A common approach used to show high mobility is a low correlation of present and past incomes is captured, for instance, by the Hart index (cov lnyt, lnyt-1). If we assume, as is often done, that an individual’s income is comprised of a transitory component (short-term blips up or down in a self-employed person’s income that we can smooth, or even measurement error), and a permanent component where each income shock is persistent (say, an income loss after an involuntary job change (an AR (1) process with autoregressive coefficient, ρ), then the Hart index can be broken into three parts.
Social welfare functions that assign weights to individuals based on their income levels can be used to document the relative importance of growth and inequality changes for changes in social welfare. This method is applied in a new working paper by David Dollar, Tatjana Kleineberg, and Aart Kraay. They find that, in a large panel of industrial and developing countries over the past 40 years, most of the cross-country and over-time variation in changes in social welfare is due to changes in average incomes. In contrast, the changes in inequality observed during this period are on average much smaller than changes in average incomes, are uncorrelated with changes in average incomes, and have contributed relatively little to changes in social welfare.