Within-Group Heterogeneity and Civil War∗ Nobuhiro Mizuno† Faculty of Economics, Osaka University of Economics

Ryosuke Okazawa‡ Graduate School of Economics, Osaka City University

December 2016

Abstract This study offers a bargaining model of conflict in which the government offers a transfer to an opposition group to preclude civil war. Members of the opposition are heterogeneous in income and ideology, and heterogeneity generates disagreement about whether to accept the government’s offer. We assume that the probability that the government’s offer will preclude conflict increases continuously with the number of opposition group members who agree to accept it. When within-group heterogeneity is large, the number of members who are receptive to the government’s offer is less responsive to an increase in the transfer level. In this situation, the government must substantially increase its transfer to attract the support of the opposition. Subsequently, as peace becomes more costly for the government, negotiations are likely to break down. JEL classification: C78; D31; D74 Keywords: Bargaining; Civil war; Heterogeneity

∗ We are grateful to the editor, Amihai Glazer, and an anonymous referee for their useful comments. We also appreciate the comments made by Akihisa Shibata, Kazuhiro Yuki, Naoto Jinji, and Yuta Kamahara, as well as conference and seminar participants at the Japan Public Choice Society Meeting 2015, the Institute of Developing Economies JETRO, and Fukuoka University. † E-mail: [email protected] ‡ E-mail: [email protected]

1

Introduction

According to Blattman and Miguel (2010), 20 % of the world’s countries were engaged in civil war for at least 10 years during the 1960–2006 period. Civil war threatens human rights and welfare and damages economies.1 Since the seminal study of Collier and Hoeffler (1998), many studies have found a negative relationship between per-capita income and the risk of civil war.2 In contrast, most empirical studies find no significant relationship between economic inequality and the risk of civil war (Fearon and Laitin 2003; Collier and Hoeffler 2004). However, recent empirical studies cite “within-group” inequality, not overall inequality, as a significant cause of civil war. Using subnational data for sub-Saharan Africa, Østby et al. (2009) find that intra-regional inequality in household assets and education increases the onset of civil conflict. As the failure of negotiations between Israel and Palestine during the 1990s suggests, heterogeneity in ideology among within-group members also affects the likelihood of conflict. Although Israel–Palestine negotiations began with bilateral popular support, the extremist Palestinian faction Hamas hindered them by attacks against Israel (Kydd and Walter 2002). This study presents a bargaining model of civil conflict that illustrates the manner in which within-group heterogeneity hinders peace negotiations and leads to the outbreak of costly conflicts. Our model follows the standard environment in the literature of bargaining models of conflict. If the government and an opposition group initiate civil war, both bear its cost, but the winner deprives the loser of a portion of its resources. The government has little to gain and much to lose from civil war, and it can thus offer the opposition group transfers in order to preclude civil war. If the opposition accepts the government’s offer, war is precluded. As per Fearon (1995), as long as each group is treated as a unitary player, conflict can be precluded through negotiation, because there is no private information, issue indivisibility, or commitment problem. We extend the standard bargaining model of conflict by introducing heterogeneity into the opposition group, and explicitly consider the manner in which conflicting interests among members in the opposing group affect bargaining outcomes.3 Income is the opportunity cost of war, and ideology is the payoff from waging war (e.g., antagonism toward the government). Given their heterogeneity, members of the opposition group have different preferences for civil war, and whether the opposition group accepts the government’s offer depends on 1 See,

for example, Rodrik (1999) and Cerra and Saxena (2008). the quantity of rainfall as an instrument, Miguel et al. (2004) show that poverty exerts causal effects on the risks of civil war. 3 Bueno de Mesquita (2005) presents a model in which an opposition group comprises moderates and extremists, which is similar to this study in the sense that within-group heterogeneity of political preferences are explicitly analyzed. Unlike this study, however, Bueno de Mequita (2005) does not analyze how increasing heterogeneity affects negotiation outcomes. 2 Using

1

the distribution of members’ preferences. Therefore, within-group heterogeneity matters with respect to the outbreak of civil conflict. Although many studies treat groups involved in conflict as unitary players, Jackson and Morelli (2007) analyze a situation wherein the net value of conflict for a pivotal decision-maker differs from that for the entire group. In their study, the discrepancy between the pivotal agent’s net value and that of the group is represented as “political bias,” and they show that negotiations cannot forestall conflict if the political bias is large. We present a benchmark model based on an argument similar to that in Jackson and Morelli (2007), to show that extensive within-group income inequality raises the prospect of civil war if the opposition group makes decisions by majority rule. Although our analysis shows the link between within-group heterogeneity and the onset of conflict, the assumption of majority rule is not plausible in the context of civil war. More importantly, although the benchmark model assumes that only pivotal agents affect the outcomes of a peace process—as the failure of Israel–Palestine negotiations indicates—a faction opposed to peace can derail negotiations. In the main part of this paper, we consider the likelihood that negotiations will be unsuccessful when a faction in one of the negotiating parties opposes peace. Specifically, we assume that the probability of negotiations failing will increase continuously as the number of members who reject the government’s offer increases. The greater the number of opponents, the greater their influence is on the peace process. Hence, the probability of civil war increases as their number increases. Under this assumption, we argue that extensive heterogeneity within an opposition group leads to the onset of civil war, via the following mechanism. The net payoff to each member of the opposition from accepting the government’s offer depends on his or her heterogeneous characteristics, and the payoff increases as the amount offered by the government increases. Government can bolster support for peace by increasing the amount of transfer offered, which can in turn reduce the risk of a civil conflict. However, when heterogeneity within the opposition is large, member preferences are dispersed and support for the peace process is less responsive to any change in the proposed transfer. Then, the government’s marginal cost from increasing support for the peace process will increase. In this situation, the government offers the opposition a small transfer, and the equilibrium probability of peace is small.4 This study is inspired by that of Mizuno et al. (2017), and the theoretical mechanism herein is similar to their model. However, the current study addresses a research question that differs entirely from that of Mizuno et al. 4 This

mechanism is similar to the probabilistic voting model (Lindbeck and Weibull 1987; Dixit and Londregan 1996; Persson and Tabellini 2000).

