Interaction term as an IV?

[Donovan Pollack]

Hello,

I have read a few posts on here that discuss IV when the model has interaction terms, but I have not seen advice on the model where the IV is an interaction term. For instance:

ivregress 2sls dep_var control_vars (endogenous_var=c.Z1##c.X)

Where Z1 is a continuous variable that I consider to be an instrumental variable, however it is aggregated at a state level so I want to interact it with an individual level variable X to get more variation.

This command will run, however I am unsure if my coefficients are biased from a mispecification of my model?

Thank you,
Donovan

[Donovan Pollack]

Or perhaps by generating an interaction term and including the product as the IV this can get around the inclusion of other vars that stata includes when ## is used?

[FernandoRios]

Hi Donovan,
I would say that interactions shouldnt cause any problem in your IV implementation. If you think about the first stage simply as an auxiliary regression, you want to fit that auxiliary regression the best way possible using your desired instrument. In nonparametric literature, people argue that instruments that seem to be week when used in linear regressions, may actually be strong if the correct functional form is used. I would say the same principle applies here.
Assuming your instrument is exogenous to the main model, i would say that adding interactions should have no negative effect, other than reducing the efficiency of the model, if the interaction was in fact not needed.
HTH
Fernando

[Donovan Pollack]

ok great thanks!