commitment, threat perceptions, and expenditures in a defense alliance

Commitment, Threat Perceptions, and Expenditures in a Defense AllianceAuthor(s): William R. Gates and Katsuaki L. TerasawaSource: International Studies Quarterly, Vol. 36, No. 1 (Mar., 1992), pp. 101-118Published by: Wiley on behalf of The International Studies AssociationStable URL: http://www.jstor.org/stable/2600918 .

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Intemnational Studies Quarterly (1992) 36, 101-118

Commitment, Threat Perceptions, and Expenditures in a Defense Alliance

WILLIAM R. GATES

AND

KATSUAKI L. TERASAWA

U.S. Naval Postgraduate School

The economic theory of alliances is based on public goods theory. This theory has been modified to include defense resources with mixed public/private benefits. This paper develops a defense alliance model that distinguishes public from private benefits based on the degree to which defense resources are committed to the alliance. Resources fully committed to the alliance (e.g., U.S. troops stationed abroad) provide public benefits. Partially committed resources (e.g., U.S.-based NATO reinforcements) provide mixed public/private benefits. Finally, resources committed to uses outside the alliance (e.g., internal security and unrelated international interests) provide mostly private benefits. Threat perceptions are also used in explaining alliance defense expenditures. This model provides plausible explanations for recent defense expenditure trends. It also suggests important policy implications. In particular, free riding is an inherent characteristic of defense alliances and aggregate defense expenditure data cannot measure the distribution of the defense burden.

The economic theory of alliances is based on the theory of public goods. A public good is any good where consumption is nonrivalrous and nonexcludable (Samuelson, 1954). Nonrivalrous consumption means that consumption of one unit of the good by an individual does not detract from the value other individuals receive from the same unit of the good. Nonexcludability means that it is impossible, or prohibitively expensive, to deny access to any consumers irrespective of their payments for the good.

Voluntary provision of public goods typically creates two problems: disproportionality and suboptimality. Once a public good has been provided, nonexcludability makes the benefits available to all individuals. As a result, all individuals have an incentive to "free ride." Thus, nonexcludability creates disproportionality by shifting the cost burden to those who place the highest absolute value on the

Authors' note: The authors are grateful for the helpful comments of the editor and two anonymous referees. Their comments helped improve the paper's quality. Any remaining errors, omissions, or misrepresentations are the authors' responsibility. This work was sponsored by the Office of the Chief of Staff of the Army.

? 1992 International Studies Association



102 Defense Alliance

good (as determined by both preferences for the good and income, or ability to pay). It also creates suboptimality by reducing the quantity of the public good provided.1

This paper examines the public goods paradigm as applied to defense alliances. It distinguishes public from private benefits using commitment levels within the alliance. It also incorporates threat perceptions into the explanation of alliance defense expenditures. This characterization provides a plausible explanation for defense expenditures over the past two decades.

Pure Public Goods and Joint Products in Defense Alliances

Whereas national defense has always been considered a classic example of a public good within a country, Mancur Olson and Richard Zeckhauser (1966) were the first to apply this paradigm to international alliances. They hypothesized that the primary purpose of international alliances is to provide public goods. Using the public goods paradigm, they concluded that suboptimality and disproportionality are inherent characteristics in international alliances such as the North Atlantic Treaty Organization (NATO).

As an indication of suboptimality, Olson and Zeckhauser cited NATO's system- atic failure to achieve their total goal for allied forces. To test for disproportionality, they examined the relationship between GNP and defense expenditures for each NATO member in 1964. They found that defense expenditures as a percent of GNP increased as GNP increased. Assuming that GNP and defense expenditures, as officially measured in a nation's national income accounts, are good proxies for defense benefits and contributions, respectively, this indicates that nations placing a higher value on defense were bearing a disproportionate share of the allied defense burden. Thus, NATO data indicated that there was suboptimality and disproportionality. Olson and Zeckhauser concluded that actual NATO behavior is not inconsistent with the public goods paradigm.

Later authors found that more recent data do not support the pure public goods paradigm. In particular, Sandler and Forbes (1980) observed that the relationship between defense expenditures and GNP began to deteriorate around 1967. Using data from 1967 to 1975, they tested the hypothesis that GNP and defense expenditures were independent across select NATO allies. In this sample, there was only one year when this hypothesis was statistically rejected. Further- more, comparing actual expenditures to estimates of defense benefits indicated that the defense burden had partially shifted from the United States to Western Europe during this time period.

These observations led to the development of the joint products model, where defense expenditures are characterized as providing both public and private benefits (Sandler and Cauley, 1975; Sandler, 1977, 1988; Sandler, Cauley, and Forbes, 1980; Sandler and Forbes, 1980). In this model, defense expenditures are typically divided into deterrence, protective, and mixed weapons. Deterrence weapons rely on a credible threat of retaliation to deter aggression. Strategic nuclear weapons are deterrence weapons. Tactical nuclear and conventional weapons are either protective or mixed weapons. Protective weapons shelter, repel, retard, or forewarn against an attack (e.g., early warning systems, air raid shelters, antiballistic missiles, and antitank guided weapons). Mixed weapons can function

1 Individuals making independent decisions will provide a public good until the marginal cost of the last increment they provide is equal to the marginal benefit they receive from that increment. In this decision, individuals ignore the benefit that their expenditures provide to others. Societal optimality requires that individuals provide the public good until the marginal cost of their last increment equals the marginal benefit that all consumers receive from that increment.



WILLIAM R. GATES AND KATSUAKI L. TERASAWA 103

in varying degrees as both deterrence and protective weapons (e.g., submarines, tanks, multipurpose aircraft, and cruise missiles).

