Atkinson Index Research Articles

Atkinson Index Detector for Spectrum Sensing

Recently, a new approach for designing detectors for cooperative spectrum sensing has been coined. It applies an incoming inequality index, which is normally used in economic and social sciences, to build a test statistic that operates on the entries of the received signal sample covariance matrix. The first detector designed using this approach was the Gini index detector (GID). This letter devises the Atkinson index detector (AID), which is shown to outperform the GID in many situations, with the special attribute of attaining a time complexity that grows linearly with the number of secondary users.

Modeling the Population Equity of Alzheimer Disease Treatments in the US

The arrival of new medications for Alzheimer disease (AD) has prompted efforts to measure their value using conventional cost-effectiveness analyses; however, these analyses focus on how much health improvement new medications generate per dollar spent. As AD disproportionately affects older adults, women, racial and ethnic minority individuals, and individuals with lower socioeconomic and educational levels, it is critical to also examine the health equity outcomes of treatment. To estimate the health equity impact of a hypothetical disease-modifying treatment for early AD in the US and to examine targeted policies to mitigate health care disparities. This economic evaluation, which used a distributional cost-effectiveness analysis, was conducted from June 16, 2022, to January 11, 2024. The study included subgroups defined by race and ethnicity and by social vulnerability quintiles in the US. A hypothetical disease-modifying treatment compared with best supportive care. The main outcomes were population-level quality-adjusted life-years (QALYs), lifetime costs, and net health benefits. The social welfare impact and change in health inequality were estimated using the Atkinson index. The distributional cost-effectiveness analysis simulated 316 037 100 individuals from the US population, including 25 subgroups defined by 5 categories of race and ethnicity and population quintiles of social vulnerability, with the fifth quintile representing the most socially vulnerable group. At an opportunity cost benchmark of $150 000 per QALY, treatment was associated with improved population health, adding 28 197 QALYs per year to the US population. Accounting for health inequality preferences (using an aversion level of 11, based on an Atkinson inequality aversion parameter that can range from 0 to infinity, with higher values assigning greater weight to health gains that accrue to the population with the lowest lifetime quality-adjusted life expectancy), treatment was associated with a 0.009% reduction in existing population health inequalities annually. Scenario analyses examining earlier and expanded treatment access suggested a population health improvement of up to 221 358 QALYs. The findings of this economic evaluation suggest that treatment for AD could improve population health and health equity. Policies to enable earlier diagnosis and treatment initiation, as well as expanded access to treatment, may further improve treatment and health equity impacts.

Assessment of Spatial Proportions of the Tax Potential of Small and Medium Enterprises in a Resource Type Region

Purpose of the study – to determine the spatial structure and concentration of tax revenues from the activities of small and medium enterprises (SMEs) in municipal entities of the resource-type region (based on materials from the Kemerovo Region – Kuzbass), to characterize their compliance with the needs of local budgets.Materials and methods. The data on total tax revenues from SMEs, specific revenues per small and medium enterprise, in relation to population indexes, the total number of SMEs, the presence or absence of coal mining in the municipality were used. The coefficients of variation and oscillation, Atkinson index, the coefficient of paired correlation, Gatev coefficient, and the paired Student t-test were applied. The calculations were performed in the SPSS 19.0 program and the free software “R”.Results. The Kemerovo region – Kuzbass is characterized by high levels of spatial concentration of revenues from SMEs by municipalities, spatial inequality for this index. This is explained by not only the differences in the level of economic and business development between the centers and the periphery, but also by a large gap between municipalities in terms of population (10 times or more). The concentration and inequality of tax potential by municipalities in 2023 increased compared to 2021. The absolute values of revenues from special tax regimes and the population of municipalities have a very high level of correlation. Gatev coefficient (where another calculation method related to specific weights is used) showed a moderate degree of difference in the structures of these indexes. The center is ahead of the periphery in terms of the share of SMEs in the tax potential. Spatial inequality in revenues per one SME entity is moderate; in 2023, compared to 2021, a tendency towards an increase in this index was revealed. The leading positions are occupied by the Novokuznetsk municipal district (which is partly explained by the agglomeration effect of Novokuznetsk), Tashtagolsky municipal district (rapid development of the national resort of Sheregesh). The largest urban centers (Kemerovo, Novokuznetsk urban districts) occupy only third and fourth place. The absolute value of the tax potential of SMEs, as well as specific revenues from special tax regimes per one SME entity do not depend on the presence of a developed coal industry in the municipality.Conclusion. The study demonstrates spatial proportions and spatial inequality of municipalities in terms of SME tax potential, taking into account the specifics of resource-type regions. The presented methodological approach can be used to study a similar subject area in other regions dependent on mineral extraction. The findings of the study demonstrate the potential of SMEs in ensuring budget balance at the local level in the face of risks of declining coal production.

