fabrizio zilibotti. war signals: a theory of trade, trust and confict

War Signals:A Theory of Trade, Trust and Con�ict

Dominic Rohner (University of Lausanne) Mathias Thoenig(University of Lausanne) Fabrizio Zilibotti (University of Zurich)

Estonian Economic Association 2014

January 31, 2014

War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 1 / 50

Introduction

Recurrent Wars

In 1950-2000, over two third of civil con�icts are "recurrent"

Determinants of civil wars: "Greed" vs. "Grievance"

Greed : cost/bene�t analysis in presence of weak institutions,natural resource contest, etc.Grievance: fanaticism, revenge, irrationality of crowds. . .

Persistence in such factors can explain recurrence


Introduction

This paper

A rational choice theory of trust, trade and warwhere "distrust" is at the root of recurrent con�icts

War today hinders inter-ethnic trustDistrust reduces trade opportunitiesand the opportunity cost of future war fallsThis leads to recurrent war

Distrust may be "unwarranted"...without necessarily being irrational

Culprit: imperfect information / learning trap(related to information cascades)


Introduction

Institutions vs. Social Capital

Recent economic theories emphasize institutions

A number of developing countries with relativelysolid institutions plunge into recurrent con�icts,

Colombia, India, Turkey, Sri Lanka and the Philippines(WVS score 0.16)

... whereas other countries with weak institutions and highethnic cleavages experienced no civil con�icts:

Bhutan, Cameroon, Gabon, Kazahstan,Togo, China and Vietnam (WVS score 0.51)

Institutions do not appear to be the sole determinants of civil war


Introduction

War Persistence and E¤ect of Lagged Trust

LHS: civil war incidence (5-years period, annual in col. 7-8)

(1) (2) (3) (4) (5) (6) (7) (8)

War (t1) 0.36*** 0.22*** 0.30*** 0.17*** 0.24*** 0.10 0.24*** 0.05

(0.01) (0.01) (0.02) (0.014) (0.04) (0.07) (0.02) (0.04)

Trust (t1) 0.37* 0.56*** 0.48*** 0.46***

(0.21) (0.20) (0.08) (0.17)

Conflicts coded as war >25 Fatal. >1000 Fatal. >25 Fatal. >1000 Fatal. >25 Fatal. >1000 Fatal. >25 Fatal. >1000 Fatal.

Controls No No Yes Yes Yes Yes Yes Yes

Observations 1426 1426 1026 939 101 101 564 439

Pseudo Rsquared 0.304 0.322 0.363 0.358 0.575 0.572 0.695 0.597

Dependent variable: Civil war incidence (fiveyear intervals). The dependent variable is coded as 1 if a conflict causing at least 25 (1000) fatalities is recorded

in at least one of the five years. Sample period: 19492008. Number of countries for which observations are available: 174. The set of controls include:

lagged democracy, lagged GDP per capita, oil exporter, lagged population, ethnic fractionalization, mountainous terrain, noncontiguous state, region fixed

effects and time dummies. Columns 78 have as dependent variable civil war incidence at the annual level (details in the text). The table reports the marginal

effects of logit regressions with robust standard errors, clustered at the country level. Significance levels: * p<0.1, ** p<0.05, *** p<0.01.


Introduction

War Persistence and E¤ect of Lagged Trust

Controls:

democracy: often insigni�cant, negative and signif. in column 6log GDP[-1]: usually negative, sometimes insigni�cantethnic fractionalization: positive and often signi�cantoil exporter: usually insigni�cantmountainous terrain: positive and often signi�cant

See, e.g., Fearon and Laitin (2003), Collier and Hoe er (2004),Montalvo and Reynal-Querol (2005), Cederman and Girardin(2007), Collier and Rohner (2008), and Esteban et al. (2012).


Introduction

Causal Impact of War on Trust: Uganda

Rohner, Thoenig and Zilibotti (2011):

"Seeds of Distrust: Con�ict in Uganda"

Highly fractionalized country (52 groups)

Endemic ethnic con�icts


Introduction

Causal Impact of War on Trust: Uganda (cont.)

