On the Measurement of Long-Term Income Inequality and Income Mobility

This paper proposes a two-step aggregation method for measuring long-term income inequality and income mobility, where mobility is defined as an equalizer of long-term income. First, the income stream of each individual is aggregated into a measure of permanent income, which accounts for the costs associated with income fluctuations. Consequently, mobility will have an unambiguously positive impact on social welfare in the sense that for two societies that have identical short term income distributions, the social welfare will be greatest for the socie ty which exhibits most mobility. The second step consists of aggregating permanent incomes across individuals into measures of social welfare, inequality and mobility. To this end, we employ an axiomatic approach to justify the introduction of a generalized family of rank-dependent measures of inequality, where the distributional weights, as opposed to the Mehran-Yaari family, depend on income shares as well as on population shares. Moreover, a subfamily is shown to be associated with social welfare functions that have intuitively appealing interpretatio ns. Further, the generalized family of inequality measures provides several new interpretations of the Gini-coefficient. The proposed family of income mobility also proves to encompass standard measures of income mobility, depending on the assumptions made about the interpersonal preferences and the credit market.