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

Trade Policy in the Shadow of Power

Quantifying Military Coercion in the International System

1 September 2019

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: policy adjustment should occur through diplomacy
    • 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?

  • Mercantilist preferences: openness abroad and some closure at home
    • Grossman and Helpman (1994), Gawande, Krishna, and Olarreaga (2009)
  • Coercion: powerful governments impose openness abroad
    • Gunboat diplomacy (Findlay and O’Rourke 2007)

Trade Policy: Does It Matter?

  • Tariffs small, aggregate policy-induced trade frictions large
  • 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

  • Dispatch U.S. military (for example) on long-term mission to Pluto
  • 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 (power and preferences)
  • \(\bm{M}\) – 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

Model

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

Coercive International Political Economy

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

Sequence

  1. (\(\Gamma^{\bm{m}}\)) Governments set military strategies
    • allocations of effort over potential wars
  2. (\(\Gamma^{\bm{\tau}}\)) Governments make trade policy announcements
  3. (\(\Gamma^{\bm{a}}\)) Wars
    • Winners choose trade policies for vanquished governments
  4. (\(h(\bm{\tau})\)) Economic (general equilibrium) consequences of trade policies

Payoffs

\[ G_i \left( h(\bm{\tau}), \bm{a} \right) \]

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

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


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

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

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


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

\[ r_i(\color{bcOrange} \bm{w} \color{black}) = \sum_j (\tau_{ij} - 1) X_{ij}(\color{bcOrange} \bm{w} \color{black}) \]

Government Objective

\[ G_i = V_i( \color{bcOrange} \bm{w} \color{black})^{1 - b_i} r_i(\color{bcOrange} \bm{w} \color{black})^{b_i} \]

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

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


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

\[ r_i(\bm{w} \color{black}) = \sum_j (\tau_{ij} - 1) X_{ij}(\bm{w}) \]

Government Objective

\[ G_i = V_i(\bm{w})^{ \color{bcOrange} 1 - b_i \color{black} } r_i(\bm{w})^{\color{bcOrange} b_i \color{black} } \]

  • \(\color{bcOrange} b_i = 0\): government maximizes consumer welfare
  • \(\color{bcOrange} b_i = 1\): government maximizes rents
  • Free Trade Counterfactual

(\(\Gamma^{\bm{a}}\)) Wars

Optimal Post-Conquest Policies

\[ \bm{\tau}_j^{i \star} = \argmax_{\bm{\tau}_j} \quad G_i(\bm{\tau}_j ; \tilde{\bm{\tau}}_{-j}) \]

(\(\Gamma^{\bm{a}}\)) Wars

Optimal Post-Conquest Policies

\[ \color{bcOrange} \bm{\tau}_j^{i \star} \color{black} = \argmax_{\bm{\tau}_j} \quad G_{\color{bcOrange} i} \color{black} (\bm{\tau}_{\color{bcOrange} j} \color{black} ; \tilde{\bm{\tau}}_{-j}) \]

  • \(\color{bcOrange} \bm{\tau}_j^{i \star}\): trade policies in \(\color{bcOrange} j\) imposed by government \(\color{bcOrange} i\) post-conquest

(\(\Gamma^{\bm{a}}\)) Wars

Optimal Post-Conquest Policies

\[ \color{bcOrange} \bm{\tau}_j^{i \star} \color{black} = \argmax_{\bm{\tau}_j} \quad G_{i}(\bm{\tau}_{j}; \tilde{\bm{\tau}}_{-j}) \]

  • \(\color{bcOrange} \bm{\tau}_j^{i \star}\): trade policies in \(j\) imposed by government \(i\) post-conquest

Conquest Values

\[ G_i(\color{bcOrange} \bm{\tau}_j^{i \star} \color{black} ; \tilde{\bm{\tau}}_{-j}) \]

(\(\Gamma^{\bm{a}}\)) Wars

Conquest Values

\[ G_i(\bm{\tau}_j^{i \star} \color{black} ; \tilde{\bm{\tau}}_{-j}) \]

Contest Function (Dyadic)

\[ \chi_{ji}(\bm{m}) = \frac{ \rho_{ji}(\bm{W}; \bm{\alpha}) m_{ji} }{ \rho_{ji}(\bm{W}; \bm{\alpha}) m_{ji} + m_{ii} } \]

(\(\Gamma^{\bm{a}}\)) Wars

Conquest Values

\[ G_i(\bm{\tau}_j^{i \star} \color{black} ; \tilde{\bm{\tau}}_{-j}) \]

