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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   Wed, 11 Jul 2007 10:26:31 -0700 (PDT)

I don't think so.  I think you need to use 2sls or 3sls for such
situations, or perhaps some other models.

HTH
Sam

On Wed, 11 Jul 2007, Mak, Timothy wrote:

> 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
>
> > 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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