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Gini-coefficient world map
.The Gini coefficient is a measure of statistical dispersion developed by the Italian statistician Corrado Gini and published in his 1912 paper "Variability and Mutability" (Italian: Variabilità e mutabilità).^ (The Gini coefficient is a measure of inequality.
  • Liberty and Equality: They Go Together 10 January 2010 3:15 UTC www.holisticpolitics.org [Source type: Original source]

^ The Gini coefficient provides a measure of: a.
  • Development Economics - Sample Test Questions 10 January 2010 3:15 UTC www.tulane.edu [Source type: Academic]

^ The traditional measurement of inequality in a society, invented in 1912, is called the Gini coefficient, named after Italian statistician Corrado Gini.
  • The Cost of Inequality (Extract) | Jerusalem Post 10 January 2010 3:15 UTC www.jpost.com [Source type: FILTERED WITH BAYES]

.It is commonly used as a measure of inequality of income or wealth.^ How do we measure income inequality?
  • Development and Trade with Prof. Sanjay Paul 10 January 2010 3:15 UTC users.etown.edu [Source type: FILTERED WITH BAYES]

^ The Gini coefficient is a measure of inequality of income distribution or inequality of wealth distribution.
  • Archive: engagement / what consumes me, bud caddell 10 January 2010 3:15 UTC whatconsumesme.com [Source type: General]
  • Passion2Publish: Measuring Participation Inequality in Social Networks 10 January 2010 3:15 UTC www.passion2publish.com [Source type: General]

^ The Gini coefficient can also be used to measure wealth inequality .
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

.It has, however, also found application in the study of inequalities in disciplines as diverse as health science, ecology, and chemistry.^ Evidence from a broad panel of recent academic studies shows the relation between income inequality and the rate of growth and investment is indeed robust however not linear..
  • Equality, Growth and Progress 10 January 2010 3:15 UTC workforall.net [Source type: Academic]

^ In his study " Inequality and Growth in a Panel of Countries " Robert J. Barro (Harvard University) found that higher inequality tends to retard growth in poor countries and encourage growth in well develloped regions.
  • Equality, Growth and Progress 10 January 2010 3:15 UTC workforall.net [Source type: Academic]

^ A 2002 study by the World Bank found inequality growing not only between nations, but within nations.
  • NOW with David Brancaccio. Politics & Economy. Losing Ground: Global Inequality | PBS 10 January 2010 3:15 UTC www.pbs.org [Source type: FILTERED WITH BAYES]

Contents

Definition

.
Graphical representation of the Gini coefficient.
^ Graphical representation of the Gini coefficient.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ The Gini Coefficient can be expressed graphically with the Lorenz curve, where: G = A/(A+B), where A is the area between the line of equality and the Lorenz curve, and B is the area under the Lorenz curve.
  • APPENDIX III [Mackinac Center] 10 January 2010 3:15 UTC www.mackinac.org [Source type: Academic]

^ Key Words: apportionment methods • Gini coefficient • Lorenz curve • malapportionment • proportional representation Journal of Theoretical Politics, Vol.
  • Proportional Representation, Gini Coefficients, and the Principle of Transfers -- Van Puyenbroeck 20 (4): 498 -- Journal of Theoretical Politics 10 January 2010 3:15 UTC jtp.sagepub.com [Source type: Academic]



The graph shows that while the Gini is technically equal to the area marked 'A' divided by the sum of the areas marked 'A' and 'B' (that is, Gini = A/(A+B)), it is also equal to 2*A, since A+B = 0.5 since the axes scale from 0 to 1, and the total surface of the graph therefore equals 1.
.The Gini coefficient is usually defined mathematically based on the Lorenz curve (below).^ The Gini coefficient is usually defined mathematically based on the Lorenz curve (below).
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ Lorenz curve is defined as follows.
  • Measures of Inequality 10 January 2010 3:15 UTC www.unesco.org [Source type: Academic]

^ The Gini coefficient then uses the integral of the Lorenz curve.
  • ImpactMinWageOnGini.nb 10 January 2010 3:15 UTC www.dataweb.nl [Source type: FILTERED WITH BAYES]

.It can be thought of as the ratio of the area that lies between the line of equality and the Lorenz curve (marked 'A' in the diagram) over the total area under the line of equality (marked 'A' and 'B' in the diagram); i.e., G=A/(A+B).^ When the population is perfectly equal, the Lorenz curve is the diagonal line, AC. When the population is most unequal, that is, in the case of this present study, one person has a HALex score equal to or greater than 0.1 and the HALex of all others is zero (dead), the Lorenz curve follows AB and BC. The Gini coefficient is the shaded area in the graph divided by the triangle, ABC. It can take a value between zero when the Lorenz curve is diagonal, thus, perfectly equal, and one when the Lorenz curve follows AB and BC, the most unequal.
  • Population Health Metrics | Full text | Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups 10 January 2010 3:15 UTC www.pophealthmetrics.com [Source type: Academic]

^ To work out the Gini coefficient we measure the ratio of the area between the Lorenz Curve and the 45 degree line to the whole area below the 45 degree line.

^ If the Lorenz curve is the 45 degree line then the Gini index would be 0; there is no area between the Lorenz curve and the 45 degree line.
  • EDS 297: Model of Distributio... 10 January 2010 3:15 UTC docs.google.com [Source type: FILTERED WITH BAYES]

.The Gini coefficient can range from 0 to 1; it is sometimes multiplied by 100 to range between 0 and 100. A low Gini coefficient indicates a more equal distribution, with 0 corresponding to complete equality, while higher Gini coefficients indicate more unequal distribution, with 1 corresponding to complete inequality.^ A low Gini coefficient indicates a more equal distribution, with 0 corresponding to complete equality, while higher Gini coefficients indicate more unequal distribution, with 1 corresponding to complete inequality.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ The Gini coefficient thus has a range between 0 and 1.
  • Concentration of Web users' online information behaviour 10 January 2010 3:15 UTC informationr.net [Source type: Academic]

^ (The Gini coefficient is a measure of inequality.
  • Liberty and Equality: They Go Together 10 January 2010 3:15 UTC www.holisticpolitics.org [Source type: Original source]

.To be validly computed, no negative goods can be distributed.^ To be validly computed, no negative goods can be distributed.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

.Thus, if the Gini coefficient is being used to describe household income inequality, then no household can have a negative income.^ The Gini coefficient thus has a range between 0 and 1.
  • Concentration of Web users' online information behaviour 10 January 2010 3:15 UTC informationr.net [Source type: Academic]

^ (The Gini coefficient is a measure of inequality.
  • Liberty and Equality: They Go Together 10 January 2010 3:15 UTC www.holisticpolitics.org [Source type: Original source]

^ Measuring inequality of household income: the Gini coefficient .
  • Measuring inequality in household income: the Gini coefficient 10 January 2010 3:15 UTC www.statistics.gov.uk [Source type: FILTERED WITH BAYES]

.When used as a measure of income inequality, the most unequal society will be one in which a single person receives 100% of the total income and the remaining people receive none (G=1); and the most equal society will be one in which every person receives the same percentage of the total income (G=0).^ How do we measure income inequality?
  • Development and Trade with Prof. Sanjay Paul 10 January 2010 3:15 UTC users.etown.edu [Source type: FILTERED WITH BAYES]

^ A Gini coefficient of 0 represents absolute income equality, while 100 represents absolute inequality.
  • Jolkona Blog » Blog Archive » Pre-Peru Economic Musings 10 January 2010 3:15 UTC www.jolkona.org [Source type: General]

^ The Gini coefficient is one of the most commonly used indicators of income inequality.