Contest Function (Dyadic)

\[ \color{bcOrange} \chi_{ji} \color{black} (\bm{m}) = \frac{ \rho_{ji}(\bm{W}; \bm{\alpha}) m_{ji} }{ \rho_{ji}(\bm{W}; \bm{\alpha}) m_{ji} + m_{ii} } \]

  • \(\color{bcOrange} \chi_{ji}\): probability \(\color{bcOrange} j\) successfully conquers \(\color{bcOrange} i\)

(\(\Gamma^{\bm{a}}\)) Wars

Conquest Values

\[ G_i(\bm{\tau}_j^{i \star} \color{black} ; \tilde{\bm{\tau}}_{-j}) \]

Contest Function (Dyadic)

\[ \chi_{ji}( \color{bcOrange} \bm{m} \color{black}) = \frac{ \rho_{ji}(\bm{W}; \bm{\alpha}) \color{bcOrange} m_{ji} \color{black} }{ \rho_{ji}(\bm{W}; \bm{\alpha}) \color{bcOrange} m_{ji} \color{black} + \color{bcOrange} m_{ii} \color{black} } \]

  • \(\chi_{ji}\): probability \(j\) successfully conquers \(i\)
  • \(\color{bcOrange} \bm{m}\): military effort
  • \(\color{bcOrange} m_{ji}\): effort \(j\) dedicates toward threatening \(i\)
  • \(\color{bcOrange} m_{ii}\): effort \(i\) dedicates toward self-defense

(\(\Gamma^{\bm{a}}\)) Wars

Conquest Values

\[ G_i(\bm{\tau}_j^{i \star} \color{black} ; \tilde{\bm{\tau}}_{-j}) \]

Contest Function (Dyadic)

\[ \chi_{ji}(\bm{m}) = \frac{ \color{bcOrange} \rho_{ji} \color{black} (\bm{W}; \bm{\alpha}) m_{ji} }{ \color{bcOrange} \rho_{ji} \color{black} (\bm{W}; \bm{\alpha}) m_{ji} + m_{ii} } \]

  • \(\chi_{ji}\): probability \(j\) successfully conquers \(i\)
  • \(\bm{m}\): military effort
  • \(m_{ji}\): effort \(j\) dedicates toward threatening \(i\)
  • \(m_{ii}\): effort \(i\) dedicates toward self-defense
  • \(\color{bcOrange} \rho_{ji} \color{black} \in [0, 1]\): loss of strength gradient

(\(\Gamma^{\bm{a}}\)) Wars

Conquest Values

\[ G_i(\bm{\tau}_j^{i \star} \color{black} ; \tilde{\bm{\tau}}_{-j}) \]

Contest Function (Dyadic)

\[ \chi_{ji}(\bm{m}) = \frac{ \rho_{ji} (\color{bcOrange} \bm{W} \color{black} ; \bm{\alpha}) m_{ji} }{ \rho_{ji} ( \color{bcOrange} \bm{W} \color{black} ; \bm{\alpha}) m_{ji} + m_{ii} } \]

  • \(\chi_{ji}\): probability \(j\) successfully conquers \(i\)
  • \(\bm{m}\): military effort
  • \(m_{ji}\): effort \(j\) dedicates toward threatening \(i\)
  • \(m_{ii}\): effort \(i\) dedicates toward self-defense
  • \(\rho_{ji} \in [0, 1]\): loss of strength gradient
  • \(\color{bcOrange} \bm{W}\): dyadic geography

(\(\Gamma^{\bm{a}}\)) Wars

Conquest Values

\[ G_i(\bm{\tau}_j^{i \star} \color{black} ; \tilde{\bm{\tau}}_{-j}) \]

Contest Function (Dyadic)

\[ \color{bcOrange} \chi_{ji} (\bm{m}) \color{black} = \frac{ \rho_{ji} (\bm{W}; \bm{\alpha}) m_{ji} }{ \rho_{ji} (\bm{W}; \bm{\alpha}) m_{ji} + m_{ii} } \]

Reservation Values

\[ \color{bcOrange} \chi_{ji} (\bm{m}) \color{black} G_j(\bm{\tau}_i^{j \star}; \tilde{\bm{\tau}}_{-j}) + \color{bcOrange} \left( 1 - \chi_{ji} (\bm{m}) \right) \color{black} G_j(\tilde{\bm{\tau}}) - c_j \]

