DOCSLIB.ORG

Comparison of the Gini and Zenga Indexes Using Some Theoretical Income Distributions Abstract

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Comparison of the Gini and Zenga Indexes Using Some Theoretical Income Distributions Abstract OPERATIONS RESEARCH AND DECISIONS No. 1 2013 DOI: 10.5277/ord130104 Katarzyna OSTASIEWICZ * Edyta MAZUREK* COMPARISON OF THE GINI AND ZENGA INDEXES USING SOME THEORETICAL INCOME DISTRIBUTIONS ABSTRACT The most common measure of inequality used in scientific research is the Gini index. In 2007, Zenga proposed a new index of inequality that has all the appropriate properties of an measure of equality. In this paper, we compared the Gini and Zenga indexes, calculating these quantities for the few distributions frequently used for approximating distributions of income, that is, the lognormal, gamma, inverse Gauss, Weibull and Burr distributions. Within this limited examination, we have ob- served three main differences. First, the Zenga index increases more rapidly for low values of the var- iation and decreases more slowly when the variation approaches intermediate values from above. Se- cond, the Zenga index seems to be better predicted by the variation. Third, although the Zenga index is always higher than the Gini one, the ordering of some pairs of cases may be inverted. Keywords: inequality, Gini index, Zenga index 1. Introduction During the last few decades, inequalities have played an important role in many branches of social science, mainly sociology and economics, being one of the key issues in the discourse regarding the well-being of societies and individuals (see, e.g. [6, 11, 13]). Thus, there appears a question of how to measure these inequalities ap- propriately. There exist many inequality indexes in the literature, e.g. the most popular ones, namely, the Gini index, Theil index and Atkinson measure [11]. Out of these, the Gini index [5] is most frequently used and also best known to non-scientists. Re- cently, a new inequality index was proposed by Zenga [15]. It has all the properties _________________________ *Department of Statistics, Wrocław University of Economics, Komandorska118/120, 53-345 Wro- cław, e-mail addresses: [email protected], [email protected] 38 K. OSTASIEWICZ, E. MAZUREK that are usually required for inequality measures (e.g. the Pigou–Dalton transfer prin- ciple or income scale independence [2, 12]). In order to decide which measure of ine- quality is most suitable for a given subject, it would be helpful to investigate and com- pare the properties of different indexes. The aim of this paper was to compare the values of the Gini and Zenga indexes by applying them to some theoretical distributions. As our main concern will be econom- ic inequalities, we will concentrate on distributions that are commonly used as approx- imations of real income distributions [4, 10], that is, the lognormal, gamma, inverse Gauss, Weibull and Burr distributions. We will present how these inequality indexes depend on skewness and variation. In four cases (lognormal, gamma, inverse Gauss, Weibull distributions) skewness is a unique, monotonic function of the variation, thus the relation between any index and either skewness or variation may be easily recov- ered from the relation between the index and the other. In the case of the Burr distribu- tion, a fixed value of skewness may correspond to various values of the variation and vice versa. Therefore, we should examine how these inequality indexes depend on the variation and skewness separately for this case. In what follows, we will also briefly analyze some examples of the generalized Burr distribution of the second kind and one instance of a bimodal distribution, to draw more conclusions regarding how ine- quality measures depend on the variation and skewness. The paper is organized as follows. In the next section, we briefly introduce the concept of the Zenga index. Section 3 is devoted to the methodology of the research, that is, the quantities and relations used in the subsequent sections have been defined. In sections 4–8 we examine the Zenga index and its relation to the Gini index for five different classes of distributions. Section 9 presents an in depth overview of the com- bined results from sections 4–8, while the final section contains some conclusions and a summary of the paper. 