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 estimate an index of sustainable economic welfare (ISEW) for a developing country, Thailand, over a 25-year period, 1975-1999, and conclude that even low-middle income countries are beginning to approach the point in which economic growth produces both diminishing and, at times, negative welfare returns as the costs of achieving economic growth begin to outweigh the benefits.
57 citations
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TL;DR: In this paper, the authors analyzed a data set from the Bank of Italy year 2006 sample survey on household budgets and introduced the L-process on which statistical inferential results about the population L-function hinges.
Abstract: L-statistics play prominent roles in various research areas and applications, including development of robust statistical methods, measuring economic inequality and insurance risks. In many applications the score functions of L-statistics depend on parameters (e.g., distortion parameter in insurance, risk aversion parameter in econometrics), which turn the L-statistics into functions that we call L-functions. A simple example of an L-function is the Lorenz curve. Ratios of L-functions play equally important roles, with the Zenga curve being a prominent example. To illustrate real life uses of these functions/curves, we analyze a data set from the Bank of Italy year 2006 sample survey on household budgets. Naturally, empirical counterparts of the population L-functions need to be employed and, importantly, adjusted and modified in order to meaningfully capture situations well beyond those based on simple random sampling designs. In the processes of our investigations, we also introduce the L-process on which statistical inferential results about the population L-function hinges. Hence, we provide notes and references facilitating ways for deriving asymptotic properties of the L-process.
57 citations
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TL;DR: A review of empirical knowledge about income inequality in the Arab region, focusing primarily on the issues of data and measurement, and the characterization of its patterns and trends is provided in this paper.
Abstract: This paper provides a review of empirical knowledge about income inequality in the Arab region, focusing primarily on the issues of data and measurement, and the characterization of its patterns and trends. The review shows good progress in the availability of data and quality of measurement. However, the region remains far behind progress being achieved worldwide in terms of coverage and comparability across countries, improvements in quality and content of data, and, more importantly, accessibility of available micro-data to scholars. Within these data constraints and limitations, the available evidence shows moderately high levels of inequality in terms of household expenditure compared to other regions of the world. The patterns of inequality show quite significant variation across countries. One striking result is the weak time variability of the inequality indexes in most of the countries of the region. Alternative measures of welfare distribution such as of horizontal inequality, polarization or in...
57 citations
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TL;DR: In this article, the main objectives of the paper are to decompose Atkinson's measure into within-group and between-group inequality and to compare it with decompositions of inequality measures, like the Gini coefficient, variance of logarithms, Theil's entropy index and the square of the coefficient of variation.
Abstract: The main objectives of the paper are to decompose Atkinson's measure into within-group and between-group inequality and to compare it with decompositions of inequality measures, like the Gini coefficient, variance of logarithms, Theil's entropy index and the square of the coefficient of variation. Atkinson's inequality index is given an interpretation of mean order β and then it is decomposed for population subgroups. Various other measures are considered for decompositions and a variety of decomposition schemes for Gini coefficient and other measures in the literature is reviewed and commented upon. Empirical analysis using U.S.A. and U.K. data are performed on the basis of income distribution data classified by family size. For various decomposition schemes, contribution to between size-group and within size-group inequalities are compared in percentage terms. Comparisons are also made over time for the years 1964 and 1974 both for U.S.A. and U.K. and the result indicates that within size-group income inequality has declined while between size group and total income inequality shows an increase. Three important properties of Atkinson's inequality index are proved in the appendix.
57 citations
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TL;DR: In this article, a geometric approach to order row stochastic matrices is presented, where a cone extension of the Lorenz zonotope and the respective inclusion ordering are introduced.
Abstract: The distribution of d commodities among n individuals is described by an n×d row stochastic matrix. We present a geometric approach to order such matrices. For a row stochastic matrix the Lorenz zonotope is investigated, which is a higher dimensional generalization of the Lorenz curve. The Lorenz zonotope is a convex polytope. The inclusion of Lorenz zonotopes defines an ordering between row stochastic matrices, which is a multivariate majorization. For a cone in nonnegative d-space, a cone extension of the Lorenz zonotope and the respective inclusion ordering are introduced. We study this class of orderings and establish equivalence with known majorizations. It is provided a finite set of inequalities to which the ordering is equivalent.
57 citations
Cites background from "On the Measurement of Inequality"
...Kolm [9], Atkinson [2] have introduced the mathematical notion of majorization to economic theory....
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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
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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
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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