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# re:RE: re:Re: st: Multiple endogenous regressors

 From Christopher Baum To "statalist@hsphsun2.harvard.edu" Subject re:RE: re:Re: st: Multiple endogenous regressors Date Thu, 20 Oct 2011 21:03:56 -0400

```<>
Dan said

I agree with Kit's sentiments, but the way I read Yuval's message in (2) is that Yuval proposes that instead of estimating

ivreg2 y (x1-x5 = z1-z5)

Suppose I only have a 1 instrument, z, and instead propose to estimate:

ivreg2 y (x1 = z)
...
ivreg2 y (x5 = z)

In this case, each model looks exactly identified, so one can get estimates (of something!).  The problem here is that if the true model includes x1-x5, each model is mis-specified and includes the other 4 endogenous x's in the error term.  If z is correlated with each x1-x5, then z will be correlated with the error in each of the 5 IV regression models.  So, z cannot be a valid instrument for any of the 5 individual structural models.  So, each of the 5 separate TSLS models will give you biased and inconsistent estimates of the include endogenous regressor.

I think it was actually Elizabeth that proposed doing something like that. Naturally I agree with Dan's logic. As I said in my previous posting, if you screw up the specification of the model, then you are very likely to fail a test of overid restrictions (assuming you have some). So even if Elizabeth had two or three  instruments, z1, z2, z3, and ran those five regressions above, Dan's logic would apply.

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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