· 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 …

$Page 1: · The Markers are Predominantly Ethnic \In much of Asia and Africa, it is only modest hyperbole to assert that the Marxian prophecy has had an …$
Distribution and Development

Debraj Ray

DSchool lecture March 22, 2010

Convergence and Divergence

Conflict

Incentives

Based on a forthcoming monograph with Joan Esteban.

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Internal Conflict is Endemic

1945–1999: 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-Muslimviolence in India.

Economic costs: 8% of world GDP (Hess (2003))

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The Markers are Predominantly Ethnic

“In much of Asia and Africa, it is only modest hyperbole toassert that the Marxian prophecy has had an ethnic fulfillment.”Horowitz (1985)

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The Markers are Predominantly Ethnic

“In much of Asia and Africa, it is only modest hyperbole toassert that the Marxian prophecy has had an ethnic fulfillment.”Horowitz (1985)

Brubaker and Laitin (1998) on “eclipse of the left-right ideo-logical axis”

Fearon (2006), 1945–1998, approx. 700 ethnic groups known,over 100 of which participated in rebellions against the state.

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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

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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 largershare

Growing evidence that instrumentalist concerns are important— maybe even dominant — in ethnic violence.

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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.

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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 con-flict is localized . . . A centrally focused system [with few groupings]possesses fewer cleavages than a dispersed system, but those itpossesses run through the whole society and are of greater magni-tude. When conflict occurs, the center has little latitude to placatesome groups without antagonizing others.”

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Statistical approach

(Collier-Hoeffler, Fearon-Laitin, Miguel-Satyanath-Sergenti)

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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?

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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

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Fractionalization

Fractionalization index widely used:

F =m∑j=1

nj(1− nj)

where nj is population share of group j.

Special case of the Gini coefficient

G =m∑j=1

M∑k=1

njnkδik

where δik is a notion of distance across groups.

Has been used in many different contexts (growth, governance,public goods provision).

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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 fractionaliza-tion are substantively and statistically insignificant . . . The empir-ical pattern is thus inconsistent with . . . the common expectationthat ethnic diversity is a major and direct cause of civil violence.”

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And yet . . . fractionalization does not seem to capture theHorowitz quote:

“In dispersed systems, group loyalties are parochial, and ethnicconflict is localized . . . A centrally focused system [with few group-ings] possesses fewer cleavages than a dispersed system, but thoseit possesses run through the whole society and are of greater mag-nitude.”

Motivates the use of polarization measures by Montalvo andReynal-Querol (2005).

Based on a measure of polarization introduced by Esteban andRay (1994) and Duclos, Esteban and Ray (2003)

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The Identity-Alienation Framework

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Society is divided into “groups” (economic, social, religious,spatial...)

Identity. There is “homogeneity” within each group.

Alienation. There is “heterogeneity” across groups.

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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 asituation is conflictual:

“We begin with the obvious question: why are we interested inpolarization? It is our contention that the phenomenon of po-larization is closely linked to the generation of tensions, to thepossibilities of articulated rebellion and revolt, and to the existenceof social unrest in general . . . ”

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Measuring Polarization

(adapted from Duclos, Esteban and Ray (2003))

Space of densities (cdfs) on income, political opinion, etc.

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Each individual located at “income” x feels

Identification with people of “similar” income (the height ofdensity n(x) at point x.)

Alienation from people with “dissimilar” income (the incomedistance |y− x| of y from x.)

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Each individual located at “income” x feels

Identification with people of “similar” income (the height ofdensity n(x) at point x.)

Alienation from people with “dissimilar” income (the incomedistance |y− x| of y from x.)

Effective Antagonism of x towards y depends on x’s alienationfrom y and on x’s sense of identification.

T (i, a)

where i = n(x) and a = |x− y|.

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View polarization as the “sum” of all such antagonisms

P (f ) =∫ ∫

T (n(x), |x− y|)n(x)n(y)dxdy

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P (f ) =∫ ∫


Not very useful as it stands. Axioms to narrow down P .

Based on special distributions, built from uniform kernels.

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P (f ) =∫ ∫


Not very useful as it stands. Axioms to narrow down P .

Based on special distributions, built from uniform kernels.

Income or Wealth

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Axiom 1. If a distribution is just a single uniform density, a“global compression” cannot increase polarization.

Income or Wealth

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Axiom 1. If a distribution is just a single uniform density, a“global compression” cannot increase polarization.

Income or Wealth

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Axiom 2. If a symmetric distribution is composed of threeuniform kernels, then a compression of the side kernels cannotreduce polarization.

Income or Wealth

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Axiom 2. If a symmetric distribution is composed of threeuniform kernels, then a compression of the side kernels cannotreduce polarization.

Income or Wealth

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Axiom 3. If a symmetric distribution is composed of four uni-form kernels, then a symmetric slide of the two middle kernels awayfrom each other must increase polarization.

Income or Wealth

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Axiom 3. If a symmetric distribution is composed of four uni-form kernels, then a symmetric slide of the two middle kernels awayfrom each other must increase polarization.

Income or Wealth

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Axiom 4. [Population Neutrality.] Polarization comparisons areunchanged if both populations are scaled up or down by the samepercentage.

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Axiom 4. [Population Neutrality.] Polarization comparisons areunchanged if both populations are scaled up or down by the samepercentage.

Theorem 1. A polarization measure satisfies Axioms 1–4 if andonly if it is proportional to∫ ∫

n(x)1+αn(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.