(\(\Gamma^{\bm{a}}\)) Wars

Conquest Values

\[ G_j(\bm{\tau}_i^{j \star} \color{black} ; \tilde{\bm{\tau}}_{-i}) \]

Contest Function (Dyadic)

\[ \chi_{ji} (\bm{m}) = \frac{ \rho_{ji} (\bm{W}; \bm{\alpha}) m_{ji} }{ \rho_{ji} (\bm{W}; \bm{\alpha}) m_{ji} + m_{ii} } \]

Reservation Values

\[ \chi_{ji} (\bm{m}) G_j(\bm{\tau}_i^{j \star}; \tilde{\bm{\tau}}_{-j}) + \left( 1 - \chi_{ij} (\bm{m}) \right) G_j(\tilde{\bm{\tau}}) - \color{bcOrange} c_j \]

  • \(\color{bcOrange} c_j\): war cost

(\(\Gamma^{\bm{a}}\)) Wars

Conquest Values

\[ G_j(\bm{\tau}_i^{j \star} \color{black} ; \tilde{\bm{\tau}}_{-i}) \]

Contest Function (Dyadic)

\[ \chi_{ji} (\bm{m}) = \frac{ \rho_{ji} (\bm{W}; \bm{\alpha}) m_{ji} }{ \rho_{ji} (\bm{W}; \bm{\alpha}) m_{ji} + m_{ii} } \]

Reservation Values

\[ \color{bcOrange} \underline{G}_{ji}(\bm{m}) \color{black} = \chi_{ji} (\bm{m})G_j(\bm{\tau}_i^{j \star}; \tilde{\bm{\tau}}_{-j}) + \left( 1 - \chi_{ji} (\bm{m}) \right) G_j(\tilde{\bm{\tau}}) - c_j \]

  • No war \(\implies G_j(\tilde{\bm{\tau}}) \geq \color{bcOrange} \underline{G}_{ji}(\bm{m})\) for all \(j, i\)
  • Proposition C1: \(\exists\) \(\left\{ c_j^\star \right\}_{j \in \left\{1,..., N \right\}}\) such that no war occurs if \(c_j > c_j^\star\) for all \(j\).

(\(\Gamma^{\bm{\tau}}\)) Trade Policy Announcements

\[ \color{bcOrange} \underline{G}_{ji}(\bm{m}) \color{black} = \chi_{ji} (\bm{m}) G_j(\bm{\tau}_i^{j \star}; \tilde{\bm{\tau}}_{-j}) + \left( 1 - \chi_{ji} (\bm{m}) \right) G_j(\tilde{\bm{\tau}}) - c_j \]

Constrained Optimal Policies

\[\begin{equation} \begin{split} \max_{ \tilde{\bm{\tau}}_i } & \quad G_i(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \end{split} \end{equation}\]

(\(\Gamma^{\bm{\tau}}\)) Trade Policy Announcements

\[ \color{bcOrange} \underline{G}_{ji}(\bm{m}) \color{black} = \chi_{ji} (\bm{m}) G_j(\bm{\tau}_i^{j \star}; \tilde{\bm{\tau}}_{-j}) + \left( 1 - \chi_{ji} (\bm{m}) \right) G_j(\tilde{\bm{\tau}}) - c_j \]

Constrained Optimal Policies

\[\begin{equation} \begin{split} \max_{ \tilde{\bm{\tau}}_i } & \quad G_i(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \\ \text{subject to} & \quad G_j(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \geq \color{bcOrange} \underline{G}_{ji}(\bm{m}) \color{black} \text{ for all } j \neq i \end{split} \end{equation}\]

(\(\Gamma^{\bm{\tau}}\)) Trade Policy Announcements

\[ \underline{G}_{ji}(\color{bcOrange} \bm{m} \color{black}) = \chi_{ji} (\color{bcOrange} \bm{m} \color{black}) G_j(\bm{\tau}_i^{j \star}; \tilde{\bm{\tau}}_{-j}) + \left( 1 - \chi_{ji} (\color{bcOrange} \bm{m} \color{black}) \right) G_j(\tilde{\bm{\tau}}) - c_j \]

Constrained Optimal Policies

\[\begin{equation} \begin{split} \max_{ \tilde{\bm{\tau}}_i } & \quad G_i(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \\ \text{subject to} & \quad G_j(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \geq \underline{G}_{ji}( \color{bcOrange} \bm{m} \color{black}) \text{ for all } j \neq i \end{split} \end{equation}\]

