I want to run a fixed effects IV regression that is also a mixed process model. If I use the linear FE-IV estimator, I am assuming linearity, which I don't want to do. However, I do not have a program that allows for both the fixed effects, the IV, and the mixed process. In a linear fixed effects regression I could de-mean the data first and then run a regression as usual. In the context of an IV estimator, can I de-mean data for non-linear processes such as a first stage ordered probit and second stage probit (using -cmp- in Stata) and get results that properly take into account the panel aspect of the data, while also accounting for the mixed process (and IV)?
Also, I am using a nonparametric kernel IV regression in R, -npregiv- in the "np" package. Can I de-mean the data in a nonparametric regression without an IV and/or in an IV regression (I assume the answer is the same) to take into account the panel nature of the data?