.Some find it more intuitive (and it is mathematically equivalent) to think of the Gini coefficient as half of the Relative mean difference.^ A model of the mean-Gini coefficient is presented.
  • Abstracts: Stochastic interest rates, transaction costs, and immunizing foreign currency risk. An empirical evaluation of the extended mean-Gini coefficient for futures hedging - Business, general 10 January 2010 3:15 UTC www.faqs.org [Source type: Academic]

^ (The Gini coefficient is equal to half of the relative mean difference .
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

^ "The relative consistency of the national Gini coefficient...
  • Mmegi Online | Business Week 10 January 2010 3:15 UTC www.mmegi.bw [Source type: News]

.The mean difference is the average absolute difference between two items selected randomly from a population, and the relative mean difference is the mean difference divided by the average, to normalize for scale.^ As half the relative mean difference, .
  • http://www.foldvary.net/works/ineq.html 10 January 2010 3:15 UTC www.foldvary.net [Source type: Academic]

^ The mean difference is the average absolute difference between two items selected randomly from a population, and the relative mean difference is the mean difference divided by the average, to normalize for scale.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ Draw a histogram to observe the difference between these two averages.
  • Chapter 5 10 January 2010 3:15 UTC wps.aw.com [Source type: FILTERED WITH BAYES]

.Worldwide, Gini coefficients for income range from approximately 0.247 (24.7) in Denmark to 0.707 (70.7) in Namibia although not every country has been assessed.^ The Gini coefficient thus has a range between 0 and 1.
  • Concentration of Web users' online information behaviour 10 January 2010 3:15 UTC informationr.net [Source type: Academic]

^ Income Gini coefficients in the world .
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

^ A country with perfect income equality would have a Gini coefficient of 0.
  • Lesson Plan: Sources of Economic Growth and Development | Welker's Wikinomics Blog 10 January 2010 3:15 UTC welkerswikinomics.com [Source type: FILTERED WITH BAYES]

As a mathematical measure of inequality, the Gini coefficient does not necessarily entail any value judgement, i.e. the "rightness" or "wrongness" of a particular level of equality.

Different uses

.Although the Gini coefficient is most popular in economics, it can in theory be applied in any field of science that studies a distribution.^ Popularity : But the most popular measure is the Gini inequality .
  • Entropy, Redundancy and Inequality Measures 10 January 2010 3:15 UTC richcity.org [Source type: FILTERED WITH BAYES]
  • Entropy, Redundancy and Inequality Measures 10 January 2010 3:15 UTC poorcity.richcity.org [Source type: FILTERED WITH BAYES]

^ The most popular of these is the Gini index (or coefficient or ratio or number).

^ Although the Gini coefficient is most popular in economics, it can in theory be applied in any field of science that studies a distribution.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

.For example, in ecology the Gini coefficient has been used as a measure of biodiversity, where the cumulative proportion of species is plotted against cumulative proportion of individuals[1].^ (The Gini coefficient is a measure of inequality.
  • Liberty and Equality: They Go Together 10 January 2010 3:15 UTC www.holisticpolitics.org [Source type: Original source]

^ The measure of health inequality across individuals is the Gini coefficient.

^ The Gini coefficient can also be used to measure wealth inequality .
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

.In health, it has been used as a measure of the inequality of health related quality of life in a population[2].^ Inequality is measured using the Gini index.
  • Ancient income inequality | vox - Research-based policy analysis and commentary from leading economists 10 January 2010 3:15 UTC www.voxeu.org [Source type: FILTERED WITH BAYES]

^ Using other measures of inequality .
  • http://www.foldvary.net/works/ineq.html 10 January 2010 3:15 UTC www.foldvary.net [Source type: Academic]

^ But measuring income inequality has its own uses.
  • Non Sequitur Economics II: The Gini in Arabian Nights | Singapore Angle 10 January 2010 3:15 UTC www.singaporeangle.com [Source type: FILTERED WITH BAYES]

.In chemistry it has been used to express the selectivity of protein kinase inhibitors against a panel of kinases[3].^ In chemistry it has been used to express the selectivity of protein kinase inhibitors against a panel of kinases [ 3 ] .
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ "Gini Coefficient: A New Way To Express Selectivity of Kinase Inhibitors against a Family of Kinases".
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

.In statistics, building decision trees, it is used to measure the purity of possible child nodes, with the aim of maximising the average purity of two child nodes when splitting.^ The Gini Coefficient is a measure of statistical dispersion developed by the Italian statistician Corrado Gini, commonly used as a measure of inequality of income or wealth.
  • The Role of B-BBEE in transformation, or can South Africa become another Zimbabwe? - Transcend Corporate Advisors 10 January 2010 3:15 UTC www.transcend.co.za [Source type: FILTERED WITH BAYES]

^ In addition, the residuals of the growth model used in chapter two are drawn to measure the Total Factor Productivity of each country (TFP).
  • Title page for ETD etd-12052007-160908 10 January 2010 3:15 UTC etd.lib.ttu.edu [Source type: Academic]

^ This statistic is easy to measure and is commonly used in econometrics to measure how wealth is distributed in human populations.
  • A New Approach to Galaxy Morphology. I. Analysis of the Sloan Digital Sky Survey 10 January 2010 3:15 UTC adsabs.harvard.edu [Source type: Academic]

Calculation

.The Gini index is defined as a ratio of the areas on the Lorenz curve diagram.^ The GINI-INDEX V. TIME plot shows the Gini index at the time that the Lorenz curve is drawn.
  • EDS 297: Model of Distributio... 10 January 2010 3:15 UTC docs.google.com [Source type: FILTERED WITH BAYES]

^ The Gini coefficient is defined as a ratio of the areas on the Lorenz curve diagram.
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

^ If the area between the line of perfect equality and the Lorenz curve is A, and the area under the Lorenz curve is B, then the Gini index is A/(A+B).
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

.If the area between the line of perfect equality and the Lorenz curve is A, and the area under the Lorenz curve is B, then the Gini index is A/(A+B).^ Thus a Gini index of 0 percent represents perfect equality—the Lorenz curve coincides with the straight line of absolute equality.
  • DEPweb: Beyond Economic Growth, Chapter 5 11 September 2009 5:58 UTC www.worldbank.org [Source type: FILTERED WITH BAYES]

^ If the Lorenz curve is the 45 degree line then the Gini index would be 0; there is no area between the Lorenz curve and the 45 degree line.
  • EDS 297: Model of Distributio... 10 January 2010 3:15 UTC docs.google.com [Source type: FILTERED WITH BAYES]

^ To calculate the Gini index, find the area between the 45 degree line of perfect equality and the Lorenz curve.
  • EDS 297: Model of Distributio... 10 January 2010 3:15 UTC docs.google.com [Source type: FILTERED WITH BAYES]

Since A+B = 0.5, the Gini index, G = A/(0.5) = 2A = 1-2B. If the Lorenz curve is represented by the function Y = L(X), the value of B can be found with integration and:
G = 1 - 2\,\int_0^1 L(X) dX.
.In some cases, this equation can be applied to calculate the Gini coefficient without direct reference to the Lorenz curve.^ In some cases, this equation can be applied to calculate the Gini coefficient without direct reference to the Lorenz curve.
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2 agree well with the data.
  • The European Physical Journal B (EPJ B) 10 January 2010 3:15 UTC epjb.edpsciences.org [Source type: Academic]

^ The Lorenz curve and Gini coefficient are typically used to measure inequality.
  • http://www.foldvary.net/works/ineq.html 10 January 2010 3:15 UTC www.foldvary.net [Source type: Academic]

For example:
  • For a population uniform on the values yi, i = 1 to n, indexed in non-decreasing order ( yiyi+1):
G = \frac{1}{n}\left ( n+1 - 2 \left ( \frac{\Sigma_{i=1}^n \; (n+1-i)y_i}{\Sigma_{i=1}^n y_i} \right ) \right )
This may be simplified to:
G = \frac{2 \Sigma_{i=1}^n \; i y_i}{n \Sigma_{i=1}^n y_i} -\frac{n+1}{n}
  • For a discrete probability function f(y), where yi, i = 1 to n, are the points with nonzero probabilities and which are indexed in increasing order ( yi < yi+1):
G = 1 - \frac{\Sigma_{i=1}^n \; f(y_i)(S_{i-1}+S_i)}{S_n}
where
S_i = \Sigma_{j=1}^i \; f(y_j)\,y_j\, and S_0 = 0\,
G = 1 - \frac{1}{\mu}\int_0^\infty (1-F(y))^2dy = \frac{1}{\mu}\int_0^\infty F(y)(1-F(y))dy
.
  • Since the Gini coefficient is half the relative mean difference, it can also be calculated using formulas for the relative mean difference.^ Can i use this procedure to calculate Gini index??
    • Nabble - SPSSX Discussion - in reply to your gini index calculation in spss 11 September 2009 5:58 UTC www.nabble.com [Source type: Reference]

