The Effect of Spillovers and Congestion on the Endogenous Formation of Jurisdictions

• DOI: http://doi.org/10.1111/jpet.12130
• Author: REMY ODDOU
• Date: 01 February 2016
• Published date: 01 February 2016

THE EFFECT OF SPILLOVERS AND CONGESTION ON THE

ENDOGENOUS FORMATION OF JURISDICTIONS

REMY ODDOU

University Paris West

Abstract

This paper analyzes the effect of interjurisdictional spillovers and con-

gestion of local public services on the segregative properties of endoge-

nous formation of jurisdictions. Households choosing to live at the

same place form a jurisdiction which produces congested local pub-

lic services, which generates positive spillovers to other jurisdictions.

In every jurisdiction, the production of the local public services is fi-

nanced through a local tax based on households’ wealth. Local wealth

tax rates are democratically determined in every jurisdiction. House-

holds consume the available amount of public services in their jurisdic-

tion and a composite private good. Any household is free to leave its

jurisdiction for another that would increase its utility. A necessary and

sufficient condition to have every stable jurisdiction structure segre-

gated by wealth is identified: the public services must be either a gross

substitute or a gross complement to the private good.

1. Introduction

There exists a widely held belief that metropolitan sectors are wealth-segregated. Rich

and poor municipalities coexist within the same urban area. The paper investigates how

congestion effects and positive spillovers affect segregation.

According to Tiebout’s intuitions (Tiebout 1956), individuals choose their place

of residence according to a trade-off between local tax rates and the amounts of public

services provided, which leads every jurisdiction to be homogeneous. The formation

of a jurisdiction structure is endogenous, due to the free mobility of households that

can “vote with their feet”; that is to say, they can leave their jurisdiction for another one

if they are unsatisfied with that jurisdiction’s tax rate and amount of public services.

Westhoff (1977) was among the first economists to provide a formal model based on

Remy Oddou, EconomiX, University Paris West, 200 Avenue de la R´

epublique, Paris, France

(remy.oddou@free.fr).

I am indebted to Richard Arnott, Francis Bloch, Pierre-Philippe Combes, and Nicolas Gravel for their

very helpful comments and suggestions. I really appreciated the comments of Myrna Wooders and two

anonymous referees on a previous article for underlining the importance of using a discrete set of

households instead of a continuumn in local public goods economies. I am also very grateful to the

participants of the Association for Public Economic Theory 2012—in particular Gareth Myles and John

Conley, and participants of the Regional Science Council 2010.

Received July 25, 2014; Accepted August 6, 2014.

C2014 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (1), 2016, pp. 67–83.

67

68 Journal of Public Economic Theory

Tiebout’s intuitions. In this model, households can enjoy two different goods: a local

public good, financed through a local tax on wealth, which is a pure club good (only

households living in the jurisdiction that produced it can consume the local public

good that does not suffer from the congestion effect), and a composite private good,

which amount is equal to the after-tax wealth. Westhoff found a condition that ensures

the existence of at least one equilibrium: the slopes of individuals’ indifference curves

must be ordered by the private wealth in the tax rate-amount of public good space. If

this condition is respected, not only will at least one equilibrium exist, but all equilibria

will be segregated, as per definition provided by Ellickson (1979).

Gravel and Thoron (2007) identified a necessary and sufficient condition that en-

sures the segregation of every stable jurisdiction structure: the public good must, for all

levels of prices and wealth, either always be a complement or a substitute to the private

good. This condition is called the gross substitutability/complementarity (GSC) condi-

tion. This condition is equivalent to the preferred tax rate being a monotonous function

of private wealth, for any level of prices and wealth. Biswas, Gravel, and Oddou (2009)

integrated a welfarist central government to the model, the purpose of which is to max-

imize a generalized utilitarian social welfare function by implementing an equalization

payment policy. They found that the GSC condition remains necessary and sufficient.

That is also the case when a land market is introduced (see Gravel and Oddou 2011).

However, none of these models allows for interjurisdictional spillovers or conges-

tion effects. To be convinced of the existence of interjurisdictional spillovers, one can

simply consider the example of an international airport in a suburban town (Newark,

for instance). Every municipality located near this town would benefit from the airport,

though it would not be located on its administrative territory. The most striking proof

of how congestion effects existence is the traffic jam: the benefit households will gain

from a public road is clearly affected by the number of its users.

As provided by Calabrese et al. (2006), empirical evidences suggest that households

mobility leads to segregation when peer effects are taken into account. One can notice

that the calibration of households’ preferences respects the GSC condition.

Wooders (1978, 1980) and Conley and Wooders(1997) provided several generaliza-

tions of Westhoff’s model by relaxing some assumptions, such as the nonrivalry of the

local public goods. They assumed that the public good suffers from congestion (called

here “crowding effect”), which means that households’ utility decreases with the num-

ber of people that consume the public good, for any given amount of produced public

good. Those papers are closer to Tiebout’s intuitions in the sense that crowding effects

are allowed in Tiebout’s paper to justify his assumption that jurisdictions would not be

too crowded.

Allowing for crowding effects is likely to affect the segregative characteristic of

the equilibrium, as presumably they would reinforce the segregative properties of

endogenous jurisdiction formation. As Wooders (1999) writes: “in general, even in the

crowding types model, where it has the best chance, players do not necessarily sort into

taste homogeneous jurisdictions.”

Nechyba (1997) developed a model within a discrete set of households. In his

model, spillovers between jurisdictions were allowed, because a household’s utility

depends not only on the amounts of local public good provided by its jurisdiction and

of the national public good, but also on the amounts of public good provided by all

other jurisdictions. After having ensured the existence of an equilibrium under certain

conditions, Nechyba identified sufficient conditions for a stable jurisdiction structure

to be segregated. Unfortunately, one of these sufficient conditions was the absence of