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This chapter describes the different ways of measuring how good a scoring system is. It clarifies that there are three different ways of measuring the systems: their ability to discriminate Goods from Bads, their prediction of the probability of a borrower defaulting, and the accuracy of their categorical calibration. Discrimination, which only requires knowledge of the scorecard itself, is measured using ROC curves, Cumulative Accuracy Profiles (CAP), Gini Coefficient, AUROC, Divergence, Mahalonobis distance, and Somers D-concordance statistic. Probability predictions, which need the population odds as well as the scorecard, are measured using the binomial and normal tests and the Hosmer-Lemeshow test. Categorical calibration, which needs the cut-off score as well as the scorecard, is measured using confusion matrix, swap sets, specificity and sensitivity, and Type I and Type II errors. The chapter also explains how, if one has built a suite of scorecards each on a different segment of the population, one can combine the measures of the different scorecards into an overall measure.

Formulas for computing the most commonly used summary measure of income distribution are given. These include the mean, median, and mode. The methodology for computing shares of total income obtained by quantiles of income recipients, and the technique to graph the Lorenz curve and compute the Gini coefficient are described.

This chapter presents national estimates of incomes and inequality for 2007 and 2013. It begins with discussion of the CHIP datasets and measurement issues. It then reports core estimates of income and inequality, which indicate a modest decline in inequality during this period. Estimates are reported separately for formal urban residents, rural residents, and rural-to-urban migrants, with discussion of the effects of migration on inequality. Incomes and inequality are decomposed among the different sources of income; the urban/rural and regional income gaps are investigated. Alternative estimates of national inequality—using different income definitions, inequality indexes, and prices—are reported, as well as estimates that adjust for the underrepresentation of incomes in the top tail of the income distribution. The estimated decline in national inequality survives some but not all of these alternative calculations and thus raises questions about the magnitude and long-term sustainability of the inequality decline.

This chapter examines a variety of theories that attempt to explain intergenerational and sibling correlations and have been developed in several disciplines, including economics, psychology, sociology, and behavioral genetics. More specifically, it addresses the relationship between intergenerational and intragenerational inequality, the dynamics of which are summarized by the relationship between “beta convergence”—related to the concept of absolute mobility—and “sigma convergence”—related to the concept of horizontal inequality. It analyzes the link between horizontal and vertical inequality in terms of the relationship between conditional and unconditional inequality. It also considers the ways in which inequality or diversity may be measured, such as standard deviation and the Gini coefficient.

Deals with the effects of income taxes on income distribution. It is widely believed that the individual income tax, with progressive tax rates, can reduce the inequality of income distribution or at least slowdown its growth. An attempt is made to correlate information about the redistribution effects of income taxes with the distribution of income.

This chapter provides estimates of income inequality, income mobility, and wealth inequality for Japan. Income and consumption inequalities that are measured by the Gini coefficient, and estimated using data from the Keio Household Panel Survey (KHPS), suggest that there was little change in income inequality in Japan during the period 2004–2008. Compared to earlier estimates of short-run transition probabilities for the 1990s and 2000–2001, the probability of a household staying in the same income quintile group was much higher in 2004–2005 and 2007–2008. Finally, using data from the KHPS and the Japan Household Panel Survey (JHPS), Japan's asset holdings were compared to those in other high-income countries. The proportion of Japanese households reporting that they own some type of financial asset, about 80 percent, is similar to that reported in most countries included in the Luxembourg Wealth Study Database.

This chapter describes a new method of facilitating inequality and poverty analysis of grouped distributional data by allowing individual income observations to be reconstructed from any feasible grouping pattern. In contrast to earlier methods, the chapter's procedure ensures that the characteristics of the synthetic sample exactly match the reported values. The performance of the algorithm is evaluated first by using household survey records to compare true income observations with their synthetic counterparts, then by comparing the true and generated values of the Gini coefficient and other inequality indices. The results indicate that the new technique is capable of reproducing individual data from grouped statistics with a high degree of accuracy.

This chapter covers a period of rising wealth followed by abrupt decline. Between 1983 and 2007, real median household wealth rose by 70 percent, from $80,000 to $136,000 (in 2013 dollars). This increase disappeared completely, however, in the Great Recession; by 2010, median wealth had dropped by 40 percent, to $82,000, and it did not improve by 2013. The typical household of 2013 was no wealthier than the typical household of 1983. In addition, the distribution became markedly more unequal during the Great Recession; the richest 10 percent experienced a smaller reduction of 10 percent. For families in the middle, the most important asset was their home, but in 2013, fewer of them were homeowners and home values dropped for those who were. The declines in home ownership and home values accounted for most of the loss in wealth for middle-wealth families as a group.

This chapter examines the use of statistics in assessing the relationship between phenotypes and genotypes. It proposes a simple data-generating process in which the phenotype of children depends on their genotype and the phenotype of their parents. The autoregressive coefficient is Francis Galton’s “beta” that expresses the causal effect of parents on their children’s outcome. Heredity is modeled by assuming that a child’s genotype is dependent on his/her parents’ genotypes and on a random draw from the gene pool. The data-generating process consists of two related first-order autoregressive processes referred to as the AR (2) model, which becomes an AR (3) model if the environments of children are correlated with their parents’ environments (in terms of religion, culture, geography, professions, etc.). The AR (2) and AR (3) models are used to solve for the transmission of inequality between generations. The chapter concludes with a discussion of other metrics for measuring inequality, including the Gini coefficient.

