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War Signals:
A Theory of Trade, Trust and Con‡ict
Dominic Rohner (University of Lausanne) Mathias Thoenig
(University of L...
Introduction

Recurrent Wars

In 1950-2000, over two third of civil con‡icts are "recurrent"
Determinants of civil wars: "...
Introduction

This paper
A rational choice theory of trust, trade and war
where "distrust" is at the root of recurrent con...
Introduction

Institutions vs. Social Capital
Recent economic theories emphasize institutions
A number of developing count...
Introduction

War Persistence and E¤ect of Lagged Trust
LHS: civil war incidence (5-years period, annual in col. 7-8)
(1)
...
Introduction

War Persistence and E¤ect of Lagged Trust

Controls:
democracy: often insigni…cant, negative and signif. in ...
Introduction

Causal Impact of War on Trust: Uganda

Rohner, Thoenig and Zilibotti (2011):
"Seeds of Distrust: Con‡ict in ...
Introduction

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

Exogenous change in the intensity
of counter-insurgency after...
Introduction

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

2000

2008
2002:
Museveni starts
“
Operation Iron Fist”

End ...
Introduction

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

Main …ndings:
Intensity of violence at the county and/or ethn...
Introduction

Trade, Trust and Con‡ict
Trade reduces the likelihood of con‡ict:
Martin, Meyer & Thoenig (ReSTud 08; JEEA 0...
Introduction

Road map
Static model
Perfect Information
Imperfect information

Dynamics
War traps

Extensions
Altruism (Ma...
Theory

The Two-Stage Game

A continuum of risk-neutral individuals belonging to
two "ethnic" groups (A and B), each of un...
Theory

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

Group B
C
C

D

c, c

h

l, h

Group A
D

h, h

l

h, h

where c > h...
Theory

Interpretation
Interpretation(s):
1

2

Defection as opportunistic ("dishonest") behavior
(Hauk and Saez Marti JET...
Theory

S2: Economic + Psychological payo¤ of trade

Group B
C
C

c + ιA,i , c + ιB ,j h

D
l + ιA,i , h

Group A
D

h, h
...
Theory

S2: Distribution of "Cooperative Spirit"

We assume ι to be a continuous random variable,
i.i.d. across agents, dr...
Theory

S2: Cooperation in Trade
The optimal strategy (C vs. D) depends on the
proportion of cooperators in the other popu...
Theory

S2: Trade Surplus
Trade surplus accruing to group A and B
k
k k
SA = h + znA nB
k
k k
SB = h + znA nB

Z ∞

l z

k...
Theory

S1: Stochastic war
War has a stochastic pay o¤
Motivation: good and bad times to make war...

˜
Discrete support, ...
Theory

Perfect Information (benchmark)

Multiple equilibria in general possible
Under some conditions on distributions, w...
Theory

Imperfect information

Assume group B does not observe:
1
2

group A’ type
s
˜
the realization of V

Characterize ...
Theory

Imperfect information (trade)
Let π P denotes the posterior belief
(after peace) that A is civic
Group A: invest i...
Theory

Imperfect information (surplus)

Surplus of group A (relevant for war waging decision)
!
Z
+

Sk

πP

k
= h + znA ...
Theory

Imperfect information (group A’ trade surplus)
s

Figure: V is pay-o¤ of war under BAU. For π P < π , group A wage...
Dynamics

Bayesian updating

Young agents acquire beliefs based on warfare history
transmission of private info within "dy...
Dynamics

Dynamic equilibrium

Let rt =

πt
1 πt

(likelihood ratio, r 2 (0, ∞))
war

peace

Trap

r

War Signals (Estonia...
Dynamics

Dynamic equilibrium (cont.)
In the informative equilibrium region,
beliefs follow an asymmetric random walk with...
Dynamics

Dynamic equilibrium (cont.)
ln rt
peace

war
Non-recurrent
states

45°

ln

λW
r
1 − λP

ln r

ln rt −1

Figure:...
Dynamics

"Unwarranted" war traps

Suppose group A is civic (k=+)
... but B does not know it
Yet, a sequence of low-probab...
Dynamics

Dynamic equilibrium (cont.)

