Equivalence of Scales and Inequality (published in Income Inequality Measurement:From Theory to Practice, J Silber (ed), Dewenter: Kluver (1999)

Instead of Inequality analysis sometimes neglects the problem of allowing differences in people's non-income characteristics in the comparison of income distribution, I would say, At the heart of any distributional analysis there is the problem of allowing for differences in people's non-income characteristics. We examine the role of standard equivalence scales in distributional comparisons and the welfare implications of the basis for constructing equivalence scales. We consider the use of alternative approaches that do not require the specification of a single scale and implement one of these in a practical comparison of Spain and the UK.Inequality, social welfare, equivalence scales

Searching by questionaire for the meaning of income inequality

Amien and Cowell (1992) have recently performed an experimental test by questionnaire to investigate whether a sample of individuals corroborate the general consensus found in the literature about a number of axioms on the meaning of 'inequality'. They obtained some mixed results. In this article we report on a replica of the experiment with some novelties: we introudce the role of political attitudes toward income redistribution to clarify the interpretation of some results; the questionnaire is enlarged in an attempt to give more room to notions of inequality imtermediate between the relative and absolute polar cases; and we provide a systematic treatment of the degree of consistency exhibited by the respondents

The measurement of inequality of opportunity : theory and an application to Latin America

What part of the inequality observed in a particular country is due to unequal opportunities, rather than to differences in individual efforts or luck? This paper estimates a lower bound for the opportunity share of inequality in labor earnings, household income per capita and household consumption per capita in six Latin American countries. Following John Roemer, the authors associate inequality of opportunity with outcome differences that can be accounted for by morally irrelevant pre-determined circumstances, such as race, gender, place of birth, and family background. Thus defined, unequal opportunities account for between 24 and 50 percent of inequality in consumption expenditure in the sample. Brazil and Central America are more opportunity-unequal than Colombia, Ecuador, or Peru."Opportunity profiles,"which identify the social groups with the most limited opportunity sets, are shown to be distinct from poverty profiles: ethnic origin and the geography of birth are markedly more important as determinants of opportunity deprivation than of outcome poverty, particularly in Brazil, Guatemala, and Peru.Inequality,Rural Poverty Reduction,Access to Finance,Equity and Development,Services&Transfers to Poor

The evolution of global inequality: absolute, relative and intermediate views

We compare absolute, relative and intermediate views on the evolution of global inequality between 1980 and 2009. According to the relative view, inequality remains invariant after a uniform proportional change of all incomes whereas the absolute view requires invariance to a uniform change of all incomes with the same amount. We use a generic intermediate view which states that an income distribution is as unequal as another one if it can be obtained as a weighted average of a uniform proportional and a uniform absolute change of the incomes. Using recent data on GDP per capita for 115 countries, we .nd considerable support for the claim that world inequality increased for the absolute view and for intermediate views which move substantially in the direction of the relative view.

The evolution of global inequality: absolute, relative and intermediate views.

We compare absolute, relative and intermediate views on the evolution of global inequality between 1980 and 2009. According to the relative view, inequality remains invariant after a uniform proportional change of all incomes whereas the absolute view requires invariance to a uniform change of all incomes with the same amount. We use a generic intermediate view which states that an income distribution is as unequal as another one if it can be obtained as a weighted average of a uniform proportional and a uniform absolute change of the incomes. Using recent data on GDP per capita for 115 countries, we .nd considerable support for the claim that world inequality increased for the absolute view and for intermediate views which move substantially in the direction of the relative view.

Friedman, Harsanyi, Rawls, Boulding - or Somebody Else?

