Large Sample Properties of Two Inequality Indices
两种不平等指数的大样本性质AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究收入分布中 Atkinson、广义熵及相关福利指标的抽样性质，直接属于收入分布度量与统计推断问题。
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两种不平等指数的大样本性质
- 研究问题
- Atkinson 指数与广义熵指数，以及对应的等分配等价收入，具有怎样的大样本抽样分布，如何据此量化收入不平等与福利差异的不确定性？
- 方法与思路
- 作者将两类指数及对应福利量表示为收入分布矩的函数，利用样本矩的大样本性质推导渐近分布，其中涉及分数阶与负阶矩。
- 材料陈述的贡献
- 摘要称，所得渐近分布支持构造不平等及福利指标的置信区间和差异检验，相关推断渐近分布无关，可用于收入微观数据分析。
- 阅读关注点
- 核对不同指数参数下所需矩条件、等分配等价收入的转换及方差估计，关注零收入、重尾与实际抽样设计对推断适用性的影响。
- 阅读边界
- 摘要未说明收入取值、矩存在性与抽样设计条件，也未给出有限样本表现；渐近分布无关不能直接理解为小样本精确有效。
原文摘要
THIS PAPER PROVIDES the large sample properties of two inequality indices, Atkinson's (1970) index and the generalized entropy index (Cowell and Kuga (1981), Shorrocks (1984)). The large sample properties of the equally-distributed-equivalent (e.d.e.) income measures associated with these indices are also derived. The asymptotic distributions of these inequality and welfare measures allow the construction of confidence intervals and tests for differences in the measures; these confidence intervals and tests are asymptotically distribution-free. Given the increasing availability of large micro-data sets on incomes, these results are directly applicable to empirical work on income distributions. The sampling distributions of some inequality indices, such as the Gini coefficient and Pietra index, are known.' But the ethical bases of these indices have been subject to criticism, and some researchers may prefer the Atkinson or generalized entropy indices on ethical grounds. These researchers are confronted with a choice between using an ethically unattractive index with a known sampling distribution, or using an ethically preferable index whose sampling properties are unknown. The increasing use of the Atkinson and generalized entropy indices in empirical analyses of income distributions suggests many are choosing the second option. It then becomes important to understand the sampling properties of these indices, so that statistical inference procedures may be applied. The analysis in this paper complements the recent research on sampling properties and inference for Lorenz curves. For example, Beach and Davidson (1983), and Gastwirth and Gail (1985) propose tests for equality of Lorenz curves, and Beach and Richmond (1985) provide joint confidence intervals for the Lorenz ordinate vector. Bishop, Chakraborti, and Thistle (1987, 1988a, 1988b) and Bishop, Formby, and Thistle (1989) provide a number of extensions. These papers utilize results from the theory of linear functions of order statistics.2 However, this approach is not directly applicable to the Atkinson and generalized entropy indices; these indices are not linear functions of order statistics. The Atkinson and generalized entropy indices are functions of fractional and negative moments of the distribution, and their large sample properties follow from the properties of the sample moments.