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Re: st: Cross-Sectional Time Series


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   anirban basu <abasu@midway.uchicago.edu>, statalist@hsphsun2.harvard.edu
Subject   Re: st: Cross-Sectional Time Series
Date   Tue, 25 Jun 2002 22:34:12 +0100 (BST)

Anirban,

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

> 
> 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.

Not quite sure what you mean, so apologies if I'm off target.  The 
coefficient estimates with -regress- won't be the same as with
-xtreg, fe- (unless the former is estimating the same model by 
explicitly including the fixed effects as dummy vars).  Both sets of 
coefficients will be different again from those produced by
-xtreg, re-.

--Mark

> 
> 
> 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

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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