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Some Properties

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Some Properties

1. Not Inequality. See Axiom 2.

2. Bimodal. Polarization maximal for bimodal distributions,but defined of course over all distributions.

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3. Global. The local “merger” of two groups has effects thatdepend on the shape of the distribution elsewhere.

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Income

Den

sity

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Income

Den

sity

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Income

Den

sity

0-36


Income

Den

sity

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3. Nonlinear. Same direction of population or income move-ments may cause polarization to go down or up, depending oncontext.

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Income

Den

sity

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Income

Den

sity

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3. Nonlinear. Same direction of population or income move-ment may cause polarization to go down or up, depending on con-text.

Income

Den

sity

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More on α

Pol =∫ ∫



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More on α

Pol =∫ ∫



Axiom 5. If p > q but p− q is small and so is r, a small shift ofmass from r to q cannot reduce polarization.

r p q

0 a 2a2ε 2ε 2ε

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More on α

Pol =∫ ∫



Axiom 5. If p > q but p− q is small and so is r, a small shift ofmass from r to q cannot reduce polarization.

r p q

0 a 2a2ε 2ε 2ε

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Theorem 2. Under the additional Axiom 5, it must be thatα = 1, so the unique polarization measure that satisfies the fiveaxioms is proportional to∫ ∫

n(x)2n(y)|y− x|dydx.

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Theorem 2. Under the additional Axiom 5, it must be thatα = 1, so the unique polarization measure that satisfies the fiveaxioms is proportional to∫ ∫

n(x)2n(y)|y− x|dydx.

Easily applicable to ethnolinguistic or religious groupings.

Say m “social groups”, nj is population proportion in group j.

If all inter-group distances are binary, then

Pol =M∑j=1

M∑k=1

n2jnk =

M∑j=1

n2j (1− nj).

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Polarization and Conflict: Behavior

Axiomatics suggest (but cannot establish) a link between po-larization and conflict.

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Polarization and Conflict: Behavior

Axiomatics suggest (but cannot establish) a link between po-larization and conflict.

Two approaches:

Theoretical. Write down a “natural” theory which links conflictwith these measures.

Empirical.Take the measures to the data and see they are re-lated to conflict.

I discuss the theory first (based on Esteban and Ray (2009)).

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A Simple Model of Conflict

m groups; Ni in group i,∑mi=1Ni = N .

They fight over a “budget”; per capita value normalized to 1.

A fraction λ of this budget is available to produce society-widepublic goods. The winning group gets to choose the goods.

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A Simple Model of Conflict

m groups; Ni in group i,∑mi=1Ni = N .

They fight over a “budget”; per capita value normalized to 1.

A fraction λ of this budget is available to produce society-widepublic goods. The winning group gets to choose the goods.

uij = public goods payoff to a member of group i if a single unitper-capita of the optimal mix for group j is produced.

The remainder 1− λ is privately divided, again among the win-ning group.

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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) = rθ/θ, with θ ≥ 2.

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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) = rθ/θ, with θ ≥ 2.

Ri is total contributions by group i. Define

R =m∑i=1

Ri.

Probability of success given by

pj =Rj

R

ρ ≡ R/N is our measure of overall conflict.

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Payoffs

Per-capita payoff to group i is

λuii + (1− λ)(N/Ni) = λuii + (1− λ)/ni

(in case i wins the conflict), and

λuij

(in case some other group j wins).

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Payoffs

Per-capita payoff to group i is

λuii + (1− λ)(N/Ni) = λuii + (1− λ)/ni

(in case i wins the conflict), and

λuij

(in case some other group j wins).

So net expected payoff to an individual k in group i is

πi(k) =m∑j=1

pjλuij + pi(1− λ)ni

− c (ri(k)) .

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How do Individuals Make Contributions?

One extreme: individuals maximize own payoff.

Another extreme: there is full intra-group cohesion and individ-ual contributions maximize group payoffs.

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How do Individuals Make Contributions?

One extreme: individuals maximize own payoff.

Another extreme: there is full intra-group cohesion and individ-ual contributions maximize group payoffs.

Intermediate situations: define person k’s extended utility by

Ui(k) ≡ (1− α)πi(k) + α∑`∈i

πi(`),

where α lies between 0 and 1.

Interpretations for α: (i) intragroup concern or altruism (ii)group cohesion.

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Equilibrium

A collection {ri(k)} of individual contributions where for everygroup i and member k, ri(k) maximizes

(1− α)πi(k) + α∑`∈i

πi(`)

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Equilibrium


(1− α)πi(k) + α∑`∈i

πi(`)

which is the same as maximizing

[(1− α) + αNi]

pi 1− λni

+ λm∑j=1

pjuij

− c(ri(k)).given the contributions of everyone else.

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Equilibrium


(1− α)πi(k) + α∑`∈i

πi(`)

which is the same as maximizing

[(1− α) + αNi]

pi 1− λni

+ λm∑j=1

pjuij

− c(ri(k)).given the contributions of everyone else.

Theorem 3. An equilibrium always exists and it is unique.

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Approximation Theorem

For each i let γi ≡ pi/ni: “correction factors”.

0-60



Theorem 4. Neglect joint impact of the deviation of correc-tion factors from unity. Then the per-capita cost of conflict isapproximately ρ, given by

ρc′(ρ) = ω1 + ω2G+ α[λP + (1− λ)F ],

where

ω1 ≡ (1− λ)(1− α)(m− 1)/N

ω2 ≡ λ(1− α)/N .