    ^ If we are using R , we can calculate the Gini coefficient (using the ineq library): .
    • The Gini Coefficient As A Measure of Software Project Risk « The Research Kitchen Weblog 10 January 2010 3:15 UTC www.theresearchkitchen.com [Source type: FILTERED WITH BAYES]
    • September « 2008 « The Research Kitchen Weblog 10 January 2010 3:15 UTC www.theresearchkitchen.com [Source type: FILTERED WITH BAYES]

    ^ Variance formulas for the mean difference and coefficient of concentration.
    • Assessment of Inequality of Root Hair Density in Arabidopsis thaliana using the Gini Coefficient: a Close Look at the Effect of Phosphorus and its Interaction with Ethylene -- HE et al. 95 (2): 287 -- Annals of Botany 10 January 2010 3:15 UTC aob.oxfordjournals.org [Source type: Academic]

    For a random sample S consisting of values yi, i = 1 to n, that are indexed in non-decreasing order ( yiyi+1), the statistic:
G(S) = \frac{1}{n-1}\left (n+1 - 2 \left ( \frac{\Sigma_{i=1}^n \; (n+1-i)y_i}{\Sigma_{i=1}^n y_i}\right ) \right )
is a consistent .estimator of the population Gini coefficient, but is not, in general, unbiased.^ (Both the Indian and the Chinese estimates here correct for spatial price variation between rural and urban areas, which is not done in the usually cited estimates of Gini coefficients.
  • How unequal a country is India?: Rediff.com Business 10 January 2010 3:15 UTC business.rediff.com [Source type: FILTERED WITH BAYES]

^ This file contains a tipsheet on data analysis tools, such as indices, the Gini coefficient and percentiles, and a tipsheet on the best source for annual Census data -- the Current Population Survey.
  • IRE - Resource Center Tipsheets 10 January 2010 3:15 UTC www.ire.org [Source type: Academic]
  • IRE - Resource Center Tipsheets 10 January 2010 3:15 UTC www.ire.org [Source type: Academic]

^ Another measure of inequality is the GINI coefficient, which estimates the distribution of income across the entire population.
  • Census Report Adds New Twist to Income Inequality Data 10 January 2010 3:15 UTC www.heritage.org [Source type: FILTERED WITH BAYES]

Like, G, G(S) has a simpler form:
G(S) = 1 - \frac{2}{n-1}\left ( n - \frac{\Sigma_{i=1}^n \; iy_i}{\Sigma_{i=1}^n y_i}\right ) .
.There does not exist a sample statistic that is in general an unbiased estimator of the population Gini coefficient, like the relative mean difference.^ Unbiased estimator of population Gini coefficient = 0.248663 .
  • Gini coefficient of inequality 10 January 2010 3:15 UTC www.statsdirect.com [Source type: Academic]

^ Like the relative mean difference , there does not exist a sample statistic that is in general an unbiased estimator of the population Gini coefficient.
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

^ As half the relative mean difference, .
  • http://www.foldvary.net/works/ineq.html 10 January 2010 3:15 UTC www.foldvary.net [Source type: Academic]

.Sometimes the entire Lorenz curve is not known, and only values at certain intervals are given.^ Sometimes the entire Lorenz curve is not known, and only values at certain intervals are given.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ G. More accurate results can be obtained using other methods to approximate the area B, such as approximating the Lorenz curve with a quadratic function across pairs of intervals, or building an appropriately smooth approximation to the underlying distribution function that matches the known data.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ Thus, the Lorenz curve is a mechanism to graphically represent the cumulative share of the total income accruing to successive income intervals.
  • The Relationship Between Primary Care, Income Inequality, and Mortality in US States, 1980-1995 -- Shi et al. 16 (5): 412 -- The Journal of the American Board of Family Medicine 10 January 2010 3:15 UTC www.jabfm.org [Source type: Academic]

.In that case, the Gini coefficient can be approximated by using various techniques for interpolating the missing values of the Lorenz curve.^ The Lorenz curve and Gini coefficient are typically used to measure inequality.
  • http://www.foldvary.net/works/ineq.html 10 January 2010 3:15 UTC www.foldvary.net [Source type: Academic]

^ This value is called the Gini coefficient.
  • Income Distribution / Financial Security / Indicators of Well-being in Canada 10 January 2010 3:15 UTC www4.rhdsc.gc.ca [Source type: FILTERED WITH BAYES]

^ The most widely used measure of inequality, the Gini coefficient, derives from the Lorenz curve.
  • CHAPTER 9: REDUCTIONS IN INEQUALITY 10 January 2010 3:15 UTC www.ntia.doc.gov [Source type: Reference]

If ( X k , Yk ) are the known points on the Lorenz curve, with the X k indexed in increasing order ( X k - 1 < X k ), so that:
  • Xk is the cumulated proportion of the population variable, for k = 0,...,n, with X0 = 0, Xn = 1.
  • Yk is the cumulated proportion of the income variable, for k = 0,...,n, with Y0 = 0, Yn = 1.
If the Lorenz curve is approximated on each interval as a line between consecutive points, then the area B can be approximated with trapezoids and:
G_1 = 1 - \sum_{k=1}^{n} (X_{k} - X_{k-1}) (Y_{k} + Y_{k-1})
is the resulting approximation for .G. More accurate results can be obtained using other methods to approximate the area B, such as approximating the Lorenz curve with a quadratic function across pairs of intervals, or building an appropriately smooth approximation to the underlying distribution function that matches the known data.^ Lorenz curve is a visual method used for the comparison of inequality.
  • Rural and Remote Health Journal - View Article 10 January 2010 3:15 UTC www.rrh.org.au [Source type: Academic]

^ G. More accurate results can be obtained using other methods to approximate the area B, such as approximating the Lorenz curve with a quadratic function across pairs of intervals, or building an appropriately smooth approximation to the underlying distribution function that matches the known data.
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ If the Lorenz curve is approximated on each interval as a line between consecutive points, then the area B can be approximated with trapezoids and: .
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

.If the population mean and boundary values for each interval are also known, these can also often be used to improve the accuracy of the approximation.^ Depreciation is often used as an approximation for this.

