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Re: st: Cross-Sectional Time Series


From   anirban basu <abasu@midway.uchicago.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Cross-Sectional Time Series
Date   Tue, 25 Jun 2002 11:52:40 -0500 (CDT)

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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