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

[Thomas Cornelissen <cornelissen@ewifo.uni-hannover.de>]

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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