Modelling of income distribution in the European Union with the Fokker–Planck equation

Abstract

Herein, we applied statistical physics to study incomes of three (low-, mediumand 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 mediumincome society class an intermediate-income society class.

Scaling in income inequalities and its dynamical origin

“…For Cluj county and Hungary we also have some indications that in the very high income limit (x/ x > 100) a second Pareto tail develops with a smaller Pareto exponent. This is in agreement with the already known fact that the "very rich" are different, and the tail has yet another scaling [40]. This second Pareto regime is however, not captured by our simple model.…”

The internal energy expression of a long-range interaction complex system and its statistical physical properties

“…Fitting United States Revenue Data by Yakovenko and Rosser, it confirms that American society has a clearly defined two-level structure [5]: the overwhelming majority of the population (middle and low income population) subjects to exponential distribution and the other (high-income population) subjects to the power law distribution. Besides, Yakovenko and Rosser advance a theory based on thermal equilibrium of statistical mechanics to solve the exponential income distribution which received more and more empirical research support [6][7][8][9][10]. Also worth noting is Banerjee and Yakovenko believe that addition and multiplication can coexist, and an income distribution formula with three parameters is deducted by using Foker-Plank Equation [11].…”

Top Incomes and Inequality Measurement: A Comparative Analysis of Correction Methods Using the EU SILC Data

“…The fit of the one-parameter Pareto distribution to European and other income distributions has been questioned (Jagielski and Kutner 2013;Jenkins 2017). In the following paragraphs we re-estimate the semi-parametric Gini coefficients assuming top incomes to be distributed as under the generalized beta distribution.…”