The Affine Wealth Model: An agent-based model of asset exchange that allows for negative-wealth agents and its empirical validation

TL;DR

This paper introduces the Affine Wealth Model, an agent-based asset exchange model that accounts for negative wealth agents, and validates it against 27 years of US wealth data with high accuracy, offering new insights into wealth inequality dynamics.

Contribution

The paper develops a novel affine wealth model allowing negative wealth and provides a method to fit it to empirical data, enhancing understanding of wealth distribution evolution.

Findings

Model matches US wealth data with less than 0.16% error over 27 years

Derived Fokker-Planck equation describes wealth distribution dynamics

Time series of model parameters serve as diagnostics for wealth inequality

Abstract

We present a stochastic, agent-based, binary-transaction Asset-Exchange Model (AEM) for wealth distribution that allows for agents with negative wealth. This model retains certain features of prior AEMs such as redistribution and wealth-attained advantage, but it also allows for shifts as well as scalings of the agent density function. We derive the Fokker-Planck equation describing its time evolution and we describe its numerical solution, including a methodology for solving the inverse problem of finding the model parameters that best match empirical data. Using this methodology, we compare the steady-state solutions of the Fokker-Planck equation with data from the United States Survey of Consumer Finances over a time period of 27 years. In doing so, we demonstrate agreement with empirical data of an average error less than 0.16\% over this time period. We present the model parameters for the US wealth distribution data as a function of time under the assumption that the distribution responds to their variation adiabatically. We argue that the time series of model parameters thus obtained provides a valuable new diagnostic tool for analyzing wealth inequality.