Bookmark and Share

Notice: On March 31, it was announced that Statalist is moving from an email list to a forum. The old list will shut down on April 23, and its replacement, statalist.org is already up and running.


[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: st: Multiple endogenous regressors


From   Yuval Arbel <yuval.arbel@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Multiple endogenous regressors
Date   Sat, 22 Oct 2011 16:07:40 +0200

Not exactly. Take, for example the following simple equation:

Yi=a+bXi+ui

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. Unfortunately, in the
system of equation I presented, you cannot generate Xhat, because the
second equation is an identity. Therefore, and if you think about it
logically, it is impossible to solve this system by 2SLS

Note, that for small samples, the two estimators are by no mean
identical. I suppose, that for large sample they are both consistent



On Sat, Oct 22, 2011 at 3:29 PM, Cameron McIntosh <cnm100@hotmail.com> wrote:
> 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.
>
> Let's move on,
> Cam
>
>> Date: Sat, 22 Oct 2011 10:34:30 +0200
>> Subject: Re: Re: Re: RE: re:Re: st: Multiple endogenous regressors
>> From: yuval.arbel@gmail.com
>> To: statalist@hsphsun2.harvard.edu
>>
>> I would like to assure you that I would not write about this matter if
>> I was not certain about my knowledge in this area.
>>
>> I believe you are confusing between 2SLS and IV estimators, which are
>> not exactly the same:
>>
>> When you are talking about 2SLS you need literally to replace
>> projected values from the solution equation - but here the second
>> equation is simply an identity, so you cannot produce here projected
>> values. I suppose what STATA did here is to use investment as
>> instrumental variable to consumption in the right-hand-side of the
>> consumption function. This is not 2SLS even if the command is 2SLS and
>> even if the output tells otherwise!!!
>>
>>
>>
>> On Fri, Oct 21, 2011 at 9:51 PM, Christopher Baum <kit.baum@bc.edu> wrote:
>> > <>
>> > Yuval said
>> >
>> > Moreover, take for example the following system of Kensian (sic) 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''m sure the inability to use 2SLS on a simple Keynesian model will come as a surprise to those of us who write econometrics lecture notes and textbooks, as it is one of the most common textbook examples of IV.
>> > An empirical counterexample:
>> >
>> > . webuse klein
>> >
>> > . ivregress 2sls consump (totinc = invest)
>> >
>> > Instrumental variables (2SLS) regression               Number of obs =      22
>> >                                                       Wald chi2(1)  =   24.24
>> >                                                       Prob > chi2   =  0.0000
>> >                                                       R-squared     =  0.8430
>> >                                                       Root MSE      =  2.8442
>> >
>> > ------------------------------------------------------------------------------
>> >     consump |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
>> > -------------+----------------------------------------------------------------
>> >      totinc |   .4593425   .0932901     4.92   0.000     .2764971    .6421878
>> >       _cons |   26.07967   5.571562     4.68   0.000     15.15961    36.99973
>> > ------------------------------------------------------------------------------
>> > Instrumented:  totinc
>> > Instruments:   invest
>> >
>> >
>> > Apparently Yuval did not take my response to his point (4) too seriously.
>> >
>> > 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
>> >
>> >
>> > *
>> > *   For searches and help try:
>> > *   http://www.stata.com/help.cgi?search
>> > *   http://www.stata.com/support/statalist/faq
>> > *   http://www.ats.ucla.edu/stat/stata/
>> >
>>
>>
>>
>> --
>> Dr. Yuval Arbel
>> School of Business
>> Carmel Academic Center
>> 4 Shaar Palmer Street, Haifa, Israel
>> e-mail: yuval.arbel@gmail.com
>>
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>



-- 
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street, Haifa, Israel
e-mail: yuval.arbel@gmail.com

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/


© Copyright 1996–2014 StataCorp LP   |   Terms of use   |   Privacy   |   Contact us   |   Site index