2

(2017). Mizuno et al. (2017) analyze relationships among inequality, institutions, and growth in nondemocratic regimes. Specifically, they analyze the decisions of an autocratic ruler who faces a tradeoff between the expropriation of citizens’ wealth and holding on to power. The contribution of this study is that it shows the link between within-group heterogeneity and failed peace negotiations. This study is also related to that of Esteban and Ray (2011), who show that greater inequalities in within-group income are associated with more intense conflicts. In their model, the poor commit their time to conflicts, whereas the rich contribute money. When intra-group income inequality is large, the group’s poorer members face lower opportunity costs by participating in the conflict, and the wealthier members contribute more money to it. However, determining the reasons why the opposing groups undertake costly conflicts exceeds the scope of their analysis. Understanding the reasons for being unable to preclude costly conflict through negotiation is a major issue in the literature; most studies cite private information and commitment problems as factors that underlie failed negotiations (Fearon 1995; Powell 1999, 2002, 2006). The role of transfers (or inclusive policies) in precluding conflict is studied by Azam (1995), Azam and Mesnard (2003), Haimanko et al. (2005), and Reynal-Querol (2005), but these studies do not examine within-group heterogeneity, nor do they undertake analyses on the basis of bargaining models. This paper proceeds as follows. In Section 2, we provide anecdotal illustrations of peace processes that have collapsed on account of internal opposition. In Section 3, we explain our model. In Section 4, we consider the case wherein the opposition group’s decision to accept the government’s offer is made by a pivotal internal agent. In Section 5, we present the study’s primary contribution. In Section 6, we conclude the study.

2

Examples of Collapsed Peace Processes

This study’s major findings arise from the assumption that peace accords between the government and an opposition group can collapse when a faction of opposition group members opposes it. This section presents three illustrations that support this assumption. All three show the significance of within-group heterogeneity in political preferences on outcomes. More importantly, they demonstrate that decisions formalized during negotiations can be overthrown by factions who reject them.

3

2.1

Israel and the Palestinian Authority

Although peaceful resolution to the conflict between Israel and the Palestinian Authority (PA) had been sought during the 1990s, negotiations under the Oslo Accords failed. Signed in 1993 by Israeli Prime Minister Yitzhak Rabin and Yasir Arafat, the leader of the Palestine Liberation Organization (PLO), the Oslo Accords declared mutual recognition by Israel and the PLO and established a framework for interim self-government in Gaza and the West Bank and finalstatus negotiations. Although most Israelis and Palestinians welcomed early negotiations, opposition within both camps was strong. Hamas, an opposing Palestinian faction, launched several attacks against Israel to impede negotiations. In particular, attacks after Arafat’s 1996 election victory killed 102 people, eroded Israeli popular support, and maimed negotiations. This shift in public opinion ousted Israel’s Labor government, installed the hawkish Likud government in 1996, and impeded the peace process (Kydd and Walter 2002). The retrogression of peace indicated Arafat’s inability to control internal opposition. Although numerous Palestinians supported him, strong Palestinian opposition revealed “the limits of Arafat’s ability to win over the Palestinian street” (Eisenberg and Caplan 2010:216). Obstruction by a violent faction can provoke distrust in negotiating partners and impede negotiations. As Eisenberg and Caplan (2010:186) note, “The PA’s reluctance or inability to crush Hamas and its refusal to extradite Palestinian fugitives to Israel confirmed for many Israelis their presumption that Arafat could not be trusted.”

2.2

Arusha

The Hutu seized power after Rwandan independence, and many Tutsi fled to escape persecution by the Hutu government. Exiled Tutsi in Uganda formed the Rwanda Patriotic Front (RPF) and invaded Rwanda in 1990. In 1991, Rwanda adopted a multi-party system and the ruling MRNDD Party formed a coalition with former opposition parties, leaving Habyarimana’s government substantially controlled by hard-line Hutus. Arusha peace negotiations began in 1992, presided over by moderate Hutus—the members of previous opposition parties and liberals in the MRNDD. Although Habyarimana’s government and the RPF signed an accord in August 1993, Hutu hard-liners obstructed its implementation (Clapham 1998). Eventually, according to Clapham (1998:204), “Habyarimana’s aircraft was shot down, almost certainly by extremists associated with his own party.” After this event, genocide against the Tutsi and moderate Hutu raged on until the RPF seized control of the country.

4

2.3

Kashmir

After 1988, numerous militant groups formed in the Jammu and Kashmir state in India, in which the majority of the population is Muslim, to force the region’s merger into Pakistan. The most powerful of those was the Hizbul Mujahideen, supported by Pakistan and the Jamaat-e-Islami political party. Facing military pressure from India, Hizbul Mujahideen began negotiations with India and declared a unilateral ceasefire in 2000 (Staniland 2012). However, negotiations collapsed under opposition from other Pakistani factions. Staniland (2012:29) notes that “Pakistani intelligence services, Kashmiri hard-liners, other jihadi groups, and even the Pakistani Jamaat-e-Islami turned on the Hizb and demanded it pull back from its peace initiative. This pressure on the Hizb and a botched negotiation led it to end its ceasefire after two weeks.”

3

The Model

Our model describes an internal conflict between a government and an opposition group. We treat the government as a single entity and the opposition group as a continuum [0, 1] of members. The government initially possesses WG > 0 quantities of resources (e.g., territory, natural resources, and rents from a political power). The opposition possesses WO ≥ 0 quantities of resources, which are evenly distributed among its members. Members of the opposition are heterogeneous with respect to income and the intensity of antagonism toward the government. We denote the income that member i ∈ [0, 1] earns via production as αi , and specify that members forfeit an opportunity to earn income if conflict with the government arises. To denote the degrees of antagonism toward the government, member i ∈ [0, 1] receives ϵi units of utility when he or she takes up arms. At the time of peace, opposition member i receives income αi . In conflict, he or she receives utility ϵi . Therefore, we can define the antiwar preferences of member i by πi ≡ αi − ϵi . That is, πi represents the degree to which member i prefers peace over conflict. We denote the cumulative distribution function of πi as F (·). Without loss of generality, we assume ∀i, j ∈ [0, 1],

i>j

=⇒

πi ≥ πj .

(1)

We formulate the process of conflict and negotiation as follows.5 When at

5 The following formulation is based on Jackson and Morelli (2007) and is similar to many studies on the bargaining model of conflict (see, among others, Fearon 1995; Powell 1999, 2002).

