On the Measurement of Inequality
TL;DR: In this paper, the problem of comparing two frequency distributions f(u) of an attribute y which for convenience I shall refer to as income is defined as a risk in the theory of decision-making under uncertainty.
About: This article is published in Journal of Economic Theory.The article was published on 1970-09-01. It has received 5002 citations till now. The article focuses on the topics: Income inequality metrics & Income distribution.
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TL;DR: In this paper, the authors model fluctuations in regional disaggregates as a nonstationary, dynamically evolving distribution, which enables study of the dynamics of aggregate fluctuations jointly with those of the rich cross-section of regional aggregates.
Abstract: This paper models fluctuations in regional disaggregates as a nonstationary, dynamically evolving distribution. Doing so enables study of the dynamics of aggregate fluctuations jointly with those of the rich cross-section of regional disaggregates. For the US, the leading state — regardless of which it happens to be — contains strong predictive power for aggregate fluctuations. This effect is difficult to understand if only aggregate disturbances affect aggregate business cycles through aggregate propagation mechanisms. Instead, a better picture might be one of a “wave” of regional dynamics, rippling across the national economy.
95 citations
Cites background from "On the Measurement of Inequality"
...Atkinson's classic paper (1970) shows how alternative inequality measures imply substantively different - and potentially contradictory - views on the inequality actually extant....
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01 Mar 1987
TL;DR: In this article, a methodology for evaluating the impact of macroeconomic adjustment on poverty has been proposed, based on the concept of crossover time, the time that it would take the average poor person to cross the poverty line if his income grew at the per capita growth rate experienced in the past.
Abstract: This paper reviews recent developments in the measurement of poverty, analyzes alternative strategies for poverty alleviation, and suggests a methodology for evaluating the impact of macroeconomic adjustment on poverty. The paper begins with the conceptual basis of alternative poverty lines and alternative indices. It then introduces the concept of "crossover time," the time that it would take the average poor person to cross the poverty line if his income grew at the per capita growth rate experienced in the past. For reasonable estimates this crossover time can exceed twenty years, which perhaps explains the concern with redistribution rather than a complete reliance on "trickle-down" effects. Regarding redistribution, the paper considers the question of targeting public expenditure on the poor. If large-scale means testing of individual households is administratively infeasible or too costly, policy must rely on instruments that measure the incomes of broadly defined groups. Although leakage is inevitable, how can it be minimized? The paper develops a methodology to answer this question and derives budgetary rules for poverty alleviation that rely only on information readily available in surveys of household income and expenditure. The paper also analyzes macroeconomic adjustment and poverty. The bottom line for most policies is to switch expenditure toward the traded goods sector and to reduce overall expenditure. The paper derives rules for when such a switch will increase or decrease poverty as well as for deciding which broad categories of income should bear the burden of reduction. Finally, the paper suggests areas for further research, especially through an application of the methodology developed in it to actual case studies. /// Le prA©sent article examine les A©tudes quantitatives qui ont A©tA© rA©cemment effectuA©es sur la pauvretA©, ainsi que diverses stratA©gies visant A y remA©dier; l'auteur propose A©galement une mA©thode de dA©termination de l'effet d'un ajustement macroA©conomique sur la pauvretA©. L'auteur commence par dA©finir diffA©rents seuils de pauvretA© et indices de pauvretA©. Puis, il introduit la notion de "temps de passage", c'est-A -dire le temps nA©cessaire A un A©conomiquement faible moyen pour quitter le seuil de pauvretA© si son revenu augmentait au mAame rythme que le taux de croissance par habitant enregistrA© dans le passA©. Il ressort d'estimations raisonnables que ce temps de passage peut Aatre supA©rieur A vingt ans, ce qui explique peut-Aatre l'importance accordA©e A la redistribution par opposition A un recours unique aux effets de retombA©e. S'agissant de la redistribution, l'auteur examine la question de l'orientation explicite des dA©penses publiques vers les A©conomiquement faibles. S'il est impossible sur le plan pratique, ou trop coA»teux, de procA©der A une vaste enquAate sur les ressources financiA¨res des mA©nages, la politique doit reposer sur des instruments