Optimal age‐dependent income taxation in a dynamic extensive model: The case for negative participation tax on young people

• Published date: 01 September 2020
• Author: Yoshihiro Takamatsu,Takao Kataoka
• Date: 01 September 2020
• DOI: http://doi.org/10.1111/jpet.12421

J Public Econ Theory. 2020;22:1338–1367.wileyonlinelibrary.com/journal/jpet1338

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© 2019 Wiley Periodicals, Inc.

Received: 27 May 2019

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Accepted: 2 December 2019

DOI: 10.1111/jpet.12421

ORIGINAL ARTICLE

Optimal age‐dependent income taxation in a

dynamicextensivemodel:Thecasefornegative

participation tax on young people

Takao Kataoka

1

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Yoshihiro Takamatsu

2

1

Faculty of Commerce, Waseda

University, Tokyo, Japan

2

Department of Economics, Faculty of

Humanities and Social Sciences,

Shizuoka University, Shizuoka, Japan

Correspondence

Yoshihiro Takamatsu, Department of

Economics, Faculty of Humanities and

Social Sciences, Shizuoka University,

836 Ohya, Suruga‐ku, Shizuoka

422‐8529, Japan.

Email: takamatsu.yoshihiro@shizuoka.

ac.jp

Funding information

Japan Society for the Promotion of

Science, Grant/Award Numbers:

15K17073, 19K01717

Abstract

We consider optimal age‐dependent income taxation in a

dynamic model where the labor‐leisurechoiceisthe

extensive margin, each household faces idiosyncratic

shocks to labor productivity and a pecuniary cost to work,

and there is no insurance market against the shocks. We

show that the well‐known property of the optimal

participation tax rate in the static model continues to hold

in our dynamic economy, that is, the participation tax rates

for some income groups with low consumption are likely

negative. In dynamic models, the optimal participation tax

rate depends on age and on labor income. Our numerical

simulations suggest that a negative participation tax should

be restricted to young households.

1

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INTRODUCTION

The optimal income taxation literature has developed models to analyze the design of income

tax/transfer programs. Following the seminal paper of Mirrlees (1971), many studies have

focused exclusively on the intensive labor margin; in other words, households choose their

hours of work or intensity of work. In such a framework, negative marginal tax rates can never

be optimal, ruling out in‐work credits.

Much recent literature has emphasized the role of the extensive margin. In the extensive labor

margin, households choose whether or not to participate in the labor force, with fixed hours of work.

In this setting, it can be optimal to adopt wage subsidies or in‐work credits, with a negative

participation tax for low‐income households (see e.g., Christiansen, 2015; Choné & Laroque, 2005,

2011; Diamond, 1980; Jacquet, Lehmann, & Van der Linden, 2013; and Saez, 2002).

1

1

Jacquet et al. (2013) and Hansen (2018) consider a model with both intensive and extensive margin. Ndiaye (2018) also investigate a life‐cycle model with an

intensive and extensive (endogenous retirement) margin.

Although these studies have provided influential findings, with both theoretical and policy

implications, a large part of the literature is static and does not directly address the

intertemporal side of the problem. A few studies employ dynamic models with an extensive

labor margin (see Laroque, 2011 and Choné & Laroque, 2017). They investigate an age‐

independent, nonlinear labor income tax/transfer in a stationary life‐cycle model with a perfect

insurance market. Laroque (2011) analytically derives the properties of an optimal tax system

and shows that a worker faces a negative participation tax rate if the worker’s social weight with

respect to lifetime permanent income is larger than the average.

2

Under the stationary

assumption, the distributions of productivity and cost to work are constant over time, and the

correlation between current and permanent income becomes a central problem.

3

Because they

also assume a perfect insurance market, personal events, such as illness or accidents, are fully

insured by the private financial market. The main objective of the government in their model is

redistribution among households that have different permanent incomes at birth, which solely

determine their social weight. Therefore, Laroque (2011) and Choné and Laroque (2017) focus

analysis on an optimal age‐independent taxation. The main purpose of our study is to explore

both the qualitative and the quantitative properties of optimal age‐dependent, nonlinear labor

income tax, without a perfect insurance market.

Recent dynamic Mirrlees literature (see Kocherlakota, 2010) examines intertemporal shocks

on labor productivity and preferences mainly in the intensive labor margin. With regard to the

extensive margin, Diamond and Mirrlees (1978) and Golosov and Tsyvinski (2006) examine

permanent disability shocks. Here, once a worker is disabled, labor status is no longer a matter

of choice. In contrast, the shocks can be temporary and a household decides whether to

participate in the labor market in each period in our model. It is important to examine these

shocks because a household that decides not to work in a period for some reason (e.g., bad

health, involuntary unemployment, or lack of ability) may change its labor status and return to

work in another period.

The results from dynamic Mirrlees literature show that an optimal income tax policy with

shocks must be history‐dependent. The history‐dependent nature is, however, complicated and

rare in the real world. We focus solely on the role of age‐dependent income taxation to consider

a more relevant policy system, which rules out the possibility of implementing a full optimal

allocation.

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As the seminal paper of Akerlof (1978) points out, some exogenously observable

characteristics are correlated with productivity or earnings. These “tagging”schemes reduce the

cost of income redistribution and enhance welfare. Age is one of the most relevant candidates

for this tagging scheme because it is easily observed by the government, and the average and the

variance of the income distribution could be correlated with age.

Several studies have analyzed age‐dependent income taxation. Using a static model,

Kremer (2002) shows that young workers should face lower marginal tax rates than older

workers do. In a dynamic homogeneous agent model, Erosa and Gervais (2002) and

Lozachmeur (2006) show an age‐dependent income taxation is optimal.

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In a dynamic

2

Laroque (2011) also examines the usefulness of a complemental positive linear tax on wealth.

3

As noted in Laroque (2011), a perfect correlation between current and permanent income would make the static and the dynamic model equivalent.

4

Some papers consider labor income tax combined with other supplemental instruments to implement the optimal allocation. For example, Grochulski and

Kocherlakota (2010) show that the optimal allocation can be implemented through a combination of a tax on current labor income until retirement, a

retrospective capital income tax only at retirement that is dependent on labor income history, and a history‐contingent payment after retirement. Michau (2014)

shows that the optimal allocation can be implemented by a history‐dependent social security system in a life‐cycle model with both intensive and extensive

(retirement) margins and without skill shocks.

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Lozachmeur (2006) incorporates education, the retirement age, and borrowing constraints in the life‐cycle model.

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