\[ \require{color} \definecolor{bcOrange}{RGB}{189,97,33} \definecolor{bcYellow}{RGB}{189,142,40} \newcommand\iddots{\mathinner{ \kern1mu\raise1pt{.} \kern2mu\raise4pt{.} \kern2mu\raise7pt{\Rule{0pt}{7pt}{0pt}.} \kern1mu }} \DeclareMathOperator*{\argmax}{arg\,max} \DeclareMathOperator*{\argmin}{arg\,min} \newcommand{\bm}[1]{\boldsymbol{\mathbf{#1}}} \newcommand{\ubar}[1]{\underline{#1}} \]

Trade Policy in the Shadow of Power

Quantifying Military Coercion in the International System

9 April 2020

Brendan Cooley

Ph.D. Candidate

Princeton University

bcooley (at) princeton.edu

These slides available at brendancooley.com/tpsp

Introduction

Power and Preferences

“A has power over B to the extent that he can get B to do something that B would not otherwise do.”

Dahl (1957)

Power in Anarchy

Anarchy: no higher authority to compel states to resolve disputes peacefully
Anarchy \(\implies\) powerful governments can impose policies on others by force
Bargaining critique: policies adjust to reflect shadow of power
- Brito and Intrilagator (1985), Fearon (1995), Art (1996); Powell (1999)

Detecting the Exercise of Power: An Inference Problem

Dahl: What would B do in the absence of A’s power?
Do observed policies reflect preferences of the governments that adopted them or constraints of anarchy?

Trade Policy and Gunboat Diplomacy

What Do Governments Want?

Protectionism at home (Grossman and Helpman 1994; Gawande, Krishna, and Olarreaga 2009)
- Domestic distributional conflict: Mayer (1984), Rogowski (1987); Grossman and Helpman (1994)
- Fiscal capacity: Rodrik (2008), Queralt (2015)
Openness abroad (Grossman 2016)
- Market access externalities: Ossa (2011), Ossa (2012)
- Lobbying and Trade Policy: Firms pressure governments to negotiate reductions in trade barriers abroad (Osgood 2016; Kim 2017)

Conflicts of Interest and Gunboat Diplomacy

Powerful governments impose openness on weaker counterparts
- Viner (1948), Findlay and O’Rourke (2007)
Peacetime regimes: empire, hegemony, and hierarchy
- Gallagher and Robinson (1953), Krasner (1976), Gilpin (1981), Kindleberger (1986), Lake (2007)
- Economic effects: Berger et al. (2013)

Does Trade Policy Matter?

Tariffs small, aggregate policy-induced trade frictions large
- ~order of magnitude larger than tariffs (Cooley 2019) (barriers)
Welfare effects of trade frictions
- Autor, Dorn, and Hanson (2013), Costinot and Rodríguez-Clare (2015), Goldberg and Pavcnik (2016)

Anarchy and Inference: Approach

A Coercive International Political Economy

\[ \left\{ \bm{\theta}, \bm{M} \right\} \rightarrow \bm{\tau} \]

Observables
- \(\bm{M}\) – governments’ military endowment (expenditure)
- \(\bm{\tau}\) – governments’ trade policies
Unobservables (\(\bm{\theta}\))
- \(\bm{v}\) – governments’ preferences for protectionism
- \(\gamma\) – returns to military force in coercive capacity
- \(\alpha\) – geographic loss of strength gradient (Boulding 1962; Bruce Bueno de Mesquita 1980; Diehl 1985; Lemke 1995; Gartzke and Braithwaite 2011; Markowitz and Fariss 2013)

Estimation: \(\left\{ \bm{\tau}, \bm{M} \right\} \rightarrow \tilde{\bm{\theta}}\)

Counterfactuals: \(\left\{ \bm{\theta}^\prime, \bm{M}^\prime \right\} \rightarrow \bm{\tau}^\prime\)

Shadow of power
- Effect of changing military endowments on trade policy
Liberal/commercial peace
- Effect of changing preferences for openness on probability of war

