Big question in this lecture

  Stockholm Doctoral Course Program in Economics Development Economics II: Lecture 4

  Civil Conflicts Masayuki Kudamatsu

  IIES, Stockholm University

20 November, 2013

  Big question in this lecture

• Why do civil conflicts occur?
• 56% of countries experienced civil conflicts (25+ deaths per annum)
• 20% of countries had 10+ years of

  civil conflicts

• Source: Armed Conflict Database

  1960-2006 (Fig. 1 in Blattman and Miguel 2010)

• Conflicts: detrimental to welfare
• Convincing evidence hard to come by,

  though ⇐

  Pre-conflict micro data hardly available Why do civil conflicts occur? (cont.)

  Literature (mainly) proposes the following three reasons: Economic factors (sec.1)

• Asymmetric information (sec.2)
• Commitment problem (sec.3)
• Also ethnic diversity is often emphasized as a source of conflict

1. Economic factors

  Poverty often cited as a cause of

• civil wars Is this true theoretically
• Use a contest model to illustrate
• Is this true empirically?
• Search for exogeneous variation
• ⇐ Conflict may cause poverty

1.1 Model

• Collective action problem: ignored

  Players: groups A & B

• Endowment: 1 unit of labor for both
• A & B Actions: both groups
• simultaneously allocate labor between production and fighting

1.1 Model (cont.)

  Technologies Production: group i produces

• w (1 − l )

  i i _i l : labor allocated to fighting

• w : labor productivity for group i _i

  Fighting: probability of group A

• winning given by l

  A

• l l A B

1.1 Model (cont.)

• Resources unaffected by labor •

  allocation (e.g. natural resource

  export revenue, foreign aid, etc.)
• Main results: robust to including labor

  Victory payoff: V

  output in victory payoff (see Garfinkel & Skaperdas 2006)

• A B

  If no fighting (l = l = 0), V is

  shared by the two groups according to some exogenous formula

  e.g. A gets sV and B gets (1 − s)V The contest model has been used in other contexts: Rent-seeking (Tullock 1980)

• Endogenous property rights
• (Skaperdas 1992)

1.2 Analysis

  = l = 0) cannot be an Peace (l A B equilibrium

  

⇐ If l = 0, l = ε > 0 makes group i

j i win for sure.

1.2 Analysis (cont.)

• Group A solves max

  l _A

  l A l

• l

  A

  B

  V + (1 − l A )w A

• Group B solves max

  l _B

  l

  B

  l A + l B V + (1 − l B )w B

1.2 Analysis (cont.)

• A

  FOC for l :

  l

  B

  V = w A

  2

  (l + l )

  A B

• B

  FOC for l :

  l

  A

  V = w B

  2 _{∂ � � l} (l A + l B ) _{1 l}

1.2 Analysis (cont.)

  V ₂ Deleting yields

• (l +l ) _{A B}

  l w

  

A B

  = l w

  

B A

  Less productive group spends more

• time in fighting

  ⇐ Lower opportunity cost of labor

1.2 Analysis (cont.)

  w

  B ∗

  l =

  V A

  2

  (w A + w B ) w

  A ∗

  l =

  V B

  2

  (w A + w B )

  V ∗ ∗

  Conflict level (l + l = ) ↑ if

  A B (w +w ) _{A B}

  V ↑ (resource curse)

• (w + w ) ↓ (poverty as a cause of
• A B

1.3 Evidence

  Tons of cross-country regressions using GDP per capita as a proxy for

• poverty natural resource export as a proxy
• for V Endogeneity is a major concern

  Conflict reduces GDP and resource

Miguel et al. (2004)

• Rainfall as instruments for GDP per capita in African countries
• GDP in Africa depends on rain-fed agriculture
• Find GDP ↓ ⇒ civil conflicts ↑
• But the mechanism is not clear

  e.g. GDP ↓ ⇒ Govt forces weaker

• Also it’s LATE
• Income ↓ due to other reasons may

Also the resource curse channel is

  not tested Recently 3 papers tackle both

• channels

i. Besley & Persson (2009): use export

  commodity price as resource effect &

import price as poverty effect

ii. Besley & Persson (2011): use UN

  Security Council membership as resource effect & natural disaster as poverty effect

