Pareto extrapolation: An analytical framework for studying tail inequality

Abstract

We develop an analytical framework designed to solve and analyze heterogeneous‐agent models that endogenously 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 (e.g., 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.

Wealth Inequality in a Low Rate Environment

“…4545 The fact that the relative proportion of each type converges in the right tail is a general result in random growth models (see, for instance, Proposition 4.1 in Gouin‐Bonenfant and Akira Toda (2022)). …”

Tail Behavior of Stopped Lévy Processes With Markov Modulation

“…See also [4] for a closely related application without Markov modulation which accurately predicts the emergence of a power law in the distribution of coronavirus disease cases across counties in the United States in the early months of 2020. Applications of (1.1) where Markov modulation plays an important role include the analyses of wealth inequality in [13,14,15], and of taxation policy in [6].…”