Size-Dependency of Income Distributions and Its Implications

TL;DR

This study demonstrates that income distributions are size-dependent and explores how this property influences macroeconomic relationships and critical phenomena, using empirical data and a generalized Lotka-Volterra model.

Contribution

It reveals the size-dependency of income distributions and derives implications for allometric growth and anomalous scaling in critical phenomena.

Findings

Income distribution curves scale with population size.

Power law relationship between population and GDP is supported.

Re-scaled income distributions match limit distributions in critical phenomena.

Abstract

This paper highlights the size-dependency of income distributions, i.e. the income distribution curves versus the population of a country systematically. By using the generalized Lotka-Volterra model to fit the empirical income data in the United States during 1996-2007, we found an important parameter $\lambda$ can scale with a $\beta$ power of the size (population) of U.S. in that year. We pointed out that the size-dependency of the income distributions, which is a very important property but seldom addressed by previous studies, has two non-trivial implications: (1) the allometric growth pattern, i.e. the power law relationship between population and GDP in different years, which can be mathematically derived from the size-dependent income distributions and also supported by the empirical data; (2) the connection with the anomalous scaling for the probability density function in critical phenomena since the re-scaled form of the income distributions has the exactly same mathematical expression for the limit distribution of the sum of many correlated random variables asymptotically.