This chapter provides estimates of income inequality, income mobility, and wealth inequality for Japan. Income and consumption inequalities that are measured by the Gini coefficient, and estimated using data from the Keio Household Panel Survey (KHPS), suggest that there was little change in income inequality in Japan during the period 2004–2008. Compared to earlier estimates of short-run transition probabilities for the 1990s and 2000–2001, the probability of a household staying in the same income quintile group was much higher in 2004-2005 and 2007–2008. Finally, using data from the KHPS and the Japan Household Panel Survey (JHPS), Japan's asset holdings were compared to those in other high-income countries. The proportion of Japanese households reporting that they own some type of financial asset, about 80 percent, is similar to that reported in most countries included in the Luxembourg Wealth Study Database.

This chapter examines long-term changes in rural household incomes, inequality, and poverty in China from the late 1980s to 2013, with a focus on changes in public policy and the structure of rural incomes from 2007 to 2013. Implementation of pro-rural (huinong) policies during the first decade of the 2000s marked a historic shift in public policy, which previously was heavily biased toward the urban areas. Rural income growth accelerated between 2007 and 2013 mainly because of an upsurge of wage earnings, asset income, and imputed rent from owner-occupied housing. The share of agricultural income in total income fell to a historic low. These shifts contributed to the increase in rural income inequality from 2007 to 2013. During this period rural poverty continued to decline. The implementation of pro-rural public policies after 2000 led to small but significant improvements in the redistributive impact of public transfers.

This chapter explores the relationship between measures of inequality based on industrial pay and those based on surveys of income and expenditure. This is important for the economist to construct a simple statistical model with a formula for translating one set of measures into the other. In this way, the economists will arrive at a consistent global dataset of estimated measures of income inequality for households, calibrated to the standard and familiar format of the Gini coefficient. The Gini coefficient is a measure of equality: a measure of zero reflects absolute equality while a measure of one means everything is concentrated in a single individual. Further studies would allow possible assessment of existing global inequality measures, their dispersion across countries, and their movement through time.

The chapter discusses the concept, statistical measurement, and determinants of income distribution and wealth distribution, highlighting that both dimensions of inequality may share some common determining features, even though the factors causing them are not necessarily the same. It reviews the role played in income distribution by the property of productive wealth in conditioning the role and position of individuals in the productive process, the role of wage-setting institutions, the degree of competition in goods markets, the impact of technical change, education, globalization, and macroeconomic crises in shaping distributive results. The chapter also examines the role of allocation of property rights, the differential savings capacities of different groups, the impact of interest rates and other factors in affecting wealth distribution. It illustrates the topics with data and examples for advanced capitalist countries, emerging economies and developing nations. The chapter touches on the role of government policies in a democratic society and closes with a discussion of the effects of inequality on economic growth and the effectiveness of democracy when permeated with the financial power of economic oligarchies.

The contribution of recent immigrants to income dispersion has grown slightly. This reflects the fact that their numbers have been rising over time and that they tend to have a higher proportion of lower-productivity individuals. Immigration policy is of course another form of human capital investment policy. In a free society, the decision to emigrate is an individual right over which government should not exercise control. But in Hong Kong, government policy decides who is allowed to emigrate here. Family reunion cases are also related to human rights, although what constitutes family is subject to policy delineation. To sum up, then, the increase in individual income dispersion is primarily affected by education. Other factors contribute, too, but none is as significant. Education policy must therefore be at the center of efforts to tackle the rising inequality in individual incomes. This sets up the analysis understand what underlies the rise of household income dispersion over this period.

This chapter evaluates the impact of the tax-benefit system on inequality and poverty in Brazil. The impact of direct taxes and government transfers has been derived using the Lorenz curve. The authors have used BRAHMS, a tax-benefit microsimulation model that generates detailed information on taxes and benefits paid and received by households in a representative sample of the Brazilian population. Social benefits, based on contributory social insurance benefits, include pensions, contributory benefits for private sector workers, noncontributory means-tested benefits, and personal/corporate income taxes and social contributions. In Brazil, the problem of poverty and inequality is not caused simply by low tax burdens but mainly by the distribution of taxes and benefits.

This chapter examines the major trends in Chinese household incomes and inequality from 2007 to 2013 and highlights key, cross-cutting findings from the book as a whole. It begins with an overview of economic and policy developments during the period and of data and measurement issues. It reports the central estimates of China’s national income inequality, with comparisons to other studies. The chapter then discusses six cross-cutting findings from the book: 1.) after 2007 national income inequality declined, a marked change from past trends; 2.) the urban/rural income gap declined, also a change from past trends; 3.) income gaps between the East, West, and Central regions were no longer a substantial source of inequality; 4.) household wealth grew markedly and unequally; 5.) the number of Chinese households with incomes comparable to middle-class households in the developed world grew rapidly; and 6.) absolute poverty in China continued to decline and by 2013 it was quite low.