2. The Zenga index of inequality In a series of papers, Zenga (e.g. [7, 9, 14, 15]) proposed a measure of inequality based on the inequality curve I(p), which is defined in terms of the lower and upper arithmetic means of a distribution. This idea of measuring income inequality consists of comparing the arithmetic means of the incomes of two groups, called the lower and upper groups. The division of the ordered data into two groups is made by choosing a point of division. At one extreme, the lower group consists of only the lowest observation. At the other ex- treme, the upper group consists of only the greatest income. Let Comparison of the Gini and Zenga indexes 39 ⎧⎫s ⎨⎬()x jj,:1,,;0nj=≤<<<=…… s xx12 x s ; ∑ nN j ⎩⎭j =1 denote the frequency distribution of a nonnegative random variable X. Next, let us divide this distribution into two parts, the lower and upper group, respectively: ()()x11,,,,,,nxn 2 2… xnjj, xnjj,, x j++11 , n j ,,,… () xn ss . For each point of { ( )} {( )( ) } + division, it is possible to define the lower mean M ()p j and upper mean M ()p j of the divided distribution as follows: 1 j M ()pxnjsjii==∑ ,1,,… (1) N j i=1 + 1 s M ()pxnjsjii==∑ ,1,,… (2) NN− j−1 ij= j N j where: Nnj = ∑ i and p j = . i=1 N + + Comparing M ( p j ) and M ()p j using the index Up()jjj= Mp()/, Mp ()we get a point measure of the uniformity of the distribution. Up( j ) × 100 gives the lower mean as a percentage of the upper mean. The point inequality index is defined in terms of Up( j ) as: Ip( j ) =−1 Up( j ) (3) The synthetic inequality measure proposed by Zenga [15] is the following weighted arithmetic mean of the point measures I( pj): s n j ZIp= ∑ ()j (4) j =1 N Both U( pj) and I( pj) take values between 0 and 1 inclusively. In particular: x1 M x1 M Up()1 = , Up()s = , Ip()1 =−1, Ip()s =−1 M xs M xs 40 K. OSTASIEWICZ, E. MAZUREK where M is the mean of all the observations. The Zenga index takes the value 0 in the case of no inequality. The shape of the Ip( j ) curve as a function of pj is not constrained by fixed points (0, 0) and (1, 1), as in the case of the Lorenz curve [3, 8] (also, see [15] for many illustrative examples). It has been proven that the Zenga index is characterized by all the main properties that any inequality measure should satisfy (see e.g. [2]). 3. Comparison of the Zenga and Gini indexes In what follows, we compare the values of the Gini and Zenga indexes, calculated for some (theoretical) income distributions. These distributions are standard distribu- tions used to simulate distributions of real incomes, that is, the lognormal, Gamma, inverse Gauss, Weibull and Burr distributions. Our aim here is to investigate the dependence of both the Gini and Zenga indexes on the variation and skewness for each family of distributions. For distributions char- acterized by a single shape parameter (i.e. the lognormal, gamma, inverse Gauss and Weibull distributions), the skewness can be obtained from the variation and vice versa and thus there should be a unique function describing each of the inequality indexes on the variation (and skewness), while in the case of distributions with two shape pa- rameters (the Burr distribution here) we can expect, in general, different relations be- tween these inequality indexes and the variation (for constant and different values of skewness) and vice versa. We will then examine the (eventual) differences in how these inequality indexes depend on the variation. We will also examine for each distri- bution the inter-dependence between the Zenga index and the Gini index. We will adopt the following quantities as measures of variation and skewness. To measure variation, we will use the classical coefficient of variation: Var()X V = EX() where Var( X ) denotes the variance and E( X ) is the expected value of the random variable X. We will measure the skewness in terms of the third standardized moment, that is: 3 EX(()− EX()) As = Var()X 3/2 where E(·) again denotes the expected value. Comparison of the Gini and Zenga indexes 41 It is well known (see e.g. [1]) that one of the most essential properties of an income distribution is the existence of only a small number of finite moments (e.g. the Burr distribution). Hence, the parametric space in which our investigations of the inequality indexes are possible is reduced (as the existence of the first moment is necessary to de- fine both the Gini and Zenga indexes). Measuring variation and skewness in terms of the classical measures defined above reduces the parametric space even more. However, as we do not claim to investigate the whole range of the parameter space thoroughly, we will still use these classical quantities to make the results easily interpretable (the orders of magnitude of these parameters for typical income distributions are known). As for calculating the Gini and Zenga indexes, and, correspondingly, the Lorenz curve and I(p) curve, we performed numerical calculations according to the general formulas. For any continuous distribution D with probability density function f ()x , x cumulative probability density function F ()xfydy= ∫ () , and mean value −∞ ∞ myfydy= ∫ () , the Gini index may be calculated using: −∞ 1 ∞ GFxFxdx=−∫ ()()1 () (5) m −∞ As for the Zenga index, the continuous counterpart of (4) reads as follows: ∞ Z = ∫ Ixfxdx()() (6) −∞ where x ∫ yf() y dy −∞ Ix()=−1 ∞ ∫ yf() y dy x 1− F ()x The Lorenz curve is expressed as a function of the cumulative distribution: Fx−1 () 1 LFx()()= ∫ xfxdx() (7) m −∞ 42 K.
