Concept: Lorenz curve
The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf’s Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto’s or Benford’s, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf’s law for the largest cities. This pathology is reflected in the fact that Zipf’s Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call ‘coherence’ and it corresponds to a ‘screening’ between various elements of the set. We show how it should be accounted for when fitting Zipf’s Law.
This paper calculates the distribution of an adjusted measure of income that deducts damages due to exposure to air pollution from reported market income in the United States from 2011 to 2014. The Gini coefficient for this measure of adjusted income is 0.682 in 2011, as compared to 0.482 for market income. By 2014, we estimate that the Gini for adjusted income fell to 0.646, while the market income Gini did not appreciably change. The inclusion of air pollution damage acts like a regressive tax: with air pollution, the bottom 20% of households lose roughly 10% of the share of income, while the top 20% of households gain 10%. We find that, unlike the case for market income, New England is not the most unequal division with respect to adjusted income. Further, the difference between adjusted income for white and Hispanics is smaller than expected. However, the gap in augmented income between whites and African-Americans is widening.
Social science research finds that the only group to have experienced real economic gains over the past four decades is the top 20 percent of the income distribution. This finding, along with greater awareness of growing inequality, has renewed interest in mobility research that identifies how individuals and their progeny move into and out of upper versus lower income categories. In this study a new mobility methodology is proposed using life course concepts and life table statistical techniques. Panel data from a prospective national sample of the U.S. population age 25 to 60 are analyzed to estimate the extent of mobility associated with top percentiles in the income distribution. Empirical results suggest high mobility associated with top-level income. For example, 11 percent of the population is found to occupy the top one percentile for one or more years between the ages of 25 and 60. The study findings suggest that many experience short-term and/or intermittent mobility into top-level income, versus a smaller set that persist within top-level income over many consecutive years. Implications of the findings are discussed in terms of inequality buffering, opportunity versus insecurity, and the demographics of income inequality.
- Proceedings of the National Academy of Sciences of the United States of America
- Published almost 7 years ago
Using multiple data sources, we establish that China’s income inequality since 2005 has reached very high levels, with the Gini coefficient in the range of 0.53-0.55. Analyzing comparable survey data collected in 2010 in China and the United States, we examine social determinants that help explain China’s high income inequality. Our results indicate that a substantial part of China’s high income inequality is due to regional disparities and the rural-urban gap. The contributions of these two structural forces are particularly strong in China, but they play a negligible role in generating the overall income inequality in the United States, where individual-level and family-level income determinants, such as family structure and race/ethnicity, play a much larger role.
The rapid increase of wealth inequality in the past few decades is one of the most disturbing social and economic issues of our time. Studying its origin and underlying mechanisms is essential for policy aiming to control and even reverse this trend. In that context, controlling the distribution of income, using income tax or other macroeconomic policy instruments, is generally perceived as effective for regulating the wealth distribution. We provide a theoretical tool, based on the realistic modeling of wealth inequality dynamics, to describe the effects of personal savings and income distribution on wealth inequality. Our theoretical approach incorporates coupled equations, solved using iterated maps to model the dynamics of wealth and income inequality. Notably, using the appropriate historical parameter values we were able to capture the historical dynamics of wealth inequality in the United States during the course of the 20th century. It is found that the effect of personal savings on wealth inequality is substantial, and its major decrease in the past 30 years can be associated with the current wealth inequality surge. In addition, the effect of increasing income tax, though naturally contributing to lowering income inequality, might contribute to a mild increase in wealth inequality and vice versa. Plausible changes in income tax are found to have an insignificant effect on wealth inequality, in practice. In addition, controlling the income inequality, by progressive taxation, for example, is found to have a very small effect on wealth inequality in the short run. The results imply, therefore, that controlling income inequality is an impractical tool for regulating wealth inequality.
We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution of wealth vs. opportunity. This picture is however dramatically ameliorated when hard constraints are imposed over agents in the form of a limiting network of transactions. There, an out of equilibrium dynamics of the networks, based on a competition between power and frustration in the decision-making of agents, leads to network coevolution. The ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of equality. It also leads, for proper values of social initiative, to the emergence of three self-organized social classes, lower, middle, and upper class. Their dynamics, which appears mostly controlled by the middle class, drives a cyclical regime of dramatic social changes.
