Economic Properties of Statistical Indices: The Case of a Multidimensional Gini Index

This paper seeks to construct a Gini index of the distribution of standard of living. Since standard of living has various dimensions, we need a multidimensional Gini index (MGI). The literature on index numbers contains two distinct approaches: the statistical and the economic. In the context of MGIs the statistical approach (which obtains the indices from conditions based on statistical or data-related considerations) seems to be open to the criticism that it sometimes yields indices that violate economic norms. However, the economic approach (where the indices are derived from norms based on economic theory) also does not seem to have succeeded so far in obtaining an MGI satisfying the various normative requirements that have been proposed in the literature. This paper shows that it is possible to obtain an MGI from the statistical approach ensuring, at the same time, that the economic norms are satisfied. In this sense it is an attempt to bring the two disparate traditions in index construction referred to above closer to each other. The index that is developed here does not appear in the existing literature. Moreover, the literature does not seem to contain any other MGI satisfying all of the proposed economic norms.

     

THE GINI-TYPE FUNCTIONS: AN ALTERNATIVE DERIVATION

The purpose of this note is to propose an alternative and intuitively simpler derivation of the Gini coefficient (in Section l), to show how it can be generalized and how then a number of coefficients (concentration coefficient, Kakwani's progressivity index) are obtained directly from this generalization (Section 2), and finally to use this approach to obtain some Gini relationships (Section 3).     

基尼系数的研究文献在过去八十年是如何拓展的

基尼系数是被最广泛应用的社会经济指标之一。它从1921年在英文的文献中出现到现在,许多学者写作并发表了大量关于基尼系数的学术文献。通览这些浩瀚的学术文献无疑是费时的。因此,这个综述的主要目的是帮助读者在比较短的时间里了解基尼系数研究的主要发展线索和理论成果,包括基尼系数的各种公式及其解释,基尼系数的社会福利涵义,以及基尼系数的收入来源和收入群体的分解。     

中国农村地区间居民收入差距及构成变化:1995—2008年——基于基尼系数的分解

本文采用分省的面板数据对农村地区间基尼系数分解结果表明,1995—2008年,中国农村地区间收入差距总体上仍然呈现上升趋势,基尼系数上升了0.0639,但增幅出现明显减弱趋势。基尼系数变化及农村居民工资性收入对基尼系数的贡献变化显示出与经济发展阶段变化一致的含义;结构性效应已不再是农村地区间收入差异的唯一构成来源,收入集中效应对基尼系数起了明显的增加作用,工资性收入的集中效应超过了其他收入来源。这些构成来源的变化蕴含着中国面临调节地区间农村收入差距的政策机遇。     

DUAL‐INDEX MEASUREMENT OF INCOME INEQUALITY

This study introduces the concept of unequally distributed income and proposes a dual‐index measurement of income inequality that evaluates the magnitude and dispersion of unequally distributed income. We use the Rawlsian index as a magnitude index and employ current income inequality indices as a dispersion index. We describe the properties of the Rawlsian and dispersion indices, and apply these indices to real income data. Further, we show that the Gini dispersion index is a weighted average of Rawlsian indices for the sub‐distributions of the unequally distributed income distribution.     

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.      

Inflation and income distribution in Central America,Mexico, Panama,and the Dominican Republic

Analyses of the impact of inflation on income distribution typically only consider the general inflation rate. However, when the consumption structure of households is shaped by its income level and inflation varies across goods and services, they are affected differently by inflation. The aim of this study is to contribute to the analysis of this effect in Central American countries (Guatemala, El Salvador, Honduras, Nicaragua, and Costa Rica), Panama, Mexico, and the Dominican Republic (CAPMDR) for the period 2007–2018. According to our findings, there have been significant differences in the inflation rates faced by different income groups. By employing these percentile‐specific inflation rates, we have computed an “inflation‐corrected Gini index.” This adjustment is important because although inequality has been decreasing during past years in the countries in our sample, on average, about half of the gains observed using the standard Gini index are lost once the Gini indices are corrected for inflation, a clearly nonnegligible magnitude.     

