Journal of Econometrics 91 (1999) 43 — 60 An ordered family of Lorenz curves J.-M. Sarabia, Enrique Castillo, Daniel J. Slottje*  Department of Economics, University of Cantabria, Avda. de los Castros s/n, 39005-Santander, Spain  Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de los Castros s/n, 39005-Santander, Spain  Department of Economics, Southern Methodist University, Dallas, TX 75275, USA Received 27 March 1997 Abstract A general method for building parametric-functional families of Lorenz curves, gener- ated 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 ¸  (p) and builds the family by increasing the number of parameters, which can be easily interpreted in terms of the elasticities of ¸  (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.  1999 Elsevier Science S.A. All rights reserved. JEL classification: D3; C5 Keywords: Inequality; Lorenz curve 1. Introduction There is a growing awareness that inequality in the size distribution of income has important ramifications for how the entire economy operates. There are * Corresponding author. 0304-4076/99/$ - see front matter  1999 Elsevier Science S.A. All rights reserved. PII: S 0 3 0 4 - 4 0 7 6 ( 9 8 ) 0 0 0 4 8 - 7