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 focus on the two most important federal policies toward housing, at least in terms of costs to the government, and focus on subsidies and urban renewal programs, respectively.
Abstract: Publisher Summary This chapter discusses housing subsidies. The American housing market is subject to a mind-boggling array of government interventions by various levels of government. These include: housing codes, that set quality standards that must be met by builders; licensure of real estate brokers and sales people; exclusionary zoning, which stipulates that land in a given area can be used only for certain purposes; open housing laws, that prohibit discrimination in the selling of housing; rent control; interest rate and other regulations on mortgage lending institutions; urban renewal programs, under which communities use their powers of eminent domain to acquire urban land, destroy “slums,” and sell the land to private developers; real estate taxation; and interventions in the credit market to increase the flow of credit to housing. The chapter focuses on the two most important federal policies toward housing, at least in terms of costs to the government.
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TL;DR: In this paper, an instructional theory of music practice is presented, focusing on the following components of the practice process: choice, intentionality, action, achievement outcome, and rest and recovery.
Abstract: This paper provides a summary and synthesis of the extant research related to music practicing as well as a preliminary presentation of an original instructional theory of practicing. The 119 studies reviewed in this paper are organized according to four central questions about practicing that research has begun to inform: (a) What do individuals do when they practice music? (b) How have researchers intervened with individuals' practice? (c) What individual difference variables interact with why and how musicians practice? and (d) How is self-regulated learning relevant to practicing? Figures summarizing the essential methodological components of selected studies from each category are included. An instructional theory is presented as opposed to a descriptive theory in an attempt to more closely align research and teaching efforts. The instructional theory that is proposed makes considerations for theoretical frameworks employed in previous research. The following components of the practice process in regards to both student's and teacher's influence are included in the new theory: choice, intentionality, action, achievement outcome, and rest and recovery.
40 citations
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TL;DR: This paper reviewed methods for summarizing and comparing wealth distributions and showed that many of the tools commonly used to summarize income distributions can also be applied to wealth distributions, albeit adapted in order to account for the distinctive features of wealth distributions: zero and negative wealth values; spikes in density at or around zero; right-skewness with long and sparse tails combined with non-trivial prevalence of extreme values.
Abstract: This paper reviews methods for summarizing and comparing wealth distributions. We show that many of the tools commonly used to summarize income distributions can also be applied to wealth distributions, albeit adapted in order to account for the distinctive features of wealth distributions: zero and negative wealth values; spikes in density at or around zero; right-skewness with long and sparse tails combined with non-trivial prevalence of extreme values. Illustrations are provided using data for Finland.
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26 Sep 2017
TL;DR: The authors showed that the difference in the rank order of donor and recipient is usually the most important factor determining the change in the Gini index due to the transfer, which implies that transfers from an upper income household to a low income household receive more weight that transfers involving the middle.
Abstract: The Gini index is the most commonly used measure of income inequality. Like any single summary measure of a set of data, it cannot capture all aspects that are of interest to researchers. One of its widely reported flaws is that it is supposed to be overly sensitive to changes in the middle of the distribution. By studying the effect of small transfers between households or an additional increment in income going to one member of the population on the value of the index, this claim is re-examined. It turns out that the difference in the rank order of donor and recipient is usually the most important factor determining the change in the Gini index due to the transfer, which implies that transfers from an upper income household to a low income household receive more weight that transfers involving the middle. Transfers between two middle-income households do affect a higher fraction of the population than other transfers but those transfers do not receive an excessive weight relative to other transf...
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Cites background or methods from "On the Measurement of Inequality"
...…of them will be used in Section 3 to examine the effect on the Gini index of a small order-preserving transfer, e.g., an infinitesimal transfer from a high income household to one with less income, discussed by Atkinson (1970) or a small additional increment given to one household (Hoffman 2001)....
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...Thus, the relationship between the choice of measure and its underlying social welfare function, stressed by Atkinson (1970), Newbery (1970), Sheshinski (1972), and Sen (1974) remains very important....
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...Thus, for small increments analogous to the transfers considered by both Atkinson (1970) and Allison (1978), the Gini index will decrease the most when the household with the lowest income is the recipient....
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...Thus, the results in this section are applicable to the “infinitesimal” transfers considered by Atkinson (1970) and the “small ones” discussed by Allison (1978)....
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...As Atkinson (1970) noted, the Gini index is sensitive to changes at all levels and a reason for this is that the change has two components, one of which is more sensitive to transfers when the donor and recipient are from different parts of the distribution and the other when they are both in the…...
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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