Income, Inequality, and Social Welfare: A Study of the U.S. States

Abstract

Amartya Sen (Journal of Public Economics, 1974; Review of Economic Studies, 1976) proposed a social welfare index defined as mean income multiplied by (1-Gini coefficient) and provided an axiomatic basis for the index. The index can also be interpreted as inequality-adjusted income or, as Bishop, Chakraborti, and Thistle (Oxford Bulletin of Economics and Statistics, 1990) note, equally-distributedequivalent income measure for Gini. Anthony Atkinson (Scandinavian Journal of Economics, 1999, p. 181) treated the index as a measure of real income. The index has been used in several studies of income and welfare. For example, Berrebi and Silber (Economics Letters, 1987) did a decomposition of the change in the index for the United States over the periods 1960–1970 and 1970–1980. Bishop et al. (1990) provided distribution-free tests for the index and did an application to the U.S. from 1980 census data. Ram (Economic Development and Cultural Change, 1992) computed the index for two cross-country samples and showed that the index correlated highly with income, but weakly with the Gini coefficient. Since Bishop et al. focused on significance tests for the index and worked with 1980 census data for the U.S., it is useful to construct the index from more recent state-level information and, like Ram (1992), consider how the welfare index correlates with mean income and the Gini coefficient. The index may be written as W0Y(1−G), where W is Sen’s welfare index, Y denotes mean income, and G stands for the Gini coefficient of each state. Data on mean household income and the household Gini coefficient for each state are taken from Census Bureau’s American Fact Finder and are based on American Community Surveys (ACS) for the five-year period of 2006–2010. Since information is derived from five rounds of ACS, it is likely to be more stable and reliable than the usual annual numbers from ACS or even the census. The welfare index is calculated for each state by using the foregoing expression. Int Adv Econ Res (2013) 19:65–67 DOI 10.1007/s11294-012-9378-8