RE: st: Fixed Effects GLS

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Andrea,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Andrea Morescalchi
> Sent: Tuesday, April 12, 2011 9:57 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Fixed Effects GLS
> 
> Dear Ada and Maysa,
> I was trying too to estimate the FEGLS as presented in 
> Wooldridge (2002), but with only one error component.
> 
> Anyway, I cannot understand properly the first line of 
> Ada's response: "Fixed Effects model is a kind of GLS 
> model. Use the basic FE commands and you will be fine."
> I red carefully the Chapter 10 in Wooldridge, but I cannot 
> see among the - xtreg, FE - options available which is 
> that for doing FEGLS. In particular, the options available 
> for vce are: conventional, robust, cluster, bootstrap, or 
> jackknife.
> FEGLS implies a particular structure for the (T-1)*(T-1) 
> covariance matrix for the errors, i.e. the matrix is 
> estimated after a standard FE in the first step where this 
> matrix is an identity matrix multiplicated for the 
> T-constant variance parameter.
> Among FE Stata options the most proper to do FEGLS would 
> seem: "vce(conventional), the default, uses the 
> conventionally derived variance estimator for generalized 
> least squares regression". This line is a bit strange to 
> me since it seems to imply that the standard FE Stata 
> regression is actually a FEGLS!

It is indeed, and not just in Stata.  The FE estimator is, by
definition, a GLS estimator.

I am sure this is discussed in Jeff Wooldridge's book somewhere (there's
a 2010 edition out, by the way), but I don't have it handy and can't
direct you to the right chapter/page.  Another place you might look is
Arellano's 2003 book, "Panel Data Econometrics".  In chapter 2 (I think)
he shows that the FE estimator is the GLS estimator obtained after
applying the first-differencing transformation.

--Mark

> I computed the FE and the 
> FEGLS separately in Matlab and it turns out that the 
> "conventional" Stata FE is identical to that with error 
> v-c matrix equal to an identity matrix (multiplicated for 
> sigma_u). But which is the option which tells Stata to 
> estimate the v-c matrix in the first step?
> 
> Thanks in advance
> Andrea
> 
> On Tue, 12 Apr 2011 00:09:11 +0000
>   "Ada Ma" <heu034@googlemail.com> wrote:
> >Fixed Effects model is a kind of GLS model. Use the basic 
> >FE commands and you will be fine. 
> > 
> > There are user written commands for two way FEs but I 
> >can't remember the commands' names, sorry! There are two 
> >of them and they r both featured in the Stata Journal, 
> >one of the authors for one command is Upward. HTH.
> > 
> > 
> > Sent using BlackBerry(r)
> > 
> > -----Original Message-----
> >From: May Ster <mayfrank@gmail.com>
> > Sender: owner-statalist@hsphsun2.harvard.edu
> > Date: Mon, 11 Apr 2011 23:10:06 
> > To: <statalist@hsphsun2.harvard.edu>
> > Reply-To: statalist@hsphsun2.harvard.eduSubject: st: 
> >Fixed Effects GLS
> > 
> > Dear Statalist,
> > 
> > I tried reading Woolridge (2002), Chapter 10 after he 
> >mentioned
> > choosing between Random effects model and Fixed effects 
> >model, he does
> > mentioned 'Fixed Effects GLS".
> > 
> > I'm not sure how does this apply to STATA command if i 
> >want to use
> > 'Fixed Effects GLS".
> > 
> > If my model is a two-way fixed effects model, Basically, 
> >is the 'Fixed
> > Effects GLS" can be written like this (i've checked for 
> >serial
> > correlation in error terms) ;
> > 
> > xi: xtgls var1 var2 var3 i.year , panel(hetero) 
> >corr(psar1)
> > 
> > 
> > Please help.
> > 
> > Thank you very much in advance
> > 
> > Maysa
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