Income inequalities, social support and depressive symptoms among older adults in Europe: a multilevel cross-sectional study

This study analysed the association between income inequality and depression from a multilevel perspective among older adults in Europe, including an examination of the role of social support. The data came from Eurostat’s European Health Interview Survey (EHIS). Selected participants were aged 65 years or above (n = 68,417) and located in 24 European countries. The outcome variable (depression) was measured using the eight-item Patient Health Questionnaire (PHQ-8). The resulting dataset included individual-level (level-1) and aggregate-level (level 2) exposure variables. Level-1 included income quintiles and social support as exposure variables and sex, age, living alone, limitation in activities of daily living and general activity limitation as control variables. Level 2 included the Gini coefficient, healthcare expenditure and dependency ratio. A multilevel linear regression analysis was performed with maximum likelihood (ML) estimation. All the income quintiles from 1 to 4 showed higher average scores for depression than quintile 5 (the highest). Higher social support scores were associated with lower scores for depression. An interaction was found between income quintile and social support, with higher levels of social support associated with lower scores for depression in quintiles 1 and 2. Higher Gini coefficient scores were associated with higher scores for depression. A significative random slope for social support was also found, meaning that the relationship between social support and depression differed across countries. No significant interaction was found between the Gini coefficient and social support. The study findings suggest that more unequal societies provide a less favourable context for the mental health of older adults. There are also significant country-dependent differences in terms of the relationship between support and mental health among older adults.

Group averaging and the Gini deviation

It is known that partitioning a society into groups with subsequent averaging in each group decreases the Gini coefficient. The resulting Lorenz function is piecewise linear. This study deals with a natural question: by how much the Gini coefficient could decrease when passing to a piecewise linear Lorenz function? Obtained results are quite illustrative (since they are expressed in terms of the geometric parameters of the polygon Lorenz curve, such as the lengths of its segments and the angles between successive segments) upper bound estimates for the maximum possible change in the Gini coefficient with a restriction on the group shares, or on the difference between the averaged values of the attribute for consecutive groups. It is shown that there exist Lorenz curves with the Gini coefficient arbitrarily close to one, and at the same time with the Gini coefficient of the averaged society arbitrarily close to zero.

Timetable and Headway Adherence Assessment using the Gini Coefficient and the Lorenz Curve

Adherence to the schedule is of prime importance in public transport. This paper presents a specific application of the Gini coefficient, well known indicator in economics, for the headway adherence assessment. The paper shows that Lorenz curve, which is usually used to define mathematically the Gini coefficient, is a good indicator of the users' waiting time when it is based on the bus schedule. When it is computed on the basis of the ratio of observed headway to the schedule, it is a powerful visual tool that can be used by operators to detect the existence of irregularities on a bus line at a glance. An equation gives, in an idealistic case, the impact of any single traffic disturbance on the Gini coefficient, making this coefficient comprehensive. A detailed analysis is developed, based on the bus proportions according to the headway adherence level. These proportions are obtained from new indices coming from the derivative of the Lorenz curve. The values of these indexes alert the operator of any adherence disturbance. The examination of the Lorenz curve takes more time, but is worthwhile, giving the types of the irregularities The application of these indicators is carried on real-time data from the New Delhi bus network.

The Robin Hood Index Adjusted for Negatives and Equivalised Incomes

Indisputable figures on income and wealth inequality are indispensable for politics, society and science. Although the Gini coefficient is the most common measure of inequality, the straightforward concept of the Robin Hood index (namely, the income share that has to be transferred from the rich to the poor to make everyone equally well off) makes it a more attractive measure for the general public. In a distribution with many negative values – particularly wealth distributions – the Robin Hood index can take on values larger than 1, indicating an intuitively impossible income transfer of more than 100%. This article proposes a method to normalise the Robin Hood index. In contrast to the original index, the normalised Robin Hood index always takes on values between 0 and 1 and ends up as the original index in a distribution without negatives. As inequality measures are commonly applied to equivalised income, we also introduce a method for adequately transferring equivalised incomes from the rich to the poor within the framework of the (normalised) Robin Hood index. An empirical application shows the effect of normalisation for the Robin Hood index, and compares it to the normalisation of the Gini coefficient from previous research.

Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas

Small area estimation is receiving considerable attention due to the high demand for small area statistics. Small area estimators of means and totals have been widely studied in the literature. Moreover, in the last years also small area estimators of quantiles and poverty indicators have been studied. In contrast, small area estimators of inequality indicators, which are often used in socio-economic studies, have received less attention. In this article, we propose a robust method based on the M-quantile regression model for small area estimation of the Theil index and the Gini coefficient, two popular inequality measures. To estimate the mean squared error a non-parametric bootstrap is adopted. A robust approach is used because often inequality is measured using income or consumption data, which are often non-normal and affected by outliers. The proposed methodology is applied to income data to estimate the Theil index and the Gini coefficient for small domains in Tuscany (provinces by age groups), using survey and Census micro-data as auxiliary variables. In addition, a design-based simulation is carried out to study the behaviour of the proposed robust estimators. The performance of the bootstrap mean squared error estimator is also investigated in the simulation study.

Fracture Network Localization Preceding Catastrophic Failure in Triaxial Compression Experiments on Rocks

We quantify the spatial distribution of fracture networks throughout six in situ X-ray tomography triaxial compression experiments on crystalline rocks at confining stresses of 5–35 MPa in order to quantify how fracture development controls the final macroscopic failure of the rock, a process analogous to those that control geohazards such as earthquakes and landslides. Tracking the proportion of the cumulative volume of fractures with volumes >90th percentile to the total fracture volume, ∑v90/vtot indicates that the fracture networks tend to increase in localization toward these largest fractures for up to 80% of the applied differential stress. The evolution of this metric also matches the evolution of the Gini coefficient, which measures the deviation of a population from uniformity. These results are consistent with observations of localizing low magnitude seismicity before large earthquakes in southern California. In both this analysis and the present work, phases of delocalization interrupt the general increase in localization preceding catastrophic failure, indicating that delocalization does not necessarily indicate a reduction of seismic hazard. However, the proportion of the maximum fracture volume to the total fracture volume does not increase monotonically. Experiments with higher confining stress tend to experience greater localization. To further quantify localization, we compare the geometry of the largest fractures, with volumes >90th percentile, to the best fit plane through these fractures immediately preceding failure. The r2 scores and the mean distance of the fractures to the plane indicate greater localization in monzonite than in granite. The smaller mean mineral diameter and lower confining stress in the granite experiments may contribute to this result. Tracking these various metrics of localization reveals a close association between macroscopic yielding and the acceleration of fracture network localization. Near yielding, ∑v90/vtot and the Gini coefficient increase while the mean distance to the final failure plane decreases. Macroscopic yielding thus occurs when the rate of fracture network localization increases.

Fairness of the Distribution of Public Medical and Health Resources

The fairness of health services is an important indicator of the World Health Organization's performance evaluation of health services, and the fairness of health resource allocation is the prerequisite for the fairness of health services. The research in this article aims to explore how to use health and medical resources fairly and effectively to allocate health resources in different fields, populations and projects, in order to achieve the maximization of social and economic benefits of health and medical resources. In the study of the distribution and equity of public health and medical resources, we comprehensively apply Gini coefficient, Theil index, Lorentz curve and difference index, based on the theory of health resource allocation and the theory of health equity, the province's health service resources have been researched and evaluated, combined with regional health planning theories and public health theories, a variety of scientific methods were used to analyze community health service resources at all levels across the country. At the same time, we reviewed the journal literature about the treatment of patients and children, and analyzed the patients admitted to medical institutions in various regions. The research in this paper found that from 2016 to 2020, the Gini coefficient of the province's health institutions according to population distribution has been fluctuating between 0.14 and 0.17. During this 5-year period, the Gini coefficient of the distribution of medical and health expenditures by population shows a downward trend year by year. From 2019, reach below 0.1, this shows that the fairness of the allocation of health resources according to population has a clear trend of improvement.

