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st: Fwd: rank condition in a simultaneous equations system


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Fwd: rank condition in a simultaneous equations system
Date   Fri, 12 Oct 2007 10:53:15 -0400

After an off-list discussion, we have reached a few conclusions that we want
to share with the list.

The iterated feasible generalized least squares (IFGLS) procedure used when
the -ireg3- option is specified to the -reg3- command will not converge when
the model does not satisfy the rank condition. So, specifying -ireg3-
checks the rank condition.

The IFGLS procedure can fail to converge for reasons besides a failure of
the rank condition. If the procedure does not converge, it might not be due
to a failure of the rank condition.

Models that pass the order condition and fail the rank condition have
special structures. For instance, the model defined by

. reg3 (price mpg weight displacement turn) (mpg price displacement)
(weight displacement trunk turn length)

adapted from Wooldridge (2002), passes the order condition and fails the
rank condition because the the third equation has no endogenous variables on
the left-hand side. When one equation is a linear combination of other
equations is another special structure that causes the rank condition to
fail when the model passes the order condition.

--Kit --David
baum@bc.edu ddrukker@stata.com


References
----------

J. M. Wooldridge. 2002. "Econometric Analysis of Cross Section and Panel Data".
Cambridge:The MIT Press.


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