A general theory of inverse welfare functions

This paper develops a general theory to recover the inverse welfare function that rationalizes a given tax schedule as optimal. Our theory allows for complex environments including the presence of multidimensional tax schedules, bunching/jumping behavior, optimization frictions, general equilibrium effects, and externalities. We show that inverse welfare functions can be used to test for Pareto efficiency, construct Pareto improving reforms, and characterize the set of welfare improving local reforms, thereby extending previous results to more general environments. We show numerically that allowing for such generalities can have meaningful impacts on inverse welfare functions.