scispace - formally typeset
Search or ask a question
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
More filters
Journal ArticleDOI
TL;DR: A small and very volatile fraction of total domestic food production is a small fraction of the average price of cereals, and domestic price fluctuations tend to be an amplified version of international price fluctuations as mentioned in this paper.
Abstract: a small and very volatile fraction of total domestic food production. Many countries aim at food self-sufficiency, with the consequence that the country may be an exporter in good years, but an importer in bad years. International and domestic transport and handling costs are a significant fraction of the average price of cereals, so the domestic price fluctuations will tend to be an amplified version of international price fluctuations - the difference between the domestic price in exporting and importing years will be twice the transport costs if the world price is unchanged. It would require a strong negative correlation between domestic and world supply to offset this additional source of instability.1

93 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that weakly upper semicontinuous concave Schur concave functions coincide with concave Fenchel transform and Hardy and Littlewood's inequality.
Abstract: A representation result is provided for concave Schur concave functions on L∞(Ω). In particular, it is proven that any monotone concave Schur concave weakly upper semicontinuous function is the infinimum of a family of nonnegative affine combinations of Choquet integrals with respect to a convex continuous distortion of the underlying probability. The method of proof is based on the concave Fenchel transform and on Hardy and Littlewood's inequality. Under the assumption that the probability space is nonatomic, concave, weakly upper semicontinuous, law-invariant functions are shown to coincide with weakly upper semicontinuous concave Schur concave functions. A representation result is, thus, obtained for weakly upper semicontinuous concave law-invariant functions.

93 citations

Journal ArticleDOI
TL;DR: This paper derives requirements for an aggregation method through the Squale model for metric aggregation, a model specifically designed to address the needs of practitioners, and empirically validate the adequacy of Squale through experiments on Eclipse.
Abstract: With the growing need for quality assessment of entire software systems in the industry, new issues are emerging. First, because most software quality metrics are defined at the level of individual software components, there is a need for aggregation methods to summarize the results at the system level. Second, because a software evaluation requires the use of different metrics, with possibly widely varying output ranges, there is a need to combine these results into a unified quality assessment. In this paper we derive, from our experience on real industrial cases and from the scientific literature, requirements for an aggregation method. We then present a solution through the Squale model for metric aggregation, a model specifically designed to address the needs of practitioners. We empirically validate the adequacy of Squale through experiments on Eclipse. Additionally, we compare the Squale model to both traditional aggregation techniques (e.g., the arithmetic mean), and to econometric inequality indices (e.g., the Gini or the Theil indices), recently applied to aggregation of software metrics. Keywords: software metrics; software quality; aggregation; inequality indices

93 citations

Journal ArticleDOI
TL;DR: Slesnick et al. as discussed by the authors presented a detailed decomposition of the differences between estimates of poverty rates based on consumption and the official estimates based on income, and concluded that the war on poverty was a failure.
Abstract: Was the War on Poverty a failure or a success? Official U.S. poverty statistics based on household income imply that the War on Poverty ended in failure. According to the Bureau of the Census, the proportion of the U.S. population below the poverty level of income reached a minimum of 11.1 percent in 1973. This ratio rebounded to 15.2 percent in 1983 and has fluctuated within a narrow range since then, giving rise to the widespread impression that the elimination of poverty is difficult or even impossible. 1 However, poverty estimates based on household consumption imply that the War on Poverty was a success. Jorgenson and Slesnick (1989) showed that the proportion of the U.S. population below the poverty level of consumption fell to 10.9 percent in 1973, only slightly below the poverty incidence as measured by income in that year; the poverty ratio for consumption declined further, reaching 6.8 percent in 1983. Slesnick (1993) presents estimates of poverty ratios incorporating consumption data from the Consumer Expenditure Survey, conducted by the Bureau of Labor Statistics. The poverty rate for consumption fell to 9.7 percent in 1973 and reached a low of 8.7 percent in 1978 before rising to 12.0 percent in 1980. The consumptionbased poverty rate then declined to a new low of 8.3 percent in 1986, ending at 8.4 percent in 1989. Calibrating consumption to levels reported in the U.S. National Income and Product Accounts, Slesnick obtained a poverty rate of 4.1 percent in 1978 and a postwar low in 1989 of only 2.2 percent. 2 1 The persistence of poverty, as reflected in the official statistics, is discussed by Sawhill (1988). 2 Slesnick (1993) presented a detailed decomposition of the differences between estimates of poverty rates based on consumption and the official estimates based on income. Neither measures of consumption from the Consumer Expenditure Survey nor measures of income used by the Bureau of the Census include in-kind transfers. Slesnick (1996) discussed the effects of these transfers on measures of poverty.

93 citations

Journal ArticleDOI
TL;DR: In this paper, the authors provide asymtotically distribution-free statistical inference procedures for generalized Lorenz curves, given appropriate measures of income and the income recipient unit are chosen appropriately.
Abstract: This paper provides asymtotically distribution-free statistical inference procedures for generalized Lorenz curves. Given appropriate measures of income and the income recipient unit are chosen appropriately, the tests allow consensually valid statements regarding social welfare to be made from sample data on the basis of sound inferential procedures. More generally, the results presented here can be applied to test for second degree stochastic dominance. Copyright 1989 by MIT Press.

92 citations

References
More filters
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