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To compare income and wealth distributions and to assess the effects of policy that affect those distributions require reliable inequality‐measurement tools. However, commonly used inequality measures such as the Gini coefficient have an apparently counter‐intuitive property: income growth among the rich may actually reduce measured inequality. We show that there are just two inequality measures that both avoid this anomalous behavior and satisfy the principle of transfers. We further show that the recent increases in US income inequality are understated by the conventional Gini coefficient and explain why a simple alternative inequality measure should be preferred in practice. [ABSTRACT FROM AUTHOR]

In this paper, we examine trends in inequality of Chinese rural household income from 1989 through 2015 using log power function lognormal composite distribution. Six inequality measures, Gini coefficient, Generalized entropy index, Theil's entropy index, Atkinson index, Bonferroni index, and Zenga index, were computed by numerical methods. The results show that the all the inequality measures exhibit a similar pattern, and a steadily increased tendency through a slight slowdown for some in the time period of our analysis. [ABSTRACT FROM AUTHOR]

Evidence from micro-data shows that capital incomes are exceedingly volatile, which makes up a disproportionately high contribution to the overall inequality in populations with the heavy-tailed nature on the income distributions for many countries. The quintile share ratio (QSR) is a recently introduced measure of income inequality, also forming part of the European Laeken indicators and which cover four important dimensions of social inclusion (health, education, employment and financial poverty). In 2001, the European Council decided that income inequality in the European Union member states should be described using a number of indicators including the QSR. Non-parametric estimation has been developed on the QSR index for heavy-tailed capital incomes distributions. However, this method of estimation does not give satisfactory statistical performances, since it suffers badly from under coverage, and so we cannot rely on the non-parametric estimator. Hence, we need another estimator in the case of heavy-tailed populations. This is the reason why we introduce, in this paper, a class of semi-parametric estimators of the QSR index of economic inequality for heavy-tailed income distributions. Our methodology is based on the extreme value theory, which offers adequate statistical results for such distributions. We establish their asymptotic distribution, and through a simulation study, we illustrate their behavior in terms of the absolute bias and the median squared error. The simulation results clearly show that our estimators work well. [ABSTRACT FROM AUTHOR]

A two-parameter unit distribution and its regression model plus its extension to 0 and 1 inflation is introduced and studied. The distribution is called the unit upper truncated Weibull (UUTW) distribution, while the inflated variant is called the 0−1 inflated unit upper truncated Weibull (ZOIUUTW) distribution. The UUTW distribution has an increasing and a J-shaped hazard rate function. The parameters of the proposed models are estimated by the method of maximum likelihood estimation. For the UUTW distribution, two practical examples involving household expenditure and maximum flood level data are used to show its flexibility and the proposed distribution demonstrates better fit tendencies than some of the competing unit distributions. Application of the proposed regression model demonstrates adequate capability in describing the real data set with better modeling proficiency than the existing competing models. Then, for the ZOIUUTW distribution, the CD34+ data involving cancer patients are analyzed to show the flexibility of the model in characterizing inflation at both endpoints of the unit interval.

The aim of this paper is to classify the post-transition OECD countries according to the Gini coefficient for income inequality, the S80/S20 ratio, the income share of the bottom 40% of the population, educational attainment – tertiary education, and labor force participation rate using factor and cluster analyses. Factor analysis resulted in two extracted factors, and factor scores were calculated. Hierarchical and non-hierarchical cluster analysis was performed on factor scores to classify eight posttransition OECD countries and three candidate countries. The research question of this paper is to investigate whether there are similarities/differences between existing members and candidates for membership in the OECD, among the selected post-transition countries of Europe, in the context of income inequality. Based on the dendrogram obtained by the hierarchical Ward’s method, a three cluster solution was selected. The non-hierarchical k-means method for the three-cluster solution clustered Croatia with Bulgaria and Romania. These three countries are OECD candidate countries. Our findings confirm that the three candidate countries remain behind because of historical reasons and the non-implementation of structural reforms.

