Arms build‐up and arms race in optimal economic growth

• Published date: 01 June 2016
• DOI: http://doi.org/10.1111/ijet.12087
• Author: Juan M. C. Larrosa
• Date: 01 June 2016

doi: 10.1111/ijet.12087

Arms build-up and arms race in optimal economic growth

Juan M. C. Larrosa∗

I analyze a model of strategic interdependence between two economies linked by investments

in defensive capital for deterrence purposes. I adapt a two-agent dynamic setting where weapon

production affects consumption. Individually both economies determine their balanced growth

path by taking this interdependence into account in different grades of awareness. I associate

two types of equilibria with internal or external determinants for defense production analogous

to scenarios of arms build-up or arms race. I find that a defense sector is compatible with

economic growth but a tight arms race can harm growth.

Key wor ds arms race, arms build-up, economic growth, difference game

JEL classification C73, F52, O41

Accepted 19 February 2015

1 Introduction

Investment in defense without affecting social welfare has been a concern of most economies. It

implies a sacrifice of private consumption and would represent a benefit in cases of preventing an

attack or providing a decisivew inning position when following an aggressive policy.Several modeling

approaches have been used in attempting to capture the interaction between competing economies,

synthesized mostly in reaction functions (Brito and Intriligator 1995). On the other hand, the

political science literature has identified two causes for defense expenditure (see Glaser 2000). First,

driven by internal factors, defense investment can be pursued in order to provide basic protection

for the socioeconomic infrastructure and other related issues such as internal security or national

prestige. Here, the defense industry is embedded in the economic infrastructure and produces so

as to accomplish an agenda set internally in the country. Secondly, and driven by external factors,

defense investment can be pursued in order to match the capabilities of another country considered

as an actual or potential threat. While very similar in nature to the former,this second cause requires

the observation of and response to another economy’s behavior. They end up “living a parallel life”,

to paraphrase Bester and Konrad (2005, p. 199).

I propose a dynamic model of growth where these two causes (internal and external)are modeled

as different type of equilibria of a game. Twoeconomies attempt to grow while maintaining a defense

industry. I model a dynamic framework in the form of a game in difference that allows us to capture

∗Department of Economics, National University of the South and Economic and Social Research Institute of the South

(IIESS), Bah´

ıa Blanca, Argentina. Email: jlarrosa@criba.edu.ar

I thank Fernando Tohm´

e and Daniel Heymann and two anonymous referees for comments on an early version of this

paper. All remaininger rorsare mine.

International Journal of Economic Theory 12 (2016) 167–182 © IAET 167

International Journal of Economic Theory

Arms build-up and arms race Juan M. C. Larrosa

the grade of interaction between them. If the interaction in sporadic, I will assume that the defense

industry is promoted through internal determinants in an arms build-up scenario, modeled as an

open-loop equilibrium. If interaction is periodic, then I will assume that investment in the defense

industry is promoted by external reasons in an arms race scenario, and this case will be modeled as

a Markovian perfect equilibrium.

The main findings of the model are that equilibria exist under the open-loop and Markov

strategies. Given that economies internalize and update period to period information on the other

economy’s defensivecapital investment, if economies integrate their productive sectors with the de-

fense industry they tend to obtain a higher rate of growth. However,if the utilit y of the representative

consumer is affected because the rate of sacrifice of internal consumption is higher than the intensity

of production of private goods, then the rate of growth could be negative.

The paper is organized as follows. Section 2 surveys the relevant literature. Section 3 describes

the model and definitions. Section 4 presents the results in the strategic growth model and its main

outcomes. Section 5 analyzes and discusses both results. Section 6 presents the paper’sconclusions.

2 Defense expenditure and economic growth

Some investment in capital formation is specifically decided by strategic considerations. This is the

case where two (or more) economies closely observe the realization of another nation’s variable

for assessing its own performance. Under more specific circumstances, a tangible variable is the

weapon stock of a country. However, nations decide how to investin defense by considering multiple

dimensions. Following Glaser (2000), two broad determinants for these dimensions are enumerated

as external and internal causes. For instance, a specific internal agenda could foster a policy of arms

build-up independently of changes in the defense policy of any other related economy; that is, an

internal process leads to an increase in investment in defense. On other hand, economies could

engage in an arms race by reacting to any change in the defense capabilities of another economy

taken as a relevant threat for them; this would represent an external cause for investingin defense.

The internal cause approach considers that each nation is not a unitary actor representedby some

representative agent. Instead, each economyhas its own institutions and actors that follow their own

interests and encourage weapons production for diverse reasons. Buzan and Herring (1998), for

example, analyze how (internal) strategic and political goals tend to drive massive arms build-ups

that are not fuelled by any external threat. A state decision to enhance its military institutions and

structures gives raise to new actors such as bureaucracies (political and military), arms producers,

and lobbyists, among others. They have their own agenda and pursue their own interests. This process

will be referred as an “arms build-up.” The internal cause in defense expenditure is associated with

a level of suboptimality in many dimensions but will focus specifically on its effect on economic

performance.

On the other side, external causes are main drivers in “armr aces.” Several economies in the world

keep a close eye on their neighbors for fear of falling victim to an attack. Under this circumstance,

any given country evaluates positively enhancing economic growth that allows for constant levels of

consumption for an increasing population but at the same time it is afraid of a potential threat and

accumulates defensive capital (weapons) for keeping a level of power parity (deterrence) constant.

This special capital is assumed to adopt a strategic role. Its absence is a potential danger for sustaining

the production conditions in the economy in the long run. For instance, countries build arsenals

for stockpiling weapons and training personnel. This capital stock fulfills the social function of

protecting the reproduction of traditional capital. This capital is produced in order tocreate negative

168 International Journal of Economic Theory 12 (2016) 167–182 © IAET