Evidence for the Independence of Waged and Unwaged Income, Evidence for Boltzmann Distributions in Waged Income, and the Outlines of a Coherent Theory of Income Distribution

TL;DR

This paper analyzes income data from the UK and USA, demonstrating that Boltzmann and log-normal distributions accurately model income, and argues for treating waged and unwaged income separately within a coherent theoretical framework.

Contribution

It provides evidence for the independence of waged and unwaged income and advocates for Boltzmann distributions as a better fit, proposing a unified theory of income distribution.

Findings

Boltzmann distribution fits income data well

Waged and unwaged incomes are mathematically separate

A coherent theory of income distribution is proposed

Abstract

Two sets of high quality income data are analysed in detail, one set from the UK, one from the USA. It is firstly demonstrated that both a log-normal distribution and a Boltzmann distribution can give very accurate fits to both these data sets. The absence of a power tail in the US data set is then discussed. Taken in conjunction with detailed evidence from the UK and Japanese income data, a strong case is made for the mathematically separate treatment of waged and unwaged income. The authors present a case for preferring the use of the Boltzmann distribution over the log-normal function, this leads to a brief review of the work of a number of researchers, which shows that a coherent theory for the distribution of all income can be postulated.