Gini Coefficient

11 Key excerpts on "Gini Coefficient"

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  The Politics of Inequality

  • Carsten Jensen, Kees Van Kersbergen(Authors)
  • 2016(Publication Date)
  • Red Globe Press

    (Publisher)

  If everybody has the same income, the Gini Coefficient is 0 (perfect equality), and it is 1 if all income belongs to one person alone (perfect inequality). These extremes are never approached. In modern societies, the Gini Coefficient normally ranges between 0.2 and 0.5, and year-on-year changes rarely exceed 0.01. Despite its popularity, the Gini Coefficient has some shortcomings. The most important one is that there is little information about the shape of the income distribution contained in the Gini Coefficient. The prob- lem is that many different income distributions can generate the same coefficient. Table 4.1 provides an example of this. The five quintiles in Person no.1 Accumulated income 50 99 B A 100% 50% 80 15% 70% 90 Source: Created by the authors. Figure 4.2 The Lorentz curve 40 The Politics of Inequality both Distributions I and II have an accumulated income of 10,000 and a Gini Coefficient of 0.2. This means that to obtain perfect equality, the same amount of money needs to be reallocated in the two distributions. This is valuable knowledge, but looking more closely at the distribu- tions, it becomes clear that they are very different from each other. In Distribution I, the poorest quintile makes 1000 and the richest 3000, leading to a 5:1 ratio of 3. In Distribution II, the poorest quintile earns 450, compared with 2750 for the richest. This implies a 5:1 ratio of 6.11, or twice the size of the one in Distribution I. In this example, then, the same Gini Coefficient masks dramatically different ratios of top vs. bottom earners. A related shortcoming is that the Gini Coefficient is particularly sensi- tive to changes in the middle of the income distribution (Atkinson 1970: 256–7). Table 4.1 illustrates the problem. In Distribution III, quintile 3, i.e. the median income segment, only earns 1600 rather than 2000 as in Distribution I. The total income is still 10,000 and the 5:1 ratio remains 3, as in Distribution I.

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  Societal Problems as Public Bads

  • Nan Dirk de Graaf, Dingeman Wiertz, Nan de Graaf(Authors)
  • 2019(Publication Date)
  • Routledge

    (Publisher)

  Figure 7.1 . This curve essentially plots how much of the total national income is earned by the poorest X percent of the country’s population. If income is distributed completely equally across all citizens, the curve will be a straight diagonal line: e.g., the poorest ten percent of the population earn ten percent of the national income, the poorest 50 percent earn 50 percent of the national income, the poorest 90 percent earn 90 percent of the national income. The larger the degree of curvature of the Lorenze curve, the more unequal the income distribution: e.g., the poorest ten percent of the population earn 0.0001 percent of the national income, the poorest 50 percent earn one percent of the national income, the poorest 90 percent earn three percent of the national income (leaving 97 percent of the national income for the richest ten percent). As such, the Lorenz curve provides a convenient way of eyeballing how much inequality there is within a group, a society, or across a selection of countries.

  Figure 7.1     The Lorenz curve and the Gini Coefficient

  The Gini Coefficient or Gini index , in turn, provides a quantitative measure of inequality. It ranges from zero to one, where zero corresponds to a situation of complete equality (sticking to the example of the income distribution within a country, this would mean that every citizen earns the same income) and one corresponds to a situation of complete inequality (one citizens earns all of the income and everyone else earns nothing). In between zero and one, higher values correspond to a greater degree of inequality. Therefore, the Gini Coefficient can broadly be interpreted as the percentage of national income that needs to be redistributed in order to achieve a perfectly equal distribution.

  The Gini Coefficient bears a direct relationship to the Lorenz curve. That is, it can be calculated by dividing the size of area A (i.e., the area between the diagonal line of equality and the Lorenz curve) by the sum of areas A plus B; see Figure 7.1 . In equation form: Gini = A / (A + B)

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  World on the Move

  Consumption Patterns in a More Equal Global Economy

  • Paolo Mauro, Tomas Hellebrandt, Jan Zilinsky(Authors)
  • 2016(Publication Date)
  • Peterson Institute for International Economics

    (Publisher)

  This chapter examines how economists measure inequality. It discusses the challenges posed by survey data and explains a novel method of reconciling surveys with national account measures of household consumption. This method results in higher estimates of inequality within countries than indicated by survey data alone. The chapter then discusses recent trends in inequality within countries and the cross-country relationship between inequality and the level of development. The results can be used to inform projections of within-country inequality into the future.

