st: RE: RE: RE: RE: Robust Hausman test

[Veronica Veleanu <lexvsv1@nottingham.ac.uk>]

This has cleared all my doubts now. Thank you very much!!

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Schaffer, Mark E
Sent: 09 November 2011 14:36
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: RE: RE: Robust Hausman test

Veronica, 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Veronica 
> Veleanu
> Sent: 09 November 2011 13:41
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: RE: Robust Hausman test
> 
> Dear Professor Schaffer,
> 
> Thank you very much for your reply and clarifications.
> 
> In terms of "fitting the model" I was actually referring to the 
> variance-covariance matrix - apologies for the confusion.
> 
> Regarding Daniel Hoechle's paper after he implements the Hausman test 
> robust to cross-sectional dependence with xtscc, the p-value is above 
> the 10% level and he concludes the estimates from pooled OLS should be 
> consistent. So I am not clear whether the test actually compares FE 
> versus pooled or FE versus RE.

I think he is drawing conclusions about consistency of pooled OLS, but he isn't actually estimating it.  Pooled OLS uses an inefficient combination of the same orthogonality conditions as RE, so generally if RE is consistent, pooled OLS will be as well.

The results at the bottom of p. 307 of Hoechle's paper fit the auxiliary regression using xtscc.  You'll see the variables all have _fe and _re extensions, because these are the demeaned and quasi-demeaned versions.
The test statistic is for FE vs RE.

Cheers,
Mark


> Thank you very much again for your feedback!
> 
> Regards,
> 
> Veronica
> 
> 
>  
> 
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Schaffer, 
> Mark E
> Sent: 09 November 2011 12:56
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: Robust Hausman test
> 
> Veronica,
> 
> A few misunderstandings here... 
> 
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Veronica 
> > Veleanu
> > Sent: 02 November 2011 17:43
> > To: statalist@hsphsun2.harvard.edu
> > 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 whatever.
> 
> 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.
> 
> --Mark
> 
> > > 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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