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st: RE: Test coefficients across equations


From   "Mike Hollis" <mehla@earthlink.net>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Test coefficients across equations
Date   Fri, 27 Jun 2003 07:53:58 -0700

On option I suggested to Borsant was that he consider using software that
includes routines explicitly for multiple group analysis.  Lisrel, Amos and
Mplus (included in the software links on Stata's home page) are among the
possibilities.  The features in these full information ML estimators include
the ability to explicitly estimate and test for a variant of coefficient
constraints within and between groups.  Correlations for residuals between
equations (i.e., groups) can also be estimated, as with Zellner's method.

The new piece of information provided by Borsant that causes me to now
question the appropriateness of the multi-group strategy is his statement
that groups may have transitioned from one to another over time.  Allowing
the simple correlation of error terms, as in Zellner's method, is unlikely
to be an adequate strategy for handling the effects of this type of
non-independence.  At this point, he may need to consider multi-group
hierarchical modeling (features that software like Mplus and Amos) with the
higher-order effects essentially accounting for the transition of firms from
one group to the next.

I've been out of the field for some time, but there was some work involving
growth models and the analysis of change that might be helpful in this area.
Most of that work was being done in the area of cognitive development and
testing.  You might take a look through this literature -- or check Bengt
Muthen's web page at ULCA (Muthen developed Mplus) -- for possible leads.
Another possibility would be to ask this questions of the people involved
with structural or hierarchical modeling since they seem to have done the
most work in the area of multiple group analysis.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Bersant
Hobdari
Sent: Friday, June 27, 2003 2:52 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: Test coefficients across equations


Hi Everyone,

Many thanks to Scott Merryman, David Moore and Mike
Hollis for their comments on my original message. I
however have still some doubts regarding the way I
should follow. I will explain it in more detail taking also into
account comments of Scott, David and Mike.

I am estimating the same specification on different
samples and want to test coefficients equality across the
samples. The main gist of Scott, Davis and Mike
argument was that I introduce ownership dummies and
respective interactions in the pooled sample and then
apply Chow type tests on individual equations. This
however, as they themselves stress, needs sub-samples
to be independent.

I have serious doubts that my sub-samples are
independent. More specifically, I divide the big sample into
smaller ones based on majority ownership. Given that
ownership changes over time a given firm might be
present at different sub-samples over time. I assume this
is enough to state that sub-samples are not independent.
The reason for sample separation is the endogeneity of
ownership structures to the left hand side variable, labor
productivity in this case. If I ignore this problem I will be in
a bigger problem that the one I am trying to solve.

Given non-independence then what is the way to test
coefficient equality across equations. One suggestion
would be to use Zellner's SUR method, suggested by
Scott. To my knowledge however SUR estimates equation
by equation OLS
accounting for cross equation correlation. I however have
used GMM (through ivreg2 procedure) to obtain
estimates. Can SUR be used with GMM?

The big question then becomes: how do I test  coefficients
equality across equations estimated on different samples
when samples are not independent?

Any help is highly appreciated.
Sincerely,
Bersant Hobdari
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