Interpolating the Lorenz Curve: Methods to Preserve Shape and Remain Consistent with the Concentration Curves for Components

C¹‐class interpolation methods that preserve monotonicity and convexity and are thus suitable for the estimation of the Lorenz curve from grouped data are not widely known. Instead, parametric models are usually applied for such estimation. Parametric models, however, have difficulty in accurately approximating every part of income/expenditure distributions. This paper proposes two types of C¹‐class shape‐preserving interpolation methods. One is a piecewise rational polynomial interpolation (proposed independently by Stineman and Delbourgo) that enables consistent interpolation of the concentration curves for income/expenditure components, attaining approximately the same accuracy as that of the existing methods when applied to decile‐grouped data or to more detailed aggregation. Another is a Hybrid interpolation that employs pieces of curves derived from parametric models on end intervals. Empirical comparisons show that the Hybrid interpolation (with the assistance of parametric models for class‐boundary estimation) outperforms the existing methods even when applied to quintile‐grouped data without class boundaries.     

On the Measurement of the Overall Degree of Income Stratification between Groups

This paper proposes a new class of indices that measure overall stratification between groups in a population and can be decomposed as population‐weighted averages of pairwise indices. The indices capture not only the extent to which groups form well‐defined strata in the income distribution but also the scale of the resultant differences in equally distributed equivalent incomes between them, where these two factors play the same role as identification and alienation respectively in the measurement of polarization. The properties of the class as a whole are investigated as well as those of selected members of it: zeroth and first power indices may be interpreted as measuring the overall incidence and depth of stratification respectively, while second and higher power indices members are directly sensitive to the severity of stratification between groups. An illustrative application provides an empirical analysis of global income stratification by regions in 1993.     

Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind

There are three reasons why estimation of parametric income distributions may be useful when empirical data and estimators are available: to stabilize estimation; to gain insight into the relationships between the characteristics of the theoretical distribution and a set of indicators, e.g. by sensitivity plots; and to deduce the whole distribution from known empirical indicators, when the raw data are not available. The European Union Statistics on Income and Living Conditions (EU‐SILC) survey is used to address these issues. In order to model the income distribution, we consider the generalized beta distribution of the second kind (GB2). A pseudo‐likelihood approach for fitting the distribution is considered, which takes into account the design features of the EU‐SILC survey. An ad‐hoc procedure for robustification of the sampling weights, which improves estimation, is presented. This method is compared to a non‐linear fit from the indicators. Variance estimation within a complex survey setting of the maximum pseudo‐likelihood estimates is done by linearization (a sandwich variance estimator), and a simplified formula for the sandwich variance, which accounts for clustering, is given. Performance of the fit and estimated indicators is evaluated graphically and numerically.     

Inequality of Income and Consumption in the U.S.: Measuring the Trends in Inequality from 1984 to 2011 for the Same Individuals

This paper examines the distribution of income and consumption in the U.S. using one dataset that obtains measures of both income and consumption from the same set of individuals. We develop a set of inequality measures that show the increase in inequality during the past 27 years using the 1984–2011 Consumer Expenditure Survey. We find that the trends in income and consumption inequality are similar between 1984 and 2006, and diverge during and after the Great Recession. For the entire 27‐year period we find that consumption inequality increases almost as much as does income inequality.     

Understanding Rising Income Inequality in Germany, 1999/2000–2005/2006

We examine the factors behind rising income inequality in Europe's most populous economy. From 1999/2000 to 2005/2006, Germany experienced an unprecedented rise in net equivalized income inequality and poverty. At the same time, unemployment rose to record levels, part‐time and marginal part‐time work grew, and there was evidence for a widening distribution of labor incomes. Other factors that possibly contributed to the rise in income inequality were changes in the tax and transfer system, changes in the household structure (in particular the rising share of single parent households), and changes in other socio‐economic characteristics (e.g., age or education). We address the question of which factors were the main drivers of the observed inequality increase. Our results suggest that the largest part of the increase was due to increasing inequality in labor incomes, but that changes in employment outcomes and changes in the tax system also contributed considerable shares. By contrast, changes in household structures and household characteristics, as well as changes in the transfer system only seem to have played a minor role.     

