Dynamics of wealth inequality

Zdzislaw Burda; Pawel Wojcieszak; Konrad Zuchniak

doi:10.1016/j.crhy.2019.05.011

From statistical physics to social sciences / De la physique statistique aux sciences sociales

Dynamics of wealth inequality
[Dynamique de l'inégalité de richesse]

Zdzislaw Burda ¹ ; Pawel Wojcieszak ¹ ; Konrad Zuchniak ¹

¹ Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30059 Kraków, Poland

Comptes Rendus. Physique, Volume 20 (2019) no. 4, pp. 349-363.

Résumé
Abstract

Nous étudions un modèle d'évolution de la répartition de la richesse dans un système macro-économique basé sur les agents. L'évolution est mue par des fluctuations stochastiques multiplicatives régies par la loi de la croissance proportionnelle et des interactions entre agents. Nous nous intéressons principalement aux interactions qui accroissent les inégalités de richesse, c'est-à-dire à une mise en œuvre locale du principe de l'avantage accumulé. De telles interactions déstabilisent le système. Elles sont confrontées dans le modèle à un mécanisme réglementaire mondial qui réduit les inégalités de richesse. Différents scénarios se dessinent, comme un effet net de ces deux mécanismes concurrents. Lorsque l'effet de la régulation globale (interventionnisme économique) est trop faible, le système est instable et n'atteint jamais l'équilibre. Lorsque l'effet est suffisamment fort, le système évolue vers une distribution stationnaire limitante avec une queue de Pareto. Entre les deux, il y a une phase critique. Dans cette phase, le système peut évoluer vers un état stable avec une répartition multimodale des richesses. La fonction de densité cumulative correspondante suit un motif d'escalier caractéristique qui reflète l'effet de la stratification économique. Les escaliers représentent les niveaux de richesse des classes économiques séparées par des écarts de richesse. Comme nous le montrons, le schéma est typique des systèmes macro-économiques avec une liberté économique limitée. On peut trouver un tel modèle multimodal dans les données empiriques, par exemple, dans le percentile le plus élevé de la répartition des richesses pour la population des zones urbaines de la Chine.

We study an agent-based model of evolution of wealth distribution in a macroeconomic 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 that 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 that 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 macroeconomic 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.

Publié le : 2019-05-01

DOI : 10.1016/j.crhy.2019.05.011

Keywords: Wealth inequality, Wealth distribution, Population dynamics, Stochastic evolution, Agent-based modelling, Monte Carlo methods
Mot clés : Inégalité de richesse, Répartition de la richesse, Dynamique de la population, Évolution stochastique, Modélisation basée sur les agents, Méthodes de Monte-Carlo

Affiliations des auteurs :

Zdzislaw Burda ¹ ; Pawel Wojcieszak ¹ ; Konrad Zuchniak ¹

¹ Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30059 Kraków, Poland

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Zdzislaw Burda; Pawel Wojcieszak; Konrad Zuchniak. Dynamics of wealth inequality. Comptes Rendus. Physique, Volume 20 (2019) no. 4, pp. 349-363. doi : 10.1016/j.crhy.2019.05.011. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2019.05.011/

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