(\(\Gamma^{\bm{\tau}}\)) Trade Policy Announcements

\[ \underline{G}_{ji}(\color{bcOrange} \bm{m} \color{black}) = \chi_{ji} (\color{bcOrange} \bm{m} \color{black}) G_j(\bm{\tau}_i^{j \star}; \tilde{\bm{\tau}}_{-j}) + \left( 1 - \chi_{ji} (\color{bcOrange} \bm{m} \color{black}) \right) G_j(\tilde{\bm{\tau}}) - c_j \]

Constrained Optimal Policies

\[\begin{equation} \begin{split} \tilde{\bm{\tau}}_i^\star( \color{bcOrange} \bm{m} \color{black}) = \argmax_{ \tilde{\bm{\tau}}_i } & \quad G_i(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \\ \text{subject to} & \quad G_j(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \geq \underline{G}_{ji}( \color{bcOrange} \bm{m} \color{black}) \text{ for all } j \neq i \end{split} \end{equation}\]

(\(\Gamma^{\bm{m}}\)) Military Strategies

\[ \underline{G}_{ji}(\color{bcOrange} \bm{m} \color{black}) = \chi_{ji} (\color{bcOrange} \bm{m} \color{black}) G_j(\bm{\tau}_i^{j \star}; \tilde{\bm{\tau}}_{-j}) + \left( 1 - \chi_{ji} (\color{bcOrange} \bm{m} \color{black}) \right) G_j(\tilde{\bm{\tau}}) - c_j \]

Constrained Optimal Policies

\[\begin{equation} \begin{split} \tilde{\bm{\tau}}_i^\star( \color{bcOrange} \bm{m} \color{black}) = \argmax_{ \tilde{\bm{\tau}}_i } & \quad G_i(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \\ \text{subject to} & \quad G_j(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \geq \underline{G}_{ji}( \color{bcOrange} \bm{m} \color{black}) \text{ for all } j \neq i \end{split} \end{equation}\]

Optimal Military Strategies

\[\begin{equation} \begin{split} \max_{ \color{bcOrange} \bm{m}_i \color{black} } & \quad G_i \left(\tilde{\bm{\tau}}^\star( \color{bcOrange} \bm{m}_i \color{black} ; \bm{m}_{-i}) \right) \end{split} \end{equation}\]

\[ \color{bcOrange} \bm{m}_i = \begin{pmatrix} m_{i1} & \cdots & m_{iN} \end{pmatrix} \]

  • \(\color{bcOrange} m_{ij}\): military effort \(i\) dedicates toward threatening \(j\)

(\(\Gamma^{\bm{m}}\)) Military Strategies

\[ \underline{G}_{ji}(\bm{m}) = \chi_{ji} (\bm{m}) G_j(\bm{\tau}_i^{j \star}; \tilde{\bm{\tau}}_{-j}) + \left( 1 - \chi_{ji} (\bm{m}) \right) G_j(\tilde{\bm{\tau}}) - c_j \]

Constrained Optimal Policies

\[\begin{equation} \begin{split} \tilde{\bm{\tau}}_i^\star(\bm{m}) = \argmax_{ \tilde{\bm{\tau}}_i } & \quad G_i(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \\ \text{subject to} & \quad G_j(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \geq \underline{G}_{ji}(\bm{m}) \text{ for all } j \neq i \end{split} \end{equation}\]

Optimal Military Strategies

\[\begin{equation} \begin{split} \max_{ \bm{m}_i } & \quad G_i \left(\tilde{\bm{\tau}}^\star( \bm{m}_i ; \bm{m}_{-i}) \right) \\ \text{subject to} & \quad \sum_j m_{ij} \leq \color{bcOrange} M_i \end{split} \end{equation}\]

(\(\Gamma^{\bm{m}}\)) Military Strategies

\[ \underline{G}_{ji}(\bm{m}) = \chi_{ji} (\bm{m}) G_j(\bm{\tau}_i^{j \star}; \tilde{\bm{\tau}}_{-j}) + \left( 1 - \chi_{ji} (\bm{m}) \right) G_j(\tilde{\bm{\tau}}) - c_j \]

Constrained Optimal Policies

\[\begin{equation} \begin{split} \tilde{\bm{\tau}}_i^\star(\bm{m}) = \argmax_{ \tilde{\bm{\tau}}_i } & \quad G_i(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \\ \text{subject to} & \quad G_j(\tilde{\bm{\tau}}_i; \tilde{\bm{\tau}}_{-i}) \geq \underline{G}_{ji}(\bm{m}) \text{ for all } j \neq i \end{split} \end{equation}\]

