Towards an Analytical Solution for Agent Based Models: An Application to a Credit Network Economy

Abstract

In this paper we present a model with heterogeneous and interacting firms and banks, which is solved analytically. Methodologically, the economy is modelled as a network, a theoretical structure which is particularly suitable to represent the interactions among different agents. In this credit network firms interact directly with banks and, indirectly, among themselves. The main novelty is the use of the master equation to perform the aggregation over a population of heterogeneous firms and to describe the endogenous evolution of the network. The asymptotic solution of the master equation provides a system of coupled equations, governing the dynamics of growth and fluctuations of the aggregate output and the network degree.

Keywords: heterogeneity, financial fragility, master equation, interaction, dynamic aggregation

JEL Classification: E1, E6