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

 From "Austin Nichols" To statalist@hsphsun2.harvard.edu Subject Re: st: Intepreting: "IV estimates are biased towards OLS estimates with weak instruments" Date Thu, 10 Jul 2008 09:43:43 -0400

```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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