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st: RE: Hausman test for clustered random vs. fixed effects (again)


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Hausman test for clustered random vs. fixed effects (again)
Date   Sat, 27 Jun 2009 18:31:32 +0100

Steve,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Steven Archambault
> Sent: 27 June 2009 00:26
> To: statalist@hsphsun2.harvard.edu; austinnichols@gmail.com; 
> Alfred.Stiglbauer@oenb.at
> Subject: st: Hausman test for clustered random vs. fixed 
> effects (again)
> 
> Hi all,
> 
> I know this has been discussed before, but in STATA 10 (and 
> versions before 9 I understand) the canned procedure for 
> Hausman test when comparing FE and RE models cannot be run 
> when the data analysis uses clustering (and by default 
> corrects for robust errors in STATA 10).
> This is the error received
> 
> "hausman cannot be used with vce(robust), vce(cluster cvar), 
> or p-weighted data"
> 
> My question is whether or not the approach of using xtoverid 
> to compare FE and RE models (analyzed using the clustered and 
> by default robust approach in STATA 10) is accepted in the 
> literature. This approach produces the Sargan-Hansen stat, 
> which is typically used with analyses that have 
> instrumentalized variables and need an overidentification 
> test. For the sake of publishing I am wondering if it is 
> better just not to worry about heteroskedaticity, and avoid 
> clustering in the first place (even though heteroskedaticity 
> likely exists)? Or, alternatively one could just calculate 
> the Hausman test by hand following the clustered analyses.
> 
> Thanks for your insight.

It's very much accepted in the literature.  In the -xtoverid- help file,
see especially the paper by Arellano and the book by Hayashi.

If you suspect heteroskedasticity or clustered errors, there really is
no good reason to go with a test (classic Hausman) that is invalid in
the presence of these problems.  The GMM -xtoverid- approach is a
generalization of the Hausman test, in the following sense:

- The Hausman and GMM tests of fixed vs. random effects have the same
degrees of freedom.  This means the result cited by Hayashi (and due to
Newey, if I recall) kicks in, namely...

- Under the assumption of homoskedasticity and independent errors, the
Hausman and GMM test statistics are numerically identical.  Same test.

- When you loosen the iid assumption and allow heteroskedasticity or
dependent data, the robust GMM test is the natural generalization.

Hope this helps.

Cheers,
Mark (author of -xtoverid-)

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