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From |
Cameron McIntosh <cnm100@hotmail.com> |

To |
STATA LIST <statalist@hsphsun2.harvard.edu> |

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 > >> > > >> > > >> > * > >> > * 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/ * * 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/

**References**:**re: Re: Re: RE: re:Re: st: Multiple endogenous regressors***From:*Christopher Baum <kit.baum@bc.edu>

**Re: Re: Re: RE: re:Re: st: Multiple endogenous regressors***From:*Yuval Arbel <yuval.arbel@gmail.com>

**RE: st: Multiple endogenous regressors***From:*Cameron McIntosh <cnm100@hotmail.com>

**Re: st: Multiple endogenous regressors***From:*Yuval Arbel <yuval.arbel@gmail.com>

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