Results: Preview

Economic Consequences of Coercion: Increases value of global trade 63 percent

Results: Preview

Economic Consequences of Coercion: Increases value of global trade 63 percent

Data

Economic Effects of Endogenous Trade Frictions

Choice variables

\[ \bm{\tau} = \begin{pmatrix} \tau_{11} & \cdots & \cdots & \cdots & \tau_{1N} \\ \vdots & \ddots & \vdots & \iddots & \vdots \\ \vdots & \cdots & \tau_{ij} & \cdots & \vdots \\ \vdots & \iddots & \vdots & \ddots & \vdots \\ \tau_{N1} & \cdots & \cdots & \cdots & \tau_{NN} \end{pmatrix} \]

\(\tau_{ij}\) – tax government \(i\) imposes on imports from country \(j\)
\(\bm{\tau}_i\) – government \(i\)’s policy vector
Measurement: Cooley (2019) (magnitudes)

Economy

\[ h(\bm{\tau}; \bm{Z}_h, \bm{\theta}_h) \rightarrow \begin{pmatrix} w_1 \\ \vdots \\ w_N \end{pmatrix} = \bm{w} \]

Model: variant of Eaton and Kortum (2002) workhorse
\(\bm{Z}_h\) – economic data
- national accounts, price levels, trade flows, freight costs
\(\bm{\theta}_h\) – economic parameters (calibration)

Coercive International Political Economy: Data

Sample Countries

Year: 2011
RoW: Aggregate outside economy
- cannot coerce or be coerced
- Non-ROW countries: 72 percent of world GDP
EU: Aggregate trade policies and military capacities

War Costs

\[ c_{ij} \sim F \left( \bm{\theta}_m; \bm{Z}_m \right) \]

\(c_{ij}\) – cost government \(i\) pays to attack government \(j\)
\(\bm{Z}_m\) – observable dyadic features
- \(M_{i} / M_{j}\) – military expenditure ratio (data)
- \(W_{ij}\) – centroid-centroid distance between \(i\) and \(j\)
\(\bm{\theta}_m\) – estimand

Reduced Form Evidence

Model

Model (Overview)

Governments indexed \(i \in \left\{ 1, ..., N \right\}\)

Sequence

(\(\tilde{\bm{\tau}}\)) Governments make trade policy announcements
Wars
- Winners impose free trade on conquered governments
(\(h(\bm{\tau})\)) Economic consequences of announced/imposed trade policies

Payoffs

\[ V_i \left( h(\bm{\tau}); \color{bcOrange} v_i \color{black} \right) \]

\(\color{bcOrange} v_i\) - latent preference for protectionist policies

Government Objective

Wars

Directed dyad-specific war costs held as private information to prospective attacker
- \(c_{ji}\) – cost \(j\) incurs to invade \(i\)
Wars fought to impose free trade on target

\[ \bm{\tau}_i^\prime = \left( 1, \dots, 1 \right) = \bm{1}_i \]

Conquest Values

\(V_j(\bm{1}_i; \tilde{\bm{\tau}}_{-i})\) – \(j\)’s value for imposing free trade on \(i\)

Peace Condition

\[ V_j \left( \bm{1}_i, \tilde{\bm{\tau}}_{-i}; v_j \right) - c_{ji} \leq V_j \left( \tilde{\bm{\tau}}, v_j \right) \]

Probability of Peace

\[ \text{Pr}\left( \frac{1}{c_{ji}} \leq \frac{1}{V_j \left( \bm{1}_i, \tilde{\bm{\tau}}_{-i}; v_j \right) - V_j \left( \tilde{\bm{\tau}}, v_j \right)} \right) = F_{ji} \left( \frac{1}{V_j \left( \bm{1}_i, \tilde{\bm{\tau}}_{-i}; v_j \right) - V_j \left( \tilde{\bm{\tau}}, v_j \right)} \right) \]

Cost Distribution, Functional Form

Optimal Policies

Risk-return tradeoff: ideal policies balance policy optimality against threat of war
- Lower tariffs on goods from countries that pose military threats