  How Do Economists Measure Inequality? Key Concepts and Issues

  The most straightforward way of finding out about individuals’ incomes or consumption is to ask them directly. A household survey can provide a good approximation of the distribution of living standards in the population at large, provided that its sample is nationally representative and respondents answer honestly.

  The Gini Index

  Suppose all households participating in a survey are lined up in ascending order of household income. How would one capture the income disparities between them in a single number? Many measures have been put forward over the years, with different properties and varying degrees of relevance, depending on the specific question one is trying to answer (see Cowell 2011 for a discussion).

  The best-known and most widely used measure of inequality is the Gini index (also referred to as the Gini Coefficient). It is presented by means of the Lorenz curve, which plots the proportion of the total income of the population that is cumulatively earned by the bottom x percent of the population. The Gini index is equal to the ratio of the area (G) between the Lorenz curve and the line of perfect equality to the area of the triangle ABC in figure 3.1 . It takes values between 0 and 100. Perfect equality is achieved when the bottom x percent of the population receives x percent of total income, in which case the Lorenz curve overlaps with the line of perfect equality and the Gini index equals zero. Perfect inequality occurs when all income goes to a single person, in which case the Lorenz curve is ABC in figure 3.1

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  Occupational and Residential Segregation

  • Jacques Silber, Yves Fluckiger, Sean F. Reardon, Jacques Silber, Yves Fluckiger, Sean F. Reardon(Authors)
  • 2009(Publication Date)
  • Emerald Group Publishing Limited

    (Publisher)

  Based on the areas under the line of equality identified in Fig. 1 , the Gini Coefficient of income inequality ( G i ) is defined by: G i ¼ A 1 þ A 2 A 1 þ A 2 þ B (1) The Gini Coefficient and Segregation on a Continuous Variable 59 G i has a minimum of zero if all households have equal income and approaches 1 as the population increases if all income is possessed by a single household. The Gini Coefficient of neighborhood inequality ( G j ) is between-group inequality ( Pyatt, 1976 ; Silber, 1989 ) and is calculated in an analogous manner to G i : G j ¼ A 1 A 1 þ A 2 þ B (2) G j has a minimum of zero if all neighborhoods have identical mean incomes, so that the area A 1 that separates L j from the line of equality is zero. However, it has a maximum of G i if no neighborhood contains households with different levels of income, so that the area A 2 that separates L i and L j is zero. This form of Gini has been used to describe unevenness in the spatial distribution of health-care providers ( Brown, 1994 ; Schwartz, Newhouse, Bennett, & Williams, 1980 ). However, G j is not a pure measure of segregation, because it simply measures the inequality of the neighborhoods, Cumulative Households Cumulative Income A 2 A 1 B 100% 100% L i L j Fig. 1 . Lorenz Curves for Individual Households and Neighborhoods. JEONGDAI KIM AND PAUL A. JARGOWSKY 60 which results from an interaction of the sorting of households (segregation) and the underlying degree of income inequality. The upper bound of G j varies depending on the inequality of the individual units. When there is maximal segregation – every household living in neighborhoods with other households of the same income – the Lorenz curve for neighborhoods ( L j ) converges to the Lorenz curve for individuals ( L i ) and the upper bound of G j is determined by G i . A version of Gini that depends solely on the sorting of households into neighborhoods can be obtained by normalizing G j by G i .

