Distribution and Development

Transcription

1 Distribution and Development Debraj Ray DSchool lecture March 22, 2010 Convergence and Divergence Conflict Incentives Based on a forthcoming monograph with Joan Esteban.

2 Internal Conflict is Endemic : battle deaths in 25 interstate wars approx. 3.33m 127 civil wars in 73 states (25 ongoing in 1999). (over 1/3 of all countries) 16m+ dead as a direct result Does not count displacement and disease. Does not count ongoing ethnic violence, such as Hindu-Muslim violence in India. Economic costs: 8% of world GDP (Hess (2003))

3 The Markers are Predominantly Ethnic In much of Asia and Africa, it is only modest hyperbole to assert that the Marxian prophecy has had an ethnic fulfillment. Horowitz (1985)

4 The Markers are Predominantly Ethnic In much of Asia and Africa, it is only modest hyperbole to assert that the Marxian prophecy has had an ethnic fulfillment. Horowitz (1985) Brubaker and Laitin (1998) on eclipse of the left-right ideological axis Fearon (2006), , approx. 700 ethnic groups known, over 100 of which participated in rebellions against the state.

5 Primordial or Instrumental? Ancient hatreds, reinforced by myth/legend/discourse: Samuel Huntington s Clash of Civilizations (1993, 1996). Similar position adopted by many other social scientists (e.g., orientalists such as Bernard Lewis). Cultural fundamentalism close to primordialism

6 Primordial or Instrumental? Ancient hatreds, reinforced by myth/legend/discourse: Samuel Huntington s Clash of Civilizations (1993, 1996). Similar position adopted by many other social scientists (e.g., orientalists such as Bernard Lewis). Cultural fundamentalism close to primordialism Instrumentalism Ethnicity broadly construed a marker for carving a larger share Growing evidence that instrumentalist concerns are important maybe even dominant in ethnic violence.

7 Do Ethnic Divisions Matter? Two ways to approach this question. Historical study of conflicts, one by one. Bit of a wood-for-the-trees problem.

8 Do Ethnic Divisions Matter? Two ways to approach this question. Historical study of conflicts, one by one. Bit of a wood-for-the-trees problem. Horowitz (1985) summarizes: In dispersed systems, group loyalties are parochial, and ethnic conflict is localized... A centrally focused system [with few groupings] possesses fewer cleavages than a dispersed system, but those it possesses run through the whole society and are of greater magnitude. When conflict occurs, the center has little latitude to placate some groups without antagonizing others.

9 Statistical approach (Collier-Hoeffler, Fearon-Laitin, Miguel-Satyanath-Sergenti)

10 Statistical approach (Collier-Hoeffler, Fearon-Laitin, Miguel-Satyanath-Sergenti) Typical variables for conflict: demonstrations, processions, strikes, riots, casualties and on to civil war. Explanatory variables: Economic. per-capita income, inequality, resource holdings... Geographic. mountains, separation from capital city... Political. democracy, prior war... And, of course, Ethnic. But how measured?

11 Information on ethnolinguistic diversity from: World Christian Encyclopedia Encyclopedia Britannica Atlas Narodov Mira CIA FactBook Or religious diversity from: L Etat des Religions dans le Monde World Christian Encyclopedia The Statesman s Yearbook

12 Fractionalization Fractionalization index widely used: F = m n j (1 n j ) j=1 where n j is population share of group j. Special case of the Gini coefficient G = m M n j n k δ ik j=1 k=1 where δ ik is a notion of distance across groups. Has been used in many different contexts (growth, governance, public goods provision).

13 But it shows no correlation with conflict. See Collier and Hoeffler (2002), Fearon and Laitin (2003), Miguel-Satyanath-Sergenti (2004). Fearon and Laitin (APSR 2003) The estimates for the effect of ethnic and religious fractionalization are substantively and statistically insignificant... The empirical pattern is thus inconsistent with... the common expectation that ethnic diversity is a major and direct cause of civil violence.

14 And yet... fractionalization does not seem to capture the Horowitz quote: In dispersed systems, group loyalties are parochial, and ethnic conflict is localized... A centrally focused system [with few groupings] possesses fewer cleavages than a dispersed system, but those it possesses run through the whole society and are of greater magnitude. Motivates the use of polarization measures by Montalvo and Reynal-Querol (2005). Based on a measure of polarization introduced by Esteban and Ray (1994) and Duclos, Esteban and Ray (2003)

15 The Identity-Alienation Framework

16 The Identity-Alienation Framework Society is divided into groups (economic, social, religious, spatial...) Identity. There is homogeneity within each group. Alienation. There is heterogeneity across groups.

17 The Identity-Alienation Framework Society is divided into groups (economic, social, religious, spatial...) Identity. There is homogeneity within each group. Alienation. There is heterogeneity across groups. In our 1994 Econometrica paper, we presumed that such a situation is conflictual: We begin with the obvious question: why are we interested in polarization? It is our contention that the phenomenon of polarization is closely linked to the generation of tensions, to the possibilities of articulated rebellion and revolt, and to the existence of social unrest in general...

18 Measuring Polarization (adapted from Duclos, Esteban and Ray (2003)) Space of densities (cdfs) on income, political opinion, etc.

19 Measuring Polarization (adapted from Duclos, Esteban and Ray (2003)) Space of densities (cdfs) on income, political opinion, etc. Each individual located at income x feels Identification with people of similar income (the height of density n(x) at point x.) Alienation from people with dissimilar income (the income distance y x of y from x.)

20 where i = n(x) and a = x y. Measuring Polarization (adapted from Duclos, Esteban and Ray (2003)) Space of densities (cdfs) on income, political opinion, etc. Each individual located at income x feels Identification with people of similar income (the height of density n(x) at point x.) Alienation from people with dissimilar income (the income distance y x of y from x.) Effective Antagonism of x towards y depends on x s alienation from y and on x s sense of identification. T (i, a)

21 View polarization as the sum of all such antagonisms P (f) = T (n(x), x y ) n(x)n(y)dxdy

22 View polarization as the sum of all such antagonisms P (f) = T (n(x), x y ) n(x)n(y)dxdy Not very useful as it stands. Axioms to narrow down P. Based on special distributions, built from uniform kernels.

