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RE: st: Clustered standard errors in -xtreg-


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Clustered standard errors in -xtreg-
Date   Thu, 28 Dec 2006 13:55:02 -0000

Thomas,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Thomas Cornelißen
> Sent: 28 December 2006 12:29
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Clustered standard errors in -xtreg-
> 
> > Thomas Cornelissen wrote:
> 
> 
> > >> I am comparing two different ways of estimating a linear 
> > >> fixed-effects
> > >> model:
> > >>
> > >> Method 1: Use -regress- and include dummy variables for the panels.
> > >> Method 2: Use -xtreg, fe-.
> > >>
> > >> These two deliver exactly the same estimates of coefficients and 
> > >> their standard errors (if I do not cluster the standard errors).
> > >>
> > >> However, if I use the option -cluster- in order to get clustered 
> > >> standard errors (clustered on the panel ID), I get different 
> > >> results with the two ways of estimating the model.
> > >>
> > >> Why is this ?

<snip>

> Is there a rationale for not counting the absorbed regressors 
> when standard errors are clustered ?
> 
> Haven't degrees of freedom been used for absorbing the 
> variables and therefore the absorbed regressors should always 
> be counted as well?

The short answer to your first question is "yes" - you don't have to include the number of absorbed regressors in a degrees of freedom adjustment for the cluster-robust covariance estimator.  The slightly longer answer is to appeal to authority, e.g., Wooldridge's 2002 textbook.  The cluster-robust covariance estimator is given in eqn. 10.59 on p. 275, and you will see there is no dof adjustment.  The standard covariance estimator is discussed on pp. 271-2, and the dof adjustment is given explicit attention.

This is why the more recent versions of Stata's official -xtreg- have the -nonest- and -dfadj- options for fixed effects estimation.

-nonest- relates to nesting panels within clusters; the cluster-robust cov estimator doesn't require a dof adjustment but only if panels are nested within clusters.  If panels are not nested within clusters, then some kind of dof adjustment is needed.

-dfadj- will impose the full dof adjustment on the cluster-robust cov estimator.  If panels are nested within clusters, then you would never need to use this.  But since some kind of dof adjustment is needed if panels are not nested within clusters, you can use this option to go all the way and impose the full dof adjustment.

Cheers,
Mark

Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes

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