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  Imagine There's No Country

  Poverty, Inequality, and Growth in the Era of Globalization

  • Surjit S. Bhalla(Author)
  • 2002(Publication Date)
  • Peterson Institute for International Economics

    (Publisher)

  By definition, therefore, the Lorenz curve starts at zero and ends at unity (figure 3.1 plots such a curve for three different years—1960, 1980, and 2000). If incomes are equally distributed, then the Lorenz curve is described by the diagonal (i.e., the share of income at each point is equal to the share of population). If all the income in society accrued to just one person, then the Lorenz curve would be the zero line (A to B) and then at the end the share would ‘‘spike’’ up to 1 (B to C). The Gini Coefficient 2 is equal to 1 in the latter case (perfect inequality) and 0 in the former (perfect equality). For the curve shown in the figure (world distribution in 2000), the Gini Coefficient is 0.651 (or 65.1). 2. The Gini Coefficient is the ‘‘area between the Lorenz curve and the diagonal, relative to the whole triangle below the diagonal, or half the mean difference relative to the mean’’ (Atkinson and Brandolini 1999, 6). 32 IMAGINE THERE’S NO COUNTRY Figure 3.1 World Lorenz curve, 1960, 1980, and 2000 1960 1980 100 80 60 40 20 0 100 60 percent income percent population 40 20 A B C 80 2000 Note: World income inequality is computed by the simple accounting procedure (SAP) method of aggregating individual country data on distributions of incomes into a world distribution of individuals; see chapter 11 for the details. Sources: Deininger and Squire (1996); World Income Inequality Database, available at http://www.wider.unu.edu/wiid; Asian Development Bank (2002); Milanovic and Yitzhaki (2001). Measuring Intertemporal Inequality Along with the Gini, researchers have used other definitions of inequal-ity—the share in incomes of a particular quintile (e.g., the bottom 20 percent) or the ratio in incomes of different groups (e.g., the ratio in incomes of the top vs. the bottom decile). This logic has even been extended to the study of incomes of the richest country relative to the poorest country, as we saw in the previous chapter.

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  Themes in Economic Analysis

  Theory, policy and measurement

  • Subrata Guha, Rajendra Prasad Kundu, S. Subramanian(Authors)
  • 2015(Publication Date)
  • Routledge India

    (Publisher)

  Part VI Social and Economic Measurement Passage contains an image

  14 On a Family of Indices for Envy in Situations of Income Inequality

  Ravindra Ranade and Yukie Shimono

  The coefficient of inequality in Gini (1912) was initially defined for a finite population—a discrete income distribution. Its calculation was a statistician’s exercise. The income distribution in larger societies, on the other hand, was always thought to be of the lognormal variety. In the literature, including Sen (1973), these two different situations are pooled together by assuming the latter case as an approximation for the former. The lognormal distribution is not very amenable to explicit analysis and manipulability. Making complete sense of the Lorenz curve (Lorenz 1905) and the Gini Coefficient for a continuous distribution is not the easiest of things to achieve for a student exposed to these matters for the first time (see item A1 in the Appendix for some interesting personal history). In this essay, as an approximation, we assume the simplest unimodal income distribution—the triangular one. After all, societies do not have zero and infinity as the extreme incomes as required in the lognormal case. This assumption here allows us to use the minimum level, modal level and the maximum level as parameters for further analysis. The essay is an attempt to propose a family of envy indices based on the Lorenz curve which can be seen to be a quantification of the magnitude of society-wide relative deprivation (or envy) arising from the presence of inequality in an income distribution. In the context of the particular distribution we employ, the index can be related to a number of other elementary statistical measures of central tendency and dispersion.

  Assumptions and Formal Analysis

  We assume a triangular income distribution with the minimum, modal and maximum income as a$, d$ and b$ respectively—all positive and distinct. Also, the distribution is assumed to be skewed to the left. The density is given by:

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  Equality, Participation, Transition

