Size-Dependency of Income Distributions and Its Implications

Jiang Zhang and You-Gui Wang

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Abstract: This paper highlights the size-dependency of income distributions, i.e. the income distribution curves versus the population of a country systematically. By using the generalized Lotka-Volterra model to fit the empirical income data in the United States during 1996-2007, we found an important parameter $\lambda$ can scale with a $\beta$ power of the size (population) of U.S. in that year. We pointed out that the size-dependency of the income distributions, which is a very important property but seldom addressed by previous studies, has two non-trivial implications: (1) the allometric growth pattern, i.e. the power law relationship between population and GDP in different years, which can be mathematically derived from the size-dependent income distributions and also supported by the empirical data; (2) the connection with the anomalous scaling for the probability density function in critical phenomena since the re-scaled form of the income distributions has the exactly same mathematical expression for the limit distribution of the sum of many correlated random variables asymptotically.

Date: 2010-12, Revised 2011-01
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Published in Chinese Physics Letters, 2011,28(2):038901

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1012.2279

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