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

 From Hanley Chiang To statalist@hsphsun2.harvard.edu Subject st: xtreg, fe and cluster-robust standard errors Date Tue, 13 May 2008 16:57:44 -0400

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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