qui mesurent les revenus de groupes dA©finis de maniA¨re gA©nA©rale. S'il est impossible de limiter les effets de cette politique aux groupes pour lesquels elle a A©tA© conA§ue, comment minimiser ces fuites? L'A©tude prA©sente une mA©thode qui rA©pond A cette question et A©tablit des normes budgA©taires destinA©es A allA©ger la pauvretA©, qui s'appuient uniquement sur des donnA©es provenant d'enquAates sur le revenu et les dA©penses des mA©nages. L'auteur analyse A©galement l'ajustement macroA©conomique et la pauvretA©. La plupart des politiques consistent, en fin de compte, A rA©orienter les dA©penses vers le secteur des biens A©changA©s et A rA©duire les dA©penses globales. L'A©tude prA©sente certaines normes permettant de dA©terminer quand cette rA©orientation peut provoquer un accroissement ou une diminution de la pauvretA© et de dA©cider quelles sont les grandes catA©gories de revenus qui doivent supporter le fardeau de la rA©duction. Enfin, l'auteur suggA¨re divers domaines susceptibles d'Aatre d'A©tudiA©s de maniA¨re plus approfondie, notamment par l'application A des cas spA©cifiques de la mA©thode mise au point dans le cadre de la prA©sente A©tude. /// En este trabajo pasamos revista a la evoluciA³n mAis reciente de la mediciA³n de la pobreza, analizando estrategias alternativas para mitigarla y proponiendo una metodologAa para evaluar los efectos que el ajuste macroeconA³mico tiene sobre la misma. El artAculo empieza presentando el fundamento conceptual de las distintas lAneas de pobreza y de los diferentes Andices; a continuaciA³n aborda el concepto de "perAodo de traspaso", es decir, el tiempo que tardarAa la persona pobre media en traspasar la lAnea de pobreza si sus ingresos aumentaran al ritmo de crecimiento per cAipita experimentado en el pasado. Con arreglo a unas estimaciones razonables, dicho perAodo podrAa superar los veinte aA±os, lo que explica quizAi la preocupaciA³n por la redistribuciA³n, en vez de fiarse por completo de los efectos del "goteo de los beneficios". En lo relativo a la redistribuciA³n, el presente trabajo considera la cuestiA³n de volcar el gasto pAoblico en los pobres. Si no es factible desde el punto de vista administrativo contrastar a gran escala los medios econA³micos de cada una de las unidades familiares, o resulta demasiado costoso, la polAtica habrAi de apoyarse en instrumentos que midan el ingreso de grupos definidos de forma amplia. Aunque la filtraciA³n es inevitable, Â?cA³mo reducirla al mAnimo? Se presenta aquA una metodologAa para contestar a esa pregunta y que permite formular unas reglas presupuestarias para mitigar la pobreza exclusivamente en la informaciA³n disponible directamente de las encuestas sobre ingresos y gastos de las unidades familiares. El presente artAculo analiza tambiA©n el ajuste macroeconA³mico y la pobreza. La finalidad de muchas medidas de polAtica consiste en trasladar el gasto hacia el sector de bienes comerciados y reducir el gasto global. MAis adelante se formulan las reglas a aplicar cuando dicha traslaciA³n aumente o disminuya la pobreza, asA como para decidir quA© categorAas generales de ingresos habrAin de soportar la carga de la reducciA³n. Por Aoltimo, se proponen algunos temas en los que puede continuarse la investigaciA³n, especialmente mediante la aplicaciA³n a casos concretos de la metodologAa aquA formulada.
94 citations
01 Jan 1999
TL;DR: A general survey of multidimensional approaches to the measurement and comparisons of welfare situations is provided in this paper, where the authors emphasize implementability issues and statistical methods in the context of a comparative analysis of the philosophical and theoretical desirability of alternative approaches.
Abstract: A general survey of multidimensional approaches to the measurement and comparisons of welfare situations is provided. The survey covers some aspects of welfare representation, data availability and experience, axiomatic characterization of inequality measures, existing multidimensional indices, the stochastic dominance alternative for comparing welfare situations, and mobility. Applications to national and international data are described. The paper emphasizes implementability issues and statistical methods in the context of a comparative analysis of the philosophical and theoretical desirability of alternative approaches.
94 citations
Cites background from "On the Measurement of Inequality"
...Kolm (1969) and Atkinson (1970) have provided clear and influential formalizations of the relationship between SWFs and inequality measures2 ....
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...Atkinson (1970) and Kolm (1969) argued that, see also Blackorby and Donaldson (1978), I(X) = 1−Xe/µx (2.1) may be a good measure of “relative” inequality....
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Posted Content•
TL;DR: In this article, it was shown that the use of η is preferable to the pure time discount parameter ρ when a balanced distribution of utility across generations is to be brought about.
