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

[Kit Baum <baum@bc.edu>]

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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