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Journal ArticleDOI

On the Measurement of Inequality

01 Sep 1970-Journal of Economic Theory (Academic Press)-Vol. 2, Iss: 3, pp 244-263
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.
Citations
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TL;DR: Income distribution and inequalities in the southern United States are analyzed and compared with data for the rest of the country as mentioned in this paper, and the evidence presented in this paper reveals that in the 1970s the Souths income distribution either converged or moved significantly closer to the income distribution of the restof the country.
Abstract: Income distribution and inequalities in the southern United States are analyzed and compared with data for the rest of the country. "The evidence presented in this paper reveals that in the 1970s the Souths income distribution either converged or moved significantly closer to the income distribution of the rest of the country. The degree of convergence depends on the definition of the recipient unit and to a degree on the particular cost-of-living index used to deflate Southern and non-Southern incomes." The convergence is attributed in part to the labor unionization in the Northeast and the resulting relocation of companies to the South. Data are from the 1970 and 1980 censuses and concern total household income. (EXCERPT)

167 citations

Journal ArticleDOI
TL;DR: In this paper, a new concept of inequality-equivalence, called intermediate, is presented, which allows one to vary the value judgement on inequality between the well-known relative and absolute views.

166 citations

ReportDOI
TL;DR: In this article, an index of inequality is proposed which decomposes into two components, corresponding to vertical and horizontal equity respectively, and an application to data for 5895 UK households is presented.
Abstract: Horizontal equity and social mobility are discussed in terms of a non-utilitarian social welfare function which takes account of the process by which an ex ante distribution is mapped into an ex post distribution (by the tax system, for example). An index of inequality is proposed which decomposes into two components, corresponding to vertical and horizontal equity respectively. A functional form for the social welfare function is derived for the purposes of empirical work, and an application to data for 5895 UK households is presented. The paper contains a theoretical application of the index to a model of optimal taxation. IT IS CONVENTIONAL to assess the merits of alternative public policies in terms of a trade-off between equity and efficiency. In practice, however, a change in, say, the tax system involves three effects. First, it may have incentive or disincentive effects leading to efficiency gains or losses. Secondly, it may alter the distribution of welfare levels. Thirdly, it may alter the ranking of individuals (or households) within the distribution. These three effects correspond to efficiency, vertical equity, and, we shall argue, certain aspects of horizontal equity, respectively, and any assessment of a tax change must take into account all three. The principal assumption of this paper is that government is concerned about the trade-off between these three effects. A strict utilitarian is concerned only with the consequences of an action, and in the evaluation of a particular reform a utilitarian measure of social welfare is defined over the vector of ex post utilities. No account is taken of the process by which the vector of ex ante utilities is mapped into the ex post vector, and no ethical status is awarded to the ex ante distribution. One does not have to adopt an entitlement theory of justice to believe that the utilitarian approach may ignore some relevant considerations, such as the fairness of the redistributive process. A striking example of this arises in the model used by Mirrlees [11] to examine optimal income taxation. In that model individuals have identical preferences (defined over consumption and leisure) and differ only in respect of their potential wage rates or ability levels. Clearly, in the absence of taxation individual utility is an increasing function of ability. Suppose the government uses redistributive lump-sum taxes to achieve the first-best optimum. Then as Mirrlees [11, 12] shows, the first-best optimum for a utilitarian social welfare

165 citations

Journal ArticleDOI
31 Jul 2020-Science
TL;DR: Overall, absolute disparities have fallen, but relative disparities persist, and differences in PM2.5 between more and less polluted areas declined substantially between 1981 and 2016, however, the most polluted census tracts in 1981 remained the least polluted in 2016.
Abstract: Air pollution at any given time is unequally distributed across locations. Average concentrations of fine particulate matter smaller than 2.5 micrometers in diameter (PM2.5) have fallen over time. However, we do not know how the spatial distribution of PM2.5 has evolved. Here, we provide early evidence. We combine 36 years of PM2.5 concentrations measured over ~8.6 million grid cells with geographic, economic, and demographic data from ~65,000 U.S. census tracts. We show that differences in PM2.5 between more and less polluted areas declined substantially between 1981 and 2016. However, the most polluted census tracts in 1981 remained the most polluted in 2016. The least polluted census tracts in 1981 remained the least polluted in 2016. The most exposed subpopulations in 1981 remained the most exposed in 2016. Overall, absolute disparities have fallen, but relative disparities persist.

164 citations

Posted Content
TL;DR: In this article, the authors provide a critical, but constructive, discussion of the various methods used for the valuation of non-renewable resource depletion and long-term environmental damage and for the weighting of consumption expenditures for income inequalities.
Abstract: Existing country studies of the Index of Sustainable Economic Welfare (ISEW), the Genuine Progress Indicator (GPI) and related measures, while sharing the same basic methodological approach, differ with respect to the valuation of important items. This paper provides a critical, but constructive, discussion of the various methods used for the valuation of non-renewable resource depletion and long-term environmental damage and for the weighting of consumption expenditures for income inequalities. Several recommendations are given on how to improve the methodology for future updates of existing studies or for the construction of new measures. Sensitivity analysis shows that if these recommendations are followed for the valuation of resource depletion and long-term environmental damage, then the so-called "threshold" hypothesis, which seemed to have gained empirical support from all studies undertaken so far, fails to materialise. This suggests that, as far as factors related to the environment are concerned, the widening gap between ISEW and GPI on the one hand and gross national product (GNP) on the other, might be an artefact of highly contestable methodological assumptions.

163 citations

References
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Journal ArticleDOI
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]....

    [...]

Journal ArticleDOI

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...

    [...]

Journal ArticleDOI
TL;DR: JSTOR as discussed by the authors is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship, which is used to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources.
Abstract: you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org.

1,544 citations

Journal ArticleDOI
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