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# RE: st: Multiple endogenous regressors

 From Cameron McIntosh To STATA LIST Subject RE: st: Multiple endogenous regressors Date Sat, 22 Oct 2011 13:01:42 -0400

```So I guess you think Batalgi's text (now in its 5th edition, actually) should be retracted?Cam

> Date: Sat, 22 Oct 2011 16:07:40 +0200
> Subject: Re: st: Multiple endogenous regressors
> From: yuval.arbel@gmail.com
> To: statalist@hsphsun2.harvard.edu
>
> 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
> >> >
> >> >
> >> > *
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> >> > *   http://www.ats.ucla.edu/stat/stata/
> >> >
> >>
> >>
> >>
> >> --
> >> 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
> 4 Shaar Palmer Street, Haifa, Israel
> e-mail: yuval.arbel@gmail.com
>
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