Wealth Inequality and the Ergodic Hypothesis : Evidence from the United States

Many studies of wealth inequality make the ergodic hypothesis that rescaled wealth converges rapidly to a stationary distribution. Changes in distribution are expressed through changes in model parameters, reflecting shocks in economic conditions, with rapid equilibration thereafter. Here we test the ergodic hypothesis in an established model of wealth in a growing and reallocating economy. We fit model parameters to historical data from the United States. In recent decades, we find negative reallocation, from poorer to richer, for which no stationary distribution exists. When we find positive reallocation, convergence to the stationary distribution is slow. Our analysis does not support using the ergodic hypothesis in this model for these data. It suggests that inequality evolves because the distribution is inherently unstable on relevant timescales, regardless of shocks. Studies of other models and data, in which the ergodic hypothesis is made, would benefit from similar tests