Exogenous change in the intensityof counter-insurgency after 9/11

Explosion of violence in 2002-04ending with defeat of main rebel movements

We exploit geolocalized information on con�ict events (ACLED);we know where ethnic violence took placeand which ethnic groups it involved

"Pre" and "Post" district-level survey measuresof trust and ethnic identity (Afrobarometer)


Introduction


13

2000 2008

End of 2001:US Patriot Act declaresLRA and ADF to be

Terrorists(+end of Congo War)

2002:Museveni starts

“Operation Iron Fist”

2002 2004:Escalation of violence

by rebels andgovernment

2005:ADF defeated,LRA weakened

2006:Ceasefire,

less fighting


Introduction


Main �ndings:

Intensity of violence at the county and/or ethnic leveldecreases trust towards other Ugandansand increases ethnic identityIntensity of violence at the district/ethnic leveldecreases post-con�ict economic cooperationin ethnically fractionalized areas


Introduction

Trade, Trust and Con�ict

Trade reduces the likelihood of con�ict:

Martin, Meyer & Thoenig (ReSTud 08; JEEA 08)India and East Asia: Horowitz (2000), Jha (2008),Varshney (2001, 2002), Bardhan (1997)Rwanda: Ingelaere (2007), Pinchotti and Verwimp (2007)

Trade and economic cooperation hinges on trustand perceived trustworthyness:

Inter-ctry evidence (Guiso, Sapienza & Zingales QJE 09,Felbermayr & Toubal EER 10)Social/trade networks help enforcement ofreputation and retaliation (Rauch JIE 99, Greif JPE 94)


Introduction

Road map

Static model

Perfect InformationImperfect information

Dynamics

War traps

Extensions

Altruism (Markov Perfect Equilibrium)Stochastic typesPeace trapsLearning from trade


Theory

The Two-Stage Game

A continuum of risk-neutral individuals belonging totwo "ethnic" groups (A and B), each of unit mass

Between-groups interactions are described by a two-stage game:

S1 Group A decides whether or not to wage war against group BS2 (WAR) No economically interesting decisions

(payo¤ of war to group A is equal to V )S2 (PEACE) Each agent in group A is randomly matched

to trade with an agent in group B


Theory

S2: Economic Payo¤ of Trade (stag hunt game)

Group B

C D

C c, c h� l , hGroup A

D h, h� l h, h

where c > h


Theory

Interpretation

Interpretation(s):1 Defection as opportunistic ("dishonest") behavior(Hauk and Saez Marti JET 02; Tabellini QJE 08)

2 Human capital investment

1 A "successful" partnership requires a costly (l) human capitalinvestment, e.g., familiarizing oneself with the other group�slanguage and customs

2 Cooperation=invest; defection=not invest3 In line with the classic stag-hunt game

In either interpretation, cooperation is risky (if the other sidedefects, the cooperator neither hunts the stag nor the rabbit)


Theory

S2: Economic + Psychological payo¤ of trade

Group B

C D

C c + ιA,i , c + ιB ,j h� l + ιA,i , hGroup A

D h, h� l + ιB ,j h, h

where c > h


Theory

S2: Distribution of "Cooperative Spirit"

We assume ι to be a continuous random variable,i .i .d . across agents, drawn from a distributionwith c.d.f. F J : R ! [0, 1]

Group A can be of two types: FA 2 fF+,F�g,where F+ �rst-order stochastically dominates F�

Group A is civic (trustworthy) if FA = F+,and is uncivic if FA = F�

FB has a unique realization (for tractability)


Theory

S2: Cooperation in Trade

The optimal strategy (C vs. D) depends on theproportion of cooperators in the other population

Let z � c � (h� l)Cooperation is chosen by all agents in group A for whom

ιA � l � z � nB ,

where nB is the proportion of cooperators in group B

Cooperation is chosen by all agents in group B for whom

ιB � l � z � nA.

where nA is the of proportion cooperators in group A


Theory

S2: Trade Surplus

Trade surplus accruing to group A and B

SkA = h+ znkAnkB �

Z ∞

l�z �nkB(l � ι) � dF k (ι)

SkB = h+ znkAnkB �

Z ∞

l�z �nkA(l � ι) � dF k (ι)

where k 2 f+,�g denotes group A�s typeWithin-group transfers rule out (within-group) ine¢ ciencies

Note: S+A � S�A and S+B � S

�B


Theory

S1: Stochastic war

War has a stochastic pay o¤

Motivation: good and bad times to make war...

Discrete support, V 2 fVH ,V ,V Lg such thatif V = V H

�V = V L

�war (peace) is always optimal

We call these states war shocks and peace shocksThe associated probabilities are λW and λP

If V = V war or peace may be chosen depending on theeconomic surplus. We call this state "business as usual" (BAU)

If Sk > V group A chooses peace under BAUIf Sk < V group A chooses war under BAU

The realization of V is observed before war decision


Theory

Perfect Information (benchmark)

Multiple equilibria in general possible

Under some conditions on distributions, we prove that

the Nash equilibrium of the trade game is uniqueif k = +, group A keeps peace under BAUif k = �, group A wages war under BAU


Theory

Imperfect information

Assume group B does not observe:1 group A�s type2 the realization of V

Characterize the PBE

Solve the game backwards


Theory

Imperfect information (trade)

Let πP denotes the posterior belief(after peace) that A is civicGroup A: invest if

ιA,i � l � z � nB ) nkA = Fk (znB )

Group B: invest if

ιB ,i � z �E [nA j πP ]) nB = FB�

πP � zn+A +�1� πP

�� zn�A

�Fixed point yields:

nB = nB

+

πP

!, n+A = n

+A

+

πP

!, n�A = n

�A

+

πP

!