Abstract: Based on the Ramsey equation and an ethically motivated rejection of pure utility time discount, the Stern Review on the Economics of Climate Change concentrates on the use of the elasticity of marginal utility η in the intergenerational social welfare function. We support this position by showing that, also from the view point of sustainability, application of η is preferable to the use of the pure time discount parameter ρ when a balanced distribution of utility across generations is to be brought about. After reviewing empirical studies on the size of η we develop a novel axiomatic approach based on non-envy criteria by which we obtain values for η lying in a range between 1 and 2. Whereas the starting point of the Stern Review quite explicitly is an ethical one, many critics of the Review deny this ethical stance and thus - as described in our paper - miss a crucial element of the Stern Review.
94 citations
01 Jan 2005
TL;DR: In this article, the authors explore the correlation among selected measures of vertical and horizontal inequality in Indonesia using census survey data and show that there is very high correlation among the vertical inequalities and high correlation between the horizontal inequalities, while the correlation between HI and VI measures is less clear.
Abstract: This paper considers why inequalities between groups (horizontal inequalities -HIs) matter, as well as inequalities between individuals (vertical inequality VI). It argues that HIs matter both from the perspective of the wellbeing of individuals within groups, who are concerned about how their group is faring relative to others, and instrumentally, through the impact of group inequalities in reducing growth potential and provoking violence. The paper reviews a set of measures for HI. We explore the correlation among selected measures of vertical and horizontal inequality in Indonesia using census survey data and show that there is very high correlation among the VI measures and high correlation among the HI measures, while the correlation between HI and VI measures is less clear. Using data over time for South Africa and the United States we illustrate differences between alternative HI measures. The most appropriate measure depends on the purpose for which it is intended. For empirical research on the consequences of group inequalities, the more descriptive measures are preferable. We conclude that group Ginis and the group coefficient of variation weighted by the population size of the group are to be preferred from this perspective. However, in some contexts a simple ratio of group performance among the two groups of interest may be most informative. The Authors: Frances Stewart is the Director of the Centre for Research on Inequality, Human Security and Ethnicity (CRISE) and Professor of Development Economics, Queen Elizabeth House Department for International Development, University of Oxford. Email: frances.stewart@qeh.ox.ac.uk Graham Brown is the Southeast Asia Research Officer at the Centre for Research on Inequality, Human Security and Ethnicity (CRISE), Queen Elizabeth House Department for International Development, University of Oxford. Email: graham.brown@qeh.ox.ac.uk Luca Mancini is the Research Officer in Applied Econometrics at the Centre for Research on Inequality, Human Security and Ethnicity (CRISE), Queen Elizabeth House Department for International Development, University of Oxford. Email: luca.mancini@qeh.ox.ac.uk
94 citations
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TL;DR: In this article, a measure of risk aversion in the small, the risk premium or insurance premium for an arbitrary risk, and a natural concept of decreasing risk aversion are discussed and related to one another.
Abstract: This paper concerns utility functions for money. A measure of risk aversion in the small, the risk premium or insurance premium for an arbitrary risk, and a natural concept of decreasing risk aversion are discussed and related to one another. Risks are also considered as a proportion of total assets.
5,207 citations
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1,748 citations
"On the Measurement of Inequality" refers background in this paper
...3 See Rothschild and Stiglitz [13], Hadar and Russell [ 5 ], and Hanoch and Levy [6]....
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1,738 citations
"On the Measurement of Inequality" refers methods in this paper
...Then by applying the results of Pratt [l 11, Arrow [ 2 ], and others, we can see that this requirement (which may be referred to as constant (relative) inequality-aversion) implies that U(y) has the form...
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TL;DR: In this paper, an analysis of the first step of the decision-making process of an individual decision maker among alternative risky ventures is presented, in terms of a single dimension such as money, both for the utility functions and for the probability distributions.
Abstract: Publisher Summary The choice of an individual decision maker among alternative risky ventures may be regarded as a two-step procedure. The decision maker chooses an efficient set among all available portfolios, independently of his tastes or preferences. Then, the decision maker applies individual preferences to this set to choose the desired portfolio. The subject of this chapter is the analysis of the first step. It deals with optimal selection rules that minimize the efficient set by discarding any portfolio that is inefficient in the sense that it is inferior to a member of the efficient set, from point of view of each and every individual, when all individuals' utility functions are assumed to be of a given general class of admissible functions. The analysis presented in the chapter is carried out in terms of a single dimension such as money, both for the utility functions and for the probability distributions. However, the results may easily be extended, with minor changes in the theorems and the proofs, to the multivariate case. The chapter explains a necessary and sufficient condition for efficiency, when no further restrictions are imposed on the utility functions. It presents proofs of the optimal efficiency criterion in the presence of general risk aversion, that is, for concave utility functions.
1,160 citations