Econometrica: Nov 2018, Volume 86, Issue 6
Identifying Effects of Multivalued Treatments
Sokbae Lee, Bernard Salanié
Multivalued treatment models have typically been studied under restrictive assumptions: ordered choice, and more recently, unordered monotonicity. We show how treatment effects can be identified in a more general class of models that allows for multidimensional unobserved heterogeneity. Our results rely on two main assumptions: treatment assignment must be a measurable function of threshold‐crossing rules, and enough continuous instruments must be available. We illustrate our approach for several classes of models.
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Supplement to "Identifying Effects of Multivalued Treatments"
Appendix A gives an identification result for the zero-index case, which was not dealt with in the text. It also provides a characterization of Heckman and Pinto's unordered monotonicity property as a subcase of our more general framework. Appendix B collects proofs of some of the results in the main text. Finally, Appendix C fills in the details of the entry game introduced in Section 2, and Appendix D compares our results with those of Heckman, Urzua, and Vytlacil (2008) in more detail. Appendix E discusses a more general form of threshold conditions than the "rectangular"
threshold conditions in Assumption 2.1.