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

Trade Policy in the Shadow of Power

Quantifying Military Coercion in the International System

20 February 2020

Brendan Cooley

Ph.D. Candidate

Princeton University

bcooley (at) princeton.edu

Power and Preferences

Anarchy and Inference

  • Anarchy \(\implies\) powerful governments can impose policies on others by force
  • Bargaining critique: policies reflect shadow of power
    • Brito and Intrilagator (1985), Fearon (1995), Art (1996)
  • Question: Do observed policies reflect preferences of the governments that adopted them or constraints of anarchy?

Trade Policy: What Do Governments Want?

  • Heterogeneity in desired protectionism
    • Grossman and Helpman (1994), Gawande, Krishna, and Olarreaga (2009)
  • Mercantilism induces conflicts of interest between governments
    • Gunboat diplomacy: powerful impose openness abroad (Findlay and O’Rourke 2007)

Trade Policy: Does It 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

Ideal Experiment

  • Exogenously manipulate governments’ military capacity
  • Attribute changes in trade policy to latent effect of military coercion

A Coercive International Political Economy

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

  • \(\bm{\theta}\) – structural parameters (preferences and power projection)
  • \(\bm{M}\) – governments’ military endowment (expenditure)
  • \(\bm{\tau}\) – governments’ trade policies

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 military strategies

Coercive International Political Economy

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

Sequence

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

Payoffs

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

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

Peaceful Equilibrium

\[\begin{equation*} \begin{split} \max_{ \tilde{\bm{\tau}}_i } & \quad G_i \left( h( \tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i} ) \right) \\ \text{subject to} & \quad \underbrace{\tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) G_j \left( h( \bm{1}_i; \tilde{\bm{\tau}}_{-i} ); v_j \right) + \left( 1 - \tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) \right) G_j \left( h (\tilde{\bm{\tau}} ); v_j \right) - c_j \geq 0}_{\text{war constraint}} \quad \text{for all } j \end{split} \end{equation*}\]

Peaceful Equilibrium

\[\begin{equation*} \begin{split} \max_{ \tilde{\bm{\tau}}_i } & \quad G_i \left( h( \tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i} ) \right) \\ \text{subject to} & \quad \color{bcOrange} \tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) \color{black} G_j \left( h( \bm{1}_i; \tilde{\bm{\tau}}_{-i} ); v_j \right) + \left( 1 - \color{bcOrange} \tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) \color{black} \right) G_j \left( h (\tilde{\bm{\tau}} ); v_j \right) - c_j \geq 0 \quad \text{for all } j \end{split} \end{equation*}\]

Contest Function

\[ \color{bcOrange} \tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) \color{black} = \frac{ \rho_{ji}(\bm{W}; \bm{\alpha}) M_j }{ \rho_{ji}(\bm{W}; \bm{\alpha}) M_j + M_i } \]

  • \(\rho_{ji}(\bm{W}; \bm{\alpha})\) loss of strength gradient
  • \(M_i\) military strength

Peaceful Equilibrium

\[\begin{equation*} \begin{split} \max_{ \tilde{\bm{\tau}}_i } & \quad G_i \left( h( \tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i} ) \right) \\ \text{subject to} & \quad \tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) \color{bcOrange} G_j \left( h( \bm{1}_i; \tilde{\bm{\tau}}_{-i} ); v_j \right) \color{black} + \left( 1 - \tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) \right) G_j \left( h (\tilde{\bm{\tau}} ); v_j \right) - c_j \geq 0 \quad \text{for all } j \end{split} \end{equation*}\]

Contest Function

\[ \tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) = \frac{ \rho_{ji}(\bm{W}; \bm{\alpha}) M_j }{ \rho_{ji}(\bm{W}; \bm{\alpha}) M_j + M_i } \]

  • \(\rho_{ji}(\bm{W}; \bm{\alpha})\) loss of strength gradient
  • \(M_i\) military strength

Conquest Values

\[ \color{bcOrange} G_j \left( h( \bm{1}_i; \tilde{\bm{\tau}}_{-i} ); v_j \right) \]

Peaceful Equilibrium

\[\begin{equation*} \begin{split} \max_{ \tilde{\bm{\tau}}_i } & \quad G_i \left( h( \tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i} ) \right) \\ \text{subject to} & \quad \tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) G_j \left( h( \bm{1}_i; \tilde{\bm{\tau}}_{-i} ); v_j \right) + \left( 1 - \tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) \right) G_j \left( h (\tilde{\bm{\tau}} ); v_j \right) - c_j \geq 0 \quad \text{for all } j \end{split} \end{equation*}\]

Contest Function

\[ \tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) = \frac{ \rho_{ji}(\bm{W}; \bm{\alpha}) M_j }{ \rho_{ji}(\bm{W}; \bm{\alpha}) M_j + M_i } \]

  • \(\rho_{ji}(\bm{W}; \bm{\alpha})\) loss of strength gradient
  • \(M_i\) military strength

Conquest Values

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

Equilibrium

\[ \bm{\tau}^\star(\color{bcOrange} \bm{\theta} \color{black}) \]

  • \(\color{bcOrange} \bm{\theta} \color{black}\) - estimand

Estimation

Data

  • \(\tau_{ij}\) - aggregate policy barrier to trade imposed by country \(i\) on goods from country \(j\)
    • Measurement: Cooley (2019)

Measurement Error

\[ \tau_{ij} = \tau_{ij}^\star(\bm{\theta}) + \epsilon_{ij} \]