23 View polarization as the sum of all such antagonisms P (f) = T (n(x), x y ) n(x)n(y)dxdy Not very useful as it stands. Axioms to narrow down P. Based on special distributions, built from uniform kernels. Income or Wealth

24 Axiom 1. If a distribution is just a single uniform density, a global compression cannot increase polarization. Income or Wealth

25 Axiom 1. If a distribution is just a single uniform density, a global compression cannot increase polarization. Income or Wealth

26 Axiom 2. If a symmetric distribution is composed of three uniform kernels, then a compression of the side kernels cannot reduce polarization. Income or Wealth

27 Axiom 2. If a symmetric distribution is composed of three uniform kernels, then a compression of the side kernels cannot reduce polarization. Income or Wealth

28 Axiom 3. If a symmetric distribution is composed of four uniform kernels, then a symmetric slide of the two middle kernels away from each other must increase polarization. Income or Wealth

29 Axiom 3. If a symmetric distribution is composed of four uniform kernels, then a symmetric slide of the two middle kernels away from each other must increase polarization. Income or Wealth

30 Axiom 4. [Population Neutrality.] Polarization comparisons are unchanged if both populations are scaled up or down by the same percentage.

31 Axiom 4. [Population Neutrality.] Polarization comparisons are unchanged if both populations are scaled up or down by the same percentage. Theorem 1. A polarization measure satisfies Axioms 1 4 if and only if it is proportional to n(x) 1+α n(y) y x dydx, where α lies between 0.25 and 1. Compare with the Gini coefficient / fractionalization index: Gini = n(x)n(y) y x dydx, It s α that makes all the difference.

32 Some Properties

33 Some Properties 1. Not Inequality. See Axiom Bimodal. Polarization maximal for bimodal distributions, but defined of course over all distributions.

34 3. Global. The local merger of two groups has effects that depend on the shape of the distribution elsewhere.

35 3. Global. The local merger of two groups has effects that depend on the shape of the distribution elsewhere. Density Income

36 3. Global. The local merger of two groups has effects that depend on the shape of the distribution elsewhere. Density Income

37 3. Global. The local merger of two groups has effects that depend on the shape of the distribution elsewhere. Density Income

38 3. Global. The local merger of two groups has effects that depend on the shape of the distribution elsewhere. Density Income

39 3. Nonlinear. Same direction of population or income movements may cause polarization to go down or up, depending on context.

40 3. Nonlinear. Same direction of population or income movements may cause polarization to go down or up, depending on context. Density Income

41 3. Nonlinear. Same direction of population or income movements may cause polarization to go down or up, depending on context. Density Income

42 3. Nonlinear. Same direction of population or income movement may cause polarization to go down or up, depending on context. Density Income

43 More on α Pol = n(x) 1+α n(y) y x dydx, where α lies between 0.25 and 1.

44 More on α Pol = n(x) 1+α n(y) y x dydx, where α lies between 0.25 and 1. Axiom 5. If p > q but p q is small and so is r, a small shift of mass from r to q cannot reduce polarization. r p q 2ε 2ε 2ε 0 a 2a

45 More on α Pol = n(x) 1+α n(y) y x dydx, where α lies between 0.25 and 1. Axiom 5. If p > q but p q is small and so is r, a small shift of mass from r to q cannot reduce polarization. r p q 2ε 2ε 2ε 0 a 2a

46 Theorem 2. Under the additional Axiom 5, it must be that α = 1, so the unique polarization measure that satisfies the five axioms is proportional to n(x) 2 n(y) y x dydx.

47 Theorem 2. Under the additional Axiom 5, it must be that α = 1, so the unique polarization measure that satisfies the five axioms is proportional to n(x) 2 n(y) y x dydx. Easily applicable to ethnolinguistic or religious groupings. Say m social groups, n j is population proportion in group j. If all inter-group distances are binary, then Pol = M M n 2 j n k = j=1 k=1 M n 2 j (1 n j ). j=1

48 Polarization and Conflict: Behavior Axiomatics suggest (but cannot establish) a link between polarization and conflict.

49 Polarization and Conflict: Behavior Axiomatics suggest (but cannot establish) a link between polarization and conflict. Two approaches: Theoretical. Write down a natural theory which links conflict with these measures. Empirical.Take the measures to the data and see they are related to conflict. I discuss the theory first (based on Esteban and Ray (2009)).

50 A Simple Model of Conflict m groups; N i in group i, m i=1 N i = N. They fight over a budget ; per capita value normalized to 1. A fraction λ of this budget is available to produce society-wide public goods. The winning group gets to choose the goods.

51 A Simple Model of Conflict m groups; N i in group i, m i=1 N i = N. They fight over a budget ; per capita value normalized to 1. A fraction λ of this budget is available to produce society-wide public goods. The winning group gets to choose the goods. u ij = public goods payoff to a member of group i if a single unit per-capita of the optimal mix for group j is produced. The remainder 1 λ is privately divided, again among the winning group.

52 Conflict Resources Individual resource contribution r at utility cost c(r): smooth, thrice differentiable, with c (r) > 0, c (r) > 0, c (r) 0. Example: c(r) = r θ /θ, with θ 2.

53 Conflict Resources Individual resource contribution r at utility cost c(r): smooth, thrice differentiable, with c (r) > 0, c (r) > 0, c (r) 0. Example: c(r) = r θ /θ, with θ 2. R i is total contributions by group i. Define R = m R i. i=1 Probability of success given by p j = R j R ρ R/N is our measure of overall conflict.

54 Payoffs Per-capita payoff to group i is λu ii + (1 λ)(n/n i ) = λu ii + (1 λ)/n i (in case i wins the conflict), and λu ij (in case some other group j wins).

55 Payoffs Per-capita payoff to group i is λu ii + (1 λ)(n/n i ) = λu ii + (1 λ)/n i (in case i wins the conflict), and λu ij (in case some other group j wins). So net expected payoff to an individual k in group i is π i (k) = m j=1 p j λu ij + p i (1 λ) n i c (r i (k)).

56 How do Individuals Make Contributions? One extreme: individuals maximize own payoff. Another extreme: there is full intra-group cohesion and individual contributions maximize group payoffs.

57 How do Individuals Make Contributions? One extreme: individuals maximize own payoff. Another extreme: there is full intra-group cohesion and individual contributions maximize group payoffs. Intermediate situations: define person k s extended utility by U i (k) (1 α)π i (k) + α l i π i (l), where α lies between 0 and 1. Interpretations for α: group cohesion. (i) intragroup concern or altruism (ii)

58 Equilibrium A collection {r i (k)} of individual contributions where for every group i and member k, r i (k) maximizes (1 α)π i (k) + α l i π i (l)

59 Equilibrium A collection {r i (k)} of individual contributions where for every group i and member k, r i (k) maximizes (1 α)π i (k) + α l i π i (l) which is the same as maximizing [(1 α) + αn i ] p i 1 λ n i + λ m p j u ij c(r i (k)). j=1 given the contributions of everyone else.

60 Equilibrium A collection {r i (k)} of individual contributions where for every group i and member k, r i (k) maximizes (1 α)π i (k) + α l i π i (l) which is the same as maximizing [(1 α) + αn i ] p i 1 λ n i + λ m p j u ij c(r i (k)). j=1 given the contributions of everyone else. Theorem 3. An equilibrium always exists and it is unique.

