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. 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.

Wealth distribution and optimal taxation with idiosyncratic investment risk:

This paper studies the equilibrium wealth distribution and the optimal taxation of capital using a simple model that features persistent idiosyncratic investment risk and an endogenous Pareto-tailed wealth distribution. We show that Markov switching between productivity types is important for generating a realistic wealth distribution. When the model is calibrated to the U.S. economy, we find that the capital income tax rate that maximizes the social welfare of agents with risk aversion between 1 and 5 ranges from 44% to 60%, which contains the historical effective rates in U.S. from 1981 to 2017