Exploring the fundamental properties and MGF of a 3-component mixture of power distributions: a simulation study

This paper estimates the parameters of the 3-component mixture of power distributions. The expressions of fundamental properties of the said distribution are presented, and for judgment, the numerical results of mean, median, variance, mode and skewness are evaluated. The closed-form expressions of the reliability properties, the statistical properties and necessary inequality measures are discussed. The trend of reliability measures is shown with the help of numerical results and graphs by taking different values of parameters and proportion parameters. The mathematical expressions of certain related statistical functions are derived from the reliability functions, the moment generating function, the characteristics function, the probability generating function, and the factorial moment generating function. The expressions of essential entropies, Shannon’s entropy, the B-entropy and Renyi’s entropy, are derived. The mathematical expressions of inequality indexes, the Gini index, the Lorenz curve, the Bonferroni curve, the Zinga index, the Atkinson index and the generalized entropy index are also analysed. The RF, the HRF, the CHR, the RHR, the MRL, and the MWT functions are derived in reliability analysis. The numerical values and graphs for different parameters and proportion components are discussed to judge the behaviour of reliability properties.

The Impact of Tocilizumab Coverage on Health Equity for Inpatients with COVID-19 in the USA: A Distributional Cost-Effectiveness Analysis.

We conducted a distributional cost-effectiveness analysis to evaluate how coverage of tocilizumab for inpatients with COVID-19 from 2021 to present impacted health equity in the USA. A published, payer-perspective, distributional cost-effectiveness analysis for inpatient COVID-19 treatments was adapted to include information on baseline health disparities across 25 equity-relevant subgroups based on race and ethnicity (5 census-based groups), and county-level social vulnerability (5 geographic quintiles). The underlying cost-effectiveness analysis was updated to reflect patient characteristics at admission, standard of care outcomes, tocilizumab efficacy, and contemporary unit costs. The distributional cost-effectiveness analysis inputs for COVID-19 hospitalization and subgroup risk adjustments based on social vulnerability were derived from published estimates. Opportunity costs were estimated by converting total tocilizumab spend into quality-adjusted life-years (QALYs), distributed equally across subgroups. Tocilizumab treatment was cost effective across all subgroups. Treatment resulted in larger relative QALY gains in more socially vulnerable subgroups than less socially vulnerable subgroups, given higher hospitalization rates and inpatient mortality. Using an opportunity cost threshold of US$150,000/QALY and an Atkinson index of 11, tocilizumab was estimated to have improved social welfare by increasing population health (53,252 QALYs gained) and reducing existing overall US health inequalities by 0.003% since 2021. Use of tocilizumab for COVID-19 since 2021 increased population health while improving health equity, as more patients with lower baseline health were eligible for treatment and received larger relative health gains. Future equitable access to tocilizumab for inpatients with COVID-19 is expected to lead to continued increases in population health and reductions in disparities.