Addressing inequality is recognized a worldwide development objective. The literature has primarily focused on examining economic or social inequality, but rarely on environmental inequality. Centering the discussion on economic or social factors does not provide a holistic view of inequality because it is multidimensional and several facets may overlap imposing a disproportionate burden on vulnerable communities. This study investigates the magnitude of air quality inequality in conjunction with economic and social inequalities in Bogotá (Colombia). It explores where inequalities overlap and assesses alleviation measures by tackling air pollution. We develop a composite index to estimate performance in socioeconomic and air quality characteristics across the city and evaluate inequality with a variety of measures. Using an atmospheric chemical transport model, we simulate the impact of three air pollution abatement policies: paving roads, industry fuel substitution, and diesel-vehicle renewal on fine particle concentrations, and compute their effect on inequality. Results show that allocation of air quality across Bogotá is highly unequal, exceeding economic or social inequality. Evidence also indicates that economic, social and air quality disparities intersect, displaying the southwest as the most vulnerable zone. Paving roads is found to be the most progressive and cost-effective policy, reducing overall inequality between 11 and 46 percent with net benefits exceeding US$1.4 billion. [ABSTRACT FROM AUTHOR]

This article proposes three new decompositions of inequality measures, drawn from the framework of cooperative game theory. It allows the impact of players' interactions, rather than players' contributions to inequality, to be taken into consideration. These innovative approaches are especially suited for the study of income inequality when the income has a hierarchical structure: the income is composed of several primary sources, with the particularity that each of them is also composed of secondary sources. We revisit the Shapley–Owen value that quantifies the importance of each of these secondary sources in the overall income inequality. Our main contribution is to decompose this importance into two parts: the pure marginal contribution of the considered source and a weighted sum of pairwise interactions. We then provide an axiomatic characterization of each additive interaction decomposable (AID) coalitional value considered in this paper. We give an application of these decompositions in the context of inequality theory. [ABSTRACT FROM AUTHOR]

Inequality indices are quantitative scores that take values in the unit interval, with a zero score denoting complete equality. They were originally created to measure the heterogeneity of wealth metrics. In this study, we focus on a new inequality index based on the Fourier transform that demonstrates a number of intriguing characteristics and shows great potential for applications. By extension, it is demonstrated that other inequality measures, such as the Gini and Pietra indices, can be usefully stated in terms of the Fourier transform, allowing us to illuminate characteristics in a novel and straightforward manner. [ABSTRACT FROM AUTHOR]

Abstract Background An analysis of the regional distribution of health resources is one of the tools for evaluating equal geographic access to health care. The usual analytical approach to an assessment of regional differences is to evaluate each health resource separately. This is a sensible approach, because there may be systematic reasons for any differences, for example, higher salaries in urban areas. However, a separate evaluation of the regional distribution of health resource capacities may be misleading. We should evaluate all health resource capacities as a whole and consider the substitutability of resources. Objective This study aims to measure regional inequalities in the Czech Republic with the help of alternative approaches to the evaluation of regional inequalities in the case of several substitutable health resources. Methods Five alternative evaluation methods (models) are described and applied: the separate evaluation, expert model, market model, common weights model, and production frontier model. Results The regional distribution of physicians and nurses in the Czech Republic in 2017 was evaluated. In spite of many regulations at the national and regional levels, we have found inequalities in regional resource distribution. The models that consider all health resources and the possibility of a resource substitution show lower inequalities between regional health resource capacities. Conclusion Both researchers and policy-makers should always consider the possibility of resource substitutions in the assessment of regional inequalities.

