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From |
"Erasmo Giambona" <e.giambona@gmail.com> |

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

Subject |
Re: st: Intepreting: "IV estimates are biased towards OLS estimates with weak instruments" |

Date |
Thu, 10 Jul 2008 17:26:19 +0200 |

Dear Austin and Rodrigo, Thanks very much for you helpful insights and reference suggestions. Erasmo On Thu, Jul 10, 2008 at 4:27 PM, Rodrigo Alfaro A. <ralfaro@bcentral.cl> wrote: > > /// > > Erasmo, > > This is not a Stata question, but I would like to remark some Austin's > points. > > (1) Usually, IV estimator does not have expected value. > > Wooldridge (2002) on page 101 discusses this topic in a clear way: > "udner standard distributional assumptions, the expected value of the > 2SLS estimator does not even exist". Moreover, under normality the > existence of moments of 2SLS depends on the number of overidentifying > restriccions (how much instruments you have for the endogenous > variables). > > Then talking about biased is somehow an approximation with Edgeworth > expanssion and/or in asyntotic terms. For example, using an > approximation of the distribution of IV estimator, Nagar (1959) showed > that the bias of the approximation is proportional to the number of > instruments. Staiger and Stock (1997) takes care of the theoretical > background of weak instruments, but their results are asymptotically!! > Indeed, they showed that LIML and not 2SLS is consistent, we could > relate consistency with asyntotic unbiaseness for this case. Anyway LIML > does not have any well-defined moments at all, so in finite-samples LIML > could be even worse than 2SLS!! > > > (2) Theoretical and Empirical > > Austin pointed you that it is wrong making conclusions from empirical > applications. In other words, you cannot conclude that humans likes > coffee and muffins for breakfast if you are survering only americans!! > You can post questions from empirical issues, then you can try to > generalize that issue with theory or doing some experiments (Monte Carlo > simulations). > > > Finally, I would like to recommend you some readings that introduces the > topic from simple examples in Hausman webpage > (http://econ-www.mit.edu/faculty/hausman/papers) > > IV Estimation with Valid and Invalid Instruments > Jinyong Hahn and Jerry Hausman > July 2003 > > Weak Instruments: Diagnosis & Cures in Empirical Econometrics > Jerry Hausman > December 2002 > > Notes on Bias in Estimators for Simultaneous Equation Models > Jerry A. Hausman and Jinyong Hahn > June 2001 > > > Best regards, Rodrigo. > > > > Nagar, A. (1959) ``The Bias and Moment Matrix of the General $k$-class > estimators of the Parameters in Simultaneous Equations," {\it > Econometrica}, 27, 575-595. > > Staiger, D., and Stock, J. (1997) ``Instrumental Variables Regression > with Weak Instruments," {\it Econometrica}, 65, 557-586. > > > -----Mensaje original----- > De: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] En nombre de Austin > Nichols > Enviado el: Jueves, 10 de Julio de 2008 09:44 a.m. > Para: statalist@hsphsun2.harvard.edu > Asunto: Re: st: Intepreting: "IV estimates are biased towards OLS > estimates with weak instruments" > > Erasmo Giambona <e.giambona@gmail.com>: > > There are more references to read in > http://www.stata.com/meeting/5nasug/wiv.pdf > (Bound Jaeger Baker is a good starting place for further reading) but > the basic point is simple enough. In some models, if the true causal > parameter beta is 3 and the expected OLS betahat is 1, for a OLS bias of > -2, then the IV estimator's expected value is somewhere between 1 and 3, > biased away from the true value in the direction of the OLS estimator's > expectation (i.e. both have neg bias). When you report getting an OLS > estimate of 1.2 and an IV estimate of 2.4, say, that is hardly > inconsistent with the expected outcomes. > > But in other models, the IV estimator has no expected value, or has a > very strange finite-sample distribution. So while the phrase "IV > estimates are biased towards OLS estimates with weak instruments" is a > useful heuristic device, and useful in interpreting the IV results > someone is advertising as unbiased (rather than consistent, and > high-variance, as they should advertise), it does not hold with > certainty in every setting. > > Moreover, the observed IV and OLS estimates you get in any real data > tell you nothing about their expectations or bias--you would need to > fully specify the DGP and run simulations (or do some analytical > derivations) to say something about those. > > On Thu, Jul 10, 2008 at 7:27 AM, Erasmo Giambona <e.giambona@gmail.com> > wrote: >> Dear Statalisters, >> >> Practically, any textbooks that talk about instrumental variable >> methods emphasize that with weak instruments, IV estimates will be >> biased towards OLS estimates. The way I interpret this statement is >> that the IV and OLS coefficients should have a very similar size. >> However, this intepretation is not confirmed (at least apparently) by >> my experience with IV methods. In fact, I usually find that the >> F-statistics for the excluded instruments and/or Donald-Cragg >> statistics (see Stock and Yogo, 2004) used to test for weak >> instruments are low or lower than the critical values tabulated by >> Stock and Yogo (2004), but the IV estimates are 2 or 3 times as large >> as the OLS estimates. >> >> Most likely, this implies that I am misinterpreting the statement that > >> "IV estimates are biased towards OLS estimates with weak instruments". >> Can anyone provide any hints on how I should interpret this statement? >> Thanks and best regards, >> >> Erasmo >> >> Reference >> Stock and Yogo, 2004, Testing for Weak Instruments in Linear IV >> Regressions, (can be found at: >> http://ksghome.harvard.edu/~jstock/ams/websupp/rfa_7.pdf ) > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > > ******************************************************************************** > ADVERTENCIA: La información contenida en esta transmisión, y en cualquier archivo adjunto, está sujeta a reserva legal conforme a la normativa aplicable al Banco Central de Chile, y no puede ser usada o difundida por personas distintas de su o sus destinatarios. 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**References**:**st: Intepreting: "IV estimates are biased towards OLS estimates with weak instruments"***From:*"Erasmo Giambona" <e.giambona@gmail.com>

**Re: st: Intepreting: "IV estimates are biased towards OLS estimates with weak instruments"***From:*"Austin Nichols" <austinnichols@gmail.com>

**RE: st: Intepreting: "IV estimates are biased towards OLS estimates with weak instruments"***From:*"Rodrigo Alfaro A." <ralfaro@bcentral.cl>

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