Detailed simulation results for some wealth distribution models in Econophysics

TL;DR

This paper presents detailed simulation results for a wealth distribution model with quenched saving propensities, revealing non-ergodic behavior and the significance of single realization statistics in understanding wealth distributions.

Contribution

It demonstrates that the wealth distribution model with quenched saving propensities is non-ergodic and that single realization statistics differ fundamentally from ensemble averages.

Findings

Single realization wealth distributions differ from ensemble averages.

The model is not ergodic or self-averaging.

Pareto law emerges as a convolution of single member distributions.

Abstract

In this paper we present detailed simulation results on the wealth distribution model with quenched saving propensities. Unlike other wealth distribution models where the saving propensities are either zero or constant, this model is not found to be ergodic and self-averaging. The wealth distribution statistics with a single realization of quenched disorder is observed to be significantly different in nature from that of the statistics averaged over a large number of independent quenched configurations. The peculiarities in the single realization statistics refuses to vanish irrespective of whatever large sample size is used. This implies that previously observed Pareto law is essentially a convolution of the single member distributions.