A mean-field approximation to stock-flow consistent agent-based models with state-dependent transition rates

Authored by Matheus R Grasselli, Patrick X Li

Date Published: 2017

DOI: 10.1166/jcsmd.2017.1128

Sponsors: No sponsors listed

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Model Documentation: Other Narrative

Model Code URLs: Model code not found

Abstract

We build a stock-flow consistent agent-based macroeconomic model with state-dependent transition probabilities between types of agents. We then propose a mean-field approximation, obtain the master equation associated with it, and the corresponding first and second order terms in a series expansion with respect to an appropriate scaling of the total number of agents. The first order term corresponds to the ordinary differential equation governing the deterministic mean of the fraction of agents of one type, whereas the second order term is the partial differential equation satisfied by the density of random perturbations around the mean. We perform numerical experiments to test the accuracy of the approximation and give examples of sensitivity analyses with respect to some of the parameters. We then use the model to investigate the relationship between stock markets with low returns and high volatility and the proportion of firms with fragile financial positions.
Tags
mean-field approximation Macroeconomics Stock-flow consistency Master equation