Age, Wealth Inequality and Life-Cycle Modelling

Abstract

Most of the main observed features of the distribution of wealth have been studied in detail. We know much about the possible reasons for the long upper tail of the distribution, the age profile of mean wealth, portfolio composition, changes in the distribution over time, differences between countries, and the very low wealth-holdings observed for some people at all ages (see Davies and Shorrocks, forthcoming). Yet one of the most interesting stylized facts about the distribution of wealth ‐ that wealth inequality follows a pronounced U-shaped age profile ‐ has received hardly any attention and has not been satisfactorily explained. In all countries where data are available, wealth inequality declines at least until middle age, and in almost all datasets it increases from middle age through retirement. The fact that the age profile of wealth inequality is U-shaped contrasts with the behaviour of inequality in earnings, income, and consumption. While inequality in earnings declines for the first five to ten years of the working lifetime, the dominant pattern is that inequality in all three of these variables rises over the lifetime. This is such a strong and well-known empirical regularity that it may have drawn attention away from the finding of a U-shaped profile for wealth inequality. This paper explores alternative possible explanations for the U-shaped age profile of wealth inequality. Aside from satisfying our curiosity, such an investigation may help us understand processes of wealth accumulation better. Deaton and Paxson (1994) obtained valuable insights requiring just that a saving model should predict rising income and consumption inequality over the lifetime. But a satisfactory model must be capable of more. It should predict not only that inequality in income and consumption will rise with age but also that wealth inequality will initially decline with age before rising over the latter portion of the life-cycle. As argued by Friedman (1957), the ability to reproduce the stylized facts of wealth inequality is an important test of models of consumption. The only previous attempt to model a U-shaped age profile of wealth inequality of which I am aware is Shorrocks (1975a). Shorrocks investigated a queuing model of wealth accumulation and illustrated the model through an application to the age profiles of mean wealth and wealth inequality. In his model there are two sources of shocks to wealth at a point in time. One is independent of current wealth, and arises due to earnings innovations. The other is proportional to current wealth (in expected value). The independent shocks act to reduce wealth inequality over time, whereas the proportional shocks do the opposite. Initially