Bayesian estimators and highest posterior density credible intervals are obtained for two popular inequality measures, viz. the Gini index and the Bonferroni index in the case of the Dagum distribution. The study considers informative and non-informative priors, i.e. the Mukherjee-Islam prior and the extension of Jeffrey's prior, respectively, under the presumption of the Linear Exponential (LINEX) loss function. A Monte Carlo simulation study is carried out in order to obtain the relative efficiency of both the Gini and Bonferroni indices while taking into consideration different priors and loss functions. The estimated loss proves lower when using the Mukherjee-Islam prior in comparison to the extension of Jeffrey's prior and the LINEX loss function outperforms the squared error loss function (SELF) in terms of the estimated loss. Highest posterior density credible intervals are also obtained for both these measures. The study used real-life data sets for illustration purposes. [ABSTRACT FROM AUTHOR]

We propose a new four-parameter lifetime model with flexible hazard rate called the Burr XII Power Cauchy (BXII-PC) distribution. We derive the BXII-PC distribution via (ⅰ) the T-X family technique and (ⅱ) nexus between the exponential and gamma variables. The new proposed distribution is flexible as it has famous sub-models such as Burr XII-half Cauchy, Lomax-power Cauchy, Lomax-half Cauchy, Log-logistic-power Cauchy, log-logistic-half Cauchy. The failure rate function for the BXII-PC distribution is flexible as it can accommodate various shapes such as the modified bathtub, inverted bathtub, increasing, decreasing; increasing-decreasing and decreasing-increasing-decreasing. Its density function can take shapes such as exponential, J, reverse-J, left-skewed, right-skewed and symmetrical. To illustrate the importance of the BXII-PC distribution, we establish various mathematical properties such as random number generator, moments, inequality measures, reliability measures and characterization. Six estimation methods are used to estimate the unknown parameters of the proposed distribution. We perform a simulation study on the basis of the graphical results to demonstrate the performance of the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling estimators of the parameters of the BXII-PC distribution. We consider an application to a real data set to prove empirically the potentiality of the proposed model.

Data from the Household Income and Labour Dynamics in Australia Survey is used to estimate distributions for the level of educational attainment for Australian indigenous and nonindigenous populations for the years 2001, 2006, 2014 and 2017. Bayesian inference is used to analyse how these ordinal categorical distributions have changed over time and to compare indigenous and nonindigenous distributions. Both the level of educational attainment and inequality in educational attainment are considered. To compare changes in levels over time, as well as inequality between the two populations, first order stochastic dominance and an index of educational poverty are used. To examine changes in inequality over time, two inequality indices and generalised Lorenz dominance are considered. Results are presented in terms of posterior densities for the indices and posterior probabilities for dominance for the dominance comparisons. We find some evidence of improvement over time, especially in the lower parts of the indigenous distribution and that inequality has significantly increased from 2001 to 2017. [ABSTRACT FROM AUTHOR]

Copyright of Kölner Zeitschrift für Soziologie und Sozialpsychologie ( KZfSS) is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Top incomes are often related to Pareto distribution. To date, economists have mostly used Pareto Type I distribution to model the upper tail of income and wealth distribution. It is a parametric distribution, with interesting properties, that can be easily linked to economic theory. In this paper, we first show that modeling top incomes with Pareto Type I distribution can lead to biased estimation of inequality, even with millions of observations. Then, we show that the Generalized Pareto distribution and, even more, the Extended Pareto distribution, are much less sensitive to the choice of the threshold. Thus, they can provide more reliable results. We discuss different types of bias that could be encountered in empirical studies and, we provide some guidance for practice. To illustrate, two applications are investigated, on the distribution of income in South Africa in 2012 and on the distribution of wealth in the United States in 2013. [ABSTRACT FROM AUTHOR]

Copyright of Revista de Economia Contemporânea is the property of Revista de Economia Contemporanea and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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. [ABSTRACT FROM AUTHOR]

Background: An analysis of the regional distribution of health resources is one of the tools for evaluating equal geographic access to health care. The usual analytical approach to an assessment of regional differences is to evaluate each health resource separately. This is a sensible approach, because there may be systematic reasons for any differences, for example, higher salaries in urban areas. However, a separate evaluation of the regional distribution of health resource capacities may be misleading. We should evaluate all health resource capacities as a whole and consider the substitutability of resources.Objective: This study aims to measure regional inequalities in the Czech Republic with the help of alternative approaches to the evaluation of regional inequalities in the case of several substitutable health resources.Methods: Five alternative evaluation methods (models) are described and applied: the separate evaluation, expert model, market model, common weights model, and production frontier model.Results: The regional distribution of physicians and nurses in the Czech Republic in 2017 was evaluated. In spite of many regulations at the national and regional levels, we have found inequalities in regional resource distribution. The models that consider all health resources and the possibility of a resource substitution show lower inequalities between regional health resource capacities.Conclusion: Both researchers and policy-makers should always consider the possibility of resource substitutions in the assessment of regional inequalities. [ABSTRACT FROM AUTHOR]

