RE: re:Re: st: Multiple endogenous regressors

["Millimet, Daniel" <millimet@mail.smu.edu>]

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.

Finally, it should go without saying, that IV is a complex estimator (like any estimator is).  Unless the researcher has a solid understanding of the assumptions needed to yield consistent estimates, one should keep studying before acting.  There are way too many bad IV papers.  IMHO.


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Daniel L. Millimet, Professor
Department of Economics
Box 0496
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-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Christopher Baum
Sent: Thursday, October 20, 2011 7:03 PM
To: statalist@hsphsun2.harvard.edu
Subject: re:Re: st: Multiple endogenous regressors

<>
Yuval said, in response to Elizabeth's numbered questions,

> (2) If I can't find sufficient instruments to run all 5 endogenous regressors at the same time, what potential problems might arise if I run each of the 5 endogenous regressors independently in 5 different 2SLS models?
>

Yuval: this is a very serious problem, which is known as "unidentified equations" - in which case you get biased and inconsistent estimates.
For further details I suggest to look at the unidentified supply and demand equations presented in Ramu Ramanathan. But anyway you have to be sure that your model is correctly specified


Wrong.  If an equation is unidentified or underidentified, you don't get biased nor inconsistent estimates -- you get NO estimates. You cannot estimate such an equation by any means.


> (4) Again assuming that I can find adequate instruments, I want to run the overidentification test akin to Basmann's F test and Hansen's J test. Can I still use these same overidentification tests for multiple endogenous variables?
>

Yuval: See my answer below. I don't see any reason to run an overidentification test.


Strongly disagree. If you have an overidentified equation you should ALWAYS perform the test of overidentifying restrictions to see if there is evidence against the maintained hypothesis that the instruments are uncorrelated with the error process. Use -estat overid- after ivregress. The test is built in to Baum-Schaffer-Stillman -ivreg2- on SSC. The latter program will also do the equivalent of the Hausman test referred to, with less hassle than -hausman-, with its -endog()- option. See the ivreg2 help file or the B-S-S papers mentioned by Cam, both of which are freely available.

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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