The limitations of negative incomes in the Gini coefficient decomposition by source

Lerman and Yitzhaki (1985) developed a decomposition of the Gini coefficient by income source that has been extensively used in the literature. This method has strong limitations in the presence of negative incomes, which were not discussed by the original authors and have been widely overlooked in successive studies. Through theoretical argumentation and practical examples, this article shows that, when using negative incomes, (1) the original decomposition formulae become inappropriate, (2) the marginal effects analysis may yield erroneous results and (3) the Pigou–Dalton ‘principle of transfers’ is not always met. This has critical implications for policy development, given that strategies based upon incorrect analyses could actually result in undesired greater income inequalities. The Gini source decomposition should be carefully applied by researchers and policymakers, especially in rural developing areas, where negative incomes are common due to financial losses from agricultural activities.     

A new approach to the decomposition of the Gini income inequality ratio

The purpose of this research is to introduce a new approach to the decomposition of the Gini ratio into three components, supporting them with economic and statistical rigorous interpretations. The three components are: (i) the Gini inequalitywithin subpopulations; (ii) thenet contribution of the extended Gini inequalitybetween subpopulations; and (iii) the contribution of theintensity of transvariation between subpopulations. These components are weighted by the product of the population shares times the income shares of the corresponding subpopulations where the weights add to one.The decomposition introduced in this research is applied to the 1990 U.S. family income distribution. The population of families is disaggregated by types into the following subpopulations: (a) married-couple families; (b) male householder, no wife present; and (c) female householder, no husband present.     

Gini playing soccer

The level of income inequality in a European country influences the competitive balance of its major soccer leagues. We test this hypothesis using cointegration techniques for seven male professional soccer leagues (the Dutch, English, French, German, Italian, Spanish and Ukrainian soccer leagues) from the 1980/1981 season to the 2011/2012 season. Controlling for the level of income inequality using variables such as real GDP per capita, trade openness and the emigration rate, we conclude that income inequality (measured by the Gini index) causes changes in the measures of competitive balance that we employ (the Hirschman–Herfindahl index and the SD) concerning the final number of points scored by the various teams.     

How large is income inequality in China: assessment on different estimates of Gini coefficient

The rising income inequality in China has attracted social attentions, especially since SWUFE published the unbelievably high Gini coefficient in December 2012. In order to answer the question how large income inequality in current China is, this paper compares existing different Gini coefficients estimated from four different household surveys, which are the NBS household survey, the CHIP survey, the CHFS of SWUFE, and the CFPS of Peking University, and then assesses these household surveys themselves. The relevant evidences indicate that the national Gini coefficient in current China is between 0.47~0.52. The sampling defects of the CHFS are significantly major and that the national Gini coefficient of 0.61 published by SWUFE is seriously overestimated.     

ICT and income inequality: a cross-national perspective

The importance of information and communications technology (ICT) for economic growth and development is widely researched and seemingly well understood, but the effect of such investments on income inequality is less well documented. On the one hand, improvements in infrastructure are expected to expand economic opportunities for previously underserved populations. On the other hand, ICT growth may exacerbate inequality due to differential access and skill premiums. We use panel data from 109 countries during the period 2001–2014 to examine the empirical connection between ICT and income inequality in a cross-national context. Our results suggest that the effect of ICT on income inequality depends both on the specific type of ICT and on the measure of income inequality. In addition, the magnitude of ICT’s effect on income inequality is comparable to that of more traditional forms of economic infrastructure. Finally, we find that the association between ICT and income inequality is conditional on other economic and political characteristics.     

On factor decomposition of cross-country income inequality: some extensions and qualifications

In a recent paper in this journal Duro and Esteban [Econom. Lett. 60 (1998) 269] have proposed a factor decomposition of the Theil [Economics and Information Theory, Amsterdam, North-Holland, 1967] index of inequality over per capita incomes into the (unweighted) sum of the inequality indexes of the factors in order to measure the contribution of each individual factor to the overall inequality. The purpose of this little note is to extend and qualify the meaning of such a decomposition, to show that the decomposition also holds for another Theil [Economics and Information Theory, Amsterdam, North-Holland, 1967], index of inequality and that both decompositions offer qualitatively the same general results about the contribution of the factors to aggregate inequality when applied to a particular data set, the OECD countries, although quantitative results differ.     

