The possibility to analyze everyday monetary transactions is limited by the scarcity of available data, as this kind of information is usually considered highly sensitive. Present econophysics models are usually employed on presumed random networks of interacting agents, and only some macroscopic properties (e.g. the resulting wealth distribution) are compared to real-world data. In this paper, we analyze Bitcoin, which is a novel digital currency system, where the complete list of transactions is publicly available. Using this dataset, we reconstruct the network of transactions and extract the time and amount of each payment. We analyze the structure of the transaction network by measuring network characteristics over time, such as the degree distribution, degree correlations and clustering. We find that linear preferential attachment drives the growth of the network. We also study the dynamics taking place on the transaction network, i.e. the flow of money. We measure temporal patterns and the wealth accumulation. Investigating the microscopic statistics of money movement, we find that sublinear preferential attachment governs the evolution of the wealth distribution. We report a scaling law between the degree and wealth associated to individual nodes.

/pdf/do-the-rich-get-richer-an-empirical-analysis-of-the-bitcoin-4a5a1x2onm.pdf

Do the rich get richer? An empirical analysis of the Bitcoin transaction network.

Increasingly, a huge amount of statistics have been gathered which clearly indicates that income and wealth distributions in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium. However, it also deviates in the low income and more significantly for the high income ranges. Application of physics models provides illuminating ideas and understanding, complementing the observations.

pdf/kinetic-exchange-models-for-income-and-wealth-distributions-sv0pe9ndaj.pdf

Kinetic Exchange Models for Income and Wealth Distributions

Kinetic exchange models for income and wealth distributions

Power law distributions in entrepreneurship: : Implications for theory and research

We use data on the wealth of the richest persons taken from the ‘rich lists’ provided by business magazines like Forbes to verify if the upper tails of wealth distributions follow, as often claimed, a power-law behaviour. The data sets used cover the world’s richest persons over 1996–2012, the richest Americans over 1988–2012, the richest Chinese over 2006–2012, and the richest Russians over 2004–2011. Using a recently introduced comprehensive empirical methodology for detecting power laws, which allows for testing the goodness of fit as well as for comparing the power-law model with rival distributions, we find that a power-law model is consistent with data only in 35% of the analysed data sets. Moreover, even if wealth data are consistent with the power-law model, they are usually also consistent with some rivals like the log-normal or stretched exponential distributions.

/pdf/do-wealth-distributions-follow-power-laws-evidence-from-rich-180x5tlpy8.pdf

Do wealth distributions follow power laws? Evidence from ‘rich lists’

We analyse the data from the recently published lists of the richest Chinese from the year 2003 to 2005. The results confirm that in these years the wealth is distributed according to a power law with exponents between 1.758 and 2.285 in the high end. The power distribution is found to be quite robust although the persons in the list change drastically and the wealth increases rapidly. The relation between the wealth and the absolute change of wealth rejects the notion that the wealth evolution is a multiplicative stochastic process.

https://iopscience.iop.org/article/10.1088/0256-307X/24/8/076/pdf

Power-Law Tail in the Chinese Wealth Distribution

With income data from Chinese household income projects in 1998–2002, we study the functional form of Chinese income distribution. The fitting results suggest a log-normal distribution plus a power-law tail. This distributional form has changed a lot from its appearance in the early stage of China's reform and turns out to be consistent with that of some complete market economies. The uncertainty and diversity of income growth rate aroused by marketing reform are the main causes of current Chinese income distribution.

https://iopscience.iop.org/article/10.1088/0256-307X/27/7/078901/pdf

Evidence of Scaling in Chinese Income Distribution

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Power-Law Tail in the Chinese Wealth Distribution

Evidence of Scaling in Chinese Income Distribution