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

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. We illustrate the use of our results by applying them to the wealth distribution in a heterogeneous-agent general equilibrium model, in which agents engage in private enterprise and trade risk-free bonds while subject to Markov-switching productivity and mortality risk. A plausible numerical calibration yields a Pareto exponent of 1.39 for the upper tail of the wealth distribution, similar to estimates obtained from cross-sectional data.