In this classification, only deterrence is considered purely public. Assuming a credible threat of retaliation is extended equally to all members of the alliance, deterrence benefits are indivisible and nonexcludable.2 Protective and mixed weapons, on the other hand, are considered impurely public. They provide some public benefits (they increase deterrence by increasing the cost of aggression against the alliance), but they are not perfectly indivisible and nonexcludable. Rivalry in consumption is introduced because tactical nuclear and conventional weapons have a limited range. Members cannot be added to the alliance without detracting from the protection of the existing allies because resources deployed in one area are unavailable to protect other areas. Thus, these weapons are subject to "thinning" as the area defended by an arsenal of protective weapons increases. Furthermore, protective weapons are excludable because they can be withdrawn and redeployed elsewhere at the will of the provider. Finally, protective weapons provide some purely private benefits because they can be used for purely nation- alistic objectives (e.g., internal security, disaster relief, border protection). Thus, protective and mixed weapons provide some private benefits.

The joint products model distinguishes among deterrence, protective, and mixed weapons by assuming that defense expenditures produce both public and private benefits. An alliance member's utility is a function of the private and public benefits produced by that member and the public benefits produced by other alliance members.

Complementarity between Weapons

Murdoch and Sandler (1982, 1984) believe that deterrent and protective weapons have become complementary.3 In particular, they contend that nuclear and conventional weapons are synergistic under the flexible response doctrine, making them complements. Later, Hansen, Murdoch, and Sandler (1990) suggest that conventional weapons among non-nuclear allies have become complementary. This is explained as follows: "In fact, an increase in other allies' conventional expenditures should induce the non-nuclear ally to spend more on conventional armaments so that it does not appear weak" (Hansen et al., 1990:41). Appearing weak would presumably increase the probability of becoming the initial battleground. If some alliance members increase their defense expenditures, this threat allegedly drives the other alliance members to increase defense expenditures as well.4

In theory, if weapons are complementary, alliance members would increase defense expenditures as their allies' defense expenditures increase. This result contrasts with earlier alliance models, which assumed that defense goods are substitutes. Empirical analysis indicates that defense expenditures for many NATO allies were positively correlated during the late 1970s and early 1980s (Murdoch and

2 The authors recognize that deterrence weapons may not be fully nonexcludable (for example, Sandler, 1988:30-31). The U.S. controls most nuclear weapons and may decide that damage from an attack on its allies does not justify a nuclear response (i.e., commitment may be imperfect, in this paper's parlance). However, there is no way to explicitly incorporate excludability into the joint products model.

3 These models use the Hicksian definition of substitutes and complements extended to cases where there are three or more goods (Samuelson, 1974).

4 In actuality, the incentive to maintain one's strength relative to other alliance members is more complicated. If one alliance member doesn't match defense expenditure increases by other alliance members, that member becomes relatively weaker. However, that member has not become weaker in absolute terms. In fact, that member's security should increase with the alliance's strength. The probability of becoming the initial battleground may increase, but the probability of a conflict should decrease. Furthermore, the probability of becoming the initial battleground depends on both relative strength and geographic location. Considering these additional factors, there may be little incentive to maintain one's relative strength in the alliance.




Sandler, 1982, 1984; Hansen et al., 1990). This is consistent with the complementary joint products model.

A Commitnent-Based Distinction between Public and Private Benefits

There is an alternative distinction between public and private benefits which may provide additional insights into alliance defense expenditures. To motivate this distinction, it is important to understand the concept of deterrence. According to the National Security Strategy of the United States, "Deterrence works by persuading potential adversaries that the costs of their aggression will exceed any probable gains. Deterrence is the basis of our military strategy against conventional as well as nuclear forces." (U.S., Executive Office of the President, 1988:13. See also Betts, 1985; Bajasz, 1986/87; Freedman, 1987; and U.S. Commission on Integrated Long Term Strategy, 1988.)

Considering this, deterrence can be viewed as the primary objective of all alliance resources, including strategic nuclear, tactical nuclear, and conventional forces. All weapons increase military capability and either raise the potential costs for aggression against the alliance, or reduce the potential gains. As Palmer (1990:156) states:

The primary function of the Western alliance is to deter war, and the mutual commitment that underlies that deterrence is non-rival. Further, even if the alliance's deterrence is achieved through conventional means, necessitating tactical and rival movement of military capabilities, the purpose of the alliance remains the deterrence of war.

However, deterrence requires more than the military capability to impose unacceptable costs on potential aggressors. It also requires commitment to exercise that capability. If adversaries perceive that the U.S. is not committed to using nuclear force in retaliation for aggression against alliance members, nuclear deterrence is not credible regardless of the capability. On the other hand, if adversaries perceive the U.S. as committed to using conventional forces in a conventional confron- tation in Western Europe, conventional deterrence is credible.

This leads to a distinction between public and private benefits based on commitment rather than a weapon's technological characteristics. According to Hildebrandt (1990), purely public defense goods provide the same benefits to all members of the alliance, regardless of which member supplies the good. In other words, there are no distinct benefits associated with ownership of purely public defense goods. "To the extent, however, that specific characteristics of these goods generate a higher level of defense activity for the provider than they do for other member nations, the goods contain a private element" (Hildebrandt, 1990:7).

