Jan Tinbergen's legacy for economic networks: from the gravity model to quantum statistics

Jan Tinbergen, the first recipient of the Nobel Memorial Prize in Economicsin 1969, obtained his PhD in physics at the University of Leiden under thesupervision of Paul Ehrenfest in 1929. Among many achievements as an economistafter his training as a physicist, Tinbergen proposed the so-called Gravity Model ofinternational trade. The model predicts that the intensity of trade between two countriesis described by a formula similar to Newton’s law of gravitation, where massis replaced by Gross Domestic Product. Since Tinbergen’s proposal, the GravityModel has become the standard model of non-zero trade flows in macroeconomics.However, its intrinsic limitation is the prediction of a completely connected network,which fails to explain the observed intricate topology of international trade.Recent network models overcome this limitation by describing the real network as amember of a maximum-entropy statistical ensemble. The resulting expressions areformally analogous to quantum statistics: the international trade network is foundto closely follow the Fermi-Dirac statistics in its purely binary topology, and therecently proposed mixed Bose-Fermi statistics in its full (binary plus weighted)structure. This seemingly esoteric result is actually a simple effect of the heterogeneityof world countries, that imposes strong structural constraints on the network.Our discussion highlights similarities and differences between macroeconomics andstatistical-physics approaches to economic networks.