The gravity equation has been successful in establishing a connection between the amount of trade between two countries, their respective gross domestic products and "distance" (a complex notion including geographical, historical, linguistic and sociological components). We take the inverse route and show that it is possible to construct a meaningful 'distance' without any external information simply from knowing the bilateral trade volumes between countries. The main tool is a non-standard interpretation of trade flows data as a set of high-dimensional points and the use of mathematical tools to perform dimensionality reduction. This may have further applications for problems in long-term economic analysis, cartel detection and others.
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