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Theorem 4. Neglect joint impact of the deviation of correc-tion factors from unity. Then the per-capita cost of conflict isapproximately ρ, given by

ρc′(ρ) = ω1 + ω2G+ α[λP + (1− λ)F ],

where

ω1 ≡ (1− λ)(1− α)(m− 1)/N

ω2 ≡ λ(1− α)/N .

So for large N : only P and F matter if α > 0:

ρc′(ρ) ' α[λP + (1− λ)F ]

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Proof. Recall maximization problem

[(1− α) + αNi]

pi 1− λni

+ λ

m∑j=1

pjuij

− c(ri(k)).

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σi

pi 1− λni

+ λ

m∑j=1

pjuij

− c(ri(k))where σi ≡ (1− α) + αNi.

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σi

[λuii +

1− λni

]− σi

∑j 6=i

pj

(λδij +

1− λni

)− c(ri(k))

where σi ≡ (1− α) + αNi

where δij ≡ uii − uij.

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Proof. So maximize

σi

[λuii +

1− λni

]− σi

∑j 6=i

pj

(λδij +

1− λni

)− c(ri(k))


where δij ≡ uii − uij.

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Proof. So maximize

−σim∑j=1

pj∆ij − c(ri(k))


where δij ≡ uii − uij

where ∆ii ≡ 0, and ∆ij ≡ λδij + (1− λ)/ni for all j 6= i.

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Proof. So maximize

−σim∑j=1





First-order condition:

σi

R

m∑j=1

pj∆ij = c′(ri(k))

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Proof. So maximize

−σim∑j=1





First-order condition (ri(k) = ri for all k ∈ i):

σi

R

m∑j=1

pj∆ij = c′(ri)

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Proof. So maximize

−σim∑j=1





First-order condition (multiply both sides by ρpi):

ρ

R

m∑j=1

pipjσi∆ij = ρpic′(ri)

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Proof. So maximize

−σim∑j=1





First-order condition using ρ = R/N :

1

N

m∑j=1

pipjσi∆ij = ρpic′(ri)

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Proof. So maximize

−σim∑j=1





First-order condition using ρ = R/N :

1

N

m∑j=1

γiγjninjσi∆ij = ρpic′(γiρ)

recalling that γi = pi/ni.

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From previous slide:

1

N

m∑j=1


0-73


1

N

m∑j=1


Multiply both sides by c′(ρ)/c′(γiρ), sum over all i:

m∑i=1

m∑j=1

φ(γi, γj , ρ)ninjσi∆ijN

= ρm∑i=1

pic′(ρ) = ρc′(ρ),

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1

N

m∑j=1



m∑i=1

m∑j=1


= ρm∑i=1


where

φ(γi, γj , ρ) ≡c′(ρ)γiγjc′(γiρ)

.

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1

N

m∑j=1



m∑i=1

m∑j=1


= ρm∑i=1


where


.

Ignore the φ term (which is 1 when all γ equal 1):

ρc′(ρ) 'm∑i=1

m∑j=1

ninjσi∆ijN

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1

N

m∑j=1



m∑i=1

m∑j=1


= ρ

m∑i=1


where


.

Ignore the φ term (which is 1 when all γ equal 1), open up:

ρc′(ρ) 'm∑i=1

∑j 6=i

ninj[(1− α) + αNi][λδij + (1− λ)/ni]

N.

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How Good is the Approximation?

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Holds exactly when there are just two groups and all goods arepublic.

Holds exactly when all groups the same size and public goodslosses are symmetric.

Holds almost exactly for contests when conflict is high enough.

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Holds exactly when there are just two groups and all goods arepublic.

Holds exactly when all groups the same size and public goodslosses are symmetric.

Holds almost exactly for contests when conflict is high enough.

Can numerically simulate to see how good the approximationis.

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Contests, quadratic costs, large populations, λ various:

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Distances, quadratic costs, large populations, λ various:

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Small populations, λ various:

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Nonquadratic costs, large populations, λ various:

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Empirical Investigation

Based on Montalvo and Reynal-Querol, AER (2005).

Pol =M∑j=1

n2j (1− nj).

Compare with fragmentation:

Frag =M∑j=1

nj(1− nj).

The two measures are very different, even empirically:

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ethnic polarization index

Eth

nic

fra

ctio

nal

izat

ion

ind

ex

Figure 8: Ethnic fractionalization versus polarization. Source: WCE.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1 1.2

Religious polarization index

Rel

igio

us

frac

tio

nal

izat

ion

ind

ex

Figure 9: Religious fractionalization versus polarization. Source: ET.

22

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Guatemala, Sierra Leone: ethnic polarization high but ethnicfractionalization low

(Guatemala: 55% Mestizo or Ladino, 42% Maya, 3% other)

Nigeria, Bosnia: religious polarization high but religious frac-tionalization low

( 49–45 split on Christians and Muslims in Nigeria, 50–40 in Bosnia)

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New regression as in Fearon-Laitin (2003) and Collier-Hoeffler(2004) but with polarization included.

138 countries, 1960–1999.

Dependent variable: incidence of a civil war over a five yearperiod.

PRIO dataset for civil wars, 25 yearly deaths criterion (and 1000overall).

