Nonparametric and Consistent Empirical Welfare Analysis Using Functional Methods

最近，人们重新对社会福利和不平等的衡量产生了兴趣。特别令人感兴趣的是对各国之间的贫穷和不平等进行比较。与此同时，经济学家一直对一个国家的福祉随时间的演变感兴趣。现在非常需要有一种方法，既可以用来审查最近的经济繁荣在多大程度上改善了总体福祉，如社会福利所衡量的，也可以用来审查改善的分布方式，如不平等指数和洛伦兹曲线所衡量的。此外，审查不同人口阶层的福利和不平等随时间变化的程度也是有意义的。为审查福利和不平等而开发的大多数统计工具都没有考虑到收入的全部分配，而是只侧重于一小部分收入水平。因此，例如，在这些措施中，最贫穷者不断变化的情况通常会被忽视。此外，目前使用的大多数方法在考虑人口各部分内部的不平等时都有很强的假设。本提案中的研究目的是开发一套完整的统计工具，用于衡量福利、不平等和贫困。新方法将考虑到分布的所有特征。这将通过使用统计函数的方法来实现，这些方法允许人们在衡量和比较福利和不平等时考虑整个收入分配。拟议的研究的第二个特点是制定方法，使人们能够以相对灵活的方式衡量人口各阶层的福利和不平等。这是通过采用非参数方法来实现的，这些方法在实践中非常灵活且易于使用。这些方法将使人们能够灵活地比较人口不同部分的福利、不平等或贫穷。所提出的研究将主要依赖于大样本近似，如大数定律和中心极限定理，发展所提出的技术的理论特性。此外，拟议中的研究将检查这些方法在人工情况下的工作程度，这些情况类似于人们可能会发现的真实的世界数据。最后，这些方法将被用来检查福利的变化，不平等和贫困随着时间的推移，在美国和加拿大的人口使用各种来源的数据的各个部分。

Recently there has been a renewed interest in the measurement of social welfare and inequality. Of particular interest have been comparisons of poverty and inequality across countries. At the same time economists have been interested in the evolution of a nations well being across time. There is a great need for methods that can be used to examine both the extent to which recent economic booms have improved overall well being, as measured by social welfare, as well as the way in which improvements have been distributed, as measured by inequality indices and Lorenz curves. Moreover it is of interest to examine the extent to which welfare and inequality have changed over time within different segments of the population. Most of the statistical tools that have been developed for examination of welfare and inequality do not consider the complete distribution of income, instead focusing on only a small set of income levels. Thus, for instance, the changing circumstances of the poorest would generally be ignored in such measures. Additionally, most currently used methods impose strong assumptions when considering inequality within segments of the population. The aim of the research in this proposal is to develop a complete set of statistical tools for measurement of welfare, inequality and poverty. The new methods will be such that all features of the distribution will be taken into account. This will be achieved by using methods for statistical functionals which allow one to consider the whole income distribution when measuring and comparing welfare and inequality. A second feature of the proposed research is the development of methods that allow one to measure welfare and inequality within segments of the population in a relatively flexible fashion. This is achieved by employing non-parametric methods that are quite flexible and easy to use in practice. The methods would then permit one to compare welfare, inequality or poverty across different segments of the population in a flexible manner. The proposed research will develop the theoretical properties of the proposed techniques mostly relying on large sample approximations such as the law of large numbers and central limit theorem. In addition the proposed research will examine the extent to which the methods work in artificial situations similar to what one might find with real world data. Finally, the methods will be used to examine changes in welfare, inequality and poverty across time and across segments of the population in the United States and Canada using data from a variety of sources.