Optimal nonlinear taxation of income and savings without commitment

• Published date: 01 February 2019
• Author: Craig Brett,John A. Weymark
• DOI: http://doi.org/10.1111/jpet.12328
• Date: 01 February 2019

5

Journal of Public Economic Theory. 2019;21:5–43. wileyonlinelibrary.com/journal/jpet © 2018 Wiley Periodicals, Inc.

Received: 13 December 2017 Accepted: 3 July 2018

DOI: 10.1111/jpet.12328

ARTICLE

Optimal nonlinear taxation of income and savings

without commitment

Craig Brett1John A. Weymark2

1Departmentof Economics, Mount Allison Uni-

versity,New Brunswick, Canada

2Departmentof Economics, Vanderbilt Univer-

sity,Nashville, Tennessee

Correspondence

JohnA. Weymark, Department of Economics,

VanderbiltUniversity,VU Station B #351819,

2301Vanderbilt Place, Nashville, TN 37235-

1819.

Email:john.weymark@vanderbilt.edu

Abstract

When a government is unable to commit to its future tax poli-

cies, information about taxpayers'characteristics revealed by their

behavior may be used to extractmore taxes from them in the future.

We examine the implications of this ratchet effect for the design of

redistributive income and savings tax policies in a two-period model

with two types of individuals who only differ in their skill levels.

When commitment is not possible, it may be optimal to separate,

pool, or partially pool different types in period one. The nature of the

distortions to labor supplies and savings are investigated for each of

thesethree regimes. The identification of the optimal regime is inves-

tigated numerically.

KEYWORDS

asymmetric information, commitment, optimal income taxation,

ratchet effect, savings taxation

JEL CLASSIFICATION:

D82, H21

1INTRODUCTION

Ever since the pathbreaking work of Mirrlees (1971), a government's lack of full information about the tax-relevant

characteristics of those subject to its taxation authority has been viewed as a fundamental constraint on the design

of tax policy. In the context of redistributive nonlinear income taxation, a government's egalitarian intentions may

be hampered by its inability to identify the labor productivities of different taxpayers (their “types”).1The asymmet-

ric information approach to taxation was originally developed for atemporal environments. A major impediment to

extending the Mirrlees model to dynamic settings is that information revealedby taxpayers in one period can be used

by the government in subsequent periods. Aware of this possibility, rationaltaxpayers may modify their behavior in

early periods in an attempt to better conceal their characteristics. In particular, more able taxpayers might fear the

ratchet effect (Roberts, 1984; Weitzman, 1980), whereby the government may use anyknowledge revealed by their

behavior to extract more taxes from them in the future. The ratchet effect would not arise if the governmentcould

1SeeTuomala (2016) for an introduction to optimal nonlinear income taxation using the Mirrlees framework.

2BRETT AND WEYMARK

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commit to forgetting any information it learns at the beginning of each new tax year.However, such a commitment is

not credible and therefore the optimal tax schedule with commitment is time inconsistent.2

In this article, we investigatethe implications for redistributive tax policy of a government's inability to commit to its

future actions. In particular,we focus on how individual decisions are distorted at the margin. We consider an economy

inwhich a continuum of individuals of two productivity types work and consume in each of two periods. Individuals may

also transfer resources forward in time through saving. A utilitarian governmentoptimally chooses nonlinear taxes on

income and savings in a dynamically consistent way taking into account the budget and incentive constraints that it

faces. Thus, the government is unable to commit to its second-period tax policy in advance, and so any information

about individual productivities revealed in the first period can be used when designing second-period taxes. Equiva-

lently, the governmentsets a joint tax on income and savings based on all observable variables up to the time period

in question.3The dependence of second-period taxes on information revealed through behavior in the first period is

rationally anticipated by the taxpayers. As is the case with the government, individuals cannot make commitments

about second-period behavior in the first period.

In order to focus on the interactionbetween information revelation and redistribution, we set aside the social insur-

ance motive for taxation by assuming that productivities do not change over time.4We also assume that the prefer-

ences of individuals are additively separable both across time and between consumption and leisure. An implication of

the Atkinson–Stiglitz (1976) Theorem is that these preference separability assumptions imply that there is no value to

supplementing an optimal nonlinear income tax with savings taxation when the government can commit to its future

tax policies. Weshow that in the absence of this commitment, taxing or subsidizing savings helps to mitigate the distor-

tions in the labor market. Other policy instruments can also serve this purpose. Forexample, Boadway, Marceau, and

Marchand (1996) show that mandating a minimum amount of time spent in publicly observable education is such an

instrument.

Laffont and Tirole (1987) show that the design of an optimal two-period incentive contract without commitment is

complicated by the fact that there may be different kinds of optima depending on which of the incentive constraints

bind in the first period. The same is true here. In a two-type atemporal model of nonlinear income taxation with a util-

itarian objective, it is optimal for the incentive constraint of the high skilled to bind and that of the low skilled to be

slack. This need not be the case in the first period in our dynamic tax problem. Although it is always optimal for at least

one of the first-period incentive constraints to bind, it could be that either or both of them do so. With a separating

regime, type information is revealed in the first period. Separation is consistent with either one or both of the first-

period incentive constraints binding. If they both bind and both types make the same first-period choices, we havea

pooling regime in which type information remains hidden for all individuals after the first period. If a type has a binding

first-period incentive constraint, it ispossible for some, but not all, individuals of this type to reveal their type informa-

tion in the first period, with the other individuals of this type mimicking the behavior of the other type. In this case, the

regime is one of semi-pooling.5

There are three kinds of separating regimes and three kinds of semi-pooling regimes; each of them is distinguished

by which of the first-period incentive constraints bind. The optimal regime depends on a discrete comparison among

the best tax policies for each of the possible regimes. Such a comparison requires additional assumptions about the

2Thereis a vast literature on the time consistency of economic policies beginning with the seminal work of Kydland and Prescott (1977).

