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From |
DE SOUZA Eric <eric.de_souza@coleurope.eu> |

To |
"'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: Re: How to correct standard errors of a 2sls performed by |

Date |
Sat, 6 Feb 2010 14:21:18 +0100 |

What you have is a simultaneous equation system (SEM). A SEM can be estimated equation by equation by single equation methods (2SLS, LIML, ...) In your system, the endogenous variables are y, x1, x2, m1, m2. The exogenous variables are n1, n2, q1, q2, p1, p2. In your first stage, you would estimate each of the endogenous variables on all of the exogenous variables In your second stage, you use the predicted values of the endogenous variables to replace the endogenous variables on the right hand side of each equation. This means that you can estimate Eq2 by 2SLS, specifying all of the exogenous variables above as instruments. m1 and m2 would be the included exogenous, and the others would be the excluded exogenous Idem for Eq3 Eq4 and Eq5 can be estimated by OLS Eric de Souza College of Europe BE-8000 Brugge (Bruges) Belgium -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of John Antonakis Sent: 06 February 2010 14:04 To: statalist@hsphsun2.harvard.edu Subject: Re: st: Re: How to correct standard errors of a 2sls performed by Thanks Kit--I am aware of the problem regarding system-wide estimators and the fact that a misspecification in one part of the model may bias another part of the model; in fact, I always compare 2sls estimates (which I refer to as a "safe-bet" estimator) to those of a systems estimator (e.g., 3sls or ML). However, there is the efficiency problem on the one hand; on the other, how does one do single-equation estimation with in the context of a non-recursive system. Again, here is the example: Eq1: y = x1 + x2 + z Eq2: x1 = m1 + m2 + x2 + z Eq3: x2 = n1 + n2 + x1 + z Eq4: m1 = q1 + q2 + z Eq5: m2 = p1 + p2 + z The predicted value of x2 enters in Eq. 2; however, the predicted value of x1 enters in Eq. 3. So, how does one go about estimating this non-recursive model using a single-equation estimator? Thanks, John. ____________________________________________________ Prof. John Antonakis, Associate Dean Faculty of Business and Economics Department of Organizational Behavior University of Lausanne Internef #618 CH-1015 Lausanne-Dorigny Switzerland Tel ++41 (0)21 692-3438 Fax ++41 (0)21 692-3305 Faculty page: http://www.hec.unil.ch/people/jantonakis Personal page: http://www.hec.unil.ch/jantonakis ____________________________________________________ On 06.02.2010 13:39, Kit Baum wrote: > On Feb 6, 2010, at 2:33 AM, John wrote: > > >> What if the system is non-recursive (with feedback loops) and with >> multiple equations, e.g., >> >> y = x1 + x2 + z >> x1 = m1 + m2 + x2 + z >> x2 = n1 + n2 + x1 + z >> m1 = q1 + q2 + z >> m2 = p1 + p2 + z >> >> Here one would need reg3, but how would one ensure consistency of >> standard errors (in the presence of heteroskedasticity), apart from >> bootstrapping (and Roodman's -cmp- would not here as it is only for >> recursive systems)? >> > > > No, you don't _need_ reg3. A systems estimator is never needed unless you want to impose constraints across equations on the coefficients. There is nothing wrong with limited-information (single-equation) estimation of each equation in turn. A systems estimator can provide efficiency; but on the other hand any misspecification means that every equation's coefficients can become inconsistent if one equation is flawed. > > 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/ > * * 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**:**st: Re: How to correct standard errors of a 2sls performed by***From:*Kit Baum <baum@bc.edu>

**Re: st: Re: How to correct standard errors of a 2sls performed by***From:*John Antonakis <john.antonakis@unil.ch>

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