A Quantitative Bargaining Theory of War Key concepts in bargaining - - PowerPoint PPT Presentation

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A Quantitative Bargaining Theory of War Key concepts in bargaining - - PowerPoint PPT Presentation

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Kristopher W. Ramsay Brenton Kenkel September 3, 2016 A Quantitative Bargaining Theory of War Key concepts in bargaining model of war: Military strength Resolve/cost of fighting Prior beliefs/uncertainty How can we measure these

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SLIDE 1

A Quantitative Bargaining Theory of War

Brenton Kenkel Kristopher W. Ramsay September 3, 2016

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SLIDE 2

Introduction

Key concepts in bargaining model of war:

  • Military strength
  • Resolve/cost of fighting
  • Prior beliefs/uncertainty

How can we measure these theoretical quantities in terms of

  • bservable characteristics of states?
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SLIDE 3

Approach

  • 1. Write down bargaining model of war
  • 2. Model exogenous parameters as functions of data
  • 3. Assume data generated by equilibrium behavior
  • 4. Structurally estimate
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SLIDE 4

Bargaining model

Sides A and B, each with ≥ 1 constituent states

  • 1. Side A offers x ∈ R
  • 2. Side B accepts or rejects
  • Accept → A gets x, B gets 1 − x
  • Reject → each pays θk, war occurs

War costs θA, θB i.i.d. Exponential(λ)

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SLIDE 5

War-fighting model

Each state expends effort ei ≥ 0 Probability Side A wins: pA = ∑

j∈A mjej

∑

j∈A mjej + ∑ j∈B mjej

War payoffs: uA = pA − θA − ∑

j∈A

cjej uB = 1 − pA − θB − ∑

j∈B

cjej

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SLIDE 6

Empirical parameterization

Crisis level

  • Shape of prior beliefs: λ

exp W

  • Contiguity
  • Preference Similarity
  • Rivalry
  • Major Power Involvement
  • Peace Years

State level

  • Military effectiveness: mi

exp Xi

  • GDP
  • Population
  • Military Quality
  • Marginal cost of effort: ci

exp Zi

  • Imports/GDP
  • Democracy
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SLIDE 7

Empirical parameterization

Crisis level

  • Shape of prior beliefs: λ = exp(Wα)
  • Contiguity
  • Preference Similarity
  • Rivalry
  • Major Power Involvement
  • Peace Years

State level

  • Military effectiveness: mi

exp Xi

  • GDP
  • Population
  • Military Quality
  • Marginal cost of effort: ci

exp Zi

  • Imports/GDP
  • Democracy
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SLIDE 8

Empirical parameterization

Crisis level

  • Shape of prior beliefs: λ = exp(Wα)
  • Contiguity
  • Preference Similarity
  • Rivalry
  • Major Power Involvement
  • Peace Years

State level

  • Military effectiveness: mi

exp Xi

  • GDP
  • Population
  • Military Quality
  • Marginal cost of effort: ci

exp Zi

  • Imports/GDP
  • Democracy
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SLIDE 9

Empirical parameterization

Crisis level

  • Shape of prior beliefs: λ = exp(Wα)
  • Contiguity
  • Preference Similarity
  • Rivalry
  • Major Power Involvement
  • Peace Years

State level

  • Military effectiveness: mi = exp(Xiβ)
  • GDP
  • Population
  • Military Quality
  • Marginal cost of effort: ci

exp Zi

  • Imports/GDP
  • Democracy
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SLIDE 10

Empirical parameterization

Crisis level

  • Shape of prior beliefs: λ = exp(Wα)
  • Contiguity
  • Preference Similarity
  • Rivalry
  • Major Power Involvement
  • Peace Years

State level

  • Military effectiveness: mi = exp(Xiβ)
  • GDP
  • Population
  • Military Quality
  • Marginal cost of effort: ci

exp Zi

  • Imports/GDP
  • Democracy
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SLIDE 11

Empirical parameterization

Crisis level

  • Shape of prior beliefs: λ = exp(Wα)
  • Contiguity
  • Preference Similarity
  • Rivalry
  • Major Power Involvement
  • Peace Years

State level

  • Military effectiveness: mi = exp(Xiβ)
  • GDP
  • Population
  • Military Quality
  • Marginal cost of effort: ci = exp(Ziγ)
  • Imports/GDP
  • Democracy
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SLIDE 12

Empirical parameterization

Crisis level

  • Shape of prior beliefs: λ = exp(Wα)
  • Contiguity
  • Preference Similarity
  • Rivalry
  • Major Power Involvement
  • Peace Years

State level

  • Military effectiveness: mi = exp(Xiβ)
  • GDP
  • Population
  • Military Quality
  • Marginal cost of effort: ci = exp(Ziγ)
  • Imports/GDP
  • Democracy
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SLIDE 13

Data

Militarized Interstate Disputes, 1816–2001

  • N = 2,295 disputes, with 5,451 total participants
  • War: 0 or 1
  • Winner: A, B, or censored
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SLIDE 14

Data structure

Crisis level

Dispute War Winner Contiguity Rivalry ...

  • 1

. 2 1 A 1 3 . 1 ...

State level

Dispute Side GDP Population ...

  • 1

A 0.4 6.4 1 B 7.8 3.1 2 A 0.8 5.6 2 A 4.2 6.4 2 B 6.2 8.6 3 A 1.3 2.0 3 B 7.9 8.4 ...

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SLIDE 15

Parameter estimates

α: ln(1 + Peace Years) α: Major Power–Both α: Major Power–Either α: Rivalry α: Preference Similarity α: Contiguity β: ln(1 + Military Quality) β: ln(Population) β: ln(GDP) γ: Democracy γ: ln(1 + Import Percentage) Prior Beliefs

  • Mil. Effectiveness

Effort Cost

  • 1.0
  • 0.5

0.0 0.5 1.0

Estimate ± 1.96se

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SLIDE 16

Equilibrium quantities: USA vs. Russia

0.4 0.5 0.6 0.7 1850 1900 1950 2000

Probability USA wins war

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SLIDE 17

Equilibrium quantities: USA vs. Russia

1.0 1.5 1850 1900 1950 2000

Optimal offer by USA

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SLIDE 18

Equilibrium quantities: USA vs. Russia

0.00 0.05 0.10 0.15 1850 1900 1950 2000

Probability of war

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SLIDE 19

Conclusions and next steps

Conclusions

  • Bargaining model has empirical content
  • Major powers, similar preferences → more uncertainty
  • Rivals, long time at peace → less uncertainty
  • No discernible effects of economic/political characteristics on

states’ ability and willingness to wage war Next steps

  • Different variables in the effectiveness/cost equations?
  • Benchmark models for predictive comparison?
  • Other substantive applications of estimator?