(will be discussed in Political Recently 3 papers tackle both

• channels

iii. Dube & Vargas (2013): look at

  subnational-level evidence from Colombia

1.4 Dube & Vargas (2013)

• Use 978 municipality panel data on conflict incidents from Colombia (1988-2005)

  (based on newspapers & reports by Catholic priests)

• where civil wars ongoing since 1960s
• 3-way conflict (govt, guerilla, &

  paramilitary), but govt & paramilitary collude

• Columbia exports oil & coffee
• Oil price: proxy for V

y = λ(OP ∗ Oil ) + ρ(CP ∗ Cof ) jrt t j t j

  �

  ρ + α + β

  

j t

• x jt
• δ t + γ(Coca ∗ t) + ε

  r j jrt

• jrt : # of guerilla attacks,

  y

  paramilitary attacks, clashes, or y jrt = λ( OP t ∗ Oil j ) + ρ(CP t ∗ Cof j )

  �

  ρ + α j + β t

• x jt
• δ + γ(Coca ∗ t) + ε

  r t j jrt

• t

  OP : int’l price of oil in year t

• j

  Oil : oil production level in y jrt = λ(OP t ∗ Oil j ) + ρ( CP t ∗ Cof j )

  �

  ρ + α j + β t

• x jt
• δ + γ(Coca ∗ t) + ε

  r t j jrt

• t

  CP : domestic coffee price in year t

• j

  Cof : hectares of land devoted to

  = λ(OP ∗ Oil ) + ρ(CP ∗ Cof ) y jrt t j t j

  �

  ρ + α β + +

  

j t

x jt

• δ t + γ(Coca ∗ t) + ε

  r j jrt

• jt

  : vector of controls, incl. log

  x

  population y jrt = λ(OP t ∗ Oil j ) + ρ(CP t ∗ Cof j )

  �

  ρ + α j + β t

• x jt

  δ + + γ( ∗ t ) + ε r t Coca j jrt

• r

  δ t: region-specific linear trends

• j

  Coca ∗ t: linear trends for

1.4 Dube & Vargas (2013) (cont.)

  λ ∗ Oil ρ ∗ Cof

  y jrt = (OP t j ) + (CP t j )

  �

  ρ + α + β

  j t

• x

  jt

• δ t + γ(Coca ∗ t) + ε

  r j jrt

  Theoretical predictions λ > 0: resource curse effect

jrt

  ∗ t) + ε

  � jt

  j

  t + γ(Coca

  r

  t

  j

  ρ + α

  )

  y jrt = λ (OP

  j

  ∗ Cof

  t

  ) + ρ (CP

  j

  ∗ Oil

  t

• β
• x
• δ
• Now OLS estimation of this equation would lead to bias in

1.4 Dube & Vargas (2013) (cont.)

• t

  No need to instrument OP

  Int’l price is used • Columbia produces <1% of world oil

• production
• j

  No need to instrument Oil

  

measured at the 1st year of the

• sample

  ⇒ No endogenous change in response to conflict

1.4 Dube & Vargas (2013) (cont.)

  Instrument for CP t Int’l coffee price: not suitable

• Columbia is a major coffee exporter
• Log foreign coffee exports from 3
• largest producers (Vietnam, Brazil, Indonesia), denoted by FE

  t Is this really exogeneous? •

1.4 Dube & Vargas (2013) (cont.)

• j

  Need to instrument Cof

  Measured in 1997, when CP peaked • _t (i) Usually low-production municipalities may produce coffee a lot in 1997 ⇒ Non-classical measurement error

  (ii) Municipalities w/ downward pre-1997 trend in ε _mt e.g. Govt effort in security may have started coffee production by _C 1997, because P � _t ⇒ Spurious corr. btw CP & y for _{t jrt}

1.4 Dube & Vargas (2013) (cont.)

  Instrument for Cof :

  j

  rainfall and temperature at j

  ⇐ Coffee grows well if _m

T < 26 (degrees Celcius)

