Identification of treatment effects using control functions in models with continuous, endogenous treatment and heterogeneous effects

<p><p><p><p>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.</p> </p><p> </p><p></p><b>Copyright Notice</b> The copyright to this Article is held by the Econometric Society. It may be downloaded, printed and reproduced only for educational or research purposes, including use in course packs. No downloading or copying may be done for any commercial purpose without the explicit permission of the Econometric Society. For such commercial purposes contact the Office of the Econometric Society (contact information may be found at the website <a href="http://www.econometricsociety.org">http://www.econometricsociety.org </a> or in the back cover of Econometrica). This statement must the included on all copies of this Article that are made available electronically or in any other format.</p></p></p>