Re: st: Re: ivreg2 questions

[Robert Davidson <rhd773@gmail.com>]

Thank you for the response; it is quite helpful.

Rob

On Tue, Mar 20, 2012 at 8:02 AM, Christopher Baum <kit.baum@bc.edu> wrote:
> <>
> 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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