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
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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