In this paper, we establish  sufficient conditions for identifying the treatment effects on continuous outcomes in endogenous and multi-valued discrete treatment settings with unobserved heterogeneity. We employ the monotonicity assumption for multi-valued discrete treatments and instruments, and our identification condition is easy to interpret economically. Our result contrasts with related work by Chernozhukov and Hansen (2005) for thispoint. We also establish identification of the local treatment effects in multi-valued treatment settings and derive the closed-form expressions of the identified treatment effects. We give examples to verify the usefulness of our result.
In this paper, we establish the sufficient conditions for identifying treatment effects on continuous outcomes in endogenous and multi-valued discrete treatment settings with unobserved heterogeneity. We employ the monotonicity assumption for multi-valued discrete treatments and instruments, and our identification condition is easy to interpret economically. Our result contrasts with related work by Chernozhukov and Hansen (2005) with regard to this. In addition, we identify the local treatment effects in multi-valued treatment settings and derive a closed-form expression of the identified treatment effects. We provide examples to illustrate the usefulness of our result.
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