> I have panel data on 32 countries and am estimating a fixed-effects
> model with country-specific time trends. I found evidence of
> autocorrelation (using the command xtdw), so I am using areg with
> robust standard errors clustered on country. However, when I test for
> the equality of the time trends using "testparm timetrendcountry*, e",
> I get that all but one of the 31 constraints are dropped. I also
> tried using reg with country dummies and the robust standard errors
> clustered on country, but the same thing happens. Without specifying
> robust standard errors, the test for equality works as usual. Does
> anybody know what is going on?
The way -, cluster()- option works is that the varcov matrix of the
estimated coefficient consists of #clusters terms (in this case, 32). If
you are estimating more than 32 parameters (as you do in this case), it
won't be positive definite (although of course it will be non-negative
definite; it just won't be of full rank). When you are asking Stata to
test your 31 restrictions, Stata looks up at the VCE matrix and figures
out that those restrictions are exactly in the null linear subspace of the
VCE matrix, since your country-specific slopes are collinear with the
cluster identifiers, and drops them. At any rate, when you do -something,
cluster()-, you've got only 32 effective degrees of freedom to test
anything, and that anything should be varying between clusters to be
identified by the -test-.
Think of the worst case: all your observations within a cluster are
identical (or you simply have one observation per cluster). That is indeed
the worst case, but -cluster- will still give you asymptotically correct
standard errors. If you were running regression with 32 observations and
specify 32 parameters to estimate, you won't have any degrees of freedom
to test anything. When you add country dummies, you do pretty much the
same thing: everything Stata could have used to estimate the standard
errors is being absorbed by those dummies.
By the way, the meaning of the asymptotic standard errors here is that the
number of clusters goes to infinity. You trust your standard errors just
as much as you believe 32 to be infinity.
--- Stas Kolenikov
-- Ph.D. student in Statistics at UNC-Chapel Hill
- http://www.komkon.org/~tacik/ -- [email protected]
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