The study of income inequality is important for predicting the wealth of a country. There is an increasing number of publications where the authors call for the use of several indices simultaneously to better account for the wealth distribution. Due to the fact that income data are usually collected through sample surveys, the sampling properties of income inequality measures should not be overlooked. The most widely used inequality measure is the Gini index, and its inferential aspects have been deeply investigated. An alternative inequality index could be the Bonferroni inequality index, although less attention on its inference has been paid in the literature. The aim of this paper is to address the inference of the Bonferroni index in a finite population framework. The Bonferroni index is linearized by differentiation with respect to the sample indicators which allows for conducting a valid inference. Furthermore, the linearized variables are used to evaluate the effects of the different observations on the Bonferroni and Gini indices. The result demonstrates once for all that the former is more sensitive to the lowest incomes in the distribution than the latter. [ABSTRACT FROM AUTHOR]

Inequality indices are quantitative scores that take values in the unit interval, with a zero score denoting complete equality. They were originally created to measure the heterogeneity of wealth metrics. In this study, we focus on a new inequality index based on the Fourier transform that demonstrates a number of intriguing characteristics and shows great potential for applications. By extension, it is demonstrated that other inequality measures, such as the Gini and Pietra indices, can be usefully stated in terms of the Fourier transform, allowing us to illuminate characteristics in a novel and straightforward manner.

In this study, we have discussed various statistical properties for 3-component mixture of Rayleigh distributions. Here initially, the main properties of mixture distributions are presented and analyzed. Second, some of the famous entropies, measures of inequality are also discussed. Also, the statistical properties of the density functions of rth-, 1st- and nth-order statistics are derived. Moreover, the parameters estimation of the considered mixture model under the maximum likelihood (ML) estimation is also performed using censored and complete data scheme. Finally, the results on ML estimation are also computed via Monte Carlo simulation study and as well as by using a real-life data set.

It is argued that the political feasibility of climate mitigation policies depends heavily on their distributional effects. This paper therefore studies the distributional effects of the European Commission's Fit-for-55 package at the household level in seven EU countries, analyzing a carbon tax on transport and heating fuels as well as variations of a lump-sum refund. Based on the resulting income distributions, different inequality measures are computed. The paper aims to extend previous methodological approaches by including inequality measures such as the Theil index and Atkinson index and comparing the results of carbon taxes on transport and heating fuels for seven EU countries in a consistent manner. I find that a household-size specific lump-sum refund not only mitigates the negative distributional effects of a carbon tax but also reduces overall inequality compared to the baseline scenario without a tax. [ABSTRACT FROM AUTHOR]

The purpose of the article is to present ways to measure inequality. The article describes the last three ways to measure inequality, i.e. based on the Lorenz curve, generalized entropy and the social welfare function. It omits, however, the share and division measures, i.e. the absolute and relative differences, variance, quartile and standard deviations, or positional inequality measures based on percentiles, deciles, quartiles, quantiles, the coefficient of variation and the McLoone index, which results from the fact that although they are often used in empirical research, they illustrate division rather than inequality sensu stricto [i.a. Park 1984, pp. 42-44; Heshmati 2004; Jóźwiak, Podgórski 2012; Jabkowski 2009, pp. 32-35]. Thus, the article does not include a wider presentation of these measures.

