Econometrica: Jul 2022, Volume 90, Issue 4

Determination of Pareto exponents in economic models driven by Markov multiplicative processes
p. 1811-1833

Brendan K. Beare, Alexis Akira Toda

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.

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