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.
`
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