61 Approximation Theorem For each i let γ i p i /n i : correction factors.

62 Approximation Theorem For each i let γ i p i /n i : correction factors. Theorem 4. Neglect joint impact of the deviation of correction factors from unity. Then the per-capita cost of conflict is approximately ˆρ, given by ˆρc ( ˆρ) = ω 1 + ω 2 G + α[λp + (1 λ)f ], where ω 1 (1 λ)(1 α)(m 1)/N ω 2 λ(1 α)/n.

63 Approximation Theorem For each i let γ i p i /n i : correction factors. Theorem 4. Neglect joint impact of the deviation of correction factors from unity. Then the per-capita cost of conflict is approximately ˆρ, given by ˆρc ( ˆρ) = ω 1 + ω 2 G + α[λp + (1 λ)f ], where ω 1 (1 λ)(1 α)(m 1)/N ω 2 λ(1 α)/n. So for large N: only P and F matter if α > 0: ˆρc ( ˆρ) α[λp + (1 λ)f ]

64 Proof. Recall maximization problem [(1 α) + αn i ] p i 1 λ n i m + λ p j u ij c(r i (k)). j=1

65 Proof. Recall maximization problem σ i p i 1 λ n i m + λ p j u ij c(r i (k)) j=1 where σ i (1 α) + αn i.

66 Proof. Recall maximization problem [ σ i λu ii + 1 λ ] ( σ i p j λδij + 1 λ ) c(r i (k)) n i n j =i i where σ i (1 α) + αn i where δ ij u ii u ij.

67 Proof. So maximize [ σ i λu ii + 1 λ ] ( σ i p j λδij + 1 λ ) c(r i (k)) n i n j =i i where σ i (1 α) + αn i where δ ij u ii u ij.

68 Proof. So maximize σ i m j=1 p j ij c(r i (k)) where σ i (1 α) + αn i where δ ij u ii u ij where ii 0, and ij λδ ij + (1 λ)/n i for all j = i.

69 Proof. So maximize σ i m j=1 p j ij c(r i (k)) where σ i (1 α) + αn i where δ ij u ii u ij where ii 0, and ij λδ ij + (1 λ)/n i for all j = i. First-order condition: σ i R m p j ij = c (r i (k)) j=1

70 Proof. So maximize σ i m j=1 p j ij c(r i (k)) where σ i (1 α) + αn i where δ ij u ii u ij where ii 0, and ij λδ ij + (1 λ)/n i for all j = i. First-order condition (r i (k) = r i for all k i): σ i R m p j ij = c (r i ) j=1

71 Proof. So maximize σ i m j=1 p j ij c(r i (k)) where σ i (1 α) + αn i where δ ij u ii u ij where ii 0, and ij λδ ij + (1 λ)/n i for all j = i. First-order condition (multiply both sides by ρp i ): ρ R m p i p j σ i ij = ρp i c (r i ) j=1

72 Proof. So maximize σ i m j=1 p j ij c(r i (k)) where σ i (1 α) + αn i where δ ij u ii u ij where ii 0, and ij λδ ij + (1 λ)/n i for all j = i. First-order condition using ρ = R/N: 1 N m p i p j σ i ij = ρp i c (r i ) j=1

73 Proof. So maximize σ i m j=1 p j ij c(r i (k)) where σ i (1 α) + αn i where δ ij u ii u ij where ii 0, and ij λδ ij + (1 λ)/n i for all j = i. First-order condition using ρ = R/N: 1 N m γ i γ j n i n j σ i ij = ρp i c (γ i ρ) j=1 recalling that γ i = p i /n i.

74 From previous slide: 1 N m γ i γ j n i n j σ i ij = ρp i c (γ i ρ) j=1

75 From previous slide: 1 N m γ i γ j n i n j σ i ij = ρp i c (γ i ρ) j=1 Multiply both sides by c (ρ)/c (γ i ρ), sum over all i: m m i=1 j=1 φ(γ i, γ j, ρ)n i n j σ i ij N m = ρ p i c (ρ) = ρc (ρ), i=1

76 From previous slide: 1 N m γ i γ j n i n j σ i ij = ρp i c (γ i ρ) j=1 Multiply both sides by c (ρ)/c (γ i ρ), sum over all i: m m i=1 j=1 φ(γ i, γ j, ρ)n i n j σ i ij N m = ρ p i c (ρ) = ρc (ρ), i=1 where φ(γ i, γ j, ρ) c (ρ)γ i γ j c (γ i ρ).

77 From previous slide: 1 N m γ i γ j n i n j σ i ij = ρp i c (γ i ρ) j=1 Multiply both sides by c (ρ)/c (γ i ρ), sum over all i: m m i=1 j=1 φ(γ i, γ j, ρ)n i n j σ i ij N m = ρ p i c (ρ) = ρc (ρ), i=1 where φ(γ i, γ j, ρ) c (ρ)γ i γ j c (γ i ρ). Ignore the φ term (which is 1 when all γ equal 1): ρc (ρ) m m i=1 j=1 n i n j σ i ij N

78 From previous slide: 1 N m γ i γ j n i n j σ i ij = ρp i c (γ i ρ) j=1 Multiply both sides by c (ρ)/c (γ i ρ), sum over all i: m m i=1 j=1 φ(γ i, γ j, ρ)n i n j σ i ij N m = ρ p i c (ρ) = ρc (ρ), i=1 where φ(γ i, γ j, ρ) c (ρ)γ i γ j c (γ i ρ). Ignore the φ term (which is 1 when all γ equal 1), open up: ρc (ρ) m i=1 j =i n i n j [(1 α) + αn i ][λδ ij + (1 λ)/n i ] N.

79 How Good is the Approximation?

80 How Good is the Approximation? Holds exactly when there are just two groups and all goods are public. Holds exactly when all groups the same size and public goods losses are symmetric. Holds almost exactly for contests when conflict is high enough.

81 How Good is the Approximation? Holds exactly when there are just two groups and all goods are public. Holds exactly when all groups the same size and public goods losses are symmetric. Holds almost exactly for contests when conflict is high enough. is. Can numerically simulate to see how good the approximation

82 Contests, quadratic costs, large populations, λ various:

83 Distances, quadratic costs, large populations, λ various:

84 Small populations, λ various:

85 Nonquadratic costs, large populations, λ various:

86 Empirical Investigation Based on Montalvo and Reynal-Querol, AER (2005). Pol = M n 2 j (1 n j ). j=1 Compare with fragmentation: Frag = M n j (1 n j ). j=1 The two measures are very different, even empirically:

87 Ethnic fractionalization index Ethnic polarization index

88 Guatemala, Sierra Leone: fractionalization low ethnic polarization high but ethnic (Guatemala: 55% Mestizo or Ladino, 42% Maya, 3% other) religious polarization high but religious frac- Nigeria, Bosnia: tionalization low ( split on Christians and Muslims in Nigeria, in Bosnia)

89 New regression as in Fearon-Laitin (2003) and Collier-Hoeffler (2004) but with polarization included. 138 countries, Dependent variable: period. incidence of a civil war over a five year PRIO dataset for civil wars, 25 yearly deaths criterion (and 1000 overall).

