Convolutional Gravitational Models for Economic Exchanges: Mathematical Extensions for Dynamic Processes and Knowledge Flows

Abstract

The Gravity Model of trade is a regression model for exchanges between countries. The model comprises a measure of exchange as its dependent variable, a measure of mass for each of the two exchanging parties, and a distance. Typically, the dependent variable represents exports, the measures of mass are the GDPs of two countries, and the distance is geographical distance. The analysis in this paper yields a number of simplifying assumptions, which if relaxed may yield a stronger model. The paper focuses on knowledge flows as measured through citations as a use case of a new convolutional gravitational model, which includes an element of delay in between the production of a good and its acquisition. The convolutional model further extends the concept of a distance between two entities to include a measure of affinity. These extensions clarify some limits of the basic model and conditions when it is appropriate.