^ If the population mean and boundary values for each interval are also known, these can also often be used to improve the accuracy of the approximation.
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ G. More accurate results can be obtained using other methods to approximate the area B, such as approximating the Lorenz curve with a quadratic function across pairs of intervals, or building an appropriately smooth approximation to the underlying distribution function that matches the known data.
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

.The Gini coefficient calculated from a sample is a statistic and its standard error, or confidence intervals for the population Gini coefficient, should be reported.^ The Gini coefficient calculated from a sample is a statistic and its standard error, or confidence intervals for the population Gini coefficient, should be reported.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ Gini coefficients of new bootstrap samples.
  • Assessment of Inequality of Root Hair Density in Arabidopsis thaliana using the Gini Coefficient: a Close Look at the Effect of Phosphorus and its Interaction with Ethylene -- HE et al. 95 (2): 287 -- Annals of Botany 10 January 2010 3:15 UTC aob.oxfordjournals.org [Source type: Academic]

^ International Statistics : Income - gini coefficients .
  • Browse By Subject - NZSTATS - The University of Auckland Library 10 January 2010 3:15 UTC www.nzstats.auckland.ac.nz [Source type: Academic]

.These can be calculated using bootstrap techniques but those proposed have been mathematically complicated and computationally onerous even in an era of fast computers.^ These can be calculated using bootstrap techniques but those proposed have been mathematically complicated and computationally onerous even in an era of fast computers.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ To overcome these two difficulties, I use a bootstrap method modified for survey data with the complex design: the two-stage with-replacement bootstrap [ 20 - 22 ].
  • Population Health Metrics | Full text | Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups 10 January 2010 3:15 UTC www.pophealthmetrics.com [Source type: Academic]

^ But the most accurate estimates of the distributions of earnings and capital ownership come from the 2000 census and a 2001 wealth survey, and so these years are used to calibrate those distributions.
  • Eastern Economic Journal - Socialism vs Social Democracy as Income-Equalizing Institutions 10 January 2010 3:15 UTC www.palgrave-journals.com [Source type: Academic]

Ogwang (2000) made the process more efficient by setting up a “trick regression model” in which the incomes in the sample are ranked with the lowest income being allocated rank 1. The model then expresses the rank (dependent variable) as the sum of a constant A and a normal error term whose variance is inversely proportional to yk;
k = A + \ N(0, s^{2}/y_k)
.Ogwang showed that G can be expressed as a function of the weighted least squares estimate of the constant A and that this can be used to speed up the calculation of the jackknife estimate for the standard error.^ Ogwang showed that G can be expressed as a function of the weighted least squares estimate of the constant A and that this can be used to speed up the calculation of the jackknife estimate for the standard error.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ We cannot just use our calculators to find the power function y = ax^n, since this does not necessarily pass through (1,1).
  • AP Central - After the Exam: The Gini Index Activity (Statistics and Calculus) 11 September 2009 5:58 UTC apcentral.collegeboard.com [Source type: FILTERED WITH BAYES]

^ With a few assumptions, it can estimate the standard error for any statistic.
  • Population Health Metrics | Full text | Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups 10 January 2010 3:15 UTC www.pophealthmetrics.com [Source type: Academic]

.Giles (2004) argued that the standard error of the estimate of A can be used to derive that of the estimate of G directly without using a jackknife at all.^ Giles (2004) argued that the standard error of the estimate of A can be used to derive that of the estimate of G directly without using a jackknife at all.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ These facts have sometimes been used to argue that land is the ideal thing to tax--there is no excess burden, and all of the tax is borne by the landowners.
  • Price Theory: Chapter 14 D. Friedman 11 September 2009 5:58 UTC daviddfriedman.com [Source type: Original source]

^ With a few assumptions, it can estimate the standard error for any statistic.
  • Population Health Metrics | Full text | Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups 10 January 2010 3:15 UTC www.pophealthmetrics.com [Source type: Academic]

.This method only requires the use of ordinary least squares regression after ordering the sample data.^ This method only requires the use of ordinary least squares regression after ordering the sample data.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ Bootstrap is a simulation method only using data at hand.
  • Population Health Metrics | Full text | Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups 10 January 2010 3:15 UTC www.pophealthmetrics.com [Source type: Academic]

^ Data collected from the samples will be used to draw inferences for the entire population.
  • DSEC - FAQ 10 January 2010 3:15 UTC www.dsec.gov.mo [Source type: FILTERED WITH BAYES]

.The results compare favorably with the estimates from the jackknife with agreement improving with increasing sample size.^ The results compare favorably with the estimates from the jackknife with agreement improving with increasing sample size.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ Finally, we provide detailed experimental evidence testifying for the claimed increased accuracy, precision, and efficiency of the proposed SJS estimation method, compared to the other methods.

^ PubMed ] Lake S, Kammann E, Klar N, Betensky R. Sample size re-estimation in cluster randomization trials.
  • Planning a cluster randomized trial with unequal cluster sizes: practical issues involving continuous outcomes 10 January 2010 3:15 UTC www.ncbi.nlm.nih.gov [Source type: Academic]

The paper describing this method can be found here: http://web.uvic.ca/econ/ewp0202.pdf
.However it has since been argued that this is dependent on the model’s assumptions about the error distributions (Ogwang 2004) and the independence of error terms (Reza & Gastwirth 2006) and that these assumptions are often not valid for real data sets.^ However it has since been argued that this is dependent on the model’s assumptions about the error distributions (Ogwang 2004) and the independence of error terms (Reza & Gastwirth 2006) and that these assumptions are often not valid for real data sets.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ However, the joint distribution of the errors (u t – u t–1 ) is no longer as in the original model.
  • Population health and income inequality: new evidence from Israeli time-series analysis -- Shmueli 33 (2): 311 -- International Journal of Epidemiology 10 January 2010 3:15 UTC ije.oxfordjournals.org [Source type: Academic]

^ (While Lorenz curves can have many different shapes, depending on what is being modeled, in this setting models of the form y = x^n are typically used.
  • AP Central - After the Exam: The Gini Index Activity (Statistics and Calculus) 11 September 2009 5:58 UTC apcentral.collegeboard.com [Source type: FILTERED WITH BAYES]

.It may therefore be better to stick with jackknife methods such as those proposed by Yitzhaki (1991) and Karagiannis and Kovacevic (2000).^ It may therefore be better to stick with jackknife methods such as those proposed by Yitzhaki (1991) and Karagiannis and Kovacevic (2000).
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ I will offer several proposals in the conclusion for what those reasons could be, although they may not be convincing, to myself or others.
  • Eastern Economic Journal - Socialism vs Social Democracy as Income-Equalizing Institutions 10 January 2010 3:15 UTC www.palgrave-journals.com [Source type: Academic]

^ We may need to teach more research methods to gain a better understanding of how people use and view content — specifically — news content.
  • Advertising : Hot Topics 10 January 2010 3:15 UTC aejmc.org [Source type: Academic]

The debate continues.
.The Gini coefficient can be calculated if you know the mean of a distribution, the number of people (or percentiles), and the income of each person (or percentile).^ Income Gini coefficients in the world .
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

^ The closer the Gini coefficient is to one, the greater the inequality of income distribution.
  • Assessment of Inequality of Root Hair Density in Arabidopsis thaliana using the Gini Coefficient: a Close Look at the Effect of Phosphorus and its Interaction with Ethylene -- HE et al. 95 (2): 287 -- Annals of Botany 10 January 2010 3:15 UTC aob.oxfordjournals.org [Source type: Academic]

^ The Gini coefficient is a measure of inequality of income distribution or inequality of wealth distribution.
  • gini coefficient for online participation / what consumes me, bud caddell 10 January 2010 3:15 UTC whatconsumesme.com [Source type: General]
  • Passion2Publish: Measuring Participation Inequality in Social Networks 10 January 2010 3:15 UTC www.passion2publish.com [Source type: General]

Princeton development economist Angus Deaton (1997, 139) simplified the Gini calculation to one easy formula:
G = \frac{N+1}{N-1}-\frac{2}{N(N-1)u}(\Sigma_{i=1}^n \; P_iX_i)
where u is mean income of the population, .Pi is the income rank P of person i, with income X, such that the richest person receives a rank of 1 and the poorest a rank of N. This effectively gives higher weight to poorer people in the income distribution, which allows the Gini to meet the Transfer Principle.^ P i is the income rank P of person i, with income X, such that the richest person receives a rank of 1 and the poorest a rank of N. This effectively gives higher weight to poorer people in the income distribution, which allows the Gini to meet the Transfer Principle.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ Geographers and many others have used the Gini coefficient in numerous instances, such assessing income distribution among a set of contiguous regions (or countries) or to measure other spatial phenomena such as racial segregation and industrial location.

