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st: RE: Robust Hausman test

From   "Schaffer, Mark E" <>
To   <>
Subject   st: RE: Robust Hausman test
Date   Wed, 9 Nov 2011 12:56:28 -0000


A few misunderstandings here... 

> -----Original Message-----
> From: 
> [] On Behalf Of 
> Veronica Veleanu
> Sent: 02 November 2011 17:43
> To:
> Subject: st: Robust Hausman test
> > Dear Statalist,
> >
> > I am writing with a query related to an older post from 
> 2011-07 archive.
> >
> >
> > I understand that the robust version of the Hausman test 
> (Wooldridge 2002) compares FE versus pooled OLS, while 
> xtoverid compares FE versus RE.

No, that's not right.  The robust version of the Hausman test proposed
by Arellano (not Wooldridge - see the xtoverid help file for the
references) is what xtoverid implements.  The standard interpretation is
FE vs. RE (but if you read up on the literature, you'll find there are
other interpretations available).  Pooled OLS doesn't figure here.

> > How do you suggest comparing FE versus RE when the model is 
> fitted in the following ways:
> > -Pooled OLS:with newey2 or xtscc
> > -FE:with xi: newey2 i.panelid lag(#) force or xtscc , fe lag(#) 
> > -RE:with xtreg, re cluster(panelid) [as there is no other 
> way to fit newey = or xtscc with RE]

There is a confusion here between the estimation of the coeffs and the
estimation of the var-cov matrix.

When you say the model is "fitted" using FE, for example, it means you
are "fitting" a line to the data, i.e., you are estimating coefficients.
You get the same FE coeffs whether you specify kernel-robust SEs (e.g.,
Newey-West), or cluster-robust SEs, or Driscoll-Kraay SEs (xtscc), or

You want to compare the FE and RE estimates (not pooled OLS) and have
the comparison - the Hausman test - be robust to various violations of
the assumptions about the disturbances.  This is where the VCE comes in,
and why you might want to use cluster-robust, or Newey-West, or
Driscoll-Kraay, or whatever, when constructing the test statistic.

This is what Arellano did - he showed how to construct the test
statistic for FE vs RE using an artificial regression, and in such a way
that it is cluster-robust, i.e., robust to arbitrary within-group serial
correlation.  The way this is done is to estimate an artificial
regression and then use Stata's -test-.

> >
> >
> > So I can compare FE versus pooled OLS in this manner:

No - see above.

> >
> > * Robust version of the Hausman test (Wooldridge 2002) 
> quietly xtreg y x1 x2 x3 x4, re by id: gen T=3D_N gen 
> theta=3D1-sqrt(e(sigma_e)^2/(e(sigma_e)^2+ T*e(sigma_u)^2)) 
> foreach x in y x1 x2 x3 x4 { by id: egen mean`x' =3D 
> mean(`x') generate md`x' =3D `x' - mean`x'
> > generate red`x' =3D `x' - theta*mean`x'
> > }
> > quietly xtscc  redy  redx1 redx2 redx3 redx4  mdx1 mdx2 mdx3 mdx4, 
> > lag(#) test mdx1 mdx2 mdx3 mdx4
> >
> > But I can only compare FE versus RE by using xtoverid which 
> assumes the FE  model is fitted only with clustered standard 
> errors (not taking account forcross-sectional dependence or 
> MA(h) lag in residuals) so the inference fro= m xtoverid 
> would not be completely correct, right?

That's true.  But see Daniel Hoechle's Stata Journal paper (2007, vol. 7
no. 3) on Driscoll-Kraay SEs as implemented in xtscc.  He has a section
on how to extend the Arellano approach to this case.


> > Lastly, related to the older post in the archive I 
> mentioned earlier, given that these 2 tests test different 
> things, how can you finally decide betwe= en Pooled, FE or 
> RE? Should one just use all of them?
> >
> >
> > Thanks very much in advance!
> >
> >
> > Veronica
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