st: How does xtreg calculate clustered standard error?

[Ting JIANG <econjiang@gmail.com>]

Dear all,

I'm using Stata 13. When I try the following two lines,

reg y x i.id, cluster(id)

xtreg y x, fe robust

I noticed that they give the same coefficient estimates as expected,
but the clustered standard errors are different.

I checked that when doing OLS with reg, Stata has a multiplier (finite
sample adjustment) for clustered variance G/(G-1) *(n-1)/(n-k), where
G is the number of clusters.

but when I manually calculate clustered std err for the fixed-effect
model, the results do not match those reported after doing xtreg.

So my questions are:

(1) Does Stata make finite sample adjustment in the ``xtreg +
cluster'' case? How?

(2) Can I expect reg and xtreg to give exactly the same answer, when
properly specified?

By the way, I noticed that the t-statistic produced after xtreg with
cluster option does not follow Stock & Watson's (ECMA, 2008)
suggestion -- multiply the traditional t-statistic by sqrt(n/(n-1)),
where n is the number of entities.

(3) Am I correct that Stata does not adjust t-statistic in the
``xtreg+cluster''case?

Thanks.

Ting JIANG
Beijing, China
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