Tail Of Income Distribution Research Articles

Inequality of Opportunity and the Probability of Being Very Rich or Very Poor

This paper models the effects of individuals' background variables on the chances they end up in the extremes of the income distribution. Taking high‐quality Australian panel data, we show that factors like the education of one's father have a much stronger impact on belonging to the top 1 per cent than they have on the conditional mean. Similarly, individuals from immigrant families are more likely to belong to both the left and the right tails of income distribution. Identifying the drivers of extreme incomes is important as individuals with very high incomes exert disproportionate political power, while those with very low incomes may drive prejudice and perceptions of disadvantage.

A simple method for measuring inequality

To simultaneously overcome the limitation of the Gini index in that it is less sensitive to inequality at the tails of income distribution and the limitation of the inter-decile ratios that ignore inequality in the middle of income distribution, an inequality index is introduced. It comprises three indicators, namely, the Gini index, the income share held by the top 10%, and the income share held by the bottom 10%. The data from the World Bank database and the Organization for Economic Co-operation and Development Income Distribution Database between 2005 and 2015 are used to demonstrate how the inequality index works. The results show that it can distinguish income inequality among countries that share the same Gini index but have different income gaps between the top 10% and the bottom 10%. It could also distinguish income inequality among countries that have the same ratio of income share held by the top 10% to income share held by the bottom 10% but differ in the values of the Gini index. In addition, the inequality index could capture the dynamics where the Gini index of a country is stable over time but the ratio of income share of the top 10% to income share of the bottom 10% is increasing. Furthermore, the inequality index could be applied to other scientific disciplines as a measure of statistical heterogeneity and for size distributions of any non-negative quantities.

Inferential results for a new measure of inequality

Summary In recent decades, substantial changes have been observed in the left and right tails of income distributions in countries like the USA, Germany, the UK, and France. These changes are a major concern for policy makers. Here, we derive inferential results for a new inequality index that is specifically designed for capturing such significant shifts. We propose two empirical estimators for the index and show that they are asymptotically equivalent. Afterward, we adopt one estimator and prove its consistency and asymptotic normality. Finally, we introduce an empirical estimator for its variance and provide conditions for its consistency. An analysis of real data from the Bank of Italy Survey of Income and Wealth is also presented on the basis of the obtained inferential results.

Envy, inequality and fertility

This study seeks to examine the consequences of “keeping up with the Joneses” on household fertility outcomes. “Envy” is introduced in a simple “quality-quantity” trade-off type of fertility model, where the trade-off is induced by the fact that being out of the labor market due to child-bearing is more expensive for people with higher human capital levels. The effect of introducing upward-looking “envy” in the model is that households, notably low-income ones, reduce fertility in an attempt to emulate consumption levels of their high-income neighbors. This effect is stronger the larger the reference consumption—that is, in areas with higher income inequality, which are characterized by longer right tails of income distributions. It follows that if households indeed tend to “keep up with the Joneses,” one should expect lower fertility rates in areas with higher income inequality compared to more equal areas. The empirical analysis using the American Community Survey confirms that indeed, households residing in more unequal metropolitan areas tend to have fewer children than households residing in more equal metropolitan areas.

Optimal threshold for Pareto tail modelling in the presence of outliers

The Pareto distribution is widely applied in many areas of studies such as economics and sciences. An important issues related to Pareto tail modelling is to determine the optimal threshold of the Pareto distribution. One of the methods used for determining the optimal threshold of Pareto distribution is by choosing the threshold that minimizes the goodness-of-fit statistics found based on empirical distribution function (EDF). This study involves determination of the shape parameter of the Pareto distribution using the maximum likelihood method and robust method based on the probability integral transform statistics. In addition, given the particular estimates of the shape parameter, comparison of the performance of several EDF statistics, namely, Kolmogorov–Smirnov, Kuiper, Anderson–Darling, Cramer–von Misses and Watson statistics in determining the optimal threshold in the presence of outliers is studied based on Monte Carlo simulation. Since the EDF statistics are found smallest for Kolmogorov–Smirnov or Kuiper statistics, these two EDF statistics outperformed other EDF statistics considered. The findings are illustrated using a sample of household income data of the Malaysian population. The optimal threshold found can be used to classify the high income earners in Malaysia since Pareto distribution is one of the most frequently used model to describe the upper tail of income distribution.

Heavy tails and upper-tail inequality: The case of Russia

Motivated, in part, by the recent surge of interest in robust inequality measurement, cross-country inequality comparisons, applications of heavy-tailed distributions and the study of global and upper-tail inequality, this paper focuses on robust analysis of heavy-tailedness properties and inequality in the upper tails of income distribution in Russia, as measured, mainly, by its tail indices. The study is based on recently developed approaches to robust inference on the degree of heavy-tailedness and their implications for the analysis of upper-tail inequality discussed in the paper. Among other results, the paper provides robust estimates of heavy-tailedness parameters and tail indices for Russian income distribution and their comparisons with the benchmark values in developed economies reported in the previous literature. The estimates point out to important similarity between heavy-tailedness properties of income distribution and their implications for the analysis of upper-tail income inequality in Russia and those in developed markets.