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st: RE: RE: Negative Hausman value?


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   "Pavlos C. Symeou" <p.symeou@jbs.cam.ac.uk>, <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: Negative Hausman value?
Date   Tue, 17 Oct 2006 07:49:41 +0100

Pavlos,

> -----Original Message-----
> From: Pavlos C. Symeou [mailto:ps414@hermes.cam.ac.uk] On 
> Behalf Of Pavlos C. Symeou
> Sent: 16 October 2006 21:35
> To: statalist@hsphsun2.harvard.edu
> Cc: Schaffer, Mark E; gsanchez@stata.com
> Subject: RE: RE: Negative Hausman value?
> 
> Dear Mark and Gustavo,
> 
> Thank you for your advice. Your recommendations have actually 
> helped me generate positive results which culminated in 
> rejecting the Ho for the Hausman test. Yet, the two 
> respective options sigmamore and sigmaless, produced 
> different results; namely, Sigmaless produced:
> chi2(46) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 794.29
> Prob>chi2 =      0.0000
> 
> and
> 
> sigmamore produced:
> chi2(46) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 678.25
> Prob>chi2 =      0.0000
> 
> I therefore have two questions:
> 
> 1) Which result should I include in my analysis?

Both estimates of the error variance are consistent under the null, so
either H stat is reportable.  I think -sigmamore- is more traditional
but it doesn't matter.  Of course, in your case both H stats are
enormous and it doesn't matter which you report.

> 2) Shouldn't they have different Df since the two options are 
> based on different covariance matrices?

No.  It is not the vcv that is different, it is the estimate of sigma,
the error variance.  Under the null, both the sigma from the RE
estimation and the sigma from the FE estimation are consistent.  The
formula for the vcv uses sigma.  For example, in a RE estimation you
automatically use the RE sigma in the vcv.  But there is nothing
stopping you from replacing it with the FE sigma and getting a slightly
different, but also consistent, vcv.  Have a look at
Baum-Schaffer-Stillman 2003 (Stata Journal, also Boston College working
paper).

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


> 
> Yours truly,
> 
> Pavlos
> 
> 
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Gustavo Sanchez
> Sent: Monday, October 16, 2006 8:37 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: Negative Hausman value?
> 
> Pavlos C. Symeou [p.symeou@jbs.cam.ac.uk] asked about the 
> Hausman test produced by -hausman-,
> 
> 
> > I attempt to compare between FE and RE transformations in 
> Stata using 
> > the hausman command, yet the chi^2 for the test is negative 
> (how can a 
> > square
> be
> > negative?).
> 
> 
> Mark Schaffer [M.E.Schaffer@hw.ac.uk] diagnosed the problem when he
> explained:
> 
> > This can happen in finite samples, unless the same estimate of the 
> > error variance is used throughout the H statistic - see, 
> e.g., Baum et al.
> > (2003) in the Stata Journal or the Boston College working 
> paper version.
> 
> > This can generally be handled in Stata with the -sigmamore- or
> > -sigmaless- options to the -hausman- command.  What I am 
> not sure of 
> > is whether -xtreg- stores the right sigma internally in the right 
> > place where -hausman- can make use of it.  I have a vague 
> memory that 
> > in earlier version of Stata, -xtreg- did not store sigma in 
> a way that 
> > was compatible with this option, but maybe that's been fixed.  You 
> > need to check.
> 
> Those two options (sigmamore and sigmaless) are actually 
> supported by the
> -hausman- command after fitting the model with -xtreg-. They 
> were part of the features incorporated in Stata 9.1
> 
> -- Gustavo
>    gsanchez@stata.com
> 
> 
> 
> 
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