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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

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First run a logit of war on ethnic fractionalization

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[1] [2] [3] [4]

EthFrac 0.81 0.22 -0.18 0.49(2.04) (0.53) (0.16) (0.97)

LogPcGdp -0.62 -0.76 -0.79 -0.93(5.07) (5.90) (5.96) (5.40)

Constant 2.47 -0.42 -0.18 1.57(2.47) (0.38) (0.16) (0.94)

LogPop 0.46 0.46 0.35(6.75) (6.03) (3.69)

PrimExp 0.25 0.50(0.26) (0.48)

Mountains 0.00(1.67)

NonContiguous -0.20(0.61)

Democracy 0.49(1.87)

Pseu R2 0.07 0.15 0.15 0.14Obs 860 860 840 741

0-91

[1] [2] [3] [4]

EthPol 1.56 1.95 1.98 1.82(3.31) (3.76) (3.71) (3.23)

LogPcGdp -0.71 -0.77 -0.78 -0.93(6.16) (6.53) (6.57) (5.50)

Constant 2.65 -1.56 -1.43 -0.93(3.01) (1.47) (1.27) (0.16)

LogPop 0.49 0.48 0.38(7.15) (6.46) (4.33)

PrimExp -0.09 0.17(0.09) (0.16)


NonContiguous -0.00(0.00)


Pseu R2 0.09 0.17 0.17 0.16Obs 860 860 840 741

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Ethnic polarization not just significant; the effect is pretty bigtoo.

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 conflictprobability by 50%.]

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Try the same logit with religious variables instead

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[1] [2] [3] [4]

RelFrac 1.41 0.53 0.35 0.92(2.31) (0.76) (0.49) (1.17)

LogPcGdp -0.61 -0.84 -0.87 -1.03(4.91) (5.75) (5.85) (5.27)

Constant 1.53 -1.24 -1.15 0.45(1.42) (0.97) (0.86) (0.25)

LogPop 0.50 0.51 0.41(6.41) (5.88) (4.09)

PrimExp 0.63 1.15(0.61) (1.04)


NonContiguous 0.10(0.31)


Pseu R2 0.10 0.16 0.16 0.16Obs 853 853 833 734

0-95

[1] [2] [3] [4]

RelPol 1.09 0.71 0.65 1.06(2.93) (1.71) (1.50) (2.20)

LogPcGdp -0.57 -0.76 -0.78 -0.98(4.46) (5.22) (5.26) (5.08)

Constant 1.17 -1.93 -1.85 0.17(1.10) (1.52) (1.40) (0.10)

LogPop 0.49 0.50 0.39(6.36) (5.75) (3.94)

PrimExp 0.41 0.93(0.39) (0.84)




Pseu R2 0.10 0.17 0.17 0.17Obs 853 853 833 734

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Robustness to Different Specifications

Ethnic polarization significant when in same regression withethnic fractionalization; latter is not.

Same true if a measure of ethnic dominance (Collier 2001 andCollier 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.

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Robustness: Datasets and Classifications

World Christian Encyclopedia (used here), Encyclopedia Bri-tannica, Atlas Nadorov Mira, alternative classifications in Alesinaet 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 1960–1995 with base variables from 1960.

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Intergroup Distances

Esteban, Mayoral and Ray (2010) [EMR] compute inter-groupdistances by using responses from the World Values Survey.

Polarization measures derived from these — both ethnic andreligious — are highly correlated with conflict.

But endogeneity a major concern.

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Intergroup Distances

Esteban, Mayoral and Ray (2010) [EMR] compute inter-groupdistances by using responses from the World Values Survey.

Polarization measures derived from these — both ethnic andreligious — 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 con-flict directly but only via its correlation with people’s tolerance orintolerance of other groups.

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Follow Fearon (2003) and Desmet et al. (2009, 2010): distancebetween languages i and j is

d′ij = 1−(l

m

)δ,

where l is the number of common branches between i and j, mis the maximum number of shared branches between any two lan-guages, and δ is a decay parameter.

Pop-weighted average over all languages is the instrument:

WAD =K∑i=1

K∑j=1

sisjd′ij ,

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Follow Fearon (2003) and Desmet et al. (2009, 2010): distancebetween languages i and j is

d′ij = 1−(l

m

)δ,

where l is the number of common branches between i and j, mis the maximum number of shared branches between any two lan-guages, and δ is a decay parameter.

Pop-weighted average over all languages is the instrument:

WAD =K∑i=1

K∑j=1

sisjd′ij ,

Use additional definition of conflict, as opposed to civil war:

W. av. of 8 different domestic conflicts: assassinations, gen-eral strikes, guerrilla war, government crises, purges, riots, rev-olutions, anti-govt demonstrations. (Cross-National Time-SeriesData Archive.)

0-102

War Incidence Social Unrest[1] [2] [3] [4] [5] [6]

EthPolER 1.24(0.01)

1.19(0.01)

3.66(0.00)

3.61(0.00)

1.75(0.03)

1.81(0.02)

EthPolRQ −0.22(0.33)

- −0.43(0.51)

- 0.27(0.54)

-

LogPcGdp −0.10(0.03)

−0.10(0.04)

−0.27(0.11)

−0.26(0.12)

−0.51(0.00)

−0.52(0.00)

LogPop 0.00(0.98)

0.01(0.81)

−0.00(0.98)

0.01(0.91)

0.12(0.13)

0.11(0.15)

PrimExp −0.29(0.20)

−0.30(0.22)

−1.34(0.18)

−1.36(0.17)

−1.20(0.10)

−1.19(0.11)


0.00(0.14)

0.01(0.09)

0.012(0.10)

0.01(0.38)

0.01(0.21)


0.14(0.29)

0.52(0.18)

0.57(0.13)

0.82(0.01)

0.78(0.01)


0.01(0.89)

−0.07(0.78)

−0.08(0.76)

0.13(0.49)

0.14(0.47)

Pseu R2 - - - - 0.25 0.25Obs 385 385 385 385 344 344

0-103

Why Ethnicity?