5

least one group prefers conflict over peace, conflict erupts.6 The winner deprives the loser of fraction D ∈ (0, 1) of its resources, but fighting costs both groups a fraction C ∈ (0, 1 − D] of their own resources.7 Therefore, conflict is costly for both. The cost of conflict and the loss from defeat are borne evenly by all members. The probability that the government wins is denoted by q ∈ (0, 1). Before conflict breaks out, negotiation is available. To preclude conflict, one group can offer the other transfer T . Note that positive transfer occurs only if, when there is no transfer, one group prefers conflict and the other prefers peace. As stated below, we consider the case wherein only the government has the incentive to offer transfers. Transfer T can comprise a transfer of not only resources, but also of territory, political concessions, and so on. We assume the resources derived from the government DWG and transfers T are divided evenly among recipients. The government’s transfer cannot target a subset of the opposition. When the government offers transfer T , the payoff of the government, PG (T ), is given by { WG − T if peace. PG (T ) = (2) (1 − C)WG − [(1 − q)DWG − qDWO ] if conflict. The payoff of member i in the opposition group Pi (T ) is given by { WO + T + αi if peace. Pi (T ) = (1 − C)WO + [(1 − q)DWG − qDWO ] + ϵi if conflict.

(3)

Let VO ≡ [(1−q)WG −qWO ]D denote the expected value of resources transferred from the government to the opposition after conflict. Concerning the parameters above, we assume the following. Assumption 1. (Inefficiency of Conflict) C(WG + WO ) + α ¯ > ϵ¯, where α ¯ and ϵ¯ denote the mean values of αi and ϵi , respectively. Assumption 2. If the government makes no transfer, the expected gain of war exceeds its cost for the average member of the opposition group. That is given as follows: VO + ϵ¯ > CWO + α ¯. 6 The

process by which the decisions by the opposition group members are aggregated into the group-wide decision will be explained below. 7 We assume C ≤ 1 − D to ensure that the winner cannot deprive more amounts of the loser’s resources than the remaining amounts after conflict.

6

Assumption 1 means that society’s total payoff during peacetime exceeds that during conflict. Assumption 2 means that when there is no transfer, the aggregate payoff to the opposition group from conflict is greater than that in peacetime. Therefore, under Assumption 2, barring any transfer, the opposition chooses war if that decision is made by an agent who maximizes the total payoff to the group.8 When both assumptions hold, the government prefers peace with no transfers over conflict. Consider the situation in which negotiation is unavailable; therefore, T = 0. From Assumption 1, the total payoff to society is greater under peace. Nevertheless, from Assumption 2, the opposition group receives a larger payoff from conflict. Then, the payoff to the government from conflict must be less than the payoff from peace. Because the government does not wage war when there is no transfer, the opposition group has no incentive to offer transfers. Because in most cases only the opposition has an incentive to initiate civil war, these assumptions would be appropriate. In summary, we consider the following bargaining process: 1. The government offers transfer T ≥ 0 to the opposition (take-it-or-leave-it offer). 2. The opposition decides whether to accept the offer. 3. If the offer is accepted, the transfer is implemented and civil war is precluded. If rejected, civil war breaks out. Because the members of the opposition have heterogeneous preferences, the manner in which each member’s decision is aggregated into a group decision is crucial to the equilibrium outcome. The following sections investigate differing aggregations.

4

Group Decision by a Pivotal Agent

First, we consider that the group’s decision is made by a pivotal decision-maker. We consider two types of pivotal decision-makers. The first type of agent maximizes the aggregate payoff to the group; we call this individual a “group welfare maximizer.” In this case, heterogeneity within the opposition group does not affect the decision to accept the government’s offer. In the absence of private information, issue indivisibility, commitment problems, or political bias, results show that civil war is always precluded by negotiation between the government and the group welfare maximizer (Fearon 1995; Jackson and Morelli 2007). 8 Of

course, whether the opposition group decides to wage civil war when T = 0 will depend upon the decision-making rule.

7

The second type of pivotal agent is a median voter. In this case, the opposition makes its decision by majority rule. Distributions of income and ideology in the opposition group can affect the outcome of negotiations. Results show that civil war cannot be precluded by negotiation when the median value of πi is sufficiently small. As Jackson and Morelli (2007) argue, a difference of interests between the pivotal agent and the group causes a negotiation failure. This section assumes a pivotal decision-maker. More importantly, we assume that the members of the opposition honor the agreement between the government and the pivotal decision-maker.

4.1

Bargaining with a Group Welfare Maximizer

We assume that the decision of the opposition is made by a group welfare maximizer who maximizes the total payoff of the group. Given the offer T , the group welfare maximizer accepts the offer if and only if ∫ 1 WO + T + (αi − ϵi )dF ≥ (1 − C)WO + VO . (4) 0

This condition can be rewritten as T ≥ TGW ≡ VO − CWO + ϵ¯ − α ¯.

(5)

From Assumption 2, TGW > 0. Anticipating the behavior of the group welfare maximizer, the government offers a transfer in the amount that maximizes its payoff: { WG − T if T ≥ TGW PG (T ) = (6) (1 − C)WG − VO otherwise. From (5) and (6), we derive the following proposition. Proposition 1. Let Assumptions 1 and 2 hold. Assume that the decision of the opposition group is made by the group welfare maximizer. Then, • Civil war is always precluded through negotiation. • The government transfers the TGW of its resources to the opposition. Proof. See Appendix. The intuition behind Proposition 1 is as follows. Consider the payoff to the government by offering transfer T ≥ TGW to preclude war. Since the government seeks an agreement that minimizes transfers, it offers T = TGW . Then, the payoff to the opposition group under the agreement is the same as that under conflict. From Assumption 1, peace increases society’s total payoff. This means that the government receives a larger payoff by offering T = TGW than by accepting civil war. Because conflict is socially inefficient, negotiations between the government and the group welfare maximizer can preclude it. 8

4.2

Bargaining with the Median Voter

Assume that the opposition group’s decision is made by the median agent, who has the median value of πi . In this situation, the majority rule determines the collective decision of the opposition group. Let πm denote the median value of πi . Then, the median agent accepts the offer T if and only if WO + T + αm ≥ (1 − C)WO + VO + ϵm .

(7)

This condition can be rewritten as T ≥ TM ≡ VO − CWO + ϵm − αm .