Considering this, public and private defense goods can be distinguished based on the degree to which they are committed to the alliance. For example, consider the case of NATO. Resources fully committed to the alliance (e.g., U.S. troops stationed abroad) can be considered as providing public benefits. Resources partially committed to the alliance (e.g., U.S. troops stationed in Japan and U.S. troops stationed in the U.S. but identified as early reinforcements for NATO) provide both public and private benefits. Finally, resources committed to uses outside the alliance (e.g., internal security, border protection, and unrelated international security interests) provide mostly private benefits.5

5 Not all resources committed to uses outside the alliance are purely private. For example, U.S. involvement in non-NATO regional confrontations, such as Operation Desert Shield/Desert Storm, may help reaffirm the U.S. commitment to assist both formal and informal allies. If allies and potential adversaries increase their perception of the U.S. commitment, then the alliance receives a public benefit from these resources, even though they are committed outside the alliance.




Commitment in this usage refers to the degree to which the member providing the resource relinquishes control over that resource. If the provider has trans- ferred all control over an asset to the alliance, alliance members will consider that the defense good is fully committed to the alliance. This ensures that the resource will be deployed in a way that best achieves the alliance's objectives. If the provider retains some control over the asset, alliance members will perceive that the defense good is only partially committed to the alliance. The provider has the ability to deploy the resource in a way that benefits the provider at the alliance's expense. In accounting for partially committed resources, alliance members are likely to consider the assets at less than their full potential value. Finally, if the provider retains complete control over the resource, and its expected deployment is not likely to provide any benefit to the alliance, the resource is purely private. Alliance members perceive no benefit from these resources.

There is an interesting and possibly realistic case where a country's allies and adversaries have different perceptions of the country's commitment. For example, suppose the NATO allies doubt the U.S. commitment to use its nuclear arsenal, while the Soviet Union considers the commitment small but non-negligible. The uncertainty perceived by the Soviets may deter Soviet aggression by creating a small probability of an unacceptable outcome. This would provide the alliance with a public benefit. However, if the allies perceive the U.S. commitment as negligible, they may consider the benefit of U.S. strategic nuclear weapons as mostly private. The actual balance between public and private benefits depends on the commitment perceived by potential adversaries. However, alliance members' expenditures are influenced by their perception of their allies' commitment, not the actual proportion of public and private benefits.

Even if deterrence fails and weapons are used defensively, their benefits are public if the resources are deployed to most effectively secure the alliance's objectives. Due to limited range and mobility, conventional resources may only be able to defend a small area. Nevertheless, the benefit is public if this deployment most effectively defeats the adversary or deters further aggression. A resource is partially private if its deployment provides the owner distinct benefits at the expense of the alliance's objectives (e.g., if the alliance would have repositioned the resource, ex ante, had the alliance been given control of the asset).6

Distinguishing between public and private benefits on the basis of commitment has significant implications for burden sharing, the incidence of free riding, and measures of fairness in defense alliances. These will be discussed after describing the model.

A Commitment-Based Model of Defense Alliances

Consider a two-country model, where each country (i) produces a private nondefense good (Xi) and a defense good (Yi). The defense good is nonrivalrous in consumption. The utility functions of Country One and Two are represented by U = U(X1, ZI) and V = V(X2, Z2), respectively. Zi (i = 1, 2) represents country i's total consumption of the defense good. Zi depends on the country's own production of the defense good (Yi) and the spillover benefits it receives from other countries (EjY): Zi = Yi + E.Y. (i = 1, 2; j ? i) . Country j produces Y' of the defense good, but country i perceives that only Ej of Y is credibly committed (or relevant) to country i's defense.

In general, E is expected to take on values between zero and one. If E. = 1, defense expenditures by country j are purely public goods. This corresponds to

6 Because of its limited applicability, the remainder of this paper will ignore rivalry in consumption for resources fully committed to the alliance.




Olson and Zeckhauser's model of alliances. Conversely, if Ej = 0, defense expenditures are pure private goods. This corresponds to the case where country i perceives that j has no commitment to i's defense, and i cannot depend on j's assistance in its defense calculations. As E. varies from one to zero, private benefits become relatively more important. This case reflects countries such as the U.S. where only part of the total defense expenditures are committed to the alliance. Finally, although not specifically modeled in this paper, countryj might be able to influence i's perception of j's commitment (Palmer, 1990). For example, the flexible response doctrine was designed in part to reaffirm the U.S. commitment to Western Europe in all types of contingencies. A similar argument can be made for U.S. forward-deployed forces in Western Europe. Conversely, many analysts believe that the Strategic Arms Limitations Talks (SALT) eroded Western Europe's perception of the U.S. nuclear commitment (Wolfe, 1979; Yost, 1981).

Each country maximizes its own utility subject to its resource constraint, assuming that its ally's defense expenditures and commitment level are given.7 Each country's resource constraint is expressed as: Gi = PiX, + Yi (i = 1, 2), where Gi denotes i's GNP, and Pi is the relative price of the private good measured in terms of the defense good. The first order conditions for utility maximization for Country One are given by

UX/UZ = P1 (1)

G1 - PIX, - Y1 = 0 (2)

Similar first order conditions characterize utility maximization for Country Two. These are the familiar first order conditions for voluntary, independent contri-

butions for a public good. According to condition (1), utility maximization occurs when the ratio of the marginal utilities for the defense and nondefense goods (i.e., the marginal rate of substitution) equals the ratio of their marginal costs (i.e., the marginal rate of transformation).8 The second condition is the resource constraint.

