My panel model is of the following form where x1 is the endogenous regressor and z is the moderator.
y = f(x1, x1^2, x1z)
The instrument for x1 is M (based on averages of similar observations except the one under consideration). Based on the paper by Haans et al.(2015) https://onlinelibrary.wiley.com/doi/full/10.1002/smj.2399, I am instrumenting both the linear and quadratic terms with M and M^2.
The instrument for the interaction term x1z is N (again, based on averages of similar observations except the one under consideration).
I am not sure if I should include the instrument for the interaction term in the instruments for the linear and quadratic terms. Can someone please advise. Thanks.
