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From |
"Rodrigo Alfaro A." <ralfaro@bcentral.cl> |

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

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

Date |
Thu, 10 Jul 2008 10:27:22 -0400 |

/// 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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**Follow-Ups**:**Re: st: Intepreting: "IV estimates are biased towards OLS estimates with weak instruments"***From:*"Erasmo Giambona" <e.giambona@gmail.com>

**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>

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