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 provide a macroeconomic model with non-Gorman preferences that rationalizes three facts: the share of goods in total expenditure declines at a constant rate over time, the price of goods relative to services, and poor households spend a larger fraction of their budget on goods than do rich households.
Abstract: U.S. data reveal three facts: (1) the share of goods in total expenditure declines at a constant rate over time, (2) the price of goods relative to services declines at a constant rate over time, and (3) poor households spend a larger fraction of their budget on goods than do rich households. I provide a macroeconomic model with non-Gorman preferences that rationalizes these facts, along with the aggregate Kaldor facts. The model is parsimonious and admits an analytical solution. Its functional form allows a decomposition of U.S. structural change into an income and substitution effect. Estimates from micro data show each of these effects to be of roughly equal importance.
157 citations
Cites background from "On the Measurement of Inequality"
...φ is a (negative) monotonic transformation of an Atkinson index (Atkinson, 1970) with relative inequality aversion ǫ (see Online Appendix B....
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01 Jan 2013
TL;DR: In this article, the authors survey the literature on income mobility, aiming to provide an integrated discussion of mobility within and between-generations, and review mobility concepts, descriptive devices, measurement methods, data sources, and recent empirical evidence.
Abstract: We survey the literature on income mobility, aiming to provide an integrated discussion of mobility within- and between-generations. We review mobility concepts, descriptive devices, measurement methods, data sources, and recent empirical evidence.
156 citations
Cites background or methods from "On the Measurement of Inequality"
...Atkinson et al. (1992), Burkhauser and Couch (2009), Fields and Ok (1999a), Jenkins and Van Kerm (2009), and Maasoumi (1998). For intergenerational mobility, important earlier reviews are provided by Solon (1999), Björklund and Jäntti (2009), Black and Devereux (2011), and Piketty (2000). Many of the reviews just cited appear in volumes with ‘Handbook’ in their title....
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...For inequality measurement, the use of an explicit model of social welfare is known to yield dividends: see, notably, Atkinson’s (1970) demonstration of how the ‘cost’ of income inequality can be summarised in social welfare terms and how inequality comparisons based on Lorenz curves are intimately linked to orderings by social welfare functions that are additive, increasing, and concave function of individuals’ incomes. The corresponding literature on the social welfare foundations of mobility measurement is small, with contributions including Atkinson (1981a), reprinted as Atkinson (1983), Atkinson and Bourguignon (1982), Markandya (1984), and Gottschalk and Spolaore (2002)....
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...Atkinson et al. (1992), Burkhauser and Couch (2009), Fields and Ok (1999a), Jenkins and Van Kerm (2009), and Maasoumi (1998). For intergenerational mobility, important earlier reviews are provided by Solon (1999), Björklund and Jäntti (2009), Black and Devereux (2011), and Piketty (2000)....
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...Mobility is the percentage change in social welfare (measured by the equally-distributed equivalent income, defined in the Atkinson (1970) sense) of the actual distribution of longitudinally-averaged incomes compared to what social welfare would have been in the completely immobile benchmark…...
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...(10) where I is a relative inequality index equal to one minus an index of relative equality (as is the case with the Atkinson (1970) class of inequality indices)....
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TL;DR: This paper proposed an alternative approach that allows for differences in social judgements regarding the treatment of different types of families and examines the relation with the choice of poverty measure. But their approach cannot provide a complete ranking but allow the extent of disagreement to be identified.
Abstract: The equivalence scales used to adjust for differences in family composition when measuring poverty exhibit considerable variation This paper suggests an alternative approach that allows for differences in social judgements regarding the treatment of different types of family and examines the relation with the choice of poverty measure The resulting dominance criteria cannot provide a complete ranking but allow the extent of disagreement to be identified Their application is illustrated by the example of changes in child benefits Copyright 1992 by The London School of Economics and Political Science
154 citations
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TL;DR: In this article, both income-based and access-based measurement approaches are employed to gain a broader picture of wellbeing in South Africa, and the authors compare the measured changes in well being that emerge from the income and access approaches.
Abstract: The paper analyses poverty and inequality changes in South Africa for the period 1996 to 2001 using Census data. To gain a broader picture of wellbeing in South Africa, both income-based and access-based measurement approaches are employed. At the national level, findings from the income-based approach show that inequality has unambiguously increased from 1996 to 2001. As regards population group inequality, within-group inequality has increased; while between-group inequality has decreased (inequality has also increased in each province and across the rural/urban divide). The poverty analysis reveals that poverty has worsened in the nation, particularly for Africans. Provincially, the Eastern Cape and Limpopo have the highest poverty rates while the Western Cape and Gauteng have the lowest poverty rates. Poverty differs across the urban-rural divide with rural areas being relatively worse off than urban areas. However, due to the large extent of rural-urban migration, the proportion of the poor in rural areas is declining. The access-based approach focuses on type of dwelling, access to water, energy for lighting, energy for cooking, sanitation and refuse removal. The data reveal significant improvements in these access measures between 1996 and 2001. The proportion of households occupying traditional dwellings has decreased while the proportion of households occupying formal dwellings has risen slightly (approximately two-thirds of households occupy formal dwellings). Access to basic services has improved, especially with regard to access to electricity for lighting and access to telephones. On a provincial level, Limpopo and the Eastern Cape display the poorest performance in terms of access to basic services. The paper concludes by contrasting the measured changes in well being that emerge from the income and access approaches. While income measures show worsening well being via increases in income poverty and inequality, access measures show that well being in South Africa has improved in a number of important dimensions.
154 citations
01 Jun 1991
TL;DR: In this article, the authors discuss reasons why interpersonal comparisons of utility have been eschewed in the past and argue that most existing approaches, both empirical and ethical, to ICU's are flawed, either confound facts with values, or they are based on unrealistic hypothetical decisions in an original position.
Abstract: A satisfactory complete normative criterion for individualistic ethical decisionmaking under uncertainty such as Harsanyi’s (Journal of Political Economy , 1955) requires a single fundamental utility function for all individuals which is fully interpersonally comparable. The paper discusses reasons why interpersonal comparisons of utility (ICU’s) have been eschewed in the past and argues that most existing approaches, both empirical and ethical, to ICU’s are flawed. Either they confound facts with values, or they are based on unrealistic hypothetical decisions in an “original position”. Instead ICU’s need to be recognized for what they really are — preferences for different kinds of people. INTERPERSONAL COMPARISONS OF UTILITY . . . I still believe that it is helpful to speak as if inter-personal comparisons of utility rest upon scientiAEc foundations – that is, upon observation or introspection. . . . I still think, when I make interpersonal comparisons . . . that my judgments are more like judgments of value than judgments of veriAEable fact. Nevertheless, to those of my friends who think differently, I would urge that, in practice, our difference is not very important. They think that propositions based upon the assumption of equality are essentially part of economic science. I think that the assumption of equality comes from outside, and that its justiAEcation is more ethical than scientiAEc. But we all agree that it is AEtting that such assumptions should be made and their implications explored with the aid of the economist’s technique. — Robbins (1938, pp. 640–641)
154 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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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
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