Diffusion Approximation of Distribution Dynamics in an Agent-Based Economic Model with a Banking Sector

Александр Мартыненко, Olga Krivorotko

Keywords: agent-based model (ABM), mean-field Markov particles, nonlinear diffusion approximation, defaults and crisis regimes

TL;DR: An agent-based economy with households, firms, and a bank is analyzed via empirical state distributions. In the large-population limit, a mean-field evolution equation and a nonlinear diffusion approximation capture macro-dynamics and crisis regimes.

Abstract:

Thesis:
This study examines an agent-based model (ABM) of an economy comprising households, firms, and a banking sector with stock-flow consistent balance sheets. Each simulation step encompasses interest accrual, labor market dynamics, production and wage payments, the consumer market, and household and firm defaults, followed by an update of the banking sector's balance sheet.
Household Behavior: Governed by a consumption rule defined as a fraction of current savings and expected income, with access to credit subject to debt constraints and default thresholds.
Firm Behavior: Firms employ markup pricing, adapt employment levels to expected demand, and utilize credit to finance production. Technical default is triggered when debt exceeds a revenue-linked threshold.
Banking Sector Rules: The bank limits lending based on its capital adequacy; in the event of negative capital, bail-in and bailout mechanisms are applied.
The model output consists of aggregated time series for employment, output, prices, debt, defaults, and banking regimes. To analyze these, empirical distributions of household and firm states are introduced, with macroeconomic indicators treated as functionals of these distributions and the bank's state. Agent interaction occurs through aggregates, allowing the model to be framed as a system of a large number of mean-field Markov particles. In the large-population limit, this system yields an evolution equation for distributions and admits a nonlinear diffusion approximation.
This formulation allows the agent-based model to serve as a data source for training models of distribution dynamics and provides an interpretable link between micro-level behavioral rules and macro-dynamics. A comparison between the diffusion approximation and the original simulation identifies regimes where the mean-field approach adequately describes the dynamics, as well as regimes where discrete thresholds and rare crisis events—such as default cascades and banking insolvency—play a significant role.
This work was supported by the grant of the state program of the «Sirius» Federal Territory «Scientific and technological development of the «Sirius» Federal Territory» (Agreement № 26-03 date 07.07.2025).

Submission Number: 85