect model against fixed effect model


From   "Jian Zhang" <jzh@ucdavis.edu>
To   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>, statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   RE: st: RE: a question on testing for random effect model against fixed effect model
Date   Mon, 17 Jul 2006 17:44:53 -0700 (PDT)

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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