• _m

  R ≥ 1800 (mm)

1.4 Dube & Vargas (2013) (cont.)

  ⇒ ∗ Cof

  CP t j is instrumented by: _t

• _{t j}

  FE

  ∗ R FE

• FE ∗ T • _{t j t j j} FE ∗ R ∗ T
• R : mean annual rainfall in municipality j _j T : mean annual temperature in _j

  municipality j First-stage (page 20)

• Kleibergen-Paap F statistic: 15.94
• Exceeds Stock-Yogo critical value

Digression: Detecting weak instruments

• Stock & Yogo (2005) provide critical values of F-statistic or Cragg-Donald statistic (if # of endogenous variables > 1) for
• Bias in 2SLS is > 10% of bias in OLS (available only for # of instruments ≥ 3)
• Actual size of 5% test being less than 10%

• • (Baum, Schaffer,

  Stata ivreg2 authors

  Stillman 2007: 489-491) take the i.i.d.

  assumption seriously, and if you cluster standard errors, it reports Kleibergen-Paap statistics Not clear if Stock & Yogo (2005)

• critical values are relevant in this case

Findings (Tables II, III): ρ < 0 for all types of conflict ˆ

• ˆ

  λ > 0 for paramilitary attacks only

• ρ > 0 if y ˆ is agricultural wage
• jrt

  

⇒ Evidence for opportunity cost

mechanism

  ˆ λ > 0 if y is municipality govt

• jrt

  revenue

  ⇒ Evidence for resource mechanism

1.5 Recent studies on

  opportunity cost mechanism

  Jia (2012): Sweet potato mitigated

• the impact of droughts on peasant revolts in China (1470-1900) Bueno de Mesquita (2013):
• Guerrilla & terrorism should have an inverse U-shaped relation with opportunity cost

1.6 Limitation of the contest

  model

  Fighting is always an equilibrium

• Does not distinguish arming from
• fighting

  ∗ ∗ ∗

• A A B

  /(l By setting s = l + l ), both

  parties should prefer peace ⇒ Need for other explanations for

2. Asymmetric information

  War breaks out if you overestimate your strength

• you underestimate the opponent’s
• strength

  Below we illustrate the latter with a simple model of bargaining

2.1 Model (Fearon 1995)

  Players: groups A & B

• V : Pie to share or fight over
• Actions:
• A proposes V − x as transfer to B
• B then decides whether to accept
• V − x or go to war

  p: Probability of group A winning if

• war breaks out
• A B : Cost of war for A & B,

  , c c

2.1 Model (cont.)

  {u , u }: Payoffs A B

  If B accepts A’s offer, {x, V − x}

• If B fights, {pV − c , (1 − p)V − c }
• A B

  With complete info., peace achieved by x = pV + c (which makes B indifferent)

  B

2.2 Analysis

• B : only

  Suppose A does not know c

  knows its distribution F (c B ) B accepts peace if

• − x ≥ (1 − p)V − c

  V B ⇐⇒ c ≥ x − pV

  B

  A solves

• max [1 − F (x − pV )]x

  x FOC (assuming interior solution) 1 − F (K )

  = K + c

  A

  f (K ) where K ≡ x − pV RHS: increases w/ K

• LHS: decreases w/ K if F yields the
• monotone increasing hazard rate.

  ⇒ Unique K satisfying FOC

2.3 Limitation

  Information story may explain the

• onset of a war But both parties should learn about
• each other over time

  ⇒ cannot explain a long-lasting war Which is typically the case for civil • wars, e.g. Colombia, Sudan, Angola, DR Congo

3. Commitment

  In the previous model, peace is

• achieved w/ complete info. This, however, assumes group A’s
• ability to commit to x If A’s winning probability goes up
>tomorrow, it will renege on the promise B then decides to fight t

3.1 Model (Powell 2006)

• 2-period model
• Players: groups A & B
• V : Pie to share or fight over in each period
• If war breaks out in period t:
• A wins w/ prob. p _t
• Fraction (1 − d) of V : destroyed forever
• The loser eliminated forever (payoff 0)