0-104

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:

0-105

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”.

0-106

1. Incomplete Information.

Myerson-Satterthwaite (1983), Fearon (1995), Esteban and Ray (2001),

Bester and Warneryd (2006), Sanchez-Pages (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.

0-107

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.

0-108

Two-Group Version



Two groups. Either group can initiate conflict.

Group i is of size ni and contributes resources ri per capita.

Win probability pi = niri/R.

Cost function c(r) = (1/θ)rθ for θ ≥ 2.

0-109

Two-Group Version



Two groups. Either group can initiate conflict.

Group i is of size ni and contributes resources ri per capita.

Win probability pi = niri/R.

Cost function c(r) = (1/θ)rθ for θ ≥ 2.

Assume cohesion α > 0 from previous exercise.

0-110

Under conflict, group i chooses ri to maximize

niri

RP (ni)− (rθi /θ).

where P (n) = [λG+ (1− λ)(G/n)] is per-capita prize to group.

First-order condition is

P (ni)[ni

R−n2i ri

R2

]= rθ−1

i ,

0-111


niri




P (ni)[ni

R−n2i ri

R2

]= rθ−1

i ,

P (ni)ni

R

[1−

niri

R

]= rθ−1

i ,

0-112


niri




P (ni)[ni

R−n2i ri

R2

]= rθ−1

i ,

P (ni)ni

R

[1−

niri

R

]= rθ−1

i ,

P (ni)ninj = R2 rθ−1i

rj.

0-113


rj.

0-114


rj.

If θ = 2, we see right away that

R4 = P (ni)n2iP (nj)n2

j

= [λG+ (1− λ)(G/n1)] [λG+ (1− λ)(G/n2)]n2in

2j ,

This is inverted-U in population division.

0-115


rj.

If θ = 2, we see right away that

R4 = P (ni)n2iP (nj)n2

j

= [λG+ (1− λ)(G/n1)] [λG+ (1− λ)(G/n2)]n2in

2j ,

This is inverted-U in population division.

For general θ result is still true, but more complex:

Rθ = [P (ni)niP (nj)nj ]1/θ (ninj)(θ−1)/θ

{P (nj)1/θnj + P (ni)1/θni

}θ−2.

also inverted-U.

Polarization affects conflict intensity (no approx. needed), con-ditional on it happening in the first place.

0-116

Initiation

But conflict may not happen to begin with — too costly.

0-117

Initiation


Let peacetime share of group i be si. Then i initiates if

P (ni)niri

R− (rθi /θ) > siP (ni),

where ri and R are “subgame” values.

0-118

Initiation



P (ni)niri



Recall first-order condition P (ni)niR

[1− niri

R

]= rθ−1

i .

0-119

Initiation



P (ni)niri



Recall first-order condition P (ni)pipj = rθi .

0-120

Initiation



P (ni)niri




pi −1

θpi(1− pi) > si.

0-121

Initiation



P (ni)niri




pi −1

θpi(1− pi) > si.

kpi + (1− k)p2i > si

where k ≡ (θ− 1)/θ.

0-122

The Case of Public Goods

Assume that λ = 1. Then P (n) = G, and FOC is

Gninj = R2 rθ−1i

rj

Proves right away that ri = rj for public goods, so pi = ni.

0-123



Gninj = R2 rθ−1i

rj


Recall condition for conflict initiation:

kpi + (1− k)p2i > si

0-124



Gninj = R2 rθ−1i

rj


Condition for conflict initiation:

kni + (1− k)n2i > si.

0-125

Public Goods, Summary

0-126


Observation 1.

Public resources; payoffs equally divided under peace.

Then there is m∗ ∈ ( 12, 1) so that group with size m > m∗ wants

conflict.

0-127


Observation 1.

Public resources; payoffs equally divided under peace.

Then there is m∗ ∈ ( 12, 1) so that group with size m > m∗ wants

conflict.

For public goods, si = 1/2 for equal treatment.

Conflict initiation:

kni + (1− k)n2i > 1/2.

Threshold for intersection is m∗ > 1/2.

Note that ni ≤ 1/2 never works and ni >√

1/2 is sufficient.

0-128

The Case of Private Goods

Recall first order condition:


rj.

0-129


Recall first order condition; remember P (ni) = G/ni:

G

nininj = R2 r

θ−1i

rj.

0-130



Gnj = R2 rθ−1i

rj.

0-131



Gnj = R2 rθ−1i

rj.

Divide by first-order condition for group j:

ri

rj=(nj

ni

)1/θ

=(nj

ni

)1−k,

Olson intuition: small groups lobby more per-capita.

So probability that i wins the conflict is given by

pi ≡niri

niri + njrj=

nkinki + nkj

0-132

Write this out as function of initiating group size ni = m:

p(m) =mk

mk + (1−m)k.

Condition for initiation:

kp(m) + (1− k)p(m)2 > s(m)

where s(m) is share function under peace.

0-133


p(m) =mk

mk + (1−m)k.


kp(m) + (1− k)p(m)2 > s(m)


Observation 2.

Privately divisible resources; payoffs equally divided under peace.

Then there is m∗ ∈ (0, 12) so that marker m < m∗ wants conflict.

0-134


p(m) =mk

mk + (1−m)k.


kp(m) + (1− k)p(m)2 > s(m)


Observation 2.

Privately divisible resources; payoffs equally divided under peace.

Then there is m∗ ∈ (0, 12) so that marker m < m∗ wants conflict.