^ Netherlands 32.6 7.3 40.1 NOTE: Countries are ranked according to the Gini index (or coefficient), a measure of income inequality within a country.
  • http://www.infoplease.com/ipa/A0908770.html 11 September 2009 5:58 UTC www.infoplease.com [Source type: FILTERED WITH BAYES]

Income Gini indices in the world

.While most developed European nations and Canada tend to have Gini indices between 24 and 36, the United States' and Mexico's Gini indices are both above 40, indicating that the United States and Mexico have greater inequality.^ On the evolution of income inequality in the United States.
  • http://www.infoplease.com/ipa/A0908770.html 11 September 2009 5:58 UTC www.infoplease.com [Source type: FILTERED WITH BAYES]

^ European countries generally have lower inequality than the United States.
  • Fiscal Policy and Inequality: Latin American Lessons for the U.S. by Charles P. Oman - The Globalist 10 January 2010 3:15 UTC www.theglobalist.com [Source type: FILTERED WITH BAYES]

^ Gini coefficient, income distribution by country While most developed European nations tend to have Gini coefficients between 0.24 and 0.36, the United States Gini coefficient is above 0.4, indicating that the United States has greater inequality.
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

.Using the Gini can help quantify differences in welfare and compensation policies and philosophies.^ Using the Gini can help quantify differences in welfare and compensation policies and philosophies.
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ Last year the United Nations, using a different scale, ranked Canada's overall Gini index as one of the best in the world.
  • Lies, damn lies - and Statistics Canada 10 January 2010 3:15 UTC www.canada.com [Source type: General]

^ (The Gini coefficient is a measurement used to gauge the concentration of different variables, mainly income, mortality, and the distribution of health services (10, 11).
  • PAHO Revista/Journal 10 January 2010 3:15 UTC journal.paho.org [Source type: Academic]

.However it should be borne in mind that the Gini coefficient can be misleading when used to make political comparisons between large and small countries (see criticisms section).^ The Gini coefficient thus has a range between 0 and 1.
  • Concentration of Web users' online information behaviour 10 January 2010 3:15 UTC informationr.net [Source type: Academic]

^ The other type of comparison is between countries.
  • EastSouthWestNorth: Gini Index in Hong Kong 10 January 2010 3:15 UTC www.zonaeuropa.com [Source type: Original source]

^ However, if a country has the gini-coefficient at zero, then it is next to heaven.
  • National Assembly of Zambia - Debates- Tuesday, 5th August, 2008 10 January 2010 3:15 UTC www.parliament.gov.zm [Source type: FILTERED WITH BAYES]

The Gini index for the entire world has been estimated by various parties to be between 56 and 66.[4][5]
The change in Gini indices has differed across countries. <a name=.Some countries have change little over time, such as Belgium, Canada, Germany, Japan, and Sweden.^ Look up population densities (people per square mile) and income figures for China, Japan, India, West Germany, Belgium, Taiwan, and Mexico.
  • Price Theory: Chapter 14 D. Friedman 11 September 2009 5:58 UTC daviddfriedman.com [Source type: Original source]

^ Inequalities are also low in Austria, Belgium, France, Germany, Luxemburg, Norway, Sweden, and Switzerland, where the Gini coefficients range from between 0.25 and 0.3.
  • Africa: Urban Inequality in Global Perspective, 10/24/2009 10 January 2010 3:15 UTC www.africa.upenn.edu [Source type: FILTERED WITH BAYES]

^ The same general trends are also visible in wage data for other developed countries, including Sweden, the United Kingdom, the Netherlands, France, and Canada.
  • Growing Income Inequality: Roots and Remedies 10 January 2010 3:15 UTC www.urban.org [Source type: FILTERED WITH BAYES]

Brazil has oscillated around a steady value. France, Italy, Mexico, and Norway have shown marked declines. China and the US have increased steadily. Australia grew to moderate levels before dropping. India sank before rising again. The UK and Poland stayed at very low levels before rising. Bulgaria had an increase of fits-and-starts. .svg‎ alt text" src="http://images-mediawiki-sites.thefullwiki.org/08/3/6/9/215962606317409.png" width="720" height="521" class="thumbimage" />

US income Gini indices over time

Gini indices for the United States at various times, according to the US Census Bureau:[6][7]
  • 1929: 45.0 (estimated)
  • 1947: 37.6 (estimated)
  • 1967: 39.7 (first year reported)
  • 1968: 38.6 (lowest index reported)
  • 1970: 39.4
  • 1980: 40.3
  • 1990: 42.8
  • 2000: 46.2 [8]
  • 2005: 46.9
  • 2006: 47.0 (highest index reported)
  • 2007: 46.3
  • 2008: 46.6

EU Gini index

.In 2005 the Gini index for the EU was estimated at 31.[9].^ EU Gini index .
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ In 2005 the Gini index for the EU was estimated at 31.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ State media estimated that China's Gini index could now be as high as 0.47, up from 0.454 in 2002 and 0.437 in 1995.
  • yax-452 Privacy rights and heads in the sand 10 January 2010 3:15 UTC www.yawningbread.org [Source type: Original source]

Advantages of Gini coefficient as a measure of inequality

.
  • It can be used to compare income distributions across different population sectors as well as countries, for example the Gini coefficient for urban areas differs from that of rural areas in many countries (though the United States' urban and rural Gini coefficients are nearly identical).
  • It is sufficiently simple that it can be compared across countries and be easily interpreted.^ It is sufficiently simple that it can be compared across countries and be easily interpreted.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Income distribution was measured by the Gini coefficient, a commonly used indicator of income inequality.
    • The Relationship Between Primary Care, Income Inequality, and Mortality in US States, 1980-1995 -- Shi et al. 16 (5): 412 -- The Journal of the American Board of Family Medicine 10 January 2010 3:15 UTC www.jabfm.org [Source type: Academic]

    ^ A country with perfect income equality would have a Gini coefficient of 0.
    • Lesson Plan: Sources of Economic Growth and Development | Welker's Wikinomics Blog 10 January 2010 3:15 UTC welkerswikinomics.com [Source type: FILTERED WITH BAYES]

    .GDP statistics are often criticized as they do not represent changes for the whole population; the Gini coefficient demonstrates how income has changed for poor and rich.^ Gini coefficient is a Statistical measure for Income Distribution.
    • Organizaciju vadyba: sisteminiai tyrimai Nr. 27 10 January 2010 3:15 UTC www.vdu.lt [Source type: Academic]

    ^ GDP statistics are often criticised as they do not represent changes for the whole population; the Gini coefficient demonstrates how income has changed for poor and rich.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ Income Gini coefficients in the world .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    If the Gini coefficient is rising as well as GDP, poverty may not be improving for the majority of the population.
  • The Gini coefficient can be used to indicate how the distribution of income has changed within a country over a period of time, thus it is possible to see if inequality is increasing or decreasing.
  • The Gini coefficient satisfies four important principles[10]:
    • Anonymity: it does not matter who the high and low earners are.
    • Scale independence: the Gini coefficient does not consider the size of the economy, the way it is measured, or whether it is a rich or poor country on average.
    • Population independence: it does not matter how large the population of the country is.
    • Transfer principle: if income (less than the difference), is transferred from a rich person to a poor person the resulting distribution is more equal.

Disadvantages of Gini coefficient as a measure of inequality

.
  • The Gini coefficient of different sets of people cannot be averaged to obtain the Gini coefficient of all the people in the sets: if a Gini coefficient were to be calculated for each person it would always be zero.^ The Gini coefficient of different sets of people cannot be averaged to obtain the Gini coefficient of all the people in the sets: if a Gini coefficient were to be calculated for each person it would always be zero.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Obtain a Gini coefficient: .