In the long run, the economy can fall into the trap
... but can as well, alternativ...
Dynamics

Proposition
Assume that V > S + (0) , S (∞) < V < S + (∞) , and r0 > r.
(i) If group A is uncivic,
then the DSE ...
Dynamics

Proof (sketch)

The proof is based on the Martingale Convergence Theorem:
π t converges almost surely to a limit...
Dynamics

Proof (sketch)
Suppose A is uncivic
Then, limt !∞ π t = 1 induces a contradiction
(i.e., the economy converges t...
Dynamics

Taking stock

In summary, supposing A is civic:
With a positive probability
the economy converges to perfect (co...
Extensions

Extensions
Altruistic agents:
Internalize the negative e¤ect of war on future generations
Characterize the Mar...
Extensions

Stochastic types

Cultural shocks drive shifts of group A’ type
s
(e.g., ancient Vikings vs modern Scandinavia...
Extensions

Stochastic types (cont.)
Two-state Markov chain:

+

k

+

1

θ
φ

θ
1

φ

φ 1/2 and θ 1/2, implying a positiv...
Extensions

Stochastic types (cont.)
Posterior at t now di¤ers from prior at t+1
Bayes rule yields

(1 θ )rt 1 + φ
θrt 1 +...
Extensions

Stochastic types (cont.)
CASE 1: TRAP
r(t+1)

r(t)
uninformative
region
War Signals (Estonian Economic Associa...
Extensions

Stochastic types (cont.)
CASE 2: NO TRAP
r(t+1)

ergodic set

r(t)
uninf.
region
War Signals (Estonian Economi...
Extensions

Stochastic types (cont.)
CASE 3: CYCLES
r(t+1)

ergodic set

r(t)
uninform.
region
War Signals (Estonian Econo...
Extensions

Peace Traps

Figure: Surplus from trade and war bene…ts; the case of two traps.
War Signals (Estonian Economic...
Extensions

Peace Traps
ln rt
peace

Non-recurrent
states

Non-recurrent
states

war

45°

ln

λW
r
1 − λP

ln r

ln r *

...
Extensions

Learning from trade
Agents can acquire and retain some information
through their individual family trade histo...
Extensions

Learning from trade
Suppose the proportion of informed players is exogenous
Informed players reduce the scope ...
Extensions

Learning from trade
Suppose k=+ and ι is endogenous
Now, peace periods have the additional virtue
that some pe...
Extensions

Learning from trade

Result no. 2:
Cycles are a generic feature of the equilibrium:
the economy enters the uni...
Conclusions

Conclusions
A rational theory of persistent (ine¢ cient) wars
Business relations are key to preserve stable p...
Conclusions

In progress
Limitation (common in the literature):
con‡ict as a two-group game
Yet, in many con‡icts there ar...
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Fabrizio Zilibotti. War Signals: A Theory of Trade, Trust and Conf‡ict

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Fabrizio Zilibotti (Institute for Empirical Research in Economics)
Estonian Economic Association 2014
January 31, 2014

Published in: Economy & Finance
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Fabrizio Zilibotti. War Signals: A Theory of Trade, Trust and Conf‡ict

