A matrix approach to the Gini index decomposition by subgroup and by income source

The literature offers two main ways of decomposing the Gini index: decomposition by population subgroup and by income source. This article proposes merging the two decomposition dimensions by suggesting a matrix formula for the Gini index which permits the simultaneous decomposition by subgroup and by income source. Using this multi‐decomposition, one can investigate the role of the interaction between the subgroup and the source components in determining the overall inequality. We apply the methodology to sample data on Italian household incomes collected in 2008.     

影响我国农村居民收入差距的主要因素:从收入构成角度的分解分析

This paper attempts to explore the causes behind the change of the inequality in China rural areas at the very beginning of this century by decomposing the inequality of the total per capita income into the contributions from different income components. Furthermore, we develop the decomposition method of Gini coefficients from the income components and use it not only in the static analysis but also in comparative static analysis. Namely it can be used to explore the change of the overall inequality by decomposing the change of Gini Coefficient from income components. The empirical results show that the wage from local employment, the income from agricultural household business and the incomes from non-agricultural household business are the three income components that made the largest contributions to the inequality of the total per capita income. The total contribution to the overall inequality of non-agricultural incomes was much more than that of agricultural incomes. The incomes from agricultural household business, the incomes from non-agricultural household business and the wages from migration made the positive impact on the increase of the overall inequality. The incomes donated by relatives and friends made the most important negative impact on the increase of the overall inequality.     

Decomposing World Income Distribution: Does The World Have A Middle Class?

Using the national income/expenditure distribution data from 111 countries, we decompose total inequality between the individuals in the world, by continents and regions. We use Yitzhaki's Gini decomposition which allows for an exact breakdown of the Gini. We find that Asia is the most heterogeneous continent; between-country inequality is much more important than inequality in incomes within countries. At the other extreme is Latin America where differences between the countries are small, but inequalities within the countries are large. Western Europe/North America is fairly homogeneous both in terms of countries' mean incomes and income differences between individuals. If we divide the world population into three groups: the rich (those with incomes greater than Italy's mean income), the poor (those with incomes less than Western countries' poverty line), and the middle class, we find that there are only 11 percent of people who are "world middle class"; 78 percent are poor, and 11 percent are rich.     

The Changing Pattern of Sources of Income and its Impact on Inequality: The Method and its Application to Australia, 1975–94

This paper proposes a new method of explaining the temporal change in economic inequality in terms of changes in the sources of income. The method is based on the decomposition of the Gini coefficient by source of income. Using this method, the paper also examines changes of the sources of private income in Australia over the last two decades and their impact on the distribution of income. It will be seen that not only have the shares of income from different sources changed, but that there has been significant change in inequality of distribution of the components themselves.     

POVERTY AND INCOME INEQUALITY IN PUERTO RICO, 1969–89: TRENDS AND SOURCES

The paper examines Puerto Rican trends in income distribution during the 1970s and 1980s, then attempts to ascertain the source of the changes in income inequality through a decomposition of the Gini coefficient by factor income source. The study finds that poverty and inequality declined unambiguously during the twenty-year period. The source of the fall in income concentration was found to have been tied, not to changes in the distribution or share of earned income, but to that of unearned income, particularly transfers. These appear to have also accounted for the decline in poverty.     

二元经济中城乡混合基尼系数的计算与分解

关于基尼系数计算方法的文献已经十分丰富,但专门计算城乡混合基尼系数的理论方法,却一直没有得到很好的解决,这导致全国收入分配长期变化方面的某些研究难以深入。本文建立了城乡混合基尼系数的新算法,并给出新的分解形式,同时还提出并论证了度量城乡差距的新指标。该分解形式具有明确的经济含义和理论意义,并且不依赖于“城乡收入分布不重叠”的假定。利用这一分解形式的经济含义,我们分析了几个重要理论问题。最后,应用新算法计算并分解了中国个别年份的城乡混合基尼系数,以检验新算法的有效性。     

Disparities in Australian Regional Incomes: Are They Widening or Narrowing?