New technologies and income inequalities into Sub-Saharan Africa: Using a new technological indicator

The studies which analyzed the impact of technology innovation on income inequalities have considered only one factor of change at a time. The results are overall inconclusive: technology innovation appears to either reduce or increase inequality, depending on which factor is considered. In the literature of technological change, there is a technology innovation indicator that comprises multiple factors simultaneously. Using this technology innovation indicator and three different measures of income inequality (Gini index, Atkinson index, and the ratio of Palma), the paper analyzed the effect of technology innovation on income inequalities into Sub-Saharan Africa countries. A dynamic panel model was specified and estimated with the Generalized Moments Method (GMM) in System. The data used come from the Global Consumption and Income Project (GCIP), the World Development Indicator (WDI) and the World Governance Indicator (WGI). They were observed over the period 1996–2014 of 30 Sub-Saharan Africa countries. The paper finds robust evidence that technology innovation contributes to reducing income inequalities into Sub-Saharan Africa countries. The implementation of learning policy through improving education condition associated with social policy can contribute to limit the income inequalities due to technologies change into Sub-Saharan Africa countries.

Исследование неоднородности социально-экономического пространства России на уровне макрорегионов

Introduction. This article examines the problem of differentiation of the economic space of Russia. This problem originates during the collapse of the Soviet Union, when, during the transition from a command economy to a market economy, the state was faced with an uneven distribution of natural, territorial, demographic and other resources across the country's regions. The destruction of industrial, financial and social ties of the regions occurred as a result of the policy pursued by Yeltsin B., who pursued a course of strengthening the sovereignty of the subjects of Russia. In the Decree of the President of the Russian Federation No. 803 dated 06/03/1996 "On the main provisions of regional policy in the Russian Federation", the task was set to smooth out significant imbalances in the socio-economic development of the regions. In this paper, the question is considered: has the task regulated by the decree of the President of the Russian Federation been achieved? The purpose of the work is to assess the differences in the socio-economic development of Russian regions grouped into federal districts.Materials and methods. The information base of this study consists of the works of domestic authors and data from the State Statistics Service (Rosstat). The Thale index, its structural decomposition, and the Atkinson index were used to analyze the socio-economic inequality of the regions.Results. The article provides a structural analysis of the socio-economic development of Russia (at the level of macro-regions) from 2000-2020 using the above indices. The results of the study showed significant intergroup differences in the macro-regions of Russia, as well as increased regional inequality in most of the considered indicators. An analysis of the regions within the federal districts showed that the regions of the Central Federal District differ significantly in terms of socio-economic development. In other federal districts, there is a low level of regional inequalityConclusions. As a result of the study, proposals were developed to reduce the socio-economic differentiation of the regions. The conclusions of this work can be used to improve the state regional policy in the field of balanced development of territories.

Small-Sample Bias Correction of Inequality Estimators in Complex Surveys

Income inequality estimators are biased in small samples, leading generally to an underestimation. This aspect deserves particular attention when estimating inequality in small domains and performing small area estimation at the area level. We propose a bias correction framework for a large class of inequality measures comprising the Gini Index, the Generalized Entropy, and the Atkinson index families by accounting for complex survey designs. The proposed methodology does not require any parametric assumption on income distribution, being very flexible. Design-based performance evaluation of our proposal has been carried out using EU-SILC data, their results show a noticeable bias reduction for all the measures. Lastly, an illustrative example of application in small area estimation confirms that ignoring ex-ante bias correction determines model misspecification.

Towards Efforts to Equalize Income in Africa: The Role of Tourism Development

ABSTRACT A vast literature has investigated the nexus between tourism and income inequality in developing and developed countries. Unfortunately, the literature on the impact of tourism on income inequality in Africa is sparse. Hence, this study examines the influence of tourism on income inequality in 30 African countries over the period 1996–2020. In addition to international tourism arrivals and international tourism receipts which have been widely used by previous studies, this study uses a plethora of tourism indicators, namely business tourism spending, leisure tourism spending, internal travel and tourism consumption, domestic tourism spending, and visitor exports. Moreover, unlike previous studies that have extensively used the Gini index with its inadequacy as a measurement of income inequality; this study uses the Atkinson index and Palma ratio to capture extreme points of the inequality distribution. The empirical evidence is based on the panel-corrected standard error (PCSE) estimation technique. The results reveal that tourism contributes to the equalization of income in Africa, contingent on the type of tourism. Policy implications are discussed.

