Machine Learning the Gravity Equation for International Trade

42 Pages Posted: 15 Mar 2022 Last revised: 18 Mar 2022

Date Written: March 8, 2022

Abstract

Machine learning (ML) is becoming more and more important throughout the mathematical and theoretical sciences. In this work we apply modern ML methods to gravity models of pairwise interactions in international economics. We explain the formulation of graphical neural networks (GNNs), models for graph-structured data that respect the properties of exchangeability and locality. GNNs are a natural and theoretically appealing class of models for international trade, which we demonstrate empirically by fitting them to a large panel of annual-frequency country-level data. We then use a symbolic regression algorithm to turn our fits into interpretable models with performance comparable to state of the art hand-crafted models motivated by economic theory. The resulting symbolic models contain objects resembling market access functions, which were developed in modern structural literature, but in our analysis arise ab initio without being explicitly postulated. Along the way, we also produce several model-consistent and model-agnostic ML-based measures of bilateral trade accessibility.

Keywords: gravity, bilateral accessibility, market access function, graph theory, graph neural network, black-box model interpretation

Suggested Citation

Verstyuk, Sergiy and Douglas, Michael R., Machine Learning the Gravity Equation for International Trade (March 8, 2022). Available at SSRN: https://ssrn.com/abstract=4053795 or http://dx.doi.org/10.2139/ssrn.4053795

Sergiy Verstyuk (Contact Author)

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Michael R. Douglas

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

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