Generalized Beta Prime Distribution: Stochastic Model of Economic Exchange and Properties of Inequality Indices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866909167475752960 |
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| author | Moghaddam, M. Dashti Mills, Jeffrey Serota, R. A. |
| author_facet | Moghaddam, M. Dashti Mills, Jeffrey Serota, R. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_04822 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Generalized Beta Prime Distribution: Stochastic Model of Economic Exchange and Properties of Inequality Indices Moghaddam, M. Dashti Mills, Jeffrey Serota, R. A. Econometrics Theoretical Economics Mathematical Finance Statistical Finance 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. |
| title | Generalized Beta Prime Distribution: Stochastic Model of Economic Exchange and Properties of Inequality Indices |
| topic | Econometrics Theoretical Economics Mathematical Finance Statistical Finance |
| url | https://arxiv.org/abs/1906.04822 |