Factor decomposition of cross-country income inequality, 1960–1990

In this paper we present Esteban's 1994 [Esteban, J., 1994. La desigualdad interregional en Europa y en España: descripción y análisis. In: Esteban, J.M^a., Vives, X. (dirs.), Crecimiento y convergencia regional en España y en Europa, Vol. 2, Instituto de Análisis Económico] decomposition of the Theil index of inequality over per capita incomes into the (unweighted) sum of the inequality indices of (i) the productivity per employed worker, (ii) the employment rate, (iii) the active over working-age population rate, and (iv) the working-age over total population rate. Each of these factors clearly have different meanings for analysis as well as for policy. We apply this factoral decomposition to a set of 120 countries. We also contrast the empirical findings with the results obtained for the 23 OECD countries. [OECD, Labour Force Statistics, Several issues, Paris].     

Cointegration with structural changes between per capita product and income inequality in Mexico

The long-run relationship between per capita product and income inequality in Mexico is assessed for the period 1963–2010. The methodology consists of stochastic unit root techniques with structural changes. The integration and cointegration tests suggest that it is not possible to understand this link if the possibility of structural changes is not taken into account. Causality, running from per capita product to income inequality, and a negative and significant overall effect are estimated. However, after the regime shifts – mainly estimated to occur in the 1980s – the connection is no longer meaningful. This result seems to be linked to the slow growth of the Mexican economy after these structural breaks, affecting, in turn, the reductions in income inequality.     

Empirical likelihood confidence intervals for the Gini measure of income inequality

Gini coefficient is among the most popular and widely used measures of income inequality in economic studies, with various extensions and applications in finance and other related areas. This paper studies confidence intervals on the Gini coefficient for simple random samples, using normal approximation, bootstrap percentile, bootstrap-t and the empirical likelihood method. Through both theory and simulation studies it is shown that the intervals based on normal or bootstrap approximation are less satisfactory for samples of small or moderate size than the bootstrap-calibrated empirical likelihood ratio confidence intervals which perform well for all sample sizes. Results for stratified random sampling are also presented.     

A refinement of the relationship between economic growth and income inequality

There is mixed evidence in the literature of a clear relationship between income inequality and economic growth. Most of that work has focused almost exclusively on developed economies. In what we believe to be a first effort, our emphasis is solely on developing economics, which we classify as high-income and low-income developing countries (HIDC and LIDC). We make such distinction on theoretical and empirical grounds. Empirically, the World Bank has classified developing economies in this manner since 1978. The data in our sample are also supportive of such classifications. We provide theoretical scaffolding that uses asymmetric credit constraints as a premise for separating developing economies in such a way. We find strong evidence of a negative relationship between income inequality and economic growth in LIDC to be in stark contrast with a positive inequality–growth relationship for HIDC. Both correlations are statistically significant across multiple econometric specifications. Using international data from 1960 to 2010, this article explores the effect of income inequality on economic growth using dynamic panel technique, such as system generalized method of moments (GMM) that is believed to mitigate endogenous problem. These results are strikingly contrasting to the previous estimation results of Forbes (2000) displaying significant positive correlation between two variables in the short to medium term.     

The contribution of minimum wage valorization policy to the decline in household income inequality in Brazil: A decomposition approach

There is a vast literature that estimates the effect of the minimum wage on wage inequality in various countries. However, as the minimum wage directly affects nonlabor income of families in some countries (in the Brazilian case via the benefits of the pension system and of certain social programs), this article extends the empirical analysis by studying the effects of the minimum wage on the level of inequality of household income as a whole. To accomplish that we employ a decomposition method that gauges the contribution of the increases in the minimum wage that occurred in recent decades in Brazil through the labor and nonlabor sources of household income. The results show that the minimum wage had a contribution of 64 percent to the observed fall in income inequality between 1995 and 2014 and that pensions were the most relevant channel over this period.     

