On the precarious link between the Gini coefficient and the incentive to migrate

We offer an explanation for the inconclusive results of empirical studies into the relationship between the magnitude of the Gini coefficient of income distribution at origin and the intensity of migration. Bearing in mind the substantial literature that identifies relative deprivation as an important determinant of migration behavior, we study the relationship between aggregate or total relative deprivation, TRD, the Gini coefficient, G, and migration. We show that for a given change of incomes, TRD and G can behave differently. We present examples where, in the case of universal increases in incomes, TRD increases while G does not change; G decreases while TRD does not change; and G decreases while TRD increases. We generalize these examples into formal criteria, providing sufficient conditions on the initial and final income vectors under which incongruence between the directions of changes of G and of TRD occur. Our analysis leads us to infer that when the incentive to migrate increases with TRD, then this response can co-exist with no change of G or with a decrease of G. @We offer an explanation for the inconclusive results of empirical studies into the relationship between the magnitude of the Gini coefficient of income distribution at origin and the intensity of migration. Bearing in mind the substantial literature that identifies relative deprivation as an important determinant of migration behavior, we study the relationship between aggregate or total relative deprivation, TRD, the Gini coefficient, G, and migration. We show that for a given change of incomes, TRD and G can behave differently. We present examples where, in the case of universal increases in incomes, TRD increases while G does not change; G decreases while TRD does not change; and G decreases while TRD increases. We generalize these examples into formal criteria, providing sufficient conditions on the initial and final income vectors under which incongruence between the directions of changes of G and of TRD occur. Our analysis leads us to infer that when the incentive to migrate increases with TRD, then this response can co-exist with no change of G or with a decrease of G.