In this study we examine Australian census data on regional incomes for the period 1976–91. Following a discussion of theories and empirical evidence regarding regional income adjustment, the regional dispersion of per capita income is analysed for the six Australian states and at the sub-state level (statistical divisions, SDs). The coefficient of variation is used as the measure of dispersion, and Gini coefficients are also calculated to analyse income equality within regions. For Australia, the cross-state dispersion of per capita incomes increased over the period, whereas there was neither convergence nor divergence of incomes among Australia's 57 SDs. In addition, the intrastate dispersion of per capita incomes across SDs remained largely unaltered over the period. Gini coefficients indicated that across income strata, the distribution of incomes both within states and within SDs has become more equal.     

A Consistent Poverty Approach to Assessing the Sensitivity of Income Poverty Measures and Trends

This paper examines the sensitivity of estimates of income poverty rates and trends to variations in the poverty line and to whether or not certain households are included or excluded from the sample used to estimate poverty. The approach draws on the concept of consistent poverty, which has been used to identify those with incomes below the poverty line who also experience deprivation. Our approach involves excluding households with incomes below the poverty line if they report zero or negative income or are self‐employed, have expenditure well in excess of their income, have substantial wealth holdings, or if they do not report having experienced financial stress over the past year. The combined impact of all four exclusions is to reduce the half‐median income poverty rate from 9.9 per cent to 5.4 per cent, but also suggests that poverty increased by more over the decade to 2003–04 than the original estimates indicate.     

Decomposition of the Gini Index by Sources of Income

The Gini concentration coefficient is considered to be the best synthetic inequality measure and is widely used in economic research. In this paper, we present its decomposition by factor components with an application to income distributions in Poland. Income inequality measures proposed by Gini, Zenga and Bonferroni are calculated for different socio-economic groups based on their exclusive or primary source of maintenance. For theoretical income distribution, the Dagum type-I model was used. The basis for the calculations was the individual data coming from the Household Budgets Survey conducted quarterly by the Polish Central Statistical Office. Using the decomposition of inequality by source, we were able to examine how changes in particular income components affected overall inequality.      

AN UPPER BOUND OF THE GINI INDEX IN THE ABSENCE OF MEAN INCOME INFORMATION

In this paper, an upper bound of the Gini index, based on grouped data, is proposed assuming that there is no information on all the group mean incomes as well as the overall mean income but the limits of the income brackets are known. An important advantage of this proposal is that conventional formulas for the upper bound of the Gini index could be applied directly by substituting the (unknown) mean income for each income bracket with the corresponding value that maximizes the grouping correction for that income bracket. The effects of varying the number and size of income brackets are investigated.     

Bounds of the Gini Index Using Sparse Information on Mean Incomes

In this paper, bounds of the Gini index, based on grouped data, are proposed assuming sparse information on mean incomes in the sense that data on either the overall mean income or some of the group mean incomes are not reported. It turns out that the proposed bounds are identical to those proposed by other authors that have more stringent information requirements with respect to mean incomes.     

AN ESTIMATE OF AVERAGE INCOME AND INEQUALITY IN BYZANTIUM AROUND YEAR 1000

Using recent economic statistics from the peak period of Byzantine political and economic influence, we estimate the average income around the year 1000 to have been about 6 nomismata per capita per annum. This is then translated into current prices using two independent methods. They both yield an estimate around $PPP 640–680 in 1990 international prices. It is argued that this amount is some 20 percent below an average estimate of Roman incomes at the time of Augustus (around year one). Assuming that most of income differences in Byzantium were due to the differences in average incomes between social classes, we estimate the Gini coefficient to have been in the range between 40 and 45.     

