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Inequality has become a malignant, contagious disease. It feeds, it grows, it attaches itself to nearly all aspects of life. It poisons or impedes many of our relationships. Above all, it is a threat to the health and stability of our democratic republic. It has become the major issue of our time. We can see more clearly how and why it has become so as we review eight major features of our society. Refer to the diagram below as you read.

Inequality often appears in linked pairs of variables. Examples include schooling and income, income and consumption, and wealth and happiness. Consider the famous words of Veblen: "wealth confers honor." Understanding inequality requires understanding input inequality, outcome inequality, and the relation between the two—in both inequality between persons and inequality between subgroups. This article contributes to the methodological toolkit for studying inequality by developing a framework that makes explicit both input inequality and outcome inequality and by addressing three main associated questions: (1) How do the mechanisms for generating and altering inequality differ across inputs and outcomes? (2) Which have more inequality—inputs or outcomes? (3) Under what conditions, and by what mechanisms, does input inequality affect outcome inequality? Results include the following: First, under specified conditions, distinctive mechanisms govern inequality in inputs and inequality in outcomes. Second, input inequality and outcome inequality can be the same or different; if different, whether inequality is greater among inputs or outcomes depends on the configuration of outcome function, types of inputs, distributional form of and inequality in cardinal inputs, and number of and associations among inputs. Third, the link between input inequality and outcome inequality is multiform; it can be nonexistent, linear, or nonlinear, and if nonlinear, it can be concave or convex. More deeply, this work signals the formidable empirical challenges in studying inequality, but also the fast growing toolbox. For example, even if the outcome distribution is difficult to derive, fundamental theorems on the variance make it possible to analyze the input–outcome inequality connection. Similarly, within specified distributions, the general inequality parameter makes it possible to express results in terms of both measures of overall inequality and measures of subgroup inequality.

"We revisit to what extent the increase in income inequality over the last 30 years has been mirrored by consumption inequality. We do so by constructing two alternative measures of consumption expenditure, using data from the Consumer Expenditure Survey (CE). We first use reports of active savings and after tax income to construct the measure of consumption implied by the budget constraint. We find that the consumption inequality implied by savings behavior largely tracks income inequality between 1980 and 2007. Second, we use a demand system to correct for systematic measurement error in the CE's expenditure data. Specifically, we consider trends in the relative expenditure of high income and low income households for different goods with different income (total expenditure) elasticities. Our estimation exploits the difference in the growth rate of luxury consumption inequality versus necessity consumption inequality. This "double-differencing,'' which we implement in a a regression framework, corrects for mis-measurement that can systematically vary over time by good and income group. This second exercise indicates that consumption inequality has closely tracked income inequality over the period 1980-2007. Both of our measures show a significantly greater increase in consumption inequality than what is obtained from the CE's total household expenditure data directly"--National Bureau of Economic Research web site

We revisit to what extent the increase in income inequality since 1980 was mirrored by consumption inequality. We do so by constructing an alternative measure of consumption expenditure using a demand system to correct for systematic measurement error in the Consumer Expenditure Survey. Our estimation exploits the relative expenditure of high- and low-income households on luxuries versus necessities. This double differencing corrects for measurement error that can vary over time by good and income. We find consumption inequality tracked income inequality much more closely than estimated by direct responses on expenditures. (JEL D31, D63, E21)

This article analyzes the mathematical connections between two kinds of inequality: inequality between persons (e.g., income inequality) and inequality between subgroups (e.g., racial inequality). The authors define a general inequality parameter in two-parameter continuous distributions. This parameter governs all measures of personal inequality (e.g., the Gini coefficient) and governs as well the gap (difference or ratio) between the means of subdistributions. It is thus established that in the distributions analyzed here, as personal inequality increases, so does inequality between subgroups. This general inequality parameter also governs Lorenz dominance and all quantities in the decomposition of Theil's mean logarithmic deviation into between-subgroup and within-subgroup components in the Pareto case. Thus, the general inequality parameter captures the ``deep structure'' of inequality. Finally, a whole-distribution graphical tool is introduced for assessing personal and subgroup inequality. Substantively, this work suggests that in societies characterized by special income distributions, whenever inequality disrupts social cohesion, it attacks on two fronts, via subgroup inequality as well as personal inequality.

Social scientists study two kinds of inequality: inequality between persons (as in income inequality) and inequality between subgroups (as in racial inequality). This paper analyzes the mathematical connections between the two kinds of inequality. The paper proceeds by exploring a set of two-parameter continuous probability distributions widely used in economic and sociological applications. We define a general inequality parameter, which governs all measures of personal inequality (such as the Gini coefficient), and we link this parameter to the gap (difference or ratio) between the means of subdistributions. In this way we establish that, at least in the two-parameter distributions analyzed here, and for the case of two nonoverlapping subgroups, as personal inequality increases, so does inequality between subgroups. This general inequality parameter also governs Lorenz dominance. Further, we explore the connection between subgroup inequality (in particular, the ratio of the bottom subgroup mean to the top subgroup mean) and decomposition of personal inequality into between-subgroup and within-subgroup components, focusing on an important decomposable measure, Theil's MLD, and its operation in the Pareto case. This allows us to establish that all the quantities in the decomposition are monotonic functions of the general inequality parameter. Thus, the general inequality parameter captures the deep structureʺ of inequality. We also introduce a whole-distribution graphical tool for assessing personal and subgroup inequality. Substantively, this work suggests that in at least some societies, characterized by special income distributions, whenever inequality disrupts social harmony and social cohesion, it attacks on two fronts, via subgroup inequality as well as personal inequality.

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