Load more

Recommended publications
  • Inequality Measurement Development Issues No
    Development Strategy and Policy Analysis Unit w Development Policy and Analysis Division Department of Economic and Social Affairs Inequality Measurement Development Issues No. 2 21 October 2015 Comprehending the impact of policy changes on the distribu- tion of income first requires a good portrayal of that distribution. Summary There are various ways to accomplish this, including graphical and mathematical approaches that range from simplistic to more There are many measures of inequality that, when intricate methods. All of these can be used to provide a complete combined, provide nuance and depth to our understanding picture of the concentration of income, to compare and rank of how income is distributed. Choosing which measure to different income distributions, and to examine the implications use requires understanding the strengths and weaknesses of alternative policy options. of each, and how they can complement each other to An inequality measure is often a function that ascribes a value provide a complete picture. to a specific distribution of income in a way that allows direct and objective comparisons across different distributions. To do this, inequality measures should have certain properties and behave in a certain way given certain events. For example, moving $1 from the ratio of the area between the two curves (Lorenz curve and a richer person to a poorer person should lead to a lower level of 45-degree line) to the area beneath the 45-degree line. In the inequality. No single measure can satisfy all properties though, so figure above, it is equal to A/(A+B). A higher Gini coefficient the choice of one measure over others involves trade-offs.
    [Show full text]
  • Inequality of Opportunity: a Parametric Approach
    23rd Public Economics Meeting, University of Vigo February 4 and 5, 2016 Inequality of Opportunity: a Parametric Approach Jos´eMar´ıaSarabia1, Vanesa Jord´a,Faustino Prieto Department of Economics, University of Cantabria, Avda de los Castros s/n, 39005-Santander, Spain Abstract In this paper we measure the extent of inequality of opportunity us- ing a new parametric approach. We rely on the idea that differences in earning can be ethically fair if they come from choices that indi- viduals are completely responsible for, called efforts. Unacceptable disparities are those come from external factors called circumstances. We use a flexible parametric form to model the joint distribution of circumstances and efforts. Our model avoids the need to break con- tinuous variables of circumstances into groups, while also allowing for the use of categorical variables such as gender or race. Using data from Living Conditions Survey, we estimate the level of inequality of opportunity in Spain in 2005. Our results are robust to different parametric functional forms and indicators of parental education. JEL Classification: D31, D63, J62 Key Words: Multivariate distributions; Inequality of opportunity; Theil in- dices; Decompositions 1 Introduction Income inequality has been of great interest in the economic literature, be- ing also a sort of concern as regards redistribution policies. It is however argued that disparities driven by different levels of efforts of individuals are 1E-mail addresses: [email protected] (J.M. Sarabia). 1 less objectionable than those arise from differences in the characteristics of these individuals which are exogenous to them. Among the last kind of fea- tures we can highlight race, gender, familiar background or region, among others.