If spending on nondefense goods increases with GNP, then Country One's defense expenditure is a decreasing function of Country Two's defense expenditure (Pauly, 1970). By examining the impact that changes in Y2 have on Y1, it is possible to derive Country One's reaction function. This shows the amount of defense Country One will provide for all possible levels of defense expenditures by Country Two. Country Two's reaction function can be derived in a similar manner. These functions can be expressed as

Y1 = Y1 (G1, P1, E2Y2) (3)

Y2 = Y2 (G2, P2, E1Y1) (4)

In an alliance where contributions to the mutual defense are voluntary and independently determined, equilibrium will occur where the members' reaction curves intersect. This is the only point where country i's expectation regarding

7 This is a Nash equilibrium. This equilibrium concept is typically used to describe alliance interactions, and has been used in the pure public goods and joint products models described above. If alliance members are concerned with maintaining long-term mutual commitment, interactions between alliance members may involve cooperative behavior such as bargaining (Palmer, 1990).

8 This trade-off is affected by a country's threat perception. Threat perceptions presumably affect the marginal rate of substitution between expenditures on defense and nondefense goods. Thus, threat perceptions are incorporated as the income elasticity of total effective defense expenditures (a country's own defense expenditures plus those expenditures committed by the country's allies).




country j's contribution is consistent with country j's actual contribution, and vice versa.9

For example, assume Cobb-Douglas utility functions of the form: U = (XIAl) (ZIBl), and V = (X2A2) (Z2B2), where A, and Bi represent i's utility elasticity of the nondefense and defense goods, respectively. The value of Bi relative to Ai reflects the country's threat perception. With these utility functions, and the first order conditions for utility maximization given above, the reaction functions for both countries can be expressed as

Yi = {BiGi - AiE.Yj}/(Ai + Bil i,j = 1, 2;j i (5)

Full Commitment

Figure 1 illustrates the reaction functions and equilibrium defense expenditures for the two countries, assuming Cobb-Douglas utility functions, full and symmetric commitment (E1 =E2 = 1), equal GNP (G1 = G2 = 10), identical preferences (A1 = A2 = 0.2; B1 = B2 = 0.2), and equal relative marginal costs for the nondefense good (P1 = P2 = 0.5). Because both countries exhibit full commitment, this model corresponds to the pure public goods model, where both countries are identical in all respects. In this case, both countries will spend one third of their GNP on defense and the equilibrium is stable (i.e., if actual and expected contributions by the allies are not equal, both countries adjust their expenditures in a way that moves toward equilibrium).

In fact, the equilibrium level of defense expenditures for a Cobb-Douglas utility function is given by

Yi = {aiGi - biEjGj}/D i,j = 1, 2;j i (6)

where ai = (Aj + B.)B.; bi = AiB-; and D = {(A, + Bi) (Aj + B.) - AAjEiEj}

The Nash equilibrium level of defense output falls short of the optimum output, where the optimum output equates the marginal cost of defense expenditures to the sum of the marginal rate of substitution for all member countries.10 However, when both countries are identical, there is no disproportionality. The defense burden is shared equally (i.e., both countries spend one third of their GNP on defense).

Disproportionality, as traditionally measured (i.e., defense expenditures as a percentage of GNP), arises if GNP differs across countries, ceteris paribus. From equation (6), assuming full commitment, it is easy to see that relative defense expenditures (Yi/Gi) would be larger for a country with a higher utility elasticity-weighted GNP, (Bi/A,) Gi. In other words, the country with the highest elasticity-weighted GNP will contribute relatively more toward defense. If both countries have identical preferences, the distribution of the defense burden is determined by relative GNP.

9 Equations (3) and (4) implicitly define a country's defense expenditures in terms of its GNP, the price of the private good relative to the defense good, and the benefits it receives from its allies' defense expenditures. This is identical to the functional form empirically estimated by Murdoch and Sandler (1984:88). Using Murdoch and Sandler's data to empirically estimate equations (3) and (4) would yield similar parameter estimates and functional fit. However, there would be significant differences in interpreting the variables. In Murdoch and Sandler's model, the coefficient of the term for the allies' defense expenditures indicates complementarity. In the commitment model described here, these coefficients would indicate commitment and threat perception. Rather than duplicate Murdoch and Sandler's empirical analysis, this paper will focus on describing the intuition behind the commitment model.

10 Suboptimality for Nash equilibrium defense spending was noted by Olson and Zeckhauser (1966) and later proved by Pauly (1970).




4.0

cm 3.9 _\

> 3.8 _ ~ \ Country One V

c 3.7 w a) 3.6 U)

Country Two '~3.5

o 3.4 H D 3.33 0 O 3.2

3.1

3.0

3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00

Country One's Defense Expenditure, Y1

FIG. 1. Reaction functions and equilibrium defense spending.

This case of disproportionality is illustrated in Figure 2. Keeping Country Two's GNP constant, Country One's GNP is increased along the horizontal axis from 10 to 120 percent of Country Two's GNP. The resulting equilibrium defense expenditures for both countries (measured as a percentage of GNP) are shown in Figure 2. Country One devotes a smaller share of GNP to the mutual defense as long as its GNP is less than that of Country Two. Only when G1 = G2 do both countries devote the same percent of GNP to defense. Thus, when Ei = 1 for all i, this model's results are the same as the pure public goods model.