Mathematical Program with Equilibrium Constraints (Su and Judd 2012)

\[\begin{equation*} \begin{split} \min_{\bm{\theta}, \bm{\tau}^\star} & \quad \sum_i \sum_j \left( \epsilon_{ij}(\bm{\theta}) \right)^2 \\ \text{subject to} & \quad \color{bcOrange} \nabla_{\bm{\tau}_i} \mathcal{L}_i(\bm{\theta}) \color{black} = 0 \quad \text{for all } i \end{split} \end{equation*}\]

  • \(\color{bcOrange} \nabla_{\bm{\tau}_i} \mathcal{L}_i(\bm{\theta})\) - gradient of Lagrangian

Estimates

\[ \hat{\bm{\theta}} = \left( \hat{\bm{v}}, \hat{\bm{\alpha}}, \hat{c} \right) \]

  • \(\hat{\bm{v}}\) preference for protectionism
  • \(\hat{\bm{\alpha}}\) loss of military strength over geographic distance
  • \(\hat{c}\) (relative) costs of war

Results

Dyadic War Cost-Benefit Ratios

Thank You

brendancooley.com

[email protected]

Table of Contents

(\(h(\bm{\tau})\)) 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 \(j\)
  • \(\color{bcOrange} \tau_{ij} \color{black} - 1\): ad-valorem tariff equivalent
  • \(\tau_{ij} = 1 \implies\) free trade
  • \(\tau_{ii} = 1\) for all \(i\)

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

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

Back

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

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


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

Back

Government Objective

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


  • \(V_i( \color{bcOrange} \bm{w} \color{black})\): welfare of representative consumer in \(i\)
  • \(X_{ij}(\color{bcOrange} \bm{w} \color{black})\): \(i\)’s imports of goods from \(j\)
  • Rents (tariff revenue):

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

Government Objective

\[ G_i = V_i( \color{bcOrange} \bm{w} \color{black}) r_i(\color{bcOrange} \bm{w} \color{black}; v_i) \]

Back

Economy (Consumption)

Consumer’s Problem

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

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

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

Back

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

Policy Problem in Changes

Government Welfare

\[ \hat{G}_i(\hat{\bm{\tau}}; v_i) = \hat{V}_i \left( \hat{h}(\hat{\bm{\tau}}) \right) \hat{r}_i \left(\hat{h}(\hat{\bm{\tau}}); v_i \right) \]

Constrained Policy Problem in Changes

\[\begin{equation*} \begin{split} \max_{ \hat{\tilde{\bm{\tau}}}_i } & \quad \hat{G}_i(\hat{\tilde{\bm{\tau}}}_i; \hat{\tilde{\bm{\tau}}}_{-i}) \\ \text{subject to} & \quad \hat{G}_j(\hat{\tilde{\bm{\tau}}}) - \hat{G}_j(\bm{1}_i; \hat{\tilde{\bm{\tau}}}_{-i}) + \hat{c} \left( \tilde{\chi}_{ji}(\bm{Z}; \bm{\theta}) \right)^{-1} \geq 0 \quad \text{for all } j \neq i \end{split} \end{equation*}\]

Back

Multilateral Contest Function

\[ \chi_{ij}(\bm{a}, \bm{m}) = \frac{ a_{ij} \rho_{ij}(\bm{W}; \bm{\alpha}) M_i }{ \sum_k a_{kj} \rho_{kj}(\bm{W}; \bm{\alpha}) M_k } \]

Back

Military Expenditure

Back

Protectionism Estimates

Preference Parameter (\(\tilde{\bm{v}}\)) Estimates
iso3 Country Name \(\tilde{v}_i\)
CHN China 1.106036
EU European Union 1.354114
JPN Japan 1.996520
RoW Rest of World 1.125184
RUS Russia 1.000000
USA United States 1.292219

Back

Conquest Values

Conquest Values

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

Back

Probability of Successful Conquest

Back


Art, Robert J. 1996. “American foreign policy and the fungibility of force.” Security Studies 5 (4): 7–42.

Autor, David H, David Dorn, and Gordon H Hanson. 2013. “The China syndrome: Local labor market effects of import competition in the United States.” The American Economic Review 103 (6): 2121–68.

Brito, Dagobert L., and Michael D. Intrilagator. 1985. “Conflict, War, and Redistribution.” American Political Science Review 79 (4).

Cooley, Brendan. 2019. “Estimating Policy Barriers to Trade.”

Costinot, Arnaud, and Andrés Rodríguez-Clare. 2015. “Trade Theory with Numbers: Quantifying the Consequences of Globalization.” Handbook of International Economics 4: 197–261.

Eaton, Jonathan, and Samuel Kortum. 2002. “Technology, geography, and trade.” Econometrica 70 (5): 1741–79.

Fearon, James D. 1995. “Rationalist explanations for war.” International Organization 49 (03): 379–414.

Findlay, Ronald., and Kevin H. O’Rourke. 2007. Power and plenty : trade, war, and the world economy in the second millennium. Princeton University Press.

Gawande, Kishore, Pravin Krishna, and Marcelo Olarreaga. 2009. “What governments maximize and why: the view from trade.” International Organization 63 (03): 491–532.

Goldberg, P K, and N Pavcnik. 2016. “The Effects of Trade Policy.” Handbook of Commercial Policy 1: 161–206.

Grossman, Gene M, and Elhanan Helpman. 1994. “Protection for Sale.” The American Economic Review, 833–50.

Su, Che Lin, and Kenneth L. Judd. 2012. “Constrained Optimization Approaches to Estimation of Structural Models.” Econometrica 80 (5): 2213–30.