(8)

Anticipating the behavior of the median agent, the government offers T to maximize its payoff: { WG − T if T ≥ TM PG (T ) = (9) (1 − C)WG − VO otherwise. The difference between this case and the one involving the group welfare maximizer is the amount of transfer the government must offer to preclude conflict. To persuade the median agent, the government must provide a transfer at least equal to TM . From (5) and (8), TM can be written as TM = TGW + π ¯ − πm ,

(10)

where π ¯ = α ¯ − ϵ¯. Hence, the greater the extent to which πm falls below π ¯, the larger is the transfer the government must provide to preclude conflict, compared to the case with the group welfare maximizer. When the median agent substantially prefers conflict over peace, the government’s cost of precluding conflict is very large. Therefore, if πm is sufficiently small, the government prefers civil war to precluding it by providing transfer TM . Although civil war is always precluded through negotiation if the pivotal agent is a group welfare maximizer, negotiation fails when the pivotal agent is the median agent and his or her net payoff from conflict is sufficiently large. Proposition 2. Let Assumptions 1 and 2 hold. Assume that a median agent makes the decision of the opposition group. Then, civil war cannot be precluded through negotiation if and only if πm < −C(WO + WG ).9 Proof. See Appendix. 9 From Assumption 1, −C(W + W ) < π ¯ . Hence, when πm ≥ π ¯ , civil war is always O G precluded through negotiation. Note that when πm ≥ π ¯ , the transfer the government must offer to preclude conflict does not exceed that which it must offer the group welfare maximizer.

9

Note that πm is increasing in αm and decreasing in ϵm , and that the threshold −C(WO + WG ) is decreasing in C, WO , and WG . Hence, Proposition 2 means that civil war is likely in the following situations. • The median agent earns a low income during peacetime (αm is small) and obtains a large ideological payoff from war (ϵm is large). • The resources of each group, WG and WO , are small. • The cost of conflict C is small. This result implies that civil war is likely if within-group income inequality is large. This is because the median income is typically smaller than the average income, and the gap between the median and the mean incomes tends to be larger in more unequal economies.10 Therefore, given the aggregate (average) income level α ¯ , large within-group income inequality tends to reduce the median income αm and leads to smaller πm values. In such a case, the median agent substantially prefers conflict over peace, because his or her opportunity cost of conflict is small. In this situation, the government must offer a large transfer to persuade the median agent, and it prefers civil war over a peaceful settlement. The above discussion presents one explanation for the positive relation between within-group income inequality and civil war. However, the assumption of majority rule may be inappropriate in the context of civil war, as the decisions made by opposition groups are not necessarily determined democratically. Section 5 considers a different formulation that associates the decisions made by each member of the opposition group with the outcome of peace negotiations. It reflects the lack of a disciplined decision-making mechanism within the opposition group and provides another mechanism that links within-group heterogeneity to the outbreak of civil war.

5

Uncertainty about Negotiated Outcomes and Heterogeneity

In Section 4, we assume that members of the opposition group honor the agreement between the delegates of the two groups. Thus, the prior analysis supposes 10 In their theoretical analysis of the relationship between inequality and economic growth, Persson and Tabellini (1994) also interpret a smaller gap between the median and the mean incomes as being indicative of a more equal income distribution. Moreover, the available data indicate a close relationship between the median–mean ratio of income and the Gini coefficient. According to UNU-WIDER (2015), the cross-country relationship between the median–mean ratio and the Gini coefficient is close to a perfect negative correlation: the correlation coefficient between them in 2010 is –0.93, which is statistically significant at the 1% level.

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a disciplined opposition whose members conform to the leader’s decisions. However, as the examples in Section 2 illustrate, certain elements in either or both parties can hinder the peace-making process, even if their delegates push for negotiations. Considering this, we abandon the assumption that precluding conflict through negotiation depends upon the actions of a pivotal decision-maker. Instead, we assume that the likelihood that the peace process will collapse is a decreasing function of the support for peace among the opposition. This assumption means that the peace process can collapse if some members oppose the government’s offer, and that collapse is more likely when opposition is vigorous. This section analyzes how within-group heterogeneity affects the occurrence of civil war in this environment.

5.1

Probability of Completing a Deal

Consider the outcome of negotiations to be uncertain. As per Section 2, the process can collapse when a faction within the opposition disavows the agreement its delegate has signed. We describe these situations as follows. Let n be the number of members of the opposition who accept the government’s offer. Let p(n) be the probability that the government’s offer is accepted and civil war is precluded when n members agree to it. Naturally, p(0) = 0 and p(1) = 1. We also assume that p(n) is continuously differentiable and that p′ > 0. The larger the number of supporters is, the greater the effect of their actions will be. Thus, the likelihood that the peace process will preclude conflict [p(n)] increases with the number of members who support it (n). Note that the government confronts the positive probability of civil war when elements within the opposition reject its offer. If the median agent is the pivotal agent and all members honor the decision of the majority (as in Section 4.2), p(n) = 1 if n ≥ 1/2, and p(n) = 0 otherwise. However, if the process can collapse when a faction rejects the government’s offer, there is the positive likelihood that negotiations will collapse, even though the majority accedes. We can imagine numerous scenarios in which factions opposed to peace derail negotiations. For example, attacks by dissidents engender hawkish reactions by the government, as was the case between Israel and the PA. Alternatively, powerful dissidents may seize the initiative from dovish factions, as the cases of Arusha and Kashmir indicate. Similarly, there is the positive likelihood that civil war will be precluded, even if the majority opposes the peace process; one such example is when a small faction that supports peace tightly controls the entire group. Evidently, it becomes more difficult for the supportive faction to suppress internal opposition as more members oppose the peace process. The popularity and leadership of the leader may also be relevant. If the leader of the peace process has significant popularity and leadership, opponents may follow 11

the leader, even if they are unconvinced by the government’s offer. The assumption that the probability of the government’s offer being accepted depends on the number of members who favor the government’s offer resembles the model of Piguillem and Riboni (2015). In their legislative bargaining model, the probability that the agenda-setter’s proposal will pass is equal to the number of legislators who support it. Piguillem and Riboni (2015: 908) justify this formulation by arguing that the opinion of the majority can be rejected on account of the veto power of the minority, vote trading, or party discipline. We think that the assumption of probabilistic acceptance is justified in the context of civil war, since the decision-making process is more uncertain and less restrained by rules than is the case in a legislature. We can also interpret this formulation in a way that is consistent with a pivotal agent making the group decision. Consider that the decision of the opposition group is made by some pivotal decision-maker, but the government does not know the identity of the pivotal decision-maker. The government knows the probability of member i ∈ [0, 1] being the pivotal decision-maker. Let ωi > 0 be the probability measure of a member i being the pivotal decisionmaker. Since the members in the opposition group are labeled according to the magnitude of πi (See (1)), p(n) can be written as11 ∫ 1 p(n) = ωi di. (11) 1−n

