Optimal Income Taxation with Risky Earnings: A Synthesis

• Published date: 01 December 2015
• Author: ROBIN BOADWAY,MOTOHIRO SATO
• DOI: http://doi.org/10.1111/jpet.12120
• Date: 01 December 2015

OPTIMAL INCOME TAXATION WITH RISKY EARNINGS:

AS

YNTHESIS

ROBIN BOADWAY

Queen’s University

MOTOHIRO SATO

Hitotsubashi University

Abstract

We study optimal nonlinear income taxation when earnings

can differ because of both ability and luck, so the income

tax has both a redistributive role and an insurance role. A

substantial literature on optimal redistribution in the ab-

sence of risk has evolved since Mirrlees’s original contribu-

tion. The literature on the income tax as a social insurance

device is more limited. It has largely assumed that house-

holds are ex ante identical so unequal earnings are due to

risk alone. We provide a general treatment of the optimal

income tax under risk when households differ in ability. We

characterize optimal marginal tax rates and interpret them

in terms of redistribution, insurance, and incentive effects.

Thecaseofex ante identical households and the no-risk case

with heterogeneous abilities come out as special cases.

1. Introduction

Redistributive income taxation serves to mitigate the social welfare conse-

quences of market-generated inequalities in earnings. These inequalities

can be characterized as having two different sources. As emphasized in the

Robin Boadway, Department of Economics, Queen’s University, Kingston, ON, K7L3N6,

Canada (boadway@econ.queensu.ca). Motohiro Sato, Graduate School of Economics,

Hitosubashi University, Kunitachi, Tokyo 186-8601, Japan (satom@econ.hit-u.ac.jp).

We thank Bas Jacobs, Chris Sanchirico, and Dirk Schindler for helpful comments. An

associate editor and two referees provided many careful comments and constructive sug-

gestions. Financial support of the Social Sciences and Humanities Research Council of

Canada (Boadway) and of Grants-in-Aid for Scientific Research of the Japan Society for

the Promotion of Science (Sato) are gratefully acknowledged.

Received February 11, 2014; Accepted February 12, 2014.

C2014 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 17 (6), 2015, pp. 773–801.

773

774 Journal of Public Economic Theory

traditional optimal income tax literature following from Mirrlees (1971),

they can be a result of differences in the endowed ability or productivity of

households. The inability of the government to observe each household’s

ability constrains the benevolent government from achieving a first-best out-

come, and limits considerably the progressivity of the tax system. Alterna-

tively, as Varian (1980) and Tuomala (1984) studied, inequality might be a

result of riskiness in the earnings obtained from a given effort. In the ab-

sence of market-provided earnings insurance, the income tax system acts as

a social insurance device, albeit an imperfect one because of the inability of

the government to observe individual effort, a sort of moral hazard. Here,

too, progressivity will be compromised by imperfect information. If the gov-

ernment were fully informed and earnings risk were the only source of in-

equality, the tax system would mimic full insurance and have 100% marginal

tax rates, which would be highly progressive indeed. The inability to observe

individual effort precludes that, and, as in the optimal income tax case, con-

strains progressivity considerably.1

The design of optimal redistributive taxation to address ability differ-

ences and to address earnings risk have largely been studied separately. The

former literature is vast, and is summarized in Atkinson and Stiglitz (1980),

Tuomala (1990), Myles (1995), and Kaplow (2008). Given the complexity

of the modeling, simulation techniques are usually relied on to shed light

on the optimal income tax structure. Early results in Mirrlees (1971) and

Tuomala (1990) found optimal marginal tax rates that are relatively constant

or slightly hump-shaped except at the two ends of the ability distribution,

where they fall to zero. However, the pattern changes with different assump-

tions about preferences, the skill distribution, and the aversion to inequality

of the government. For example, Diamond (1998) obtained a U-shaped pat-

tern of marginal tax rates above the mode when the skill distribution was

unbounded and Pareto, and preferences were quasilinear in consumption.

With maximin social preferences, Boadway and Jacquet (2008) obtained a

strictly concave tax function, implying decreasing marginal tax rates.

The literature on optimal income taxation to deal with earnings risk

is more limited, and has generally assumed away ability differences. Thus,

Tuomala (1984), Low and Maldoom (2004), and Henriet, Pintus, and Tran-

noy (2012) assume that all households are ex ante identical, so supply the

same amount of labor, but differ in earnings because of some innate idiosyn-

cratic risk that is resolved after labor is supplied. Tuomala’s (1984) simula-

tion analysis seems to indicate that the optimal degree of progressivity to

address earnings risk is qualitatively comparable to that found by Mirrlees

1A third source of earnings inequality we do not consider arises from differences in pref-

erences for work among households. This raises difficult issues with respect to how social

preferences should treat persons with different preferences, summarized in Fleurbaey and

Maniquet (2006, 2007, 2011). Different views on that can change redistribution policy sig-

nificantly, as illustrated in Boadway, Marchand, Pestieau, and Racionero (2000) and Cuff

(2000).