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Re: st: Cross-Sectional Time Series


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Cross-Sectional Time Series
Date   Tue, 25 Jun 2002 19:36:29 +0100 (BST)

Hi everybody.

Just a couple of clarifying details on -cluster- vs. -xtreg- and 
Anirban's response to John.

The -cluster- option for -regress- doesn't really impose a particular 
within-cluster correlation structure on the data.  If I understand it 
correctly, what -cluster- does instead is loosen the usual assumption 
of independence of observations to independence of clusters.  The 
correlation between observations within clusters can be arbitrary.  
The way this works is basically by treating all the observations in a 
cluster as a kind of "super-observation" and then applying the robust 
("sandwich") formula to these super-observations in order to 
calculate the standard errors of the coefficients produced by -
regress-.  See the manual entry for -regress-, p. 87.

The estimated coefficients (the betas) produced by -regress- are the 
same whether or not the -cluster- option is used; the only thing that 
is different is the standard errors.

With fixed effects, you _do_ impose a particular correlation 
structure, namely all the observations within a cluster share U(k) in 
Anirban's notation.  If you use -xtreg- with -fe- to estimate, Stata 
does not, however, use a first-difference estimator - it uses a fixed 
effects estimator.  In other words, it doesn't first-difference to 
get rid of the fixed effects, it uses the mean-deviation 
transformation to get rid of them.

Hope this helps.

--Mark

Quoting anirban basu <abasu@midway.uchicago.edu>:

> Hi John,
> 
> 
> With reg command and cluster option, one basically imposes an
> exchangeable
> correlation structure on the data. i.e assume corr (y(i),
> y(j)) = rho,
> where i ne j and  i,j are any two observation from the same
> cluster. Rho
> is constant for every pair of observation within a cluster.
> So, one can
> visuaize it in terms of a random effects model where :
> 
> Y(k) = Xb + U(k) + e, where k represents clusters and U(k) is
> a
> cluster-specific random effect that is common to all
> observation in that
> cluster. However, -reg- does not give estimates of this random
> effect. It
> just estimates -betas- assuming this structure.
> 
> However, this estimation is correct only if U(k) are
> uncorrelated with
> Xs. i.e. the unobserved characteristics of a cluster over time
> is
> uncorrelated with the X over time. If not then fixed effects
> is useful.
> 
> 
> With fixed effects, one evades the correlation problem by
> taking
> differences. i.e for any cluster k:
> 
> Y(ik) - Y(1k) = [X(ik) - X(1k)]b + [e(ik) - e(1k)]
> 
> Note that by taking the difference, the unobserved U(k) is
> eliminated.
> However, fixed effects assume the U(k) is fixed over time for
> any cluster
> k. i.e. the unobserved characteristics of a cluster is not
> changing over
> time. Also, since we are taking a difference, fixed effects
> model cannot
> estimate the betas for baseline covariates since they cancel
> out in the
> difference.
> 
> Hope this helps,
> 
> Anirban
> 
> 
> 
> ______________________________________
> ANIRBAN BASU
> Doctoral Student
> Harris School of Public Policy Studies
> University of Chicago
> (312) 563 0907 (H)
> ________________________________________________________________
> 
> 
> On Tue, 25 Jun 2002, John Neumann wrote:
> 
> > Hello all,
> > 
> > Since I frequently see panel data questions flying around
> the
> > list, I'm thinking that some of you can provide me with a
> > very succinct answer to the following question, and in so
> > doing clarify conceptually for me the data-related issue:
> > 
> > I have data on investment products, by year.  Not all
> > products have data in each year.  The dependent
> > variable is scaled in such a way as to make time series
> > variation in its levels of no concern.  Here's the question:
> > 
> > What is the difference between using the reg command,
> > with the robust and cluster option, vs. the xtreg command
> > fixed effects model?  The cluster variable using reg would
> > naturally be the i( ) parameter for xtreg ...
> > 
> > Thanks!
> > 
> > John Neumann
> > Boston University
> > 
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Prof. Mark Schaffer
Director, CERT
Department of Economics, School of Management
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3008
email: m.e.schaffer@hw.ac.uk
web: http://www.som.hw.ac.uk/ecomes
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