    ^ A Gini Coefficient of 1 would mean one person had all the money and power.
    • Runic Games • View topic - The Gini-Coefficient: Examining Fairness in PvP 10 January 2010 3:15 UTC forums.runicgames.com [Source type: General]

    .For a large, economically diverse country, a much higher coefficient will be calculated for the country as a whole than will be calculated for each of its regions.^ The Gini coefficient measured for a large economically diverse country will generally result in a much higher coefficient than each of its regions has individually.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ For a large, economically diverse country, a much higher coefficient will be calculated for the country as a whole than will be calculated for each of its regions.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Judged by international standard, a country with Gini coefficient higher than 0.
    • Emerging Income Inequalities in China 10 January 2010 3:15 UTC www.adbi.org [Source type: FILTERED WITH BAYES]

    .(The coefficient is usually applied to measurable nominal income rather than local purchasing power, tending to increase the calculated coefficient across larger areas.^ (The coefficient is usually applied to measurable nominal income rather than local purchasing power , tending to increase the calculated coefficient across larger areas.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Inequality is usually measured with the Gini coefficient.
    • Prince and pauper - Columnist - livemint.com 10 January 2010 3:15 UTC www.livemint.com [Source type: FILTERED WITH BAYES]

    ^ It measures current income rather than lifetime income.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ).March 2010" style="white-space:nowrap;">[citation needed]
  • The Lorenz curve may understate the actual amount of inequality if richer households are able to use income more efficiently than lower income households or vice versa.^ Lorenz curve is a visual method used for the comparison of inequality.
    • Rural and Remote Health Journal - View Article 10 January 2010 3:15 UTC www.rrh.org.au [Source type: Academic]

    ^ The Lorenz curve and Gini coefficient are typically used to measure inequality.
    • http://www.foldvary.net/works/ineq.html 10 January 2010 3:15 UTC www.foldvary.net [Source type: Academic]

    ^ From another point of view, measured inequality may be the result of more or less efficient use of household incomes.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .From another point of view, measured inequality may be the result of more or less efficient use of household incomes[citation needed].
  • Economies with similar incomes and Gini coefficients can still have very different income distributions.^ The measure will give different results when applied to individuals instead of households.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Economies with similar incomes and Gini coefficients can still have very different income distributions.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Income distribution was measured by the Gini coefficient, a commonly used indicator of income inequality.
    • The Relationship Between Primary Care, Income Inequality, and Mortality in US States, 1980-1995 -- Shi et al. 16 (5): 412 -- The Journal of the American Board of Family Medicine 10 January 2010 3:15 UTC www.jabfm.org [Source type: Academic]

    .This is because the Lorenz curves can have different shapes and yet still yield the same Gini coefficient.^ This is because the Lorenz curves can have different shapes and yet still yield the same Gini coefficient.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ The Gini coefficient then uses the integral of the Lorenz curve.
    • ImpactMinWageOnGini.nb 10 January 2010 3:15 UTC www.dataweb.nl [Source type: FILTERED WITH BAYES]

    ^ The Lorenz curve and Gini coefficient are typically used to measure inequality.
    • http://www.foldvary.net/works/ineq.html 10 January 2010 3:15 UTC www.foldvary.net [Source type: Academic]

    .For example a society where half of individuals had no income and the other half shared all the income equally would have the same Gini coefficient as one where 75% of people equally shared 25% of income while the remaining 25% equally shared 75%[citation needed].
  • It measures current income rather than lifetime income.^ Income Gini coefficients in the world .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ The closer the Gini coefficient is to one, the greater the inequality of income distribution.
    • Assessment of Inequality of Root Hair Density in Arabidopsis thaliana using the Gini Coefficient: a Close Look at the Effect of Phosphorus and its Interaction with Ethylene -- HE et al. 95 (2): 287 -- Annals of Botany 10 January 2010 3:15 UTC aob.oxfordjournals.org [Source type: Academic]

    ^ The Gini coefficient is a measure of inequality of income distribution or inequality of wealth distribution.
    • Passion2Publish: Measuring Participation Inequality in Social Networks 10 January 2010 3:15 UTC www.passion2publish.com [Source type: General]

    .A society in which everyone earned the same over a lifetime would appear unequal because of people at different stages in their life; a society in which students study rather than save can never have a coefficient of 0. However, Gini coefficient can also be calculated for any kind of distribution, e.g.^ We can in the same way calculate everyone else's income, giving us the distribution of income for the whole society.
    • Price Theory: Chapter 14 D. Friedman 11 September 2009 5:58 UTC daviddfriedman.com [Source type: Original source]

    ^ However, Gini coefficient can also be calculated for any kind of distribution, e.g.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ If everyone had exactly the same income, the Gini coefficient would be zero.
    • Lies, damn lies - and Statistics Canada 10 January 2010 3:15 UTC www.canada.com [Source type: General]

    for wealth. [11]

Problems in using the Gini coefficient

.
  • Gini coefficients do include investment income; however, the Gini coefficient based on net income does not accurately reflect differences in wealth - a possible source of misinterpretation.^ The Gini coefficient is a measure of inequality of income distribution or inequality of wealth distribution.
    • Passion2Publish: Measuring Participation Inequality in Social Networks 10 January 2010 3:15 UTC www.passion2publish.com [Source type: General]

    ^ The Gini coefficient requires that no one have a negative net income or wealth.
    • File:Gini since WWII.svg - Wikimedia Commons 10 January 2010 3:15 UTC commons.wikimedia.org [Source type: Reference]
    • Down the O-Hole: why the present administration's plans lead to catastrophe (and there isn't anything you can do about it.) | The Agonist 10 January 2010 3:15 UTC agonist.org [Source type: FILTERED WITH BAYES]

    ^ Different quantifications of these incomes will yield different Gini coefficients.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .For example, Sweden has a low Gini coefficient for income distribution but a significantly higher Gini coefficient for wealth (for instance 77% of the share value owned by households is held by just 5% of Swedish shareholding households )[12].^ Income Gini coefficients in the world .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ The Gini coefficient is a measure of inequality of income distribution or inequality of wealth distribution.
    • Passion2Publish: Measuring Participation Inequality in Social Networks 10 January 2010 3:15 UTC www.passion2publish.com [Source type: General]

    ^ The household survey and the Gini coefficient .
    • http://www.singaporedemocrat.org/articleprivacyrights.html 11 September 2009 5:58 UTC www.singaporedemocrat.org [Source type: Original source]
    • yax-452 Privacy rights and heads in the sand 10 January 2010 3:15 UTC www.yawningbread.org [Source type: Original source]

    .In other words, the Gini income coefficient should not be interpreted as measuring effective egalitarianism.
  • Too often only the Gini coefficient is quoted without describing the proportions of the quantiles used for measurement.^ Income distribution was measured by the Gini coefficient, a commonly used indicator of income inequality.
    • The Relationship Between Primary Care, Income Inequality, and Mortality in US States, 1980-1995 -- Shi et al. 16 (5): 412 -- The Journal of the American Board of Family Medicine 10 January 2010 3:15 UTC www.jabfm.org [Source type: Academic]

    ^ Income Gini coefficients in the world .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ The Gini coefficient is a measure of inequality of income distribution or inequality of wealth distribution.
    • Passion2Publish: Measuring Participation Inequality in Social Networks 10 January 2010 3:15 UTC www.passion2publish.com [Source type: General]

    .As with other inequality coefficients, the Gini coefficient is influenced by the granularity of the measurements.^ The Gini coefficient is a measure of inequality of income distribution or inequality of wealth distribution.
    • Passion2Publish: Measuring Participation Inequality in Social Networks 10 January 2010 3:15 UTC www.passion2publish.com [Source type: General]

    ^ The Gini coefficient can also be used to measure wealth inequality .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ 'Bootstrapping the Gini coefficient of inequality'.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    .For example, five 20% quantiles (low granularity) will usually yield a lower Gini coefficient than twenty 5% quantiles (high granularity) taken from the same distribution.^ For example, five 20% quantiles (low granularity) will yield a lower Gini coefficient than twenty 5% quantiles (high granularity) taken from the same distribution.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ For example, a coefficient of 0.2 will represent a lower level of inequality than a coefficient of 0.4.
    • The Relationship Between Primary Care, Income Inequality, and Mortality in US States, 1980-1995 -- Shi et al. 16 (5): 412 -- The Journal of the American Board of Family Medicine 10 January 2010 3:15 UTC www.jabfm.org [Source type: Academic]

