Wage endogeneity, tax evasion, and optimal nonlinear income taxation

• Date: 01 June 2020
• Published date: 01 June 2020
• Author: Firouz Gahvari,Luca Micheletto
• DOI: http://doi.org/10.1111/jpet.12424

J Public Econ Theory. 2020;22:501–531. wileyonlinelibrary.com/journal/jpet © 2020 Wiley Periodicals, Inc.

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501

Received: 26 September 2019

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Accepted: 8 December 2019

DOI: 10.1111/jpet.12424

ORIGINAL ARTICLE

Wage endogeneity, tax evasion, and optimal

nonlinear income taxation

Firouz Gahvari

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Luca Micheletto

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Department of Economics, University of

Illinois at Urbana‐Champaign, Urbana‐

Champaign, Illinois

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Department of Law, University of Milan,

Milan, Italy

Correspondence

Luca Micheletto, Department of Law,

University of Milan, Milan 20122, Italy.

Email: luca.micheletto@unimi.it

Abstract

This paper studies the interaction between tax evasion

and wage endogeneity within a Mirrleesian optimal tax

framework. It characterizes the optimal marginal income

tax rates on the skilled and the unskilled workers and the

optimal amount of resources to be spent on deterring tax

evasion. It shows that tax evasion weakens the incentives

for the government to manipulate the marginal tax rates

for the purpose of exploiting general equilibrium effects

on wages. Moreover, the extent of this depends on the

curvature of the evasion cost function. It also argues that

marginal income tax rates are likely to be higher when

the government attempts to deter evasion.

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INTRODUCTION

Nearly five decades has past since Allingham and Sandmo (1972) formulated the first formal

model of tax evasion in the economics discipline. A vast literature has since emerged expanding

the subject into numerous directions.

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One strand, to which this paper belongs, has sought to

integrate tax evasion into the optimal income tax literature with variable labor supply. What

distinguishes the current paper from the previous papers is that it allows for imperfect

substitutability between skilled and unskilled workers and the endogeneity of their wages.

Previous studies have followed the traditional optimal income tax models that assume wages

are exogenously determined.

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See, for example, Cremer, Marchand, and Pestieau (1990), Cremer and Gahvari (1994, 1996, 2000), and Slemrod and Yitzhaki (2002) for a survey.

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Even though Stiglitz (1982) included a section on wage endogeneity in his two‐group formulation of the optimum general income tax, the vast body of this

general literature has focused on the original Mirrleesian assumption of fixed wages. Stiglitz (1985), Naito (1999), Huber (1999), Pirttilä and Tuomala (2002),

Blackorby and Brett (2004), Micheletto (2004), Gaube (2005), Gahvari (2014), and Bastani, Blumkin, and Micheletto (2015) are among the exceptions.Starting

with Sandmo (1981), the contributors to the optimal income taxation literature in the presence of tax evasion have generally simplified the problem by

restricting the income tax schedule to be linear. Cremer and Gahvari (1996) and Schroyen (1997) have reconsidered the problem within the Mirrleesian general

income tax framework. However, all writers in this area have assumed that wages are constant. Thus far, to the best of our knowledge, nobody has considered

tax evasion within the general income tax framework that allows for wage endogeneity.

Endogeneity of wages matters and not just for its realism; it opens up a second channel for

redistribution. The change in the relative gross‐of‐tax wages, arising from government tax

policies, plays as important a factor in income distribution as taxation itself (which aims to

change the relative net‐of‐tax wages). These general equilibrium changes can very well reduce

the burden of distortionary redistributive taxes. The point is that highly increasing marginal

income tax rates leads to decreasing labor supplies of the higher‐skilled workers. In turn, this

will lead to an increase in the gross‐of‐tax wage rate of the higher‐skilled relative to lower‐

skilled workers. By opting for a less increasing marginal income tax rate schedule, one can

mitigate this perverse redistributive effect of taxation.

The difference that wage endogeneity makes for the optimal marginal income tax rates was

demonstrated by Stiglitz (1982, 1987) in his two‐group model. One was that a marginal income

subsidy on the high‐skilled agents replaces the no‐distortion‐at‐the‐top recommendation. Second,

while the marginal tax rate on the low‐skilled is always positive, its magnitude depends on the

elasticity of substitution between the two types of labor. The smaller the elasticity of substitution,

the larger should be the marginal tax rate—with the government increasingly relying on the

changes in the gross‐of‐tax wages to redistribute income. These modification to the characterization

of the optimal marginal income tax rates are meant to bring about an increase in the labor supply

ratio of the high‐skilled relative to the low‐skilled workers and a decrease in their relative wages.

This paper focuses on the implications of tax evasion for the optimal marginal income tax

rates, particularly the component that reflects the change in the relative gross‐of‐tax wages.

Prior studies on optimal taxation and tax evasion have neglected this specific question. To keep

things simple, we adopt the riskless approach to evasion introduced in the literature by Usher

(1986) and has since been used in a number of subsequent contributions.

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It assumes taxpayers

are able to fully avoid detection by incurring a cost that depends on the amount they misreport.

In this way, we can focus on the implication of tax evasion for the marginal income tax rates

that are exclusively due to the endogeneity of wages.

We append a production function, with skilled and unskilled workers as inputs, to the two‐

group model of Stiglitz. The inputs are imperfect substitutes so that wages of the two inputs are

determined endogenously. The economic environment is competitive and wages reflect the

value of marginal product. Specifying the evasion cost as a smooth convex function of

the amount of evaded income, we characterize the optimal marginal income tax rates faced by

the two types of workers. The first lesson we learn from this exercise is that tax evasion weakens

the incentives for the government to manipulate marginal income tax rates for the purpose of

exploiting general equilibrium effects on wages. The second lesson we learn is that the effect of

tax evasion on the optimal marginal income tax rates depends on the convexity of the

concealment cost function. The tax rate decreases as the cost function becomes less convex. Put

differently, the less convex is the concealment cost function (resulting in a higher amount of

evasion), the less labor supplies should be distorted. Loosely speaking, this arises because the

easier it is for agents to misreport their true income to the tax authority, the less effective the

marginal income tax rate becomes as an instrument for changing labor supplies.

As an extension, we allow the concealment costs to also depend on government expenditures

to deter evasion. We characterize the optimal amount that the government should spend on

deterrence and discuss how this changes our earlier results under a passive government.

Numerical exercises show that optimally spending resources to deter evasion strengthens the

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See, for example, Mayshar (1991), Boadway, Marchand, and Pestieau (1994), Kopczuk (2001), Slemrod (2001), Christiansen and Tuomala (2008), Chetty (2009),

Gahvari and Micheletto (2014), and Blomquist, Christiansen, and Micheletto (2016).

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