I've noticed that when addressing the problem of linear endogeneity that the different techniques result in the same estimator for the potentially endogenous variable. Specifically, the control function approach ends up with the same estimator as instrumental variable approaches.
Considering that, I've heard it mentioned that in non-linear models these approach do not result in the same estimator. Can anyone explain or potentially provide me with a good reference with the derivations? If so, that would be very much appreciated.
I quite like the Imbens and Wooldridge notes, but they're not very general.