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st: re: do 2sls, ivreg etc. test the rank condition for identification


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: re: do 2sls, ivreg etc. test the rank condition for identification
Date   Tue, 2 Oct 2007 16:40:17 -0400

Thomas said

When I asked my question I was thinking about the rank condition for identification of an equation
of a simultaneous equation model, such as the conditions stated in Wooldridge 2002 p.218 equation
9.19 or in Greene 2003, page 393, second equation. To my understanding, a violation of these can be
asserted by looking at the structure of the model, without needing a statistical test. Am I mistaken
here?

Wooldridge 2002, Example 9.3 (p. 219) states a three-equation model which meets the order condition
but not the rank condition of identification. I replicated the model structure with variables I have
available in a data set and estimated it:

. reg3 (w tenure schooling male) (tenure w) (schooling pubsec male expft), 2sls

Two-stage least-squares regression
----------------------------------------------------------------------
...

I don't have my Wooldridge handy to check out the reference, but the Greene reference is to the rank condition on a simultaneous system: one estimated with 3SLS. You have estimated each equation with 2SLS, just as if you ran ivreg/ivregress/ivreg2 on each equation. The first equation needs 2 instruments and 2 are available. It is exactly ID by the order condition and passes the rank condition as long as the two instruments are not perfectly correlated (the rank of Z must be full). The second equation is overid by order (2 inst, 1 needed) and the third equation is not simultaneous, and could be estimated by OLS given the assertions that male pubsec expft are exogenous. Thus this is a block-recursive system, with the third equation forming one block and the first two equations forming another. In any case, you can't evaluate the condition that Greene is examining by looking at the system one equation at a time, and your estimation technique is doing just that, despite employing -reg3-.

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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