Furthermore, this example illustrates Olson's (1965) "privileged group."Il For G1 less than 50 percent of G2, Y1 = 0 and Country Two voluntarily provides all of the public good. However, it should be noted that the relative GNP level at which Country One starts spending on defense, (G1/G2) *, is determined by Country Two's commitment and the utility elasticity of the defense and nondefense goods for both countries. In particular, equation (6) indicates that Country One's threshold GNP is determined by (G1/G2)* = B2A1E2/(A2 + B2)B1. Thus, Country One's threshold GNP increases as A2 decreases or B2 increases. These changes reflect a shift in Country Two's marginal rate of substitution between defense and nondefense goods in favor of defense goods (i.e., an increase in Country Two's threat perception). This would increase defense expenditures in Country Two. In response, Country One would substitute the increase in spillover benefits from Country Two for its own defense expenditures. Thus, Country One would reduce defense expenditures, raising its threshold GNP. Conversely, an increase in A1 or a decrease in B1 indicates a shift in Country One's preferences toward nondefense goods. This increases Country One's threshold GNP. Finally, an increase in E2 increases the benefit that

11 In a "privileged group," there is great disparity in the size of the members. If some members are sufficiently large (or place a sufficiently high value on the public good), they might be the only members providing the public good. Smaller members could be satiated with the quantity provided by the larger members. The larger members' contributions and the incidence of free riding should decrease as the smaller members' relative GNP increases.



WILLiAM R. GATES AND KATSUAKI L. TERASAWA 109

0.50-_

o 0.45 Country Two

- 0.40 z

? 0.35 .a) c 0.30 a) u) 0.25 a) - 0.20 Country One CL

,xj 0.1 5-/ a)

a, 0.10 a)

c 0.05 0.05

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

Country One's GNP Relative to Country Two, G1/G2

FIG. 2. Defense spending as a function of relative GNP.

Country One derives from Country Two's defense expenditures. This would also increase Country One's threshold GNP. Thus, the occurrence of Olson's "privileged group" depends on several factors in addition to relative GNP.

Partial Commitment

Another example considers partial commitment (E1 = E2 = 0.5). As in the previous example, this case assumes Country Two's GNP is held constant and Country One's GNP varies from 10 percent to 100 percent of Country Two's GNP (all other parameters have the values given in the previous examples). Figure 3 compares equilibrium defense expenditures for the partial and full commitment cases. Because Country Two's defense expenditures have less credibility, Country One will spend more on defense in the partial commitment case than it did under full commitment, for all levels of GNP above G1/G2 = 0.25. Further comparing partial to full commitment, the percentage increase in Y1 decreases as G1 increases.

Country Two's defense expenditures are slightly more complicated. Country Two's defense expenditures decrease if the spillover benefits from Country One increase as the level of commitment decreases. With partial commitment, Country One's defense expenditures increase relative to the full commitment case. How- ever, these expenditures are only partially committed to Country Two. If commitment falls from 100 to 50 percent, Country Two only receives half of the previous benefit from each dollar that Country One spends on defense. Country Two's spillover benefit increases if the decrease in commitment more than doubles Country One's defense expenditures.

In Figure 3, Country One's defense expenditures are more than twice as high with 50 percent commitment, relative to full commitment, when 0.25 ? G1/G2 < 0.67. Thus, Country Two's defense expenditures are lower than in the full commitment case. As Country One's relative GNP increases, its percentage increase in defense expenditures decreases. When G1/G2 > 0.67, Country Two spends relatively more on defense in the partial commitment case because Country One's defense expenditures less than double.




Country Two: Full Commitment

0.50

R 0.45 - Country Two: 0.40 Partial Commitment

0 4 0.35 U)

X 0.30 75 Country One: C 0.25 Partial Commitment UD

r 0.20

Q 0.15 X w Country One: CD 0.10 --, / Full Commitment

c] 0.05-'/ 0.10

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Country One's GNP Relative to Country Two, G1/G2

FIG. 3. Effects of credible commitment.

Figure 3 also illustrates that this model can generate results similar to the joint products model. For all levels of GNP, combined defense expenditures by both countries increase as commitment decreases. Furthermore, the difference between the percentage of GNP devoted to defense by each country decreases. Thus, as the public benefits of defense expenditures decrease (i.e., the level of commitment decreases), suboptimality and disproportionality decrease.12 However, suboptimality and disproportionality cannot be completely eliminated unless both countries perceive no commitment to mutual defense (i.e., E1 = E2 = 0).

This leads to a dubious result if considered in the narrow framework of this model. We can eliminate disproportionality and suboptimality by reducing the perceived commitment between allies. This can be accomplished by threatening to withdraw or redeploy troops and procuring weapons of limited use to the alliance. However, reducing the perceived commitment increases aggregate defense spending and reduces allied security. The primary benefit provided by defense alliances is deterrence against foreign aggression. Deterrence increases because potential adversaries will encounter the combined resources of all alliance members in return for aggression against any member. Reducing commitment can reduce deterrence for alliance members, thereby increasing the probability of conflict.13

12Suboptimality is computed here for a given level of partial commitment, Ei. If the commitment level is a choice variable, then the issue of optimality must be discussed in a broader context.

13 The reduction in security is reflected by the decrease in total combined utility (U + V) as commitment decreases and aggregate defense expenditures increase. However, utility for some individual members may actually increase. In Figure 3, utility increases for Country Two when Country One's income is relatively low and a decrease in commitment results in lower defense expenditures for Country Two. Country One's utility decreases everywhere in Figure 3.




Divergent Threat Perceptions

The effects of divergent threat perceptions can also be examined in this model. In particular, Country Two's utility elasticity of defense expenditures has the same value as before (B2 = 0.2), but this parameter for Country One (B1) varies from 10 to 120 percent of Country Two's parameter (i.e., 0.02 < B1 < 0.24). Equilibrium defense expenditures are calculated assuming constant and identical GNPs for both countries.

