Wealth Distribution and Infinite Horizon

This paper presents an explicitly solved model of wealth distribution in an infinite-horizon incomplete-markets economy. The agent aims to hold a target level of wealth in order to partially buffer income shocks. The notion of buffering suggests that the agent’s wealth is less skewed and less fat-tailed than his income in the long run. Infinite-horizon setting implies that the cross-sectional joint distribution of wealth and income is equal to the long-run joint distribution of an individual’s wealth and income. Therefore, infinitehorizon models imply that cross-sectionally, wealth is also less skewed and fat-tailed than income, just the opposite of the empirical evidence. This paper also provides an analytical consumption rule and a recursive formulation for the moments of the joint distribution, which allows us to completely characterize the joint distribution of wealth and income in closed form. One implication of this paper is that a life-cycle model is necessarily the first step towards a more realistic model of wealth distribution. JEL Classification: D91, E21