From a Hierarchy of Stochastic Differential Equations to a Hierarchy of Generalized Beta Distributions
How random shocks create different income and wealth distributions
A mathematical model shows how financial systems buffeted by random events naturally produce a family of different distribution shapes—from bell curves to power-law tails—all from the same underlying mechanism. The researchers discovered that the order in which you apply mathematical transformations to these distributions matters: two seemingly equivalent procedures produce different results at the top level, revealing a hidden non-uniqueness in how we model real-world inequality.
Income and wealth distributions follow different patterns across countries and time periods, and economists have long struggled to explain why the same real-world forces produce such varied shapes. This framework unifies several competing distribution models under one stochastic foundation, making it possible to predict which distribution shape should emerge from a given set of market conditions. That could help policymakers understand whether observed inequality patterns reflect market fundamentals or require policy intervention.