Defense Strategy Transition and Economic Growth Under External Predation

Abstract

This paper develops a growth model for a country under a Hobbesian environment with international conflicts where national defense is the only way to prevent external predation. Different defense strategies result in different growth paths. The long-run growth path is determined by the equilibrium of a dynamic game with three players: the external predator, the government, and the family. The equilibrium growth path can have different phases: submissive equilibrium, tolerant equilibrium, and complete protection equilibrium. Sustainable growth will endogenously induce an adjustment of the defense strategies. As the economy keeps growing, complete protection will eventually be preferred. The optimal growth path prefers to compress the length of the transitional period between incomplete protection and complete protection. Some interesting features of the transitional dynamics are exhibited by a control model with discontinuity.

Keywords:

• Economic growth
• Defense strategy
• Predation
• Defense expenditure

JEL Codes:

• O41
• F52
• H56

Notes

¹See the discussion about the open economy in Barro and Sala-i-Martin (2004).

²There is affluent literature in history and politics that concerns the relationship between external threat and economic growth. Bernholz and Vaubel (2004) argue, based on the history of Asia, that political fragmentation will not favor innovation and growth if it leads to prolonged and highly destructive wars rather than peaceful competition among states. Also see Jones (1981) and Nye (2002).

³See Sandler and Hartley (2001).

⁴The characters of these three types of models are as follows: the basic method of a general empirical model tries to consider all factors that might have an impact on defense expenditure, including the economy, politics, and strategy. It generally applies them directly to empirical research. Macnail, Murdoch and Sandler (1995), Looney and Mehay (1990) and Kollias (1995, 1997) have primarily adopted and developed this type of model. They performed extensive research on the cases of the USA, Australia, Greece, Turkey, and other countries. The neoclassical model’s foundation is the assumption of a rational government, which considers the purpose of government to be the maximization of social welfare. Because the total resources are finite, they need to be distributed optimally to the private and public departments. In addition, in general, this model assumes that welfare consists of national security and consumption. The defense expenditure demand model, which is based on a decision process does not agree with the basic assumption that considers the government to be an independent rational agent. This type of model pays more attention to the actual process behind one country’s decision-making on defense expenditures. (See Hartley and Sandler, 2001: 70–85).

⁵Although it is controversial to describe the international order by using Hobbesian Rule, many scholars still accept it and consider it to be the most important difference between international society and domestic society. (See Nye, 2002.)

⁶Conflict economics considers the conflict process to have essential economic features similar to those of the production process. The basic means to analyze the production process is a production function; in the formal economics literature on conflict, there is generally also some function adopted to simulate the relationship between input and output of conflict behavior. These functions are called CSF. Hirshleifer (1989, 1994, 2000) introduces some general function forms. For the application of some of them, see Loury (1979), Tullock (1980), Rosen(1986), Appelbaum and Katz (1987), Dixit (1987), Hirshleifer (1989), Skaperdas (1996), Baik and Lee (2001), Hirshleifer (1989), Baik (1998) and others.

⁷It is more reasonable that p is decided by the stocks of the bilateral conflict inputs. However, this decision has no substantial effect on the theoretical conclusions of this model. For simplicity, we treat conflict inputs as flows.

⁸Because of the assumption that the predators randomly gain the chance to plunder, the predation input decision in different periods can be decided by different predators.

⁹See the proof in the appendix.

¹⁰See the proof in the appendix.

¹¹This is appropriate in the nuclear weapons period while viewing the complete protection as from SWS might be too restrictive in other situations. For instance, historically, England ensured her absolute security by maintaining the most powerful navy in the world. However, if one of the requisites for complete protection is a certain level of some type of military weapon or capital stock, which requires costly sustained investment, it is consistent with the analysis here.

¹²For details about a control problem with discontinuity, see Hull (2003).

¹³See the proof in the appendix.

¹⁴For the history of the Han Dynasty, see Sima (1993).