Determination of Pareto exponents in economic models driven by Markov multiplicative processes

Brendan Beare and Alexis Akira Toda

Papers from arXiv.org

Abstract: This article contains new tools for studying the shape of the stationary distribution of sizes in a dynamic economic system in which units experience random multiplicative shocks and are occasionally reset. Each unit has a Markov-switching type which influences their growth rate and reset probability. We show that the size distribution has a Pareto upper tail, with exponent equal to the unique positive solution to an equation involving the spectral radius of a certain matrix-valued function. Under a non-lattice condition on growth rates, an eigenvector associated with the Pareto exponent provides the distribution of types in the upper tail of the size distribution.

Date: 2017-12, Revised 2022-01
New Economics Papers: this item is included in nep-rmg
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Published in Econometrica 90(4):1811-1833 (2022)

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Journal Article: Determination of Pareto Exponents in Economic Models Driven by Markov Multiplicative Processes (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1712.01431

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