Evolution of the personal income distribution in the USA: High incomes

Abstract The personal income distribution (PID) above the Pareto threshold is studied and modeled. A microeconomic model is proposed to simulate the PID and its evolution below and above the Pareto income threshold. The model balances processes of income production and dissipation for any person above 15 years of age. The model accurately predicts the observed dependence of the number of people reaching the Pareto threshold on work experience and the functional dependence of the relationship on the per capita real GDP growth for the period from 1994 to 2002. Predictions of the income distribution depending on age are given for past and future. In future, relatively less rich people are observed in the younger age groups and the peak of the relative number shifts to older ages with time. The effect of the power law distribution extending itself to very high incomes is speculated to be the cause of low performance of socialist countries.

Key words: personal income distribution, Pareto distribution, microeconomic modeling, USA, real GDP, macroeconomics

JEL Classification: D01, D31, E17, J1, O12

Introduction A microeconomic model describing the personal income distribution (PID) in the USA was recently developed [1]. The basic approach draws from the field of geomechanics and reproduces some general features of the model for a solid with inhomogeneous inclusions [2]. The microeconomic model predicts the individual income evolution dependence on time when the person entered the economy, the work experience, the personal capability to earn money, and the effective size of the means used to earn money. When aggregated, the model predicts the PID and its evolution in time for the population above 15 years of age. The principal assumption of the model is that there is no difference between money production and money earning. In contrast to the conventional economic theories, no one produces any profit for the rest of the society s/he belongs to. So, the amount of money produced by a person in the form of goods or services is exactly equal to the amount of money earned by the person. This condition also means that there is no money that is not produced by people, i.e. the total income or GDP exactly equals the sum of the personal incomes. In turn, the personal income distribution is fixed in relative terms at a characteristic time length of several years.
One of the essential features of the observed PID described by the model is the existence of two inherently different regimes of money earning. The first regime, referred to as “subcritical”, corresponds to money income proportional to the (numerically defined) capacity of a person to earn money, i.e. to the product of the capability to earn

1 money and the size of the earning means [1]. One can consider this capacity as the effective power of money production that the person achieves by applying her/his personal capability to earn money by some mechanism (leverage) for multiplying the personal power to earn money.
The second regime, a “supercritical” one, corresponds to the personal income range described by a Pareto or power law distribution. This regime starts at some non- zero income threshold, the Pareto threshold, and is supposedly the result of a self- organized-criticality (SOC) [3]. The personal income distribution here is governed by stochastic processes and any person in this income interval can reach any income according to a power law probability. No individual capability above the Pareto threshold is important for the final result, just the probability law. However, the Pareto threshold has to be reached first by passing through the subcritical branch. The Pareto distribution has several analogies in natural and social sciences.

Mechanisms leading to the power law distributions (scale free distributions of sizes - personal incomes in the case of economics) are studied in more detail in some natural sciences. The nature of such mechanisms resulting in the power law distribution in the field of economics is still a big challenge and is not considered here. One can assume, however, that the mechanisms work rapidly and there is no delay between the moment when some personal income reaches the threshold and the moment when the income jumps to its new position in the Pareto distribution. In seismology, for example, the final size or magnitude of an earthquake is usually reached several seconds after the rupture starts. Seismic magnitude represents the size of earthquakes, and this is also distributed according to a power law. There are several problems related to the Pareto distribution that one can resolve in the framework of the developed model. One important problem is to determine the income threshold separating the subcritical and supercritical zones of income behaviour. There is a relat

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