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 article, the authors propose a framework recognizing three necessary but individually insufficient properties of diversity and propose a general quantitative non-parametric diversity heuristic to explore different possible trade-offs between diversity and other aspects of interest.
Abstract: This paper addresses the scope for more integrated general analysis of diversity in science, technology and society. It proposes a framework recognizing three necessary but individually insufficient properties of diversity. Based on 10 quality criteria, it suggests a general quantitative non-parametric diversity heuristic. This allows the systematic exploration of diversity under different perspectives, including divergent conceptions of relevant attributes and contrasting weightings on different diversity properties. It is shown how this heuristic may be used to explore different possible trade-offs between diversity and other aspects of interest, including portfolio interactions. The resulting approach offers a way to be more systematic and transparent in the treatment of scientific and technological diversity in a range of fields, including conservation management, research governance, energy policy and sustainable innovation.
735 citations
TL;DR: In this article, the authors analyzed properties of measures of inequality, applied to income inequalities but meaningful for practically any measure of dispersion in economics, and showed that these properties are equivalent to each other: positivity out of equality, rectifiance, quasi-convexity, and concavity.
710 citations
TL;DR: In this article, the authors investigated the effect of age on consumption and income inequality in the United States, Taiwan, and Great Britain, and found that within-cohort consumption and inequality measures do indeed increase with age in the three economies.
Abstract: The permanent income hypothesis implies that, for any cohort of people born at the same time, inequality in both consumption and income should grow with age. We investigate this prediction using cohort data constructed from 11 years of household survey data from the United States, 22 years from Great Britain, and 14 years from Taiwan. The data show that within-cohort consumption and income inequality measures do indeed increase with age in the three economies and that the rate of increase is similar in all three. According to the permanent income hypothesis, the increase in inequality reflects cumulative differences in the effects of luck on consumption. Other models of intertemporal choice-such as those with strong precautionary motives or liquidity constraints-can limit or even prevent the spread of inequality, as can insurance arrangements that share risk across individuals. The evidence on the spread of inequality can therefore be used to help quantify the extent to which private and social arrangements moderate the impact of risk on the distribution of individual welfare.
706 citations
TL;DR: Inequalities in health favoured the higher income groups and were statistically significant in all countries, and were particularly high in the United States and the United Kingdom.
702 citations
TL;DR: The authors derived the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare, and inequality, including estimators of most of the poverty indices currently in use, as well as estimators used to infer stochastic dominance of any order.
Abstract: We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare, and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality, or social welfare is greater in one distribution than in another for general classes of indices and for ranges of possible poverty lines. We also derive the sampling distribution of the maximal poverty lines up to which we may confidently assert that poverty is greater in one distribution than in another. The sampling distribution of convenient dual estimators for the measurement of poverty is also established. The statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes. Our results are briefly illustrated using data for four countries drawn from the Luxembourg Income Study data bases.
695 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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"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