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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Journal Article•
TL;DR: Maldistribution of GPs as measured by the Gini coefficient and Atkinson index increased from the mid-1980s to 2003, but the decile ratio showed little change over the entire 1974-2003 period.
Abstract: Background: The geographical distribution of general practitioners (GPs) is a persistent policy concern within the National Health Service. Maldistribution across family health service authorities in England and Wales fell between 1974 and the mid-1980s but then remained, at best, constant until the mid-1990s.
Aim: To estimate levels of maldistribution over the period 1994–2003 and to examine the long-term trend in maldistribution from 1974–2003.
Design: Annual snapshots from the GP census.
Setting: One hundred 2001 ‘frozen’ health authorities in England and Wales for 1994–2003 and 98 family health service authorities for 1974–1995.
Method: Ratios of GPs to raw and need-adjusted populations were calculated for each health authority for each year using four methods of need adjustment: age-related capitation payments, national age- and sex-specific consultation rates, national age- and sex-specific limiting long-term illness rates, and health authority-specific mortality. Three summary measures of maldistribution across health authorities in the GP to population ratio — the decile ratio, the Gini coefficient, and the Atkinson index — were calculated for each year.
Results: Maldistribution of GPs as measured by the Gini coefficient and Atkinson index increased from the mid-1980s to 2003, but the decile ratio showed little change over the entire 1974–2003 period. Unrestricted GP principals and equivalents were more equitably distributed than other types of GP.
Conclusion: The 20% increase in the number of unrestricted GPs between 1985 and 2003 did not lead to a more equal distribution.
99 citations
TL;DR: In this paper, the authors explored the redistributive effects of different tax benefit instruments in the enlarged European Union (EU) based on two approaches: sequential accounting and factor source decomposition.
Abstract: How do different components of the tax and transfer systems affect disposable income inequality? This article explores the redistributive effects of different tax benefit instruments in the enlarged European Union (EU) based on two approaches. Inequality analysis based on the sequential accounting approach suggests that benefits are the most important factor reducing inequality in the majority of countries. The factor source decomposition approach, however, suggests that benefits play a negligible role and sometimes even contribute slightly positively to inequality. On the contrary, here taxes and social contributions are by far the most important contributors to income inequality reduction. The authors explain these partly contradictory results with the different normative focus of the two approaches and show that benefits have other aims than redistribution.
99 citations
Cites methods from "On the Measurement of Inequality"
...Following Atkinson (1970) and Kolm (1969), a relative measure of inequality can be derived from a relationship between inequality, mean income and social welfare as:...
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TL;DR: In this article, the authors examined the distribution of sites coming within the Industrial Pollution Control (IPC) regime against patterns of deprivation and found evidence of a socially unequal distribution of IPC sites in England, with sites disproportionately located and clustered together in deprived areas and near to deprived populations.
Abstract: The local impacts of industrial pollution can take many forms and—whilst uncertain in their scale, severity and distribution—are widely recognised. The question of who in society potentially experiences these impacts through living near to emission sources has been little explored, at least in the UK. This paper reports on a study carried out for the Environment Agency, which examined the distribution of sites coming within the Industrial Pollution Control (IPC) regime against patterns of deprivation. Our analysis provides evidence of a socially unequal distribution of IPC sites in England, with sites disproportionately located and clustered together in deprived areas and near to deprived populations. In discussing these results we emphasise the methodological limitations of this form of environmental justice analysis and the crucial differences between proximity, risk and impact. We also consider the distinction between inequality and injustice and the difficult policy questions which arise when...
98 citations
TL;DR: In this article, a scaled conditional mean curve is proposed as an alternative interpretation of the information content of the Lorenz curve and furthermore proves to yield essential information on polarization in the population.
Abstract: The purpose of this paper is to justify the use of the Gini coefficient and two close relatives for summarizing the basic information of inequality in distributions of income. To this end we employ a specific transformation of the Lorenz curve, the scaled conditional mean curve, rather than the Lorenz curve as the basic formal representation of inequality in distributions of income. The scaled conditional mean curve is shown to possess several attractive properties as an alternative interpretation of the information content of the Lorenz curve and furthermore proves to yield essential information on polarization in the population. The paper also provides asymptotic distribution results for the empirical scaled conditional mean curve and the related family of empirical measures of inequality.
98 citations
Cites background from "On the Measurement of Inequality"
...Kolm [32] and Atkinson [8] to characterize the criterion of non-intersecting Lorenz curves in the case of distributions with equal mean incomes....
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TL;DR: In this article, the authors show that people of color and people living in poverty bear a disproportionate burden of urban heat exposure in almost all major cities in the continental United States and that the average person of color lives in a census tract with higher urban heat island (SUHI) intensity than non-Hispanic whites in all but 6 of the 175 largest urbanized areas in the United States.
Abstract: Urban heat stress poses a major risk to public health Case studies of individual cities suggest that heat exposure, like other environmental stressors, may be unequally distributed across income groups There is little evidence, however, as to whether such disparities are pervasive We combine surface urban heat island (SUHI) data, a proxy for isolating the urban contribution to additional heat exposure in built environments, with census tract-level demographic data to answer these questions for summer days, when heat exposure is likely to be at a maximum We find that the average person of color lives in a census tract with higher SUHI intensity than non-Hispanic whites in all but 6 of the 175 largest urbanized areas in the continental United States A similar pattern emerges for people living in households below the poverty line relative to those at more than two times the poverty line Individual exposure to heat is associated with adverse health and economic outcomes Here, the authors show that people of color and people living in poverty bear a disproportionate burden of urban heat exposure in almost all major cities in the continental United States
98 citations
References
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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
Posted Content•
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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