3Conditioning taxes on both current and past values of the variables in the tax base is a feature of actual tax practice.For example, as Kocherlakota (2006,

p.269) notes, the alternative minimum tax and the carry-forward of certain deductions introduce history dependence in the U.S. tax code. Likewise, in Canada,

informationabout behavior in previous tax years is used in setting limits for contributions to tax-deferred savings schemes.

4The role that taxation plays in providing social insurance has been a major focus of the “new dynamic public finance” literature surveyed by Golosov and

Tsyvinski(2015), Golosov, Tsyvinski, and Werning (2007), and Kocherlakota(2006, 2010). With some exceptions, this literature assumes that governments

cancommit in advance to their future tax policies. When there is no government commitment and individual productivities are stochastic over time, types may

neverbe known with certainty, thereby attenuating the ratcheteffects that are exhibited when types are unchanged over time. See, for example, Battaglini and

Coate(2008) and Golosov and Iovino (2015). If there is savings taxation, as Bisin and Rampini (2006) show, the power of the government to take advantageof

informationrevealed can be somewhat mitigated if individuals have access to capital markets that prevent the government from observing their total savings.

5Semi-poolingallows the government to implement allocations that would otherwise not be feasible. Ruling out semi-pooling a priori amounts to a restriction

onthe feasible allocations in addition to the materials balance and incentive constraints.

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functional form of the utility function or about the values of the parameters that appear in the model. We explorethe

issue of identifying the globally optimal regime numerically in an example with a Cobb–Douglas utility function. In a

model similar to our own, Guo and Krause (2015) also use numerical analysis to determine the optimal regime.

Space considerations preclude providing a detailed analysis of how the individual decisions are distorted for every

one of the possible regimes. For this reason, in our formal analysis of the optimal distortions, we restrict attention to

the cases in which either there is pooling or only the incentiveconstraint of the high skilled binds in the first period. We

focus on these cases for two reasons. First, in our numerical analysis of the Cobb–Douglas example, we never find an

instance in which the first-period incentive constraint of the low skilled binds exceptwhen there is pooling. Second, it

is optimal for only the high-skilled incentive constraint to bind in the atemporal Mirrlees optimal income tax problem

when there are two types. Nevertheless, by exploiting symmetries, it is possible to use our results to help sign the

distortions in the other cases as well. The nature of the distortions in these cases is briefly discussed informally in

Section 9.

The question of whether it is optimal to separate or pool individuals in nonlinear income tax models with a ratchet

effect is considered analytically by Roberts (1984) and Berliant and Ledyard(2014). Like us, they employ a determinis-

tic framework to analyze dynamic optimal nonlinear income taxation without commitment. Roberts shows that types

are never separated in an infinite horizon economy with a finite number of types because if a high-skilled individual

ever reveals his type, he will paythe larger full-information tax for all of the infinite future, which is not in his interest.

On the other hand, Berliant and Ledyard identify sufficient conditions for type information to be revealed in the first

period of a two-period economy with a continuum of types.6Laffont and Tirole (1987) provide a taxonomyof the vari-

ous kinds of separating, pooling, and semi-pooling equilibria in a two-period model of regulation in which the regulated

firm can be of only two types. They investigatewhich one of these cases is optimal both numerically and analytically. In

the two-type model they consider,each kind of equilibria is possible for some specifications of the model parameters.

In contrast, with a continuum of types, Laffont and Tirole (1988) show that there is no equilibrium with full separa-

tion and that there must be considerable pooling of types. None of these articles consider how individual decisions are

distorted.

The work closest to our own is that of Apps and Rees (2009).7As is the case here, Apps and Rees consider optimal

taxation without commitment a two-type, two-period model with a continuum of individuals of each type. They do not

allow for savings taxation and only consider the three tax regimes analyzed formally here. For these three regimes,

they show that the distortions on labor earnings have the same signs as is the case in our model with both income and

savings taxation. Variations of the basic structure considered here have been investigatedin Krause (2009) and in a

series of articles by Guo and Krause that are cited in Guo and Krause(2015).

The rest of this article is organized as follows. Section 2 describes the economy.In order to provide a benchmark for

our analysis of optimal taxation without commitment, in Section 3, we identify the qualitativeproperties of the solution

tothe optimal tax design problem under the assumptionthat the government can commit to a second-period tax sched-

ule before type information is revealed. Sections 4–7 consider the optimal tax design problem without commitment.

Section 4 provides an introduction to the incentive issues that arise when there is no commitment. In Section 5, we

determine the properties of the solution to the optimal tax design problem when it is optimal to separatethe two types

in the first period. In Section 6, we analyze the second-period tax design problem when some or all of the high-skilled

individuals do not truthfully reveal their type in period one. The first period of this problem is analyzed in Section 7.

In Section 8, we numerically investigate which of the tax regimes is optimal using a Cobb–Douglas utility function. We

informally discuss the optimal distortions for the cases not considered formally and consider some possible extensions

of our analysis in Section 9. The proofs of our results are gathered in Appendix A. The details of the Cobb–Douglas

example are providedin Appendix B.8

6Dillénand Lundholm (1996) also analyze when it is optimal to separate or pool types in a two-period model, but restrict attention to linear income taxation.

7Thefirst version of our article was completed before we learned of their research.

8Thecomputer code and more detail about our numerical analysis are available in the Supporting Information.