Determination of Pareto Exponents in Economic Models Driven by Markov Multiplicative Processes

• 成果类型: Article
• 署名作者: Beare, Brendan K.; Toda, Alexis Akira
• 署名单位: University of Sydney; University of California System; University of California San Diego
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA17984
• 发表日期: 2022
• 页码: 1811-1833
• 关键词: size distribution; Power laws; WEALTH; income; EQUATIONS; DYNAMICS; returns; GROWTH; cities

摘要

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 nonlattice condition on growth rates, an eigenvector associated with the Pareto exponent provides the distribution of types in the upper tail of the size distribution.