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 show that for any given cohort of people born at the same time, inequality in both consumption and income will grow with age, and that the rate of increase is broadly similar in all three economies.
Abstract: We show that standard models of intertemporal choice, including the permanent income hypothesis, imply that for any given cohort of people born at the same time, inequality in both consumption and income will grow with age. At any given date, each individual's consumption depends on the integral of unanticipated earnings shocks up to that date, so that consumption becomes more dispersed with time. If earnings are not themselves similarly dispersing, assets will do so, so that the dispersion of total income will increase, irrespective of the behavior of earnings. Because the result applies to an increase in inequality over time within a given age cohort, it has no immediate implications for the behavior of inequality in the economy as a whole, and is consistent with constant aggregate inequality over time. Cohort data are constructed from 11 years of household survey data from the U.S., 22 years from Great Britain, and 14 years from Taiwan. They show that within-cohort consumption and income inequality does indeed grow with age in all three economies, and that the rate of increase is broadly similar in all three.
137 citations
TL;DR: In this paper, a characterization of a commonly used measure of income inequality, Theil measure, is presented, which is consistent with the Lorenz criterion, when it applies, and exhibits a simple and empricically useful decomposition by population subgroup into within-group and between-group terms.
137 citations
TL;DR: The Human Development Index (HDI) as mentioned in this paper improves upon per-capita Gross Domestic Product as an indicator of development by incorporating information on health and education, but it fails to account for the inequality with which the benefits of development are distributed among the population.
Abstract: The Human Development Index (HDI) improves upon per‐capita Gross Domestic Product as an indicator of development by incorporating information on health and education. However, like its predecessor, it fails to account for the inequality with which the benefits of development are distributed among the population. Subsequent work by Anand and Sen (1993) and Hicks (1997) has led to a useful distribution‐sensitive measure of human development, but at the cost of a key property of the HDI that ensures consistency between regional and aggregate analyses. This paper presents a new parametric class of human develop-ment indices that includes the original HDI as well as a family of distribution sensitive indices that satisfy all the basic properties for an index of human development. An empirical application using the year 2000 Mexican Population Census data shows how the new measures can be applied to analyze the distribution of human development at the national level and for individual states.
136 citations
TL;DR: In this paper, the authors used the possibilities provided by the regression-based inequality decomposition (Fields in Res Labor Econ 22:1-38, 2003) to explore the contribution of different explanatory factors to international inequality in emissions per capita.
Abstract: This paper uses the possibilities provided by the regression-based inequality decomposition (Fields in Res Labor Econ 22:1–38, 2003) to explore the contribution of different explanatory factors to international inequality in $$\hbox {CO}_{2}$$
emissions per capita. In contrast to previous emissions inequality decompositions, which were based on identity relationships, this methodology does not impose any a priori specific relationship. Thus, it allows an assessment of the contribution to inequality of different relevant variables. In short, the paper appraises the relative contributions of affluence, sectoral composition, demographic factors and climate. The analysis is applied to selected years of the period 1993–2007. The results show the important (though decreasing) share of the contribution of demographic factors, as well as a significant contribution of affluence and sectoral composition.
135 citations
TL;DR: An integrated multi-objective optimization model that combines resource allocation with emergency distribution is developed, where a time space network is used to incorporate the frequent information and decision updates in a rolling horizon approach as mentioned in this paper.
Abstract: In this paper, we characterize the humanitarian objectives of emergency resource allocation and distribution in disaster response operations. We formulate the humanitarian principles as three objective functions, i.e., lifesaving utility, delay cost and fairness. An integrated multi-objective optimization model that combines resource allocation with emergency distribution is developed, where a time space network is used to incorporate the frequent information and decision updates in a rolling horizon approach. The proposed model is shown to be a convex quadratic network flow problem, for which we design an efficient Variational Inequality algorithm. Computational results are reported to illustrate the performance of the proposed model and algorithm.
135 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