An ordered family of Lorenz curves

A general method for building parametric-functional families of Lorenz curves, generated from an initial Lorenz curve (which satisfies some regularity conditions) is presented. It is shown that these families can be ordered in a manner which leads to a hierarchy of Lorenz curves. The method starts from a generating Lorenz curve L0(p) and builds the family by increasing the number of parameters, which can be easily interpreted in terms of the elasticities of L0(p). The method is applied to a family we term the Pareto family, since they use the Pareto Lorenz curves as their generating curves. The family is shown to contain an important number of classical Lorenz curves used in the existing literature. Several properties of this family are analyzed, these include the population function, inequality measures and Lorenz orderings. A general method for the estimation of these family is given and applied to the Pareto family. Finally, an application is presented for data from various countries. The results are very robust across data sources. The Pareto models fit very well in a number of applications.