The right-hand side (RHS) is increasing in n, and, therefore, p(·) is increasing in n. Concerning the probability p(n), we assume the following: Assumption 3. We assume p(n) is twice continuously differentiable and satisfies p′ > 0, p′′ ≤ 0, p(0) = 0, and p(1) = 1. Moreover, we assume the elasticity of p(n) with respect to n to be constant. That is, ∀n ∈ [0, 1]

p′ (n)n = σ. p(n)

We assume constant elasticity, to simplify the analysis and derive a unique analytical solution. The assumption is not essential to our main results.

5.2

Equilibrium

We assume the following uniform distribution for πi . Assumption 4. The distribution of π is given by [ ξ ξ] πi ∼ U π ¯ − ,π ¯ + , ξ > 0. 2 2 11 Note

that the larger πi is, the more a member i in the opposition group will prefer peace to conflict.

12

The density of the distribution is 1/ξ. Parameter ξ represents the degree of heterogeneity among the members of the opposition. Larger values for ξ indicate greater heterogeneity within the opposition group. After observing the government’s offer T , each member of the opposition decides whether to accept it. When n members agree, negotiations forestall civil war with the probability p(n). Opposition member i ∈ [0, 1] agrees with the offer if and only if WO + T + αi ≥ (1 − C)WO + VO + ϵi .

(12)

This can be written as πi ≥ π ˜ (T ) ≡ VO − CWO − T,

(13)

where π ˜ (T ) represents the threshold value of the antiwar stance when the government offers T . Thus, all members with πi ≥ π ˜ (T ) accept offer T , and others do not. Since member i = 1 has the largest value of π, π1 equals π ¯ + ξ/2. Similarly, π0 equals π ¯ − ξ/2. To simplify the analysis, we assume the following: Assumption 5. Some members of the opposition prefer peace over conflict, irrespective of a government transfer. That is, π ˜ (0) = VO − CWO ≤ π ¯ + ξ/2 = π1 . Under Assumption 5, some members of the opposition always prefer peace. Since π ¯ < π ˜ (0) from Assumption 2, the majority in the opposition prefers conflict if the government offers no transfer. Let n(T ) be the number of members who accept the government’s offer T . Because all members with πi ≥ π ˜ (T ) accept T , from (13), n(T ) can be written as ∫ π1 1 n(T ) = dπ π ˜ (T ) ξ { [ ] } 1 ξ = min π ¯ + − (VO − CWO − T ) , 1 . (14) ξ 2 From (14), we derive the number of opposition members who accept the offer T = 0 as [ ] ξ 1 π ¯ + − VO + CWO ≥ 0. (15) n0 ≡ n(0) = ξ 2 If the government’s offer satisfies π ˜ (T ) ≤ π0 , all members of the opposition accept it and n(T ) = 1. Clearly, offering π ˜ (T ) < π0 is suboptimal for the government, because it can reduce the amount of its transfers without losing opposition support. Therefore, in the following, we consider that π ˜ (T ) ≥ π0 . 13

An in rease in T

1= 0

1=

 ~ (T 0 ) ~ (T )

 

Figure 1: The marginal effect of transfer Equation (14) shows an important property of the relationship between transfers and support for peace. When the amount of the transfer increases, the threshold π ˜ (T ) decreases and the number of members receptive to the offer increases. Further, the marginal effect of the transfer on the number of supporters (n) is inverse to the degree of heterogeneity, as n′ (T ) = 1/ξ. Figure 1 shows why the transfer’s marginal effect is small when heterogeneity is great. When heterogeneity within the opposition is large, the density of the distribution of πi is small and the shift of π ˜ (T ) resulting from an increase in T does not significantly increase support for the offer. Therefore, support for the government’s offer is less responsive to an increase in transfer when the opposition is more heterogeneous. From (14), we derive the function T (n), which represents the transfer amount necessary to convince n members of the opposition to accept the offer as ( ) ξ T (n) = ξn + VO − CWO − π ¯+ , n ≥ n(0). (16) 2 Following similar logic, the necessary increment in transfer needed to secure a marginal increase in n is increasing in ξ as T ′ (n) = ξ. When heterogeneity among the opposition (ξ) is large, the effect of T on n is small, and the government must increase T significantly to secure a definite increase in n. Note that T (n) is increasing in VO and decreasing in CWO and π ¯ . This is because the value of conflict for the opposition is increasing in VO and decreasing in CWO and π ¯ . Therefore, in these situations, the government must offer a large transfer to gain support. Anticipating the opposition’s decision, the government determines the amount 14

of its proposed transfer to maximize its expected payoff. Using function T (n), the government’s objective function can be written as: p(n)[WG − T (n)] + (1 − p(n))[(1 − C)WG − VO ].

(17)

We define R(n) ≡ CWG + VO − T (n) as the government’s peace surplus. When n is large, the government offers a large transfer, and its peace surplus is small. Using function R(n), the government’s problem can be written as: max n∈[n0 ,1]

p(n)R(n) + (1 − C)WG − VO

subject to

(16).

Let n∗ be the equilibrium number of opposition group members who accept the government’s offer. We assume n∗ > n0 . From the first-order condition, n∗ satisfies: p′ (n∗ )R(n∗ ) − p(n∗ )T ′ (n∗ ) ≥ 0

with equality when n∗ < 1.

