Taxation of capital income in overlapping generations economies

• Author: Torben M. Andersen
• Published date: 01 September 2020
• DOI: http://doi.org/10.1111/jpet.12437
• Date: 01 September 2020

J Public Econ Theory. 2020;22:1245–1261. wileyonlinelibrary.com/journal/jpet © 2020 Wiley Periodicals, Inc.

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1245

Received: 22 August 2019

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Accepted: 16 February 2020

DOI: 10.1111/jpet.12437

ORIGINAL ARTICLE

Taxation of capital income in overlapping

generations economies

Torben M. Andersen

Department of Economics and Business

Economics, Aarhus University CEPR,

CESifo and IZA, Aarhus, Denmark

Correspondence

Torben M. Andersen, Department of

Economics and Business Economics,

Aarhus University CEPR, CESifo and IZA,

Aarhus 8210, Denmark.

Email: tandersen@econ.au.dk

Funding information

Independent Research Fund Denmark,

Grant/Award Number: DFF –6109‐00043

Abstract

Whether capital income should be taxed in overlapping

generations economies is vividly discussed. It is shown

that intergenerational lump‐sum taxes cannot imple-

ment the Golden Rule allocation when agents have

private information on their earnings potential. Hence,

the seminal Atkinson–Stiglitz result that optimal in-

come taxation pre‐empts any role for indirect taxation

cannot be interpreted to imply that capital income

taxation (affecting intertemporal relative prices) should

not be taxed. Specifically, capital income should un-

ambiguously be taxed in small open economies, and the

optimal tax rate depends inversely on the elasticity of

total savings to disposable income and the after‐tax rate

of return.

1|INTRODUCTION

Whether capital income should be taxed is a contested issue. With infinitely lived households,

Chamley (1986)andJudd(1985) show that the optimal tax structure has a zero tax on capital

income in the long run, leaving government activities to be financed by distortionary taxes on labor

income (and the return on accumulated assets). A capital income tax is essentially an implicit tax on

future consumption which is increasing the further into the future the consumption is planned.

Under standard assumptions, distortions would increase over time, implying that they are not

minimized. Hence, the optimal capital income tax is zero.

1

1

Capital income taxation has been considered in incomplete‐market heterogeneous‐agents infinite horizon economies.

Aiyagari (1995) showed how incomplete insurance markets and borrowing constraints lead to precautionary savings,

which in turn causes overaccumulation of capital (dynamic inefficiency). A tax on capital can reduce this problem, and

may therefore, be justified on welfare grounds. A number of contributions have extended and considered the robustness

of this result; see for example, Gottardi, Kajii, and Nakajima (2015), Chen, Chien, and Yang (2017), and Chien and

Yang (2017).

In life‐cycle models

2

it has similarly been argued that capital income should not be taxed. This

conclusion is based on a seminal contribution by Atkinson and Stiglitz (1976) on direct and indirect

taxation of income. Specifically, they consider a government with distributional objectives and a need

to finance some public sector activities in a setting with endogenous labor supply and an exogenous

distribution of earnings capabilities (private information).

3

They show that under the optimal

nonlinear income tax, there is no role for indirect taxation (commodity taxation), only labor income

should be taxed. This result has been reinterpreted to hold in a temporal setting, for example, in a

two‐period model. A capital income tax distorts the relative price between current and future

consumption. It is thus a direct corollary of the Atkinson and Stiglitz (1976)resultthatthereisno

rationale for a capital income tax if the optimal nonlinear labor income tax is implemented. Or

phrased differently, there is no welfare gain from distorting the intertemporal consumption allocation

if income taxes are set optimally. Later contributions have shown that richer environments may leave

a case for positive capital income taxation; see for example, Banks and Diamond (2010), Cremer and

Pestieau (2018), P. Diamond (2009), P. Diamond and Spinnewijn (2011), and Stiglitz (2015).

The implicit reasoning in the work cited above is that results from two‐period models also hold

in an overlapping generations setting. Although agents in both settings have a finite horizon, there

is a fundamental difference due to the explicit overlap of generations in the latter. Moreover, the

welfare effects of policies are subtle in overlapping generations economies where the standard

efficiency results do not hold. In the empirically relevant case where the market rate of return

exceeds the biological rate of return (Samuelson, 1958)—the case of dynamic efficiency—there is

“undersaving.”In competitive equilibrium, the steady state level of the capital ratio falls short of the

Golden Rule level, maximizing steady state welfare; see Diamond (1965).

The seminal contribution by Atkinson and Sandmo (1980) considers whether capital income

should be taxed in a representative agent overlapping generations setting and concludes that it

depends on the available set of policy instruments. If (intergenerational) lump‐sum taxation

4

is

possible, the Golden Rule savings level can be implemented, and there is no welfare justification

(steady state welfare) for a capital income tax.

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When such intergenerational lump‐sum taxes

are unavailable, there is in general a case for taxation of capital income, but whether the

tax should be positive or negative (subsidy) is ambiguous. In the case of log‐utility and a

Cobb–Douglas production function, they show thatcapitalincomeshouldbetaxed,sinceit

would increase savings, but “… this is a special feature of the particular example”(Atkinson and

Sandmo, 1980, p. 543). Hence, no general results or intuition as to whether capital income should be

taxed are presented. In the literature the finding that (intergenerational) lump‐sum taxes can im-

plement the Golden Rule allocation has been explicitly or implicitly used as justification for inter-

preting results from a two‐period setting as holding in an overlapping generations setting,

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and that

capital income taxation is not required to solve any “undersavings”problem.

2

While the literature has mainly featured infinitely lived household models or two‐period models, Conesa, Kitao, and

Krueger (2009) and Krueger and Ludwig (2018) are exceptions presenting overlapping generations models. Both papers

focus on the role of uninsurable risk for the determination of the optimal taxation scheme.

3

Importantly, Atkinson and Stiglitz (1976) assume preferences to be separable between consumption and leisure.

4

It is well known in the literature that there is an equivalence between lump‐sum taxes (pensions) and debt; that is, any

feasible equilibrium path involving public debt can be decentralized by appropriately designed lump‐sum taxes on

different cohorts; see for example, P. A. Diamond (1973), Gale (1990), and de la Croix and Michel (2002; Ch. 4).

5

In passing, note that intergenerational transfers have been extensively studied in the pensions literature. A flat rate

PAYG pension is a transfer from the young to the old, and it is well known that there is no welfare case for a positive

pension in a dynamically efficient economy; see Aaron (1966).

6

See for example, the references given above and Auerbach and Hines (2002), Cremer, Pestieau, and Rochet (2003), and

Kaplow (2011).

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ANDERSEN