Inequality and Panel Income Changes: Conditions for Possibilities and Impossibilities

The question of who benefits from economic growth is usually assessed by using cross section data to calculate changes in income inequality. An alternative is to assess patterns of panel income changes. We derive theoretical conditions reconciling changes in inequality together with various measures of convergent/divergent panel income changes. For a large number of inequality indices, as well as for Lorenz curves: we show that rising inequality can coexist with convergent panel changes provided the latter are "large" (and in the right direction), where the meaning of "large" varies depending on the particular regression under analysis; we show that it is impossible to have both falling inequality together with divergent panel income changes in shares or in proportions; and we establish a condition linking convergence/divergence in dollars to changes in the coefficient of variation.