Nonlinear taxation of income and education in the presence of income‐misreporting

• Published date: 01 August 2023
• Author: Spencer Bastani,Firouz Gahvari,Luca Micheletto
• Date: 01 August 2023
• DOI: http://doi.org/10.1111/jpet.12634

Received: 5 April 2022

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Accepted: 14 November 2022

DOI: 10.1111/jpet.12634

ORIGINAL ARTICLE

Nonlinear taxation of income and education

in the presence of income‐misreporting

Spencer Bastani

1,2,3

|Firouz Gahvari

4

|Luca Micheletto

5,6

1

Institute for Evaluation of Labour

Market and Education Policy (IFAU),

Uppsala, Sweden

2

UCFS, UCLS, Uppsala, Sweden

3

Research Institute of Industrial

Economics (IFN), Stockholm, Sweden

4

Department of Economics, University of

Illinois at Urbana‐Champaign,

Champaign, Illinois, USA

5

Department of Law, University of Milan,

Milan, Italy

6

Dondena Centre for Research on Social

Dynamics and Public Policy, Bocconi

University, Milan, Italy

Correspondence

Luca Micheletto, Department of Law,

University of Milan, Milan, Italy.

Email: luca.micheletto@unimi.it

Abstract

We study the joint design of nonlinear income and

education taxes when the government pursues

redistributive objectives. A key feature of our setup is

that the ability type of an agent can affect both the

costs and benefits of acquiring education. Market

remuneration of agents depends on both their innate

ability type and their educational choices. Our focus is

on the properties of constrained efficient allocations

when educational choices are publicly observable at

the individual level, but earned income is subject to

misreporting. We find that income‐misreporting (IM)

affects the optimal distortions on income and educa-

tion and shed light on the reasons for it and

mechanisms through which it is done. We show how

and why IM strengthens the case for downward

distorting the educational choices of low‐ability agents.

Finally, we find that IM provides another mechanism

that makes commodity taxation useful.

1|INTRODUCTION

The contributions growing out of Mirrlees' (1971) seminal paper on optimal income taxation have

mostly assumed that an individual's productivity or wage rate is exogenously given. More recently,

however, comparatively small literature has analyzed optimal redistributive taxation in settings

with endogenous wages. These contributions may be divided roughly into three strands. One strand

J Public Econ Theory. 2023;25:679–726. wileyonlinelibrary.com/journal/jpet

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This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial License, which permits use,

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© 2022 The Authors. Journal of Public Economic Theory published by Wiley Periodicals LLC.

maintains the assumption of perfect competition in the labor market and generates wage

endogeneity by treating workers of different skill type as separate inputs that are imperfectly

substitutable in the production function.

1

A second strand generates wage endogeneity by

introducing frictions in the labor market that may either be due to imperfect competition or to

problems of asymmetric information between workers and employers.

2

The third strand

endogenizes wages by allowing for the possibility to invest in productivity‐enhancing education.

3

Within this last strand, a number of contributions assume that educational attainment is

publicly observable at the individual level and thus can be taxed nonlinearly. These studies

have greatly enhanced our understanding of what determines the direction of the optimal

distortion on the educational choices of agents. Yet, while they differ in many aspects, they all

maintain the Mirrleesian assumption of public observability of earnings. This makes nonlinear

taxation of both incomes and educational expenditures possible. However, in reality, income‐

misreporting (IM) is often a relevant phenomenon—a fact that might very well undermine the

efficacy of the income tax in achieving redistribution.

The distinctive feature of our contribution lies in the recognition that agents can conceal

part of their earned income for tax purposes. Our main goal is to investigate if, and how, the

optimal distortion on agents' educational choices varies depending on whether or not earned

income is perfectly observable by the government at the individual level. And, to simplify our

analysis, we model IM following the so called riskless approach pioneered by Usher (1986).

As a vehicle for our study, we set up a two‐type optimal income tax model (à la Stern, 1982 and

Stiglitz, 1982) where an agent's productivity depends on his type (innate ability), and on the amount

of education he acquires. To attain a given amount of education, agents incur an effort cost which is

type‐dependent (in addition to monetary cost of education).

4

We characterize the properties of an

informationally constrained Pareto‐efficient tax policy, focusing on the so‐called “normal”case

where the direction of redistribution goes from the high‐to the low‐ability type.

Ourmainresultscanbesummarizedasfollows.First,whenanagent'sproductivityorwage

depends only on his education level and not directly on his type (i.e., the effect of one's type is

channeled only indirectly through the education level he chooses), IM does not affect the qualitative

properties of an optimal tax policy. Whether earned income is perfectly observable at the individual

level or not, all agents—high‐and low‐ability alike—faceazeromarginalincometaxrate.Tax

treatment of educational attainment, on the other hand,is not the same. Its choice is left undistorted

for high‐ability agents but downward distorted for low‐ability agents.