- Proceedings of the National Academy of Sciences of the United States of America
- Published over 6 years ago
The present paper reports results from, to our knowledge, the first study designed to examine the neuronal responses to income inequality in situations in which individuals have made different contributions in terms of work effort. We conducted an experiment that included a prescanning phase in which the participants earned money by working, and a neuronal scanning phase in which we examined how the brain responded when the participants evaluated different distributions of their earnings. We provide causal evidence for the relative contribution of work effort being crucial for understanding the hemodynamic response in the brain to inequality. We found a significant hemodynamic response in the striatum to deviations from the distribution of income that was proportional to work effort, but found no effect of deviations from the equal distribution of income. We also observed a striking correlation between the hemodynamic response in the striatum and the self-reported evaluation of the income distributions. Our results provide, to our knowledge, the first set of neuronal evidence for equity theory and suggest that people distinguish between fair and unfair inequalities.
Heritability is often estimated by decomposing the variance of a trait into genetic and other factors. Interpreting such variance decompositions, however, is not straightforward. In particular, there is an ongoing debate on the importance of genetic factors in cancer development, even though heritability estimates exist. Here we show that heritability estimates contain information on the distribution of absolute risk due to genetic differences. The approach relies on the assumptions underlying the conventional heritability of liability model. We also suggest a model unrelated to heritability estimates. By applying these strategies, we describe the distribution of absolute genetic risk for 15 common cancers. We highlight the considerable inequality in genetic risk of cancer using different metrics, e.g., the Gini Index and quantile ratios which are frequently used in economics. For all these cancers, the estimated inequality in genetic risk is larger than the inequality in income in the USA.
The spatial distribution of income shapes the structure and organisation of cities and its understanding has broad societal implications. Despite an abundant literature, many issues remain unclear. In particular, all definitions of segregation are implicitely tied to a single indicator, usually rely on an ambiguous definition of income classes, without any consensus on how to define neighbourhoods and to deal with the polycentric organization of large cities. In this paper, we address all these questions within a unique conceptual framework. We avoid the challenge of providing a direct definition of segregation and instead start from a definition of what segregation is not. This naturally leads to the measure of representation that is able to identify locations where categories are over- or underrepresented. From there, we provide a new measure of exposure that discriminates between situations where categories co-locate or repel one another. We then use this feature to provide an unambiguous, parameter-free method to find meaningful breaks in the income distribution, thus defining classes. Applied to the 2014 American Community Survey, we find 3 emerging classes-low, middle and higher income-out of the original 16 income categories. The higher-income households are proportionally more present in larger cities, while lower-income households are not, invalidating the idea of an increased social polarisation. Finally, using the density-and not the distance to a center which is meaningless in polycentric cities-we find that the richer class is overrepresented in high density zones, especially for larger cities. This suggests that density is a relevant factor for understanding the income structure of cities and might explain some of the differences observed between US and European cities.
The publication of The Spirit Level (Wilkinson and Pickett, 2009) marked a paramount moment in the analysis of health and inequality, quickly attracting a remarkable degree of attention, both positive and negative, both in academic and in public discourse. Following at least 20 years of research, the book proposes a simple and powerful argument: inequality per se, more specifically income inequality, is harmful to every aspect of social life. In order to confirm this idea, the authors present a series of bivariate, cross-sectional associations showing comparisons across countries and within the United States. Despite the methodological limitations of this approach, the authors advance causal claims concerning the detrimental effects of income inequality. They also rule out poverty as a plausible alternative explanation, without directly measuring it. Meanwhile, over the last decade stratification scholars have demonstrated the nonlinear effect of economic factors, especially income, on health. The results suggest that a relative approach is best for analyzing dynamics at the top of the income distribution, whereas an absolute approach seems most appropriate for studying the bottom of the distribution. Consistent with this perspective, here I reanalyze data from The Spirit Level, adding a measure of poverty, in order to control the effect of inequality and explore its interaction with poverty. The findings show that inequality and poverty-which I contend are two interdependent but nonetheless distinct phenomena-interact across countries, such that the detrimental effects of inequality are present or stronger in countries with high poverty, and absent or weaker in countries with low poverty; poverty replaces inequality as the favored explanation of health and social ills across states. The new evidence suggests that income distributions are characterized by a complex interplay between inequality and poverty, whose interaction deserves further analysis.