Reconciling econometrics with continuous maximum-entropy network models

TL;DR

This paper extends maximum-entropy network models to continuous link weights, integrating econometric and statistical physics approaches, and applies them to the World Trade Web to analyze international trade networks.

Contribution

It introduces two classes of continuous maximum-entropy models, the integrated and conditional, unifying probabilistic rules for link placement and weights in economic networks.

Findings

Models successfully applied to World Trade Web data

Integrated models optimize a single divergence criterion

Conditional models disentangle link placement and weight assignment

Abstract

In the study of economic networks, econometric approaches interpret the traditional Gravity Model specification as the expected link weight coming from a probability distribution whose functional form can be chosen arbitrarily, while statistical-physics approaches construct maximum-entropy distributions of weighted graphs, constrained to satisfy a given set of measurable network properties. In a recent, companion paper, we integrated the two approaches and applied them to the World Trade Web, i.e. the network of international trade among world countries. While the companion paper dealt only with discrete-valued link weights, the present paper extends the theoretical framework to continuous-valued link weights. In particular, we construct two broad classes of maximum-entropy models, namely the integrated and the conditional ones, defined by different criteria to derive and combine the probabilistic rules for placing links and loading them with weights. In the integrated models, both rules follow from a single, constrained optimization of the continuous Kullback-Leibler divergence; in the conditional models, the two rules are disentangled and the functional form of the weight distribution follows from a conditional, optimization procedure. After deriving the general functional form of the two classes, we turn each of them into a proper family of econometric models via a suitable identification of the econometric function relating the corresponding, expected link weights to macroeconomic factors. After testing the two classes of models on World Trade Web data, we discuss their strengths and weaknesses.