Optimal Military Strategies

\[\begin{equation} \begin{split} \color{bcOrange} \bm{m}_i^\star \color{black} = \argmax_{ \bm{m}_i } & \quad G_i \left(\tilde{\bm{\tau}}^\star( \bm{m}_i ; \bm{m}_{-i}) \right) \\ \text{subject to} & \quad \sum_j m_{ij} \leq M_i \end{split} \end{equation}\]

Estimation

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

Observables and Unobservables

Data

  • \(\bm{\tau}\): policy barriers to trade (barriers)
  • \(\bm{M}\): military expenditure (milex)

Structural Parameters \[ \bm{\theta} = \left\{ \bm{b}, \rho(\bm{W}) \right\} \]

Observables and Unobservables

Data

  • \(\bm{\tau}\): policy barriers to trade (barriers)
  • \(\bm{M}\): military expenditure (milex)

Structural Parameters \[ \bm{\theta} = \left\{ \color{bcOrange} \bm{b} \color{black}, \rho(\bm{W}) \right\} \]

  • \(\color{bcOrange} \bm{b}\): governments’ preferences

Observables and Unobservables

Data

  • \(\bm{\tau}\): policy barriers to trade (barriers)
  • \(\bm{M}\): military expenditure (milex)

Structural Parameters \[ \bm{\theta} = \left\{ \bm{b}, \color{bcOrange} \rho(\bm{W}) \color{black} \right\} \]

  • \(\bm{b}\): governments’ preferences
  • \(\color{bcOrange} \rho(\bm{W})\): loss of strength gradient
    • \(\bm{W}\): minimum geographic distance

Observables and Unobservables

Data

  • \(\bm{\tau}\): policy barriers to trade (barriers)
  • \(\bm{M}\): military expenditure (milex)

Structural Parameters \[ \bm{\theta} = \left\{ \bm{b}, \rho(\bm{W}) \right\} \]

  • \(\bm{b}\): governments’ preferences
  • \(\rho(\bm{W})\): loss of strength gradient
    • \(\bm{W}\): minimum geographic distance

Structural Residual \[ \epsilon_{ij}(\bm{\theta}) = \tilde{\tau}_{ij}^\star(\bm{m}^\star; \bm{\theta}) - \tau_{ij} \]

Estimation Problem

\[\begin{equation} \begin{split} \hat{\bm{\theta}} = \argmin_{\bm{\theta}} & \quad \sum_i \sum_j \left( \epsilon_{ij}(\bm{\theta}) \right)^2 \end{split} \end{equation}\]

  • Reformulate as mathematical program with equilibrium constraints (MPEC) (Su and Judd 2012)

Conclusion

Counterfactuals \[ \left\{ \left\{ \bm{b}^\prime, \hat{\rho}(\bm{W}) \right\}, \bm{M}^\prime \right\} \rightarrow \left\{ \bm{\tau}^\prime, \bm{m}^\prime \right\} \]

Conclusion

Counterfactuals \[ \left\{ \left\{ \hat{\bm{b}}, \hat{\rho}(\bm{W}) \right\}, \color{bcOrange} \bm{M}^\prime \color{black} \right\} \rightarrow \left\{ \color{bcOrange} \bm{\tau}^\prime \color{black}, \bm{m}^\prime \right\} \]

  • Shadow of power (\(\color{bcOrange} \bm{M}^\prime \rightarrow \bm{\tau}^\prime\))

Conclusion

Counterfactuals \[ \left\{ \left\{ \color{bcOrange} \bm{b}^\prime \color{black}, \hat{\rho}(\bm{W}) \right\}, \bm{M} \right\} \rightarrow \left\{ \color{bcOrange} \bm{\tau}^\prime, \bm{m}^\prime \color{black} \right\} \]

  • Shadow of power (\(\bm{M}^\prime \rightarrow \bm{\tau}^\prime\))
  • Liberal peace (\(\color{bcOrange} \bm{b}^\prime \color{black} \rightarrow \color{bcOrange} \bm{\tau}^\prime, \bm{m}^\prime \color{black}\))

Results

  • Coming soon…

Thank You

brendancooley.com

[email protected]

Policy Barriers to Trade, 2011

Back (Intro)   Back (Estimation)

Welfare Under Free Trade

Back

Conquest Values (Empirical)

Back

Military Expenditure

Back


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