90 Explanatory Variables include per-capita income population size terrain (proxy for ease of insurgency) primary exports (proxy for payoff in event of victory) democracy indicators... and of course indices of ethnic or religious polarization

91 First run a logit of war on ethnic fractionalization

92 [1] [2] [3] [4] EthFrac (2.04) (0.53) (0.16) (0.97) LogPcGdp (5.07) (5.90) (5.96) (5.40) Constant (2.47) (0.38) (0.16) (0.94) LogPop (6.75) (6.03) (3.69) PrimExp (0.26) (0.48) Mountains 0.00 (1.67) NonContiguous (0.61) Democracy 0.49 (1.87) Pseu R Obs

93 [1] [2] [3] [4] EthPol (3.31) (3.76) (3.71) (3.23) LogPcGdp (6.16) (6.53) (6.57) (5.50) Constant (3.01) (1.47) (1.27) (0.16) LogPop (7.15) (6.46) (4.33) PrimExp (0.09) (0.16) Mountains 0.00 (1.13) NonContiguous (0.00) Democracy 0.41 (1.58) Pseu R Obs

94 Ethnic polarization not just significant; the effect is pretty big too. If polarization raised from 0.51 (the average) to 0.95 (Nigeria) the predicted probability of conflict doubles. [An increase by one standard deviation (0.24) raises conflict probability by 50%.]

95 Try the same logit with religious variables instead

96 [1] [2] [3] [4] RelFrac (2.31) (0.76) (0.49) (1.17) LogPcGdp (4.91) (5.75) (5.85) (5.27) Constant (1.42) (0.97) (0.86) (0.25) LogPop (6.41) (5.88) (4.09) PrimExp (0.61) (1.04) Mountains 0.01 (2.17) NonContiguous 0.10 (0.31) Democracy 0.36 (1.29) Pseu R Obs

97 [1] [2] [3] [4] RelPol (2.93) (1.71) (1.50) (2.20) LogPcGdp (4.46) (5.22) (5.26) (5.08) Constant (1.10) (1.52) (1.40) (0.10) LogPop (6.36) (5.75) (3.94) PrimExp (0.39) (0.84) Mountains 0.01 (2.12) NonContiguous 0.16 (0.47) Democracy 0.35 (1.26) Pseu R Obs

98 Robustness to Different Specifications Ethnic polarization significant when in same regression with ethnic fractionalization; latter is not. Same true if a measure of ethnic dominance (Collier 2001 and Collier and Hoeffler 2002) is used instead. Both observations above still true if ethnic is replaced by religious. Robust to non-war measures of conflict; see Esteban-Mayoral- Ray (2010); more later.

99 Robustness: Datasets and Classifications World Christian Encyclopedia (used here), Encyclopedia Britannica, Atlas Nadorov Mira, alternative classifications in Alesina et al (2003) Joint indices of ethnic and religious polarization (measure along each dimension, pick the max) Alternative definitions of civil war (Replace PRIO criterion with Fearon-Laitin. Same results.) Works even more strongly for genocides (Montalvo and Reynal-Querol Economic Journal (2008)). Pure cross-section logits Incidence of civil war with base variables from 1960.

100 Intergroup Distances Esteban, Mayoral and Ray (2010) [EMR] compute inter-group distances by using responses from the World Values Survey. Polarization measures derived from these both ethnic and religious are highly correlated with conflict. But endogeneity a major concern.

101 Intergroup Distances Esteban, Mayoral and Ray (2010) [EMR] compute inter-group distances by using responses from the World Values Survey. Polarization measures derived from these both ethnic and religious are highly correlated with conflict. But endogeneity a major concern. EMR instrument ethnic pol using average language distances. Identification assumption: language distances do not affect conflict directly but only via its correlation with people s tolerance or intolerance of other groups.

102 Follow Fearon (2003) and Desmet et al. (2009, 2010): distance between languages i and j is d ij = 1 ( l m ) δ, where l is the number of common branches between i and j, m is the maximum number of shared branches between any two languages, and δ is a decay parameter. Pop-weighted average over all languages is the instrument: W AD = K K s i s j d ij, i=1 j=1

103 Follow Fearon (2003) and Desmet et al. (2009, 2010): distance between languages i and j is d ij = 1 ( l m ) δ, where l is the number of common branches between i and j, m is the maximum number of shared branches between any two languages, and δ is a decay parameter. Pop-weighted average over all languages is the instrument: W AD = K K s i s j d ij, i=1 j=1 Use additional definition of conflict, as opposed to civil war: W. av. of 8 different domestic conflicts: assassinations, general strikes, guerrilla war, government crises, purges, riots, revolutions, anti-govt demonstrations. (Cross-National Time-Series Data Archive.)

104 EthPol ER 1.24 (0.01) EthPol RQ 0.22 (0.33) LogPcGdp 0.10 (0.03) LogPop 0.00 (0.98) PrimExp 0.29 (0.20) Mountains 0.01 (0.12) NonContiguous 0.12 (0.36) Democracy 0.01 (0.86) War Incidence Social Unrest [1] [2] [3] [4] [5] [6] 1.19 (0.01) 3.66 (0.00) (0.51) 0.10 (0.04) 0.01 (0.81) 0.30 (0.22) 0.00 (0.14) 0.14 (0.29) 0.01 (0.89) 0.27 (0.11) 0.00 (0.98) 1.34 (0.18) 0.01 (0.09) 0.52 (0.18) 0.07 (0.78) 3.61 (0.00) 1.75 (0.03) (0.54) 0.26 (0.12) 0.01 (0.91) 1.36 (0.17) (0.10) 0.57 (0.13) 0.08 (0.76) 0.51 (0.00) 0.12 (0.13) 1.20 (0.10) 0.01 (0.38) 0.82 (0.01) 0.13 (0.49) 1.81 (0.02) (0.00) 0.11 (0.15) 1.19 (0.11) 0.01 (0.21) 0.78 (0.01) 0.14 (0.47) Pseu R Obs

105 Why Ethnicity?

106 Why Ethnicity? If ethnic polarization matters, should we adopt primordialism? No: ethnicity could just be an instrumental marker. But a logically prior question needs to be addressed:

107 Why Ethnicity? If ethnic polarization matters, should we adopt primordialism? No: ethnicity could just be an instrumental marker. But a logically prior question needs to be addressed: Why Conflict? Equilibrium conflict is Pareto inefficient Why not arrange a transfer scheme to avoid costly conflict? James Fearon (1995) refers to this as the central puzzle.

