# RE: st: What is seemingly unrelated regression?

 From SamL To Stata Listserve Subject RE: st: What is seemingly unrelated regression? Date Tue, 10 Jul 2007 09:00:43 -0700 (PDT)

```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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```