    ^ For example, five 20% quantiles (low granularity) will usually yield a lower Gini coefficient than twenty 5% quantiles (high granularity) taken from the same distribution.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .This is an often encountered problem with measurements.
  • Care should be taken in using the Gini coefficient as a measure of egalitarianism, as it is properly a measure of income dispersion.^ Income distribution was measured by the Gini coefficient, a commonly used indicator of income inequality.
    • The Relationship Between Primary Care, Income Inequality, and Mortality in US States, 1980-1995 -- Shi et al. 16 (5): 412 -- The Journal of the American Board of Family Medicine 10 January 2010 3:15 UTC www.jabfm.org [Source type: Academic]

    ^ The Lorenz curve and Gini coefficient are typically used to measure inequality.
    • http://www.foldvary.net/works/ineq.html 10 January 2010 3:15 UTC www.foldvary.net [Source type: Academic]

    ^ The Gini coefficient provides a measure of: a.
    • Development Economics - Sample Test Questions 10 January 2010 3:15 UTC www.tulane.edu [Source type: Academic]

    .For example, if two equally egalitarian countries pursue different immigration policies, the country accepting higher proportion of low-income or impoverished migrants will be assessed as less equal (gain a higher Gini coefficient).
  • The Gini coefficient is a point-estimate of equality at a certain time, hence it ignores life-span changes in income.^ Income Gini coefficients in the world .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ US income gini coefficients over time .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ US income Gini indices over time .
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .Typically, increases in the proportion of young or old members of a society will drive apparent changes in equality.^ Typically, increases in the proportion of young or old members of a society will drive apparent changes in equality.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ The extent of the increase will depend on the proportion of people that have income in the range between median income and the income of the person with the changed income, both before and after the change in income.
    • 6553.0 - Information Paper: Survey of Income and Housing, User Guide, Australia, 2005-06 10 January 2010 3:15 UTC www.abs.gov.au [Source type: Academic]

    ^ Since G is varying directly with (1-G) rather than with N, G measures little change in inequality if a large N increases while C is constant, while I F increases proportional to population.
    • http://www.foldvary.net/works/ineq.html 10 January 2010 3:15 UTC www.foldvary.net [Source type: Academic]

    .Because of this, factors such as age distribution within a population and mobility within income classes can create the appearance of differential equality when none exist taking into account demographic effects.^ Because of this, factors such as age distribution within a population and mobility within income classes can create the appearance of differential equality when none exist taking into account demographic effects.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Differences in the distribution of income, or 'income disparities', are often considered a measure of a society's fairness, how it treats the disadvantaged, and a factor in maintaining social order and peace.
    • Income Distribution / Financial Security / Indicators of Well-being in Canada 10 January 2010 3:15 UTC www4.hrsdc.gc.ca [Source type: Reference]

    ^ It is expressed as a value between 0 and 1 where 0 represents perfect equality (everyone has the same income) and 1 represents absolute inequality (one person has all of the wealth and the rest have none).
    • REPORTE DE LA JUSTICIA / CEJA - REPORT OF JUSTICE / JSCA 10 January 2010 3:15 UTC www.cejamericas.org [Source type: FILTERED WITH BAYES]

    .Thus a given economy may have a higher Gini coefficient at any one point in time compared to another, while the Gini coefficient calculated over individuals' lifetime income is actually lower than the apparently more equal (at a given point in time) economy's.^ The Gini coefficient thus has a range between 0 and 1.
    • Concentration of Web users' online information behaviour 10 January 2010 3:15 UTC informationr.net [Source type: Academic]

    ^ Income Gini coefficients in the world .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ A country with perfect income equality would have a Gini coefficient of 0.
    • Lesson Plan: Sources of Economic Growth and Development | Welker's Wikinomics Blog 10 January 2010 3:15 UTC welkerswikinomics.com [Source type: FILTERED WITH BAYES]

    [13] .Essentially, what matters is not just inequality in any particular year, but the composition of the distribution over time.
  • The Gini coefficient is a measure only of inequality.^ Income distribution was measured by the Gini coefficient, a commonly used indicator of income inequality.
    • The Relationship Between Primary Care, Income Inequality, and Mortality in US States, 1980-1995 -- Shi et al. 16 (5): 412 -- The Journal of the American Board of Family Medicine 10 January 2010 3:15 UTC www.jabfm.org [Source type: Academic]

    ^ The measure of health inequality across individuals is the Gini coefficient.
    • Population Health Metrics | Full text | Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups 10 January 2010 3:15 UTC www.pophealthmetrics.com [Source type: Academic]

    ^ The Gini coefficient for the urban-rural inequality was only 0.
    • Emerging Income Inequalities in China 10 January 2010 3:15 UTC www.adbi.org [Source type: FILTERED WITH BAYES]

    .Countries can have the same Gini coefficient but have completely different levels of wealth and indeed it is possible for a more equal country to be poorer at every level of income.^ Income Gini coefficients in the world .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ A country with perfect income equality would have a Gini coefficient of 0.
    • Lesson Plan: Sources of Economic Growth and Development | Welker's Wikinomics Blog 10 January 2010 3:15 UTC welkerswikinomics.com [Source type: FILTERED WITH BAYES]

    ^ The Gini coefficient is a measure of inequality of income distribution or inequality of wealth distribution.
    • Passion2Publish: Measuring Participation Inequality in Social Networks 10 January 2010 3:15 UTC www.passion2publish.com [Source type: General]

    Similarly, the Gini coefficient as measured over time does not measure growth in incomes.

General problems of measurement

.
  • Comparing income distributions among countries may be difficult because benefits systems may differ.^ Income distribution and poverty in OECD countries.
    • Income inequality, mortality, and self rated health: meta-analysis of multilevel studies -- Kondo et al. 339: b4471 -- BMJ 10 January 2010 3:15 UTC www.bmj.com [Source type: Academic]

    ^ Comparing income distributions among countries may be difficult because benefits systems may differ.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ For this reason the scores calculated for individual countries within the EU are difficult to compare with the score of the entire US. Comparing income distributions among countries may be difficult because benefits systems may differ.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    .For example, some countries give benefits in the form of money while others give food stamps, which might not be counted by some economists and researchers as income in the Lorenz curve and therefore not taken into account in the Gini coefficient.^ Here's an example of a Lorenz curve in a country with a relatively unequal distribution of income.
    • AG EC 450 - Inequality and Corruption in Developing Countries 10 January 2010 3:15 UTC 450.aers.psu.edu [Source type: Original source]

    ^ Income Gini coefficients in the world .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ A country with perfect income equality would have a Gini coefficient of 0.
    • Lesson Plan: Sources of Economic Growth and Development | Welker's Wikinomics Blog 10 January 2010 3:15 UTC welkerswikinomics.com [Source type: FILTERED WITH BAYES]

    .The USA counts income before benefits, while France counts it after benefits, making the USA appear slightly more unequal vis-a-vis France than it admittedly is.^ The USA counts income before benefits, while France counts it after benefits, making the USA appear slightly more unequal vis-a-vis France than it admittedly is.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ More broadly, table 4 shows that, even though before-tax-and-transfer income inequality (as measured by the Gini coefficient) is larger in Quebec and Atlantic Canada than elsewhere, after-tax-and-transfer inequality is smaller in those two regions.
    • INROADS, THE CANADIAN JOURNAL OF OPINION: Newsletter, Fall 2009 10 January 2010 3:15 UTC www.inroadsjournal.ca [Source type: FILTERED WITH BAYES]

    ^ Each of these slight pushing of spreads added up, and created situations where dollars were selling for slightly less than a dollar in one place, and slightly more than a dollar in another.
    • Down the O-Hole: why the present administration's plans lead to catastrophe (and there isn't anything you can do about it.) | The Agonist 10 January 2010 3:15 UTC agonist.org [Source type: FILTERED WITH BAYES]

