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st: Interaction terms with IV models
There are a number of postings showing that when an interaction term or a squared term is added to an IV model that the best thing to do is to directly instrument that interaction or square, and providing helpful suggestions as to variables to use as instruments.
These postings have all been written in terms of single squared terms or interactions. I have a situation where I would like to consider squared terms on a number of endogenous variables, and a substantial set of interaction terms with endogenous terms with each other and with various exogenous terms (not quite a full translog model, but a significant subset on one).
While mechanically this can be done following the previous advice, and I can maintain identification by adding in the relevant non linear forms of the instruments, this generates an extraordinarily complex model in which one would not have a great deal of faith.
Are there any easier solutions to this structural issue?
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