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 paper, two indices for measuring multidimensional inequality, derived from two underlying social evaluation functions, were proposed for Russian household data between 1995 and 2005 for four dimensions of wellbeing: expenditure, health, schooling and housing quality.
Abstract: An important aspect of multidimensional wellbeing distributions is the correlation between different dimensions. We propose two indices for measuring multidimensional inequality, derived from two underlying social evaluation functions. These functions aggregate both across dimensions and across individuals. The social evaluation functions differ only with respect to the sequencing of aggregation. Aggregating first across dimensions is more attractive since it allows the inequality index to depend on the correlation between dimensions. We illustrate both indices, and the impact of correlation sensitivity, using Russian household data between 1995 and 2005 for four dimensions of wellbeing: expenditure, health, schooling and housing quality.
75 citations
TL;DR: Results are quite promising, showing that the "Legislation Network" approach can lead towards an enhanced explanation in respect to the structure and evolution of legislation properties.
Abstract: Legislators, designers of legal information systems, as well as citizens face often problems due to the interdependence of the laws and the growing number of references needed to interpret them. Quantifying this complexity is not an easy task. In this paper, we introduce the "Legislation Network" as a novel approach to address related problems. We have collected an extensive data set of a more than 60-year old legislation corpus, as published in the Official Journal of the European Union, and we further analysed it as a complex network, thus gaining insight into its topological structure. Among other issues, we have performed a temporal analysis of the evolution of the Legislation Network, as well as a robust resilience test to assess its vulnerability under specific cases that may lead to possible breakdowns. Results are quite promising, showing that our approach can lead towards an enhanced explanation in respect to the structure and evolution of legislation properties.
75 citations
Cites methods from "On the Measurement of Inequality"
...ng the probability that a randomly selected node has k links. A popular visualization of the degree distribution is the Lorenz curve, a type of plot to measure inequality originally used in economics [41]. In a network degree plot, the Lorenz curve is a straight diagonal line when all nodes have the same degree and curved otherwise. It visualizes statements of the form X% of nodes with smallest degre...
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TL;DR: In this article, the authors show that categorical time series, covering comparable time spans, are often quite different in a number of aspects: the number of distinct states and transitions, and the distribution of duration.
Abstract: Categorical time series, covering comparable time spans, are often quite different in a number of aspects: the number of distinct states, the number of transitions, and the distribution of duration...
75 citations
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TL;DR: In this article, a new measure of horizontal equity was proposed to measure deviations from the fundamental principle that equals be treated equally. But this measure is based on the so-called marriage penalty.
Abstract: In this paper, we propose a new measure of horizontal equity that overcomes many of the shortcomings of previous proposed measures Our starting point is the observation that a well-behaved social welfare function need not evaluate global' (vertical equity) differences in after-tax income using the same weights it applies to local' (horizontal equity) differences, even though this constraint has been applied in the past Following work on the structure of individual preferences, we show that a social welfare function can imply different preferences toward horizontal and vertical equity Adopting the general approach to the measurement of inequality developed by Atkinson (1970), we use such a social welfare function to derive measures of inequality that are decomposable into components naturally interpreted as indices of horizontal and vertical equity In particular, the former index measures deviations from the fundamental principle that equals be treated equally Finally, we apply our new measure to two tax-return data sets, evaluating the degree to which the horizontal equity of the US personal income tax has changed over time, and how horizontal equity would be altered by one version of recent proposals to do away with the so-called marriage penalty'
75 citations
TL;DR: In this paper, the authors investigated how area-level income inequality is associated with an individual's assessment of happiness, based on micro-level data sourced from nationwide surveys in Japan, and confirmed from their analysis using logit models that individuals who live in areas of high income inequality tend to report themselves as being less happy, even after controlling for various individual and area level factors.
Abstract: In this study, we investigated how area-level income inequality is associated with an individual’s assessment of happiness, based on micro-level data sourced from nationwide surveys in Japan. It was confirmed from our analysis using logit models that individuals who live in areas of high income inequality tend to report themselves as being less happy, even after controlling for various individual and area-level factors. The association between inequality and happiness is modestly significant, regardless of the choice of covariates at an individual level, and stronger at a lower level of perceived happiness. Moreover, sensitivity to inequality differs substantially according to certain individual attributes. Among others, an important implication for social policy is that those with unstable occupational status are more sensitive to inequality. Given that these people tend to be less happy than others, this result indicates the risk that area-level inequality further reduces the well-being of those with unfavorable employment conditions.
75 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