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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

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
    • Findlay and O’Rourke (2007)
  • Peacetime regimes: empire, hegemony, and hierarchy
    • Gallagher and Robinson (1953), Krasner (1976), Gilpin (1981), Kindleberger (1986), Lake (2013)
    • 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)

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

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

  • Positive military capability ratio reduces costs of war, lends coercive advantage

Economic Consequences: Trade flows contract 12.4 percent in absence of coercion

Results: Preview

  • Positive military capability ratio reduces costs of war, lends coercive advantage

Economic Consequences: Trade flows contract 12.4 percent in absence of coercion

Model (Overview)

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

Sequence

  1. (\(\tilde{\bm{\tau}}\)) Governments make trade policy announcements
  2. Wars
    • Winners impose free trade on vanquished governments
  3. (\(h(\bm{\tau})\)) Economic (general equilibrium, Eaton and Kortum (2002)) 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

(\(h(\bm{\tau})\)) Economy

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

(\(h(\bm{\tau})\)) Economy

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


  • \(\color{bcOrange} \tau_{ij}\): trade barrier government \(i\) imposes on imports from \(j\)

(\(h(\bm{\tau})\)) Economy

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


\[ \color{bcOrange} \bm{\tau}_1 = \begin{pmatrix} \tau_{11} & \cdots & \cdots & \cdots & \tau_{1N} \end{pmatrix} \]


  • Government 1’s trade policy

(\(h(\bm{\tau})\)) Economy

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


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

Economy Details

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

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

  • \(\color{bcOrange} v_i \color{black} \in [1, \infty)\) 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

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

Wars I

  • 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

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

Wars II

Cost Distribution

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

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

Wars II

Cost Distribution

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

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

  • \(\color{bcOrange} \hat{C}_j\) – attacker-specific cost-shifter

Wars II

Cost Distribution

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

\[ \text{Pr}\left( \frac{1}{\hat{c}_{ji}} \leq \frac{1}{\hat{c}} \right) = \hat{F}_{ji} \left( \frac{1}{\hat{c}} \right) = \exp \left( -\frac{1}{\hat{C}_j} \left( \frac{ \color{bcOrange} M_j \color{black} }{ \color{bcOrange} M_i \color{black} } \right)^{\gamma} (Z_{ji})^{-\alpha} \hat{c}^{\eta} \right) . \]

  • \(\hat{C}_j\) – attacker-specific cost-shifter
  • \(\color{bcOrange} \frac{M_j}{M_i}\) – military capability ratio (\(\gamma = 0 \implies\) no cost advantage for military superiority)

Wars II

Cost Distribution

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

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

  • \(\hat{C}_j\) – attacker-specific cost-shifter
  • \(\frac{M_j}{M_i}\) – 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)

Probability of Peace

\[\begin{align*} \hat{H}_i \left( \hat{\tilde{\bm{\tau}}}; \bm{Z}, \bm{\theta}_m \right) &= \prod_{j \neq i} \hat{F}_{ji} \left( \left( \hat{V}_j \left( \bm{1}_i; \tilde{\bm{\tau}}_{-i} \right) - \hat{V}_j \left( \hat{\tilde{\bm{\tau}}} \right) \right)^{-1} \right) \\ &= \exp \left( - \sum_{j \neq i} - \frac{1}{\hat{C}_j} \left( \frac{M_j}{M_i} \right)^{\gamma} Z_{ji}^{-\alpha} \left( \hat{V}_j \left( \bm{1}_i; \tilde{\bm{\tau}}_{-i} \right) - \hat{V}_j \left( \hat{\tilde{\bm{\tau}}} \right) \right)^{\eta} \right) \end{align*}\]

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

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

Equilibrium

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

  • \(\bm{\theta}_m = \left( \bm{v}, \gamma, \alpha, \hat{\bm{C}} \right)\) – estimand
    • \(\bm{v}\) – revenue thresholds (preference for protectionism)
    • \(\alpha\) – loss of strength gradient (if \(\alpha > 0\))
    • \(\gamma\) – returns to military advantage (if \(\gamma > 0\))
    • \(\hat{\bm{C}}\) – country-specific cost-shifters
  • \(\bm{Z}\) – data

Identification (Intuition)

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
  • \(\alpha\) – does policy favoritism covary with distance from trade partner?
  • \(\gamma\) – does policy favoritism covary with military capability ratio?
  • \(\hat{C}_i\) – does \(i\) tend to secure favorable policies everywhere?

Data

Year: 2011

  • \(\tau_{ij}\) – aggregate policy barrier to trade imposed by country \(i\) on goods from country \(j\)
  • \(M_i\) – military expenditure
  • \(W_{ji}\) – centroid-centroid distances (Weidmann, Kuse, and Gleditsch 2010)

Economy Calibration (\(h(\bm{\tau})\))

  • Trade flows
  • National accounts (gdp, gross consumption)
  • Parameters
    • share of intermediates in traded goods
    • share of consumer expenditure spend on traded goods
    • trade elasticity

In-Sample Countries

  • RoW: Aggregate outside economy (cannot coerce or be coerced)
    • Non-ROW countriies: 72 percent of world GDP
  • EU: Aggregate trade policy and military capacity
    • Country-level estimation coming soon

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)

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

Uncertainty

  • Bootstrap policy estimates (\(\tau_{ij}\)) and recompute \(\bm{\theta}_m\) (In progress)

Results (Preferences)

Results (Power)

  • \(\gamma =\) 1.54: increasing returns to military advantage
  • \(\alpha =\) -0.55: inverse loss of strength gradient

Likelihood of War

Counterfactual: A Coercion-Free World

  • Impose \(c_{ji} = \infty\) for all \(i, j\), recompute \(\bm{\tau}^\star(\bm{\theta}_m, \bm{Z})\),
    • \(h \left( \bm{\tau}^\star(\bm{\theta}_m, \bm{Z}) \right)\) for trade flows

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]

Table of Contents

Estimated Policy Barriers to Trade

Back (Gunboats)

Back (TOC)

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)

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

Back (Economy)

Back (TOC)

Cost Distribution

Fréchet distribution. Source Back (Wars)

Back (TOC)

Military Expenditure

Back (Data)

Back (TOC)

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

Back (Data)

Back (TOC)

Conquest Values

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

Back (TOC)


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