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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Journal Article•
TL;DR: The authors examined the implications of the ranking relation generated by two non-intersecting relative deprivation curves as developed in Kakwani (1984) and showed that the dominance in terms of relative deprivation implies the Lorenz domination, hence welfare improvement property (that is, welfare increases under Pigou-Dalton type progressive income transfers).
Abstract: This paper examines the implications of the ranking relation generated by two non-intersecting relative deprivation curves as developed in Kakwani (1984). It is shown that the dominance in terms of relative deprivation implies the Lorenz domination, hence welfare improvement property (that is, welfare increases under Pigou—Dalton type progressive income transfers) , but the converse is not true. Next, the class of average relative deprivation indices that agrees with the deprivation dominance criterion is identified. It turns out that all such deprivation indices can be regarded as Lorenz consistent inequality indices, but the reverse i mplication does not follow. Key-words: Inequality, relative deprivation , social welfare. JEL classification numbers: D31, D63
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TL;DR: In this paper, a weighting factor decomposition method is proposed in order to isolate weighting factors changes in inequality growth rates and the only non-ambiguous way of decomposing inequality by source is the natural decomposition of CV2, which additionally allows the interpretation of marginal term contributions.
Abstract: Scarcities of environmental services are no longer merely a remote hypothesis. Consequently, analysis of their inequalities between nations becomes of paramount importance for the achievement of sustainability in terms either of international policy, or of Universalist ethical principles of equity. This paper aims, on the one hand, at revising methodological aspects of the inequality measurement of certain environmental data and, on the other, at extending the scarce empirical evidence relating to the international distribution of Ecological Footprint (EF), by using a longer EF time series. Most of the techniques currently important in the literature are revised and then tested on EF data with interesting results. We look in depth at Lorenz dominance analyses and consider the underlying properties of different inequality indices. Those indices which fit best with environmental inequality measurements are CV2 and GE(2) because of their neutrality property, however a trade-off may occur when subgroup decompositions are performed. A weighting factor decomposition method is proposed in order to isolate weighting factor changes in inequality growth rates. Finally, the only non-ambiguous way of decomposing inequality by source is the natural decomposition of CV2, which additionally allows the interpretation of marginal term contributions. Empirically, this paper contributes to the environmental inequality measurement of EF: this inequality has been quite stable and its change over time is due to per capita vector changes rather than population changes. Almost the entirety of the EF inequality is explainable by differences in the means between the countries of the World Bank group. This finding suggests that international environmental agreements should be attempted on a regional basis in an attempt to achieve greater consensus between the parties involved. Additionally, source decomposition warns of the dangers of confining CO2 emissions reduction to crop-based energies because of the implications for basic needs satisfaction.
46 citations
Cites background or methods from "On the Measurement of Inequality"
...To summarize, which year exhibits a more desirable situation depends on which part of the distribution is considered more relevant - this necessarily involves value judgements (Atkinson, 1970; Cowell, 2011; Shorrocks and Foster, 1987)....
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...The development of distributional analysis methods in economics has been tackled in the context of Social Welfare Theory (Atkinson, 1970; Theil, 1979; F. Cowell, 1980, 2011; Shorrocks, 1980)....
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Dissertation•
05 Jul 2006
TL;DR: In this paper, a methodique de l'impact du revenu on les pratiques de mobilite of semaine, de week-end and de longue distance is presented.
Abstract: Le contexte des dernieres decennies se caracterise par la forte croissance des mobilites et le role central qu'elles occupent dans l'insertion sociale et professionnelle des individus. La societe contemporaine produit de nouveaux imperatifs de deplacement qui modifient en profondeur notre rapport a l'espace et au temps. Pour autant, nous ne disposons pas tous de capacites identiques pour faire face a ces exigences changeantes et complexes. Les inegalites observees en matiere de mobilite meritent donc une attention particuliere dans la mesure ou elles participent a la production et a la reproduction des inegalites socio-economiques. Partant de ce constat, cette these tente de mieux cerner le lien entre inegalites de revenu et mobilites, en integrant les differentes facettes des mobilites dites « reversibles », en desagregeant l'analyse par groupe de cycle de vie et en faisant explicitement apparaitre l'influence de l'acces a l'automobile. Nous proposons ainsi d'identifier, de mesurer et d'interpreter les inegalites de mobilites grâce a des indicateurs simples permettant, sinon de recomposer la complexite du phenomene, tout au moins d'en presenter les differentes dimensions. Nous presentons une analyse methodique de l'impact du revenu sur les pratiques de mobilite de semaine, de week-end et de longue distance a partir des donnees disponibles grâce aux enquetes statistiques classiques sur la mobilite (Enquete Menages Deplacements de Lyon 1995, Enquete Nationale Transport 1994). Les resultats obtenus montrent que les effets du revenu sont tres heterogenes selon le type de mobilite observe. Notre approche apporte ainsi des elements de comprehension et d'eclaircissement sur les inegalites economiques de mobilites. Des pistes de reflexion sont egalement formulees pour une meilleure prise en compte des preoccupations en matiere d'equite sociale dans la gestion durable des mobilites.
46 citations
Posted Content•
TL;DR: In this paper, a variety of methods for measuring the actual reward and the just reward, for both self and other, including direct and indirect methods, are presented, including the one-reward-per-reeward method.
Abstract: This paper describes procedures for measuring and estimating the fundamental quantities in the study of distributive justice. We examine a variety of methods for measuring the actual reward and the just reward, for both self and other, including direct and indirect methods for measuring the just reward. Finally, we provide an extended illustration of one of the two indirect methods, the one-reward-per-rewardee method, obtaining estimates not only of ideas of the just earnings for others but also of just rates of return to personal characteristics as well as perceived overall injustice and its decomposition into poverty and inequality components.
46 citations
01 Jan 1994
TL;DR: In this article, a simple method for analyzing the distributional effects of marginal changes in commodity taxes is proposed, where the authors measure the impact of a tax by its impact on the Gini coefficient of the overall distribution of real income.
Abstract: This paper suggests a simple method for analyzing the distributional effects of marginal changes in commodity taxes. The distributional effect of a tax is measured by its impact on the Gini coefficient of the overall distribution of real income. Then the Gini coefficient is decomposed in a manner resembling the decomposition of the coefficient of variation. This decomposition yield non-parametric estimates of income elasticities of the Engel curves. The magnitudes of these elasticities determine the desired change in taxes. The method is illustrated with data from Israel.
46 citations
References
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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
Posted Content•
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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1,544 citations
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