The Affine Wealth Model: An agent-based model of asset exchange that allows for negative-wealth agents and its empirical validation
Authored by Jie Li, Bruce M Boghosian, Chengli Li
Date Published: 2019
DOI: 10.1016/j.physa.2018.10.042
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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, inter alia, the United States
Survey of Consumer Finances over a time period of 27 years. In doing so,
we demonstrate agreement with empirical data with 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. (C) 2018 Elsevier B.V. All rights reserved.
Tags
Wealth inequality
Distributions
money
Statistical-mechanics
Affine wealth model
Extended yard-sale model
Yard-sale model
Asset
exchange model
Lorenz curve
Gini coefficient
Phase
transitions
Phase coexistence
Wealth condensation
Wealth-attained
advantage
Duality