No, by definition the off-diagonal elements in the covariance matrix for an OLS
are 0. Thus, OLS is a special case of a GLS. You can see this if you write out
the formulae for an OLS solution and GLS solution.
The typical solution for the standard errors in an OLS are (X'X)^{-1}*s^2. This
is the same as (X'V^{-1}X)^{-1} when V= s^2*I, I being the identity matrix,
which is also the gls solution. But in the gls solution the off diagonal
elements of V are covariances, not 0. In the case of autocorrelation (AR1) the
off-diagonal elements decay exponentially over time.
I'm not familiar with Beck and Katz or why they would recommend that OLS be
used when the number of time units is smaller than the number of individuals in
the data. But to me, this seems rather silly, isn't this often the case?
HTH
Harold
-----Original Message-----
From: David Hugh-Jones [mailto:[EMAIL PROTECTED]
Sent: Fri 2/11/2005 5:23 AM
To: Doran, Harold
Cc: [EMAIL PROTECTED]
Subject: Re: [R] correcting for autocorrelation in models with panel
data?
Another question - is there a way to use autocorrelation with OLS,
rather than GLS?
I am really blindly following Beck and Katz (1995) here, and they
recommend OLS rather than "Feasible Generalized Least Squares" for
panel data where the number of individuals is larger than the number
of time units, which is my case.
Cheers
David
> On Thu, 10 Feb 2005 12:36:32 -0500, Doran, Harold <[EMAIL PROTECTED]>
wrote:
> > In the nlme package you can find the gls() function to account for
> > autocorrelation over time using corAR1. Syntax might look something
like
> > this:
> >
> > fm1 <- gls(response ~ IV, long, correlation=corAR1(form=~1|ID),
> > method='ML')
> >
> > You can also use weights() for heteroscedasticity.
> >
> > -Harold
> >
> > -----Original Message-----
> > From: [EMAIL PROTECTED]
> > [mailto:[EMAIL PROTECTED] On Behalf Of David Hugh-Jones
> > Sent: Thursday, February 10, 2005 12:15 PM
> > To: [email protected]
> > Subject: [R] correcting for autocorrelation in models with panel
data?
> >
> > Hi
> >
> > I have some panel data for the 50 US states over about 25 years,
and I
> > would like to test a simple model via OLS, using this data. I know
how
> > to run OLS in R, and I think I can see how to create Panel
Corrected
> > Standard Errors using
> >
> > http://jackman.stanford.edu/classes/350C/pcse.r
> >
> > What I can't figure out is how to correct for autocorrelation over
time.
> > I have found a lot of R stuff on time series models but they all
seem
> > focused on predicting a single variable from its previous values.
> > Can anyone explain to me how to detect and get round
autocorrelation?
> > Is there a package for panel data that I have missed?
> >
> > I appreciate that this is probably just as much about my ignorance
of
> > econometrics as about R itself!
> >
> > Cheers
> > David
> >
> > ______________________________________________
> > [email protected] mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide!
> > http://www.R-project.org/posting-guide.html
> >
> >
>
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