A Note on α‐Gini Measures

This note provides a characterization of α‐Gini inequality measures. These measures generalize the standard Gini index by including one sensitivity parameter α, which captures different value judgments. The α‐Gini measures are shown to be weakly decomposable and unit consistent. Weak decomposition provides within‐group and between‐group inequalities. Unit consistency keeps unchanged the ranking of two income distributions when the income units vary. It is shown that the α‐Gini measures are relevant with either “leftist” or“rightist” views.     

A Gini decomposition analysis of inequality in the Czech and Slovak Republics during the transition1

Disposable income inequality, as measured by the Gini coefficient and using the Family Budget Survey data, increased very little, and by a similar amount, from 1989 to 1993 in the Czech Republic and Slovakia. This surprising result is examined with an analysis of changes in the channels of redistribution and Gini decomposition. We find that the sizeable increase in overall inequality due to changes in the wage earnings component is mitigated by changes in the tax and transfer components in both republics. As for the relative effects of government policies, changes in the transfer component contributed more than changes in the tax component to lowering the growth of inequality in the Czech Republic, while the reverse was true for Slovakia.     

基尼系数的扩展与和谐社会的基石

笔者从稀缺资源的分配角度对基尼系数进行了有益的扩展,提出并论证了权力系数的合理性,结果表明:降低权力系数不仅能够促进社会公平,而且能够促进经济增长,开放的社会秩序是合适的权力系数的必然结果,也是国家长治久安、社会和谐、民族崛起的必然选择。借助于传统基尼系数的计算方法,论文给出了权力系数一种新的算法。针对中国当前转轨经济的现实,提出了实现和谐社会的必要步骤。     

Decomposing US regional income inequality from 1969 to 2009

This article analyses changes in levels and composition of income inequality among US counties from 1969 to 2009. It also decomposes inequality using the Theil coefficient into between-State and within-State inequality. The article finds that income inequality has increased in the period studied with between-State inequality decreasing and within-State inequality increasing. We subsequently decompose income inequality into the proportion arising from differences in productivity and employment–population ratios across counties. The results suggest that inequality arising from differentials in labour productivity has fallen over the period studied while those arising from employment–population ratio differences have increased.     

Calculation and decomposition of income inequality in low- and middle-income countries: a survey data analysis

This article estimates income inequality in a sample of four low- and middle-income (LMI) countries namely; Albania, Nepal, Tajikistan and Tanzania using the household survey data – Nepal Living Standard Measurement Survey Second. First, we estimate the income generation function for each country and calculate the income inequality using Gini index (GI). Second, we decompose the income Gini into the determinants of income generation functions. Based on the decomposition result, socio-economic factors are the most important determinants of income inequality followed by geographic factors. Demographic factors have the least effect on income inequality in all four countries. Third, we propose a new method to quantify the effect of change in each covariate of income generation function on income Gini. That allows us to quantify the effects of change in specific policy such as increase in investment in schooling or public health to specific group of the population in society on income inequality. A carefully chosen, integrated policy can significantly reduce inequality in all four countries under study.     

代际收入流动性与收入不平等——基于面板数据联立方程模型的分析

利用CHNS数据,在测度收入不平等的代际传递性的基础上,通过面板数据联立方程模型实证分析代际收入流动与收入不平等之间的关系。实证研究结果表明,收入不平等程度的上升阻碍了代际收入的流动,而代际收入弹性的提高也会导致收入不平等状况的恶化。     

On the Limitations of Some Current Usages of the Gini Index

This note constructs a simple two class example in which the Gini index is held constant while the size of the rich and poor populations change, in order to illustrate how very different societies can have the same Gini index and produce very similar estimates of standard inequality averse Social Welfare Functions. The rich/poor income ratio can vary by a factor of over 12, and the income share of the top one per cent can vary by a factor of over 16, with exactly the same Gini index. Focussing solely on the Gini index can thus obscure perceptions—e.g. of important market income trends or large changes in the redistributive impact of the tax and transfer system. Hence, analysts should supplement the use of an aggregate summary index of inequality with direct examination of the segments of the income distribution which they think are of greatest importance.     

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.