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, a general method for constructing measures (both relative and absolute) of effective tax/benefit progressivity from social-welfare functions is proposed. But this method does not consider the effect of individual taxation.
Abstract: In this paper we propose a general method for constructing measures (both relative and absolute) of effective tax/benefit progressivity from social-welfare functions. Relative measures compare the after-tax (or benefit) distribution of income with the distribution that would result if the burden were imposed proportionally. Absolute measures use the equal taxation of individuals as a benchmark. These indices are related to relative and absolute indices of inequality. Our relative indices are generalizations of the Gini-index-based Musgrave-Thin measure of effective progressivity. We compare our general indices to the proposals of Kakwani, Khetan and Poddar, and Suits.
81 citations
TL;DR: In this article, the authors consider the problem of grouping income distribution data into a given number of groups such that the concealed income differences due to grouping are minimized, i.e., minimizing the area between the grouped and ungrouped Lorenz curves.
Abstract: We consider the problem of grouping income distribution data into a given number of groups such that the concealed income differences due to grouping are minimized. When income differences are measured by Gini's pairwise differences, this means minimizing the area between the grouped and ungrouped Lorenz curves. In this case, the necessary condition for optimal grouping is that each group limit be equal to the average income in its two adjacent groups. An iterative procedure for computation and applications including fractile groupings are discussed. Alternative optimal groupings based on other measures of income differences are also considered.
81 citations
TL;DR: In this article, the authors consider non-anonymous growth incidence curves that plot income growth rates against the various quantiles of the initial distribution, which account for the inequality of individual income changes, conditional on initial income.
Abstract: The distributional incidence of growth is generally analyzed by comparing the quantiles of the pre- and post-growth income distribution—e.g. the so-called Growth Incidence Curves. Such an approach based on an implicit re-ranking of individual incomes ignores income mobility by assuming that only post-growth income matters in social welfare. By contrast, this paper takes the view that “status quo matters” and that social welfare should logically be defined on both inital and terminal income. This leads to consider ’non-anonymous’ Growth Incidence Curves that plot income growth rates against the various quantiles of the initial distribution. Dominance criteria that generalize those available for standard growth incidence curves are derived, which account for the inequality of individual income changes, conditional on initial income. An application to the cross-country distributional feature of global growth illustrates the analysis.
81 citations
TL;DR: The criteria presented in this paper provide an important theoretical foundation for empirical analysis using the concentration curve and are shown to be closely related to the concentration Curve when health and income are positively related.
81 citations
TL;DR: This article developed a model in which public capital is both an engine of growth and a determinant of the distributions of wealth, income, and welfare, and showed that public investment increases wealth inequality over time, regardless of its financing.
81 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