Wealth and Income in New Zealand: c. 1870 to c. 1939

<p>This thesis examines the level and distribution of wealth and income in New Zealand between about 1870 and 1939. To do so it draws upon the available aggregate statistics on wealth and income, and it uses a sample of wealth holders especially constructed to alleviate the data deficiencies which have arisen through New Zealand not having a wealth census. The evidence available suggests that New Zealand was correctly portrayed as having a high level of wealth with an egalitarian distribution. In 1893, the first year in which average wealth could be estimated, New Zealand was definitely wealthier than Victoria. This wealth was not evenly distributed but the gini coefficient of about 0.75 suggested that New Zealand was an egalitarian economy compared to the United States, Britain, or even Australia. Over the period to 1939 the average level of wealth increased by about 100 percent. Most of this increase took place between 1900 and 1922; the late 1920's and 1930's were periods of slow growth. But this increase was not sufficient to maintain New Zealand's high position relative to Australia, and probably to other countries. The growth of real wealth was accompanied by a redistribution of wealth and by the 1930's, the gini coefficient was only about 0.73. Most of this decline was due to the declining assets held by the very rich. In 1890 to 1895 the top one percent of wealth holders owned 55 - 60 percent of all assets, but by 1935 to 1939 this had fallen to 25 - 30 percent. The very rich had, in fact, never been rich by international standards. The case studies in the thesis did not include one millionaire. As a rule they were first generation wealthy men who came from a well-to-do background, who had superior education, but who had to achieve being wealthy through their own efforts. There were few women among the top wealth holders, and those who did appear inherited their wealth from their father or or husband. The wealthy did not show signs of being a closed elite. There was a considerable amount of upward mobility in the group, and the Scots especially tended to come from poor backgrounds. The practise of equal inheritance among all the children meant that few families remained very wealthy for more than one generation. The same social and occupational mobility was clear among our sample of estate holders. Only 50 percent of sons had the same social status as their fathers. The remaining sons were fairly evenly divided between those who rose and those who fell in status. The sample, which was constructed from probate valuations and death certificate records, suggests some of the factors which assisted and hindered upward mobility. Being born female at a time when women did not pursue careers, or own family property obviously influenced the wealth holdings of a considerable proportion of the population. For men, the place of their birth proved to be significant. The Scottish showed a marked tendency to be upwardly mobile, while being Irish or New Zealand born was a definite handicap. Those who were born overseas did better if they arrived as young adults between 1860 and 1880. Assisted migrants produced proportionately less probatable estates, but those who did had about the same estates as those not assisted. Wealth was concentrated among those involved in farming, trading and the professions throughout most of our period, but over time agricultural wealth showed signs of being replaced by industrial fortunes. The professions had the advantage of a comparatively high income which enabled people to accumulate fortunes. Lifetime income undoubtedly had the major influence on wealth at death. The level of average income increased probably three-fold in the period. Again most of this rise came between 1900 and 1920. It is probable that the distribution also became more equal, through the reduced incomes to the top earners. There was a strong trend for margins for skill to decline over time, even though they were already small relative to those found in the United States. The exception to this was teachers' salaries, which showed a marked rise as the occupation became more professional. The rise of teachers' wages, shop work and clerical jobs all changed the employment structure for women, which was reflected in a changed attitude towards higher education. The 1930's saw a reduction in incomes largely through unemployment and short-time. However, the reduction was heaviest among those in the top 10 percent. The depression had mixed effects on production levels, prices and wages, but only one of our three sample industries, butter and cheese making, showed strong evidence of wage overhang. In 1939 New Zealand was still a wealthy nation, though probably she would not have ranked as highly on an international scale as in 1890. The distribution of both wealth and income had changed over our period to being substantially more egalitarian.</p>