    [Show full text]
  • On the Accuracy of Inequality Measures Calculated from Aggregated Data
    ARGUMENTA OECONOMICA No 1 (42) 2019 PL ISSN 1233-5835 ∗ Katarzyna Ostasiewicz*, Edyta Mazurek* ON THE ACCURACY OF INEQUALITY MEASURES CALCULATED FROM AGGREGATED DATA Our aim in this study is to compare the typically used methods of calculating inequality measures for aggregated data with the modified approaches by the relative error. We start with the individual observations (obtained from the tax office) and calculate the exact values of a few inequality measures. Then, we construct the interval distribution in the form that is usually available in the statistical yearbooks. The standard approach is to treat all observations from a given class as if concentrated in the exact middle of this class. We have investigated a few other approaches, including the one that assumes the knowledge of the accurate mean values of subsequent classes (although these exact means are usually not available).The accuracy of each method is rated by comparing the results obtained by different methods with the exact ones. The inequality measures which are the matter of interest here are the Gini index which is the most commonly used, and also the Theil and Atkinson indexes. Keywords: the Gini index, the Theil index, the Atkinson index, aggregated data JEL Classifications: C4, C8, J3 DOI: 10.15611/aoe.2019.1.04 1. INTRODUCTION Measuring the inequalities of income distribution is an important issue nowadays and the accuracy of the calculations of the measures has become a challenge to be faced (Jędrzejczak, 2012). The problem of the measurement of inequalities of income distribution is relevant to the measurement of the justice and progression of the taxation (Monti, Pellegrino and Vernizzi 2015; Mazurek, Pellegrino and Vernizzi 2015; Pellegrino and Vernizzi 2013).
    [Show full text]
  • Water Use Inequality and Efficiency Assessments in the Yangtze River
    water Article Water Use Inequality and Efficiency Assessments in the Yangtze River Economic Delta of China Pius Babuna 1,2 , Xiaohua Yang 1,* and Dehui Bian 1 1 School of Environment, Beijing Normal University, Beijing 100875, China; [email protected] (P.B.); [email protected] (D.B.) 2 Department of Geography and Environmental Science, the University of Reading, Reading RG6 6AB, UK * Correspondence: [email protected]; Tel./Fax: +86-10-588-060-50 Received: 9 May 2020; Accepted: 12 June 2020; Published: 15 June 2020 Abstract: The Yangtze River Economic Delta (YRED) faces inequality in water use in large proportions due to rapid industrialization. This study adopted the Gini coefficient and Global Moran’s index to calculate inequality, its spatial spread and water use efficiency of cities in the YRED and categorized them into types based on the spatial spread of inequality. In general, inequality is reducing, but water use efficiency is poor. Inequality was rated 0–1; zero being the highest equality while 1 indicates the highest inequality. There is relatively high inequality (0.4–0.5) in Shanghai, Suzhou and Hefei. Most cities (20), however, showed equality (below 0.2). Nine (9) cities showed relative equality (0.2–0.3), while Wuxi, Bengbu and Zhenjiang were neutral (0.3–0.4). No city scored above 0.5. Water use efficiency in the majority of cities was poor. Only 11 out of 35 cities scored more than 50% efficiency. Poor irrigation, income and industrial water demand are the factors driving inefficiency and inequality. The categorization of cities into groups produced nine city types according to the spatial disposition of inequality.
    [Show full text]
  • Decomposition of the Inequality of Income Distribution by Income Types—Application for Romania
    entropy Article Decomposition of the Inequality of Income Distribution by Income Types—Application for Romania Tudorel Andrei 1,*, Bogdan Oancea 2, Peter Richmond 3, Gurjeet Dhesi 4 and Claudiu Herteliu 1,* 1 Department of Statistics and Econometrics, Bucharest University of Economic Studies, Bucures, ti 010374, Romania 2 Department of Economic and Administrative Sciences, University of Bucharest, Bucures, ti 050107, Romania; [email protected] 3 School of Physics, Trinity College Dublin, Dublin 2, Ireland; [email protected] 4 School of Business, London South Bank University, London SE1 0AA, UK; [email protected] * Correspondence: [email protected] or [email protected] (T.A.); [email protected] or [email protected] (C.H.); Tel.: +40-722-455-586 (C.H.) Received: 31 July 2017; Accepted: 16 August 2017; Published: 1 September 2017 Abstract: This paper identifies the salient factors that characterize the inequality income distribution for Romania. Data analysis is rigorously carried out using sophisticated techniques borrowed from classical statistics (Theil). Decomposition of the inequalities measured by the Theil index is also performed. This study relies on an exhaustive (11.1 million records for 2014) data-set for total personal gross income of Romanian citizens. Keywords: income inequality; Theil index; disjoint groups; decomposition 1. Introduction Many analyses of income distributions have been made over the years by economists and econophysicists (for example: [1–14]). Of special interest in all these analyses are income distribution and income inequality (see for example: [15–27]). Several distribution functions have been proposed to describe the income distribution, of which the lognormal-Pareto [28] and exponential-Pareto distributions [29,30] best fit the empirical data.
