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Re: st: Cross-Sectional Time Series


From   anirban basu <abasu@midway.uchicago.edu>
To   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
Subject   Re: st: Cross-Sectional Time Series
Date   Tue, 25 Jun 2002 14:35:47 -0500 (CDT)

Hi Mark,

Thanks for the clarifications. I knew that the cluster option does the
Huber-White correction for the standard errors but realized that the
empirical var-cov estimate used by this command is different from the
parameterized exchageable corr model. 
However, the coefficient estimates with regress are the same as the xtreg,
fe or xtreg, re command which assumes an exchangeable correlation. I
think, and please fell free to correct me, these will be different if we
use a different correlation structure model.


Anirban

______________________________________
ANIRBAN BASU
Doctoral Student
Harris School of Public Policy Studies
University of Chicago
(312) 563 0907 (H)
________________________________________________________________


On Tue, 25 Jun 2002, Mark Schaffer wrote:

> 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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