Each period t

  1. A proposes a transfer schedule

  2

  {s } to B

  τ τ =t

  

2. B decides whether to accept or to

  go to war In period 1, A cannot commit to s

• 2

  < p Suppose p

  1 2 : A is temporarily weak In period 2: A’s payoff from war: p (1 − d)V

• 2

  ⇒ Credible s must be at most

  2

  (1 − p

  2 (1 − d))V

  In period 1: A’s maximum credible concession

• to avoid war:

  = V s

  1 B’s payoff from war

• (1 − p )(1 − d)(1 + δ)V

  1

⇒ War cannot be avoided in period 1 if

  (1 − p )(1 − d)(1 + δ)V

  1

  > [1 + δ(1 − p (1 − d))]V

  2

3.3 Intuition

  Key: large shifts in future

• distribution of power (p

  2 >> p 1 )

  Party whose power will increase

• cannot commit to a large transfer in future

  

They’d rather fight otherwise

• Opponent then prefers a
• preemptive attack, even if it’s costly (d > 0)

3.4 Evidence

  Yet to come

• How to measure future shifts in relative power?

3.5 Implications on political

  institutions Acemoglu & Robinson (2000, 2001, 2006): •

model democratization as commitment

device to future transfer Bruckner & Ciccone (2011): rainfall shock • led to democratization in Africa (1980-2004)

• Chaney (2013): when the Nile flooded,

  religious leaders less likely to be replaced

4. Other explanations of war

  Leader bias (Jackson and Morelli

• 2007)

  Jones & Olken (2009) for evidence

• that leaders matter

  Grievances (key to solve collective

• action problem?) Multiple threat points (Ray 2009,
• Morelli and Rohner 2010)

5. Ethnic diversity

  Viewed as the leading source of

• civil conflict (& govt failure) Is this empirically true? (sec. 5.1 -
• 5.3) What’s the theoretical rationale?
>(sec. 5.4-5.5) Why ethnicity, rather than c

5.1 Measurement

  Ethnic diversity often measured by

• the prob. that 2 randomly chosen individuals in a country belong to different ethnic groups

_{� � �}

N π i (1 − π i ) = π i π j

  i i j

=1 �=i

_i π : pop. share of ethnic group i
This measure has become popular
• among economists because of its presumed exogeneity

  Political scientists do not agree, • though. (e.g. Posner 2004)

Michalopoulos (2012) provides

• evidence against exogeneity

  Found to be negatively correlated

• w/ govt & economic performances

  cf. Easterly & Levine (1997), La Porta et

al. (1999), Alesina et al. (2003)

5.1 Measurement (cont.)

  But no robust association w/ civil

• conflicts

  cf. Collier & Hoeffler (1998), Fearon and Laitin (2003)

  But is this the correct measure of

• ethnic diversity to predict conflict?

  This measure: highest if many ethnic

• groups of equal size Conflict: most likely if two groups of
• equal size (ie. polarization)

5.2 Polarization

  Esteban & Ray (1994) derive an index of polarization from two ideas:

  

1. Identity (how many people you are

  identified with) ↑ ⇒ Conflict ↑

  

2. Alienation (how far other people are

  from you) ↑ ⇒ Conflict ↑

5.2 Polarization (cont.)

• Polarization index:
• α i

  K

  _� n i =1

n

_�

j

  

=1

  π

  1

  π

  j

  ν

  ij

  : pop. share of group i

• π _i
• ν _ij
• α ∈ (0, α ^∗
• n: # of groups
• K > 0: constant for normalizing index

  : distance between groups i & j

  ](α ^∗ ≈ 1.6)

  π _i π

  j ^{π k}

  ν ij ^{ik π}

  i ^{> π} j

  = π

  k

  π _i π

  j ^{π k}

  ν ij ^{ik π}

  i ^{> π} k _v ij ^{> v} ik

  − ^v

  ij

  π _i ^π

  

j

_{π k}

  ν ij ^ik ν

  ij

  = ν

  ik

  2

  (2005)

  Adopt this polarization index into

• ethnic conflict by setting

  ν = 1, ∀i, j (distance between any • _ij

two ethnic groups: same)

α = 1 (perhaps for simplicity) • K = 4 (⇒1 is maximum: ie. • N = 2, π = π = 1/2) _{1 2}

  ⇒

_�

N

  2

  

5.3 Montalvo & Reynal-Querol

(2005) (cont.)

