PhD Seminar: Pareto tails of Consumption and Wealth

Title:Pareto tails of Consumption and Wealth

Abstract:Prior cross-country evidence shows that wealth distribution has a much heavier Pareto tail than consumption distribution. Prior impossibility results show that standard heterogeneous-agent (HA) models cannot generate this gap. This paper studies a constructive escape. We develop a two-asset HA model with liquid and illiquid wealth. Returns are stochastic and satisfy a return premium condition. Consumption financed from illiquid wealth requires liquidation, and liquidation costs are convex in the size of the withdrawal. Under primitive conditions, liquid wealth vanishes as a share of total wealth in the upper tail, so the two-asset problem reduces to an income-fluctuation problem with a convex consumption cost. When liquidation costs rise as a power of the withdrawal amount, the model links the observed tail index gap to how quickly liquidation costs rise with withdrawal size. Moderately convex liquidation costs account for the Australian, Chinese, and French gaps, while larger gaps point to stronger frictions or complementary wealth-preference mechanisms. Within this cost class, the distinction is sharp: costs tied to the withdrawal size can generate the tail index gap, whereas holdings-scaled costs cannot.