Pareto extrapolation: bridging theoretical and quantitative models of wealth inequality

We develop an analytical framework designed to solve and analyze heterogeneous-agent models that generate fat-tailed wealth distributions. We exploit the asymptotic linearity of policy functions and the analytical characterization of the Pareto exponent to augment the conventional solution algorithm with a theory of the tail. Our framework allows for a precise understanding of the very top of the wealth distribution (i.e., analytical expressions for top wealth shares, type distribution in the tail, and transition probabilities in and out of the tail) in addition to delivering improved accuracy and speed. We apply our framework to quantify the effect of a wealth tax on large fortunes in a general equilibrium model with borrowing constraint, portfolio choice, earnings risk, and return heterogeneity