Stochastic Earnings Growth and Equilibrium Wealth Distributions

The cross-section distribution of U.S. wealth is more skewed than the distribution of labor earnings. Stachurski and Toda (2019) explain how plain vanilla Bewley-Aiyagari-Huggett (BAH) models with infinitely lived agents can't generate that pattern because an equilibrium risk-free rate is lower than the time rate of preference and each person's wealth process is stationary. We provide two modifications of a BAH model that generate this pattern: (1) overlapping generations of agents who have low wealth at birth and pass through N life-stage transitions of stochastic lengths, and (2) labor-earnings processes that exhibit stochastic growth. With only a few parameters such a model can well approximate mappings from the Lorenz curve and Gini coefficient for cross-sections of labor earnings to their counterparts for cross sections of wealth. Three forces amplify inequality in wealth relative to inequality in labor-earnings: stochastic life-stage transitions; a precautionary savings motive for high wage earners that is especially strong after they receive positive permanent earnings shocks; and an energetic life-cycle saving motive for agents who have low wealth at birth. An equilibrium risk-free interest rate that exceeds a time preference rate fosters a fat-tailed wealth distribution.