  In pooled sample of country by

• 5-year-period (1960-1999): Ethnic polarization ↑ ⇒ Prob. of civil conflicts ↑

5.4 Esteban & Ray (2011)

  Provide a theory that links

• fractionalization and polarization indices to conflict Theory also tells when which
• measure is more important to predict conflict The key is whether the prize from
• winning is public or private goods.

5.4.1 Model: Players

• _�

  N agents

  m groups of agents

• Size of group i: N ( ⇒ N = N)
• i i i

  Denote group i’s population share

• by n ≡ N /N

  i i

5.4.1 Model: Actions

  Agent k of group i expends effort

• r (k ) to fight over a budget of size N

  i

• i � �� ���

  (r (k )) with Effort is costly: c

  c > 0, c > 0, c > 0 _���

  c > 0 ensures the uniqueness of the

• equilibrium _� Group i wins w. prob.
• r i (k ) R

  i k ∈i _{� �} ≡ R is our measure of conflict

• intensity

5.4.1 Model: Public good

  Winning group spends fraction λ

• (fixed) of the budget to produce the public good they prefer Group i’s payoff from public good is
• λu if they win _ii λu if group j �= i wins _ij

• ij ii ij : “distance” between i

  δ ≡ u − u

  and j

5.4.1 Model: Private goods

  Fraction 1 − λ of the budget will be

• shared equally by winning group members to produce private goods Group i member’s payoff is:
• (1 − λ)N/N if group i wins _i 0 otherwise

  _�

  Each individual’s payoff is therefore:

• 1 − λ

  π (k ) = p + i i p j λu ij −c i (r i (k )) n i

  j

_�

  We assume player k ∈ i maximizes:

• π (k ) + α π (l)

  i i l

∈i;l�=k

_�

  = (1 − α)π i (k ) + α π i (l)

• α is an extent of altruism to other fellow members of the same group
• α can also be the bargaining power of the group leader who maximizes _�

  l ∈i

  π

  i

  (l)

• In a political economy model, govt

  maximizes a weighted sum of

  individual utilities (cf. Persson and Tabellini (2000)) with weights different by political institutions etc.

5.4.2 Analysis

  max

  r _i (k )

  (1 − α)π i (k ) + α ^�

  l ∈i

  π i (l) = σ i ^� p i 1 − λ n i

• λ ^�

  j

  p j u ij ^� − c(r

  i

  (k )) − α ^�

  l ∈i;l�=k

  c (r

  i

  (l))

• λ ^�

  p

  l ∈i;l�=k c (r i

  (k )) − α ^�

  i

  − c(r

  ij ^�

  u

  j

  p

  j

  i

  1 − λ n

  i

  i ^�

  Ignore the last term as it doesn’t depend on r

  (l) = σ

  i

  π

  l ∈i

  (k ) + α ^�

  i

  (1 − α)π

  r _i (k )

  (l) are given max

  i

  (k ) and r

  i

  (l))

  1 − λ n i

• λ ^�
• Rewrite this term by using

  i

  c (r

  l ∈i;l�=k

  (k )) − α ^�

  i

  − c(r

  j p j u ij ^�

  i ^� p i

  max

  (l) = σ

  i

  π

  l ∈i

  (k ) + α ^�

  i

  (1 − α)π

  r _i (k )

  (l))

  � � _� 1 − λ σ + λ

  i p i p j u ij

  n

  i _{� � � � �} j

  1 − λ 1 − λ

• = σ p λu − + λp u

  i j ij i ii

  n n

  i i j _{� � � � �} �=i 1 − λ

  1 − λ

• = σ p − λδ − λu +

  i j ij ii n n i i j �=i So agent k of group i’s maximization problem becomes: _{� � � ��} 1 − λ max σ p − λδ −

