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# Re: st: Is it OK to interact an instrumented variable?

 From Tirthankar Chakravarty To statalist@hsphsun2.harvard.edu Subject Re: st: Is it OK to interact an instrumented variable? Date Wed, 31 Aug 2011 03:31:24 -0700

You have three options:

1) Instrument X2 and X1*X2 by Z and Z*X1. This is what is commonly
done, but problem with this approach is that it requires conditional
independence rather than just uncorrelatedness of the instruments
(included and excluded) with the structural error.

2) 2SLS with the second stage OLS using the regressors X2hat and
X1*X2hat, where X2hat is the projection of the endogenous regressor on
a full set of instruments. Here you will need to use a bootstrap or a
similar technique to get valid standard errors.

3) Use X2hat and X1*X2hat as _instruments_. This requires only
uncorrelatedness and gives valid standard errors.

For an excellent discussion of these issues, see pg. 143 onwards in
the 2nd edition of Prof. Woodridge's book, Econometric Analysis of
Cross Section and Panel Data.

T

On Wed, Aug 31, 2011 at 12:13 AM, Joseph B. Creek <inkind1982@yahoo.com> wrote:
> Hello,
>
> Hello,
>
> I am unsure about how to deal with this model. I want to estimate
>
> Y = B0 + B1*X1 + B2*X2 + B3*X1*X2 + controls + e
>
> X1 is exogenous and X2 is endogenous. The interaction of X1 and X2 has a clear economic interpretation that I want to investigate empirically. I intend to estimate using IV and have an instrument Z for X2. I have been told I can use Z and Z*X1 as instruments for the endogenous variables X2 and X1*X2. Is this true? Also, does it matter in this case if X1 and X2 are likely related?
>
> Is there any specific command I should use for this?
>
> Your help is much appreciated.
> *
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>

--
Tirthankar Chakravarty
tchakravarty@ucsd.edu
tirthankar.chakravarty@gmail.com

*
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