Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects

We use the control function approach to identify the average treatment effect and the effect of treatment on the treated in models with a continuous endogenous regressor whose impact is heterogeneous. We assume a stochastic polynomial restriction on the form of the heterogeneity, but unlike alternative nonparametric control function approaches, our approach does not require large support assumptions.