Optimal taxation with multiple dimensions of heterogeneity

This paper develops a general theory of optimal income taxation with multiple dimensions of agent heterogeneity. The main technical hurdle in developing this theory is the possibility that individuals have multiple optimal incomes. Using a perturbation approach, we derive optimal tax formulas that account for the possibility that individuals have multiple optima and, hence, account for the possibility that indi-viduals jump between their optimal income levels when we perturb the tax schedule. We quantify the magnitude of these effects, thereby augmenting the optimal tax formulas from Saez (2001) with addi-tional "jumping effect" terms. We provide a partial characterization of when individuals with multiple optimal incomes may exist under the optimal tax schedule. Finally, we derive a new methodology to sim-ulate optimal income tax schedules with multidimensional heterogeneity. We implement this method numerically, showing that individuals with multiple optimal income levels can exist under the optimal tax schedule. (c) 2021 Elsevier B.V. All rights reserved.