This paper will propose an index for measuring spatial concentration, which is based on the solution of a particular transportation problem. This approach extends a new index proposed for the measurement of seasonality to the spatial case, and it takes into account the level of the concentration of the phenomenon of interest according to its spatial distribution. Various properties of the proposed index, which make it a desirable measure for spatial concentration, will also be described. An empirical application, using data from selected European countries, will be provided, and the results derived from the proposed index will be compared with those derived from currently used indices. [ABSTRACT FROM AUTHOR]

The objective of the paper is to verify if income inequality impedes the growth rates in OECD countries in the period of 1990–2014 and to reveal whether the choice of the income inequality measure determines the sign and the strength of the estimated relationship. We use system GMM to estimate parameters of a dynamic panel growth model. The research indicates that income inequality negatively affects economic growth. We also find evidence that various measures of inequality bring the different scale of consequences for economic growth, with measures that give more weight to the middle part of the distribution being the weakest predictor of GDP growth. Simultaneously, we present the test of weak instruments, which helps to explain these differences. [ABSTRACT FROM AUTHOR]

In this study, we embark on measuring inequality in Iran. We compute three measures of group-based inequality (Group-weighted Coefficient of Variation, Group-weighted Gini, and Group-weighted Theil) for the following outcomes: education, assets, income, and expenditure per capita. The groups are defined based on gender, ethnicity/language (Persian, Azeri, and other ethnic minorities), and region (urban versus rural and capital city versus other places) using 23 years of annual Household Expenditure and Income Surveys from 1990 through 2012. Inequality between groups based on religion (Muslim, non-Muslim), citizenship (Iranian, non-Iranian) are also studied using the 2006 census. Our analysis of the trend of horizontal inequality reveals substantial reduction in between-group inequalities over the 1990–2012 period. Yet, gender based income inequality remains high. The implications and underlying reasons for these results are discussed. [ABSTRACT FROM AUTHOR]

Variability of a microsite contributes to the size hierarchy in tree populations. Tree size symmetry varies with the available growth resources. However, competition hierarchy may not cause size symmetry in tree populations. The identification of mechanisms that determine size hierarchy has ecological significance in the management of a forest stand. Therefore, this study investigated the tree size structure of the Teak stand in the Hilltop and Valley-Bottom stands of the Omo Forest Reserve. A ten-year-old Teak plantation was delineated into Hilltop and Valley-Bottom stands based on topography. Five (30 m × 30 m) sample plots were systematically demarcated on 1 km transects in each stand. Tree stems with diameter at breast height (dbh) ≥ 10 cm were enumerated. Diameter at breast height and total height were measured using Girth tape and Spiegel Relaskop. Stem size inequality, diversity and stand attributes of both stands were evaluated for diameter and height. Data collected were analyzed using descriptive, correlation, regression analysis and t-test at α0.05. Mean dbh and height in the Valley-Bottom stand (11.30 ± 4.82 cm dbh and 7.26 ± 3.21 m) were not significantly different from the Hilltop stand (10.19 ± 4.62 cm dbh and 7.12 ± 3.88 m). Stem density in the Hilltop stand (1431.0 stems/ha) was higher than in Valley-Bottom stand (1248.0 stems/ha). All distributions expressed unimodality, except the diameter distribution of the Valley-Bottom stand, which expressed bimodality. The inequality was strongly correlated with the diversity indices in dbh and height distributions in the Hilltop and Valley-Bottom stands, respectively. The same mechanism was responsible for the dbh and height structures of the Hilltop and Valley-Bottom stands, respectively. However, different mechanisms were responsible for the dbh and height structures of the Valley-Bottom and Hilltop stands, respectively.

The residential sector has become the second largest energy consumer in China. Urban residential energy consumption (URE) in China is growing rapidly in the process of urbanization. This paper aims to reveal the spatiotemporal dynamic evolution and influencing mechanism of URE in China. The spatiotemporal heterogeneity of URE during 2007–2018 is explored through Kernel density estimation and inequality measures (i.e., Gini coefficient, Theil index, and mean logarithmic deviation). Then, with several advantages over traditional index decomposition analysis approaches, the Generalized Divisia Index Method (GDIM) decomposition is employed to investigate the impacts of eight driving factors on URE. Furthermore, the national and provincial decoupling relationships between URE and residential income increase are studied. It is found that different provinces’ URE present a significant agglomeration effect; the interprovincial inequality in URE increases and then decreases during the study period. The GDIM decomposition results indicate the income effect is the main positive factor driving URE. Besides, urban population, residential area, per capita energy use, and per unit area energy consumption positively influence URE. By contrast, per capita income, energy intensity, and residential density have negative effects on URE. There is evidence that only three decoupling states, i.e., weak decoupling, strong decoupling, and expansive negative decoupling, appear in China during 2007–2018. Specifically, weak decoupling is the dominant state among different regions. Finally, some suggestions are given to speed up the construction of energy-saving cities and promote the decoupling process of residential energy consumption in China. This paper fills some research gaps in urban residential energy research and is important for China’s policymakers.

