Modeling of income distribution in the European Union with the Fokker-Planck equation

TL;DR

This paper introduces a unified statistical physics model using the Fokker-Planck equation to describe income distribution across three societal classes in the EU, capturing known income laws and extending previous two-class models.

Contribution

It develops a more general income distribution formula that models three society classes simultaneously, improving upon previous two-class models with better data fit.

Findings

Accurately describes low, medium, and high-income distributions.

Replicates Boltzmann-Gibbs, Pareto, and Zipf laws.

Reduces the medium-income class region in the model.

Abstract

Herein, we applied statistical physics to study incomes of three (low-, medium- and high-income) society classes instead of the two (low- and medium-income)classes studied so far. In the frame of the threshold nonlinear Langevin dynamics and its threshold Fokker-Planck counterpart, we derived a unified formula for description of income of all society classes, by way of example, of those of the European Union in year 2006 and 2008. Hence, the formula is more general than the well known that of Yakovenko et al. That is, our formula well describes not only two regions but simultaneously the third region in the plot of the complementary cumulative distribution function vs. an annual household income. Furthermore, the known stylised facts concerning this income are well described by our formula. Namely, the formula provides the Boltzmann-Gibbs income distribution function for the low-income society class and the weak Pareto law for the medium-income society class, as expected. Importantly, it predicts (to satisfactory approximation) the Zipf law for the high-income society class. Moreover, the region of medium-income society class is now distinctly reduced because the bottom of high-income society class is distinctly lowered. This reduction made, in fact, the medium-income society class an intermediate-income society class.