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Optimal Trade and Industrial Policies in the Global Economy: A Deep Learning Framework

Zi Wang, Xingcheng Xu, Yanqing Yang, Xiaodong Zhu

TL;DR

This paper tackles the challenge of computing optimal, high-dimensional trade and industrial policies in a quantifiable general-equilibrium framework with global linkages. It introduces DL-opt, a deep-learning–inspired framework that blends Nested Fixed Point (NFXP) optimization, automatic implicit differentiation, and best-response dynamics to efficiently find unilaterally optimal and Nash policies in large multi-country, multi-sector models. The authors apply DL-opt to a seven-economy, 44-sector model with sectoral scale economies, revealing key results: Nash subsidies rise with scale elasticity $oldsymbol{ ho}_j$ while Nash tariffs rise with $oldsymbol{ ho}_j$ and fall with $oldsymbol{ heta}_j$, global dual policy competition yields lower tariffs and higher welfare than tariff wars, and global cooperation drives tariffs toward zero with substantial welfare gains; imperfect implementation of subsidies can dampen or reverse these gains, underscoring the importance of precise policy design. The methodology offers a scalable, generalizable tool for evaluating policy mixes in global trade and spatial economics and can be extended to domains like carbon pricing, corporate taxes, and innovation subsidies.

Abstract

We propose a deep learning framework, DL-opt, designed to efficiently solve for optimal policies in quantifiable general equilibrium trade models. DL-opt integrates (i) a nested fixed point (NFXP) formulation of the optimization problem, (ii) automatic implicit differentiation to enhance gradient descent for solving unilateral optimal policies, and (iii) a best-response dynamics approach for finding Nash equilibria. Utilizing DL-opt, we solve for non-cooperative tariffs and industrial subsidies across 7 economies and 44 sectors, incorporating sectoral external economies of scale. Our quantitative analysis reveals significant sectoral heterogeneity in Nash policies: Nash industrial subsidies increase with scale elasticities, whereas Nash tariffs decrease with trade elasticities. Moreover, we show that global dual competition, involving both tariffs and industrial subsidies, results in lower tariffs and higher welfare outcomes compared to a global tariff war. These findings highlight the importance of considering sectoral heterogeneity and policy combinations in understanding global economic competition.

Optimal Trade and Industrial Policies in the Global Economy: A Deep Learning Framework

TL;DR

This paper tackles the challenge of computing optimal, high-dimensional trade and industrial policies in a quantifiable general-equilibrium framework with global linkages. It introduces DL-opt, a deep-learning–inspired framework that blends Nested Fixed Point (NFXP) optimization, automatic implicit differentiation, and best-response dynamics to efficiently find unilaterally optimal and Nash policies in large multi-country, multi-sector models. The authors apply DL-opt to a seven-economy, 44-sector model with sectoral scale economies, revealing key results: Nash subsidies rise with scale elasticity while Nash tariffs rise with and fall with , global dual policy competition yields lower tariffs and higher welfare than tariff wars, and global cooperation drives tariffs toward zero with substantial welfare gains; imperfect implementation of subsidies can dampen or reverse these gains, underscoring the importance of precise policy design. The methodology offers a scalable, generalizable tool for evaluating policy mixes in global trade and spatial economics and can be extended to domains like carbon pricing, corporate taxes, and innovation subsidies.

Abstract

We propose a deep learning framework, DL-opt, designed to efficiently solve for optimal policies in quantifiable general equilibrium trade models. DL-opt integrates (i) a nested fixed point (NFXP) formulation of the optimization problem, (ii) automatic implicit differentiation to enhance gradient descent for solving unilateral optimal policies, and (iii) a best-response dynamics approach for finding Nash equilibria. Utilizing DL-opt, we solve for non-cooperative tariffs and industrial subsidies across 7 economies and 44 sectors, incorporating sectoral external economies of scale. Our quantitative analysis reveals significant sectoral heterogeneity in Nash policies: Nash industrial subsidies increase with scale elasticities, whereas Nash tariffs decrease with trade elasticities. Moreover, we show that global dual competition, involving both tariffs and industrial subsidies, results in lower tariffs and higher welfare outcomes compared to a global tariff war. These findings highlight the importance of considering sectoral heterogeneity and policy combinations in understanding global economic competition.
Paper Structure (23 sections, 28 equations, 13 figures, 8 tables, 1 algorithm)

This paper contains 23 sections, 28 equations, 13 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. DL-opt: General Framework
  3. Unilaterally Optimal Policies
  4. Nash Policies
  5. Model, Calibration, and Computation
  6. Model and Equilibrium
  7. Calibration
  8. Computation
  9. Optimal Trade and Industrial Policies
  10. Sectoral Heterogeneity of Optimal Policies
  11. Trade and Industrial Policy Competitions
  12. Extension: Cooperative Policies
  13. Extension: Imperfect Implementation of Industrial Subsidies
  14. Conclusion
  15. Model, Calibration, and Computation
  16. ...and 8 more sections

Figures (13)

  • Figure 1: Analogy between Policy Optimization and Neural Networks
  • Figure 2: Calculation Flows of the DL-opt Framework
  • Figure 3: Iteration Curve for Nash Equilibrium of Global Dual Competition
  • Figure 4: Landscape Near Nash Equilibrium for Global Dual Policy Competition with Scale Economies
  • Figure 5: Unilaterally Optimal vs. Nash Policies in China
  • ...and 8 more figures

Theorems & Definitions (1)

  • Definition 1: Equilibrium