Re: st: Clustered standard errors in -xtreg-

[Thomas Cornelißen<cornelissen@ewifo.uni-hannover.de>]

With regard to the count of degrees of freedom for the 
degrees of freedom adjustment in fixed effects models
estimated by -areg- or -xtreg, fe-
Thomas Cornelissen wrote:


> > 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?

Mark Schaeffer wrote:

> 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

After doing some trial estimations I have the impression that the dof 
adjustment in -areg- and -xtreg, fe- are as follows:

1. With just the robust option, there seems to be the full dof 
adjustment, including the adjustment for the absorbed regressors.

2. With the cluster option, and panels are nested within clusters, then 
adjustment seems to be for the explicit regressors only but not for the 
absorbed regressors.

3. With the cluster option and the nonest option (panels not nested 
within cluster), then adjustment seems to be the same as before, i.e. 
for the explicit
regressors only but not for the absorbed regressors.

4. With the cluster option and the dfadj option added, there is the full 
dof adjustment also with cluster.

Provided that the four points I mentioned are correct, the bottom line 
would be that
a) there is always some dof adjustment, and
b) for the clustered VCE estimator, unless the dfadj option is 
specified, adjustment is for the explicit regressors but not for the
absorbed ones, no matter whether panels are nested within clusters or not.

I think I still don't understand why one would adjust for the explicit regressors only.

As Mark mentioned, eqn. 10.59 on p. 275 in the Wooldrige 2002 textbook 
would imply no dof

adjustment. But that would mean that one should also not adjust for the explicit regressors.

Thanks a lot for any suggestions!
Best,
Thomas
--------------------------------------
Thomas Cornelissen
Institute of Empirical Economics
University of Hannover, Germany
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