Welfare at Risk: Distributional impact of policy interventions

This paper proposes a framewrok for analyzing how the welfare effects of policy interventions are distributed across individuals when those effects are unobserved. Rather than focusing solely on average outcomes, the approach uses readily available information on average welfare responses to uncover meaningful patterns in how gains and losses are distributed across different populations. The framework is built around the concept of superquantile and applies to a broad class of models with unobserved individual heterogeneity. It enables policymakers to identify which groups are most adversely affected by a policy and to evaluate trade-offs between efficiency and equity. We illustrate the approach in three widely studied economic settings: price changes and compensated variation, treatment allocation with self-selection, and the cost-benefit analysis of social programs. In this latter application, we show how standard tools from the marginal treatment effect and generalized Roy model literature are useful for implementing our bounds for both the overall population and for individuals who participate in the program.