    [Show full text]
  • An Analysis of Inequality Measures and Common Datasets
    An Analysis of Inequality Measures and Common Datasets Chandini Sankaran – University of Wisconsin – Stevens Point Abstract Results from studies of within-country income inequality are inconclusive and sometimes contradictory. This paper emphasizes that these varied findings may be due to differences in the datasets used. There are four major indices to measure inequality within societies, income shares, income ratios, the gini index, and the theil index. Common datasets include the World Development Indicators Database (World Bank 2003b), Deininger and Squire’s (1996) database, and the theil index compiled through the University of Texas Inequality Project (UTIP 2005). This paper discusses the strengths and weaknesses of these measures, and investigates the comparability of these datasets. Findings indicate that UTIP’s (2005) theil dataset is not strongly correlated with the inequality measures from the World Bank data base (World Bank 2003b) and the Deininger and Squire’s inequality measures. Since their theil dataset is based on manufacturing wage and employment data, it does not accurately reflect society-wide income inequality. There is indication that wages within the manufacturing sector are less spread out than society-wide wages. Findings also indicate inconsistency in Deininger and Squire’s (1996) income inequality database. Finding a uniform and comprehensive dataset of income inequality still remains a challenge. Until then, researchers and policymakers should proceed with caution when interpreting the results of studies on inequality, keeping in mind the drawbacks of the existing measures. Introduction Simon Kuznets (1955) in a study of income inequality within and between the agricultural and non-agricultural sectors of three countries over the process of development, hypothesized that economic progress initially causes rising inequality within a country, but as the country develops further this inequality falls.
    [Show full text]
  • A Simple Method for Measuring Inequality ✉ Thitithep Sitthiyot 1 & Kanyarat Holasut2
    ARTICLE https://doi.org/10.1057/s41599-020-0484-6 OPEN A simple method for measuring inequality ✉ Thitithep Sitthiyot 1 & Kanyarat Holasut2 ABSTRACT To simultaneously overcome the limitation of the Gini index in that it is less sensitive to inequality at the tails of income distribution and the limitation of the inter-decile ratios that ignore inequality in the middle of income distribution, an inequality index is introduced. It comprises three indicators, namely, the Gini index, the income share held by the top 10%, and the income share held by the bottom 10%. The data from the World Bank 1234567890():,; database and the Organization for Economic Co-operation and Development Income Dis- tribution Database between 2005 and 2015 are used to demonstrate how the inequality index works. The results show that it can distinguish income inequality among countries that share the same Gini index but have different income gaps between the top 10% and the bottom 10%. It could also distinguish income inequality among countries that have the same ratio of income share held by the top 10% to income share held by the bottom 10% but differ in the values of the Gini index. In addition, the inequality index could capture the dynamics where the Gini index of a country is stable over time but the ratio of income share of the top 10% to income share of the bottom 10% is increasing. Furthermore, the inequality index could be applied to other scientific disciplines as a measure of statistical heterogeneity and for size distributions of any non-negative quantities.
