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

From   Christopher Baum <>
To   "" <>
Subject   Re: Re: RE: re:Re: st: Multiple endogenous regressors
Date   Fri, 21 Oct 2011 10:38:51 -0400

On Oct 21, 2011, at 2:33 AM, Yuval wrote:

> 1. To summarize our previous discussion: if you solve the system by
> ILS and the equation is unidentified - you might get something but it
> will be biased and inconsistent (as I suggested). On the other hand:
> if you run 2SLS on unidentified equation - you get exact
> multicollinearity (as Kit suggested)
> 2. Ramanathan has no discussion at all about statistical tests related
> to simultaneous equation model. So you should not put the blame on
> him.
> 3. Can you apply me to the stata link of this test? it seems strange
> to me that the test checks whether the specification is correct. To
> the best of my understanding the specification of the model is based
> on the logic of the researcher or the economic theory, isn't it? maybe
> you imply that the test checks the correlation between the exogenous
> variable(s) and the random disturbance term - to see whether the IV is
> a good instrument.
> 3. If you look at econometrics textbooks dealing with
> error-in-variable models (including Greene), the only test you can
> find in this context is the Wu Hausman. Also, in the footnotes of
> table 2 of Symazki (JPE, Vol. 108 Issue 3: 590-603) the author use the
> term "Wu-Hausman" to describe one of the tests he carries out.
> 4. Finally, are you familiar with the Cox Regression and survival
> rates? Can you answer the question, which I sent a few hours ago?

(1) "Solving the system with ILS" is a meaningless exercise. One does not do that in empirical work; one uses 2SLS or IV-GMM. It is meaningless to speak of bias, as in the example you gave (of a supply and demand system with no exogenous shifters) one cannot identify the individual parameters--only, for instance, the difference in the slopes--so cannot speak of their estimates as biased. They are nonexistent.

Furthermore, this has NOTHING to do with (multi)collinearity (and I did not suggest that it did!!) Perfect collinearity means the regressor matrix or instrument matrix is rank deficient. In the case of under identification, the instrument matrix is 'short', not having sufficient columns to match the X matrix. It is wise not to confuse issues by throwing out irrelevant terms.

(2) As you recommended Ramanathan's chapter on simultaneous equation models to Elizabeth, I imagined that it covered the topic of testing. As we say quite clearly in Baum-Schaffer-Stillman SJ 2003, using IV without the appropriate battery of tests is irresponsible, which is why our version of IV estimation provides a large number of test results by default.  If Ramanathan's book does not discuss the elementary tests, my advice stands.

(3) I don't know which test you mean, but if you are referring to the test of over identifying restrictions, it is clearly discussed both in Stata documentation (e.g., [R] ivregress postestimation) and in any decent econometrics textbook such as Greene, Hayashi, Wooldridge and, as Bill B. suggests, the excellent "Mostly Harmless Econometrics" of Angrist and Pischke.

(3') Agreed, Wu-Hausman or Durbin-Wu-Hausman are common terms in this literature (as we cite in B-S-S SJ 2003, 2007). "Yu-Hausman" is what you said to go look up. If you read the B-S-S SJ papers, you will find that the test produced by ivreg2's endog() option is asymptotically equivalent to the D-W-H test.

(4) I know very little about those topics, so will cautiously refrain from passing on my ignorance. Although you may not be that familiar with Statalist, you will find that most repeat Statalist posters avoid speaking about matters of which they know little.


Kit Baum   |   Boston College Economics & DIW Berlin   |
                             An Introduction to Stata Programming  |
  An Introduction to Modern Econometrics Using Stata  |

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