我国城镇居民收入分配差距的实证研究

笔者首先计算了几种度量收入分配差距的指标,从不同角度的分析得到了我国城镇居民收入分配差距不断扩大的结论;其次估计了我国城镇居民的基尼系数.通过计量经济模型,检验了高、中、低各阶层可支配收入与收入分配差距之间的关系,得出结论:增加中低收入阶层的可支配收入,遏制高收入阶层可支配收入,可以减小基尼系数,从而降低收入分配差距;进一步通过模型发现,我国发达地区的经济发展和收入分配差距呈现出倒U型规律,说明经济发展达到一定水平,收入分配差距有望缩小.     

Income inequality and income bias in voter turnout

In the era of growing income inequality around the world, it remains inconclusive how higher income inequality affects income bias in turnout (i.e., high-income citizens vote more likely than low-income citizens). Using large-scale cross-national survey data, we show that (1) strong income bias in turnout exists in many parts of the world, (2) higher income inequality is related to lower income bias in turnout by demobilizing high-income citizens and mobilizing low-income citizens, and (3) this relationship is partly explained by the pattern that vote buying is more common in societies with higher income inequality and thus mobilizes low-income citizens but decreases political efficacy among high-income citizens. Ultimately, this study suggests that growing income inequality may not exaggerate political inequality, but may challenge the legitimacy of democratic elections.     

Accounting for United States Household Income Inequality Trends: The Changing Importance of Household Structure and Male and Female Labor Earnings Inequality

Using a shift‐share analysis on March CPS data, this paper estimates the degree to which changes in labor earnings, employment, and marriage patterns account for household income inequality growth in the United States since 1979. The factors contributing to the rapid rise in income inequality in the 1980s differ substantially from those contributing to its slower increase since that time. Unlike findings for the 1980s when changes in the correlation of spouses' earnings accounted for income inequality growth, this factor is no longer a major contributor toward its continued increase. Additionally, the 2000s business cycle is the first full business cycle in at least 30 years where changes in earnings of male household heads accounted for declines in income inequality. Instead, the continued growth in income inequality in the 2000s was accounted for primarily by increases in female earnings inequality and declines in both male and female employment.     

Income comparison and happiness: The role of fair income distribution

Relative income gap is one of the most popular approaches for explaining the income–happiness relationship. We argue in this article that when people compare their incomes, they care about distributional fairness more than relative income disparity. It is difficult for us to explain China's income–happiness paradox if we simply compare the income gap and do not explore the income‐generation process leading to income inequality. We therefore employ an approach based on a responsibility‐sensitive theory of justice that decomposes individual income into fair and unfair components. As a proxy for distributional unfairness, unfair income is considered the main source of unhappiness. Using data from the Chinese Household Income Project survey, we find strong support for the negative relationship between income unfairness and happiness. We also find a significantly positive relationship between the relative income gap and income unfairness, which leads us to consider the income comparison hypothesis as the explanation for the income–happiness paradox in a new light. Sensitivity analyses confirm the robustness of our results.     

The Long‐Run History of Income Inequality in Denmark

We use historical publications and micro data from tax returns to construct internationally comparable estimates of the development in income inequality in Denmark over the last 140 years. The study shows that income inequality and top income shares have declined during several distinct phases in between periods of stability. Furthermore, the quality of the Danish data allows us to analyse not only the development in top income shares but also broader inequality measures such as the Gini coefficient. These analyses show that top income shares are a good proxy for the underlying development in inequality.     

Income inequality in China: causes and policy responses

The phenomenal economic growth in China has been accompanied by a rapid increase in income inequality. This paper reviews the historical trends and patterns of income inequality in China, discusses the potential causes underlying rising income inequality, and applies the functional distribution of income approach in understanding China’s income inequality. This analytical approach highlights how rising return to capital relative to wage incomes can be an important source for increasing income inequality in China. The paper provides the evidence which shows that the rapid economic growth in China has been relying on a model that pays high returns to various kinds of capital including financial capital and real estate, while the ownership of capital is very unequal. This finding prompts us to rethink about the causes of China’s income inequality and to formulate appropriate policies based on the new way of understanding this pressing issue of income distribution in China.     

Mobility of Top Incomes in Germany

I analyze German top income mobility using micro‐level panel data of personal income tax returns which are highly representative for top income taxpayers for the years 2001–06. Top income mobility is assessed in three dimensions: (i) persistence in top income fractiles and its stability over time, (ii) measures of individual mobility that are not dependent on the fractile size: the degree of mobility between equally sized groups and mobility in ranks, and (iii) mobility's impact on top income shares. Persistence in top income fractiles is comparatively high and fairly stable across the analyzed period. Top income recipients are less prone to downward mobility and see less variation in annual ranks than less rich tax units. Mobility's impact on income concentration is moderate. The top percentile's share is reduced by roughly 5 percent over six years.     