Second, in the more general case wherein an agent's productivity or wage depends directly

on both his type and educational attainment, IM does not change the characterization and the

sign of the marginal income tax rate faced by low‐ability agents (which should be positive), and

high‐ability agents (which should be zero). It also leaves unscathed the result that education

1

See, for example, Stiglitz (1982,1987), Allen (1987), Naito (1999), Pirttilä and Tuomala (2002), Blackorby and Brett (2004), Gaube

(2005), and Gahvari (2014).

2

See, for example, Aronsson and Sjögren (2003,2004), Hungerbühler et al. (2006), Kessing and Konrad (2006), Bastani et al. (2015), and

Aronsson and Micheletto (2021).

3

See, for example, Ulph (1977), Tuomala (1986), Brett and Weymark (2003), Bovenberg and Jacobs (2005), Blumkin and Sadka (2008), da

Costa and Severo (2008), Maldonado (2008), Jacobs and Bovenberg (2011), Guo and Krause (2013), Findeisen and Sachs (2016,2018),

and Stantcheva (2017).

4

The idea of an agent's “type”as a multidimensional characteristic which affects both a person's productivity and a person's cost of

acquiring education resonates with the concluding remarks in Hellwig (2008, p. 8): “… it makes sense to think of both the productivity of

an agent with education level

e

and the cost of achieving this education level as being unobservable, determined by one or several

hidden characteristics. The question then should be how these two information problems interact and how this interaction affects

optimal utilitarian taxation. Recognizing this as an issue provides a good basis for further research on the respective roles of

heterogeneities in productivities and in education costs.”

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should be undistorted for high‐ability agents. However, compared with a setting where earned

income is perfectly observed by the government at the individual level, it strengthens the case

for a downward distortion on the educational choice of low‐ability agents. We will explore the

various factors that are behind this later in the paper. However, it is worth pointing out here

that, with or without IM, education provides another instrument for making “mimicking”less

attractive (making the preferred choice of the low‐ability agents less desirable to high‐ability

agents), thus allowing more redistribution to low‐ability agents.

Third, in the general case wherein an agent's productivity depends directly on his type, IM

implies that consumption taxation is no longer a redundant policy instrument. We thus

reconsider our results by assuming that a linear consumption tax is used alongside a joint

nonlinear tax on education and reported income. Under this scenario, it becomes desirable to

let high‐ability agents face a negative marginal tax on reported income and also to distort

upwards their educational choice. For low‐ability agents, consumption taxation exerts a

moderating effect on the optimal marginal tax on reported income. It also generates a

mitigating effect on the tendency, attributable to the possibility of IM, to warrant a downward

distortion on the educational choice of low‐ability individuals.

The paper is related to a diverse body of literature in public economics.

(i)Tax evasion. Most of the early evasion literature, following the seminal contribution by

Allingham and Sandmo (1972), assumes that decisions about IM involve risk. Evasion may be

detected with some probability, for instance due to random audits by the tax authorities, in

which case a sanction applies (see, e.g., Cremer et al., 1990;Cremer&Gahvari,1994,1996;

Schroyen, 1997). The riskless approach to evasion, introduced in the literature by Usher (1986),

assumes that taxpayers are able to fully avoid detection by incurring a cost that depends on the

amount they misreport. The cost function may be implicitly assumed to capture some of the

elements from the uncertainty model, for instance to make the cost higher the more extensive

is the auditing activity of the tax collector. As in the uncertainty case, there is a trade‐off

between the gain from lowering the tax by IM and the cost incurred, which ismodeled as a

pure concealment cost. Following the contribution by Usher (1986), the riskless approach has

been used in a number of subsequentcontributions(e.g., Mayshar, 1991; Boadway et al., 1994;

Kopczuk, 2001;Slemrod,2001; Christiansen & Tuomala, 2008; Chetty, 2009;Gahvari&

Micheletto, 2014; Gerritsen, 2021).

(ii)Redistributive role of education policy. Beginning with Arrow (1971), a large body of

public economics literature has investigated the redistributive role of education policy.

Earlier contributions, including Arrow (1971), Green and Sheshinski (1975), and Bruno

(1976), left aside asymmetric information problems and assumed that the government

could observe an individual's type. The main goal of these contributions was to

characterize the optimal allocation of a given amount of educational expenditure amongst

a population of individuals of different ability. Considering the educational policy in

isolation, or assuming an exogenously given income tax schedule, these papers could not

shed light on the relative merits of tax‐and expenditure policy for redistributive purposes.

(iii)Interaction of income redistribution and educational policy. Ulph (1977) and Hare and

Ulph (1979) developed Bruno's work on the interaction of income redistribution and

educational policy by allowing both types of policies to be simultaneously optimized.

However, they retained the assumption that the ability to benefit from education is

observed by the education authorities. Relaxing this assumption, and assuming that a

nonlinear income tax is the only government's policy instrument, Tuomala (1986)

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