Wealth and Income in New Zealand: c. 1870 to c. 1939

<p>This thesis examines the level and distribution of wealth and income in New Zealand between about 1870 and 1939. To do so it draws upon the available aggregate statistics on wealth and income, and it uses a sample of wealth holders especially constructed to alleviate the data deficiencies which have arisen through New Zealand not having a wealth census. The evidence available suggests that New Zealand was correctly portrayed as having a high level of wealth with an egalitarian distribution. In 1893, the first year in which average wealth could be estimated, New Zealand was definitely wealthier than Victoria. This wealth was not evenly distributed but the gini coefficient of about 0.75 suggested that New Zealand was an egalitarian economy compared to the United States, Britain, or even Australia. Over the period to 1939 the average level of wealth increased by about 100 percent. Most of this increase took place between 1900 and 1922; the late 1920's and 1930's were periods of slow growth. But this increase was not sufficient to maintain New Zealand's high position relative to Australia, and probably to other countries. The growth of real wealth was accompanied by a redistribution of wealth and by the 1930's, the gini coefficient was only about 0.73. Most of this decline was due to the declining assets held by the very rich. In 1890 to 1895 the top one percent of wealth holders owned 55 - 60 percent of all assets, but by 1935 to 1939 this had fallen to 25 - 30 percent. The very rich had, in fact, never been rich by international standards. The case studies in the thesis did not include one millionaire. As a rule they were first generation wealthy men who came from a well-to-do background, who had superior education, but who had to achieve being wealthy through their own efforts. There were few women among the top wealth holders, and those who did appear inherited their wealth from their father or or husband. The wealthy did not show signs of being a closed elite. There was a considerable amount of upward mobility in the group, and the Scots especially tended to come from poor backgrounds. The practise of equal inheritance among all the children meant that few families remained very wealthy for more than one generation. The same social and occupational mobility was clear among our sample of estate holders. Only 50 percent of sons had the same social status as their fathers. The remaining sons were fairly evenly divided between those who rose and those who fell in status. The sample, which was constructed from probate valuations and death certificate records, suggests some of the factors which assisted and hindered upward mobility. Being born female at a time when women did not pursue careers, or own family property obviously influenced the wealth holdings of a considerable proportion of the population. For men, the place of their birth proved to be significant. The Scottish showed a marked tendency to be upwardly mobile, while being Irish or New Zealand born was a definite handicap. Those who were born overseas did better if they arrived as young adults between 1860 and 1880. Assisted migrants produced proportionately less probatable estates, but those who did had about the same estates as those not assisted. Wealth was concentrated among those involved in farming, trading and the professions throughout most of our period, but over time agricultural wealth showed signs of being replaced by industrial fortunes. The professions had the advantage of a comparatively high income which enabled people to accumulate fortunes. Lifetime income undoubtedly had the major influence on wealth at death. The level of average income increased probably three-fold in the period. Again most of this rise came between 1900 and 1920. It is probable that the distribution also became more equal, through the reduced incomes to the top earners. There was a strong trend for margins for skill to decline over time, even though they were already small relative to those found in the United States. The exception to this was teachers' salaries, which showed a marked rise as the occupation became more professional. The rise of teachers' wages, shop work and clerical jobs all changed the employment structure for women, which was reflected in a changed attitude towards higher education. The 1930's saw a reduction in incomes largely through unemployment and short-time. However, the reduction was heaviest among those in the top 10 percent. The depression had mixed effects on production levels, prices and wages, but only one of our three sample industries, butter and cheese making, showed strong evidence of wage overhang. In 1939 New Zealand was still a wealthy nation, though probably she would not have ranked as highly on an international scale as in 1890. The distribution of both wealth and income had changed over our period to being substantially more egalitarian.</p>

The degree of equity and coupling coordination of staff in primary medical and health care institutions in China 2013–2019

Background Primary medical and health care facilities are the first lines of defense for the health of population. This study aims to evaluate the current state and trend of equity and coupling coordination degree (CCD) of staff in primary medical and health care institutions (SPMHCI) based on the quantity and living standards of citizens in China 2013–2019. The research findings are expected to serve as a guideline for the allocation of SPMHCI. Methods The data used in this study including the quantity and living standards of citizens, as well as the number of SPMHCI in 31 provincial administrative regions of China, were obtained from the China Statistical Yearbook and the China Health Statistics Yearbook. The equity and CCD for SPMHCI were analyzed by using the Gini coefficient and the CCD model, and the Grey forecasting model GM (1, 1) (GM) was used to predict the equity and CCD from 2020 to 2022. Results Between 2013 and 2019, the number of SPMHCI increased from 3.17 million to 3.50 million, and the population-based Gini coefficient declined from 0.0704 to 0.0513. In urban and rural areas, the Gini coefficients decreased from 0.1185 and 0.0737 to 0.1025 and 0.0611, respectively. The CCD between SPMHCI and citizens’ living standards (CLS) changed from 0.5691, 0.5813, 0.5818 to 0.5650, 0.5634, 0.6088 at national, urban, and rural levels, respectively. The forecasting results of GM revealed that at the national, urban and rural levels from 2020 to 2022, the Gini coefficient would rise at a rate of − 13.53, − 5.77%, and − 6.10%, respectively, while the CCD would grow at a rate of - 0.89, 1.06, and 0.87%, respectively. Conclusions In China, the number of SPMHCI has increased significantly, with an equitable allocation based on the population. The interaction between SPMHCI and CLS is sufficient, but the degree of mutual promotion is moderate. The government could optimize SPMHCI and improve the chronic disease management services to improve CLS and to ensure the continued operation of primary medical and health care institutions in urban areas.