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Generalized Beta Prime Distribution: Stochastic Model of Economic Exchange and Properties of Inequality Indices

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  • M. Dashti Moghaddam
  • Jeffrey Mills
  • R. A. Serota

Abstract

We argue that a stochastic model of economic exchange, whose steady-state distribution is a Generalized Beta Prime (also known as GB2), and some unique properties of the latter, are the reason for GB2's success in describing wealth/income distributions. We use housing sale prices as a proxy to wealth/income distribution to numerically illustrate this point. We also explore parametric limits of the distribution to do so analytically. We discuss parametric properties of the inequality indices -- Gini, Hoover, Theil T and Theil L -- vis-a-vis those of GB2 and introduce a new inequality index, which serves a similar purpose. We argue that Hoover and Theil L are more appropriate measures for distributions with power-law dependencies, especially fat tails, such as GB2.

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  • M. Dashti Moghaddam & Jeffrey Mills & R. A. Serota, 2019. "Generalized Beta Prime Distribution: Stochastic Model of Economic Exchange and Properties of Inequality Indices," Papers 1906.04822, arXiv.org.
    • Handle: RePEc:arx:papers:1906.04822
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