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 examined the cyclical sensitivity of the distributional sensitivity of income inequality to macroeconomic changes and compared the results with previous findings by Metcalf, Mirer, and Schultz.
Abstract: DECENT years have witnessed an upswing in economists' interest in various aspects of the distnibution of income. The burgeoning of the size of econometric models has also led to inquiries into the distributional aspects of macroeconomic activity. How much do the poor gain from sustained growth, and who suffers relatively during slowdown and depression? Several attempts have been made to measure just what are the impacts of cyclical economic fluctuations on the distribution of income. Studies by Metcalf (1969), Mirer (1972), Schultz (1969), and Thurow (1970) have employed quite different approaches, and have reached differing conclusions on the cyclical sensitivity of income inequality. Clearly, a more general framework of analysis is needed to evaluate these findings in some perspective. One of the most frequently used approaches in such studies has been to characterize inequality in a distribution by a small number of summary measures (such as a Gini coefficient or an income share) and simply regress these inequality indices on such factors as an unemployment rate, a participation rate, and a per capita income measure. More preferable would be an approach that (i) explicitly lays out a model of the various channels by which macrofluctuations affect the distribution of income and (ii) examines the effects in a disaggregative fashion on individual income levels across a distribution. Such an approach, forwarded in Beach (1976), involved first modelling the behaviour of a set of individual quantile income levels and then expressing disaggregative income inequality measures in terms of these estimated income quantiles. One can then check the reasonableness of estimated inequality behaviour by examining the underlying behaviour of the individual quantile income levels. This article extends this disaggregative approach to an examination of implied aggregate inequality changes and compares the results with previous findings by Metcalf (1969) and Schultz (1969). It thus attempts to evaluate and integrate a number of disparate findings by building up summary measures of inequality from individual income quantiles. The outline of the paper is as follows. The next section reviews the "indirect quantile approach" followed here, and presents estimation results for the cyclical behaviour of a set of income quantiles. In section III the implied behaviour of relative mean incomes and income shares is discussed, and a comparison is presented with Metcalf's results. Section IV contains an aggregation of the results and a comparison with Schultz' findings. Then section V examines the behaviour of several alternative summary inequality measures. Section VI summarizes the principal findings and draws some implications.
78 citations
Cites result from "On the Measurement of Inequality"
...But, as witnessed in the estimation results (5) and (6) and as pointed out by Aigner and Heins (1967) and Atkinson (1970), different measures of income concentration can yield differing results....
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01 Jan 1999
TL;DR: For example, if the two-person income distribution (2,4) is as unequal as the distribution (1,2) because the ratios of incomes are the same, is inequality also unchanged when the distribution is transformed into the distribution by the multiplication of all incomes by the same number 10? In the transfer case, whatever its effect on inequality the transfer from richer to poorer may be good because it alleviates one person's poverty, or it may be just as discussed by the authors.
Abstract: People die in revolutions fighting inequalities. inequalities. “Men are free and equal in rights” is the political basis of democratic societies, and these rights may more or less include rights to consumption or income. Inequality, notably of incomes, is related to practically all important problems of society, as cause or as effect. But one generally has to compare unequal situations: When is one less unequal than the other? Does the transfer of one dollar from a richer to a poorer diminish inequality, given that it certainly augments inequality between the relatively poor receiver and the still poorer and equally poor, and between the relatively rich giver and the still richer and equally rich? In another respect, if the two-person income distribution (2,4) is as unequal as the distribution (1,2) because the ratios of incomes are the same, is inequality also unchanged when the distribution (0.01,1) is transformed into the distribution (0.1,10) by the multiplication of all incomes by the same number 10? In the transfer case, whatever its effect on inequality the transfer from richer to poorer may be good because it alleviates one person’s poverty, or it may be just.
78 citations
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TL;DR: In this paper, the authors present an empirical application of the distributional characteristic and its decomposition using Mexican data, showing that the welfare gains from using categorical targeting and means testing reflect improvements in redistributive and targeting efficiency respectively.
Abstract: The distributional characteristic provides an attractive alternative to conventional approaches used to evaluate the targeting performance of transfer programs. We decompose it into two components that are useful both conceptually and empirically; one capturing the targeting efficiency of the instrument, the other its redistributive efficiency. The redistributive index can also be generalized for the purposes of evaluating the degree of progressivity in tax-benefit structures. For illustrative purposes, we present an empirical application of the distributional characteristic and its decomposition using Mexican data. The welfare gains from using categorical targeting and means testing reflect improvements in redistributive and targeting efficiency respectively.
78 citations
TL;DR: In this article, the authors explore how the behaviour of welfare, income inequality and poverty changes during the course of a country's economic development, based on Kuznet's model of sectorial dualism.
Abstract: This paper explores how the behaviour of welfare, income inequality and poverty changes during the course of a country’s economic development. The analysis is based on Kuznet’s model of sectorial dualism. The various propositions proved in the paper provide conditions under which the modern sector enlargement and enrichment will lead to higher social welfare and lower income inequality and poverty. It is demonstrated that Kuznet’s U-shaped curve may not exist or even if it does, the turning point may occur at a later stage of development. The paper provides numerical illustrations of the results using Sri Lankan data.
78 citations
TL;DR: In this paper, the authors argue that, because of capital accumulation effects, the estate tax may increase inequality of income and wealth, and that the government takes actions to offset these accumulation effects.
Abstract: This paper shows that, because of capital accumulation effects, the estate tax may increase inequality of income and wealth. If the government takes actions to offset these accumulation effects, the tax will lead to an increase in equality of income and wealth. More generally, the paper argues that to evaluate the incidence of a tax in a growth context, one should compare policy changes which leave the aggregate capital labor ratio unchanged; we call this balanced growth incidence. But even with the capital labor ratio remaining unchanged, the estate tax may increase inequality in the distribution of consumption.
78 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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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