2 research outputs found
The Affine Wealth Model: An agent-based model of asset exchange that allows for negative-wealth agents and its empirical validation
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.Comment: 18 pages, 6 figure
The Nonuniversality of Wealth Distribution Tails Near Wealth Condensation Criticality
In this work, we modify the affine wealth model of wealth distributions to
examine the effects of nonconstant redistribution on the very wealthy. Previous
studies of this model, restricted to flat redistribution schemes, have
demonstrated the presence of a phase transition to a partially wealth-condensed
state, or "partial oligarchy," at the critical value of an order parameter.
These studies have also indicated the presence of an exponential tail in wealth
distribution precisely at criticality. Away from criticality, the tail was
observed to be Gaussian. In this work, we generalize the flat redistribution
within the affine wealth model to allow for an essentially arbitrary
redistribution policy. We show that the exponential tail observed near
criticality in prior work is, in fact, a special case of a much broader class
of critical, slower-than-Gaussian decays that depend sensitively on the
corresponding asymptotic behavior of the progressive redistribution model used.
We thereby demonstrate that the functional form of the tail of the wealth
distribution in a near-critical society is not universal in nature but rather
entirely determined by the specifics of public policy decisions. This is
significant because most major economies today are observed to be
near-critical.Comment: 20 pages, 2 figure