Inverse Problem for the Yard-Sale Model of Wealth Distribution
Abstract: Wealth inequality has become one of the most pressing issues throughout the world today. Among the different approaches trying to understand wealth inequality, "Econophysics" applies methods from physics to establish microscopic models from which macroeconomic wealth distributions can be derived. Asset Exchange Models (AEMs) are some of the most successful models of this kind. In this th... read moreesis, we study a particular AEM called the Yard-Sale Model (YSM). In Chapter 2, we further extend the basic YSM to include redistribution and Wealth-Attained Advantage (WAA), and we derive a Fokker-Planck equation for the resulting Extended Yard-Sale Model (EYSM). In Chapter 3, we discuss the numerical method we use to solve for steady-state solutions to the EYSM. In Chapter 4, we mainly discuss the existence of a "duality" symmetry between the supercritical and the subcritical solutions to the EYSM. In Chapter 5, we further extend the EYSM so that it allows for agents with negative wealth, which are important empirically. We show how to derive and solve the Fokker-Planck equation for the resulting Affine Wealth Model (AWM) based on the tools and methods we used for EYSM. Finally in Chapter 6, we compare our results with U.S. wealth distribution data from the Survey of Consumer Finances (SCF). We first demonstrate the superiority of the AWM to the other models for its remarkable faithfulness to the empirical data . We also compare our model results from the AWM to U.S. wealth distribution data from 1989 to 2016. We argue that the time series of model parameters thus obtained provides a valuable new diagnostic tool for analyzing wealth inequality.
Thesis (Ph.D.)--Tufts University, 2018.
Submitted to the Dept. of Mathematics.
Advisor: Bruce Boghosian.
Committee: Xiaozhe Hu, Christoph B\"ogers, and Bikas Chakrabarti.
Keywords: Mathematics, Physics, and Economics.read less