Dynamics of wealth inequality

Abstract

We study an agent-based model of evolution of wealth distribution in a macro-economic system. The evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth and interactions between agents. We are mainly interested in interactions increasing wealth inequality that is in a local implementation of the accumulated advantage principle. Such interactions destabilise the system. They are confronted in the model with a global regulatory mechanism which reduces wealth inequality. There are different scenarios emerging as a net effect of these two competing mechanisms. When the effect of the global regulation (economic interventionism) is too weak the system is unstable and it never reaches equilibrium. When the effect is sufficiently strong the system evolves towards a limiting stationary distribution with a Pareto tail. In between there is a critical phase. In this phase the system may evolve towards a steady state with a multimodal wealth distribution. The corresponding cumulative density function has a characteristic stairway pattern which reflects the effect of economic stratification. The stairs represent wealth levels of economic classes separated by wealth gaps. As we show, the pattern is typical for macro-economic systems with a limited economic freedom. One can find such a multimodal pattern in empirical data, for instance, in the highest percentile of wealth distribution for the population in urban areas of China.

Wealth Rheology

“…In Figure 1a, we compare a theoretical prediction for the Gini coefficient with the values obtained in Monte Carlo simulations of the system with σ = 0.02, 0.04, 0.08, and N = 10 4 . The theoretical prediction for the distribution (4) reads [26]…”

“…We see that all curves collapse to a single universal curve. By listing explicitly all arguments of the overlap ratio Ω n (k, σ, α, N), we see that the overlap ratio becomes a universal function of the argument x = kσ 2 (α − 1): The data is fitted with the Formula (12) with A = 0.7570 (26) and B = 0.3341 (30). The fit is shown with a solid line.…”

“…Many ideas behind agent-based modelling have been derived from concepts like kinetic theory [ 17 , 18 ], scattering [ 19 ], rate equations [ 20 ], random matrix theory [ 21 , 22 ], Brownian motion [ 23 ] which were developed in statistical physics. Using this type of ideas, one was able to model wealth or income distributions [ 24 ], dynamics of wealth inequality [ 25 , 26 ], wealth concentration [ 27 ], structure emergence [ 28 , 29 ], economic instability and corruption mechanisms [ 30 , 31 , 32 ], systemic risk in economic networks [ 33 ], emergence of heavy tails in wealth and income distributions [ 24 , 34 ], and herding behaviour [ 35 ], or to analyse statistical behaviour or rational agents [ 36 ].…”

“…The first parameter in the legend is the value of α and the second is the value of σ. The data is fitted with the Formula (12) with A = 0.7570(26) and B = 0.3341(30). The fit is shown with a solid line.…”

Power accretion in social systems

“…Some recent models have considered the effect of personal savings and taxation [29]. Other studies have focused on the appearance of social classes [30], the extraordinary velocity of growth of the top earners [31] or how inequality may induce economic crisis without requiring external shocks [32]. Many of these models are built on multiplicative stochastic processes, for which the approach to equilibrium can be extremely slow, and the validity of the ergodic hypothesis is questionable [32][33][34][35]37].…”