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Ranking intersecting distribution functions

机译：排名交叉分配功能

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摘要

Second-degree dominance has become a widely accepted criterion for ordering distribution functions according to social welfare. However, it provides only a partial ordering, and it may fail to rank distributions that intersect. To rank intersecting distribution functions, we propose a general approach based on rank-dependent theory. This approach avoids making arbitrary restrictions or parametric assumptions about social welfare functions and allows researchers to identify the weakest set of assumptions needed to rank distributions according to social welfare. Our approach is based on two complementary sequences of nested dominance criteria. The first (second) sequence extends second-degree stochastic dominance by placing more emphasis on differences that occur in the lower (upper) part of the distribution. The sequences characterize two separate systems of nested subfamilies of rank-dependent social welfare functions. This allows us to identify the least restrictive rank-dependent social preferences that give an unambiguous ranking of a given set of distribution functions. We also provide an axiomatization of the sequences of dominance criteria and the corresponding subfamilies of social welfare functions. We show the usefulness of our approach using two empirical applications; the first assesses the welfare implications of changes in household income distributions over the business cycle, while the second performs a social welfare comparison of the actual and counterfactual outcome distributions from a policy experiment.
机译：二级统治认为，根据社会福利，已成为对订购分销职能的广泛接受的标准。但是，它只提供部分排序，并且可能无法排序相交的分布。为了排列交叉分配职能，我们提出了一种基于依赖依赖理论的一般方法。这种方法避免了关于社会福利职能的任意限制或参数假设，并允许研究人员根据社会福利确定排名所需的最薄弱的假设。我们的方法是基于嵌套统治标准的两个补充序列。第一（第二）序列通过更加强调分布的下部（上）部分中发生的差异来延长二级随机优势。该序列表征了依赖依赖社会福利职能的两个嵌套亚颈部系统。这使我们能够识别最少限制依赖性的社交偏好，其给出给定的一组分发功能的明确排名。我们还提供了主导标准序列和社会福利功能的相应亚组织的公理化。我们展示了我们使用两个经验应用的方法的有用性;首先评估家庭收入分布变化对商业周期的福利影响，而第二次履行政策实验中实际和反事实成果分布的社会福利比较。

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