Best Response

\[ \max_{\bm{\tau}_i} \quad \underbrace{\hat{H}_i(\hat{\tilde{\bm{\tau}}}; \bm{Z}_m, \bm{\theta}_m) \hat{V}_i(\hat{\tilde{\bm{\tau}}})}_{\text{peace}} + \underbrace{\left( 1 - \hat{H}_i(\hat{\tilde{\bm{\tau}}}; \bm{Z}_m, \bm{\theta}_m) \right) \hat{V}_i(\bm{1}_i; \hat{\tilde{\bm{\tau}}}_{-i})}_{\text{war}} \]

Equilibrium (in changes)

\[ \bm{\tau}^\star(\bm{\theta}_m, \bm{Z}_m) \]

\(\bm{\theta}_m = \left( \bm{v}, \gamma, \alpha_1, \alpha_2 \right)\) – estimand
- \(\bm{v}\) – revenue thresholds (preference for protectionism)
- \(\gamma\) – returns to military advantage (if \(\gamma > 0\))
- \(\alpha_1\) – loss of strength gradient (if \(\alpha_1 > 0\))
- \(\alpha_2\) – returns to gdp (if \(\alpha_2 > 0\))
\(\bm{Z}_m\) – data

Calibration and Identification

Estimation

Measurement Error: \(\tau_{ij} = \tau_{ij}^\star(\bm{\theta}_m, \bm{Z}) + \epsilon_{ij}\)

Moment Estimator

\[ \min_{\bm{\theta}_m} \quad \sum_i \sum_j \left( \epsilon_{ij}(\bm{\theta}_m, \bm{Z}) \right)^2 \]

Mathematical Program with Equilibrium Constraints (MPEC) (Su and Judd 2012)

\[\begin{equation*} \begin{split} \min_{ \bm{\theta}_m, \hat{\tilde{\bm{\tau}}}, \hat{\bm{w}}, \hat{\bm{w}}^\prime, \bm{\lambda} } & \quad \sum_i \sum_j \left( \epsilon_{ij} \right)^2 & \quad \text{} \\ \text{subject to} & \quad \nabla_{\hat{\tilde{\bm{\tau}}}_i} \mathcal{L}_i(\hat{\tilde{\bm{\tau}}}, \hat{\bm{w}}, \bm{\lambda}_i; \bm{\theta}_m) = \bm{0} \text{ for all } i & \quad \text{Policy Optimality} \\ & \quad \hat{\bm{w}} = \hat{h} \left( \hat{\tilde{\bm{\tau}}} \right) & \quad \text{GE (Proposed Policies)} \\ & \quad \hat{\bm{w}}_i^\prime = \hat{h} \left( \bm{1}_i, \hat{\tilde{\bm{\tau}}}_{-i} \right) \text{ for all } i & \quad \text{GE (Imposed Policies)} \end{split} \end{equation*}\]

Best Response MPEC

Uncertainty: Nonparametric bootstrap (sample policy estimates (\(\tau_{ij}\)) and recompute \(\tilde{\bm{\theta}}_m\))

Results

Parameters

Model Fit Errors Non-Coercive Model Non-Coercive Model Fit

War Costs

Conquest Values

War Probabilities

Counterfactuals

Counterfactuals (Overview)

Counterfactual Policies \(\tilde{\bm{\tau}}^\star(\bm{\theta}_m^\prime; \bm{Z}_m^\prime)\)

\(\bm{\theta}_m^\prime\) – counterfactual parameters (e.g. preferences)
\(\bm{Z}_m^\prime\) – counterfactual data (e.g. military expenditure)

Economic Effects of Counterfactual Policies

\[ h \left( \tilde{\bm{\tau}}^\star(\bm{\theta}_m^\prime; \bm{Z}_m^\prime) \right) \]

Scenarios

A Coercion-Free World
Multipolarity, Trade Policy, and International Trade
Chinese Preference Liberalization and the Risk of War

Coercion-Free World: Policies

Coercion-Free World: Trade

Moving from pacifism to 2011 military expenditure levels \(\rightarrow\) 63 percent increase in value of world trade

Coercion-Free World: Trade

Moving from pacifism to 2011 military expenditure levels \(\rightarrow\) 63 percent increase in value of world trade

