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st: What is seemingly unrelated regression?


From   "Mak, Timothy" <Timothy.Mak@iop.kcl.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: What is seemingly unrelated regression?
Date   Tue, 10 Jul 2007 14:40:44 +0100

Hi Statalist, 

Forgive me for more of a statistical question than a Stata question, but
I only recently found out about seemingly unrelated regression (SUR). I
dug up the Zellner (1962) paper, and it says that: 

	Under conditions generally encountered in practice, it is found
that the regression coefficient estimators so obtained are at least
asymptotically more efficient than those obtained by an
equation-by-equation application of least squares. 

Interesting claim - does it imply that whenever we're doing more than
one regression on the same dataset, we should be using SUR? 

Anyway, I ran a small test. First I created a 5-dimensional multivariate
normal sample of size 10000. Correlations between the 5 variables are
all 0.3. I generated y = 0.1 * (x1+ x2 + x3 + x4 + x5) + u, where x1-x5
are the variables just created, and u is an error term generated
separately by -uniform-. And I regressed y on x1, x2, x3, etc,
separately using -reg-, and together using -sureg-. As expected the
-reg- estimates were around 0.22 (=0.1 + 4 * 0.3 * 0.1 + ...). But the
-sureg- estimates were around 0.02. If these were estimates of the
relationship between y and x1, x2, etc, then these are clearly biased. I
suppose then that these estimates are not estimating the same things as
-reg- estimates. But then what are these estimating? 

Sorry if this is really elementary. I haven't studied econometrics but
would like to learn a bit more about statistics. 

Thanks, 

Tim 

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