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, it is shown that inequality reducing taxation is equivalent to progressive taxation in the sense of an increasing average tax rate if and only if the concept of relative inequality is used.
Abstract: The paper examines different approaches to measure tax progressivity. In particular the distributional aspect of taxation is considered in some depth. For each member of a parametric class of inequality concepts, including more than only the relative and the absolute view of inequality, a necessary and sufficient condition for a tax function to be inequality reducing with respect to this concept for all admissible pre-tax income distributions is derived, both in strong and weak form. Only three very natural properties are required to prove this result: each tax liability is less than the corresponding pre-tax income, taxation does not reverse ranks on the income scale, and inequality is reduced if a rich gives to a poor such that they do not interchange their ranks. A definition of tax progressivity based on the shown equivalence is suggested. It is demonstrated that inequality reducing taxation is equivalent to progressive taxation in the sense of an increasing average tax rate if and only if the concept of relative inequality is used.
84 citations
Cites background from "On the Measurement of Inequality"
...An inequality index I: IR~_ + ~IR, X~I(X), is usually (e.g., Atkinson (1970) ,...
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TL;DR: In this paper, the authors investigate the juxtaposition of preferences with respect to income distributions and corresponding perceptions of distributional inequality, and find that even when some income distribution is judged to be more unequal than another, that distribution might be preferred, as it accords higher incomes to each individual.
Abstract: There are two categories of income distribution evaluations: first, the more-or-less “value-free” perception of income inequality as a statistical dispersion; and second, the valuation of income distributions according to an explicit social welfare function which is meant to capture all of society's value judgements. These societal value judgements can be expressed in the form of preferences. Whereas the inequality perception of income distributions appeals to an observer's sober judgement, the revelation of preferences with respect to specific income distributions appeals to his or her sentiments. This paper is an empirical analysis which investigates the juxtaposition of preferences with respect to income distributions and corresponding perceptions of distributional inequality. We do this through a questionnaire in which attitudes towards various distributional axioms are tested. The source of our data is 1773 completed questionnaires collected from five German universities. Based on our data, we observe that individuals' preference orderings over the set of income distributionssubstantially deviate from their perceptions of distributional inequality. In fact, our test responses showed that even when some income distribution is judged to be more unequal than another, that distribution might be preferred, as it accords higher incomes to each individual. We hold that the preference for these greater incomes expresses a compensation for the increased degree of inequality. This explanation applies both to equiproportional and to equal fixed-sum increases in incomes, which implies a support of Paretian ethics.
84 citations
01 Mar 2001
TL;DR: This paper explored the possibility of using the Atkinson (1970) and Kolm (1969) and Sen (1973) general ethical index in polarisation measurement and showed that inequality and polarisation are two dissimilar concepts, different indices of inequality may be used to generate alternative indices of polarisation.
Abstract: In this paper we explore the possibility of using the Atkinson (1970) ‐ Kolm (1969) ‐ Sen (1973) general ethical index in polarisation measurement. It is shown that though inequality and polarisation are two dissimilar concepts, different indices of inequality may be used to generate alternative indices of polarisation. A numerical illustration based on Indian household expenditure survey data is provided using several polarisation indices.
84 citations
01 Jan 2000
TL;DR: The EMU would provide an even greater temptation for them to do so because other economic policy instruments such as trade policy or monetary policy are kept under tight control, thereby increasing the relevance of incomes policy as an instrument at their disposal.
Abstract: Every step towards the completion of European integration appears to be greeted with renewed, not to say increasing, concern over its possible unwanted negative social side-effects, particularly as regards protection against social risks (unemployment, sickness and invalidity, age, ...) and poverty. Not only the governments of the different Member States but also the two EU Commissions headed in the past by Delors were deeply worried about the ability of the Member States, by applying incomes policies and social security measures, to pursue beggar-my-neighbour policies in an integrated market and all the more so in a monetary union. The EMU would provide an even greater temptation for them to do so because other economic policy instruments such as trade policy or monetary policy are kept under tight control, thereby increasing the relevance of incomes policy as an instrument at their disposal. Moreover the very creation of a single market would allow potentially more substantial gains from a competitive advantage as competition and the price elasticity of the demand of “tradables” increases. This applies in particular in a monetary union in which international transparency increases with the removal of transaction costs.
84 citations
TL;DR: In this article, the authors describe some basic steps in the theoretical and empirical analysis of comparison processes, processes that lead to such phenomena as happiness, self-esteem, relative deprivation, and distributive justice.
Abstract: This paper describes some basic steps in the theoretical and empirical analysis of comparison processes, processes that lead to such phenomena as happiness, self-esteem, relative deprivation, and distributive justice. Application of theoretical methods, notably solution of a system of partial differential equations, shows that the conditions embodied in the discursive accounts constrain the comparison function, for all goods and bads, to a function symmetric and additive in its two arguments, the actual holding and the comparison holding. Moreover, in the special case of a cardinal good or bad, the comparison function is constrained to the logarithmic form. Next, we describe empirical methods-based on the factorial survey pioneered by Peter H. Rossi-that enable estimation of the equation of observable comparison processes and statistical test of the associated heterogeneity hypotheses. We show that the general functional form dictated by the theoretical analysis combines with properties of Rossi's method to permit estimation of the principal theoretical quantities and, in the case of relative-rank holdings, assessment of the fit of alternative functional forms. We illustrate these methods with data on the justice of earnings. The empirical results reveal considerable variability across respondents both in the com-
84 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