Distributional Treatment Effect in Models with Multiple Unordered Outcomes

We introduce a novel set of bounds that addresses distributional heterogeneity in treatment effects within models featuring multiple unordered outcomes. By incorporating the concept of superquantiles, we derive upper and lower bounds for individual treatment effects resulting from policy interventions. From an economic perspective, these bounds enable us to assess the impact of policy interventions on specific population groups, with a focus on identifying potential adverse effects on vulnerable segments in the presence of evaluation and selection problems. Specifically, we demonstrate how the superquantile framework allows a social planner to quantify the risk of harm to particular populations, accounting for both observable and unobservable factors in the design of policy interventions.