(18)

The government faces a tradeoff between the risk of civil war and the size of its peace surplus.12 An increase in opposition support for its offer reduces the risk of war, but the larger transfer needed to obtain it reduces the peace surplus. The first term in (18) is the marginal benefit of increasing n, and the second term is the marginal cost. Because T (n0 ) = 0, the government’s peace surplus when it offers no transfer is R(n0 ) = VO + CWG , which is positive from Assumptions 1 and 2. This means R(n∗ ) > 0,13 and condition (18) can be rewritten as p′ (n∗ )n∗ ξn∗ R′ (n∗ )n∗ = σ ≥ = − . p(n∗ ) C(WG + WO ) + π ¯ + ξ/2 − ξn∗ R(n∗ )

(19)

The left-hand side (LHS) is the elasticity of the probability p(n), which equals the constant σ from Assumption 3. The RHS is the elasticity of the government’s peace surplus with respect to n. Since the government maximizes the product of p(n) and R(n), it equalizes these two elasticities. From (19), we solve for n∗ as { [ ]} σ ξ ∗ n = min 1, C(WG + WO ) + π ¯+ . (20) (1 + σ)ξ 2 12 Similar risk–return tradeoffs appear in the bargaining model of conflict with asymmetric information (see Powell 1999). In a model featuring information asymmetry, the probability of peace is less responsive to the change in transfer amounts when there is great uncertainty about the opponent’s military technology. In contrast, this study shows that support for peace negotiations is less responsive to a change in transfer amounts when within-group heterogeneity is large. 13 Since R(n ) > 0, p′ > 0, and p(n )R(n ) ≥ 0, p(n)R(n) takes a positive value if n is 0 0 0 sufficiently close to n0 . Thus, making p(n)R(n) nonpositive is suboptimal for the government.

15

The elasticity of peace surplus

An increase in ξ

σ

0

The elasticity of p(n)

1

n

Figure 2: The negative relationship between n∗ and ξ When within-group heterogeneity among the opposition (ξ) is large, n∗ is small and the probability of civil war (1 − p(n∗ )) is large. Figure 2 illustrates the relationship between ξ and n∗ . Since T ′ (n) is increasing in ξ, high degrees of heterogeneity imply that the government must increase transfers substantially to secure a marginal increase in n. Because of this effect, the elasticity of the peace surplus is increasing in ξ—that is, the peace surplus declines sharply as n increases when heterogeneity within the opposition is large. Therefore, an increase in ξ shifts the graph of the elasticity of the peace surplus upward in Figure 2. Because the elasticity of the probability p(n) is assumed to be constant and independent of ξ, the increase in ξ reduces the level of n∗ , as shown in Figure 2.14 The equilibrium number of opposition group members who support the government’s offer (n∗ ) increases with the cost of conflict C(WG + WO ) + π ¯ and σ (the elasticity of p). The result is intuitive: an increase in the cost of conflict reduces the risk of war. A large elasticity of p implies that negotiation by transfer is more effective. Hence, an increase in σ reduces the risk of war. From (16) and (20), we solve for the equilibrium transfer level offered by the

14 Assuming the constant elasticity of p(n) is not crucial to our argument. Even if the elasticity of p(n) were to depend on n, an increase in ξ shifts the graph of elasticity of the peace surplus upward, but does not change the graph of the elasticity of p(n). Therefore, n∗ would decrease as heterogeneity in the opposition group increases, as long as an interior solution is guaranteed.

16

n*

T*

1

0

ξ*

ξ

0

ξ*

ξ

Figure 3: The graph of n∗ and T ∗ . government as { ( ) ξ T = min VO − CWO − π ¯− , 2 [ ( )] } 1 ξ VO + C(σWG − WO ) − π ¯+ . 1+σ 2 ∗

(21)

The relationship between T ∗ and ξ is nonmonotonic, as described in Figure 3. When within-group heterogeneity ξ is sufficiently small, it is optimal for the government to win over all opposition group members. In this case, an increase in ξ increases the amount of the transfer needed to win over the member who most prefers conflict. The transfer, therefore, increases in ξ when ξ is sufficiently small (ξ < ξ ∗ in Figure 3). When within-group heterogeneity ξ is sufficiently large (ξ > ξ ∗ in Figure 3), ∗ n is an interior solution (i.e., n∗ < 1) and decreasing in ξ, as explained above. Due to this effect, in this case, T ∗ is decreasing in ξ. The above argument can be summarized as the following proposition: Proposition 3. Let Assumptions 1–5 hold. We also assume that the probability of civil war being precluded through negotiation is represented by the function p(n). In the case of the interior solution (n∗ < 1), the following results hold: • Opposition support for the government’s offer is decreasing in the withingroup heterogeneity (i.e., n∗ is decreasing in ξ). The risk of civil war 1 − p(n∗ ) is therefore increasing in ξ. • The risk of civil war is small when the cost of conflict C(WG + WO ) + π ¯ is large. • The risk of civil war is small when elasticity σ is large. When we consider the corner solution (n∗ = 1), the following result also holds: • The relationship between the transfer offer of the government (T ∗ ) and ξ takes an inverted-U shape. 17

Proposition 3 says that greater within-group heterogeneity in antiwar preferences increases the risk of civil war, because it makes government transfers less effective in precluding conflict.

5.3

Within-Group Income Inequality and Civil War

Østby et al. (2009) find that intraregional inequality in household assets and education increases the onset of civil conflict. Since assets and education correlate positively with income, their evidence suggests a positive relationship between within-group income inequality and civil conflict. Can the aformentioned theory explain this empirical relationship? Clearly, our model shows a positive relationship between within-group income inequality and the risk of civil war, if there is no correlation between income (αi ) and antagonism toward the government (ϵi ). In this case, the variance of antiwar preferences (the variance of πi ) is the sum of the variances of αi and ϵi . Hence, an increase in the variance of αi increases the variance of πi — which leads to a higher probability of civil war, as Proposition 3 shows. Then, does the correlation between income and antagonism toward the government change the result? In what follows, we show that as long as income level correlates positively with antiwar preferences, inequality in within-group income positively affects the risk of civil war. Furthermore, we briefly discuss the empirical relationship between income and preferences for conflict. It is theoretically possible that greater within-group income inequality leads to lower probability of civil war. To illustrate this, consider a simple example where there are only two members. Table 1 (a) refers to the case where the rich member has greater antagonism toward the government and hence the antiwar preference of the rich is smaller than that of the poor member. In this case, as Table 1 (b) shows, an increase in income inequality reduces the variance of antiwar preferences, which means a lower risk of civil war.15 Note that the positive correlation between income and antagonism toward the government is not a sufficient condition for this negative relationship between within-group income inequality and the variance of antiwar preferences. In Table 2 (a), the rich member has greater antagonism toward the government, but has a stronger antiwar preference. In this case, an increase in income inequality increases the variance of antiwar preferences.16 As these examples illustrate (and as formally demonstrated in the Appendix), within-group income inequality reduces the variance of antiwar prefer15 This

example was suggested by an anonymous referee. We greatly appreciate his or her valuable comments. 16 One can easily check for the same relationship when antagonism toward the government correlates negatively with income level.

