A microeconomic model is developed, which accurately predicts the shape of personal income distribution (PID) in the United States and the evolution of the shape over time. The underlying concept is borrowed from geo-mechanics and thus can be considered as mechanics of income distribution. The model allows the resolution of empirical and definitional problems associated with personal income measurements. It also serves as a firm fundament for definitions of income inequality as secondary derivatives from personal income distribution. It is found that in relative terms the PID in the US has not been changing since 1947. Effectively, the Gini coefficient has been almost constant during the last 60 years, as reported by the Census Bureau.
Deep Dive into Mechanical Model of Personal Income Distribution.
A microeconomic model is developed, which accurately predicts the shape of personal income distribution (PID) in the United States and the evolution of the shape over time. The underlying concept is borrowed from geo-mechanics and thus can be considered as mechanics of income distribution. The model allows the resolution of empirical and definitional problems associated with personal income measurements. It also serves as a firm fundament for definitions of income inequality as secondary derivatives from personal income distribution. It is found that in relative terms the PID in the US has not been changing since 1947. Effectively, the Gini coefficient has been almost constant during the last 60 years, as reported by the Census Bureau.
Income distribution is a fundamental process in all economic systems. Conventional economic theories provide a variety of views on the mechanism driving the division of gross domestic product among economic agents. Income distribution at personal level did not deserve the highest attention of the mainstream economists who are focused on households. We do not share this approach and consider personal income as a natural and indivisible level for theoretical consideration. Total income of families and households corresponds to a higher level of aggregation and the dynamics of their evolution is prone to all disturbances associated with fluctuations in their composition and average size over time. Therefore, we introduce and elaborate a concept describing the distribution of personal income and its evolution. Because of data availability, quality and time coverage an unavoidable choice for our study is the United States.
Redline of our investigation follows up the answer to the key question: Whether the configuration of personal incomes in the US is the result of distribution of a random part of nominal GDP growing at a rate prone to stochastic external (in economics -exogenous) shocks or there exists a deterministic and fixed hierarchy of personal incomes, which evolution defines the rate of GDP growth? If the distribution is a stochastic process together with the part of GDP related to personal incomes, i.e. with gross personal income (GPI), one should develop a statistical approach. If the distribution is fixed and defines the overall growth of economy one would be able to formulate a deterministic (e.g. mechanical) model. In this Chapter, we are trying to prove that the second answer is valid and the evolution of each and every personal income is predictable, potentially as accurate as in classical mechanics.
We do not feel that economics as a science is currently able to provide adequate concepts and methods to analyze personal incomes in quantitative terms. So, we adapt an interdisciplinary approach, which has already shown its fruitfulness in many scientific and technological areas. This success is achieved not only due to the coincidence of formal description of various physical, chemical, biological, and sociological processes, but also expresses the existence of very deep common roots in the nature. For example, the power law distribution of sizes is observed in economics (Pareto distribution), in frequencies of words in longer texts, in seismology (Guttenberg-Richter recurrence curve), geomechanics (fractured particle sizes), and many other areas. Recent studies associate the power law distribution with a realization of some stochastic processes known as “self-organized criticality” (SOC).
Economics and its numerous applications in real life demand huge amount of numerical data in order to estimate current state of a given economy and future development. Such data have been continuously gathered from the very beginning of capitalism as an economic system, but the 20 th century and especially its second part is characterized by a dramatic increase in the number of economic observations and measurements. The resulting data set has become an object of a thorough study not only for professional economists but also for specialists in many other disciplines. There are many examples of successful application of mathematical and physical methods from many adjacent disciplines for understanding economic phenomena and processes.
Personal income distribution (PID) represents one of high-quality sets of quantitative data with a history of more than sixty years of continuous measurement with increasing accuracy.
Irrelevant to the nature of these data, even the simplest scatter plot reveals some specific features, which are often observed in physics: growth and fall is well approximated by exponential and power law functions. Some of these functions are the solutions of ordinary differential equation, and thus one can presume that the processes behind the data can be also described by such equations. This makes it very attractive to apply standard methods of analysis and to model the evolution of personal incomes according to ‘first principles’ adopted in the natural sciences.
Among numerous possibilities, we selected the geomechanical model of a solid with inhomogeneous inclusions proposed and developed by V.N. Rodionov and co-authors (1982) as an analogue of an economy expressed as a set of personal incomes. The economy plays the role of a solid body and personal incomes correspond to inelastic stresses on the inclusions. We expected that some of the already available equations and solutions for a solid would provide an adequate description of incomes, and some of the equations would need modification. The intuition behind such an assumption was based not only on our professional experience in both disciplines but also on a formal equivalence of the PID in the United States and the Guttenberg-Richter recu
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