On one hand, a large class of inequality measures, which includes the generalized entropy, the Atkinson, the Gini, etc., for example, has been introduced in P.D. Mergane, G.S. Lo, Appl. Math. 4 (2013), 986–1000. On the other hand, the influence function (IF) of statistics is an important tool in the asymptotics of a nonparametric statistic. This function has been and is being determined and analyzed in various aspects for a large number of statistics. We proceed to a unifying study of the IF of all the members of the so-called Theil-like family and regroup those IF's in one formula. Comparative studies become easier.

A two-parameter unit distribution and its regression model plus its extension to 0 and 1 inflation is introduced and studied. The distribution is called the unit upper truncated Weibull (UUTW) distribution, while the inflated variant is called the 0 - 1 inflated unit upper truncated Weibull (ZOIUUTW) distribution. The UUTW distribution has an increasing and a J-shaped hazard rate function. The parameters of the proposed models are estimated by the method of maximum likelihood estimation. For the UUTW distribution, two practical examples involving household expenditure and maximum flood level data are used to show its flexibility and the proposed distribution demonstrates better fit tendencies than some of the competing unit distributions. Application of the proposed regression model demonstrates adequate capability in describing the real data set with better modeling proficiency than the existing competing models. Then, for the ZOIUUTW distribution, the CD34+ data involving cancer patients are analyzed to show the flexibility of the model in characterizing inflation at both endpoints of the unit interval., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Author(s).)

Asymptotic and bootstrap tests for inequality measures are known to perform poorly in finite samples when the underlying distribution is heavy-tailed. We propose Monte Carlo permutation and bootstrap methods for the problem of testing the equality of inequality measures between two samples. Results cover the Generalized Entropy class, which includes Theil's index, the Atkinson class of indices, and the Gini index. We analyze finite-sample and asymptotic conditions for the validity of the proposed methods, and we introduce a convenient rescaling to improve finite-sample performance. Simulation results show that size correct inference can be obtained with our proposed methods despite heavy tails if the underlying distributions are sufficiently close in the upper tails. Substantial reduction in size distortion is achieved more generally. Studentized rescaled Monte Carlo permutation tests outperform the competing methods we consider in terms of power. [ABSTRACT FROM AUTHOR]

• Quantile random forests are estimated to study stock-return predictability. • Quarterly UK data tracing back to 1977 are studied. • Data feature six different inequality measures. • Strong evidence that inequality measures predict stock returns in sample. • No systematic evidence that inequality measures predict stock returns out-of-sample. We contribute to research on the predictability of stock returns in two ways. First, we use quantile random forests to study the predictive value of various consumption-based and income-based inequality measures across the quantiles of the conditional distribution of stock returns. Second, we examine whether the inequality measures, measured at a quarterly frequency, have out-of-sample predictive value for stock returns at three different forecast horizons. Our results suggest that the inequality measures have predictive value for stock returns in sample, but do not systematically predict stock returns out of sample. [ABSTRACT FROM AUTHOR]

Two popular inequality measures used in the study of income and wealth distributions are the Gini (G) and Theil (T) indices. Several bounds on these inequality measures are available when only partial information about the distribution is available. However the correlation between them has been less studied. We derive the allowed region for the joint values of (G, T), for both continuous and discrete distributions. This has the form of a lower bound for T at given G. There is no corresponding upper bound, and T can be made as large as desired for given G by choosing an appropriate form of the Lorenz curve. We illustrate the bound for several parametric models of income distribution and Lorenz curves frequently used in the income distribution literature. [ABSTRACT FROM AUTHOR]

