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: The results of this study confirm that the social determinants of health are relevant to the mental health of OA, however, further research is required to identify which are the specific socioeconomic deprivation components at the locality and municipal levels that correlate with depression in this population group.
Abstract: Objective Depression is the second most common mental disorder in older adults (OA) worldwide. The ways in which depression is influenced by the social determinants of health – specifically, by socioeconomic deprivation, income inequality and social capital - have been analyzed with only partially conclusive results thus far. The objective of our study was to estimate the association of income inequality and socioeconomic deprivation at the locality, municipal and state levels with the prevalence of depressive symptoms among OA in Mexico. Methods Cross-sectional study based on a nationally representative sample of 8,874 OA aged 60 and over. We applied the brief seven-item version of the Center for Epidemiologic Studies Depression Scale (CES-D) to determine the presence of depressive symptoms. Additionally, to select the principal context variables, we used the Deprivation Index of the National Population Council of Mexico at the locality, municipal and state levels, and the Gini Index at the municipal and state levels. Finally, we estimated the association of income inequality and socioeconomic deprivation with the presence of depressive symptoms using a multilevel logistic regression model. Results Socioeconomic deprivation at the locality (OR = 1.28; p<0.10) and municipal levels (OR = 1.16; p<0.01) correlated significantly with the presence of depressive symptoms, while income inequality did not. Conclusions The results of our study confirm that the social determinants of health are relevant to the mental health of OA. Further research is required, however, to identify which are the specific socioeconomic deprivation components at the locality and municipal levels that correlate with depression in this population group.
64 citations
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TL;DR: In this paper, the distributional impact of Brazilian economic growth during the 1960's was examined and it was shown that the poor in Brazil did participate in the rapid economic growth of the decade and that the majority of the growth of national income over the decade was received by families that placed them above the official poverty standard.
Abstract: [Excerpt] The purpose of this paper is to reexamine one of these two challenges, namely, the distributional impact of Brazilian economic growth during the 1960's. My results lead to a quite different interpretation from the conventional one. I will show that the poor in Brazil did participate in the rapid economic growth of the decade. Estimates presented below indicate that average real incomes among families defined as poor by Brazilian standards increased by as much as 60 percent while the comparable figure for nonpoor families is around 25 percent. However, since nonpoor families receive incomes which are much greater than those of poor families, the bulk of the growth of national income over the decade was received by families whose incomes placed them above the official poverty standard. Thus, it would be incorrect to say either that 1) in achieving a high rate of economic growth in Brazil the rich got absolutely richer while the poor got absolutely poorer, or 2) the incomes of poor families increased more slowly (percentagewise) than those of nonpoor families. These and other findings are presented below in Section II, and some of the reasons for the observed changes are discussed in Section III. In assessing the distributional consequences of Brazilian economic growth, this study explicitly adopts an absolute poverty approach. In so doing, it is at odds with the bulk of the economic development literature, which while urging a poverty focus, has long relied on measures of relative income inequality and Lorenz curves. Thus, this paper does not merely offer "one more measure"; it is, rather, the use of a different type of measure that causes the divergent results. The paper concludes in Section IV by reviewing the principal findings and exploring some further questions of more general applicability raised by the Brazilian debate.
64 citations
TL;DR: In this paper, the authors derived the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare and inequality, and established the statistical results for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes.
Abstract: We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality or social welfare is greater in one distribution than in another for general classes of indices. We also derive the sampling distribution of the maximal poverty lines (or income censoring thresholds) up to which we may confidently assert that poverty or social welfare is greater in one distribution than in another. The sampling distribution of convenient estimators for dual approaches to the measurement of poverty is also established. The statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes. Our results are briefly illustrated using data for 6 countries drawn from the Luxembourg Income Study data bases.
64 citations
TL;DR: In this paper, personal comparisons of utility levels and/or utility differences are used to define equity in distributing income, and the form of these restrictions depends on whether the levels and differences of the same utility functions are being compared.
63 citations
TL;DR: This article revisited the empirical basis of the Palma Proposition (the relative stability of the "middle") with a new and expanded data set across and within developing and developed countries and found that the data reaffirmed the proposition and that the proposition is getting stronger over time.
Abstract: The Palma Proposition is that changes in income or consumption inequality are (almost) exclusively due to changes in the share of the richest 10 per cent and poorest 40 per cent because the ‘middle’ group between the richest and poorest tend to capture approximately 50 per cent of gross national income (GNI). The Palma Ratio is a measure of income or consumption concentration based on the above-mentioned proposition and calculated as the GNI capture of the richest 10 per cent divided by that of the poorest 40 per cent. In this paper we revisit the empirical basis of the Palma Proposition (the relative stability of the ‘middle’) with a new and expanded data set across and within developing and developed countries. We find the data reaffirms the Palma Proposition and that the proposition is getting stronger over time.
63 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