Nonparametric and Consistent Empirical Welfare Analysis Using Functional Methods

最近，人们对社会福利和不平等的衡量重新产生了兴趣。特别令人感兴趣的是对各国贫困和不平等的比较。与此同时，经济学家一直对一个国家福祉在不同时间的演变感兴趣。我们迫切需要一种方法，既可以用来检验最近的经济繁荣在多大程度上改善了整体福祉(以社会福利衡量)，也需要用不平等指数和洛伦茨曲线来衡量改善的分配方式。此外，有必要审查不同人口部分的福利和不平等随着时间的推移而发生变化的程度。大多数已开发的用于检查福利和不平等的统计工具并没有考虑收入的完全分配，而是只关注一小部分收入水平。因此，例如，在这类措施中，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部分内的不平等时都会强加强有力的假设。这项建议的研究目的是开发一套完整的统计工具来衡量福利、不平等和贫困。新的方法将考虑到分发的所有特点。这将通过使用统计泛函的方法来实现，这种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。拟议研究的第二个特点是开发方法，使人们能够以相对灵活的方式衡量人口部分的福利和不平等。这是通过采用非常灵活和易于在实践中使用的非参数方法来实现的。然后，这些方法将允许人们以灵活的方式比较不同人口部分的福利、不平等或贫困。拟议的研究将主要依靠大数定律和中心极限定理等大样本近似来发展所提议的技术的理论性质。此外，拟议的研究将检验这些方法在人工情况下的工作程度，类似于人们可能在现实世界数据中发现的情况。最后，这些方法将被用来使用来自各种来源的数据来检查美国和加拿大不同时期和不同人口部分的福利、不平等和贫困的变化。

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.