Coercion-Free World: Welfare

Conclusions

Conclusion

Shadow of Power in International Political Economy

Quantify governments’ welfare under counterfactual imposition of free trade abroad
- Use difference between factual welfare and welfare under this counterfactual to identify parameters governing technology of coercion in international relations

Results
- Returns to military advantage
- Loss of strength gradient

The Persistence of Hegemony/Hierarchy in International Relations

Power politics of international trade regime
- Hegemon compels openness from recalcitrant followers
- Gallagher and Robinson (1953), Krasner (1976), Gilpin (1981), Kindleberger (1986), Lake (2013)
- Largely theoretical literature due to difficulty in constructing counterfactual

What policies would governments adopt in anarchy’s absence?
- Significantly more protectionist world

Thank You

brendancooley.com

[email protected]

Appendix: Introduction

Bargaining, Trade, and War

Institutionalized Bargaining

Models of GATT/WTO: reciprocity and nondiscriminination
- Grossman and Helpman (1995), Maggi (1999), Bagwell and Staiger (1999)
Institutions and incentive compatibility: war as an outside option (Powell 1994)

Trade as Means

Governments pursue “political” ends (e.g. security), trade used as coercive instrument
- Hirschman (1945), Gowa and Mansfield (1993), Martin, Mayer, and Thoenig (2012), Seitz, Tarasov, and Zakharenko (2015)
Security and power are themselves means to achieve other ends

Power and Exchange

Prices and power in the marketplace
- Skaperdas (2001), Piccione and Rubinstein (2007), Garfinkel, Skaperdas, and Syropoulos (2011), Carroll (2018)
Trade frictions as choice variable here

Appendix: Data

Estimated Trade Frictions

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Economy (Consumption)

Consumer’s Problem

\[\begin{equation*} \begin{split} \max & \quad U_i = Q_i^{\nu_i} S_i^{1 - \nu_i} \\ \text{subject to} & \quad P_i Q_i + P_i^s S_i \leq w_i L_i \end{split} \end{equation*}\]

CES Preferences over Tradable Varieties

\[ Q_i = \left( \int_{[0,1]} \alpha_{h(\omega)}^{\frac{1}{\sigma}} q_i(\omega)^{\frac{\sigma - 1}{\sigma}} d \omega \right)^{\frac{\sigma}{\sigma - 1}} \]

Tradable Price Index

\[ P_i = \left( \int_{[0,1]} \alpha_{h(\omega)} p_i(\omega)^{1 - \sigma} d \omega \right)^{\frac{1}{1 - \sigma}} \]

Expenditure on Tradables

\[ E_i^q = \nu_i I_i + D_i = P_i Q_i^\star \]

Economy (Production)

Costs

\[\begin{equation} \label{eq:c} c_i = w_i^{1 - \beta} P_i^{\beta} \end{equation}\]

\(w_i\) - cost of labor
\(P_i\) - cost of composite intermediate good
- equivalent to composite consumption good

\[ E_i^x = \beta X_i \]

Local Prices

\[ p_{ii}(\omega) = \frac{c_i}{z_i(\omega)} \]

Technology (Fréchet)

\[ F_i(z) = \text{Pr} \left\{ z_i(\omega) \leq z \right\} = \exp \left\{ - T_i z^{-\theta} \right\} \]

Economy (Equilibrium)

Total Expenditure on Tradables

\[ X_i = \underbrace{E_i^q + E_i^x}_{E_i} - D_i \]

Trade Shares

\[ \Omega_{ij}^\star = \left\{ \omega \in [0,1] \left. \right\vert p_{ij}(\omega) \leq \min_{k \neq j} \left\{ p_{ik} \right\} \right\} \]

\[ \lambda_{ij}(\boldsymbol{w}) = \frac{1}{E_i} \int_{\Omega_{ij}^\star} p_{ij}(\omega) q_i \left( p_{ij} (\omega) \right) d \omega \]

Market Clearing

\[ X_i = \sum_{j=1}^N \lambda_{ji}(\boldsymbol{w}) E_j \]

