The Hidden Geometry of Trade Networks

The Hidden Geometry of Trade Networks


From The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013



Key Terms:

  • Trade Networks
  • Complex Networks
  • Preferential Attachment
  • Positive Feedback
  • Fractals
  • Power Laws
  • Hyperbolic Geometry
  • Economic Geography
  • Regional Trading Blocks
  • Bilateral Trade
  • Multilateral Trade
  • Free Trade Agreements
  • Metabolism of a City
  • Metabolism of a Nation
  • Metabolism of the World
  • Industrial Ecology
  • Social Ecology
  • Growth and Form



From The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013

Here, we present the World Trade Atlas 1870–2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, based on a gravity model predicting the existence of significant trade channels, are such that the closer countries are in trade space, the greater their chance of becoming connected. The atlas provides us with information regarding the long-term evolution of the international trade system and demonstrates that, in terms of trade, the world is not flat but hyperbolic, as a reflection of its complex architecture. The departure from flatness has been increasing since World War I, meaning that differences in trade distances are growing and trade networks are becoming more hierarchical. Smaller-scale economies are moving away from other countries except for the largest economies; meanwhile those large economies are increasing their chances of becoming connected worldwide. At the same time, Preferential Trade Agreements do not fit in perfectly with natural communities within the trade space and have not necessarily reduced internal trade barriers. We discuss an interpretation in terms of globalization, hierarchization, and localization; three simultaneous forces that shape the international trade system.

From The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013

When it comes to international trade, the evidence suggests that we are far from a distance-free world. Distance still matters1 and in many dimensions: cultural, administrative or political, economic, and geographic. This is widely supported by empirical evidence concerning the magnitude of bilateral trade flows. The gravity model of trade2–4, in analogy to Newton’s law of gravitation, accurately predicts that the volume of trade exchanged between two countries increases with their economic sizes and decreases with their geographical separation. The precision of that model improves when it is supplemented with other factors, such as colony–colonizer relationships, a shared common language, or the effects of political borders and a common currency5–7. Despite the success of the gravity model at replicating trade volumes, it performs very poorly at predicting the existence of a trade connection between a given pair of countries8; an obvious limitation that prevents it from explaining the striking regularities observed in the complex architecture of the world trade web9–13. One of the reasons for this flaw is that the gravity model focuses on detached bilateral relationships and so overlooks multilateral trade resistance and other network effects14.

Another drawback of the classical gravity model is that geography is not the only factor that defines distance in international trade. Here, we use a systems approach based on network science methodologies15,16 to propose a gravity model for the existence of significant trade channels between pairs of countries in the world. The gravity model is based on economic sizes and on an effective distance which incorporates different dimensions that affect international trade, not only geography, implicitly encoded on the complex patterns of trade interactions. Our gravity model is based on the connectivity law proposed for complex networks with underlying metric spaces17,18 and it can be represented in a pure geometric approach using a hyperbolic space, which has been conjectured as the natural geometry underlying complex networks19–22. In the hyperbolic trade space, distance combines economic size and effective distance into a sole distance metric, such that the closer countries are in hyperbolic trade space, the greater their chance of becoming connected. We estimate this trade distance from empirical data using adapted statistical inference techniques23,24, which allow us to represent international trade through World Trade Maps (WTMs). These define a coordinate system in which countries are located in relative positions according to the aggregate trade barriers between them. The maps are annual and cover a time span of fourteen decades. The collection as a whole, referred to as the World Trade Atlas 1870–2013, is presented via spatial projections25, Table S5, and trade distance matrices, Table S6. Beyond the obvious advantages of visualization, the World Trade Atlas 1870–2013 significantly increases our understanding of the long-term evolution of the international trade system and helps us to address a number of important and challenging questions. In particular: How far, in terms of trade, have countries traveled in recent history? What role does each country play in the maps and how have those roles evolved over time? Are Preferential Trade Agreements (PTAs) consistent with natural communities as measured by trade distances? Has the formation of PTAs led to lesser or greater barriers to trade within blocs? Is trade distance becoming increasingly irrelevant?

The answers to these questions can be summarized by asserting that, in terms of trade, the world is not flat; it is hyperbolic. Differences in trade distances are growing and becoming more heterogeneous and hierarchical; at the same time as they define natural trade communities—not fully consistent with PTAs. Countries are becoming more interconnected and clustered into hierarchical trade blocs than ever before.

Please see my related posts:

Networks and Hierarchies

Increasing Returns, Path Dependence, Circular and Cumulative Causation in Economics

Relational Turn in Economic Geography

Boundaries and Networks

Multilevel Approach to Research in Organizations

Regional Trading Blocs and Economic Integration

Increasing Returns and Path Dependence in Economics

Growth and Form in Nature: Power Laws and Fractals

Key Sources of Research:


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