  1. 1. 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
  2. 2. 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 War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 2 / 50
  3. 3. Introduction This paper A rational choice theory of trust, trade and war where "distrust" is at the root of recurrent con‡icts War today hinders inter-ethnic trust Distrust reduces trade opportunities and the opportunity cost of future war falls This leads to recurrent war Distrust may be "unwarranted"... without necessarily being irrational Culprit: imperfect information / learning trap (related to information cascades) War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 3 / 50
  4. 4. Introduction Institutions vs. Social Capital Recent economic theories emphasize institutions A number of developing countries with relatively solid 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 high ethnic 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 War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 4 / 50
  5. 5. 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) 0.36*** 0.22*** 0.30*** 0.17*** 0.24*** 0.10 0.24*** 0.05 (0.01) War (t-1) (0.01) (0.02) (0.014) (0.04) (0.07) (0.02) (0.04) -0.37* Trust (t-1) -0.56*** -0.48*** -0.46*** (0.21) Conflicts coded as war Controls >25 Fatal. >1000 Fatal. >25 Fatal. >1000 Fatal. (0.20) (0.08) (0.17) >25 Fatal. >1000 Fatal. >25 Fatal. >1000 Fatal. No No Yes Yes Yes Yes Yes Yes Observations 1426 1426 1026 939 101 101 564 439 Pseudo R-squared 0.304 0.322 0.363 0.358 0.575 0.572 0.695 0.597 Dependent variable: Civil war incidence (five-year 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: 1949-2008. 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 7-8 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. War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 5 / 50
  6. 6. Introduction War Persistence and E¤ect of Lagged Trust Controls: democracy: often insigni…cant, negative and signif. in column 6 log GDP[-1]: usually negative, sometimes insigni…cant ethnic fractionalization: positive and often signi…cant oil exporter: usually insigni…cant mountainous 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). War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 6 / 50
  7. 7. 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 War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 7 / 50
  8. 8. Introduction Causal Impact of War on Trust: Uganda (cont.) Exogenous change in the intensity of counter-insurgency after 9/11 Explosion of violence in 2002-04 ending with defeat of main rebel movements We exploit geolocalized information on con‡ict events (ACLED); we know where ethnic violence took place and which ethnic groups it involved "Pre" and "Post" district-level survey measures of trust and ethnic identity (Afrobarometer) War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 8 / 50
  9. 9. Introduction Causal Impact of War on Trust: Uganda (cont.) 2000 2008 2002: Museveni starts “ Operation Iron Fist” End of 2001: US Patriot Act declares LRA and ADF to be Terrorists (+end of Congo War) 2005: ADF defeated, LRA weakened 2002 - 2004: Escalation of violence by rebels and government 2006: Ceasefire, less fighting 13 War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 9 / 50
  10. 10. Introduction Causal Impact of War on Trust: Uganda (cont.) Main …ndings: Intensity of violence at the county and/or ethnic level decreases trust towards other Ugandans and increases ethnic identity Intensity of violence at the district/ethnic level decreases post-con‡ict economic cooperation in ethnically fractionalized areas War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 10 / 50
  11. 11. 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 trust and perceived trustworthyness: Inter-ctry evidence (Guiso, Sapienza & Zingales QJE 09, Felbermayr & Toubal EER 10) Social/trade networks help enforcement of reputation and retaliation (Rauch JIE 99, Greif JPE 94) War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 11 / 50
  12. 12. Introduction Road map Static model Perfect Information Imperfect information Dynamics War traps Extensions Altruism (Markov Perfect Equilibrium) Stochastic types Peace traps Learning from trade War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 12 / 50
  13. 13. Theory The Two-Stage Game A continuum of risk-neutral individuals belonging to two "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 B S2 (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 War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 13 / 50
  14. 14. Theory S2: Economic Payo¤ of Trade (stag hunt game) Group B C C D c, c h l, h Group A D h, h l h, h where c > h War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 14 / 50
  15. 15. Theory Interpretation Interpretation(s): 1 2 Defection as opportunistic ("dishonest") behavior (Hauk and Saez Marti JET 02; Tabellini QJE 08) Human capital investment 1 2 3 A "successful" partnership requires a costly (l) human capital investment, e.g., familiarizing oneself with the other group’ s language and customs Cooperation=invest; defection=not invest In line with the classic stag-hunt game In either interpretation, cooperation is risky (if the other side defects, the cooperator neither hunts the stag nor the rabbit) War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 15 / 50
  16. 16. Theory S2: Economic + Psychological payo¤ of trade Group B C C c + ιA,i , c + ιB ,j h D l + ιA,i , h Group A D h, h l + ιB ,j h, h where c > h War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 16 / 50
