This paper presents a weighted optimization framework that unifies the binary, multi-valued, continuous, as well as mixture of discrete and continuous treatment, under unconfounded treatment assignment. With a general loss function, the framework includes the average, quantile and asymmetric...

This paper presents a weighted optimization framework that unifies the binary, multivalued, and continuous treatment - as well as mixture of discrete and continuous treatment - under a unconfounded treatment assignment. With a general loss function, the framework includes the average, quantile,...

This article considers a Mann-Whitney test of distributional effects in a multivalued treatment. Specifically, we first show that, under the unconfoundedness condition, the counterfactual distributions are weighted averages, with weights satisfying some moment restrictions. We estimate the...