Regulation of Investments in Infrastructure: The Interplay between Strategic Behaviors and Initial Endowments

• Author: CHARLES FIGUIÈRES,MABEL TIDBALL,DENIS CLAUDE
• Date: 01 February 2012
• DOI: http://doi.org/10.1111/j.1467-9779.2011.01528.x
• Published date: 01 February 2012

REGULATION OF INVESTMENTS IN INFRASTRUCTURE:

THE INTERPLAY BETWEEN STRATEGIC BEHAVIORS

AND INITIAL ENDOWMENTS

DENIS CLAUDE

CNRS CES

CHARLES FIGUI `

ERES

INRA LAMETA

MABEL TIDBALL

INRA LAMETA

Abstract

This paper explores the dynamic properties of price-based

policies in a model of competition between two jurisdic-

tions. Jurisdictions invest over time in infrastructure to in-

crease the quality of the environment, a global public good.

They are identical in all respects but one: initial stocks of in-

frastructure. This is a dynamic type of heterogeneity that dis-

appears in the long run. Therefore, at the steady state, usual

intuitions from static settings apply: identical jurisdictions

inefficiently underinvest, calling for public subsidies. In the

short run, however, counterintuitive properties are estab-

lished: (i) the evolution of capital stocks can be nonmono-

tonic and (ii) one jurisdiction can be temporarily taxed,

even though it should increase its investment, whereas the

other is subsidized. It is shown how these phenomena are

Denis Claude, Centre d’Economie de la Sorbonne, Maison des Sciences Economiques,

106–112 Boulevard de l’Hˆ

opital, 75647 Paris Cedex 13, France. Charles Figui`

eres, INRA

LAMETA, 2 Place Viala, 34060 Montpellier, France (charles.figuieres@supagro.inra.fr).

Mabel Tidball, INRA LAMETA, 2 Place Viala, 34060 Montpellier Cedex 1, France

(tidball@supagro.inra.fr).

Weare grateful for financial assistance from NSERC Canada. We thank Alain Jean-Marie,

Erik Ansik, Ngo Van Long, and Georges Zaccour for helpful comments. Also, we thank

participants at the 15th Annual Conference of the EAERE and 7th Meeting on Game

Theory and Practice for helpful discussions. Finally, many thanks are due to an Associate

Editor of JPET and two anonymous referees for very useful comments and suggestions on

a previous version of this work. The usual disclaimer applies.

Received July 20, 2008; Accepted September 28, 2010.

C

2012 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 14 (1), 2012, pp. 35–66.

35

36 Journal of Public Economic Theory

related to initial conditions and the kind of interactions

between infrastructure capitals, complementarity or substi-

tutability.

1. Introduction

In recent years, the theoretical analysis of price-based policies for the control

of environmental externalities under imperfect competition has received a

renewed attention (see Requate 2006 for a survey). Previously, most of the

literature focused on the design of optimal tax or subsidy policies in a static

setting where several instantaneous effects of these instruments should be

balanced, e.g., with respect to taxation, the gain in terms of social welfare

arising from the reduction of pollution emissions against the loss from out-

put restriction.

However, little is known about how intertemporal externalities affect the

design and dynamic properties of price-based policies. Introducing the time

dimension raises the critical issue of credibility of public policies, namely,

how regulations should be framed to ensure that they remain optimal

in their ability to achieve social efficiency as circumstances change over

time. Such an explicit consideration of credibility requirements may qualify

substantially the intuitions about price-based regulations gained in a static

setting and may provide interesting and sometimes counterintuitive policy

advices.

An important contribution to this literature is Benchekroun and Van

Long (1998). They consider the efficiency-inducing taxation1for the regu-

lation of an oligopolistic industry which is responsible for releasing a stock

pollutant—one for which pollution accumulation generates present as well

as long-term environmental damages. They formulate a differential game of

pollution control in which the environmental regulator imposes a taxation

rule in a symmetric oligopolistic industry. In this game, the state variable is

the pollution stock, the tax policy is the control of the environmental regu-

lator, and output decisions are the controls of the firms which are assumed

to use either open-loop or Markov strategies.