Outline of Argument. Under symmetry, we have s(m) = m.

0-135

Need kp(m) + (1− k)p(m)2 > m.

p, p2

m1/2 1

1/2

1

0

0-136

Need kp(m) + (1− k)p(m)2 > m.

p, p2

m1/2 1

1/2

1

0

0-137

Need kp(m) + (1− k)p(m)2 > m.

p, p2

m1/2 1

1/2

1

0

0-138

Need kp(m) + (1− k)p(m)2 > m.

p, p2

m1/2 1

1/2

1

0

m

m*

0-139

Coase Revisited

Public goods, large groups initiate. Private goods, small groupsinitiate.

Coase: with transfers, there is some allocation that will appeasethe initiator

(conflict is inefficient, after all).

But what if there is a potential multiplicity of initiators?

0-140

Coase Revisited

Public goods, large groups initiate. Private goods, small groupsinitiate.

Coase: with transfers, there is some allocation that will appeasethe 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 comple-ment — but that a variety of initiators can formed based on “mark-ers”

class, caste, religion, geography, occupation . . .

0-141

A finite collection C of markers is balanced if there are weightsλ(M) in [0, 1], one for each marker, such that

∑M∈C,i∈M

λ(M) = 1 for every i in society

0-142


∑M∈C,i∈M


For instance, any partition is balanced.

More generally, rules out common intersection.

0-143


∑M∈C,i∈M


For instance, any partition is balanced.

More generally, rules out common intersection.

Theorem 5.

Suppose there exists a balanced collection of markers, each withm < m∗.

Then there is no peaceful allocation for society that is immuneto conflict.

0-144

Proof. Suppose there is indeed a peaceful allocation x.

0-145


For every marker M ∈ C, we have

∫i∈M

x(i) ≥ G[kp(m) + (1− k)p(m)2]

by immunity to conflict.

0-146



∫i∈M

x(i) ≥ G[kp(m) + (1− k)p(m)2]


Moreover, for each such marker,

G[kp(m) + (1− k)p(m)2] > Gm

because m < m∗ for every marker in collection C.

0-147



∫i∈M

x(i) ≥ G[kp(m) + (1− k)p(m)2]



G[kp(m) + (1− k)p(m)2] > Gm


Combine:

∫i∈M

x(i) > Gm

0-148



∫i∈M

x(i) ≥ G[kp(m) + (1− k)p(m)2]



G[kp(m) + (1− k)p(m)2] > Gm


Combine, and multiply by balancing weight:

λ(M)∫i∈M

x(i) > Gmλ(M)

0-149



∫i∈M

x(i) ≥ G[kp(m) + (1− k)p(m)2]



G[kp(m) + (1− k)p(m)2] > Gm


Combine, multiply, add over all markers:

∑M∈C,i∈M

λ(M)∫i∈M

x(i) >∑

M∈C,i∈MGmλ(M)

0-150



∫i∈M

x(i) ≥ G[kp(m) + (1− k)p(m)2]



G[kp(m) + (1− k)p(m)2] > Gm


Combine, multiply, add over all markers, simplify:

∫i∈N

x(i) > G.

0-151

Does the Same Argument Work for Public Goods?

If the complement of a marker is also a marker, there alwaysexists 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 inreligion, language, or group recognition.

0-152

Why Ethnicity? (Revisited)

0-153


Historical Institutions. Institutions set up ameliorate class con-flict can raise demands along other lines.

0-154



Redistribution versus Exclusion.

Horowitz again:

“[T]he relations of many . . . ethnic groups — on a global scale,most ethnic groups — are not accurately defined as superior-subordinate relations . . . It is not so much the politics of subor-dination that concerns them, but rather the politics of inclusionand exclusion.”

0-155



Redistribution versus Exclusion.

Horowitz again:

“[T]he relations of many . . . ethnic groups — on a global scale,most ethnic groups — are not accurately defined as superior-subordinate relations . . . It is not so much the politics of subor-dination that concerns them, but rather the politics of inclusionand exclusion.”

The Perverse Synergy of Within-Group Inequality.

(And some comments on the identity-alienation framework.)

0-156

A Tentative Model of Salience

0-157


Class.

0-158


Class.

"Rich"

"Poor"

0-159


Class.

"Rich"

"Poor"

population share nr

per-capita income yr

per-capita income yp

population share np

0-160


Class.

"Rich"

"Poor"

yr > yp

np > nr

0-161


Ethnicity.

0-162


Ethnicity.

H M

0-163


Ethnicity.

H M

Population Sharenh

Population Sharenm

0-164


Ethnicity.

H M

Population Sharenh

Population Sharenm

nh > nm

0-165

Unranked Ethnic Groups

0-166


R

P

0-167


H M

R

P

0-168


H M

R

P

0-169


H M

R

P

0-170

Class Goods and Ethnic Goods

Society produces public goods.

Some have a class character, some an ethnic character (someboth).

Potential conflict over seizing and controlling these goods.

0-171

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

0-172

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

0-173

Alliances

Consider conflicts from only two possible types of “alliances”.

0-174

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, butmaintaining distinction between H and M .

The battle, then, is over the capture of the ethnic budget.

0-175

Elements of a Strategic Approach

Stage 1. Salience. Alliances form (or not).

Stage 2. Hostility. Adoption of hostile or peaceful stances byone alliance or the other. If either side is hostile, move to Stage3. 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.