An Index Approach to Measuring Product Differentiation: A Hedonic Analysis of Airfares

The main objective of this paper is to introduce an Allen-type index of differentiation based on cost functions. With this index, we create an economic measure of product differentiation that quantifies differences between products. Applied research has some generally accepted economic measures, for example, the Herfindahl–Hirschman Index for market concentration, or the Gini coefficient for inequality. Product differentiation, however, does not yet have an established measure. Our objective is to fill that gap and introduce a measure that can be used in market-related applied research such as market power, antitrust, price indexes, or market strategy. To operationalize the index, we introduce the concept of a core product and use cost functions to measure the degree of differentiation from the core product. To demonstrate the use of the index, we study the effect of product differentiation on price formation in the airline industry using an enhanced hedonic model. The model is empirically tested on 103,980 observations of quarterly US domestic airfare data between 2002 and 2016 and shows that product differentiation has a significant effect on both price and mark-up.     

中国区域人才集聚合理性及其评价——中美500强企业地区分布的对比视角

本文采用中美500强企业地区分布统计数据,根据企业分布曲线,计算了中美500强企业的地区分布系数,并将此系数作为中美人才集聚度的测量指标。研究发现,我国500强企业的地区分布系数为0．58,远远高于可接受的国民收入分布（基尼）系数,但低于美国500强企业的地区分布系数。本文分析了产生此种状况的原因,展望了我国人才聚集的发展趋势,并提出了相对应的建议。     

Estimation of Concentration Measures and Their Standard Errors for Income Distributions in Poland

Measures of concentration (inequality) are often used in the analysis of income and wage size distributions. Among, them the Gini and Zenga coefficients are of greatest importance. It is well known that income inequality in Poland increased significantly in the period of transformation from a centrally planned economy to a market economy. High income inequality can be a source of serious problems, such as increasing poverty, social stratification, and polarization. Therefore, it seems especially important to present reliable estimates of income inequality measures for a population of households in Poland in different divisions. In this paper, some estimation methods for Gini and Zenga concentration measures are presented together with their application to the analysis of income distributions in Poland by socio-economic groups. The basis for the calculations was individual data coming from the Polish Household Budget Survey conducted by the Central Statistical Office. The standard errors of Gini and Zenga coefficients were estimated by means of the bootstrap and the parametric approach based on the Dagum model.     

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.     

On the impact of innovation and inequality in economic growth

We present robust results on the empirical relationship among income inequality, innovation, and economic growth for a panel dataset of 74 countries over the period 1996–2014. We estimate pairwise causality tests to show that there is bidirectional causality between GDP per capita and R&D, while R&D causes the Gini index of income inequality, and it causes human capital. Allowing coefficients to be different across cross-sections of countries, we get in any case a pairwise bi-directionality. By dynamic panel data estimations, when regressing R&D on GDP per capita, we obtain a threshold value of 0.16% of R&D such that for values above it there is economic growth. While regressing R&D on the Gini index, we get a threshold of 0.10% of R&D above which, the income distribution begins to improve. Finally, we estimate a growth equation that depends on R&D, income inequality, and physical capital. We obtain two thresholds, one of 38.79 for the Gini (above which the economic growth decreases), and one of 0.06% for R&D such that above it, economic growth is rising.     

Does income inequality hinder economic growth? New evidence using Australian taxation statistics

Using taxation statistics, we first derive consistently defined Gini coefficients for the period 1942–2013 for Australia as a whole as well as its eight states and territories. While income inequality exhibited a downward trend until 1979, it has since been on the rise not only over time, but also across states and territories. We then proceed to examine the effect of inequality on economic growth after controlling for changes arising from investment in physical and human capital using available panel data across all states and territories (1986–2013). We find that inequality adversely affects economic growth with a couple of years delay, an outcome consistent with similar studies undertaken in the United States and Europe. Our findings suggest that policymakers can address rising income inequality by implementing measures that support, and enhance, human capital accumulation given its long-run economic and social benefits.     