Economy (Equilibrium in Changes)

\[ \hat{r}_i = \frac{1}{r_i} \left( E_i \hat{E}_i(\hat{\bm{w}}) - \sum_j X_{ij}^{\text{cif}} \hat{X}_{ij}^{\text{cif}}(\hat{\bm{w}}) \right) \] \[ \hat{w}_i = \frac{1}{\nu_i w_i L_i} \left( \sum_j \left( (1 - \beta) X_{ji}^{\text{cif}} \hat{X}_{ji}^{\text{cif}}(\hat{\bm{w}}) \right) + (1 - \nu_i) r_i \hat{r}_i(\hat{\bm{w}}) \right) \] \[ \hat{E}_i(\hat{\bm{w}}) = \frac{1}{E_i} \left( E_i^q \hat{E}_i^q(\hat{\bm{w}}) + E_i^x \hat{E}_i^x(\hat{\bm{w}}) \right) \] \[ \hat{x}_{ij}(\hat{\bm{w}}) = \left( \hat{\tau}_{ij} \hat{w}_j^{1 - \beta} \hat{P}_j(\hat{\bm{w}})^\beta \right)^{-\theta} \hat{P}_i(\hat{\bm{w}})^{\theta} \] \[ \hat{P}_i(\hat{\bm{w}}) = \left( \sum_j x_{ij} \left( \hat{\tau}_{ij} \hat{w}_j^{1 - \beta} \hat{P}_j(\hat{\bm{w}})^\beta \right)^{-\theta} \right)^{-\frac{1}{\theta}} \] \[ 1 = \sum_i y_i \hat{w}_i \]

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Economy (Calibration I)

Trade Flows: BACI
National Accounts: OECD and WIOD

Parameters

\[ \bm{\theta}_h = \left( \bm{\nu}, \beta, \theta \right) \]

\(\nu_i\) – share of consumer expenditure spent on tradables (World Bank ICP)
\(\beta\) – share of intermediate goods in imports (WIOD)
- Average across countries in sample (0.86)
\(\theta\) – trade elasticity
- Set to 6 (Head and Mayer 2014)

Economy (Calibration II)

Deficits (Dekle, Eaton, and Kortum 2007)

\(\bm{D}\) – trade deficits
Equilibrium in changes \[ \hat{h}(\hat{\bm{\tau}}, \hat{\bm{D}}; \bm{\theta}_h) \]
Purge deficits before analysis \[ \hat{h}(\hat{\bm{\tau}}, \bm{0}; \bm{\theta}_h) \rightarrow \hat{\bm{w}}_{-D} \]
Recompute associated trade flows, price levels, etc

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Military Expenditure

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Reduced Form Evidence (Interpretive Model)

Bilateral Nash Bargaining over Trade Policy

\[\begin{equation} \begin{split} x^\star \in \argmax_x & \quad \left( u_1(x) - w_1(M_1 / M_2) \right) \left( u_2(x) - w_2(M_2 / M_1) \right) \\ \text{subject to} & \quad u_1(x) \geq w_1(M_1 / M_2) \\ & \quad u_2(x) \geq w_2(M_2 / M_1) . \end{split} \end{equation}\]

Result: Government 1’s utility increasing in \(M_1\)

Empirical Analogue

\[ \frac{u_1(x^\star; M_1, M_2)}{u_1(1)} \iff \frac{ V_i \left( h(\bm{\tau}) \right) }{ V_i \left( h(\bm{1}_j; \bm{\tau}_{-j}) \right) } \]

Empirical Conquest Value: \(V_i \left( h(\bm{1}_j; \bm{\tau}_{-j}) \right)\)

Reduced Form Evidence (Data)

Inverse Conquest Values and Military Capability Ratios
	Base	Base (Attacker FE)	Loss of Strength	Loss of Strength (Attacker FE)
Log Mil Capability Ratio	0.016***	0.033***	0.026	0.045
	(0.004)	(0.004)	(0.052)	(0.039)
Log Distance			0.003	0.002
			(0.010)	(0.008)
(Log Mil Capability Ratio) X (Log Distance)			-0.001	-0.001
			(0.006)	(0.004)
Num.Obs.	56	56	56	56
R2	0.247	0.676	0.249	0.677
R2 Adj.	0.233	0.621	0.205	0.605
F	17.720	12.251	5.739	9.421
Attacker FE?		✓		✓
* p < 0.1, p < 0.05, * p < 0.01

