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Is Inequality Statistically Inevitable? Econophysical Approaches to Modeling Wealth and Income Distributions

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Abstract

The last twenty-five years have seen the emergence of a significant trend within the subfield of econophysics which attempts to model economic inequality as an emergent property of stochastic interactions among ensembles of agents. In this thesis, the literature surrounding this approach to the study of wealth and income distributions, henceforth the "random asset exchange" literature, is thoroughly reviewed for the first time. The foundational papers of Dragulescu & Yakovenko (2000), Chakraborti & Chakrabarti (2000), and Bouchaud & Mezard (2000) are discussed in detail, and principal canonical models within the random asset exchange literature are established. The most common variations upon these canonical models are enumerated, and significant papers within each kind of modification are introduced. The successes of such models, as well as the limitations of their underlying assumptions, are discussed, and it is argued that the literature must move in the direction of more explicit representations of economic structure and processes before it can truly be seen as explanatory. In order to demonstrate what such a pivot could look like, a completely novel model formulation, principally inspired by the one introduced by Wright (2005), is proposed. By constructing the Markov process governing the expected motion of a representative unit of wealth, the equilibrium division of wealth between the three subpopulations posited by the model is derived. Monte Carlo simulation methods are used to further explore the behavior of the model and to establish the phase space bounds within which the model possesses a stable statistical equilibrium. It is found that the distributions of both wealth and income across all three subpopulations are well fit by Gamma distributions and that the equilibrium class division of wealth closely matches the Markov process prediction. When taxation is introduced into the model, it is furthermore found that wealth, income, and sales taxes all have strong equalizing effects on the equilibrium wealth distribution, while payroll and turnover taxes do not. The degree of income inequality, as measured by the Gini coefficient, is not alleviated by the introduction of any form of flat taxation, consistent with empirical findings. The thesis concludes with a discussion of the overall significance of the last 25 years of random asset exchange modeling and an identification of the most important areas for future work.

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Supplemental file(s) description: Slides used in public thesis defense., Data obtained from Monte Carlo simulations.., R code used in generating visualizations., Python code used in model simulations., Original images used in thesis and M exam..

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2023-05

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Keywords

econophysics; income distributions; inequality; kinetic exchange; wealth distributions

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Committee Chair

Gao, Huaizhu

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Alvarez Daziano, Ricardo

Degree Discipline

Systems Engineering

Degree Name

M.S., Systems Engineering

Degree Level

Master of Science

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Government Document

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Attribution 4.0 International

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dissertation or thesis

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