    [Show full text]
  • Package 'Acid'
    Package ‘acid’ February 1, 2016 Type Package Title Analysing Conditional Income Distributions Version 1.1 Date 2016-02-01 Author Alexander Sohn Maintainer Alexander Sohn <[email protected]> Description Functions for the analysis of income distributions for subgroups of the population as de- fined by a set of variables like age, gender, region, etc. This entails a Kolmogorov- Smirnov test for a mixture distribution as well as functions for moments, inequality mea- sures, entropy measures and polarisation measures of income distributions. This pack- age thus aides the analysis of income inequality by offering tools for the exploratory analy- sis of income distributions at the disaggregated level. Depends gamlss,gamlss.dist,Hmisc,stats,graphics,splines Imports grDevices,utils,datasets,methods Suggests ineq License GPL-3 NeedsCompilation no Repository CRAN Date/Publication 2016-02-01 13:34:52 R topics documented: acid-package . .2 arithmean.GB2 . .3 atkinson . .4 atkinson.den . .5 atkinson.GB2 . .6 atkinson.md . .8 cdf.mix.dag . .9 cdf.mix.LN . 10 coeffvar . 11 1 2 acid-package confband.kneib . 12 confband.pw . 13 dat.............................................. 14 den.md . 15 dist.para.t . 16 entropy . 17 entropy.GB2 . 18 entropy.md . 19 frac.ranks . 21 gini ............................................. 21 gini.Dag . 22 gini.den . 23 gini.gamma . 24 gini.md . 25 ineq.md . 26 km.GB2 . 28 midks.plot . 29 midks.test . 30 params . 32 pens.parade . 32 polarisation.EGR . 33 polarisation.ER . 35 pval.md . 37 sadr.test . 38 sd.GB2 . 46 sgini . 47 sgini.den . 48 skewness.GB2 . 49 theil.gamma . 50 weighted.atkinson . 51 weighted.coeffvar . 52 weighted.entropy .
    [Show full text]
  • Robust Estimation of Inequality from Binned Incomes
    Sociological Methodology, 2016 Robust estimation of inequality from binned incomes Paul T. von Hippel (University of Texas, Austin) Samuel V. Scarpino (Santa Fe Institute) Igor Holas (University of Texas, Austin) Correspondence: Paul T. von Hippel, LBJ School of Public Affairs, University of Texas, 2315 Red River, Box Y, Austin, TX 78712, [email protected]. Contributors: Von Hippel conceived the study, led the writing, and developed and ran the Stata code. Scarpino developed and ran the R code. Holas summarized the results. Acknowledgments: von Hippel and Holas were supported in part by a New Scholar Grant from the Stanford Center on Poverty and Inequality and by a grant from the Policy Research Institute at the University of Texas. Scarpino was supported by a National Science Foundation Graduate Research Fellowship, by the Santa Fe Institute, and by the Omidyar Group. Bios: Paul T. von Hippel’s research interests include family and school influences on academic achievement. With Holas and Scarpino, he has applied the methods here to another paper titled “Secession of the Successful or Millionaires Next Door? Trends in family income inequality, within and between school districts, 1970-2009.” Samuel V. Scarpino is an Omidyar Fellow at the Santa Fe Institute and an incoming Assistant Professor in the Department of Mathematics and Statistics and the Complex Systems Center at the University of Vermont. His research primarily focuses on the evolutionary and population dynamics of infectious diseases. Sam earned a Ph.D. in Integrative Biology from the University of Texas at Austin. Igor Holas is a PhD candidate in Human Development and Family Science at the University of Texas, and co-founder and CEO of Mentegram, which helps mental health professionals to provide remote monitoring and remote interventions.
