I have the following problem, where I would like to have an advise or a reference:
I'm estimating a model which usually (in other papers) only includes the explanatory variable in its linear form, but, in my case, I have seen that the model would be correctly specified if it also includes the quadratic form of my explanatory variable. Despite this, usually the literature only makes an instrumental variable for the linear version of my variable, but not for the quadratic term. Given this, would it be incorrect if I also instrument this last term with the quadratic form of my instrumental variable? Is there an "universal" answer to this question, or it depends on the type of instrumental variable of my model?
Thank you for your time.