Vanesa Jordá

The Lamé Class of Lorenz Curves.

ABSTRACT In this paper, the class of Lamé Lorenz curves is studied. This family has the advantage of modeling inequality with a single parameter. The family has a double motivation: it can be obtained from an economic model and from simple transformations of classical Lorenz curves. The underlying cumulative distribution functions have a simple closed form, and correspond to the Singh–Maddala and Dagum distributions, which are well known in the economic literature. The Lorenz order is studied and several inequality and polarization measures are obtained, including Gini, Donaldson–Weymark–Kakwani, Pietra, and Wolfson indices. Some extensions of the Lamé family are obtained. Fitting and estimation methods under two different data configurations are proposed. Empirical applications with real data are given. Finally, some relationships with other curves are included.

On the Estimation of the Global Income Distribution Using a Parsimonious Approach

Abstract This paper aims to estimate the global income distribution during the nineties using limited information. In a first stage, we obtain national income distributions considering a model with two parameters. In particular, we propose to use the so-called Lame distributions, which are curved versions of the Sigh-Maddala and Dagum distributions. The main feature of this family is that they represent parsimonious models which can fit income data adequately with just two parameters and whose Lorenz curves are characterized by only one parameter. In a second stage, global and regional distributions are derived from a finite mixture of these families using population shares. We test the validity of the model, comparing it with other two-parameter families. Our estimates of different inequality measures suggest that global inequality presents a decreasing pattern mainly driven by the fall of the differences across countries during the course of the study period that offsets the increase in disparities within countries.

Bivariate beta-generated distributions with applications to well-being data

The class of beta-generated distributions (Commun. Stat. Theory Methods 31:497–512, 2002; TEST 13:1–43, 2004) has received a lot of attention in the last years. In this paper, three new classes of bivariate beta-generated distributions are proposed. These classes are constructed using three different definitions of bivariate distributions with classical beta marginals and different covariance structures. We work with the bivariate beta distributions proposed in (J. Educ. Stat. 7:271–294, 1982; Metrika 54:215–231, 2001; Stat. Probability Lett. 62:407–412, 2003) for the first proposal, in (Stat. Methods Appl. 18: 465–481, 2009) for the second proposal and (J. Multivariate Anal. 102:1194–1202, 2011) for the third one. In each of these three classes, the main properties are studied. Some specific bivariate beta-generated distributions are studied. Finally, some empirical applications with well-being data are presented.Mathematics Subject Classification (2000)62E15; 60E05

The Theil Indices in Parametric Families of Income Distributions—A Short Review

The Theil indices (Theil, 1967) are widely used measures for studying the degree of concentration and inequality in size income distributions. Their property of decomposability makes these indices especially useful in applied economic analysis. This paper is a synthetic review of the Theil indices for the most important and popular parametric income distributions. Extensions to higher dimensions are sketched.

Assessing Global Inequality in Well-being Using Generalized Entropy Measures☆

Abstract In this paper we study global inequality in well-being taking as a reference the Human Development Index. One of the main changes applied to this indicator was the substitution of the arithmetic mean for a geometric mean in the construction of the index, thus assuming different substitution grades between dimensions. In order to determine the impact of the aggregation formula in the distribution of the HDI, we propose the use of multidimensional generalized entropy measures, which allow us to study the evolution of well-being inequality based on different aggregation schemes. The results obtained suggest a reduction in global inequality in human development over the period 1980- 2011. However different inequality patterns are observed depending on the substitutability parameter, thus pointing out the crucial role played by the aggregation formula of composite indices of well-being in the evolution of global inequality.

Bivariate Lorenz Curves Based on the Sarmanov–Lee Distribution

The extension of the univariate Lorenz curve to higher dimensions is not an obvious task. In this chapter, using the definition proposed by Arnold (Pareto Distributions. International Co-operative Publishing House, Fairland (1983)), closed expressions for the bivariate Lorenz curve are given, assuming that the underlying bivariate income distribution belong to the class of bivariate distributions with given marginals described by Sarmanov (Doklady Sov. Math. 168, 596–599 (1966)) and Lee (Commun. Stat. A-Theory 25, 1207–1222 (1996)). The expression of the bivariate Lorenz curve can be easily interpreted as a convex linear combination of products of classical and concentrated Lorenz curves. A closed expression for the bivariate Gini index (Arnold, Majorization and the Lorenz durve. In: Lecture Notes in Statistics, vol. 43. Springer, New York (1987)) in terms of the classical and concentrated Gini indices of the marginal distributions is given. This index can be decomposed in two factors, corresponding to the equality within and between variables. A specific model Pareto marginal distributions is studied. Other aspects are briefly discussed.

Evolution of global inequality in human well-being: a sensitivity analysis

In this paper, we study global inequality in well-being taking as a theoretical benchmark the Human Development Index (HDI), which comprises variables of income, health and education. We use a two-step methodology that involves the construction of a composite index in the first step on which inequality measures are computed. The use of these measures requires making choices on the standardisation of the variables and their weights, the rate of substitution between dimensions and the degree of inequality aversion in the society. We investigate the impact of these choices on the evolution of unweighted inequality over the period 1980-2011. We find the robust result that global inequality in human well-being decreased over the last 30 years.