Casilda Lasso de la Vega

Classical inequality indices, welfare and illfare functions, and the dual decomposition

Abstract In the traditional framework, social welfare functions depend on the mean income and on the income inequality. An alternative illfare framework has been developed to take into account the disutility of unfavorable variables. The illfare level is assumed to increase with the inequality of the distribution. In some social and economic fields, such as those related to employment, health, education, or deprivation, the characteristics of the individuals in the population are represented by bounded variables, which encode either achievements or shortfalls. Accordingly, both the social welfare and the social illfare levels may be assessed depending on the framework we focus on. In this paper we propose a unified dual framework in which welfare and illfare levels can both be investigated and analyzed in a natural way. The dual framework leads to the consistent measurement of achievements and shortfalls, thereby overcoming one important difficulty of the traditional approach, in which the focus on achievements or shortfalls often leads to different inequality rankings. A number of welfare functions associated with inequality indices are OWA operators. Specifically this paper considers the welfare functions associated with the classical inequality measures due to Gini, Bonferroni, and De Vergottini. These three indices incorporate different value judgments in the measurement of inequality, leading to different behavior under income transfers between individuals in the population. In the bounded variables representation, we examine the dual decomposition and the orness degree of the three classical welfare/illfare functions in the standard framework of aggregation functions on the [ 0 , 1 ] n domain. The dual decomposition of each welfare/illfare function into a self-dual central index and an anti-self-dual inequality index leads to the consistent measurement of achievements and shortfalls.

A class of poverty measures induced by the dual decomposition of aggregation functions

In this paper we introduce a new family of poverty measures for comparing and ordering social situations. The aggregation scheme of these poverty measures is based on the one-parameter family of exponential means. The poverty measures introduced satisfy interesting properties and the dual decomposition of the underlying exponential means induces a natural decomposition of the proposed poverty indices themselves into three underlying factors: incidence, intensity, and inequality among the poor.

Characterizing multidimensional inequality measures which fulfil the Pigou-Dalton bundle principle

The Pigou–Dalton bundle dominance introduced by Fleurbaey and Trannoy (Social Choice and Welfare, 2003) captures the basic idea of the Pigou–Dalton transfer principle, demanding that, in the multidimensional context also, “a transfer from a richer person to a poorer one decreases inequality”. However, up to now, this principle has not been incorporated to derive multidimensional inequality measures. The aim of this article is to characterize measures which fulfil this property, and to identify sub-families of indices from a normative approach. The families we derive share their functional forms with others having already been obtained in the literature, the major difference being the restrictions upon the parameters.

A New Multiplicative Decomposition for the Foster–Greer–Thorbecke Poverty Indices

This paper identifies a multiplicative decomposition for the Foster-Greer-Thorbecke poverty indices as a product of the three components which should be involved in every poverty index: the incidence of poverty, measured by the headcount ratio, the intensity of poverty, measured by the aggregate income gap ratio and the inequality among the poor measured by an increasing transformation of the corresponding inequality index of the Generalized Entropy family. Then, taking data from the Spanish Household Budget Surveys (SHB) as a basis we show the advantages and possibilities of this framework in regard to completing and detailing information in studies of poverty over time.

Segregation, informativeness and Lorenz dominance

It is possible to partially order cities according to the informativeness of neighborhoods about their ethnic groups. It is also possible to partially order cities with two ethnic groups according to the Lorenz criterion. We show that a segregation order satisfies four well-established segregation principles if and only if it is consistent with the informativeness criterion. We then use this result to show that for the two-group case, the Lorenz and the informativeness criteria are equivalent.

Measuring the Inequality of Bounded Distributions: A Joint Analysis of Attainments and Shortfalls

Abstract When health is measured by a bounded variable, differences in health can be presented as levels of attainment or shortfall. Measurement of heath inequality then usually involves the choice of either the attainment or the shortfall distribution, and this choice may affect comparisons of inequality across populations. A number of indices have been introduced to overcome this problem. This chapter proposes a framework in which attainment and shortfall distributions can be jointly analyzed. Joint distributions of attainments and shortfalls are defined from points of view consistent with concerns for relative, absolute or intermediate inequality. Inequality measures invariant according to the corresponding ethical criterion are then applied. A dominance criterion that guarantees unanimous rankings of the joint distributions is also proposed.

An Axiomatic Characterization of the Theil Inequality Ordering

We identify an ordinal decomposability property and use it, along with other ordinal axioms, to characterize the Theil inequality ordering.

Assessing Wellbeing and Deprivation in Later Life: A Multidimensional Counting Approach

The paper applies a multidimensional and comparative approach to the assessment of wellbeing and deprivation among a panel of older people in Brazil and South Africa. It develops and justifies a counting approach to rank order wellbeing and deprivation distributions. An application of this approach generates substantive findings on the dynamics of the distribution of wellbeing and deprivation in later life, on stratification, and on the importance of social policy addressing ageing.

A Simple Proof of Foster's (1983) Characterization of the Theil Measure of Inequality

We provide a simple proof of Fosters (1983) characterization of the Theil inequality index.

The Measurement of Income Segregation

We examine the problem of measuring the extent to which students with different income levels attend separate schools. Unless rich and poor attend the same schools in the same proportions, some segregation will exist. Since income is a continuous cardinal variable, however, the rich-poor dichotomy is necessarily arbitrary and renders any application of a binary segregation measure artificial. This paper provides an axiomatic characterization of two measures of income segregation that take into account the cardinal nature of income. Both measures satisfy an empirically useful decomposition by sub-districts.