RE: RE: st: Multiple endogenous regressors

["William Buchanan" <william@williambuchanan.net>]

Yuval,

Although I personally find this thread to be amazingly hilarious, I thought
I might try to offer you some help.  Keep in mind, however, that I am by no
means an economist or econometrician.  But I wanted to point you to some
more resources that I don't think you've read and which is probably why
you're continuing to argue with people who are infinitely more knowledgable
about this subject than either of us will ever be (namely one of the
coauthors of an amazingly robust instrumental variables regression program).


Angrist, J. D. and Pischke, J. (2009). Mostly Harmless Econometrics: An
Empiricist's Companion. Ch. 4 "Instrumental Variables in Action: Sometimes
You Get What You Need". P 113-220. Princeton, NJ: Princeton University
Press.

Baum, C. F. (2006). An Introduction to Modern Econometrics Using Stata. Ch.
8 "Instrumental-Variables Estimators". P. 185-218. College Station, TX:
Stata Press.

Murnane, R. J. and Willett, J. B. (2011). Methods Matter: Improving Causal
Inference in Educational and Social Science Research. Ch. 10. "Introducing
Instrumental-Variables Estimation". P. 203-264. Cambridge, MA: Harvard
University Press.

Stock, J. H. and Watson, M. W. (2007). Introduction to Econometrics. 2nd Ed.
Ch 12 "Instrumental Variables Regression". P. 421-467. Boston, MA: Pearson
Education.

Wooldridge, J. M. (2003). Introductory Econometrics: A Modern Approach. 2nd
Ed. Ch 15 "Instrumental Variables Estimation and Two Stage Least Squares".
P. 484-525. Mason, OH: Thomson South-Western Publishing.  

These are just the books that I have next to my desk and could get to
easily.  However, if you look at the help file for -ivreg2- the authors of
that package (available from SSC) provide a fairly extensive list of
references.  Additionally, Austin Nichols also has a great paper that you
can find in the stata journal on causal inference using observational data.


While you certainly are free to proclaim the merit that you find in the ILS
estimator, you have yet to cite any research that supports your case.  On
the otherhand, everyone else who has been trying to help Elizabeth out with
her problem has been trying to guide her to resources and answers that will
be helpful for her.  If you wanted to do more reading about the questions
that Elizabeth had - and that were directly relevant to the original intent
of this thread - you could try looking at Angrist and Pishcke's website
(http://www.mostlyharmlesseconometrics.com/2010/02/multiple-endogenous-varia
bles-what-now/) where they have a brief discussion specifically regarding
IVE with multiple endogenous regressors.  

- Billy




-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Yuval Arbel
Sent: Saturday, October 22, 2011 11:36 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: RE: st: Multiple endogenous regressors

I see you did not get my point: the question is how did you define Xhati???
after all you are controlling the program.

Lets try another example. Suppose you have the system:

Yi=a+bX1i+u1i

X1i=c+dYi+eX2i+u2i

where X2i is exogenous. The solution to this system is:

X1i=c'+e'X2i+u'2i

from which you prduce X1hati

Now suppose you have an instrument Zi, with numerical figures which are
totally different from X1hati. You want to tell me that
cov(Zi,Yi)/cov(Zi,X1i) and cov(X1hati,Yi)/Var(X1hati) yield identical
numbers??? I don't buy that

On Sat, Oct 22, 2011 at 7:49 PM, Christopher Baum <kit.baum@bc.edu> wrote:
> <>
> Cam said
>
>> Like Kit, I got a bit of a a surprise (and chuckle) about the example. In
the Keynesian model, 2SLS, ILS, and the simple IV estimator yield identical
results when instrumenting Y_t with I_t. See Chapter 11 in:
>>
>> Batalgi, B.H. (2008). Econometrics (3rd. ed.). Berlin - Heidelberg:
Springer-Verlag.
>>
>
>
> I don't thinl Badi has to worry too much about Yuval's challenge to 
> his book. Yuval said
>
>> Suppose Yi and Xi are endogenous, Zi is an instrumental variable and 
>> Xhati is the projected values of Xi obtained from the solution 
>> equation (in which all the right-hand-side variables are exogenous).
>>
>> The plim of the IV esimator for b is: cov(Zi,Yi)/cov(Zi,Xi). Note 
>> that to generate the IV estimator you are using all the 3 variables 
>> (Xi, Yi and Zi). I suppose this is what STATA estimated in Kit's 
>> example
>>
>> On the other hand, the plim of the 2SLS estimator for b is:
>> cov(Xhati,Yi)/Var(Xhati). The 2SLS estimator uses just Xhati and Yi, 
>> because you are literally replacing Xi by Xhati.
>> ?
>> Note, that for small samples, the two estimators are by no mean 
>> identical. I suppose, that for large sample they are both consistent
>
> Strangely enough, the two quantities he speaks of computing are exactly
the same to 8 decimals. This is hardly relying on asymptotics, as N=21. (I
suppose by the "solution equation" Yuval means what the rest of the world
calls a first stage regression).  From the Klein regression in my last
posting:
>
> . corr consump invest totinc inchat,cov
> (obs=22)
>
>             |  consump   invest   totinc   inchat
> -------------+------------------------------------
>     consump |  53.9893
>      invest |   10.634  12.1089
>      totinc |  76.5988  23.1506 117.8
>      inchat |  20.3308  23.1506  44.2607  44.2607
>
>
> . mata
> ------------------------------------------------- mata (type end to 
> exit) --------
> : cov=st_matrix("r(C)")
>
> : cov[2,1] / cov[3,2]     <== cov (Z,Y) / cov(Z,X)
>  .4593424594
>
> : cov[4,1] / cov[4,4]     <== cov(Xhat,Y) / var(Xhat)
>  .4593424594
>
> I'm not sure what criterion Yuval would use to define "no mean identical",
but they sure look the same to me? as econometric theory demands, as they
are the same quantities. Think about the fact that covariance is a linear
operator, and Xhat is a deterministic linear function of X...
>
>
> 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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