IV estimation for endogenous interaction terms

[Lieke]

Hello,

Currently I am doing research about financial economics and I am running into econometric issues for which I can not find any solution.
My model includes 4 interaction terms. One part of the interaction term is a dummy variable indicating one of the 5 groups of income inequality (middle low, middle, middle high and high, low is left out to serve as the base group). These dummies are interacted with another variable. Next to the interaction terms, income inequality and the other variable are included separately in the model.

The problem here is reverse causality. Normally you would perform IV estimation. I already have found the two instruments. Since I have both the level variables and the interaction terms (that consist of two endogenous variables) in the model, I really do not know how I can adress the endogeneity problem. Can anybody help me? Thank you in advance!

Lieke