108 1. Incomplete Information. Myerson-Satterthwaite (1983), Fearon (1995), Esteban and Ray (2001), Bester and Warneryd (2006), Sánchez-Pagés (2008). 2. The Absence of Transfers. Kirshner (2000). 3. Limited Commitment Fearon (1995), Garfinkel and Skaperdas (2000), Slantchev (2003), Leventoglu and Slantchev (2007), Powell (2007). 4. Uninternalized Costs Fearon (1995), Jackson and Morelli (2007). 5. The Multiplicity of Threats. Particularly relevant to ethnic conflict; will discuss here.

109 Two-Group Version Society has a prize G at stake, can be appropriated. λg is public, (1 λ)g is private and must be divided.

110 Two-Group Version Society has a prize G at stake, can be appropriated. λg is public, (1 λ)g is private and must be divided. Two groups. Either group can initiate conflict. Group i is of size n i and contributes resources r i per capita. Win probability p i = n i r i /R. Cost function c(r) = (1/θ)r θ for θ 2.

111 Two-Group Version Society has a prize G at stake, can be appropriated. λg is public, (1 λ)g is private and must be divided. Two groups. Either group can initiate conflict. Group i is of size n i and contributes resources r i per capita. Win probability p i = n i r i /R. Cost function c(r) = (1/θ)r θ for θ 2. Assume cohesion α > 0 from previous exercise.

112 Under conflict, group i chooses r i to maximize n i r i R P (n i) (r θ i /θ). where P (n) = [λg + (1 λ)(g/n)] is per-capita prize to group. First-order condition is P (n i ) [ ni R n2 i r ] i R 2 = r θ 1 i,

113 Under conflict, group i chooses r i to maximize n i r i R P (n i) (r θ i /θ). where P (n) = [λg + (1 λ)(g/n)] is per-capita prize to group. First-order condition is P (n i ) [ ni R n2 i r ] i R 2 = r θ 1 i, P (n i ) n i R [ 1 n ] ir i R = r θ 1 i,

114 Under conflict, group i chooses r i to maximize n i r i R P (n i) (r θ i /θ). where P (n) = [λg + (1 λ)(g/n)] is per-capita prize to group. First-order condition is P (n i ) [ ni R n2 i r ] i R 2 = r θ 1 i, P (n i ) n i R [ 1 n ] ir i R = r θ 1 i, P (n i )n i n j = R 2 rθ 1. ir j

115 P (n i )n i n j = R 2 rθ 1. ir j

116 P (n i )n i n j = R 2 rθ 1. ir j If θ = 2, we see right away that R 4 = P (n i )n 2 i P (n j )n 2 j = [λg + (1 λ)(g/n 1 )] [λg + (1 λ)(g/n 2 )] n 2 i n 2 j, This is inverted-u in population division.

117 P (n i )n i n j = R 2 rθ 1. ir j If θ = 2, we see right away that R 4 = P (n i )n 2 i P (n j )n 2 j = [λg + (1 λ)(g/n 1 )] [λg + (1 λ)(g/n 2 )] n 2 i n 2 j, This is inverted-u in population division. For general θ result is still true, but more complex: R θ = [P (n i )n i P (n j )n j ] 1/θ (n i n j ) (θ 1)/θ { P (n j ) 1/θ n j + P (n i ) 1/θ n i } θ 2. also inverted-u. Polarization affects conflict intensity (no approx. needed), conditional on it happening in the first place.

118 Initiation But conflict may not happen to begin with too costly.

119 Initiation But conflict may not happen to begin with too costly. Let peacetime share of group i be s i. Then i initiates if P (n i ) n ir i R (rθ i /θ) > s i P (n i ), where r i and R are subgame values.

120 Initiation But conflict may not happen to begin with too costly. Let peacetime share of group i be s i. Then i initiates if P (n i ) n ir i R (rθ i /θ) > s i P (n i ), where r i and R are subgame values. Recall first-order condition P (n i ) n i R [ 1 n i r i R ] = r θ 1 i.

121 Initiation But conflict may not happen to begin with too costly. Let peacetime share of group i be s i. Then i initiates if P (n i ) n ir i R (rθ i /θ) > s ip (n i ), where r i and R are subgame values. Recall first-order condition P (n i )p i p j = r θ i.

122 Initiation But conflict may not happen to begin with too costly. Let peacetime share of group i be s i. Then i initiates if P (n i ) n ir i R (rθ i /θ) > s ip (n i ), where r i and R are subgame values. Recall first-order condition P (n i )p i p j = r θ i. p i 1 θ p i(1 p i ) > s i.

123 where k (θ 1)/θ. Initiation But conflict may not happen to begin with too costly. Let peacetime share of group i be s i. Then i initiates if P (n i ) n ir i R (rθ i /θ) > s ip (n i ), where r i and R are subgame values. Recall first-order condition P (n i )p i p j = r θ i. p i 1 θ p i(1 p i ) > s i. kp i + (1 k)p 2 i > s i

124 The Case of Public Goods Assume that λ = 1. Then P (n) = G, and FOC is Gn i n j = R 2 rθ 1 i r j Proves right away that r i = r j for public goods, so p i = n i.

125 The Case of Public Goods Assume that λ = 1. Then P (n) = G, and FOC is Gn i n j = R 2 rθ 1 i r j Proves right away that r i = r j for public goods, so p i = n i. Recall condition for conflict initiation: kp i + (1 k)p 2 i > s i

126 The Case of Public Goods Assume that λ = 1. Then P (n) = G, and FOC is Gn i n j = R 2 rθ 1 i r j Proves right away that r i = r j for public goods, so p i = n i. Condition for conflict initiation: kn i + (1 k)n 2 i > s i.

127 Public Goods, Summary

128 Public Goods, Summary Observation 1. Public resources; payoffs equally divided under peace. Then there is m ( 1 2, 1) so that group with size m > m wants conflict.

129 Public Goods, Summary Observation 1. Public resources; payoffs equally divided under peace. Then there is m ( 1 2, 1) so that group with size m > m wants conflict. For public goods, s i = 1/2 for equal treatment. Conflict initiation: kn i + (1 k)n 2 i > 1/2. Threshold for intersection is m > 1/2. Note that n i 1/2 never works and n i > 1/2 is sufficient.