Inadequate Bivariate Measures of Health Inequality: The Impact of Income Distribution*

Bivariate measures of health inequality are influenced by changes in two variables: health and a socioeconomic variable, such as income. For these measures, what is reported as an increase in health inequality might just as well be a reduction in income inequality. In particular, several papers have found that socioeconomic health inequalities in Nordic countries are no less than in other European countries. The correct interpretation could just be that income inequality is no higher in Nordic countries than in the rest of Europe. The problem is especially profound when the causality is running from health to income.     

Inflation and the Income Share of the Rich: Evidence for 14 OECD Countries

This paper examines the distributional implications of inflation on top income shares in 14 advanced economies using data over the period 1920–2016. We use local projections to analyze how top income shares respond to an inflation shock, and panel regressions in which all variables are defined as 5-year averages to examine the impact of inflation on the position of the top-one-percent in the long run. Our findings suggest that inflation reduces the share of national income held by the top 1 percent. Furthermore, we find that inflation shocks and long-run inflation have similar effects on top income shares.     

On the World Distribution of Income

In this paper we demonstrate that the size distribution of the world income may be reasonably approximated by a log‐normal distribution rather then by a power law, as has previously been believed. This result has been shown to be quite persistent as we move from 1985 to 2011.     

The Sins of the Fathers: Intergenerational Income Mobility in China

This paper aims to obtain an accurate estimate of China's intergenerational income mobility and to present evidence on its distributional pattern. Using panel data from the China Health and Nutrition Survey (CHNS) over the period 1989–2009, I find that China is less mobile than most developed countries. Then, I employ five different approaches to investigate the distributional pattern of China's intergenerational mobility across income levels. The results suggest that poor families have relatively high mobility, indicating opportunities for the poor children to escape poverty. Finally, I show that while wealthy fathers are likely to pass on their favorable economic status to their sons, rich sons come from a very wide range of family economic backgrounds.     

Income Distribution,Econophysics and Piketty

Piketty, Atkinson and Saez have put the analysis of income distribution back on center stage. The distinction between property income and labor income plays a central role in this framework. Property income derives from the rate of return on stocks of income-earning wealth and is more unequally distributed than labor income. Piketty argues that, because the rate of return (r) is generally greater than the rate of growth of the economy (g), property income tends to grow more rapidly than labor income, so that rising income inequality is an intrinsic tendency of capitalism despite interruptions due to world wars and great depressions. This article argues the exact opposite. The rise of unions and the welfare state were the fruits of long-term historical gains made by labor, and the postwar constraints on real and financial capital arose in sensible reaction to the Great Depression. The ‘neoliberal’ era beginning in the 1980s significantly rolled back all of these. The article uses the econophysics two-class argument of Yakovenko to show that we can explain the empirical degree of inequality using two factors alone: the profit share and the degree of financialization of income. The rise of inequality in the neoliberal era then derives from a reduction in the wage share (rise in the profit share) in the face of assaults on labor and the welfare state, and a sharp increase in the financialization of incomes as financial controls are weakened. These are inherently socio-political outcomes, and what was lost can be regained. Hence, there is no inevitable return to Piketty’s ‘patrimonial capitalism’.     

Evaluating Patterns of Income Growth when Status Matters: A Robust Approach

This paper addresses the problem of ranking growth episodes from a microeconomic perspective. While most of the existing criteria, framed in the pro‐poor growth tradition, are either based on anonymous individuals or are used to identify them on the basis of their status in the initial period, this paper proposes new criteria to evaluate growth, which are robust to the choice of the reference period used to identify individuals. Suitable dominance conditions that can be used to rank alternative growth processes are derived by means of an axiomatic approach. Moreover, the theoretical results are used to rank the different growth episodes that have taken place in the past decade in Australia, Germany, Korea, Switzerland, and the U.S.     

经济增长与收入分配相关性研究重点转移带来的政策启示

从有关经济增长与收入分配相关性的研究内容入手,分析经济增长和收入分配研究从功能性分配向规模化分配的理论转变过程,提出了针对此种演变带给我们的政策启示:在经济增长过程中,应同时关注收入差距问题。