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Appendix: Model

Government Objective

\[ h(\bm{\tau}) \rightarrow \begin{pmatrix} w_1 \\ \vdots \\ w_N \end{pmatrix} = \color{bcOrange} \bm{w} \]

\(X_{ij}(\color{bcOrange} \bm{w} \color{black})\): \(i\)’s imports of goods from \(j\)

Revenues from Policy Distortions

\[ r_i(\color{bcOrange} \bm{w} \color{black}; v_i) = \sum_j (\tau_{ij} - v_i) X_{ij}(\color{bcOrange} \bm{w} \color{black}) \]

Government Objective

\[ h(\bm{\tau}) \rightarrow \begin{pmatrix} w_1 \\ \vdots \\ w_N \end{pmatrix} = \bm{w} \]

\(X_{ij}(\bm{w})\): \(i\)’s imports of goods from \(j\)

Revenues from Policy Distortions

\[ r_i(\bm{w}; \color{bcOrange} v_i \color{black}) = \sum_{j \neq i} (\tau_{ij} - \color{bcOrange} v_i \color{black}) X_{ij}(\bm{w}) \]

\(\color{bcOrange} v_i \color{black} > 0\) controls \(i\)’s preferences over the level of protection

Adjusted Consumer Income: \(\tilde{Y}_i(\bm{w}) = w_i L_i + r_i(\bm{w}; \color{bcOrange} v_i \color{black})\)

Indirect Utility

\[ V_i \left( h(\bm{\tau}); \color{bcOrange} v_i \color{black} \right) \]

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Equilibrium in Changes

Peace Condition

\[ \hat{c}_{ji}^{-1} \leq \left( \hat{V}_j \left( \bm{1}_i; \hat{\tilde{\bm{\tau}}}_{-i} \right) - \hat{V}_j \left( \hat{\tilde{\bm{\tau}}} \right) \right)^{-1} \]

Objective Function

\[ \hat{G}_i(\hat{\tilde{\bm{\tau}}}) = \hat{H}_i(\hat{\tilde{\bm{\tau}}}; \bm{Z}, \bm{\theta}_m) \hat{V}_i(\hat{\tilde{\bm{\tau}}}) + \left( 1 - \hat{H}_i(\hat{\tilde{\bm{\tau}}}; \bm{Z}, \bm{\theta}_m) \right) \hat{V}_i(\bm{1}_i; \hat{\tilde{\bm{\tau}}}_{-i}) \]

Equilibrium

\[ \hat{\tilde{\bm{\tau}}}^\star(\bm{\theta}_m; \bm{Z}_m) \]

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Wars II

Cost Distribution

\[ \hat{c}_{ji} = \frac{c_{ji}}{V_j \left( \bm{\tau}; v_j \right)} \]

\[ \text{Pr}\left( \frac{1}{\hat{c}_{ji}} \leq \frac{1}{\hat{c}} \right) = \hat{F}_{ji} \left( \frac{1}{\hat{c}} \right) = \exp \left( -\frac{1}{\hat{C}} \left( \frac{M_j}{M_i} \right)^{\gamma} W_{ji}^{-\alpha_1} Y_j^{\alpha_2} \hat{c}^{\eta} \right) \]

Wars II

Cost Distribution

\[ \hat{c}_{ji} = \frac{c_{ji}}{V_j \left( \bm{\tau}; v_j \right)} \]

\[ \text{Pr}\left( \frac{1}{\hat{c}_{ji}} \leq \frac{1}{\hat{c}} \right) = \hat{F}_{ji} \left( \frac{1}{\hat{c}} \right) = \exp \left( -\frac{1}{\hat{C}} \left( \color{bcOrange} \frac{ M_j }{ M_i } \color{black} \right)^{\gamma} W_{ji}^{-\alpha_1} Y_j^{\alpha_2} \hat{c}^{\eta} \right) \]

\(\color{bcOrange} \frac{M_j}{M_i}\) – military capability ratio (\(\gamma = 0 \implies\) no cost advantage for military superiority)

