Measuring trends in U. S. income inequality. Theory and applications (Q1389379)

This book presents the authors' work on income inequality measurement and more specifically, the evolution of income inequality over time. The corner stone of their methodology is the maximum entropy estimation method and the related approximation by exponential polynomials. The chapters of the book are named as follows: (1) Introduction; (2) The maximum entropy estimation method; (3) Capabilities and earnings inequality; (4) Some new functional forms for approximating Lorenz curves; (5) Comparing income distributions using index space representations; (6) Coordinate space vs. index space representations as estimation methods: An application to how macro activity affects the U.S. income distribution; (7) A new method for estimating limited dependent variables: An analysis of hunger; Bibliography; Author index. The introduction gives a general overview of the subject together with widely used measures for income inequality, a brief review of the literature, a discussion on basic questions such as how to define the income receiving unit and, having defined it, how to quantify its income. The focus in the book is on family income as the appropriate unit. Chapter 2 provides an overview of the maximum entropy method for density estimation. The maximum entropy principle can be justified in a number of ways and is widely used in the physical sciences, time series analysis and signal processing. In the present setting it leads to representation of the logarithm of the density as a polynomial and simple sufficient statistics in the form of sample moments. The first and second order polynomials give the exponential and Gaussian distribution, respectively. Chapter 3 focuses on the relationships between the observed earnings distributions and the unobserved capabilities of the individuals. The earnings potential accumulation model is used to describe the general relationship between earnings and capabilities. Various transformations of earnings to capabilities are compared on empirical data. The relevance of the normality assumption about the distribution of the capabilities is studied and a way to avoid it is proposed. Chapter 4 introduces new functional forms for approximating Lorenz curves and compares them with other existing methods. Chapter 5 introduces a new method to compare income distributions. To this end the authors define a share function to be the derivative of a Lorenz curve. They argue that income inequality measures are better represented by the share function. They extend the Theil's entropy measure and use the maximum entropy principle to obtain an estimate of the share function. The functional form of the estimate is exponential polynomial. The authors argue that Legendre polynomials are the appropriate orthonormal basis to use in this case. They interpret the terms corresponding to the Legendre functions of different orders as providing information on the structure of the income inequality. The discussion is in the spirit of spectral analysis, parallels are made in this and the following chapter. Chapter 6 applies the ideas from the preceding chapter to study the effects of macroeconomic variables on US income distribution. It is shown that the authors' methodology gives deeper insight into the evolution of income inequality than the Lorenz curve itself or other summary measures provide. The last chapter makes an analysis of hunger in US. It introduces ``a new econometric method to estimate the impact of political and socioeconomic variables on an ill-defined variable (hunger)'' and examines ``how the infrastructure of both legal and political systems, as well as the economic system, are associated with the perceived level of hunger among children across states''. In summary, this is a timely published book on a topic of active research. It advocates a methodology based on maximum entropy, relatively rarely used in economic studies, and provides empirical evidence about its merits.