Statistical mechanics of money, wealth, and income

Victor M. Yakovenko and J. Barkley Rosser, Jr.

[I mentioned the review 2 years ago in a post about the science of economic inequality].

It reviews the history and concept of econophysics, pointing out how some of the founders of statistical mechanics actually had a vision for its application to economics and sociology. Most of the review is about analogues with statistical mechanics that use the notion of money as a conserved quantity that is exchanged by individuals, leading to Boltzmann type distributions for wealth and income.

I found the article a nice accessible introduction to the field.

What is impressive is that the simple exponential distribution (Boltzmann) does describe empirical data over two orders of magnitude. Furthermore, the analysis gives some insight into economic inequality. This is summarised in the following sentences from the abstract and the figure below showing data from the USA.

Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential (“thermal”) distribution, whereas a small fraction of the population in the upper class is characterized by the power-law (“superthermal”) distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.

Another result that is interesting is the income of spouses seems to be uncorrelated leading to the distribution shown below for total household income. The solid line is the simple functional form following from two uncorrelated Boltzmann distributions.

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