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

[Yuval Arbel <yuval.arbel@gmail.com>]

On Fri, Oct 21, 2011 at 4:38 PM, Christopher Baum <kit.baum@bc.edu> wrote:
> <>
> 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.

Yuval: For students who study econometrics for the first time, the ILS
is certainly not a meaningless exercise: on one hand, if an equation
in the system in unidentified - this means that usually the ILS will
yield infinite solutions to the structural coefficients. On the other
hand, if an equation is over-identified the ILS will yield more than
one solution to the structural coefficients dependent of how many
extra exogenous variables outside the equation you have.
Moreover, take for example the following system of Kensian equations:

C=a+bY+u
Y=C+I

Note, that the only way to get consistent estimates in this case is by
the ILS (you cannot employ here the 2SLS)

I believe that what you mean is that in academic studies the 2SLS is
more common, because the ILS is less convenient to use and requires to
fully solve the system and the coefficients.

>
> 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.
>

Yuval: Note, that in most cases if you try to apply the 2SLS to
unidentified equation(s) - you get an exact collinearity. This is
because the 2SLS is based on replacing the problematic variable(s)
with the projection of the solution equation. It is thus important to
make sure there is no unidentified equations in the structural system
of equations

> (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.
>

Yuval: Ramanathan is an elementary textbook of econometrics, and as
such it does not cover many topics. However, It is a friendly book,
without matrix algebra, which, I believe, covers nicely the basic
intuition of the simultaneous equation model as well as most of the
basic topics in econometrics. Another advantage in the book is that it
encourages the students to run regressions (he calls this approach
"learning by doing"). I recommended it to Elizabeth because she seems
to be a begginer. I'm not familiar with the book you recommended, but
I'm using the textbooks of Greene, Kmenta and Johnston. I also found
an interesting discussion on the correction of the standard errors in
simultaneous equation model in Madala's textbook

> (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.
>
Yuval: I would certainly take a look. Generally speaking, however, my
advice is to be very careful while using simultaneous equation models
in research papers. As somebody said before, it is very difficult to
find good instruments. In fact, because of the complexity of the
subject and particularly the identification problem, the focal point
of time series analysis has moved to VAR models - where you have
lagged independent variables, which are clearly exogenous


> (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.

Yuval - That's what I thought. In fact the subject, which came from
medicine and bio-statistics, is relatively new to economists.
>
> 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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-- 
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street, Haifa, Israel
e-mail: yuval.arbel@gmail.com

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