John A. Bishop

Lorenz Dominance and Welfare: Changes in the U.S. Distribution of Income, 1967-1986

This paper examines income inequality in the Untied States over the period 1967-86 using recently developed tests for differences in Lorenz curves. The authors are able to rank eighteen of nineteen annual comparisons. In contrast, standard techniques are able to rank only twelve. These results suggest that the Lorenz dominance principle is more empirically relevant than previously thought. The tests reveal a sharp rise in U.S. inequality between 1978 and 1982, as well as a shift toward greater inequality over the entire period. The authors also examine changes in economic welfare using the joint mean-Lorenz dominance principle. Copyright 1991 by MIT Press.

Asymptotically Distribution-Free Statistical Inference for Generalized Lorenz Curves

This paper provides asymtotically distribution-free statistical inference procedures for generalized Lorenz curves. Given appropriate measures of income and the income recipient unit are chosen appropriately, the tests allow consensually valid statements regarding social welfare to be made from sample data on the basis of sound inferential procedures. More generally, the results presented here can be applied to test for second degree stochastic dominance. Copyright 1989 by MIT Press.

Statistical Inference and the Sen Index of Poverty

Statistical inference procedures are developed for A. K. Sens distribution-sensitive index of poverty and each of its components--the headcount ratio, income gap ratio, and the Gini index of the poor. Using results from U-statistics, the authors show that estimates of the index and its components all have a jointly asymptotically normal distribution and the variance-covariance structure can be consistently estimated. The inference tests are illustrated by applying them to the same microeconomic data set used in estimating official U.S. poverty statistics. The application reveals that the Sen index increased significantly in each of the three periods considered. Copyright 1997 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Testing for Marginal Changes in Income Distributions with Lorenz and Concentration Curves

Asymptotically distribution free statistical tests for comparing absolute and relative Lorenz and concentration curves are provided. The procedures do not require independent samples and can be used to test for marginal changes in income distributions. The tests are illustrated using a large sample of tax returns that have been randomly selected for audit by the Internal Revenue Service. The tests reveal the marginal effects of systematic underreporting of income and tax liabilities on the U.S. income distribution. Copyright 1994 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

International Comparisons of Income Inequality: Tests for Lorenz Dominance across Nine Countries

This paper examines income inequality across nine countries using the Luxembourg Income Study data set. New statistical tests and comparability of data provide an exceptionally clear picture of relative income inequality. Only 4 comparisons out of a possible 108 cannot be ranked. In most cases, differences in the definition of the recipient unit make little difference in the rankings. Irrespective of recipient units, Sweden, Norway, and Germany come out at the top of the ordinal Lorenz ranking, with Australia, Canada, and the United Kingdom in the middle, and the United States and Switzerland at the bottom. Copyright 1991 by The London School of Economics and Political Science.

Explaining Interstate Variation in Income Inequality

This paper investigates interstate variation in income inequality. By avoiding inequality indices and focusing directly on the Lorenz curve, the authors provide a more general explanation of the differences in inequality. They find that mean family income, the standard deviation of years of schooling, per capita educational expenditure, and property income are robust predictors of inequality. Of particular interest is their finding that, ceteris paribus, higher per capita education expenditures tend to be associated with states that have income inequality which is greater than the U.S. average. Copyright 1992 by MIT Press.

Inference Tests for Gini-Based Tax Progressivity Indexes

Distribution-free statistical inference procedures for changes in Lorenz- and Gini-based indexes of tax progressivity are developed and applied. Related but distinct tests for the Reynolds–Smolensky index of residual progression and the Kakwani index of liability progression are provided. The inference procedures are illustrated by applying them to Luxembourg Income Study microdata for Sweden, the United Kingdom, and the United States before and after periods of tax reform. In each country a finding of significant change depends on the choice among progressivity indexes. No single index exhibits a consistent pattern of significant change in all countries across time.

Rank dominance and international comparisons of income distributions

Abstract The rank dominance criterion for comparing income distributions assumes the Pareto principle, anonymity, and population size invariance. This paper applies rank dominance to compare international income distributions. Empirically, rank dominance is a powerful tool for ordering income distributions. Our results suggest that much of the power of generalized Lorenz dominance is due to efficiency preference, and equity preference adds only marginally to the ability to order income distributions.

Convergence and Divergence of Regional Income Distributions and Welfare

Regional income distributions are analyzed and tested for convergence and divergence in the 1970s. The methodology is the same as that recently used to show the almost complete convergence of the South and non-South. This paper disaggregates the non-South into major regions consisting of the West, Midwest, and Northeast. Tests for rank dominance reveal surprising results. Income distributions in the major regions of the non-South were equivalent in 1969, and the South was uniformly dominated. Fundamental changes in the 1970s resulted in the West rank dominating the Midwest, which dominated the South, which in turn dominated the Northeast. Copyright 1994 by MIT Press.

International Comparisons of Welfare and Poverty: Dominance Orderings for Ten Countries

Inference-based stochastic dominance procedures are applied to Luxembourg Income Study data to rank ten western countries in terms of standards of living and poverty. First-order dominance comparisons ranks more than 50 percent of all pairwise comparisons and second-order (generalized Lorenz) dominance adds another 25 percent. Truncated dominance analysis is used to make inferences about poverty and up to 98 percent of the truncated distributions are ordered. The results differ substantially from those obtained when only relative incomes and inequality are considered.