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: Simulation optimization techniques are used to develop rigorous algorithms to allocate resources equitably among some defined subgroups of a customer population and where non-closed-form functions of equity are allowed.
Abstract: Providing equal access to public service resources is a fundamental goal of democratic societies. Growing research interest in public services (e.g., health care, humanitarian relief, elections) has increased the importance of considering objective functions related to equity. This article studies discrete resource allocation problems where the decision maker is concerned with maintaining equity between some defined subgroups of a customer population and where non-closed-form functions of equity are allowed. Simulation optimization techniques are used to develop rigorous algorithms to allocate resources equitably among these subgroups. The presented solutions are associated with probabilistic bounds on solution quality. A full-factorial experimental design demonstrates that the proposed algorithm outperforms competing heuristics and is robust over various inequity metrics. Additionally, the algorithm is applied to a case study of allocating voting machines to election precincts in Franklin County, Ohio. [...
49 citations
TL;DR: In this paper, the authors examined the relationship between interregional inequality and the incidence of domestic terrorism in a panel of 48 countries over the period 1990-2010 and found that a high level of interregion inequality increases the number of domestic terror events in the sample countries.
49 citations
TL;DR: In this article, the authors extend the previous literature on the ethical links between the measurement of poverty, social welfare and inequality, and show inter alia, how, when the range of possible poverty lines is unbounded above, a robust ranking of absolute poverty may be interpreted as a robust ordering of social welfare, and this, for any order of stochastic dominance.
Abstract: This paper extends the previous literature on the ethical links between the measurement of poverty, social welfare and inequality. We show inter alia, how, when the range of possible poverty lines is unbounded above, a robust ranking of absolute poverty may be interpreted as a robust ranking of social welfare, and a robust ranking of relative poverty may be interpreted as a robust ranking of inequality, and this, for any order of stochastic dominance. © 2004 Blackwell Publishing, Inc.
49 citations
TL;DR: After rising during most, but not all, of the 1960-85 period, inequality in Chile seems to have stabilized since around 1987 as mentioned in this paper, with some compression at the bottom being 'compensated for' by a stretching at the top.
Abstract: After rising during most, but not all, of the 1960-85 period, inequality in Chile seems to have stabilized since around 1987. Following the stormy period of economic and political reforms of the 1970s and 1980s, no statistically significant Lorenz dominance results could be detected since 1987. Scalar measures of inequality confirm this picture of stability, but suggest a slight change in the shape of the density function, with some compression at the bottom being 'compensated for' by a stretching at the top. As inequality remained broadly stable, sustained economic growth led to substantial welfare improvements and poverty reduction, according to a range of measures and with respect to three different poverty lines. Poverty mixed stochastic dominance tests confirm this result. All of these findings are robust to different choices of equivalence scales.
49 citations
TL;DR: This article showed that a broad class of measures of inequality (including those of Herfindahl and Theil) can be readily (and accurately) estimated from grouped data and showed that the standard textbook grouping method of assuming that all incomes in any class are at the mid-point can lead to serious error in the resulting estimate of inequality.
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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