Figure 4 shows the results of this case, assuming full commitment, where the horizontal axis measures the ratio of the defense utility elasticities for both countries (B1/B2). An increase in Country One's threat perception increases its defense expenditures. In turn, defense expenditures in Country Two decrease. As B1 increases relative to B2, disproportionality decreases.14

Figure 5 contrasts the effects of partial commitment to full commitment over the range of varied threat perception. For different levels of threat perception, reducing the level of commitment has an effect similar to that explained in the earlier partial commitment case (Figure 3).15 With partial commitment, Country One increases its defense expenditures for all levels of the perceived threat above B1/B2 = 0.25. Country Two's response balances the effects of its ally's increased expenditures and lower commitment. When the perceived threat is 0.25 < B1/B2 < 0.67,

0.50 - Country Two

0.45

S 0.40 z ( 0.35 0

* 0.30

C 0.25 U)

~ 0.20 - / Country One V

a) a 0.15 w a) U) 0.10

c 0.05

0.00

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

Country One's Threat Perception Relative to Country Two, B1/B2

FIG. 4. Effects of threat perception: full commitment.

14 Note the similarity between Figures 2 and 4. Country One's defense expenditures increase in both cases, because of an increase in either GNP or threat perceptions. Country Two is concerned with the value of the benefits it receives from Country One, not with the reason these benefits have increased. Therefore, Country Two's response to increases in Country One's defense expenditure is the same in both cases. This is similar to the predictions of the "neutrality" theorem, as described by Warr (1983), Bergstrom, Blume, and Varian (1986), and Hildebrandt (1990). In the neutrality theorem, a consumer's expenditures on a public good can be shown to depend on the consumer's full income, where full income is personal income plus the in-kind income received from the public good provided by other consumers.

15 The same reasoning that explained the similarity between Figures 2 and 4 explains the similarity between Figures 3 and 5.




Country Two: 0.50 - Full Commitment

C 0.45 0 0 Country Two:

o0 Partial Commitment CD > 0.35

CD 0.30

V 0.25 CD Country One: -02

Partial Commitment LU CD 0.15 a).-(D ,.*Country One:

0.10 Full Commitment

0.05

0.00- I I 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Country One's Threat Perception Relative to Country Two, B1/B2

FIG. 5. Effects of threat perception: full and partial commitment.

reduced commitment elicits a relatively large increase in Country One's defense expenditures and Country Two reduces expenditures relative to the full commitment case. As Country One's perceived threat increases, the relative increase in that country's defense expenditures decreases. Eventually, the decrease in comnmit- ment outweighs the increase in Country One's defense expenditures. Country Two increases its expenditures relative to full commitment.

Interpreting the Commitment-Based Alliance Model

Figure 6 summarizes U.S., non-U.S. NATO, and total NATO defense expenditures as a percent of GNP from 1970 to 1985. Figure 6 indicates that the ratio of defense expenditures to GNP is positively correlated between U.S. and non-U.S. members of NATO for many years in this period. More specifically, the changes in defense expenditures relative to GNP were positively correlated in ten of fifteen cases in this time period. They were negatively correlated in just three cases (there were two cases where the ratio remained constant for the U.S. and/or non-U.S. NATO countries).16 This is counter to the results expected from the public goods paradigm, where free riding results in a negative correlation between changes in U.S. and non-U.S. NATO defense expenditures. Thus, total aggregate defense expenditures by NATO alliance members do not appear to provide pure public benefits.17

16 In the ten cases between 1960 and 1970, the ratio of defense expenditures to GNP was positively correlated five times, negatively correlated four times, and unchanged in the U.S. one time.

17 As observed by Olson and Zeckhauser (1966), the public goods paradigm predicts a negative correlation between changes in the ratio of defense expenditures to GNP across alliance members, ceteris paribus. In other words, this negative relationship is expected if tastes (i.e., threat perceptions and the relative priorities of defense and nondefense goods) are constant for all allies over time. The joint products model implicitly incorporates the ceteris paribus assumption because it does not allow for changes in tastes.




Defense expenditures generate public and private benefits in both the joint products and commitment-based alliance models. In the joint products model, technological attributes, particularly range, are the distinguishing characteristics. In the commitment-based model, all defense resources can provide public and/or private benefits, regardless of their technical characteristics. Public and private defense goods are distinguished by the degree to which they are committed to the alliance. Defense resources that are fully committed provide public benefits. Defense expenditures that are not fully committed generate a mixture of public and private benefits. Explanations for alliance members' defense expenditures will vary, depending on how public and private defense benefits are distinguished.

To illustrate the differences between the joint products and commitment-based alliance models, consider NATO defense expenditures between 1970 and 1979. U.S. defense expenditures decreased as a percent of GNP in seven of nine cases between 1970 and 1979 (they remained constant in the other two cases). Non-U.S. NATO defense expenditures also decreased as a percent of GNP in six of nine cases during this period (they increased in the other three). Thus, there is a relatively consistent decrease in defense expenditures for both U.S. and non-U.S. NATO members during this period.

The joint products model hypothesizes that changes in military strategy and technology explain this trend. In particular, NATO's defense strategy changed from mutual assured destruction to flexible response. The former strategy emphasized the U.S. nuclear umbrella whereas the latter strategy placed increasing emphasis on conventional arms. Thus, private benefits became more important as defense strategy shifted toward flexible response. In the joint products model, this shift was most dramatic when precision-guided munitions were introduced in the mid-1970s. This allegedly gave NATO the capability to implement the flexible

8-

7 -- U.S.

z

n. T on-U.S NATO

C

LL5 a)

(n

V

. 4 Non-U.S..NAT

w (n

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1970 1975 1980 1985 Year

FIG. 6. U.S., non-U.S. NATO, and total NATO defense expenditures as a percent of GNP: 1970-1985. (Source: Government Business Worldwide Reports (Jan. 2, 1991) Defense and Economy World Report 1196.)




response doctrine.18 According to the joint products model, the incentive to free ride decreased and defense expenditures became complementary across allies as private benefits became relatively more important during the 1970s. Thus, the joint products model predicts that U.S. and non-U.S. NATO defense expenditures should become more directly correlated, as observed.