0-176

Stage 3: Peace and Conflict Payoffs

0-177

Stage 3: Peace and Conflict Payoffs

Peace Payoffs:

Ethnic Budget E

sh sm

Class Budget C

sr

sp

0-178

Individual in group ij with i a class index and j an ethnic indexgets

u(yi) + siC + sjE.

Public goods: si unaffected by population.

0-179


u(yi) + siC + sjE.


Conflict Payoffs:

0-180


u(yi) + siC + sjE.


Conflict Payoffs:

Each alliance i contributes activists (militants, thugs . . . ) Ai.

Compensation rate for activists, wi in alliance i.

(wi generally connected to alliance incomes.)

Total expenditure for alliance i: wiAi.

0-181

Conflict Payoffs

In class alliance, C-share proportional to activists; E-share un-touched.

0-182

Conflict Payoffs

In class alliance, C-share proportional to activists; E-share un-touched.

Ethnic Budget E

sh sm

Class Budget C

Ar / Ar + Ap

Ap / Ar + Ap

0-183

Conflict Payoffs

In ethnic alliance, E-share proportional to activists; C-shareuntouched.

0-184

Conflict Payoffs

In ethnic alliance, E-share proportional to activists; C-shareuntouched.

Ethnic Budget E Class Budget C

sr

sp

Ah + Am

Ah Am

Ah + Am

0-185

Summary of Conflict Payoffs

CC payoffs to person of ethnicity j in class alliance i:

u (Income−Contributions) +Ai

Ap +ArC + sjE.

0-186




Ap +ArC + sjE.

CC payoffs to person of class i in class alliance j:

u (Income−Contributions) +Aj

Ah +AmE + siC.

0-187




Ap +ArC + sjE.

CC payoffs to person of class i in class alliance j:

u (Income−Contributions) +Aj

Ah +AmE + siC.

In each case, contributions add up to Aw.

Other costs include destruction of E and C: easy enough toincorporate.

0-188

A Symmetry Benchmark

0-189

A Symmetry Benchmark

Both goods equally important: C ' E

Peacetime shares the same: sh = sp = sh = sm = 1/2.

In each type of conflict, compensation rates the same across al-liances: wh = wm and wp = wr.

0-190

Conflict Versus Peace for a Given Alliance

0-191


Let λij = share of finance contributed by economic group i inalliance j:

(In a class alliance this ratio is always 1.)

0-192




Let σj = share of activists coming from alliance j:

0-193




Let σj = share of activists coming from alliance j:

For economic group i in alliance j to want conflict, sufficientand generally necessary that

λijσ2j + (1− λij)σj > sj .

For noncontributors σj > sj, for sole contributors, σj >√sj.

Activist share endogenous; can be linked to demography andeconomics.

0-194

Ethnic Conflict Versus Peace

0-195


Proposition. Activist shares = population shares: σj = nj.

Recall condition for economic group i to want conflict in alliancej:

λijσ2j + (1− λij)σj > sj .

0-196


Proposition. Activist shares = population shares: σj = nj.

Recall condition for economic group i to want conflict in alliancej:

λijn2j + (1− λij)nj > sj .

Clearly sufficient for conflict that nj >√sj.

Under symmetry: critical population share is approx 70%

Weaker when both contribute equally: [n2j + nj ]/2 > sj.

Critical population share is approx 62%.

0-197

Class Conflict Versus Peace

0-198


No differential contributions now within alliance, so conditionis easier: σi >

√si.

0-199



√si.

Can show that

σi =Ai

Ap +Ar=

α−iniαrnp + αpnr

where αi is approx. u′(yi)wi.

0-200



√si.

Can show that

σi =Ai

Ap +Ar=

α−iniαrnp + αpnr

where αi is approx. u′(yi)wi.

u′(y) ' cost of financial contributions; w cost of compensatingmilitants.

If mercenaries available (wr = wp), np > σp.

Harder for them to initiate class conflict, though not ruled out.

0-201

At the same time, rich unlikely to initiate class conflict.

Too little to gain.

0-202

At the same time, rich unlikely to initiate class conflict.

Too little to gain.

Mercenary army: wp = wr

u logarithmic

Then initiation condition for rich reduces to

nryr

nryr + npyp>√sr,

That is, income share of the rich >√

share of public good.

World Bank (2003): Indian per-capita income $2,500 PPP. Useto cut: np ' 70%, income share around 35%.

0-203

Salience I

0-204

Salience I

Proposition. [Ethnic salience for a majority group]

Assume low local curvature of u: u′ approx. constant acrossany person’s income and his income net of contributions.

Then an ethnic majority group i (i = poor or rich) obtainshigher payoffs from ethnic relative to class conflict if and only if(

[1− λih]nh + λihn2h − sh

)µ > σ2

i − si.

where µ = E/C.

0-205

Salience I

Proposition. [Ethnic salience for a majority group]

Assume low local curvature of u: u′ approx. constant acrossany person’s income and his income net of contributions.

Then an ethnic majority group i (i = poor or rich) obtainshigher payoffs from ethnic relative to class conflict if and only if(

[1− λih]nh + λihn2h − sh

)µ > σ2

i − si.

where µ = E/C.

Ethnic Conflict:([1− λih]nh + λihn

2h − sh

)> 0.

Class Conflict: σ2i − si > 0.

“Compare” these terms, weighted by µ.

0-206

Two Implications

0-207

Two Implications

Implication 1. Poor ethnic majority prefer ethnic to class con-flict.

0-208

Two Implications


([1− λph]nh + λphn

2h − sh

)µ > σ2

p − sp.