  Essays in Honour of Branko Horvat

  • V. Franicevic, M. Uvalic, V. Franicevic, M. Uvalic(Authors)
  • 2000(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  ‘Gini (eq. 7)’ is the Gini coeffi- cient calculated from the full formulation of equation 7. Points represent the actual GINIs. substantially altered. The line labeled ‘Gini (income alone)’ in Figure 4.4 shows the calculated Gini Coefficients that would obtain if income alone determined inequality. An upward and short bulge in inequality is followed by a prolonged and slow decrease in inequality as income levels rise. The Figure also shows that, if income alone mattered, the differences in inequality between rich and poor countries would be rel- atively small. While the standard deviation of the actual GINI in our sample is 11.7, the standard deviation of the thus calculated GINI is only 3.4 (see Table 4.4). The distance between the ‘Gini (income alone)’ line and the line obtained from our regression (6) is due, save for the statisti- cal discrepancy, to the role of social choice variables. The distance widens around $5000 per capita. For all countries with higher incomes (except for Hong Kong; see point HK in Figure 4.4), the divergence, and hence the role of social factors, is substantial. One can therefore propose two turning points of inequality: the first would occur at the level of approximately $2100 where, as noted before, the standard Kuznets curve linking income and GINI begins to turn downward. The second occurs at around $5000 when social choice variables become significantly more important than before and reinforce the downward trend in inequality. The difference between the unweighted Gini based on ‘income alone’ and the actual Gini in the whole sample amounts to 14.3 Gini points (Table 4.4).

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  Income Distribution Theory

  • Martin Bronfenbrenner(Author)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  CHAPTER THREE

  Topics in Personal Income Distribution

  Statistical Measurement of Inequality

  1. To measure the degree of inequality of a personal income distribution—a frequency distribution of incomes by size—we have mentioned two statistics, the standard deviation and the coefficient of variation, defined as the standard deviation divided by the arithmetic mean. (To measure the degree of equality , we could have used the reciprocals of the same statistics.) The attraction of these particular statistics is their simplicity, but they are not widely used in practical work. The coefficient of variation, for example, takes no account of the skewness of the income distribution; it has a lower bound (at zero) but no finite upper bound; and it is influenced by extreme values.

  Of the infinite variety of conceivable measures of personal income equality and inequality, many of those used in Western Europe and America have been compared and summarized by Bowman.1 The most familiar of these are the Pareto α and the Gini Coefficient of concentration, R . We consider these in order.

  2. Pareto’s “Law of Income Distribution” appeared in 1897 in his Cours d’économie politique; 2 at that time, supporting statistical data were still widely scattered, unreliable, and difficult to obtain. Pareto’s generalization relates only to the upper tail of the personal income distribution, to values above the mode. Its overall usefulness is reduced by its omission of the lower income brackets.

  Pareto’s law is in two parts, one relating to the mathematical form of the income distribution’s upper tail and the other to the arithmetical value of one of its coefficients. Let F be a level of income (above the mode), and let N be the proportion of income receivers with incomes equal to or greater than Y

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  Income Inequality in Singapore

  • Pundarik Mukhopadhaya(Author)
  • 2014(Publication Date)
  • Taylor & Francis

    (Publisher)

  k , the higher the weight given to the lower income group.

  Kakwani (1986) used Sen’s definition of the Gini Coefficient to propose a generalized version. It can be seen in equation (2.13) that Sen proposed the weight

  vi

  to depend on rank order of all individuals. To Sen

  vi

  = (N + 1 − j ). Kakwani introduced a parameter s to define the weight

  vi

  = (N + 1 − j )s . Clearly when s =1, the parameter turns out to be the Gini Coefficient and for higher values of s more weight is attached to the lower income group and less weight to the top.

  The generalized Gini Coefficient has some further normative appeal because of its favourable consideration for the low-income group. However, the mathematical exercise destroys the coefficient’s visual nicety.

  Welfare-based inequality measures

  A convenient approach to measuring the degree of income inequality is the use of a welfare function of income which incorporates normative assumptions concerning the welfare level associated with a certain level of income. The level of welfare corresponds to alternative distributions of the same mean income, and can then be used to derive the degree of inequality. Let W be a fully specified welfare function.44 Following Dalton (1920) a welfare-based equality measure of prevailing distribution can be defined by comparing the actual welfare level W′ with the maximum welfare level

  Wmax

  , obtainable with the given total income N̄x of N units with average income ̄x . The associated welfare-based inequality measure can, then, be written as:

  (A2.2)

  the measure is defined in the interval [0, 1], clearly the maximum equality is defined as the situation in which the optimum welfare level attainable with income N̄x is reached (in this case value of D is equal to 0). Similarly D approaches 1 (i.e., total inequality) as W′ approaches 0. Thus, D measures the relative welfare loss associated with a prevailing distribution, as compared with the maximum attainable level. To satisfy the homogeneity (mean invariant) principle by the measure D , the welfare function W

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  Development Economics

  • Gérard Roland, Gerard Roland(Authors)
  • 2016(Publication Date)
  • Routledge

    (Publisher)

  G is thus:

  G=1−2S.

