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".