130 The Case of Private Goods Recall first order condition: P (n i )n i n j = R 2 rθ 1. ir j

131 The Case of Private Goods Recall first order condition; remember P (n i ) = G/n i : G n i n i n j = R 2 rθ 1 ir j.

132 The Case of Private Goods Recall first order condition; remember P (n i ) = G/n i : Gn j = R 2 rθ 1. ir j

133 The Case of Private Goods Recall first order condition; remember P (n i ) = G/n i : Gn j = R 2 rθ 1. ir j Divide by first-order condition for group j: r i r j = ( nj n i ) 1/θ = ( nj n i ) 1 k, Olson intuition: small groups lobby more per-capita. So probability that i wins the conflict is given by p i n i r i n i r i + n j r j = n k i n k i + nk j

134 Write this out as function of initiating group size n i = m: p(m) = m k m k + (1 m) k. Condition for initiation: kp(m) + (1 k)p(m) 2 > s(m) where s(m) is share function under peace.

135 Write this out as function of initiating group size n i = m: p(m) = m k m k + (1 m) k. Condition for initiation: kp(m) + (1 k)p(m) 2 > s(m) where s(m) is share function under peace. Observation 2. Privately divisible resources; payoffs equally divided under peace. Then there is m (0, 1 2 ) so that marker m < m wants conflict.

136 Write this out as function of initiating group size n i = m: p(m) = m k m k + (1 m) k. Condition for initiation: kp(m) + (1 k)p(m) 2 > s(m) where s(m) is share function under peace. Observation 2. Privately divisible resources; payoffs equally divided under peace. Then there is m (0, 1 2 ) so that marker m < m wants conflict. Outline of Argument. Under symmetry, we have s(m) = m.

137 Need kp(m) + (1 k)p(m) 2 > m. 1 p, p 2 1/2 0 1/2 1 m

138 Need kp(m) + (1 k)p(m) 2 > m. 1 p, p 2 1/2 0 1/2 1 m

139 Need kp(m) + (1 k)p(m) 2 > m. 1 p, p 2 1/2 0 1/2 1 m

140 Need kp(m) + (1 k)p(m) 2 > m. 1 p, p 2 m 1/2 0 m* 1/2 1 m

141 Coase Revisited Public goods, large groups initiate. Private goods, small groups initiate. Coase: with transfers, there is some allocation that will appease the initiator (conflict is inefficient, after all). But what if there is a potential multiplicity of initiators?

142 Coase Revisited Public goods, large groups initiate. Private goods, small groups initiate. Coase: with transfers, there is some allocation that will appease the initiator (conflict is inefficient, after all). But what if there is a potential multiplicity of initiators? Formalize this idea for private goods: Say all conflicts are bilateral between initiator and complement but that a variety of initiators can formed based on markers class, caste, religion, geography, occupation...

143 A finite collection C of markers is balanced if there are weights λ(m) in [0, 1], one for each marker, such that M C,i M λ(m) = 1 for every i in society

144 A finite collection C of markers is balanced if there are weights λ(m) in [0, 1], one for each marker, such that M C,i M λ(m) = 1 for every i in society For instance, any partition is balanced. More generally, rules out common intersection.

145 A finite collection C of markers is balanced if there are weights λ(m) in [0, 1], one for each marker, such that M C,i M λ(m) = 1 for every i in society For instance, any partition is balanced. More generally, rules out common intersection. Theorem 5. Suppose there exists a balanced collection of markers, each with m < m. Then there is no peaceful allocation for society that is immune to conflict.

146 Proof. Suppose there is indeed a peaceful allocation x.

147 Proof. Suppose there is indeed a peaceful allocation x. For every marker M C, we have i M x(i) G[kp(m) + (1 k)p(m) 2 ] by immunity to conflict.

148 Proof. Suppose there is indeed a peaceful allocation x. For every marker M C, we have i M x(i) G[kp(m) + (1 k)p(m) 2 ] by immunity to conflict. Moreover, for each such marker, G[kp(m) + (1 k)p(m) 2 ] > Gm because m < m for every marker in collection C.

149 Proof. Suppose there is indeed a peaceful allocation x. For every marker M C, we have i M x(i) G[kp(m) + (1 k)p(m) 2 ] by immunity to conflict. Moreover, for each such marker, G[kp(m) + (1 k)p(m) 2 ] > Gm because m < m for every marker in collection C. Combine: i M x(i) > Gm

150 Proof. Suppose there is indeed a peaceful allocation x. For every marker M C, we have i M x(i) G[kp(m) + (1 k)p(m) 2 ] by immunity to conflict. Moreover, for each such marker, G[kp(m) + (1 k)p(m) 2 ] > Gm because m < m for every marker in collection C. Combine, and multiply by balancing weight: λ(m) i M x(i) > Gmλ(M)

151 Proof. Suppose there is indeed a peaceful allocation x. For every marker M C, we have i M x(i) G[kp(m) + (1 k)p(m) 2 ] by immunity to conflict. Moreover, for each such marker, G[kp(m) + (1 k)p(m) 2 ] > Gm because m < m for every marker in collection C. Combine, multiply, add over all markers: M C,i M λ(m) i M x(i) > M C,i M Gmλ(M)

152 Proof. Suppose there is indeed a peaceful allocation x. For every marker M C, we have i M x(i) G[kp(m) + (1 k)p(m) 2 ] by immunity to conflict. Moreover, for each such marker, G[kp(m) + (1 k)p(m) 2 ] > Gm because m < m for every marker in collection C. Combine, multiply, add over all markers, simplify: i N x(i) > G.

153 Does the Same Argument Work for Public Goods? If the complement of a marker is also a marker, there always exists an allocation which is immune to conflict. Enough superadditivity to deal with a rich array of threats, provided private transfers are available. But private transfers may not compensate for public loss in religion, language, or group recognition.

154 Why Ethnicity? (Revisited)

155 Why Ethnicity? (Revisited) Historical Institutions. Institutions set up ameliorate class conflict can raise demands along other lines.

156 Why Ethnicity? (Revisited) Historical Institutions. Institutions set up ameliorate class conflict can raise demands along other lines. Redistribution versus Exclusion. Horowitz again: [T]he relations of many... ethnic groups on a global scale, most ethnic groups are not accurately defined as superiorsubordinate relations... It is not so much the politics of subordination that concerns them, but rather the politics of inclusion and exclusion.

157 Why Ethnicity? (Revisited) Historical Institutions. Institutions set up ameliorate class conflict can raise demands along other lines. Redistribution versus Exclusion. Horowitz again: [T]he relations of many... ethnic groups on a global scale, most ethnic groups are not accurately defined as superiorsubordinate relations... It is not so much the politics of subordination that concerns them, but rather the politics of inclusion and exclusion. The Perverse Synergy of Within-Group Inequality. (And some comments on the identity-alienation framework.)