    [Show full text]
  • Income Inequality Within Smallholder Irrigation Schemes in Sub-Saharan Africa
    International Journal of Water Resources Development ISSN: 0790-0627 (Print) 1360-0648 (Online) Journal homepage: http://www.tandfonline.com/loi/cijw20 Income inequality within smallholder irrigation schemes in Sub-Saharan Africa Ana Manero To cite this article: Ana Manero (2017) Income inequality within smallholder irrigation schemes in Sub-Saharan Africa, International Journal of Water Resources Development, 33:5, 770-787, DOI: 10.1080/07900627.2016.1152461 To link to this article: https://doi.org/10.1080/07900627.2016.1152461 © 2016 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group Published online: 02 Mar 2016. Submit your article to this journal Article views: 723 View Crossmark data Citing articles: 4 View citing articles Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=cijw20 INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT, 2017 VOL. 33, NO. 5, 770–787 https://doi.org/10.1080/07900627.2016.1152461 Income inequality within smallholder irrigation schemes in Sub-Saharan Africa Ana Maneroa,b aCrawford School of Public Policy, Australian National University, Canberra; bSchool of Commerce, University of South Australia, Adelaide ABSTRACT ARTICLE HISTORY Equitable income distribution is recognized as critical for poverty Received 8 September 2015 reduction, particularly in developing areas. Most of the existing Revised 20 January 2016 literature is based on region- or country-wide data; fewer empirical Accepted 6 February 2016 studies exist at community levels. This article examines income KEYWORDS disparities within six smallholder irrigation schemes in Zimbabwe, Income inequality; Tanzania and Mozambique, comparing inequality at local and national agriculture; poverty; Gini levels, as well as decomposing inequality by group and by source.
    [Show full text]
  • EASYPOL MODULE 051 Theil Index and Enropy Class Indexes
    Describing Income Inequality Theil Index and Entropy Class Indexes Module 051 Describing Income Inequality Theil Index and Entropy Class Indexes Describing Income Inequality Theil Index and Entropy Class Indexes by Lorenzo Giovanni Bellù, Agricultural Policy Support Service, Policy Assistance Division, FAO, Rome, Italy and Paolo Liberati, University of Urbino, "Carlo Bo", Institute of Economics, Urbino, Italy for the Food and Agriculture Organization of the United Nations, FAO About EASYPol EASYPol is a an on-line, interactive multilingual repository of downloadable resource materials for capacity development in policy making for food, agriculture and rural development. The EASYPol home page is available at: www.fao.org/tc/easypol. EASYPol has been developed and is maintained by the Agricultural Policy Support Service, Policy Assistance Division, FAO. The designations employed and the presentation of the material in this information product do not imply the expression of any opinion whatsoever on the part of the Food and Agriculture Organization of the United Nations concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. © FAO December 2006: All rights reserved. Reproduction and dissemination of material contained on FAO's Web site for educational or other non-commercial purposes are authorized without any prior written permission from the copyright holders provided the source is fully acknowledged. Reproduction of material for resale or other commercial purposes is prohibited without the written permission of the copyright holders. Applications for such permission should be addressed to: [email protected]. Describing Income Inequality Theil Index and Entropy Class Indexes Table of contents 1.
    [Show full text]
  • An Integrated Approach for Top-Corrected Ginis
    DISCUSSION PAPER SERIES IZA DP No. 10573 An Integrated Approach for Top-Corrected Ginis Charlotte Bartels Maria Metzing FEBRUARY 2017 DISCUSSION PAPER SERIES IZA DP No. 10573 An Integrated Approach for Top-Corrected Ginis Charlotte Bartels DIW Berlin and IZA Maria Metzing DIW Berlin FEBRUARY 2017 Any opinions expressed in this paper are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but IZA takes no institutional policy positions. The IZA research network is committed to the IZA Guiding Principles of Research Integrity. The IZA Institute of Labor Economics is an independent economic research institute that conducts research in labor economics and offers evidence-based policy advice on labor market issues. Supported by the Deutsche Post Foundation, IZA runs the world’s largest network of economists, whose research aims to provide answers to the global labor market challenges of our time. Our key objective is to build bridges between academic research, policymakers and society. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author. IZA – Institute of Labor Economics Schaumburg-Lippe-Straße 5–9 Phone: +49-228-3894-0 53113 Bonn, Germany Email: [email protected] www.iza.org IZA DP No. 10573 FEBRUARY 2017 ABSTRACT An Integrated Approach for Top-Corrected Ginis* Household survey data provide a rich information set on income, household context and demographic variables, but tend to under report incomes at the very top of the distribution.
    [Show full text]