  

i j ij

r (k ) _i n i j �=i

  − c(r (k ))

  i

  Now we have ∂p j R j p j

  = − = −

  2 Therefore, the FOC is σ i R ^�

  j �=i

  p j ∆

  ij

  = c

  �

  (

  r i (k ) )

  where ∆ ij ≡ λδ ij +

  1 −λ n _i

  for j �= i

• LHS is the same for all k ∈ i

  ⇒ r i (k ) = r i , ∀k ∈ i

5.4.3 Linking conflict to

  

population distribution indices

_�

  σ

  i �

  p ∆ = c (r )

  j ij i

  R

  j �=i

  Now we transform this FOC under the assumption of p i = n i , to derive per capita conflict intensity ρ ≡ R/N as a function of Gini,

  � σ

  i �

  p j ∆ ij = c (r i ) R

  j �=i

  If we assume p = n , ∀i,

  i i

  R R R R R R

  i i

  r i = = · = p i · = n i = ≡ ρ N i R N i N i N i N so we have _�

  σ i

  �

  σ

  i

  �

  = ρc

  ij

  ∆

  

j

  n

  i

  n

  j �=i

  σ i N ^�

  over all i, _�

  i

  i and sum

  ρn

  (ρ) Now multiply both sides by

  �

  = c

  

ij

  ∆

  j

  n

  j �=i

  R ^�

  (ρ)

  � � σ

  i �

  n n ∆ = ρc (ρ)

  i j ij

  N

  i j �=i

  RHS: Monotonically increases with

• per capita conflict intensity ρ LHS: Linear combination of Gini,
• Polarization, and Fractionalization
Substituting σ (≡ (1 − α) + αN ) and

  i i

  1 −λ

  ∆ + ij (≡ λδ ij ) into LHS yields: _{� �} n _i

  n i n j [ (1 − α) + αN i ][ λδ ij + (1 − λ)/n i ] N i j �=i _{� �}

• i j ij i j �=i

  Gini n n δ

  Multiplied by (1 − α)λ/N

• (1 − λ)/n

  � i ^� j �=i n i n j

  [(1 − α) + αN

  i

  ][ λδ

  ij

  i

  ]

  N

• Polarization: ^�
• Multiplied by αλ

  i

^�

j �=i

  n

  2 i

  n

  j

  δ

  ij

  � i ^� j �=i n i n j

  [(1 − α) + αN

• (1 − λ)/n

  i

  ][λδ

  ij

  i

  ]

  N

  n i n j

• Fractionalization: ^�

  i ^� j �=i

• Multiplied by α(1 − λ)
In summary, conflict increases with (1 − α)λ
• α[λP + (1 − λ)F ] G N If α > 0 (altruism to other members
• of the same group), P & F matter P matters more, the higher λ (the
• prize is more public)

  

5.5 Esteban, Mayoral, & Ray

(2012)

  Estimate this equation with

• cross-country data To measure δ
• ij , use linguistic

  distances on language trees

  cf. Desmet et al. (2012) To measure λ by country, use

• PUB ∗ GDP

  PUB ∗ GDP + OIL

  PUB: degree of un-democraticness of

• government OIL: per capita value of oil reserves
>GDP: per capita GDP
To measure α by country, use World
• Value Surveys in which respondents answer to the questions on:

  Adherence to social norms

• Identification to local community

>Importance of helping others
Then estimate

  P F

  ρ =β α λ + β α (1 − λ )F

  c c c P c c c c G �

• β λ c (1 − α c )G c /N c κ + ε c
• x c

  P F

  Results: β & β positive and

• significant Coefficients on P
• c & F c : becomes

  insignificant once these interaction

  For the onset of conflict,

  polarization does correlate, but fractionalization does not robustly (Table 6)

  But Esteban and Ray (2011) use the

• contest model, which has no

  predictive power on the initiation of conflict

  Why do people tend to start fighting

• along the ethnic divisions, instead

5.6 Esteban & Ray (2008)

  Why is ethnic conflict more

• prevalent than class conflict?

