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

 From "Erasmo Giambona" To statalist 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 )
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