Theory

Imperfect information (surplus)

Surplus of group A (relevant for war waging decision)

Sk +

πP

!= h+ znkA

�πP�nB�

πP��Z ∞

l�z �nB (p)(l � ι) �dF k (ι)

Note: due to strategic complementarity, pessimistic beliefs yielda collapse of trade surplus irrespective of the true type


Theory

Imperfect information (group A�s trade surplus)

Figure: V is pay-o¤ of war under BAU. For πP < π�, group A wages war(under BAU) irrespective of its type. For πP � π�, group A does notwage war (under BAU) if it is of the civic type


Dynamics

Bayesian updating

Young agents acquire beliefs based on warfare history

transmission of private info within "dynasties" in an extension

Posterior beliefs at t are prior beliefs at t+1, etc.

In the "informative" region (of priors)

After peace:�πPt =

�πt+1 > πt

After war: πt+1 < πt

In the "uninformative" region:

πt+1 = πt no matter what


Dynamics

Dynamic equilibrium

Let rt = πt1�πt

(likelihood ratio, r 2 (0,∞))

Trapwar peace

r


Dynamics

Dynamic equilibrium (cont.)

In the informative equilibrium region,beliefs follow an asymmetric random walk with drift

ln rt =

8>><>>:ln rt�1 + ln

�1�λW

λP

�if Peace

ln rt�1 � ln�1�λP

λW

�if War

Pr (WAR) =

8<:1� λP if k=-

λW if k=+

In the war trap

ln rt = ln rt�1Pr (WAR) = 1� λP


Dynamics


ln tr

ln r 1ln tr −

war

peace

Nonrecurrentstates

ln1

W

P

rλλ−

45°

Figure: Dynamics of beliefs


Dynamics

"Unwarranted" war traps

Suppose group A is civic (k=+)... but B does not know it

Yet, a sequence of low-probability war shockscan drive the economy into a (permanent) war trap

Trap

War shock

r

War shockWar shock


Dynamics


In the long run, the economy can fall into the trap

... but can as well, alternatively, escape the trap forever

If A is civic, the process is a random walk with positive drift,and the drift pushes the economy away of the "slippery" region

We characterize the prob. distribution over long-run outcomes


Dynamics

Proposition

Assume that V > S+ (0) , S� (∞) < V < S+ (∞) , and r0 > r .(i) If group A is uncivic,then the DSE enters the war trap in �nite time with probability one.(ii) If group A is civic,then the DSE enters the war trap in �nite time w. prob. PTRAP > 0,and stays out of the war trap forever with prob. 1�PTRAP > 0.If the economy stays out of the trap, the DSE converges to perfectlearning, i.e., rt ! ∞, and war incidence stays low ( λW ).(iii) The probability PTRAP has the following bounds:

0 <λW1� λP

rr0< PTRAP �

rr0< 1.


Dynamics

Proof (sketch)

The proof is based on the Martingale Convergence Theorem:πt converges almost surely to a limit

It is easy to prove that the limit cannot liein the interior of the informative region,thus either πt enters the trap or limt!∞ πt = 1


Dynamics

Proof (sketch)

Suppose A is uncivicThen, limt!∞ πt = 1 induces a contradiction(i.e., the economy converges to a war trap with prob. one)

Suppose limt!∞ πt = 1, thenthe economy must remain forever in the informative regionBut, then, the Law of Large Numbers would imply that B couldobserve an in�nite no. of realizations of the war/peace process,and eventually learn the truth, i.e., that A is uncivicA contradiction

Suppose A is civicThen, group B can learn asymptotically the truth (i.e.,limt!∞ πt = 1) with positive probabilityHowever, a �nite no. of war shocks precipitates the economyinto the war trap. This happens with positive probability(since it takes a �nite no. of steps to enter the traps)


Dynamics

Taking stock

In summary, supposing A is civic:

With a positive probabilitythe economy converges to perfect (correct) learningWith a positive probability the economy stops learningWe can provide bounds to theprobability that the economy falls into the trap

Economic development hinges on luck, i.e.,the realization of the stochastic process of peace/war(similar to Acemoglu and Zilibotti JPE 1997).


