Intertemporal Choice and Inequality

We show that standard models of intertemporal choice, including the permanent income hypothesis, imply that for any given cohort of people born at the same time, inequality in both consumption and income will grow with age. At any given date, each individual's consumption depends on the integral of unanticipated earnings shocks up to that date, so that consumption becomes more dispersed with time. If earnings are not themselves similarly dispersing, assets will do so, so that the dispersion of total income will increase, irrespective of the behavior of earnings. Because the result applies to an increase in inequality over time within a given age cohort, it has no immediate implications for the behavior of inequality in the economy as a whole, and is consistent with constant aggregate inequality over time. Cohort data are constructed from 11 years of household survey data from the U.S., 22 years from Great Britain, and 14 years from Taiwan. They show that within-cohort consumption and income inequality does indeed grow with age in all three economies, and that the rate of increase is broadly similar in all three.