158 A Tentative Model of Salience

159 A Tentative Model of Salience Class.

160 A Tentative Model of Salience Class. "Rich" "Poor"

161 A Tentative Model of Salience Class. "Rich" population share n r per-capita income y r "Poor" population share n p per-capita income y p

162 A Tentative Model of Salience Class. "Rich" y r > y p "Poor" n p > n r

163 A Tentative Model of Salience Ethnicity.

164 A Tentative Model of Salience Ethnicity. H M

165 A Tentative Model of Salience Ethnicity. H M Population Share n h Population Share n m

166 A Tentative Model of Salience Ethnicity. H M Population Share n h Population Share n m n h > n m

167 Unranked Ethnic Groups

168 Unranked Ethnic Groups R P

169 Unranked Ethnic Groups R H M P

170 Unranked Ethnic Groups R H M P

171 Unranked Ethnic Groups R H M P

172 Class Goods and Ethnic Goods Society produces public goods. Some have a class character, some an ethnic character (some both). Potential conflict over seizing and controlling these goods.

173 Class Goods Overall budget of C for class-based public goods. health: public versus private education: primary versus higher infrastructure: transportation, electricity, communications foreign investment legislation: land reform, squatter rights, taxation

174 Ethnic Goods Overall budget of E for ethnic-based public goods. natural resources for group-based public goods occupational categories dominated by certain ethnic groups tagged public goods: temples, mosques, madrasas reservations in jobs or political positions ideologies, political power, ethnic supremacy

175 Alliances Consider conflicts from only two possible types of alliances.

176 Alliances Consider conflicts from only two possible types of alliances. A class alliance is a merging of interests over ethnic groups, but maintaining distinction between P and R. The battle, then, is over the capture of the class budget. An ethnic alliance is a merging of interests over classes, but maintaining distinction between H and M. The battle, then, is over the capture of the ethnic budget.

177 Elements of a Strategic Approach Stage 1. Salience. Alliances form (or not). Stage 2. Hostility. Adoption of hostile or peaceful stances by one alliance or the other. If either side is hostile, move to Stage 3. Otherwise receive peace payoffs. Stage 3. Conflict. Each alliance finances activists or militants. Militants enter into conflict. Each side receives conflict payoffs. Approach: work backwards from Stage 3.

178 Stage 3: Peace and Conflict Payoffs

179 Stage 3: Peace and Conflict Payoffs Peace Payoffs: Ethnic Budget E Class Budget C s r s h s m s p

180 Individual in group ij with i a class index and j an ethnic index gets u(y i ) + s i C + s j E. Public goods: s i unaffected by population.

181 Individual in group ij with i a class index and j an ethnic index gets u(y i ) + s i C + s j E. Public goods: s i unaffected by population. Conflict Payoffs:

182 Individual in group ij with i a class index and j an ethnic index gets u(y i ) + s i C + s j E. Public goods: s i unaffected by population. Conflict Payoffs: Each alliance i contributes activists (militants, thugs... ) A i. Compensation rate for activists, w i in alliance i. (w i generally connected to alliance incomes.) Total expenditure for alliance i: w i A i.

183 Conflict Payoffs In class alliance, C-share proportional to activists; E-share untouched.

184 Conflict Payoffs In class alliance, C-share proportional to activists; E-share untouched. Ethnic Budget E Class Budget C A r / A r + A p s h s m A p / A r + A p

185 Conflict Payoffs In ethnic alliance, E-share proportional to activists; C-share untouched.

186 Conflict Payoffs In ethnic alliance, E-share proportional to activists; C-share untouched. Ethnic Budget E Class Budget C A h A h + A m A m A h + A m s r s p

187 Summary of Conflict Payoffs CC payoffs to person of ethnicity j in class alliance i: u (Income Contributions) + A i A p + A r C + s j E.

188 Summary of Conflict Payoffs CC payoffs to person of ethnicity j in class alliance i: u (Income Contributions) + A i A p + A r C + s j E. CC payoffs to person of class i in class alliance j: u (Income Contributions) + A j A h + A m E + s i C.

189 Summary of Conflict Payoffs CC payoffs to person of ethnicity j in class alliance i: u (Income Contributions) + A i A p + A r C + s j E. CC payoffs to person of class i in class alliance j: u (Income Contributions) + A j A h + A m E + s i C. In each case, contributions add up to Aw. Other costs include destruction of E and C: incorporate. easy enough to

190 A Symmetry Benchmark

191 A Symmetry Benchmark Both goods equally important: C E Peacetime shares the same: s h = s p = s h = s m = 1/2. In each type of conflict, compensation rates the same across alliances: w h = w m and w p = w r.

192 Conflict Versus Peace for a Given Alliance

193 Conflict Versus Peace for a Given Alliance Let λ ij = share of finance contributed by economic group i in alliance j: (In a class alliance this ratio is always 1.)

194 Conflict Versus Peace for a Given Alliance Let λ ij = share of finance contributed by economic group i in alliance j: (In a class alliance this ratio is always 1.) Let σ j = share of activists coming from alliance j:

195 Activist share endogenous; can be linked to demography and economics. Conflict Versus Peace for a Given Alliance Let λ ij = share of finance contributed by economic group i in alliance j: (In a class alliance this ratio is always 1.) Let σ j = share of activists coming from alliance j: For economic group i in alliance j to want conflict, sufficient and generally necessary that λ ij σ 2 j + (1 λ ij )σ j > s j. For noncontributors σ j > s j, for sole contributors, σ j > s j.

196 Ethnic Conflict Versus Peace

197 Ethnic Conflict Versus Peace Proposition. Activist shares = population shares: σ j = n j. j: Recall condition for economic group i to want conflict in alliance λ ij σ 2 j + (1 λ ij )σ j > s j.

198 Ethnic Conflict Versus Peace Proposition. Activist shares = population shares: σ j = n j. j: Recall condition for economic group i to want conflict in alliance λ ij n 2 j + (1 λ ij )n j > s j. Clearly sufficient for conflict that n j > s j. Under symmetry: critical population share is approx 70% Weaker when both contribute equally: [n 2 j + n j]/2 > s j. Critical population share is approx 62%.

199 Class Conflict Versus Peace

200 Class Conflict Versus Peace No differential contributions now within alliance, so condition is easier: σ i > s i.

201 Class Conflict Versus Peace No differential contributions now within alliance, so condition is easier: σ i > s i. Can show that σ i = A i A p + A r = α i n i α r n p + α p n r where α i is approx. u (y i )w i.

202 Class Conflict Versus Peace No differential contributions now within alliance, so condition is easier: σ i > s i. Can show that σ i = A i A p + A r = α i n i α r n p + α p n r where α i is approx. u (y i )w i. u (y) cost of financial contributions; w cost of compensating militants. If mercenaries available (w r = w p ), n p > σ p. Harder for them to initiate class conflict, though not ruled out.

