Nonparametric and Consistent Empirical Welfare Analysis Using Functional Methods

Trustees Of Boston University, Boston

Investigators

Abstract

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.