This paper investigates distributive justice using a fourfold experimental design : The ignorance and the risk scenarios are combined with the self-concern and the umpire modes. We study behavioral switches between self-concern and umpire mode and investigate the goodness of ten standards of behavior. In the ignorance scenario, subjects became on average less inequality averse as umpires. A within-subjects analysis shows that about one half became less inequality averse, one quarter became more inequality averse and one quarter left its behavior unchanged as umpires. In the risk scenario, subjects become on average more inequality averse in their umpire roles. A within-subjects analysis shows that half of them became more inequality averse, one quarter became less inequality averse, and one quarter left its behavior unchanged as umpires. As to the standards of behavior, several prominent ones (leximin, leximax, Gini, Cobb-Douglas) experienced but poor support, while expected utility, Boulding's hypothesis, the entropy social welfare function, and randomization preference enjoyed impressive acceptance. For the risk scenario, the tax standard of behavior joins the favorite standards of behavior. --Distributive justice,income distributions,veil of ignorance

Modeling inequality and spread in multiple regression

We consider concepts and models for measuring inequality in the distribution of resources with a focus on how inequality varies as a function of covariates. Lorenz introduced a device for measuring inequality in the distribution of income that indicates how much the incomes below the u$^{th}$ quantile fall short of the egalitarian situation where everyone has the same income. Gini introduced a summary measure of inequality that is the average over u of the difference between the Lorenz curve and its values in the egalitarian case. More generally, measures of inequality are useful for other response variables in addition to income, e.g. wealth, sales, dividends, taxes, market share and test scores. In this paper we show that a generalized van Zwet type dispersion ordering for distributions of positive random variables induces an ordering on the Lorenz curve, the Gini coefficient and other measures of inequality. We use this result and distributional orderings based on transformations of distributions to motivate parametric and semiparametric models whose regression coefficients measure effects of covariates on inequality. In particular, we extend a parametric Pareto regression model to a flexible semiparametric regression model and give partial likelihood estimates of the regression coefficients and a baseline distribution that can be used to construct estimates of the various conditional measures of inequality.Comment: Published at http://dx.doi.org/10.1214/074921706000000428 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Measurement of Income Inequality : The η;−invariance and its Associated Lorenz Dominance

In a recent paper, Yoshida (Social Choice and Welfare 24 : 557−574 ; 2005) has proposed a new concept of intermediate inequality which is referred to as the η−inequality equivalence. The aim of this paper is to characterize the class of inequality measures possessing this property in terms of the associated Lorenz dominance. For each η ∈ [0,1], we place a class М(η) of inequality measures satisfying the η−inequality　equivalence. Then we show that a necessary and sufficient condition for two income distributions to be ranked unambiguously according to the class М(η) is that the associated η−Lorenz curves do not intersect.所得不平等度尺度は異なった状態にある所得分配の間で不平等度を比較するうえで欠かせない統計的用具であり，今日に至るまで数多くの不平等度尺度が提案され実証分析に用いられている。これらの不平等度尺度は，各構成員の所得がどのように変化した場合に不平等が不変に保たれるかという性質に応じて，（i）相対的不平等度尺度，（ii）絶対的不平等度尺度，（iii）中間的不平等度尺度，に大別することが可能である。相対的尺度とは，全構成員の所得の比例的変化に対して不平等度が不変に保たれる性質を有する尺度のことをいう。これに対して絶対的尺度とは，全構成員の所得の絶対的な同一金額の変化に対して不平等度が不変に保たれる性質を持つ尺度のことをす。中間的不平等尺度とは，文字通り，相対的尺度と絶対的尺度のどこか中間に不平等不変経路が位置しているような尺度の総称である。より形式的には，全構成員の所得の比例的な増加に対しては不平等度は上昇するが，全構成員の所得の同一額の増加に対しては不平等度は減少するような性質を有する尺度のことをいう。中間的不平等度尺度が有すべきこの性質はBossert and Pfingsten（１９９０）によって折衷的性質compromise propertyと名付けられている。中間的不平等度概念に関しては，Kolm（１９７６a, b）による独創的な研究が著わされたのを契機に論者の間で徐々に関心が高まり，特に１９９０年代以降，Pfingsten（１９８６，１９８８）Bossert and Pfingsten（１９９０），Krtscha（１９９４），Seidl and　Pfingsten（１９９７），Del Río and Ruiz−Castillo（２０００) Zoli（１９９８，１９９９），Ebert（２００４），Zheng（２００４，２００７），Yoshida（２００５）等により，異なった中間的不平等度概念とそれに基づく様々な不平等度尺度が提案されている。本論文は近年筆者が提唱した中間的不平等概念であるη−不平等不変性（Yoshida，２００５）を仮定する。η−不平等不変性はKrtscha（１９９３）が公平な折衷概念fair compromsise concept と名付けた非線形の中間的不平等概念を一般化してより厳密に定式化したものであって，相対的不平等概念と絶対的不平等概念を両端に含むパラメトリックな中間的不平等概念である。筆者は前論文（Yoshida，２００５）において，この新しい不平等概念を，所得分布の社会的厚生基準によるランキングにかかわるフレームワークの中で性格付けることを試みた。本論文では社会的厚生から不平等度計測そのものに焦点を移動させることとする。より具体的には，η−不平等不変性を有する不平等度尺度関数のクラスをそれに対応するローレンツ優越によって性格付けることを本論文の目的とする