18

πi αi ϵi The poor 10 15 5 The rich 8 20 12 (a) Low income inequality

πi The poor 9 The rich 9 (b) High income

αi ϵi 14 5 21 12 inequality

Table 1: The case of negative correlation between αi and πi . πi αi ϵi The poor 7 15 8 The rich 8 20 12 (a) Low income inequality

πi The poor 6 The rich 9 (b) High income

αi ϵi 14 8 21 12 inequality

Table 2: The case where αi positively correlates with ϵi and πi . ences if and only if antiwar preferences correlate negatively with income level. Since πi − πj = (αi − αj ) − (ϵi − ϵj ), antiwar preferences decrease with the income level if and only if (i) antagonism toward the government increases with the income level and (ii) the difference in antagonism between the rich and poor members exceeds the income difference. Hence, if at least one of the two conditions does not hold and richer members have a greater preference for peace than poorer ones, within-group income inequality relates to a high probability of civil war. Although it is difficult to observe directly the relationship between income and antiwar preferences, existing empirical evidence is consistent with the view that poorer agents are more likely to choose conflict than richer ones. Miguel et al. (2004), Besley and Persson (2011), and Dube and Vargas (2013) each show that poverty causes civil conflict. Using the survey data of combatants and noncombatants in the civil war in Sierra Leone, Humphreys and Weinstein (2008) investigate the types of individuals who (voluntarily) participate in the conflict, and they show that an individual is more likely to participate in conflict when he or she is poor and lacks education.17 To summarize the above discussion, although the negative relationship between within-group income inequality and the risk of civil war is theoretically possible when the rich prefer conflict more than the poor, it is more plausi17 Some

empirical studies investigate the determinants of support for terrorism. While Krueger and Male˘ ckov´ a (2003) show that there is no evidence that the poor support and engage in terrorism, Shafiq and Sinno (2010) and Mousseau (2011) show that the relationship between individual income and support for violence varies across countries. Although support for violence as used in these studies—which is based on individual survey data—does not necessarily coincide with the taste for conflict in our model, this evidence does not indicate that the rich tend to have a strong taste for conflict.

19

ble that the poor prefer conflict more than the rich; this suggests a positive relationship between within-group income inequality and the risk of civil war.

5.4

Discussion

This section analyzes whether our main conclusions hold when we change the two important assumptions of the model—namely, the uniform distribution of antiwar preferences and the inability of the opposition to initiate a war after receiving a transfer. Section 5.4.1 considers a more general distribution of πi , rather than the uniform distribution, and it shows conditions under which our main conclusions hold. Section 5.4.2 considers an environment in which the opposition can go to war even after it has received a transfer from the government.18 5.4.1

General Distribution

In the previous section, we assumed πi is uniformly distributed. This section analyzes the model in more general environments. Let f and F denote the density and cumulative distribution function of the distribution of πi . Then, the number of opposition group members who support the government offer is given by 1 − F (˜ π (T )). For simplicity, assume 19 that p(n) = n. Then, the government’s problem can be written as max T

n(T )(WG − T ) + [1 − n(T )][(1 − C)WG − VO ].

(22)

From the first-order condition, the optimal transfer level T ∗ satisfies n′ (T ∗ )R(T ∗ ) = n(T ∗ ).

(23)

The LHS is the marginal benefit the government receives by increasing the size of the transfer it offers. It is the product of the increase in the probability of peace and the peace surplus. As seen in the previous section, in the case of a uniform distribution, this marginal benefit declines with within-group heterogeneity. The RHS is the marginal cost of increasing the transfer offer. An increase in the offered transfer reduces the government’s payoff from peace, which is realized with probability n(T ). Equation (23) can be written as f (˜ π (T ∗ )) 1 = . 1 − F (˜ π (T ∗ )) R(T ∗ )

(24)

The LHS is the hazard rate of the distribution at πi = π ˜ (T ∗ ). Since the RHS is increasing in T ∗ , a unique solution exists when the hazard rate function is 18 See

Jackson and Morelli (2007) for similar discussion. is, we assume σ = 1.

19 That

20

nondecreasing in πi .20 Further, if the hazard rate declines with variance in the distribution, the relationship between degrees of within-group heterogeneity and risk of civil war is positive. In addition to the uniform distribution analyzed in the previous section, this property holds under, for example, an exponential distribution. Proposition 4. Let Assumptions 1–3 hold. In the general environment described above, the risk of civil war relates positively to the degree of within-group heterogeneity in the unique equilibrium when the hazard rate function of the distribution of πi , f (πi )/(1 − F (πi )), is nondecreasing in πi and decreasing in its variance. 5.4.2

No-Commitment Case

Thus far, we have assumed that the opposition group can commit not to wage a war once they accept the transfer from the government. However, it may be the case that the opposition still has an incentive to go to a war, even after it receives the transfer. Hence, if there is no mechanism that enforces the peace agreement—such as international organizations—the opposition may choose to initiate a war after receiving the transfer. This section considers an environment in which the opposition can choose a war, even after it receives a transfer from the government. In this environment, the government makes a transfer to reduce the opposition’s incentives to wage a war. We will show that our main result regarding the relationship between within-group heterogeneity and civil war still holds under this alternative environment. To analyze the opposition’s incentive to wage a war after receiving a transfer, we consider the following timing of events: 1. The government makes a transfer T ≥ 0 to the opposition. 2. After receiving the transfer, the members of the opposition decide whether to wage a war. 3. Civil war is precluded with probability p(n), where n is the number of members who prefer peace to war. In this case, what matters is whether the conflict is in the interest of the members of the opposition after they receive the transfer T . The payoff of the government after the transfer is made is given by { WG − T if peace. PG (T ) = (1 − C)(WG − T ) − [(1 − q)D(WG − T ) − qD(WO + T )] if conflict. (25) 20 Note

that π ˜ (T ) is decreasing in T .