  17. 17. Theory S2: Distribution of "Cooperative Spirit" We assume ι to be a continuous random variable, i.i.d. across agents, drawn from a distribution with c.d.f. F J : R ! [0, 1] Group A can be of two types: F A 2 fF + , F g, where F + …rst-order stochastically dominates F Group A is civic (trustworthy) if F A = F + , and is uncivic if F A = F F B has a unique realization (for tractability) War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 17 / 50
  18. 18. Theory S2: Cooperation in Trade The optimal strategy (C vs. D) depends on the proportion 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 War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 18 / 50
  19. 19. Theory S2: Trade Surplus Trade surplus accruing to group A and B k k k SA = h + znA nB k k k SB = h + znA nB Z ∞ l z k nB l z k nA Z ∞ (l ι) dF k (ι) (l ι) dF k (ι) where k 2 f+, g denotes group A’ type s Within-group transfers rule out (within-group) ine¢ ciencies + + Note: SA SA and SB SB War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 19 / 50
  20. 20. Theory S1: Stochastic war War has a stochastic pay o¤ Motivation: good and bad times to make war... ˜ Discrete support, V 2 fV H , V , V L g such that ˜ ˜ if V = V H V = V L war (peace) is always optimal We call these states war shocks and peace shocks The associated probabilities are λW and λP ˜ If V = V war or peace may be chosen depending on the economic surplus. We call this state "business as usual" (BAU) If S k > V group A chooses peace under BAU If S k < V group A chooses war under BAU ˜ The realization of V is observed before war decision War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 20 / 50
  21. 21. 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 unique if k = +, group A keeps peace under BAU if k = , group A wages war under BAU War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 21 / 50
  22. 22. Theory Imperfect information Assume group B does not observe: 1 2 group A’ type s ˜ the realization of V Characterize the PBE Solve the game backwards War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 22 / 50
  23. 23. Theory Imperfect information (trade) Let π P denotes the posterior belief (after peace) that A is civic Group A: invest if l ιA,i k z nB ) nA = F k (znB ) Group B: invest if ιB ,i + z E [nA j π P ] ) nB = F B π P znA + 1 πP znA Fixed point yields: nB = nB + P π ! War Signals (Estonian Economic Association 2014) + + , nA = nA War Signals + P π ! , nA = nA + P π ! January 31, 2014 23 / 50
  24. 24. Theory Imperfect information (surplus) Surplus of group A (relevant for war waging decision) ! Z + Sk πP k = h + znA π P nB π P ∞ (l l z nB (p ) ι) dF k (ι) Note: due to strategic complementarity, pessimistic beliefs yield a collapse of trade surplus irrespective of the true type War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 24 / 50
  25. 25. Theory Imperfect information (group A’ trade surplus) s Figure: V is pay-o¤ of war under BAU. For π P < π , group A wages war (under BAU) irrespective of its type. For π P π , group A does not wage war (under BAU) if it is of the civic type War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 25 / 50
  26. 26. 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: π P = π t +1 > π t t After war: π t +1 < π t In the "uninformative" region: π t +1 = π t no matter what War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 26 / 50
  27. 27. Dynamics Dynamic equilibrium Let rt = πt 1 πt (likelihood ratio, r 2 (0, ∞)) war peace Trap r War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 27 / 50
  28. 28. Dynamics Dynamic equilibrium (cont.) In the informative equilibrium region, beliefs follow an asymmetric random walk with drift 8 > ln rt 1 + ln 1 λW if Peace > λP < ln rt = > > : ln rt 1 ln 1 λP if War λW 8 < 1 λP if k=Pr (WAR ) = : λW if k=+ In the war trap ln rt = ln rt 1 Pr (WAR ) = 1 λP War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 28 / 50
  29. 29. Dynamics Dynamic equilibrium (cont.) ln rt peace war Non-recurrent states 45° ln λW r 1 − λP ln r ln rt −1 Figure: Dynamics of beliefs War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 29 / 50
  30. 30. Dynamics "Unwarranted" war traps Suppose group A is civic (k=+) ... but B does not know it Yet, a sequence of low-probability war shocks can drive the economy into a (permanent) war trap War shock War shock War shock Trap r War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 30 / 50
  31. 31. Dynamics Dynamic equilibrium (cont.) 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 War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 31 / 50
  32. 32. 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 perfect learning, i.e., rt ! ∞, and war incidence stays low ( λW ). (iii) The probability PTRAP has the following bounds: 0< λW r < PTRAP 1 λP r0 War Signals (Estonian Economic Association 2014) War Signals r < 1. r0 January 31, 2014 32 / 50
  33. 33. Dynamics Proof (sketch) The proof is based on the Martingale Convergence Theorem: π t converges almost surely to a limit It is easy to prove that the limit cannot lie in the interior of the informative region, thus either π t enters the trap or limt !∞ π t = 1 War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 33 / 50