Are there things that ordinary people can do in their private lives to reduce economic inequality? And, if so, how would these things work? To be sure, there are macro societal mechanisms for reducing inequality. But are there micro mechanisms for reducing inequality? This article first examines inequality measures and behavioral models that produce inequality effects, identifying five sets of inequality mechanisms which lead to levers that ordinary people can use to reduce income inequality, and next discusses the levers, with special attention to their feasibility, ease of use, and side effects. The five levers highlight transfers, equal additions, negative assortative mating, wage schedules that reward multiple personal characteristics, and compensation procedures with voting rules, many voters, diversity of thought, and secret ballots. This work raises new questions for research, such as the sources of diversity of thought. [ABSTRACT FROM AUTHOR]

In this paper, we consider an extended version of new generalized Lindley distribution (NGLD). We refer to this new generalization as the extended new generalized Lindley distribution (ENGLD). A comprehensive account of the mathematical properties of the new distribution including estimation is presented. A real life data set is considered here to illustrate the relevance of the new model and compared it with other forms of Lindley models using method of moment estimation and method of maximum likelihood estimation.

This paper analyses the gross inland energy consumption (EC) in the European Union countries (EU-15) over the period 2005-2014. The standard tools in the measurement of income inequality such as Lorenz curves, Gini index, Generalized Entropy indices and Atkinson ones are applied. Our empirical results, obtained through the decomposition of the generalized entropy indices, confirm that there are a small inward shift in the corresponding Lorenz curves, that the inequality distribution of EC across the EU-15 countries has decreased (the Gini coefficient falls from 44,27% in 2005 to 42,16% in 2014) and there are huge differences among the countries’ clusters: Mediterranean, Continental, Nordic and Anglo-Saxon. This paper makes a good contribution to knowledge since it uses a very up-to-dated database (Eurostat) and fills a gap in the literature.

This study exploits unprecedented access to income data and a combination of newly developed statistical methods to evaluate income inequality in Egypt and test for potential top incomes biases. Income inequality in Egypt is found to be low by regional and world standards; top incomes are found to follow the Pareto distribution and do not show anomalies compared to surveys worldwide. Correcting for top incomes biases increases the Gini coefficient significantly. The magnitude of the upward correction varies between 1.1 and 4.1 percentage points depending on the choice of correction method and welfare measure. [ABSTRACT FROM AUTHOR]

This paper contributes to the sparse literature on inequality convergence by empirically testing convergence across states in the U.S. This sample period encompasses a series of different periods that the existing literature discusses — the Great Depression (1929-1944), the Great Compression (1945-1979), the Great Divergence (1980-present), the Great Moderation (1982-2007), and the Great Recession (2007-2009). This paper implements the relatively new method of panel convergence testing, recommended by Phillips and Sul (2007). This method examines the club convergence hypothesis, which argues that certain countries, states, sectors, or regions belong to a club that moves from disequilibrium positions to their club-specific steady-state positions. We find strong support for convergence through the late 1970s and early 1980s, and then evidence of divergence. The divergence, however, moves the dispersion of inequality measures across states only a fraction of the way back to their levels in the early part of the twentieth century. [ABSTRACT FROM AUTHOR]

Economic inequality is, nowadays, frequently perceived as following a growing trend with impact on political and religious agendas. However, there is a wide range of inequality measures, each of which pointing to a possibly different degree of inequality. Furthermore, regardless of the measure used, it only acknowledges the momentary population inequality, failing to capture the individuals evolution over time. In this paper, several inequality measures were analyzed in order to compare the typical single time instant degree of wealth inequality (population perspective) to the one obtained from the individuals’ wealth mean over several time instants (individuals perspective). The proposed generalization of a simple addictive model, for limited time average of individual’s wealth, allows us to verify that the typically used inequality measures for a given snapshot instant of the population significantly overestimate the individuals’ wealth inequality over time. Moreover, that is more extreme for the ratios than for the indices analyzed. [ABSTRACT FROM AUTHOR]