The commitment-based model suggests other plausible explanations. For example, the trends in U.S. and non-U.S. NATO defense expenditures in the 1970s can be attributed to changes in the U.S.'s military capability and commitment to NATO. With regard to U.S. military capability, Figure 6 illustrates that U.S. defense expenditures declined as a percent of GNP throughout the 1970s. This corresponds to the U.S. withdrawal from Vietnam and the post-Vietnam era. During this time, relative priorities began shifting from defense to social objectives. Furthermore, military capability decreased even more than indicated by the aggregate defense expenditure data because the U.S. eliminated conscription in 1973 and moved to an all-volunteer force. This increased average personnel costs, reducing both the number of personnel and the funds available for non-personnel expenditures. At the same time, Soviet conventional and strategic power continued to increase. Thus, U.S. military capability eroded significantly relative to the Soviet Union. 19

The U.S.'s perceived commitment to Western Europe also decreased during this period. The relative decline of the U.S. military capability was matched with an increasing emphasis on d6tente. D6tente initiatives were largely unilateral. For example, the U.S. and the Soviet Union were involved in the Strategic Arms Limitations Talks. Western Europeans perceived this as a signal that the U.S. nuclear umbrella was weakening. Despite increasing Soviet strategic capabilities, many Western Europeans still viewed the nuclear umbrella as the pillar of NATO's deterrence strategy (Wolfe, 1979; Yost, 1981; Calleo, 1987). As Treverton (1983: 106-107) notes:

West German Chancellor Helmut Schmidt's celebrated speech in October 1977 was a reflection of his concern about the course of SALT II. Europeans like Schmidt had more qualms about the political symbolism of the emerging SALT II treaty than about specific provisions. Measures that were agreed upon before or during the SALT "breakthroughs" in September 1977 ... all seemed to suggest to the Soviet Union that the security of the United States and that of Europe could be treated separately.

The Vietnam experience also eroded the U.S.'s desire to enter another conflict on foreign soil, particularly in Third World countries. This hesitancy was indicated when the Southeast Asian Treaty Organization (SEATO) and the Central Treaty Organization (CENTO) were allowed to lapse. Though these treaties had never been particularly vital, their demise did symbolically signal that the U.S. was shedding its international defense commitments in the post-Vietnam era.

The decrease in perceived commitment during the mid-1970s is supported by surveys of public and expert opinions in Western Europe (Eichenberg, 1983; Domke, Eichenberg, and Kelleher, 1987). In particular, these surveys indicate that support for NATO in France, Great Britain, West Germany, the Netherlands, and the U.S., which had been relatively high in 1971, had fallen significantly by the

18 Oneal and Elrod (1989) assert that there is reason to question this scenario. They believe that technological developments in precision-guided munitions during the 1970s were not that significant, particularly compared with technological improvements in Soviet munitions. They also question whether Western Europe has ever fully embraced the flexible response doctrine. Calleo (1987:44-71) agrees that Western Europe didn't embrace flexible response and asserts that the U.S. strategic nuclear advantage extended until the mid- to late 1970s. The U.S. derived its strategic advantage from its Multiple Independently Targeted Re-entry Vehicles (MIRV), which gave the U.S. a significant advantage in deliverable warheads until the early 1980s.

19 For further discussion of this period see Calleo (1987, Chapter 4), Adelman (1980), and West (1980).




mid-1970s. In Western Europe, this is consistent with a decline in the perceived U.S. commitment and a recognition that Western Europe must be more self-suffi- cient. In the U.S., this reflects the U.S.'s reluctance to enter conflicts to protect other countries and an increasing emphasis on d6tente.

If decreases in the U.S.'s military capabilities and commitment to the NATO alliance are incorporated in the commitment-based alliance model, the model can simulate trends similar to those observed between 1970 and 1979 in Figure 6. In particular, these effects can be incorporated by adjusting both B2 (the U.S. relative threat perception) and E2 (the U.S.'s perceived commitment to NATO).20

Between 1979 and 1982, U.S. and non-U.S. defense expenditures both increased relative to GNP, though the increase for non-U.S. NATO members was small. The commitment-based model can also provide a plausible explanation for this period. In particular, the U.S. defense build-up in the 1980s can be seen as a change in the U.S. threat perception. Events in the late 1980s, including the revolution in Iran, the Soviet invasion of Afghanistan, and suppression of the Solidarity movement in Poland, indicated that U.S. power was eroding and U.S. d6tente initiatives were fail- ing. In addition, there was growing concern that relative conventional and strategic power were shifting from the U.S. to the Soviet Union. These trends led to an increase in the perceived threat, both in the U.S. and in non-U.S. NATO countries. In the U.S., this was signaled by the 1980 presidential election, in which the pledge for a stronger defense was a major factor in Ronald Reagan's successful cam- paign.21 It is also evident for the non-U.S. NATO members, where Western Europe became increasingly concerned about failures in U.S. d6tente and the Reagan administration's seemingly aggressive U.S. foreign policy (Calleo, 1987). Public and expert opinion surveys show increasing support for NATO, which also suggests that the perceived threat increased (Eichenberg, 1983; Domke et al., 1987). The pattern of actual defense expenditures as a percent of GNP between 1979 and 1982 is consistent with a general increase in threat perceptions throughout NATO.

