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st: Re: xtreg, fe and cluster-robust standard errors


From   Hanley Chiang <hchiang@fas.harvard.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: xtreg, fe and cluster-robust standard errors
Date   Wed, 14 May 2008 14:45:01 -0400

Thanks, Clive. After some trial and error, it turns out that the cluster-robust covariance matrix in xtreg, fe is:

{[(N-1)/(N-k-1)][M/(M-1)]}V

where V is the asymptotic cluster-robust covariance matrix from xtivreg2. I assume that xtreg is making a degrees-of-freedom adjustment for (k+1) regressors rather than k regressors because xtreg also estimates an intercept.

Best,
Hanley

Clive Nicholas wrote:

Kit Baum's answer to Garrett Glasgow's poser in July 2004 might be
of help here:
http://www.stata.com/statalist/archive/2004-07/msg00616.html Also,
have a look at Mark Schaffer's contribution to the thread, as well.
If none of this helps, I can't assist any further. -- Clive Nicholas


Hanley Chiang wrote:


Dear all,

Does anyone know the exact degrees of freedom adjustment for obtaining the clustered standard errors in the command
xtreg y x, i(id) fe cluster(id)?
This issue has been discussed previously (see http://www.stata.com/statalist/archive/2006-12/msg00867.html), but I don’t think the exact adjustment was ever specified.

More precisely, let V be the cluster-robust estimator for the asymptotic variance-covariance matrix of the fixed effects estimator. V is specified in Wooldridge (2002, p.275). The command
xtivreg2 y x, i(id) fe cluster(id)
gives a variance-covariance matrix equal to V. The command
xtivreg2 y x, small i(id) fe cluster(id)
gives a variance-covariance matrix equal to {[(N-1)/(N-k)][M/(M-1)]}V where N is the sample size, k is the number of regressors (excluding the fixed effects), and M is the number of clusters. Finally, the command
areg y x, absorb(id) cluster(id)
gives a variance-covariance matrix equal to {[(N-1)/(N-G-k)][M/(M-1)]}V where G is the number of fixed effects. (In my case, G=M.)

However, in Stata version 10.0, the clustered standard errors in xtreg, fe are equal to none of the above. Does anyone know the adjustment factor that multiplies V?

Thanks,
Hanley Chiang

References

Wooldridge, Jeffrey (2002). Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press.

--
Hanley S. Chiang
Ph.D. Candidate
Harvard University Economics Dept.
Littauer Center
Cambridge, MA 02138
Phone: (617) 613-1251
http://www.people.fas.harvard.edu/~hchiang

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