Investigating the Inequality Trend in Health Resource Distribution in Iran: A Case Study in Bushehr Province

Background: Equity in access to health resources is a fundamental goal of health systems worldwide. Objectives: This study aims to assess the distribution of essential health resources necessary for healthcare provision in Bushehr Province. Methods: This cross-sectional study spans ten years and utilizes several widely recognized indices in health resource distribution equity and equality, including the Gini Coefficient, Concentration Index, Horizontal Inequity, Robin Hood Index, Theil Index, Atkinson Index, and Quantile Ratio. These indices were calculated based on both the population level and the proposed resource allocation model (PRAM) using Excel Software 2018 and Stata version 18. Results: The findings indicate a degree of inequality in the distribution of all health resources examined, with special beds exhibiting much higher levels of inequality than others. The sensitivity of the studied indices varied across the distributed resources. Moreover, the trend of inequality generally decreased for all examined resources. The PRAM results suggest that adopting a different approach to resource distribution can significantly reduce inequality levels. Conclusions: Despite a downward trend in the inequality of health resource distribution, significant disparities persist. Altering the resource distribution system from the conventional geographical division could aid in achieving equity and equality in healthcare. Such changes could also reduce the costs associated with the health system.

Economic growth and income inequality in sub-Saharan African countries: A test of Kuznets’ hypothesis

In this study, the influence of economic growth on income disparities in 29 sub-Saharan African (SSA) countries is investigated for the period 2005-2015. The primary objective of the study is to empirically test Kuznets? hypothesis, which holds that there is an inverted U-shaped relationship between economic growth and income inequality. The study examined this relationship using four proxies for income inequality: the composite inequality index, the Atkinson index, the Gini coefficient, and the Palma ratio. Using a modified version of a difference generalised method of moments (GMM) estimation technique, it was found that regardless of the proxy used to measure income inequality, there is a consistently significant negative relationship between income per capita (y) and income inequality in the countries under study. A consistent positive relationship was also found between the square of income per capita (y2) and income inequality across all the proxies used in the study. The study found that the relationship between economic growth and income inequality follows a U-curve. The result suggests that while economic growth initially lowers income inequality, inequality eventually rises in tandem with growth. This suggests that the bulk of the studied economies in the SSA region are situated on the downward portion of the U-curve. The policy implications are discussed.

Carbon emission inequality and fairness from energy consumption by prefecture-level cities in China

This paper focuses on the conceptualization and quantification of carbon emission inequality and fairness from energy consumption. In order to more accurately measure the carbon emissions generated by electricity consumption in each city, we firstly propose a new method for calculating the carbon emission factor for electricity, and calculates the carbon emissions from energy consumption in 282 prefecture-level cities in China from 2003 to 2019. Through the application of the Theil-Kaya decomposition mechanism and the improved Atkinson index, we conducted an in-depth study of the carbon emission inequality and fairness indicators from energy consumption. The results show that (1) Although China's overall inequality has declined, it remains significant in the western region, with its inequality indicator fluctuating from 0.548 in 2003 to 0.683 in 2019.(2) The decomposition of the drivers of inequality indicators shows that the contribution of GDP per capita to inequality is increasingly being replaced by energy intensity and the energy carbon emission factor, with energy intensity emerging as the main driver, contributing more than 40% to inequality in 2019, both overall and in the three regions.(3) The results for the fairness indicator, on the other hand, show a certain degree of divergence. Further Dynamic Time Warping fitting analysis shows that regardless of how the public's sensitivity to carbon emissions varies, the change trends of the fairness and inequality indicators for carbon emissions in the eastern region show a high degree of convergence, even in the two most extreme cases. The fit is poorest in the western region, but improves significantly if public's sensitivity to carbon emissions increases. (4)To sum up, some policies that are consistent with the context of the times, such as the East-West regional counterparts and the construction of a new type of power system, are worthy of priority consideration by the Government.