  Many conflicts these days are ethnic

• in nature

  Show higher income inequality

• increases the likelihood of ethnic conflict Go beyond 2-player conflict m
each group

  Model: Players 1. ph: Poor ethnic majority 2. rh: Rich ethnic majority 3. pm: Poor ethnic minority 4. rm: Rich ethnic minority e.g

h: Hindu, m: Muslim in India

• No collective action problem within
• n ij : Population share of class i of ethnicity j

  ≡ n _ph + n

_pm

• n _p
• n _r

  ≡ n _rh + n

_rm

  ≡ n _ph + n

_rh

> n _m ≡ n _pm + n _rm
• n _h
• Per-capita income
• Rich y _r
• Poor y _p (< y

  _r

  

)

  rh

  /n

  h

  = n

  rm

  /n

  

m

⇒ Same per-capita income for each

• n
Model: Public goods
• C: class budget
• used for funding class public good
• health care
• education
• infrastructure
• E: ethnic budget
• used for funding ethnic public good
• religious festivals
• temples
• job reservations in govt.
Model: Group ij’s Payoff

  If peace is achieved,

• u (y i ) + s i C + s j E

  i ∈ {r , p}, j ∈ {h, m}

• s
• i ∈ [0, 1]: class i’s share of class

  budget in peace time ∈ [0, 1]: ethnicity j’s share of s

• j
Model: Group ij’s Payoff (cont.)

  If class alliances form,

• w i A i A i

  (y − ) + + s u i C j E n A + A

  i p r

• i

  A : # of activists financed by class i

• i : compensation for each activist

  w

  in class alliance i Total compensation shared equally

Model: Group ij’s Payoff (cont.)

  If ethnic alliances form

• w A A

  j ij j

• u (y − ) + s C E

  i i

  n A + A

  ij h m

• ij : # of activists financed by class i

  A

  in ethnic alliance j ≡ A + A

• j ij (−i)j

  A

• j

  w : compensation for each activist

  Notice: in ethnic alliances,

• compensation is shared equally within each class of an ethnic group

  ⇐ Otherwise, forming an ethnic

  alliance involves regressive redistribution, which is unlikely Utility cost of being an activist: fully

• compensated by w i or w j ⇒ Doesn’t show up in the payoff

1. Players form alliances.

  Randomly chosen player: either

• proposes (i) class alliance, (ii) ethnic alliance, or (iii) peace If an alliance proposed, the other
• player in the proposed alliance decides whether to accept or reject

  e.g. If rh proposes class (ethnic) alliance,

then rm (ph) responds

  If accepted, move to stage 2 (ie. • conflict). If rejected or peace proposed, a new

Model: Timing of events (cont.)

1. Players form alliances (cont.)

  If all the 4 players propose peace or if

• proposals rejected endlessly, peace payoffs realize

• Players reject or never make a

  Assumption D:

• proposal yielding the worst possible payoff

  ie. Delaying such a proposal so the worst payoff is discounted

  Players accept a proposal yielding the

Model: Timing of events (cont.) 2a. If class alliances are formed,

  each alliance simultaneously chooses A (k = {p, r })

  k ⇐ There’s no asymmetry between h & m in terms of payoffs.

  2b. If ethnic alliances are formed,

  each class in each alliance simultaneously chooses A ik (i = {p, r }, k = {h, m}) Analysis: how to proceed

  

1. Prove that, under Propositions 2-5,

  ethnic conflict is unique outcome of the game (Proposition 6)

  

2. Check if a higher income inequality

  makes propositions 2-5 more likely to hold

  The paper proceeds in the reverse

• order, but this way motivates us to care about propositions 2-5 better.

