Econometrica: Jul, 2022, Volume 90, Issue 4
Determination of Pareto exponents in economic models driven by Markov multiplicative processes
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.