Does educational inequality lead to income inequality? Evidence from Pakistan

One of the main issues that developing nations like Pakistan are dealing with is income inequality. Education, inter Alia, plays a key role in reducing income inequality. Theoretically, in developing countries, it is anticipated that there exist two groups: the bourgeoisie (have) and the proletariat (have not), as suggested by Karl Marx, and there is an educational difference between these two groups, and Pakistan is no exception. This study aims to investigate the impact of educational inequality on income inequality at the provincial level of Pakistan with a rural-urban break up for the period from 1998-99 to 2018-19 (pooled data). Keeping in view the nature of the data, panel data techniques are applied. Appropriate tests (i.e., the F-test and the Hausman Specification test) suggest that Fixed Effect Model is the preferred model. The results show that there is a statistically significant positive link between educational inequality and income inequality. The results are robust to various proxies of educational inequality and income inequality (i.e., Gini coefficient, Generalized Entropy, and Atkinson Index) as well as to control variables (i.e., income and poverty). Further, the study found the negative relation between income and income inequality to be statistically significant, indicating that an increase in income leads to a decrease in income inequality. Moreover, the impact of poverty on income inequality is positive and statistically significant. The policy insinuation is that the government should focus on reducing educational inequality to reduce income inequality in Pakistan.

Inequality beyond income quantiles: Distributional effects of climate mitigation policies

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.

Income Redistributive Propensities of Self-Employment, ICT and Remittances: Panel Quantile Regression with Nonadditive Fixed Effects Perspective

This study provides updated modalities for ensuring equitable income distributions in developing countries. This was achieved through the lens of self-employment, information and communication technologies (ICT), and remittances. To circumvent the dark spots in prior studies, this study harnesses annual panel series for 52 African countries. The study engaged both the system generalized method of moments (sGMM) and the panel quantile regression with nonadditive fixed effects (QRPD) techniques to elicit updated insights. Meanwhile, three metrics of income inequality, the Gini coefficient, the Atkinson index, and the Palma ratio, were explored for robust insights. A key discovery from both panel computations is the self-exacerbating inclinations of income disparities in the continent. Furthermore, it was discovered that both self-employment and ICT are significant income equalization factors. However, their influence is most effective at the upper quantiles of inequality. The influence of remittance inflows is predominantly unfavorable for equitable income distribution. Both financial inclusion and government effectiveness provided varying inequality-reducing effects. Notably, their influence is more formidable at the upper quantiles. Human capital development provides some noticeable income equalization effects, particularly at the lower quantiles. Policy insights for minifying income inequality in the continent are highlighted herein.

Inequality in the Distribution of Air Pollution Attributable Mortality Within Canadian Cities.

Recent studies have identified inequality in the distribution of air pollution attributable health impacts, but to our knowledge this has not been examined in Canadian cities. We evaluated the extent and sources of inequality in air pollution attributable mortality at the census tract (CT) level in seven of Canada's largest cities. We first regressed fine particulate matter (PM2.5) and nitrogen dioxide (NO2) attributable mortality against the neighborhood (CT) level prevalence of age 65 and older, low income, low educational attainment, and identification as an Indigenous (First Nations, Métis, Inuit) or Black person, accounting for spatial autocorrelation. We next examined the distribution of baseline mortality rates, PM2.5 and NO2 concentrations, and attributable mortality by neighborhood (CT) level prevalence of these characteristics, calculating the concentration index, Atkinson index, and Gini coefficient. Finally, we conducted a counterfactual analysis of the impact of reducing baseline mortality rates and air pollution concentrations on inequality in air pollution attributable mortality. Regression results indicated that CTs with a higher prevalence of low income and Indigenous identity had significantly higher air pollution attributable mortality. Concentration index, Atkinson index, and Gini coefficient values revealed different degrees of inequality among the cities. Counterfactual analysis indicated that inequality in air pollution attributable mortality tended to be driven more by baseline mortality inequalities than exposure inequalities. Reducing inequality in air pollution attributable mortality requires reducing disparities in both baseline mortality and air pollution exposure.

Inequality in COVID-19 vaccination in Africa.