  FIGURE 2.3 The Lorenz Curve and the Gini Coefficient

  The Gini Coefficient G is equal to twice the area between the diagonal and the Lorenz curve.

  Figure 2.1 contains information on the quintile distribution of income with the first quintile having 5% of income, the first two having 15%, the first three having 35%, and the first four having 60%, with the richest quintile holding the remaining 40%. The area S is formed from one triangle and four trapezoids. The triangle has an area 0.5(0.2 × 0.05) = 0.005. Recall that the formula of a trapezoid is its base multiplied by half of the sum of its two heights. Given that all four trapezoids have the same base, their area is equal to:

  0.2[(0.05+0.15)/2+(0.15+0.35)/2+(0.35+0.6)/2+(0.6+1)/2]=0.2(.05/2+0.15+0.35+0.6+1/2)=0.325.

  S is then equal to 0.325 + 0.005 = 0.33. The Gini Coefficient is equal to 1 − 2 × 0.33 = 0.34. We can calculate Gini Coefficients once we have information on the quantiles of income distribution.

  Real-world Gini Coefficients. Figure 2.4 provides Gini Coefficients (expressed in percentages between 0 and 100) for a selected group of countries, primarily from 2010, but also from various other years.9 The Gini Coefficients shown in Figure 2.4 take values between 25 for Sweden on the low end, and 59 for Haiti on the high end. Latin American countries, African countries, and China have relatively high income inequality. India’s Gini (33.4) is nearly 10 percentage points lower than that of China (42.5). The United States is among the most inegalitarian wealthy countries with a Gini of 40.8. Russia’s income distribution is roughly that of the United States with a Gini of 40.1. The average for developed OECD countries is around 35. The other countries shown in Figure 2.4

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  Economic Inequality and Poverty

  International Perspectives

  • Lars Osberg(Author)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  1 The Measurement of Income Inequality

  Stephen Jenkins

  1. Introduction

  In Douglas Adams' science fiction comedy classic The Hitchhiker's Guide to the Galaxy, supercomputer Deep Thought revealed that the Answer to the Ultimate Question of Life, the Universe, and Everything was "42." But unfortunately no one knew what the Question was! Newcomers to the economic inequality literature might justifiably claim to have the opposite problem. There are well-defined important questions—for example, is inequality increasing or decreasing, and by how much?—but what on earth does it mean (if anything) when the Gini Coefficient is 42 percent? The aim of this chapter is to help resolve such problems and thereby provide a theoretical framework for the empirical chapters following.

  An essential preliminary to any inequality (or poverty) study is clarification of the nature of the distribution to be analyzed to ensure that it represents the appropriate concept of economic power and does so for each constituent unit. Important questions are: What is the economic variable of interest? What is the demographic unit to which this pertains, and how does one ensure variables are comparable across households? These issues are the subject of section 2.

  The subsequent sections consider inequality measurement per se, focusing on two sorts of Ultimate Question, The first is: under what conditions can one say unambiguously that one distribution is more or less unequal than another? This covers issues such as whether or not inequality has increased over the last decade, is larger in the United States than in the United Kingdom, or whether the post-tax income distribution is more equal than the pretax one. A more demanding requirement is not only the ability to rank the distributions in terms of their inequality, but also to know how much more or less unequal one is relative to the other. On this basis a distinction can be made between ordinal inequality measures (the first case), and cardinal ones (the second). The advantage of the first sort of measures is that the set of basic assumptions underpinning them is smaller than for the second sort—which increases the possibility of having society-wide agreement about their use—but the penalty is that there are situations where unambiguous rankings cannot be made. However, using measures incorporating extra assumptions (the second class) extends the range of potential conclusions that can be drawn. Note that two summary measures may rank a set of distributions in exactly the same way, but represent this using different numerical scales; in this situation the measures are said to be ordinally, but not cardinally, equivalent.

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