Dynamic dissolutions and unifications

• Date: 01 June 2017
• Author: Christopher J. Ellis
• Published date: 01 June 2017
• DOI: http://doi.org/10.1111/jpet.12236

Received: 9 September 2016 Accepted: 27 September 2016

DOI: 10.1111/jpet.12236

ARTICLE

Dynamic dissolutions and unifications

Christopher J. Ellis

Universityof Oregon

ChristopherJ. Ellis, Department of Eco-

nomics,University of Oregon, Eugene, OR

(cjellis@uoregon.edu).

Ithank Tom Groll, Jiabin Wu, Stefano Barbieri,

andparticipants at seminars given at Tulane,

Oregon,Ifo Institute Munich, and the annual

meetingsof the Association for Public Economic

Theory.

I reexamine the key results from the literatureon the size and num-

ber of countries under different political institutions in a simple

dynamic model. I find that the canonical static results that democra-

cies lead to too many too-small countries and that Leviathans lead

to too few too-large countries no longer necessarily hold. The key

dynamic element that drives the new results is that public goods

are modeled as public capital; this changes the incentives to unify or

divide countries. I also show that there are hysteresis effects on the

size and number of countries; that is, arbitrary initial configurations

of national boundaries may tend to persist because of the initial pub-

lic capital location decisions they promote.

1INTRODUCTION

There is an extensive literature that exploresthe determinants of the size and number of countries. The key features

are that there are benefits to greater size due to the sharing of fixed costs, but there are also costs if increased size

involves greater heterogeneity in a population.1The upshot of this argument is that equilibria existcharacterized by a

specific number of countries of a specific size. Depending on the mechanism by which the tension between the costs

and benefits of size is arbitrated, these equilibria may involve smaller or larger countries than would be chosen by a

utilitarian social planner. The central results in this literature,due to Alesina and Spolaore (2003), are that if the size

of countries is determined by the preferences of the median voter then there will be too many countries of less than

optimal size.2However,if the decision-making process involves joint rent maximizing Leviathans then there will be too

few countries that are greater than optimal size. There are of course many clever caveats to these results, and they

depend on a number of somewhat restrictive assumptions. While acknowledging that this has become a rich literature,

I take as my starting point the results obtained from the simple standard model of Alesina and Spolaore (2003).3This

allows me to bring my contribution into sharper focus.4,5

1Fora discussion of costs, see Alesina and Wacziarg (1998); on the question of the relationship between size and population heterogeneity, see Easterly and

Levine (1997), La Porta, Lopez de Silanes,Shleifer, and Vishny (1999), Alesina, Devleeschauwer, Wacziarg, Kurlat, and Easterly (2003), and AlesinaandLa

Ferrara(2005).

2This echoes the pioneering results of Cremer,De Kerchove, and Thisse (1985), who model the spatial provision of a public good. They find that if the public

goodis financed by a benefits tax then majority voting supports a utilitarian welfare optimum. However, if financing is via an income tax then the extremevot er

ispivotal, and the number of locations at which the public good is supplied exceeds the number at a welfare optimum.

3Fora nice intuitive introduction to the various strands of this literature, see Spolaore (2009).

4There is also a strand of this literature where the advantages of size involve the reduction in tradingcosts associated with bigger markets (see Alesina,

Spolaore, & Wacziarg,2005). I do not model these mechanisms here, not because they are uninteresting but because they do not seem to involvethe same

dynamicissues I wish to explore.

5I do not consider the relationships between realized or potential conflicts and the size and number of countries. For a nice review of this literature, see

Spolaore(2012).

Journal of Public Economic Theory 2017; 19: 692–712 wileyonlinelibrary.com/journal/jpet c

2017 Wiley Periodicals,Inc. 692

ELLIS 693

The canonical results, if they may be called that, are obtained in a static framework. However,one interpretation

of the sharing of fixed costs is that they involve sharing the tax burden of financing public goods which takethe form

of public capital investments. It thus makes sense to think about the determination of the size and number of coun-

tries as a dynamic problem. In such a setting elements such as the rate of technological progress, the rate of income

growth, and the population growth rate become important. The purpose of this paper is to introduce these elements

into the analysis. I developa simple two-period version of the standard model that incorporates these dynamic features

together with the assumption that the public good supplied is public capital. The resultant subgame perfect equilibria

havea number of interesting features. First, for some parameter values, the keyresults of the canonical model are pre-

ciselyreversed. Decision making by the median voter can lead to too few too-large countries relative to the appropriate

welfare optimum, whereas a Leviathan maychoose too many countries that are too small. Second, if there is represen-

tative democracy then the equilibrium is not unique, and is determined by agents’ prior beliefs. Expectations over the

number of countries that will exist in the future can be self-fulfilling; beliefs today determine public capital decisions

that produce outcomes that verify these original beliefs. The number of countries maythen depend on extrinsic events

or “sun-spots.”6Third, I show that under very unrestrictive assumptions dissolutions tend to be more frequent and

unifications tend to be less frequent under democratic as opposed to autocratic governments.This correlates with the

observation that the number of countries has increased overthe same period as there has been an increase in the num-

ber of democratic governments. However,this does not preclude the number of new countries created under democ-

racy and a Leviathanboth being inefficiently high or low. Finally, the model displays a form of hysteresis result in that, if

the number of countries in the first period is determined by history,then there can be a tendency for this configuration

to persist. This perhaps then gives some insights into the seemingly surprising persistence of the boundaries drawnby

the colonial powers in Africa.

The rest of this paper is organized as follows. In the next section, I introduce a modified two-period version of

the Alesina and Spolaore (2003) model and derive results concerning the efficient size and number of countries as

determined by a utilitarian social planner. I compare these result to those obtained in a static model. In Section 3,

I allow the size and number of countries to be determined by simple majority voting over public good provision

locations and the number of countries. A comparison with the static results is given, and I also examine the effi-

ciency of majority voting in a dynamic model. I also consider a version of representative democracy and show that

this may lead to a multiplicity of equlibria. In Section 4, I let the size and number of countries, together with pub-

lic good provision locations, be determined by joint rent maximizing Leviathans. These too are compared to the effi-

ciency results of Section 3. In Section 5, I compare the behavior of democracies and Leviathans to each other.In Sec-

tion 6, I explore the possibility of hysteresis in national boundaries. In Section 7, a brief conclusion and discussion is

provided.

2A SIMPLE TWO-PERIOD MODEL

2.1 Preliminaries

The world in this analysis is represented by the unit line, a partition of which into subintervals represents a division of

the world into countries. Within each country/subintervala public good is supplied and the taxes required to finance

its provision are levied. I consider an economy that exists for two periods, indexedt=1,2. In each period, members

of the population may consume combinations of two goods, a public good, g, and a composite private good, x.An

exogenously determined quantity of the public good is supplied in each country in each period, and is assumed to be

infinitely divisible such that it may be “spread” along the unit line. The location(s) of the public good supply is best

interpreted as in geographic space, although interpretations involving attribute space may in some circumstances be

6Representativedemocracy will mean that voting takes place over a combination of “measures” that are jointly adopted or rejected.