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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
Subject   RE: st: RE: a question on testing for random effect model against fixed effect model
Date   Thu, 27 Jul 2006 12:51:38 -0700 (PDT)

Dear Statalisters,

If the hausman test for random effect model against fixed effect model is not valid, Wooldridge 
textbook(2002, pp 290-291) suggests that one use  a regression version of test that is robust to 
heteroskadasticity and serial correlation.  But it neither mentions any rationale for doing so nor 
any references.  Is there anyone that understands the rationale for doing so and can provide 
some references on this.  I have been looking for the reference but couldn't really find one that is 
very relevant to this.  Many thanks. 

Best regards,
Jian Zhang


> Jian Zhang,
> 
> Can you post the output of -hausman- to the list?  I think I know what
> might be going on, but it's easiest to see by looking at the output.
> 
> Cheers,
> Mark
> 
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu 
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> > Rodrigo A. Alfaro
> > Sent: 19 July 2006 04:06
> > To: statalist@hsphsun2.harvard.edu
> > Subject: Re: st: RE: a question on testing for random effect 
> > model against fixed effect model
> > 
> > Is the Hayashi proof valid for unbalanced-panel?
> > R
> > 
> > ----- Original Message -----
> > From: "Jian Zhang" <jzh@ucdavis.edu>
> > To: "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>; 
> > <statalist@hsphsun2.harvard.edu>;
> <statalist@hsphsun2.harvard.edu>
> > 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: 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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