Abstract

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 individuals 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 additional “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 simulate 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.

Highlights

  • The canonical Mirrlees (1971) optimal income taxation problem examines how to best redistribute labor income among a population of individuals who differ only in terms of how productive they are

  • While it turns out to be impossible to rule out the existence of individuals with multiple optima when we have multiple dimensions of heterogeneity, with one dimension of heterogeneity, we can rule out individuals having multiple optimal income levels

  • 34We found that small changes in the tax schedule which cause individuals to jump were not handled well numerically. 35Any tax schedule we find to be optimal within the class of functions that are smooth except at multiple optimal income levels so that the optimal tax schedule is everywhere twice continuously differentiable

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Summary

Introduction

The canonical Mirrlees (1971) optimal income taxation problem examines how to best redistribute labor income among a population of individuals who differ only in terms of how productive they are. The fundamental challenge with extending the results from Mirrlees’s optimal tax problem to settings where individuals differ on many (unobservable) dimensions is the possibility that some individuals have multiple optimal income levels under the optimal tax schedule.. If some individuals have multiple optimal income levels, these individuals will not respond smoothly to a small variation in the tax schedule; instead, they will “jump” between their initially optimal income levels, which complicates the analysis of optimal taxation. While we will show that, under standard assumptions, one can rule out the possibility that individuals have multiple optimal income levels when they differ only in terms of how productive they are, we show that it is, in general, impossible to rule out the presence of individuals with multiple optima when heterogeneity is multidimensional The optimal income taxation literature (both in settings with unidimensional agent heterogeneity and with multidimensional agent heterogeneity) has assumed away the presence of individuals with multiple optimal income levels. While we will show that, under standard assumptions, one can rule out the possibility that individuals have multiple optimal income levels when they differ only in terms of how productive they are, we show that it is, in general, impossible to rule out the presence of individuals with multiple optima when heterogeneity is multidimensional

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