International Security, Multiple Public Good Provisions, and The Exploitation Hypothesis

Abstract

Since the 1960s Olson-Zeckhauser’s (1966) analysis, its ‘exploitation of the great by the small’ has provided economists’ core model of alliance’s provision of security/defense. But with the end of the Cold War, countries’ allocative behavior has diverged markedly from OZ’s predictions for defense as a homogeneous pure public good voluntarily provided. This paper suggests a replacement for OZ, with the essential difference that ‘defense’ rather than being aggregated into their single public good is disaggregated into more realistic categories of self-insurance and self-protection. Because allocative behavior in public good groups is essentially driven by income effects, we concentrate on these, which become complex and conflicted, giving much greater scope for goods-inferiority. The analysis is followed by numerical simulations, which conform to actual experienced allocations in NATO much better than the conventional ‘exploitation’ model.

Keywords:

• Self-insurance
• Self-protection
• Inferior goods
• Exploitation hypothesis
• Multiple public goods

JEL Codes:

• F50
• H41
• H50
• D81

Acknowledgments

The authors thank Robin Boadway, Richard Cornes, Magnus Hoffman, Jun-ichi Itaya, Kai Konrad, Ioana Petrescu, and other conference participants for insightful comments on the earlier paper. The authors wish to acknowledge the helpful comments of the editor and two anonymous referees. If there should be any errors these remain the sole responsibility of the authors.

Notes

1 On the other hand, Oneal and Diehl (1994) argued that Olson’s original emphasis on the public nature of the good supplied by the alliance remains valid using pooled regression analysis for 1950–1986.

2 Our ‘baseline risk’ corresponds to what is sometimes referred to as ‘background risk’ in economics of insurance analyses. Background risk distinguishes ‘independent’ background risk where p(0) is not influenced by the value of L(0) as in our model here, vs. ‘non-independent’ background risk where p(0) and L(0) are interdependent, and asks how the choice of protection or insurance varies with the independence property (See Schlesinger, 2000).

3 In an example of flood protection and insurance, as greater quantities of consumables are set aside during dry years, their costs of preservation and delivery during good years might increase more than proportionately.

4 Note if self-insurance is fair and therefore (1−p) = p, then the numerator of (13) becomes p(U¹_YY− U⁰_YY).

5 Our simple solution to the problem of diminishing returns and distribution of infra marginal costs/gains in a public good spillover environment will be to assume a ‘summation finance aggregator,’ , in the provision of public good, even though p(M), represents a ‘non-summation consumption aggregator’ (e.g. ). Then, importing an idea from contest theory we take primitive preferences as being over contributions to insurance or to risk reduction, rather than insurance coverage or risk reduction itself.

6 To conduct the numerical simulations, we used Mathematica 7.0.0.

7 Equation (20) can be rewritten as . The RHS can be interpreted as a convex combination of unity and Tullock’s contest success function where the weight of the former is p₀ and that of the latter is 1−p₀. We can think of a Tullock contest with two competitors: one is the alliance of countries A and B, and the other is an opposing adversary. The effort of the former is M₁ and that of the latter is fixed at . Equation (20) implies that even if the alliance of A and B loses the Tullock contest, still A-B will enjoy the good state with probability . Specifying the risk reduction function as Equation (20), we suppose that even if the alliance of A and B loses the Tullock contest with the opponent, there remains some chance to keep the opponent from say invading the territory of the alliance and thus some chance to enjoy the good state.

8 If we treat national security as a whole with no disaggregation into self-insurance and self-protection (as in the conventional framework of public good provision), a decrease in the threat from an enemy reduces contribution (as a % of GDP), where the decline in the percent contribution of the smaller country is greater than that of the larger country. This outcome is consistent with the exploitation hypothesis. But we cannot explain the change of security outlays in 1990s by using this model. Thus, if the loss in bad state increases, the conventional framework of single public good is inadequate.

9 One could argue that the big country will move first as a Stackelberg-leader. In other calculations (available on request), we considered a leader–follower model with country A the leader and B the follower. It turned out that those results of simulated NATO burden sharing were less consistent with the actual burden sharing history than the results reported here.

This paper extends parts of ‘National Adversity: Managing insurance and protection,’ presented to a Conference on ‘The Causes and Consequences of Conflict,’ Wissenschaftszentrum Berlin (WZB), Germany, 28–29 March 2008, PET conferences 2008, Seoul, Korea, 28 June 2011, Indiana, USA., 4 June, IIPF conference 2011, Michigan, USA, 8 August 2011, and ANU, Australia, 24 March 2012.