Investigates three ordering criteria for measures of income inequality: Lorenz-ordering, R-ordering, and power-scale ordering. R-ordering is a new criterion based on Wohlstetter and Coleman's ratio of income at quantiles function. The relationship of the three orderings is determined. Then, two new summary measures of income inequality are introduced. Both derive from the ratio of incomes at quantiles function. The first, W, has the properties desired of an inequality measure. The second, omega, is useful for describing the ratio of incomes at quantiles function when it is nearly linear, but lacks the ordering properties needed for a good measure of inequality. Ordering properties are determined for the new measures and for the familiar Gini coefficient, variance of the logarithm, two information measures, and the coefficient of variation. Dichotomous distributions are presented as a convenient family of distributions for providing counter-examples. (See also R-578.)
This report is part of the RAND Corporation Report series. The report was a product of the RAND Corporation from 1948 to 1993 that represented the principal publication documenting and transmitting RAND's major research findings and final research.
This research in the public interest was supported by RAND, using discretionary funds made possible by the generosity of RAND's donors, the fees earned on client-funded research, and independent research and development (IR&D) funds provided by the Department of Defense.
Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/principles.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.