Identifying effects of multivalued treatments

Multivalued treatment models have only been studied so far under restrictive assumptions: ordered choice, or more recently unordered monotonicity. We show how marginal treatment effects can be identified in a more general class of models. 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. On the other hand, we do not require any kind of monotonicity condition. We illustrate our approach on several commonly used models; and we also discuss the identification power of discrete instruments.