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


From   Thomas Cornelissen <cornelissen@ewifo.uni-hannover.de>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   st: re: do 2sls, ivreg etc. test the rank condition for identification
Date   Sun, 07 Oct 2007 14:37:31 +0200

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?
Thomas


Kit said:
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-.


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
----------------------------------------------------------------------
...

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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