0-209

Two Implications



2h − sh

)µ > σ2

p − sp.

Assume symmetry. Then suffices to check

[1− λph]nh + λphn2h > n2

p.

0-210

Two Implications



2h − sh

)µ > σ2

p − sp.

Assume symmetry. Then suffices to check

[1− λph]nh + λphn2h > n2

p.

If nh (India: 85%) ≥ np (India: 70%), then done.

Poor don’t make the financial contributions, so condition eveneasier: approx. nh > n2

p.

0-211

Now drop symmetry of ethnic versus class goods. Sufficientcondition:

0-212


µ >n2p − (0.5)

(1− λph)nh + λphn2h − (0.5)

0-213


µ >n2p − (0.5)

(1− λph)nh + λphn2h − (0.5)

If nh = np = 80% and λph = 1/2:

Ethnic conflict preferred if E is 65% of C.

0-214


µ >n2p − (0.5)

(1− λph)nh + λphn2h − (0.5)

If nh = np = 80% and λph = 1/2:


If rich contribute all finance, threshold drops to 47%.

0-215


µ >n2p − (0.5)

(1− λph)nh + λphn2h − (0.5)

If nh = np = 80% and λph = 1/2:


If rich contribute all finance, threshold drops to 47%.

If np drops to 70%, threshold drops to zero.

0-216

Or drop equal access to class and ethnic goods, but retain otheraspects of symmetry.

0-217


sp > sh + [n2p − n2

h]− (1− λph)(nh − n2h).

0-218


sp > sh + [n2p − n2

h]− (1− λph)(nh − n2h).

nh = 80-85%, np = 70%.

0-219


sp > sh + [n2p − n2

h]− (1− λph)(nh − n2h).

nh = 80-85%, np = 70%.

sh = 1/2 and poor finance half: ethnic conflict preferred even ifclass good share as low as 20-25%.

0-220


sp > sh + [n2p − n2

h]− (1− λph)(nh − n2h).

nh = 80-85%, np = 70%.

sh = 1/2 and poor finance half: ethnic conflict preferred even ifclass good share as low as 20-25%.

If poor don’t finance ethnic conflict, threshold drops to 15-20%.

0-221

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

0-222


([1− λrh]nh + λrhn

2h − sh

)µ > σ2

r − sr.

0-223



2h − sh

)µ > σ2

r − sr.

Suppose that poor majority prefer class conflict to peace.

Then σp ≥ sp, so σr ≤ sr. So sufficient to check([1− λrh]nh + λrhn

2h − sh

)µ > −sr(1− sr).

If LHS nonnegative, condition automatically satisfied.

0-224



2h − sh

)µ > σ2

r − sr.



2h − sh

)µ > −sr(1− sr).


If LHS negative, condition reduces to

µ <sr(1− sr)

sh − [1− λrh]nh − λrhn2h

0-225



2h − sh

)µ > σ2

r − sr.



2h − sh

)µ > −sr(1− sr).


If LHS negative, condition reduces to

µ <sr(1− sr)

sh − [1− λrh]nh − λrhn2h

Met whenever nh exceeds sh and sr, and µ ≤ 1.

0-226

Salience II: Alliance Formation

Based on Bloch (1996), Ray-Vohra (1997, 1999).

0-227



Rich-H, Rich-M, Poor-H and Poor-M.

0-228




At each stage a group is “given the floor”, according to someprotocol.

0-229





Every group has uniformly positive probability of seizing thefloor.

0-230






Group can either make a proposal or pass, at which point flooris “re-seized”.

0-231






Group can either make a proposal or pass, at which point flooris “re-seized”.

If all groups relinquish the opportunity to make a proposal, thegame is over and peace payoffs are received.

0-232

Otherwise some group makes a proposal.

0-233


Proposal made to a “compatriot group” (same ethnicity orsame class) to form an alliance.

0-234



If the compatriot group agrees, the game is over. The corre-sponding alliance forms, and society enters into conflict. Receiveconflict payoffs.

0-235




If the proposal is rejected, a fresh probability distribution deter-mines a new proposer (previous rejector must get role with positiveprobability).

0-236





Endless rejections ≡ no proposals ≡ peace payoffs.

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Endless rejections ≡ no proposals ≡ peace payoffs.

Arbitrary history-dependence, but assume some discounting.

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Proposition. Assume strict preferences, and the implicationsso far:

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The poor majority prefer ethnic conflict to class conflict.

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The rich majority prefer ethnic conflict to class conflict when-ever the poor majority prefer class conflict to peace.

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The rich prefer peace to class conflict.

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The rich prefer peace to class conflict.

Then it is possible to have ethnic conflict or peace, but neverclass conflict, as the equilibrium outcome.

Proof. See Esteban and Ray (2008).

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Summary

Why might conflict be ethnicized?

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Summary


Simple model of ethnic salience to address this question.

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Summary



The model permits both peace, as well alliance-formation.

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Summary




The poor and rich members of the dominant ethnic group aredecisive in precipitating conflict or peace, but in different ways.

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Summary





The poor ethnic majority are unilaterally decisive for class con-flict (but need the lead of the rich for ethnic alliances).

The rich ethnic majority are often only too relieved to providethat lead.

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Summary





The poor ethnic majority are unilaterally decisive for class con-flict (but need the lead of the rich for ethnic alliances).

The rich ethnic majority are often only too relieved to providethat lead.

Economic inequality is synergistic: the rich provide resources,the poor provide conflict labour. Thus ethnic conflict may besalient precisely in the presence of economic inequality.

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Documents

· 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 …