st: Fwd: rank condition in a simultaneous equations system

[Kit Baum <baum@bc.edu>]

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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