The Time‐Consistent Public Goods Provision

• Author: SHIGEO MORITA
• DOI: http://doi.org/10.1111/jpet.12209
• Published date: 01 December 2016
• Date: 01 December 2016

THE TIME-CONSISTENT PUBLIC GOODS PROVISION

SHIGEO MORITA

Osaka University

Abstract

In this study, we reconsider the optimal nonlinear tax problem with

the public good from the perspective of the commitment issue and ex-

amine how it affects the condition of the public good provision. We

show that the Samuelson rule should be modified when the govern-

ment cannot commit and the skill types of taxpayers are revealed in

the first period. This is true even if the preference of the taxpayers is

separable and additive with respect to consumption and leisure. Our

analysis also shows how the lack of commitment affects the formula of

the marginal cost of public funds and the level of public good provi-

sion. Our findings imply that the level of the public good may be exces-

sive in comparison to the case where the government can commit to its

tax policy.

1. Introduction

It is known that the Samuelson rule for the optimal provision of the public good, which

equates the sum of marginal willingness to pay for the public good to the marginal

cost of providing the public good, breaks down in the presence of the distortionary

cost of taxation required to finance the public good. Pigou (1928) stated that when

the public good is financed by a distortionary tax, the dead weight loss raises the social

marginal cost of public goods above the case of a nondistortionary tax (referred to as the

Pigou effect). More recently, Boadway and Keen (1993) considered the case in which

the public good is financed using nonlinear income taxation ´

alaMirrlees (1971). They

showed that it is generally optimal to deviate from the Samuelson rule in providing the

public good, except when the utility function of taxpayers is separable in leisure. On

the other hand, since some public goods have the property of durable goods, a dynamic

setting is necessary in order to analyze the optimal condition of the public good. The

traditional dynamic Samuelson rule implies that the marginal social benefit of public

Shigeo Morita, Graduate School of Economics, Osaka University,1-7, Machikaneyama, Toyonaka, Osaka

560-0043, Japan (ngp024ms@student.econ.osaka-u.ac.jp).

I would like to express my sincere gratitude to the editors John P. Conley and Myrna Wooders, the

associate editor Helmuth Cremer, and anonymous referees for their helpful comments that greatly

improved the paper.I am especially grateful to Yukihiro Nishimura and participants at the Kansai Public

Economic Workshop.

Received May 29, 2016; Accepted June 9, 2016.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (6), 2016, pp. 923–941.

923

924 Journal of Public Economic Theory

goods should be equal to the marginal cost, the static Pigou effect, and the dynamic

efficiency effect.

This paper analyzes the issue of time consistency. Aronsson and Grandlund (2011)

focused on the situation where taxpayers have a time-inconsistent preference for the

public good. Assuming a paternalistic government, they showed that the social optimal

condition of the public good provision should deviate from the Samuelson rule. Gaube

(2007) pointed out two types of issues in the nonlinear income tax problem with two

periods. The first issue is the choice of the tax base. In other words, do the nonlinear

tax functions depend on a current income or incomes in both periods? In the model

of Gaube (2007), a nonlinear tax is a function of current income, and the government

can commit to its policy in the future. Under such formulation, he showed that the

nondistortion at the top result, namely that the high-skill consumer should face a zero

marginal tax rate and the low-skill consumer should face a positive marginal tax rate at

the optimum, should be violated. The second issue concerns the ratchet effect, which

is the focus of this paper. In using information revealed by taxpayers in the first period,

the government can re-optimize its tax schedule in the second period to allow the in-

crease of the social welfare. However, if the taxpayers are aware of this re-optimization,

then they may adjust their behavior in the first period to conceal their information.

The ratchet effect never appears if the government can commit its policy to all peri-

ods in the first period. However, this commitment is not credible and, therefore, not

time-consistent. Roberts (1984) analyzed this issue by studying the optimal income tax-

ation under noncommitment and an infinite time horizon. Proposition 8 in the paper

posited that the separation of types will not occur under an infinite horizon. More re-

cent studies on this topic include those of Apps and Rees (2006), Bisin and Rampini

(2006), Brett and Weymark (2008), Krause (2009), Guo and Krause (2011, 2013), and

Berliant and Ledyard (2014). However, no previous studies have examined how the

ratchet effect affects the public good provision. Therefore, we analyze how the public

good provision is impacted by the ratchet effect. To the best of our knowledge, this

paper is the first to examine the implications of the ratchet effect for the public good

provision.

To clarify the effect, we utilize two periods and the partial equilibrium version of the

model discussed in Pirttil¨

a and Tuomala (2001). The new dynamic public finance (here-

after NDPF) approach produces interesting lines of thought within macroeconomics

and pubic finance. It includes studies by Golosov, Tsyvinski, and Werning (2006) and

Acemoglu, Golosov, and Tsyvinski (2008). The model applied in such studies is a non-

linear tax problem with multiperiods, and stochastic-type changes are assumed to occur.

In this paper, for simplicity, there are no stochastic-type changes over time. We show

that, when the government cannot commit to its policy and the skill types of taxpayers

are revealed in the first period, the Samuelson rule no longer applies even if the utility

function is separable in labor. Moreover, this paper examines how the lack of commit-

ment by the government affects the formula of the marginal cost of public funds (here-

after MCPF), which plays an important role in assessing the optimality of government

spending.

The remainder of this paper is organized as follows. Section 2 describes the model

and considers the commitment case as the benchmark case. Section 3 analyzes the time-

consistent public goods provision. As an additional analysis, numerical examples in

Section 4 confirm that the ratchet effect also impacts the level of social welfare and

public goods. Section 5 concludes. The proofs of our main results are presented in the

Appendix.