离散分布收入数据基尼系数的矩阵向量形式及相关问题

本文旨在给出离散分布收入数据基尼系数的很一般的矩阵向量形式,并以此为基础,在一般的意义上讨论基尼系数的按组分解及按类分解问题。本文的结论是,借助矩阵向量形式,我们可以确切地说明基尼系数"完全分解"的含义,更直观地表述目前已有的各种并组或并类基尼系数按组或按类分解的意义,简洁地揭示它们内在的数理结构;通过矩阵向量的运算法则,我们可以直接发现,不可能一般性地实现并组或并类基尼系数按组或按类"完全分解",且使分解后各项均有明确的经济意义;除非进一步给出特殊假定,各种分解的运算量与直接计算并组或并类基尼系数的运算量是相当的。     

Some Ethnic Dimensions of Income Distribution from Pre- to Post-reform New Zealand, 1984–1998*

Based on unit record data from four household surveys conducted by Statistics New Zealand for the years 1983/1984, 1991/1992, 1995/1996 and 1997/1998, this paper addresses some ethnic dimensions of income inequality among New Zealanders over the period of the surveys. It applies alternative techniques of decomposition of the Gini coefficient of inequality by subgroups of population. It then analyses how changes in the incomes of specific population subgroups affect the overall inequality. The results help quantify the economic distances among the different ethnic populations of New Zealand, and indicate how and why these distances have been changing over time.     

Averaging Income Distributions

Various inequality and social welfare measures often depend heavily on the choice of a distribution of income. Picking a distribution that best fits the data involves throwing away information and does not allow for the fact that a wrong choice can be made. Instead, Bayesian model averaging utilizes a weighted average of the results from a number of income distributions, with each weight given by the probability that a distribution is ‘correct’. In this study, prior densities are placed on mean income, the mode of income and the Gini coefficient for Australian income units with one parent (1997–8). Then, using grouped sample data on incomes, posterior densities for the mean and mode of income and the Gini coefficient are derived for a variety of income distributions. The model‐averaged results from these income distributions are obtained.     

GINI DECOMPOSITION AND GINI INCOME ELASTICITY UNDER INCOME VARIABILITY

The Gini income elasticity has been used to assess the impact of marginal proportional changes in income from a given source on inequality in total income. This note extends the methodology to take into account income variability.     

Inequality and economic growth: the role of initial income

We estimate a panel model where the relationship between inequality and GDP per capita growth depends on countries’ initial incomes. Estimates of the model show that the relationship between inequality and GDP per capita growth is significantly decreasing in countries’ initial incomes. Results from instrumental variables regressions show that in Low Income Countries transitional growth is boosted by greater income inequality. In High Income Countries inequality has a significant negative effect on transitional growth. For the median country in the world, that in the year 2015 had a PPP GDP per capita of around 10000USD, IV estimates predict that a 1 percentage point increase in the Gini coefficient decreases GDP per capita growth over a 5-year period by over 1 percentage point; the long-run effect on the level of GDP per capita is around ??5%.     

CHANGES IN INCOME INEQUALITY: AUSTRALIA, 1968–69 TO 1973–74

The period 1968–69 to 1973–74 saw a redistribution of incomes in Australia. This is evidenced first by declining differentials between dissimilar persons and secondly by changes in two measures of income inequality, the Gini and Theil coefficients.
The inequality coefficients are decomposed into components which distinguish between that part of total inequality due to income differences between dissimilar persons and that part due to inequality between similar persons. It is found that the reduction in inequality was due to the reduction in differentials between dissimilar persons and that inequality between similar persons probably did not change over the period.     

中国现行统计方法基尼系数的推算及结果

根据中国统计年鉴城镇居民和农村居民收入数据的特点,对相应的基尼系数计算进行了研究和探讨,并给出了一种推算方法,计算了1982-2001年城镇、农村和全国居民的基尼系数。对推算出的城镇和农村居民基尼系数结果进行了经济分析。     

新疆城市居民收入不平等现状分析

本文采用基尼系数及其分解公式对新疆2003年城市居民收入调查的2828个样本数据进行分析，根据新疆的地理特征将基尼系数按南疆与北疆进行分解计算，并按收入来源对基尼系数进行集中度分解分析，结果表明新疆的收入不平等状况并不严重，南疆的收入差距大于北疆，工资收入和转移收入是收入差距增大的主要原因。