st: Re: ivreg2 questions

[Christopher Baum <kit.baum@bc.edu>]

<>
On Mar 20, 2012, at 2:33 AM, Rob wrote:

> Sorry for what is purely an econometric question at this point
> (removed from Stata) but there is still one thing that I am
> misunderstanding.  In every text I can read, it basically says the
> instrument must be correlated with the endogenous regressor (including
> Mostly Harmless Econometrics and an Introduction to Modern
> Econometrics Using Stata to name 2 - the latter stating the instrument
> must be highly correlated).  These texts do not state that the
> instrument must have a high correlation with the endogenous regressor
> with the effect of a set of controlling variables removed (partial
> correlation).  Is this just a simplification on the part of these
> texts or again is there something I am missing?  And does this
> basically mean that the validity of an instrument is conditional on
> the other independent variables included in the primary model and not
> just the dependent variable and the endogenous regressor?

Yes. It should be understood that when we say that an excluded instrument be highly correlated with the endogenous variable(s),
that correlation is a partial correlation, reflected by the partial regression coefficient in the 'first stage regression'. Consider
a case where Fahrenheit temp is an included exogenous regressor, and you attempt to use Celsius temp as an excluded
instrument. The instrument matrix will be rank-deficient. Now consider using Fahrenheit temp + epsilon as an excluded instrument,
where epsilon is random noise. The 'first-stage regression' (projection of endog on all exog) will be computable, but
the marginal value of your excluded instrument is very low, as it really contains no marginal information that can be used
to identify the model. So even though temperature may be highly correlated to the endogenous regressor (say, quantity traded
in the market), and you have satisfied the rank and order conditions, the model has weak instrument problems which relate
to the very low partial correlation. I suppose we could speak of the simple correlation between endogenous and excluded
instrument if we added the caveat that the instrument matrix was far from ill-conditioned, but that is a harder concept 
to motivate and test.

Kit

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
                             An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
  An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html


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