Wealth distribution with random discount factors

To explain the Pareto tail behavior empirically observed in wealth distributions, the quantitative macro literature has occasionally assumed that agents have random discount factors. This paper formally proves that the stationary wealth distribution in a simple Huggett model with random discounting has power law tails and characterizes the Pareto exponents analytically. I find that in general there is no clear relationship between the return on wealth and inequality and that the Pareto exponent is highly sensitive to the persistence of the discount factor process. I also provide a practical guidance for how to characterize the Pareto exponents in richer models