Re: st: ivreg2: No validity tests if just-identified?

[Michael Hanson <mshanson@mac.com>]

On Apr 15, 2009, at 7:46 PM, Jennifer Beardsley wrote:

> Dear Stata-list,
>
> I worked quite carefully through the various options in ivreg2 and  
> ivregress for testing (a) instrument validity (orthogonality etc)  
> and (b) instrument strength (correlatedness with endogenous  
> regressors). After doing so, I seem to be arriving at the  
> conclusion that there is no way to test (a) if the model is just- 
> identified, i.e. if I have the same number of excluded instruments  
> as I have endogenous regressors). For example, the Sargan overid  
> statistic, the C-statistic, the LR IV redundancy test statistic,  
> etc. all don't get produced unless the model is overidentified. Is  
> that true?! If yes, I would need to rely on persuasion using  
> economic intuition to make my case that the instruments are valid,  
> and there are no statistical tools to use?
>
> In contrast, there do seem to be ready statistics I can draw on to  
> examine instrument weakness/strength.
>
> Thanks for any response,
> Jennifer

Jennifer:

The short answer to your question is "yes", as most the tests you  
reference are tests of over-identifying restrictions.  Think of it  
this way:  you cannot test assumptions required to just identify a  
model, as -- by definition -- these assumptions are necessary in  
order to merely proceed with estimation.  But, if you have more  
instruments than you need to just identify a model, you *can* test  
certain properties given the "extra" (I'm speaking loosely here)  
instruments.  That's what many of the tests you cite above do, in so  
many words.

I'm not sure what you are looking for, but it sounds like you have  
some concern about the first-stage fit of your instruments.  A useful  
rule of thumb is to look at the F-statistic for the first-stage  
regression in 2SLS:  if it is larger than about 10, then you are  
unlikely to suffer from problems that arise with weak instruments.   
See the discussion in ch. 12 of Stock & Watson (2007); -estat  
firststage- after -ivregress- (in Stata 10) gives more precise  
critical values from Stock & Yogo (2005).  I believe recent versions  
of -ivreg2- also report these statistics if you use Stata 9.

To your concern about "economic persuasion": one would use  
instrumental variables if OLS is expected to yield biased results --  
that is, if E[X'u] ~= 0.  Of course, this moment condition is not  
testable:  you must use economic theory and/or intuition  
("persuasion") to argue for the need for an IV estimator in the first  
place.  Similarly, an IV estimator requires the moment conditions E 
[Z'u] = 0 and E[Z'X] ~= 0.  The second of these is "verifiable"  
through weak instrument tests as discussed above.  The first cannot  
be tested, but the existence of "extra" moments beyond those needed  
to just identify the model allows one to test for over-identifying  
restrictions.  (Again, speaking loosely.)

Hope that is helpful.  In light of your questions, you might find it  
worthwhile to review textbook treatments of IV -- such as ch. 15 in  
Wooldridge (2006) or ch. 12 in Stock & Watson (2007).  Both do a good  
job, in my opinion, of developing intuition for the IV estimator.   
For further discussion of the problems associated with weak  
instruments, you might start with Stock, Wright & Yogo (2002).  There  
are many other folks on this list with expertise in this area who may  
chime in (such as Kit, who I see has already gave a pithy reply while  
I was composing this more prolix one).

Best,
Mike


Sources:

Stock, James, Jonathan Wright & Motohiro Yogo, "A Survey of Weak  
Instruments and Weak Identification in Generalized Method of  
Moments," Journal of Business & Economic Statistics, v.20 n.4,  
October 2002.

Stock, James & Mark Watson, Introduction to Econometrics, 2nd ed.,  
Pearson Education: Boston. 2007.

Stock, James & Motohiro Yogo, "Testing for Weak Instruments in Linear  
IV Regression," Identification and Inference in Econometric Models:  
Essays in Honor of Thomas J. Rothenberg, Ed: Andrews & Stock,  
Cambridge University Press: Cambridge. 2005.

Wooldridge, Jeffrey.  Introductory Econometrics, 3rd ed., Thomson  
Higher Education: Mason, OH. 2006.

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/