Inequality, Poverty, Two Invariance Conditions, and a Product Rule

Full Text / Article completTwo axioms in the measurement of inequality and poverty which are widely perceived to be innocuous and unexceptionable - although they have both been challenged in the literature - are the Scale Invariance Axiom and the Replication Invariance Axiom. These axioms have endorsed an essentially relative approach (with respect to income-size and population-size respectively) to the measurement of inequality and poverty. The present paper is an expository essay which aims to clarify the logical and ethical limitations of either a purely relative or a purely absolute approach to distributional measurement. In the process, it also reviews two proposals - due to Manfred Krtscha and Eduardo Arriaga respectively - for ‘intermediate’ measures of inequality and poverty, which moderate the ‘extreme’ values underlying relative and absolute measures by combining these opposing values in a simple product formula.Les axiomes d’échelle invariante et de réplication invariante, sont deux axiomes de la mesure de l'inégalité et de la pauvreté largement perçus comme inoffensifs et irrécusables, bien qu'ils aient tous deux été contestés dans la littérature. Ces axiomes ont appuyé une approche essentiellement relative (par rapport au revenu et à la population, respectivement) de l'inégalité et de la pauvreté. Cet article vise à clarifier les limites logiques et éthiques d’une mesure soit purement relative, soit purement absolue. Il examine également deux propositions - suivant Manfred Krtscha et Eduardo Arriaga respectivement - des mesures «intermédiaires» de l'inégalité et de la pauvreté, qui modèrent les valeurs «extrêmes» des mesures sous-jacentes relatives et absolues en combinant ces valeurs opposées dans une formule simple

The Measurement of Educational Inequality: Achievement and Opportunity

This paper proposes two related measures of educational inequality: one for educational achievement and another for educational opportunity. The former is the simple variance (or standard deviation) of test scores. Its selection is informed by consideration of two measurement issues that have typically been overlooked in the literature: the implications of the standardization of test scores for inequality indices, and the possible sample selection biases arising from the Program of International Student Assessment (PISA) sampling frame. The measure of inequality of educational opportunity is given by the share of the variance in test scores that is explained by pre-determined circumstances. Both measures are computed for the 57 countries in which PISA surveys were conducted in 2006. Inequality of opportunity accounts for up to 35 percent of all disparities in educational achievement. It is greater in (most of) continental Europe and Latin America than in Asia, Scandinavia, and North America. It is uncorrelated with average educational achievement and only weakly negatively correlated with per capita gross domestic product. It correlates negatively with the share of spending in primary schooling, and positively with tracking in secondary schools.educational inequality, educational achievement, inequality of opportunity