As can be seen, the commitment-based alliance model provides plausible explanations for the post-World War II trends in NATO's defense expenditures. Furthermore, these explanations are consistent with other research describing relations within NATO during this period. The commitment-based model indicates that defense expenditures depend critically on each NATO member's GNP, defense expenditures, threat perceptions, and relative priorities between defense and nondefense goods. They also depend on the level of commitment between alliance members. Many of these explanations cannot be considered in the joint products model because the model does not explicitly include commitment and threat perceptions. Further empirical research is needed to test the commitment model more rigorously and verify its explanatory power.

Implications and Conclusions

The policy implications of the commitment-based and joint products models are significantly different. The joint products model implies that suboptimality and disproportionality become increasingly insignificant as private benefits become relatively more important. Furthermore, optimal membership is strictly limited

20 The adjustment in E2 balances two effects. The non-U.S. NATO allies will discount more heavily the U.S. defense resources available to NATO. However, a higher proportion of U.S. resources will be available to NATO, because the Vietnam withdrawal involved resources committed outside NATO. These two effects will move E2 in opposite directions.

21 Research by Domke, Eichenberg, and Kelleher (1983) confirms that defense expenditures in the U.S. are responsive to changes in threat perceptions.




because of rivalry in consumption (thinning). In the joint products model, recent and planned changes in technology and strategy have increased the relative importance of private benefits. Thus, there is no reason to restructure NATO on effi- ciency grounds (though closer integration might be desirable if it is justified by more effective military planning or improvements in interoperability).22 If the evolution of strategy and technology continue to increase the relative importance of private benefits, suboptimality and disproportionality should be naturally eliminated.

In a commitment-based model of defense alliances, the balance between public and private benefits is determined by the level of commitment. Any resource that is perceived as committed to the alliance contributes to deterrence (or to deterrence of further aggression if deterrence initially fails). Thus, any committed resource provides public benefits to all members of the alliance, regardless of its technical characteristics (e.g., range and mobility). If a resource is not perceived as fully committed to the alliance, it is not a pure public good. If all resources fully committed to the alliance provide public benefits, then the primary purpose of an alliance is to provide public goods.

IncreasingEquity

To the extent that resources committed to an alliance cannot be withheld or withdrawn, disproportionality is an inherent characteristic of a commitment-based alliance model, as in the pure public goods model. Furthermore, it cannot be reduced through moral suasion, a popular U.S. tactic (Fallows, 1989; U.S. Congress, Burdensharing Panel, 1988; Watson, 1988). This intransigence results because free riding is firmly grounded in the participants' national interests, not because of different moral attitudes (Olson and Zeckhauser, 1966:278). Disproportionality can be reduced by decreasing the level of commitment. However, decreasing commitment among allies could be counterproductive because it would compromise the alliance's integrity. It reduces disproportionality at the expense of effectiveness.23

Instead, disproportionality and suboptimality should be addressed through institutional changes that alter the members' incentives.24 For example, if members value an ongoing, long-term relationship, they may have less incentive to free ride. Free riding creates a short-term gain but it mayjeopardize long-term relationships. If commitment can be withheld or withdrawn, this "excludability" may reduce the incentive to free ride. Alternatively, cooperative development and pro- curement programs, which provide participants with economic and technological benefits, could help increase the contributions of alleged "free riders." Finally, private goods (such as favored trading status) might be offered as side payments to encourage defense contributions (Williams, 1966; Russett and Sullivan, 1971).

22 Developments increasing the relative importance of private defense benefits include: changes in defense strategy from mutual assured destruction to flexible response, technological developments (e.g., precision-guided munitions), nuclear disarmament, modernizing strategic forces in Britain and France, the Strategic Defense Initiative (SDI), and increases in disputes exogenous to the East-West split (Sandler and Forbes, 1980; Sandler, 1988).

23 Disproportionality would, in fact, be completely eliminated if there were no commitment among alliance members. However, without commitment there would be no alliance.

24 In fact, Olson and Zeckhauser (Olson, 1965; Olson and Zeckhauser, 1966; Olson, 1971) suggest a marginal cost pricing scheme. Members share the marginal costs of each increment of defense in the same proportion as they share the marginal benefits. With this pricing scheme, members will agree to increase defense expenditures until they reach the optimal level and each member contributes in proportion to the benefits received. Unfortunately, this scheme is impossible to implement. Marginal contributions and marginal benefits cannot be quantified, and alliance members have an incentive to free ride by overstating their contributions and understating their benefits. Thus, marginal cost pricing is not an operational concept (Loehr, 1973).




Increasing Effectiveness

In addition to equity, it may be beneficial to increase effectiveness by increasing the level of perceived commitment. As commitment increases, total defense expenditures can be reduced. This will increase total utility in this model.25 There are several ways to affect the perceived commitment. For example, foreign military bases and foreign-based troops increase commitment by involving several allies in conflicts that are geographically confined to a single country. Similarly, the U.S. adoption of the flexible response doctrine can be viewed as an attempt to increase the perceived U.S. commitment and revitalize the U.S. nuclear deterrence. Con- versely, the Strategic Arms Limitations Talks and the Intermediate Range Nuclear Forces (INF) treaty were viewed by many Western Europeans as indicating a reduction in the U.S. commitment (Wolfe, 1979; Yost, 1981). Thus, commitment can be affected by the level and content of a nation's defense expenditures and by political relationships both within the alliance and between alliance members and adversaries.

Commitment-increasing activities may be significant in mature alliances. This may manifest itself both in the actions taken by alliance members to increase their perceived commitment and in the process through which alliance members set their defense expenditures (i.e., it may be appropriate to alter the Nash equilibrium to incorporate commitment-increasing activities explicitly) (Kuenne, 1988; Palmer, 1990).

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