My question is how to use an instrumental variable in the setting of interaction terms. In my research, the regression equation is as follows:
corruption=a+b1*FDI+b2*GDP+b3*FDI*GDP+BiXi+e. Because I assume endogeneity between corruption and FDI, then I use geographic distance as instrument for FDI. But the problem is that I have an interaction term between FDI and GDP. How should I use the instrument in this case? I haven’t found anybody doing it in this way. Does the conventional method still work, like I obtain the predicted FDI from the distance and other excluded variables for the first stage regression, and then interact predicted FDI with GDP in the second stage? The problem is getting even complicated if I want to instrument both FDI and GDP.
My reply: I’m not sure, but my general advice here is to consider this as an observational study with the instrument (geographic distance) as your “treatment”, and then corruption and FDI as a joint outcome. I think everything falls out from here (following the principles of chapter 10).