Benchekroun and Van Long (1998) analyze a Markovian tax policy

whereby the output tax rate faced by a firm at any given time depends solely

on the current pollution stock. By construction, such an instrument is cred-

ible in the strong sense, i.e., it is subgame perfect. The authors provide a

characterization of the optimal tax rule that is shown to be increasing in the

pollution stock and to “decentralize” the socially optimal time path of pro-

duction. As for the dynamic properties of the tax, they obtain a surprising

result. In an initial time interval where the stock of pollution is low, the tax

rate may be negative implying a subsidy. Paradoxically, this subsidy induces

1On efficiency-inducing taxation, see also Bergstrom, Cross, and Porter (1981), Karp and

Livernois (1992), Ko, Lapan, and Sandler (1992), Karp and Livernois (1994), and Legras

(2010).

Regulation of Investments in Infrastructure 37

the firms to produce less than they would have if the industry had not been

regulated. Upon reflection, the explanation for this result is clear. Since the

tax rate at any given time depends solely on the pollution stock, firms antic-

ipate that an increase in their production will lead to reduced subsidies in

the future, and eventually precipitate the turn of the subsidy into a tax. As

noted by Benchekroun and Van Long (1998), this is an instance of “carrot

and stick” policy.

Motivated by a long standing concern for infrastructure competition,

this paper elaborates on Benchekroun and Van Long’s (1998) seminal con-

tribution by studying how differences in initial stocks of infrastructure alter

the dynamic properties of the optimal and credible tax or subsidy policy.

We consider a stylized dynamic extension of the model of interjurisdictional

spillovers introduced by Wildasin (1991). The focus of our attention is on

two jurisdictions located in the same watershed or airshed.2Each jurisdic-

tion invests in public (or green) infrastructure3in order to provide a public

good to its own residents. However, the public good produced by one ju-

risdiction also benefits the residents in the other jurisdiction who cannot

be excluded from “its” consumption once it is provided.4In the absence of

any regulation initiative, the presence of positive interjurisdictional spillovers

will result in the underprovision of public infrastructure. Indeed, local ju-

risdictions will not take into account the positive spillovers that benefit the

nonresidents when setting their investment policies. A first remedy is to

elevate the decision-making process to a higher level of jurisdiction so

that external benefits of public infrastructure become internal to the

2Here, we depart from the original meaning of the terms “watershed” and “airshed” and

adopt the North American usage in which they have come to describe the geographical

boundary for water and air quality standards.

3Most confusingly, the term “green infrastructure” is often used to refer to different en-

vironmental management solutions. Following Benedict and MacMahon (2002), the en-

vironmental conservation literature defines green infrastructure as “an interconnected

network of green space that conserves natural ecosystem values and functions and pro-

vides associated benefits to human populations.” However, it is not uncommon to use this

term to refer to engineered systems that mimic nature in function (e.g., porous pave-

ments or biological wastewater treatment facilities) or even all conventional engineered

systems aimed at environmental conservation (e.g., traditional wastewater treatment facili-

ties). In this paper, we adopt the latter usage, and define “green infrastructure” as an array

of products, technologies, and practices, relying on either natural or engineered systems,

that a local public authority can use to improve environmental quality.Furthermore, as the

model is abstract enough to cover a broad range of publicly funded goods with positive

externalities, we shall use the terms “public” and “green,” interchangeably.

4The prototypical situation we have in mind is the planning and development of the

Green-Blue Meander in the Netherlands. This major project aims at the creation of a

strong ecological and recreational buffer zone in the Randstad area, covering more than

200 km2of land between Rotterdam and The Hague. Responsibilities are divided as fol-

lows: (i) the Dutch government provides funding for the project, (ii) Rotterdam and The

Hague are in charge of land acquisition and conversion decisions, and (iii) the province

of South-Holland is responsible for the coordination of the decisions taken by the two

agglomerations.