The COVID-19 pandemic has spread rapidly to all countries with significant health, socioeconomic, and political consequences. Several safe and effective vaccines have been developed. However, it is not certain that all African countries have successfully vaccinated their populations. To study the distribution and determinants of COVID-19 vaccination in Africa from March 2021 to June 2022. Using reliable open-access data, we used the proportion of fully vaccinated people with a complete schedule as a reference variable. To analyze the level of inequality in COVID-19 vaccination, we computed common inequality indicators including two percentile ratios, the Generalized Entropy index, the Gini coefficient, and the Atkinson index. We also estimated the Lorenz curve. To identify drivers of COVID-19 vaccination, we estimated univariate and multivariate regression models as a function of COVID-19-related variables, demographic, epidemiologic, socioeconomic, and health system-related variables. To overcome a potential endogeneity bias, we checked our results using simultaneous equation models. 53 African countries with available data were included in the study. The proportion of fully vaccinated people increased during the study period. However, this increase remained unequal across African countries. Based on the inequality indicators and the Lorenz curve, inequalities in COVID-19 vaccination across African countries were high, although they have decreased in recent months. Total COVID-19 cases and human development index were identified as significant determinant factors that were independently associated with COVID-19 vaccination. Inequality in COVID-19 vaccination in Africa was high. Promoting adequate information to the general population and providing financial and logistical support to low-income countries can help expand COVID-19 vaccination in Africa.

Revisiting the finance-growth nexus in sub-Saharan Africa: Does the level of income inequality matter?

In this paper, the modulating effect of income inequality in the finance–growth nexus using data from 29 sub-Saharan African (SSA) countries is examined. The study examines i) whether financial development still spurs economic growth in the studied countries, and ii) whether income inequality modulates the effect of financial development on economic growth. Three proxies of financial development and four income inequality indicators are used. The financial development indicators used include the financial development index, financial institutions index, and financial markets index, while income inequality is measured by the Palma ratio, the Gini coefficient, the Atkinson index, as well as the composite inequality (Comp) derived from the principal component analysis (PCA). The Generalised Method of Moments (GMM) has been used to examine this linkage. The study found that, on the whole, the beneficial effect of financial sector development on economic growth in the studied countries is weak, at best. This finding has been corroborated by the results of the interaction models, which show that income inequality interacts with financial development to yield a net negative effect on economic growth in four specifications, but a net positive effect in only two specifications. This finding is not surprising given the high level of income inequality that is currently ravaging some of the SSA countries. Policy implications are discussed.

Inequality measures based on log power function-lognormal composite distribution

ABSTRACT 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.

Disparities in colorectal cancer time-to-treatment and survival time associated with racial and economic residential segregation surrounding the diagnostic hospital, Georgia 2010–2015

PurposeTo evaluate patient-level colorectal cancer outcomes in relation to residential income and racial segregation and composition of the neighborhood surrounding the diagnosing hospitals, and characterize presence of cancer-relevant diagnosis and treatment modalities that might contribute to these associations. MethodsWe utilized Georgia state cancer registry data (2010–2015), matching diagnosis information to hospital technology provided by the American Hospital Association and spatial information to the US Census. We modeled time-to-treatment and survival time, using Cox proportional hazards models, stratified by segregation. Segregation was examined as residential economic and racial evenness (Atkinson index) and isolation (isolation index) and mean income at the Census tract level. To assess possible contributing factors, analysis of hospital diagnosis and treatment technologies in relation to segregation was conducted. ResultsAverage income of the Census tract and racial residential segregation of the diagnosing hospital’s neighborhood was generally unassociated with time-to-treatment or survival time. Higher income evenness around the diagnosing hospital was associated with shorter time-to-treatment, with no association with time-to-death. Higher income isolation for the diagnosing hospital, conversely, was associated with longer times to treatment, but also longer survival times. Hospitals in regions with higher level of residential income segregation were less likely to have a particular diagnosing or treatment technologies, such as virtual colonoscopy and chemotherapy. ConclusionHospital resources may be a function of their immediate economic environment, and this may have influence on cancer outcomes. Future work should evaluate patient outcomes in light of technologies or therapies utilized within particular economic environments.