Almost Lorenz dominance

This paper extends Leshno and Levy’s (Manag Sci 48:1074–1085, 2002) approach of “almost stochastic dominance” to inequality orderings. We define and characterize the notion of “almost Lorenz dominance” (ALD) and illustrate it with the US income data. An income distribution is said to “almost” Lorenz dominate another distribution when its Lorenz curve lies almost everywhere but not entirely above the other Lorenz curve. We show that this condition is equivalent to requiring that “almost” all Gini-type inequality measures rank the former distribution to have less inequality than the latter distribution; the condition on the Gini-type inequality measures has a clear interpretation and is easy to apply. We further define an almost composite transfer (ACT) and show that ALD amounts to a sequential application of such transfers. The empirical illustration with the US income data (1967–1986) demonstrates the utility of this generalized notion of inequality ordering.