# RE: st: What is seemingly unrelated regression?

 From "Mak, Timothy" To Subject RE: st: What is seemingly unrelated regression? Date Wed, 11 Jul 2007 17:04:23 +0100

Thanks Sam.

If you don't mind, one more question: When using SUR, can we have
variables being both independent and dependent, ie dependent in one
equation and independent in another? Ie, can we use it to fit some
simple structural equation models?

Tim

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of SamL
Sent: 10 July 2007 17:01
To: Stata Listserve
Cc: SamL@demog.berkeley.edu
Subject: RE: st: What is seemingly unrelated regression?

Responses below:

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

> 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.

Correct.

> So do you imply that SUR is only useful when at least one independent
> variable is shared across equations?
>

No.  As I said, the efficiency increase only occurs if at least one of
the variables differs across equations.  However, the ability to test
coefficients across equations remains.

Second, none of the variables need to be shared across equations.  But,
because the usual researcher finds themselves placing some of the
independent variables in two different equations, I included X in both
to indicate that was allowed.

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

I tried to clarify that SUR is not for a situation where there is only
one Y.  If I understand, your simulation produces only one Y.  Thus, the
simulation is not appropriate.

HTH
Sam

>
> 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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