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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

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

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

Economy

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

Coercive International Political Economy: Data

Sample Countries

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

Thank You

brendancooley.com

[email protected]

Table of Contents

Appendix

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

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)

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

Back

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

Military Expenditure

Back

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)

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
Attacker FE?
* p < 0.1, ** p < 0.05, *** p < 0.01

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