21

On the other hand, the payoff of member i in the opposition group Pi (T ) is given by { WO + T + α i if peace. Pi (T ) = (1 − C)(WO + T ) + [(1 − q)D(WG − T ) − qD(WO + T )] + ϵi if conflict. (26) Note that the transfer T is included in the payoff from conflict, since conflict arises after the government makes a transfer to the opposition group. The member i chooses to preclude conflict if and only if WO + T + αi ≥ (1 − C)WO + VO + ϵi + (1 − C − D)T,

(27)

where the LHS of (27) represents the payoff from peace and the RHS represents the payoff from conflict. Equation (27) can be written as πi ≥ −CWO + VO − (C + D)T ≡ π ˆ (T ),

(28)

where π ˆ (T ) is the threshold value of the antiwar preference when the government offers T . Members with higher πi than π ˆ (T ) prefer peace, and members with lower πi than π ˆ (T ) prefer conflict. Condition (28) shows that the government transfer can reduce the incentive of the opposition to wage war. The government transfer increases the cost of conflict of the opposition, since the fraction C of transfer is lost in the conflict. Moreover, the government transfer reduces the resources of the government and increases the resources of the opposition. Hence, from the opposition’s perspective, the government transfer reduces the gain from winning and increases the loss from losing. Note that the previous argument holds in this model. The government can increase the probability of peace by increasing the transfer, but the share of members preferring peace is less responsive to the change in transfer when the distribution of πi is dispersed. As in the previous model, we can show that the risk of civil war is increasing in the within-group heterogeneity of antiwar preferences (see Appendix).

6

Conclusion

This study presents a bargaining model of conflict in which the government offers an opposition group a transfer to preclude civil war. Members of the opposition group are heterogeneous in income and ideology, which engenders disagreement about accepting the government’s offer. We assume that the probability that the government’s offer will preclude conflict increases continuously with the number of members who accept the offer. When within-group heterogeneity is large, the number of members who accept the government’s offer will be less responsive 22

to an increase in its amount. In this situation, the government must increase its offer substantially to increase support among the opposition. Peace becomes costly for the government, and peace negotiations are prone to breakdown.

Appendix Proof of Proposition 1 Proof. It is suboptimal for the government to offer a transfer larger than TGW . Therefore, it chooses either offer T = TGW to preclude conflict, or offer T < TGW and goes to war. The government offers T = TGW if and only if WG − TGW ≥ (1 − C)WG − VO .

(A1)

The LHS is the payoff the government receives by offering T = TGW to preclude conflict. The RHS is the government’s payoff when conflict occurs. Condition (A1) can be rewritten as C(WG + WO ) + α ¯ − ϵ¯ ≥ 0.

(A2)

By Assumption 1, the LHS of (A2) is positive and, therefore, (A2) always holds.

Proof of Proposition 2 Proof. Because it is suboptimal for the government to offer a transfer larger than TM , it chooses either to offer T = TM to preclude conflict, or to offer T < TM and accepts war. The government offers T = TM if and only if WG − TM ≥ (1 − C)WG − VO .

(A3)

This condition can be rewritten as C(WO + WG ) + πm ≥ 0.

(A4)

If πm is sufficiently small such that πm < −C(WO + WG ), the government chooses war.

Within-Group Income Inequality and Variance of Antiwar Preferences To examine the impact of within-group income inequality on the risk of civil war, we represent income of individual i as follows αi = α ¯ + γηi , 23

(A5)

where ηi captures the heterogeneity of earning ability among the opposition. Assuming E(η) = 0 and V ar(η) = 1, we can interpret the parameter γ > 0 as the degree of income inequality, since the standard deviation of the income distribution is given by γ. The antiwar preference of member i can now be written as πi = α ¯ + γηi − ϵi ,

(A6)

and the variance of antiwar preferences is given by V ar(πi ) = γ 2 + V ar(ϵi ) − 2γCov(ηi , ϵi ).

(A7)

The effect of within-group income inequality on the variance of antiwar preferences is given by dV ar(πi ) = 2(γ − Cov(ηi , ϵi )). (A8) dγ This equation shows that an increase in within-group income inequality increases the variance of antiwar preferences if and only if γ > Cov(ηi , ϵi ), which can be rewritten as V ar(αi ) > Cov(αi , ϵi ). Therefore, if (i) there is a positive correlation between antagonism toward the government and income and (ii) the covariance between antagonism and income is greater than the variance of income, greater within-group income inequality will reduce the variance of antiwar preferences. When at least one of the two conditions does not hold, greater within-group income inequality increases the variance of antiwar preferences and thereby increases the risk of civil war. Finally, we show that the condition γ > Cov(ηi , ϵi ) holds if and only if there is a positive correlation between income and antiwar preferences. To see this, note that Cov(αi , πi ) = V ar(αi ) − Cov(αi , ϵi ) = γ (γ − Cov(ηi , ϵi )) .

(A9)

Therefore, if income and antiwar preferences correlate positively, the sign of (A8) must be positive, and hence within-group income inequality increases the variance of antiwar preferences.

The Risk of Civil War in the No-Commitment Case The number of members who prefer peace when the government offers T is now given by ∫ π1 1 n(T ) = dπ π ˆ (T ) ξ (A10) [ ] 1 ξ = π ¯ + − (VO − CWO − (C + D)T ) . ξ 2 24

The amount of transfer necessary to convince n members of the opposition is T (n) =

ξn + VO − CWO − (¯ π + ξ/2) , n ≥ n(0), C +D

(A11)

and T ′ (n) = ξ/(C + D). The government’s objective function can be written as PG =p(n)[WG − T (n)] + (1 − p(n))[(1 − C)WG − VO − (1 − C)T (n) + DT (n)] =WG − T (n) + (1 − p(n))[−CWG − VO + (C + D)T (n)]

(A12)

and the first-order condition for the maximization of PG is −T ′ (n)−p′ (n)[−CWG −VO +(C +D)T (n)]+(1−p(n))(C +D)T ′ (n) = 0. (A13) Assuming p(n) = n for simplicity, the equilibrium number of opposition members who prefer peace is given by ( ) 1 3 1 1 ∗ n = − + (C(WG + WO ) + π ¯) . (A14) 2 2 C +D 2ξ Equation (A14) shows that the equilibrium number of opposition members who prefer peace decreases with the degree of heterogeneity ξ. Therefore, the risk of civil war is increasing in the within-group heterogeneity of the opposition group.

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