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# Re: st: Multiple endogenous regressors

 From Yuval Arbel 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 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
>> >
>> >
>> > *
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>> >
>>
>>
>>
>> --
>> Dr. Yuval Arbel
>> 4 Shaar Palmer Street, Haifa, Israel
>> e-mail: yuval.arbel@gmail.com
>>
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>
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--
Dr. Yuval Arbel