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 effects of government programs on the distribution of participants? earnings is reported. But, the authors focus on the first-step estimation of a nuisance function and do not consider the second-step estimate of the nuisance function.
Abstract: The effect of government programs on the distribution of participants? earnings is important for program evaluation and welfare comparisons. This paper reports estimates of the effects of JTPA training programs on the distribution of earnings. The estimation uses a new instrumental variable (IV) method that measures program impacts on the quantiles of outcome variables. This quantile treatment effects (QTE) estimator accommodates exogenous covariates and reduces to quantile regression when selection for treatment is exogenously determined. The QTE estimator can be computed as the solution to a convex linear programming problem, although this requires first-step estimation of a nuisance function. We develop distribution theory for the case where the first step is estimated nonparametrically. For women, the empirical results show that the JTPA program had the largest proportional impact at low quantiles. Perhaps surprisingly, however, JTPA training raised the quantiles of earnings for men only in the upper half of the trainee earnings distribution.
530 citations
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01 Jan 2008
TL;DR: In this paper, the authors define fairness as "defining fairness" and distribute fairly, based on a set of incentive issues: risk, insurance, and option luck.
Abstract: Introduction 1. Defining Fairness 2. Distributing Fairly 3. Introduction to Incentive Issues 4. Unequal skills 5. Income Redistribution 6. Risk, Insurance, and Option Luck 7. Fresh Starts 8. Utilitarian Reward 9. Inequalities of Opportunity and Social Mobility 10. Responsibility, Freedom, and Social Justice
527 citations
01 Jan 1986
TL;DR: The relationship between measures of population diversity and measures of segregation are shown, to describe the salient properties of these indexes, and to demonstrate the empirical interrelationships among them.
Abstract: The purposes of the present paper are to show the relationship between measures of population diversity and measures of segregation to describe the salient properties of these indexes and to demonstrate the empirical interrelationships among them. Some measures not frequently used in population studies are considered and empirical illustrations are given of the significance of using one measure rather than another. In particular the author stresses proportional reduction of error interpretations for an index and considers its ability to handle more than two groups. The primary geographic focus is on the United States. The "introductory section of the paper treats conceptual issues in more detail. The second section reviews selected measures and recent critical viewpoints while the third section tests their empirical performance. The conclusion makes some recommendations about the selection of an index. A detailed bibliography follows." (EXCERPT)
526 citations
TL;DR: In this paper, the effects of JTPA training programs on the distribution of earnings were investigated using a new instrumental variable (IV) method that measures program impacts on quantiles, and the quantile treatment effects estimator reduces to quantile regression when selection for treatment is exogenously determined.
Abstract: This paper reports estimates of the effects of JTPA training programs on the distribution of earnings. The estimation uses a new instrumental variable (IV) method that measures program impacts on quantiles. The quantile treatment effects (QTE) estimator reduces to quantile regression when selection for treatment is exogenously determined. QTE can be computed as the solution to a convex linear programming problem, although this requires first-step estimation of a nuisance function. We develop distribution theory for the case where the first step is estimated nonparametrically. For women, the empirical results show that the JTPA program had the largest proportional impact at low quantiles. Perhaps surprisingly, however, JTPA training raised the quantiles of earnings for men only in the upper half of the trainee earnings distribution.
525 citations
Posted Content•
TL;DR: For helpful comments on earlier drafts, the authors thank, without implicating, Moses Abramovitz, Yves Balcer, John Bishop, Alan Blinder, Richard Burkhauser, Michael Darby, Irwin Garfinkel, Alan Gustman, Daniel Hamermesh, Martin Holmer, George Jakubson, Robert Lampman, Paul Menchik, Robert Moffitt, Michael Murray, Joseph Quinn, Timothy Smeeding, Eugene Smolensky, Barbara Wolfe and two anonymous referees.
Abstract: For helpful comments on earlier drafts, we thank, without implicating, Moses Abramovitz, Yves Balcer, John Bishop, Alan Blinder, Richard Burkhauser, Michael Darby, Irwin Garfinkel, Alan Gustman, Daniel Hamermesh, Martin Holmer, George Jakubson, Robert Lampman, Paul Menchik, Robert Moffitt, Michael Murray, Joseph Quinn, Timothy Smeeding, Eugene Smolensky, Barbara Wolfe and two anonymous referees.
518 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
Posted Content•
1,748 citations
"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