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


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: re: do 2sls, ivreg, etc. check the rank condition for identification?
Date   Tue, 9 Oct 2007 23:26:26 -0400

David Drukker said

Thomas Cornelissen <cornelissen@ewifo.uni-hannover.de> gave an example of
-reg3- estimating the parameters of a model that fails the rank condition.

Kit Baum <baum@bc.edu> and "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
commented on this topic as well. Kit privately sent me an example using the
auto dataset in which -reg3- produced estimates of the parameters of model
that fails the rank condition.

. webuse auto
. reg3 (price mpg weight displacement turn) (mpg price displacement)
(weight displacement trunk turn length)

It is unusual for the order conditions to hold and the rank conditions to
fail. In fact, both Thomas' and Kit's examples rely on introducing an
equation that is not simultaneous with the other equations to achieve this
result. See, for example, Kit's last equation.


First of all, note that this is not my contrived example, but rather a reworking of Jeff Wooldridge's Example 9.3 (Failure of the Rank Condition) from his 2002 textbook, Econometric Analysis of Cross Section and Panel Data, p. 219.

Second, David is mistaken in stating that the failure of the rank condition arises because the system is block-recursive, that is, the third equation above is actually not simultaneous. I believe that this system would still fail the rank condition if the third equation was simultaneous:


. checkreg3 (price mpg turn headroom weight trunk) (mpg price headroom) (turn price headroom trunk weight)

Endogenous coefficients matrix

price mpg turn
price 1
mpg -.5 1
turn -.5 0 1

Exogenous coefficients matrix

headroom weight trunk
price .5 .5 .5
mpg .5 0 0
turn .5 .5 .5
Equations : 3
Rank(endog): 3
Rank(exog) : 2
Rank deficiency: system is not identified

The endogenous coefficients matrix now has a coefficient on price in the turn equation, but that does not alter the exogenous coefficients matrix, which by inspection is rank-deficient. However, -reg3- will fail to run in this case, as the first equation fails the order condition.

But here is a system that does not fail the order condition:

reg3 (price mpg headroom weight trunk) (mpg price headroom length) (turn price headroom trunk weight)

executes successfully, but my calculations show that it should fail the rank condition:

checkreg3 (price mpg headroom weight trunk) (mpg price headroom length) (turn price headroom trunk weight)

Endogenous coefficients matrix

price mpg turn
price 1 -.5 0
mpg -.5 1 0
turn -.5 0 1

Exogenous coefficients matrix

headroom weight trunk length
price .5 .5 .5 0
mpg .5 0 0 .5
turn .5 .5 .5 0
Equations : 3
Rank(endog): 3
Rank(exog) : 2
Rank deficiency: system is not identified

Contrary to David's comment about -ireg3- catching this problem, reg3 converges:

. reg3 (price mpg headroom weight trunk) (mpg price headroom length) (turn price
> headroom trunk weight),ireg3

Iteration 1: tolerance = .2964587
Iteration 2: tolerance = .00593547
Iteration 3: tolerance = .00015316
Iteration 4: tolerance = 3.975e-06
Iteration 5: tolerance = 1.032e-07

...

So I think the issue is still open.

There is naturally the possibility that the logic of -checkreg3- is flawed. I welcome any independent evaluation of its logic versus the exposition of this issue in Wooldridge and Greene, as cited in help checkreg3.

Kit

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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