Wars II

Cost Distribution

\[ \hat{c}_{ji} = \frac{c_{ji}}{V_j \left( \bm{\tau}; v_j \right)} \]

\[ \text{Pr}\left( \frac{1}{\hat{c}_{ji}} \leq \frac{1}{\hat{c}} \right) = \hat{F}_{ji} \left( \frac{1}{\hat{c}} \right) = \exp \left( -\frac{1}{\hat{C}} \left( \frac{M_j}{M_i} \right)^{\gamma} \color{bcOrange} W_{ji}^{ \color{black} -\alpha_1} \color{black} Y_j^{\alpha_2} \hat{c}^{\eta} \right) \]

\(\frac{M_j}{M_i}\) – military capability ratio (\(\gamma = 0 \implies\) no cost advantage for military superiority)
\(\color{bcOrange} W_{ji}\) – geographic distance between \(j\) and \(i\) (\(\alpha=0 \implies\) no loss of strength gradient)

Wars II

Cost Distribution

\[ \hat{c}_{ji} = \frac{c_{ji}}{V_j \left( \bm{\tau}; v_j \right)} \]

\(\frac{M_j}{M_i}\) – military capability ratio (\(\gamma = 0 \implies\) no cost advantage for military superiority)
\(W_{ji}\) – geographic distance between \(j\) and \(i\) (\(\alpha_1=0 \implies\) no loss of strength gradient)
\(\color{bcOrange} Y_j\) – attacker gdp (\(\alpha_2=0 \implies\) no advantage for larger countries)

Probability of Peace

\[ \hat{H}_i \left( \hat{\tilde{\bm{\tau}}}; \bm{Z}_m, \bm{\theta}_m \right) = \prod_{j \neq i} \hat{F}_{ji} \left( \left( \hat{V}_j \left( \bm{1}_i; \tilde{\bm{\tau}}_{-i} \right) - \hat{V}_j \left( \hat{\tilde{\bm{\tau}}} \right) \right)^{-1} \right) \]

Fréchet Distribution

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Cost Distribution

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Calibration and Identification (Intuition)

Calibration

\(\hat{C}=\) 25
\(\eta=\) 1.5

Preferences (\(\bm{v}\))

Holding military technology fixed, \(i\)’s overall level of protectionism informs about \(v_i\)
Governments with higher trade policies (more protectionist) have higher \(v_i\)

Military Technology

Holding preferences fixed, heterogeneity in observed policies informs about military parameters
\(\alpha_1\) – does policy favoritism covary with distance from trade partner?
\(\gamma\) – does policy favoritism covary with military capability ratio?

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Appendix: Estimation

Best Response MPEC

Choice Variables

\[ \hat{\bm{x}}_i = \left( \hat{\tilde{\bm{\tau}}}_i, \hat{\bm{w}} \right) \]

Best Response

\[\begin{equation*} \begin{split} \max_{\hat{\bm{x}}_i} & \quad \hat{G}_i(\hat{\bm{w}}; \bm{\theta}_m) \\ \text{subject to} & \quad \hat{\bm{w}} = \hat{h}(\hat{\tilde{\bm{\tau}}}) \end{split} \end{equation*}\]

Lagrangian: \(\mathcal{L}_i(\hat{\bm{x}}_i, \bm{\lambda}_i)\)

Optimality Condition

\[ \nabla_{\hat{\tilde{\bm{\tau}}}_i} \mathcal{L}_i(\hat{\bm{x}}_i, \bm{\lambda}_i; \bm{\theta}_m) = \bm{0} \]

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Appendix: Results

Model Fit

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Errors

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Non-Coercive Model

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Non-Coercive Model Fit

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Appendix: Counterfactuals

Multipolarity, Trade Policy, and International Trade (I)

Multipolarity, Trade Policy, and International Trade (II)

Value of global trade under multipolarization is 110.3 percent its baseline value

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Chinese Preference Liberalization and the Risk of War

\(\hat{v}_{\text{CHN}}=\) 2.77, \(v_{\text{CHN}}^\prime=\) 1.52
Reduces probability of U.S.-China war from 33.3 percent to 5.9 percent

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