  34. 34. Dynamics Proof (sketch) Suppose A is uncivic Then, limt !∞ π t = 1 induces a contradiction (i.e., the economy converges to a war trap with prob. one) Suppose limt !∞ π t = 1, then the economy must remain forever in the informative region But, then, the Law of Large Numbers would imply that B could observe an in…nite no. of realizations of the war/peace process, and eventually learn the truth, i.e., that A is uncivic A contradiction Suppose A is civic Then, group B can learn asymptotically the truth (i.e., limt !∞ π t = 1) with positive probability However, a …nite no. of war shocks precipitates the economy into the war trap. This happens with positive probability (since it takes a …nite no. of steps to enter the traps) War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 34 / 50
  35. 35. Dynamics Taking stock In summary, supposing A is civic: With a positive probability the economy converges to perfect (correct) learning With a positive probability the economy stops learning We can provide bounds to the probability 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). War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 35 / 50
  36. 36. Extensions Extensions Altruistic agents: Internalize the negative e¤ect of war on future generations Characterize the Markov equilibrium of the dynamic game Stochastic types With a positive probability group A’ type changes s (Markov switching probability) Peace trap together with war traps Learning from trade Traders acquire some private information about the other group’ type s War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 36 / 50
  37. 37. Extensions Stochastic types Cultural shocks drive shifts of group A’ type s (e.g., ancient Vikings vs modern Scandinavians) As time goes by the discredit of group B washes away Can war traps be averted? War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 37 / 50
  38. 38. Extensions Stochastic types (cont.) Two-state Markov chain: + k + 1 θ φ θ 1 φ φ 1/2 and θ 1/2, implying a positive autocorrelation The unconditional (long run) likelihood ratio that A is civic is r = φ/θ ˆ The type shock is realized at the beginning of each period, before war decision War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 38 / 50
  39. 39. Extensions Stochastic types (cont.) Posterior at t now di¤ers from prior at t+1 Bayes rule yields (1 θ )rt 1 + φ θrt 1 + 1 φ In the informative region, after war and peace 8 > r (rt 1 ) 1 λλW if peace < ˜ P rt = > λW : r (r ) ˜ t 1 if war 1 λP r (rt ˜ 1) = In uninformative region (irrespective of war/peace) rt = r (rt ˜ 1) = (1 θ )rt 1 + φ θrt 1 + 1 φ Three possibilities War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 39 / 50
  40. 40. Extensions Stochastic types (cont.) CASE 1: TRAP r(t+1) r(t) uninformative region War Signals (Estonian Economic Association 2014) informative region War Signals January 31, 2014 40 / 50
  41. 41. Extensions Stochastic types (cont.) CASE 2: NO TRAP r(t+1) ergodic set r(t) uninf. region War Signals (Estonian Economic Association 2014) informative region War Signals January 31, 2014 41 / 50
  42. 42. Extensions Stochastic types (cont.) CASE 3: CYCLES r(t+1) ergodic set r(t) uninform. region War Signals (Estonian Economic Association 2014) informative region War Signals January 31, 2014 42 / 50
  43. 43. Extensions Peace Traps Figure: Surplus from trade and war bene…ts; the case of two traps. War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 43 / 50
  44. 44. Extensions Peace Traps ln rt peace Non-recurrent states Non-recurrent states war 45° ln λW r 1 − λP ln r ln r * ln r ln rt −1 Figure: Dynamics of beliefs with two traps War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 44 / 50
  45. 45. Extensions Learning from trade Agents can acquire and retain some information through 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, the child of an informed parent fails to receive the information. War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 45 / 50
  46. 46. Extensions Learning from trade Suppose the proportion of informed players is exogenous Informed players reduce the scope of learning traps Figure: Trade surplus with di¤erent proportion of informed players, ι. War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 46 / 50
  47. 47. Extensions Learning from trade Suppose k=+ and ι is endogenous Now, peace periods have the additional virtue that 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, ι t +1 = (1 θ )[ιt + (1 Wt ) τ (1 ιt )] Result no. 1: For large enough θ a war trap continue to exist War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 47 / 50
  48. 48. 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 scant wars make fall the economy "deeper" into the uninformative region however, a sequence of peace shocks (by inducing trade and learning) can rescue the economy War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 48 / 50
  49. 49. 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 about successful inter-ethnic business partnerships targeted human capital subsidies reducing the cost of trading with the other groups (e.g., learning languages, customs) changes in social norms (persuasion campaign?) War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 49 / 50
  50. 50. 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 externalities in …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 rivalries Nash equilibrium)e¤ort depends on groups’centrality structural estimation based on Congo (DRC) war policy: key player analysis War Signals (Estonian Economic Association 2014) War Signals January 31, 2014 50 / 50

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