Extensions

Extensions

Altruistic agents:

Internalize the negative e¤ect of war on future generationsCharacterize the Markov equilibrium of the dynamic game

Stochastic types

With a positive probability group A�s type changes(Markov switching probability)

Peace trap together with war traps

Learning from trade

Traders acquire some private information aboutthe other group�s type


Extensions

Stochastic types

Cultural shocks drive shifts of group A�s type(e.g., ancient Vikings vs modern Scandinavians)

As time goes by the discredit of group B washes away

Can war traps be averted?


Extensions

Stochastic types (cont.)

Two-state Markov chain:

k + �

+ 1� θ θ

� φ 1� φ

φ � 1/2 and θ � 1/2, implying a positive autocorrelationThe unconditional (long run) likelihood ratiothat A is civic is r = φ/θ

The type shock is realized at thebeginning of each period, before war decision


Extensions


Posterior at t now di¤ers from prior at t+1Bayes rule yields

r (rt�1) =(1� θ)rt�1 + φ

θrt�1 + 1� φ

In the informative region, after war and peace

rt =

8><>:r (rt�1)� 1�λW

λPif peace

r (rt�1)� λW1�λP

if war

In uninformative region (irrespective of war/peace)

rt = r (rt�1) =(1� θ)rt�1 + φ

θrt�1 + 1� φ

Three possibilitiesWar Signals (Estonian Economic Association 2014) War Signals January 31, 2014 39 / 50

Extensions


r(t)

r(t+1)

r(t)

CASE 1: TRAP

uninformativeregion

informativeregion


Extensions


r(t)

r(t+1)

r(t)

uninf.region

informativeregion

CASE 2: NO TRAP

ergodic set


Extensions


r(t)

r(t+1)

r(t)

uninform.region

informativeregion

CASE 3: CYCLES

ergodic set


Extensions

Peace Traps

Figure: Surplus from trade and war bene�ts; the case of two traps.


Extensions

Peace Traps

ln tr

ln r 1ln tr −

war

peace

Nonrecurrentstates

ln rln1

W

P

rλλ−

*ln r

Nonrecurrentstates

45°

Figure: Dynamics of beliefs with two trapsWar Signals (Estonian Economic Association 2014) War Signals January 31, 2014 44 / 50

Extensions

Learning from trade

Agents can acquire and retain some informationthrough their individual family trade history

Simplifying assumption:as soon as an agent trade, she observes the true k

This "hard" information is transmitted to the o¤spring

Without additional assumptions,all agents would learn perfectly k over time.

We assume that the inter-generational transmission of"hard" information is imperfect: with probability θ, thechild of an informed parent fails to receive the information.


Extensions

Learning from trade

Suppose the proportion of informed players is exogenousInformed players reduce the scope of learning traps

Figure: Trade surplus with di¤erent proportion of informed players, ι.


Extensions

Learning from trade

Suppose k=+ and ι is endogenous

Now, peace periods have the additional virtuethat some people "learn through trade"

However, during war, there is no direct learning,and in fact some information from past trade gets lost

More formally,

ιt+1 = (1� θ)[ιt + (1�Wt)� τ � (1� ιt)]

Result no. 1:

For large enough θ a war trap continue to exist


Extensions

Learning from trade

Result no. 2:

Cycles are a generic feature of the equilibrium:

the economy enters the uninformative region,where war is frequent and trade is scantwars make fall the economy "deeper"into the uninformative regionhowever, a sequence of peace shocks(by inducing trade and learning) can rescue the economy


Conclusions

Conclusions

A rational theory of persistent (ine¢ cient) wars

Business relations are key to preserve stable peace

Peace-keeping forces can be ine¢ cient when trust has collapsed,since they fail to restore trade and economic cooperation(consistent with the empirical evidence)

Policies aimed to restore trade and trust are more promising

positive campaigns aboutsuccessful inter-ethnic business partnershipstargeted human capital subsidies reducing the cost of tradingwith the other groups (e.g., learning languages, customs)changes in social norms (persuasion campaign?)


Conclusions

In progress

Limitation (common in the literature):con�ict as a two-group game

Yet, in many con�icts there are complicated network of alliances

Complementarity, substitution and externalitiesin �ghting and sharing the "prize"

Work in progress with M. Koenig, D. Rohner, and M. Thoenig

contest success function (Tullock game)an explicit network of alliances and rivalriesNash equilibrium)e¤ort depends on groups�centralitystructural estimation based on Congo (DRC) warpolicy: key player analysis


fabrizio zilibotti. war signals: a theory of trade, trust and confict

Economy & Finance

extensions stochastic types

dynamics dynamic equilibrium

civil war incidence

theory imperfect information

region war signals

extensions learning

war signals

informed players