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Re: st: What is seemingly unrelated regression?


From   SamL <saml@demog.berkeley.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: What is seemingly unrelated regression?
Date   Tue, 10 Jul 2007 07:28:56 -0700 (PDT)

This is my favorite model.  SUR is a multi-equation model.  If you have
more than one y y's (y1 and y2, say), you could run multiple regressions:

y1=f(X+Z)+e_1
y2=g(X+Q)+e_2

If Z and Q differ, it is asymptotically more efficient to estimate the
equations jointly.  If Z and Q do not differ, it is not more efficient to
estimate the equations jointly, but it can still be advantageous to do so
because joint estimation allows an appropriate test of coefficients across
equations.

I do not have my econometrics textbooks here (I am traveling) but I
believe this model is discussed in the usual suspect textbooks (e.g.,
Maddala, Goldberger, Judge et. al.)  The Zellner citation is:

Zellner, A.  1962.  "An Efficient Method of Estimating Seemingly Unrelated
Regressions and Tests for Aggregation Bias."  Journal of the American
Statistical Association.  57: 348-368

HTH
Sam

On Tue, 10 Jul 2007, Mak, Timothy wrote:

> 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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