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st: RE: Do 2sls, ivreg etc. test the rank condition of identification?


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Do 2sls, ivreg etc. test the rank condition of identification?
Date   Tue, 2 Oct 2007 09:40:09 +0100

Thomas,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Thomas Cornelissen
> Sent: Tuesday, October 02, 2007 8:55 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Do 2sls, ivreg etc. test the rank condition of 
> identification?
> 
> I am wondering how Stata would react if I trid to estimate an 
> unidentified equation of a simultaneous equations model.
> 
> I tried it out, and got "Equation is not identified -- does 
> not meet order conditions".
> 
> Do -2sls-, -3sls- and -ivreg- also test the rank condition? 
> (In case the order condition is met, but not the rank 
> condition.) In any case, I imagine I wouldn't get any 
> estimation results if the model is not identified. So, at 
> least implicitly the rank condition must be checked.

The rank condition is not deterministic, like the order condition.  It's
formulated in terms of expectations - E(Z'X) has full rank - and whereas
the number of columns is observable (order condition), the true value of
this expectation is not.  Instead, you formulate a null hypothesis and
see if the data reject at some p value.  The null is that the sample
counterpart to the expectation - 1/n Z'X - is rank-deficient (has
rank=#columns minus 1), and if you can reject the null, you conclude the
rank condition is satisfied with some probability p.

The rank condition is not automatically checked by -ivreg- (Stata 9.2
and earlier).  -estat firststage- after -ivregress- (Stata 10) will
report identification statistics, but these are valid only for the
i.i.d. case and not if you are using some sort of robust vcv.  -ivreg2-
reports identification tests based on Anderson's canonical correlation
statistic (F form = Cragg-Donald statistic) in the i.i.d. case, and the
Kleibergen-Paap rk statistic for robust case.

-ivreg2- calls -ranktest- to do this, but you can use -ranktest- to do
the test by hand if, e.g., you are doing a 3sls estimation.  -help
ranktest- is perhaps worth reading - the examples show the equivalence
between tests of the rank condition and various regression formulations.

Cheers,
Mark

> Or should a separate command for that be used, such as -ranktest- ?
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