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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/

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

**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>

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