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RE: st: What is seemingly unrelated regression?


From   "Mak, Timothy" <Timothy.Mak@iop.kcl.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: What is seemingly unrelated regression?
Date   Tue, 10 Jul 2007 16:15:06 +0100

Dear Sam, 

I'm not sure I understand your notation. Supposedly X is an independent
variable that is shared between the equations, whereas Z and Q are
variables that are not shared. So do you imply that SUR is only useful
when at least one independent variable is shared across equations? 

In any case, the question why using SUR produces markedly biased
estimates in my simple illustration still begs an answer. 

Thanks for your help. 

Tim 

 

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of SamL
Sent: 10 July 2007 15:29
To: statalist@hsphsun2.harvard.edu
Cc: SamL@demog.berkeley.edu
Subject: Re: st: What is seemingly unrelated regression?

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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