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st: identification status of a linear simultaneous equations system


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: identification status of a linear simultaneous equations system
Date   Sun, 7 Oct 2007 12:14:09 -0400

Thomas said
Kit, thanks a lot for your reply!
Isn't the question of identification independent from the question of
whether I chose a system estimator or an equation-by-equation estimator?
When I use the option 3sls with that model,
reg3 (w tenure schooling male) (tenure w) (schooling pubsec male expft)
if welle==2000, 3sls
it's the same, Stata estimates the model and doesn't complain.
I understand that in the first equation there are 2 endogenous variables
on the right hand side (tenure and schooling), and that there are 2
exogenous variables
excluded from the first equation. But should the 2 instruments really be
used as instruments for the tenure variable in that particular model? I
am wondering, because they are explicitly excluded from the tenure
equation. And that exclusion from the tenure equation causes zeros in
the (A3, A5) matrix in Greene 2003, page 393, which make the matrix not
full rank and make the rank condition analyzed by Greene fail. If I
recall right, in Greene there is also a rule of thumb for
identification: "Each equation should have its own exogenous variable
excluded from the other equations." And this is violated for the first
and second equation in this model.
As I understand it, failing the rank condition analyzed by Greene means
that there are different sets of structural parameters consistent with
the same reduced form.
Does that mean that I should worry about whether the structural
estimates of the above model are unique? And does it imply that before
estimating a system of equations by 3sls, one should always check
identification of the model, maybe at least by Greene's rule of thumb
mentioned above?


Yes, you are absolutely right, working with a simultaneous system without checking this condition is
dangerous. The issue does not arise in limited-information (single equation) estimation, for there the
only concern is that the rank of the instrument matrix is sufficient. But in that context we don't know where
else in the system the instruments do (or do not) appear.

Stata's -reg3- should check this condition and warn the user if the condition is not satisfied. As -reg3- does not (yet) do that (perhaps StataCorp developers will consider it!) I have written -checkreg3-, which I believe is capable of determining whether the conditions laid out in Greene's and Wooldridge's examples are satisfied:

TITLE
'CHECKREG3': module to check identification status of simultaneous equations system

DESCRIPTION/AUTHOR(S)

checkreg3 checks whether the coefficients of a linear
simultaneous equations system to be estimated by reg3 are
identified.

KW: simultaneous system
KW: reg3
KW: identification

Requires: Stata version 9.2

Distribution-Date: 20071007

Author: Christopher F Baum, Boston College
Support: email baum@bc.edu


INSTALLATION FILES (type net install checkreg3)
checkreg3.ado
checkreg3.hlp
------------------------------------------------------------------------ ---------
(type -ssc install checkreg3- to install)


The routine requires Mata, thus the requirement for Stata 9.2.

Thanks to Thomas for cogently explaining this issue and citing the relevant literature.

Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


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