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 $F_ij$ between two countries $i$ and $j$ as $$ F_{ij} = G frac{M_i M_j}{D_{ij}},$$ where $G$ is a constant, $M_i, M_j$ denote the economic mass (often simply the gross domestic product) and $D_{ij}$ the distance between countries $i$ and $j$, where distance is a complex notion that includes geographical, historical, linguistic and sociological components. We take the textit{inverse} route and ask ourselves to which extent it is possible to reconstruct meaningful information about countries simply from knowing the bilateral trade volumes $F_{ij}$: indeed, we show that a remarkable amount of geopolitical information can be extracted. The main tool is a spectral decomposition of the Graph Laplacian as a tool to perform nonlinear dimensionality reduction. This may have further applications in economic analysis and provides a data-based approach to trade distance.