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re:Re: Re: st: Multiple endogenous regressors


From   Christopher Baum <kit.baum@bc.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   re:Re: Re: st: Multiple endogenous regressors
Date   Thu, 20 Oct 2011 20:58:24 -0400

<>
Yuval said

Yuval: I don't see the point of this test, because overidentification
is a structural problem of the system. In my opinion the Yu-Hausman
test is much better


First of all, it is a Durbin - WU - Hausman test, not a "Yu-Hausman" test. See the references in Baum-Schaffer-Stillman SJ 2003, 2007, or any decent econometrics text.

If what you have learned from Ramanathan is what you state above, then burn the book.

The Durbin-Wu-Hausman test contrasts two estimators of the same y = X b + u model: OLS and IV. Under the null hypothesis that X \perp u,  OLS is both consistent and efficient. Under the alternative hypothesis, IV is consistent (albeit biased). In a "Hausman test", you must have one estimator whose consistency is maintained.

If you cannot pass a test of overidentifying restrictions in an IV context, then you do not have a consistent IV estimator, and comparing it to OLS is a comparison of two inconsistent estimators. Thus the FIRST thing you should do with an overidentified IV model is check the overid restrictions. If you can't pass that test, then go back to the drawing board. Failure of an overid test is not a "structural problem" of an equation; it merely means that your assertion that instruments Z \perp u does not seem to be valid in the current sample. The test has the joint null that the instruments are valid AND the specification of the model is correct. A rejection can occur because the latter maintained hypothesis is not valid.

Kit

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
                              An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
   An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html




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