  

Preference conditions for ethnic

conflict to be unique outcome

  P2. ph: ethnic � class P3. If ph: class � peace

  ⇒ rh: ethnic � class

  P4. r : peace � class P5. p: class � peace If P5 does not hold, peace is also an

• equilibrium, but class conflict is NOT.
Peace won’t be an eq. outcome

  Suppose otherwise

• ph prefer proposing class
• � peace By P5, ph: class
• pm accepts this proposal
• ph: ethnic � peace (by P2, P5) ⇒ σ > s ⇒ σ < s

  _{h h m m}

  ⇒ pm: peace � ethnic ⇒ pm’s best outcome: class (by P5) ⇒ Accepts immediately (by D)

  Suppose otherwise

• r never initiate class conflict
• rh: ethnic � class (by P5 & P3)
• ⇒ rh’s worst outcome: class (by P4) ⇒ rh never proposes/accepts class (by D)
• ph: ethnic � class (by P2)

  ph prefers proposing ethnic

• Peace won’t be an eq. outcome

  rh accepts this proposal

  Poor ethnic majority: want ethnic

• conflict (P2) Issue: whether rich ethnic majority
• accept this even when rich prefer peace the most When poor can credibly threaten
• rich with class conflict (1st part of the proof), peace no longer possible
Propositions 2-5

  Paper shows P2-P5 hold under

• reasonable set of parameter values Here we focus on why
• within-ethnicity inequality helps satisfying P2 Proposition 1a: specifies condition
>for conflict � peace Proposition 1b: specifies condi
• Assume that contributions x are small relative to income y i .

  ie. u (y _i ) − u(y _i − x) ≈ u ^� (y _i − x)x

• Then class i in alliance k prefers conflict to peace iff

  λ

  σ

  2 k

• (1 − λ

  ik

  ik

  )σ

  k

  > s

  k

• λ _ik

  ≡ A _ik /A _k Proposition 1a: Intuition

• ik

  λ = 1 if k is class alliance

• 2

  Then the condition boils down to

  σ > s

  k k

  Conflict should increase the budget

• share sufficiently to compensate resources spent (A ik )
Proposition 1a: Intuition (cont.)
• ik = 0 if class i in ethnic alliance k

  λ

  does not contribute Then the condition boils down to

• σ > s

  k k

  Conflict should increase the budget

• share
• Let G ∈ {C, E}

  Proof of Proposition 1a

• Conflict � ik Peace if _�

  σ

  k

  − s

  k ^�

  G > u

  

�

^�

  y

  i

  − w k A ik n

  ik ^�

  w k A ik n

  ik

• LHS: Gain from conflict
• RHS: Cost of conflict
_{� � � �} ik Peace if

  � Conflict

  w A w A

  k ik k ik

�

  σ k − s k G > u y i − n ik n ik By FOC on A

• _{� �}

  ik , we have

  w k A ik w k A l

  �

  u y − = G

  i

  2

  n n (A + A )

  ik ik k l

• ik = λ ik A k with both sides

  Multiply A

  of FOC and replace cost of conflict

• _{� �}

  � Conflict

  ik Peace if

  A A

  k l

  σ − s G > λ G

  k k ik

  2

  (A k + A l ) = λ σ (1 − σ )G

  ik k k

• 2

  Rearranging this inequality yields:

  λ σ + (1 − λ )σ > s

  ik ik k k k Notice: this proof only uses the

• inequality that compares the payoffs from conflict and peace

  ⇒ Difference between both sides of

  inequality: Net payoff of conflict This allows us to derive Proposition

• 1b:
Proposition 1b

  Class i of ethnicity j prefers ethnic

• alliance to class alliance iff

  2

  2

  [λ + (1 − λ )n − s ]µ > σ − s

  ij n ij j j i j i

  where µ ≡ E/C LHS: Gain from ethnic conflict

• relative to peace RHS: Gain from class conf

  Class i prefers class conflict (so

• λ ik = 1) to peace iff

  

2

  σ > s i

  

i

  Class i of ethnicity j prefers ethnic

• conflict to peace iff

  2

  λ n + (1 − λ )n > s

  ij ij j j j

  λ = 0 as an implication of pk within-ethnicity inequality

• ik = 0 if class i in ethnic alliance k

  λ

  does not finance any activists: _{� �} w A w A

  

k ik k l

�

  u y − > E , ∀A ≥ 0

  i ik

  n ik n ik A k + A l _i

  This is more likely if y is very small

• ⇒ If income inequality very high

  (y >> y ), then _{r p}

• 2

  Condition for ethnic � class,

  2

  [λ n + (1 − λ )n − s ]µ > σ − s ,

  ij ij j j i j i