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。     

EVIDENCE ON RELATIONSHIPS AMONG ALTERNATIVE MEASURES OF CONCENTRATION: A TOOL FOR ANALYSIS OF LDC INEQUALITY

The evidence on economic inequality in nearly all developing countries is both seriously incomplete and of moderate to poor quality. In addition, information often corresponds to distributions which appear to be less revealing and useful than other ones; thus it can be argued that the frequently available distribution of income among households ranked by household income is less helpful than the seldom found distribution of consumption among persons ranked by per capita household consumption. Whether one's objective is to assess inequality in some absolute sense or (especially) to make comparisons across countries or evaluate trends over time, it is useful to know whether systematic relationships exist among various measures of inequality, in particular between those most commonly available and those conceptually most interesting. Illustrative comparisons of a variety of inequality indicators are presented. They suggest that in developing countries the concentration of income among persons (assuming equal distribution within the family) does not differ much from the concentration among households. They also suggest that the concentration of consumption is somewhat less unequal than that of income, the ratio of the respective Gini coefficients tending to cluster around 0.85 to 0.90.     

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 COMPARISON OF DISTRIBUTIONS OF ANNUAL AND LIFETIME INCOME: SWEDEN AROUND 1970.

The concern with income distribution has always mainly existed because of a concern with individuals' economic welfare. In recent years, the question has arisen whether the distribution of annual income—the distribution most often studied—is the best proxy for the distribution of economic welfare. Other measures, such as lifetime income, have been proposed instead.
The paper starts with a discussion of how to define and measure the distribution of lifetime income. By using a simulation model, which partly consists of estimated functions and partly of tax functions taken directly from tax laws, distributions of lifetime income, variously defined, are then constructed. These distributions are compared with each other, and with distributions of annual income. The simulations indicate that the distribution of lifetime income is considerably less unequal than the distribution of annual income. Whether inheritances are included or not seems to be of no importance for the inequality of lifetime income. If, on the other hand, we include the value of leisure time in lifetime income, inequality increases by about 10–15 percent. Distributions of income after tax have Gini coefficients which are approximately 25 percent less than the Ginis for the before-tax distributions. We thus find that the picture of inequality we get is very much dependent on which income concept we use.     

产业地理集中度测度方法研究

产业空间集聚研究对于制定产业政策、促进区域经济发展具有重要意义。其研究依赖于对产业地理分布状况的准确测度。产业空间分布一直是经济地理学研究的热点,因此发展了多种产业地理集中测度方法。传统的Herfindahl指数、区位Gini系数是衡量产业地理集中程度最为常用的方法。近年来新发展的E—G指数、M—S指数、L函数、D函数、M函数是对传统方法的重要补充和提高,极大促进了产业地理集中研究的发展。上述方法可以分成两类:单一地理尺度方法和基于距离的多空间尺度方法。不同的方法各有成功和不足之处。文章对已有方法进行了全面分析,并对进一步发展的方向提出了一些见解,以促进对这些方法的正确理解和运用。     

Distributional national accounts for the Netherlands and a comparison with 12 other countries

Most inequality studies rely on micro data that do not capture a substantial share of income identified in the national accounts. In the Netherlands, almost one fifth of household disposable income is missed by current inequality statistics. In this paper, we present inequality statistics for the Netherlands that capture all of household income, so-called distributional national accounts. Compared to the current inequality statistics, the Gini coefficient for disposable income increases substantially from 0.289 to 0.337. Cross-country comparisons show that such a change between Gini coefficients based on micro-data versus Gini coefficients based on distributional national accounts does not apply to all countries. The difference between both Gini coefficients varies not only between countries in the size, but also in the sign of the difference.     

我国地区间公共福利基尼系数及其经济增长效应研究

本文采用1995—2007年我国31个省(市)的福利性财政支出数据,应用基尼系数方法测算了我国省(市)间的公共福利差距。通过分解计算基尼系数的地区构成,发现东、中、西部地区间的经济差距是我国福利性财政支出差异的主要表现方面。鉴于此,本文利用VAR模型和脉冲响应函数,计算并比较东、中、西部地区福利性财政支出基尼系数的经济增长效应差异性。结果表明:东、中部地区公共福利基尼系数的经济增长效应正负交替出现,但最终负向且趋于平稳;而西部地区公共福利的经济增长效应则一直是负向且稳定的。