203 At the same time, rich unlikely to initiate class conflict. Too little to gain.

204 At the same time, rich unlikely to initiate class conflict. Too little to gain. Mercenary army: w p = w r u logarithmic Then initiation condition for rich reduces to n r y r n r y r + n p y p > s r, That is, income share of the rich > share of public good. World Bank (2003): Indian per-capita income $2,500 PPP. Use to cut: n p 70%, income share around 35%.

205 Salience I

206 Salience I Proposition. [Ethnic salience for a majority group] Assume low local curvature of u: u approx. constant across any person s income and his income net of contributions. Then an ethnic majority group i (i = poor or rich) obtains higher payoffs from ethnic relative to class conflict if and only if ( [1 λih ]n h + λ ih n 2 h s ) h µ > σ 2 i s i. where µ = E/C.

207 Salience I Proposition. [Ethnic salience for a majority group] Assume low local curvature of u: u approx. constant across any person s income and his income net of contributions. Then an ethnic majority group i (i = poor or rich) obtains higher payoffs from ethnic relative to class conflict if and only if ( [1 λih ]n h + λ ih n 2 h s ) h µ > σ 2 i s i. where µ = E/C. Ethnic Conflict: ( [1 λ ih ]n h + λ ih n 2 h s h) > 0. Class Conflict: σi 2 s i > 0. Compare these terms, weighted by µ.

208 Two Implications

209 Two Implications Implication 1. Poor ethnic majority prefer ethnic to class conflict.

210 Two Implications Implication 1. Poor ethnic majority prefer ethnic to class conflict. ( [1 λph ]n h + λ ph n 2 h s ) h µ > σ 2 p s p.

211 Two Implications Implication 1. Poor ethnic majority prefer ethnic to class conflict. ( [1 λph ]n h + λ ph n 2 h s ) h µ > σ 2 p s p. Assume symmetry. Then suffices to check [1 λ ph ]n h + λ ph n 2 h > n2 p.

212 Two Implications Implication 1. Poor ethnic majority prefer ethnic to class conflict. ( [1 λph ]n h + λ ph n 2 h s ) h µ > σ 2 p s p. Assume symmetry. Then suffices to check [1 λ ph ]n h + λ ph n 2 h > n2 p. If n h (India: 85%) n p (India: 70%), then done. Poor don t make the financial contributions, so condition even easier: approx. n h > n 2 p.

213 Now drop symmetry of ethnic versus class goods. condition: Sufficient

214 Now drop symmetry of ethnic versus class goods. condition: Sufficient µ > n 2 p (0.5) (1 λ ph )n h + λ ph n 2 h (0.5)

215 Now drop symmetry of ethnic versus class goods. condition: Sufficient µ > n 2 p (0.5) (1 λ ph )n h + λ ph n 2 h (0.5) If n h = n p = 80% and λ ph = 1/2: Ethnic conflict preferred if E is 65% of C.

216 Now drop symmetry of ethnic versus class goods. condition: Sufficient µ > n 2 p (0.5) (1 λ ph )n h + λ ph n 2 h (0.5) If n h = n p = 80% and λ ph = 1/2: Ethnic conflict preferred if E is 65% of C. If rich contribute all finance, threshold drops to 47%.

217 Now drop symmetry of ethnic versus class goods. condition: Sufficient µ > n 2 p (0.5) (1 λ ph )n h + λ ph n 2 h (0.5) If n h = n p = 80% and λ ph = 1/2: Ethnic conflict preferred if E is 65% of C. If rich contribute all finance, threshold drops to 47%. If n p drops to 70%, threshold drops to zero.

218 Or drop equal access to class and ethnic goods, but retain other aspects of symmetry.

219 Or drop equal access to class and ethnic goods, but retain other aspects of symmetry. s p > s h + [n 2 p n 2 h ] (1 λ ph)(n h n 2 h ).

220 Or drop equal access to class and ethnic goods, but retain other aspects of symmetry. s p > s h + [n 2 p n 2 h ] (1 λ ph)(n h n 2 h ). n h = 80-85%, n p = 70%.

221 Or drop equal access to class and ethnic goods, but retain other aspects of symmetry. s p > s h + [n 2 p n 2 h ] (1 λ ph)(n h n 2 h ). n h = 80-85%, n p = 70%. s h = 1/2 and poor finance half: ethnic conflict preferred even if class good share as low as 20-25%.

222 Or drop equal access to class and ethnic goods, but retain other aspects of symmetry. s p > s h + [n 2 p n 2 h ] (1 λ ph)(n h n 2 h ). n h = 80-85%, n p = 70%. s h = 1/2 and poor finance half: ethnic conflict preferred even if class good share as low as 20-25%. If poor don t finance ethnic conflict, threshold drops to 15-20%.

223 Implication 2. Rich ethnic majority prefer ethnic conflict to class conflict whenever the poor prefer class conflict to peace.

224 Implication 2. Rich ethnic majority prefer ethnic conflict to class conflict whenever the poor prefer class conflict to peace. ( [1 λrh ]n h + λ rh n 2 h s ) h µ > σ 2 r s r.

225 Implication 2. Rich ethnic majority prefer ethnic conflict to class conflict whenever the poor prefer class conflict to peace. ( [1 λrh ]n h + λ rh n 2 h s ) h µ > σ 2 r s r. Suppose that poor majority prefer class conflict to peace. Then σ p s p, so σ r s r. So sufficient to check ( [1 λrh ]n h + λ rh n 2 h s ) h µ > sr (1 s r ). If LHS nonnegative, condition automatically satisfied.

226 Implication 2. Rich ethnic majority prefer ethnic conflict to class conflict whenever the poor prefer class conflict to peace. ( [1 λrh ]n h + λ rh n 2 h s ) h µ > σ 2 r s r. Suppose that poor majority prefer class conflict to peace. Then σ p s p, so σ r s r. So sufficient to check ( [1 λrh ]n h + λ rh n 2 h s ) h µ > sr (1 s r ). If LHS nonnegative, condition automatically satisfied. If LHS negative, condition reduces to µ < s r (1 s r ) s h [1 λ rh ]n h λ rh n 2 h

227 Implication 2. Rich ethnic majority prefer ethnic conflict to class conflict whenever the poor prefer class conflict to peace. ( [1 λrh ]n h + λ rh n 2 h s ) h µ > σ 2 r s r. Suppose that poor majority prefer class conflict to peace. Then σ p s p, so σ r s r. So sufficient to check ( [1 λrh ]n h + λ rh n 2 h s ) h µ > sr (1 s r ). If LHS nonnegative, condition automatically satisfied. If LHS negative, condition reduces to µ < s r (1 s r ) s h [1 λ rh ]n h λ rh n 2 h Met whenever n h exceeds s h and s r, and µ 1.