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

 From "Rodrigo Alfaro A." To 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 )
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