Treatment Effects with Multidimensional Unobserved Heterogeneity: Identification of the Marginal Treatment Effect

This paper establishes sufficient conditions for the identification of the marginal treatment effects with multivalued treatments. Our model is based on a multinomial choice model with utility maximization. Our MTE generalizes the MTE defined in Heckman and Vytlacil (2005) in binary treatment models. As in the binary case, we can interpret the MTE as the treatment effect for persons who are indifferent between two treatments at a particular level. Our MTE enables one to obtain the treatment effects of those with specific preference orders over the choice set. Further, our results can identify other parameters such as the marginal distribution of potential outcomes.