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

Brendan K. Beare; Alexis Akira Toda

doi:10.3982/ecta17984

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arXiv · 1712.01431

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

Brendan K. Beare·Alexis Akira Toda

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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.

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BibTeX RIS

Brendan K. Beare, Alexis Akira Toda. 2017-12-05. Determination of Pareto exponents in economic models driven by Markov multiplicative processes. https://doi.org/10.3982/ecta17984

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