Johannes, thank you again for another very cogent explanation of
clustering, which I looked up on the archive for today. Your description
of the state of the art of modern econometricians is very helpful for a
political scientist.
And let me apologize for posting the same question to the list twice. I
stopped receiving Statalist emails this morning for some unresolved
reason, but remain free to post.
Jason Webb Yackee, PhD Candidate; J.D.
Fellow, Gould School of Law
University of Southern California
jyackee@law.usc.edu
Cell: 919-358-3040
Let's discuss this with an example: suppose you want to measure the
effect of union status on wages and you have a panel of workers that
you observe over time. There are (at least) two concerns with just
using OLS on the whole sample: you think that there are omitted
variables in your regression such as unobserved ability. If ability is
correlated with union status and wages then the coefficient on union
status will be biased. Note that this is not a problem of error terms
not being independent from each other, but of error terms being
correlated with one of your right hand side variables. If ability is
constant over time for an individual, then including individual fixed
effects will solve the problem, as this indirectly controls for
ability. Clustering can never solve this problem. In fact clustering
doesn't affect your coefficient estimates only the standard errors, so
obviously it cannot deal with omitted variable "bias", as this shifts
the estimates. The other problem that when you observe individuals
over time there is no reason why the error term should not be
correlated over time for this individual. This means that you have in
fact less independent observations and thus less information.
Clustering will adjust your standard errors for this problem. Since it
takes account of the fact that there is less information than if the
errors where all independent, standard errors nearly always go up.
There are other methods of course, such as FGLS. Fixed effects can
also deal with correlated error terms but it is pretty restrictive
(e.g. it allows only a positive uniform correlation among the errors
in one "cluster"), so usually the reason for FE is the stated omitted
variable bias, not correlation of error terms with each other.
I would say that in applied microeconometricians it is very much
standard today to always cluster your standard error on the same level
on which you would use fixed effects. Of course if you use several
fixed effects (e.g. in an education framework you might have grade,
school and year fixed effects) you have to put some thinking into the
question on which level it is best to cluster. Generally it is not
only fine to use FE and cluster together, I would go as far as saying
that not doing it is a bit fishy. I think this trend in economics is
only a couple of years old when a paper by duflo, bertrand and
mullainathan pointed out the severity of this problem. Maybe in other
disciplines this is not (yet) standard.
best, Johannes
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