Extracting geography from trade data

Understanding international trade is a fundamental problem in economics—one standard approach is via what is commonly called the “gravity equation”, which predicts the total amount of trade Fij between two countries i and j as Fij=GMiMjDij,where G is a constant, Mi,Mj denote the “economic mass” (often simply the gross domestic product) and Dij is the “distance” between countries i and j. Here “distance” is a complex notion that includes geographical, historical, linguistic and sociological components. We take the inverse route and ask ourselves to what extent it is possible to reconstruct meaningful information about countries simply from knowing the bilateral trade volumes Fij: indeed, we show that a remarkable amount of geopolitical information can be extracted. The main ingredient is a spectral decomposition of the Graph Laplacian as a tool to perform nonlinear dimensionality reduction.