    .In another example, USSR appeared to have relatively high income inequality: by some estimates, in the late 70's, Gini coefficient of its urban population was as high as 0.38[14], which is higher than many Western countries today.^ Income Gini coefficients in the world .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ The closer the Gini coefficient is to one, the greater the inequality of income distribution.
    • Assessment of Inequality of Root Hair Density in Arabidopsis thaliana using the Gini Coefficient: a Close Look at the Effect of Phosphorus and its Interaction with Ethylene -- HE et al. 95 (2): 287 -- Annals of Botany 10 January 2010 3:15 UTC aob.oxfordjournals.org [Source type: Academic]

    ^ The Gini coefficient is a measure of inequality of income distribution or inequality of wealth distribution.
    • Passion2Publish: Measuring Participation Inequality in Social Networks 10 January 2010 3:15 UTC www.passion2publish.com [Source type: General]

    .This apparent inequality ignored the fact that many benefits received by Soviet citizens were nonmonetary and were afforded regardless of income: these benefits included, among others, free child care for children as young as 2 months, free elementary, secondary and higher education, free cradle-to-grave medical care, free or heavily subsidized housing.^ This apparent inequality ignored the fact that many benefits received by Soviet citizens were nonmonetary and were afforded regardless of income: these benefits included, among others, free child care for children as young as 2 months, free elementary, secondary and higher education, free cradle-to-grave medical care, free or heavily subsidized housing.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ "Although cities in the United States of America have relatively lower levels of poverty than many other cities in the developed world, levels of income inequality ...
    • Africa: Urban Inequality in Global Perspective, 10/24/2009 10 January 2010 3:15 UTC www.africa.upenn.edu [Source type: FILTERED WITH BAYES]

    ^ The literature on income inequality and health has, by and large, not included serious examination of the role of health services on mitigating the health burden imposed by income and other social inequalities.
    • The Relationship Between Primary Care, Income Inequality, and Mortality in US States, 1980-1995 -- Shi et al. 16 (5): 412 -- The Journal of the American Board of Family Medicine 10 January 2010 3:15 UTC www.jabfm.org [Source type: Academic]

    .In this example, an accurate comparison between the 1970s USSR and Western countries would require one to assign monetary values to such benefits (a difficult task in the absence of free markets).^ In this example, an accurate comparison between the 1970s USSR and Western countries would require one to assign monetary values to such benefits (a difficult task in the absence of free markets).
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ The other type of comparison is between countries.
    • EastSouthWestNorth: Gini Index in Hong Kong 10 January 2010 3:15 UTC www.zonaeuropa.com [Source type: Original source]

    ^ However it should be borne in mind that the Gini coefficient can be misleading when used to make political comparisons between large and small countries (see criticisms section).
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .Similar problems arise whenever a comparison between pure free-market economies and partially socialist economies is attempted.^ Similar problems arise whenever a comparison between pure free-market economies and partially socialist economies is attempted.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ In this example, an accurate comparison between the 1970s USSR and Western countries would require one to assign monetary values to such benefits (a difficult task in the absence of free markets).
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Most free market nations have a Gini coefficient between 0.25 and 0.50.
    • Down the O-Hole: why the present administration's plans lead to catastrophe (and there isn't anything you can do about it.) | The Agonist 10 January 2010 3:15 UTC agonist.org [Source type: FILTERED WITH BAYES]

    .Benefits may take various and unexpected forms: for example, major oil producers such as Venezuela and Iran provide indirect benefits to its citizens by subsidizing the retail price of gasoline.
  • Similarly, in some societies people may have significant income in other forms than money, for example through subsistence farming or bartering.^ For example, some countries give benefits in the form of money while others give food stamps , which may not be counted as income in the Lorenz curve and therefore not taken into account in the Gini coefficient.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ "Although cities in the United States of America have relatively lower levels of poverty than many other cities in the developed world, levels of income inequality ...
    • Africa: Urban Inequality in Global Perspective, 10/24/2009 10 January 2010 3:15 UTC www.africa.upenn.edu [Source type: FILTERED WITH BAYES]

    ^ The education and income variables predicted age adjusted mortality for males better (R 2 adj=0.54) than for females (R 2 adj=0.34).
    • Education, income inequality, and mortality: a multiple regression analysis -- Muller 324 (7328): 23 -- BMJ 10 January 2010 3:15 UTC www.bmj.com [Source type: Academic]

    .Like non-monetary benefits, the value of these incomes is difficult to quantify.^ Like non-monetary benefits, the value of these incomes is difficult to quantify.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ In this example, an accurate comparison between the 1970s USSR and Western countries would require one to assign monetary values to such benefits (a difficult task in the absence of free markets).
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Comparing income distributions among countries may be difficult because benefits systems may differ.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .Different quantifications of these incomes will yield different Gini coefficients.
  • The measure will give different results when applied to individuals instead of households.^ The measure will give different results when applied to individuals instead of households.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Gini coefficients for individual states were not available by householder's race or sex.
    • Education, income inequality, and mortality: a multiple regression analysis -- Muller 324 (7328): 23 -- BMJ 10 January 2010 3:15 UTC www.bmj.com [Source type: Academic]

    ^ Income Gini coefficients in the world .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    .When different populations are not measured with consistent definitions, comparison is not meaningful.
  • As for all statistics, there may be systematic and random errors in the data.^ When different populations are not measured with consistent definitions, comparison is not meaningful.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ As for all statistics, there will be systematic and random errors in the data.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ All variables are measured in first-differences.
    • Population health and income inequality: new evidence from Israeli time-series analysis -- Shmueli 33 (2): 311 -- International Journal of Epidemiology 10 January 2010 3:15 UTC ije.oxfordjournals.org [Source type: Academic]

    .The meaning of the Gini coefficient decreases as the data become less accurate.^ The meaning of the Gini coefficient decreases as the data become less accurate.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Gini coefficients do include investment income; however, the Gini coefficient based on net income does not accurately reflect differences in wealth - a possible source of misinterpretation.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Since the Gini coefficient is a mathematical construct, one should note with caution how the metric is computed out from the data.
    • Non Sequitur Economics II: The Gini in Arabian Nights | Singapore Angle 10 January 2010 3:15 UTC www.singaporeangle.com [Source type: FILTERED WITH BAYES]

    Also, countries may collect data differently, making it difficult to compare statistics between countries.
.As one result of this criticism, in addition to or in competition with the Gini coefficient entropy measures are frequently used (e.g.^ The Gini coefficient can also be used to measure wealth inequality .
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

^ Why using Entropy Measures?
  • Entropy, Redundancy and Inequality Measures 10 January 2010 3:15 UTC poorcity.richcity.org [Source type: FILTERED WITH BAYES]

^ Advantages of Gini coefficient as a measure of inequality .
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

the .Theil Index and the Atkinson index).^ The table shows that the Atkinson indexes, but not the Gini or Theil measures, are sensitive to small changes, in dollar terms, to the lowest incomes in the Australian data set.
  • 6553.0 - Information Paper: Survey of Income and Housing, User Guide, Australia, 2005-06 10 January 2010 3:15 UTC www.abs.gov.au [Source type: Academic]

^ The Gini coefficient is compared with the Theil index and a number of Atkinson indexes.
  • 6553.0 - Information Paper: Survey of Income and Housing, User Guide, Australia, 2005-06 10 January 2010 3:15 UTC www.abs.gov.au [Source type: Academic]

.These measures attempt to compare the distribution of resources by intelligent agents in the market with a maximum entropy random distribution, which would occur if these agents acted like non-intelligent particles in a closed system following the laws of statistical physics.^ These measures attempt to compare the distribution of resources by intelligent agents in the market with a maximum entropy random distribution , which would occur if these agents acted like non-intelligent particles in a closed system following the laws of statistical physics.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ If all A i /E i would be same, the entropy would be ln(A total /E total ), which is the maximum entropy of the system.
  • Entropy, Redundancy and Inequality Measures 10 January 2010 3:15 UTC richcity.org [Source type: FILTERED WITH BAYES]

^ These measures attempt to compare the distribution of resources by intelligent players in the market with a maximum entropy random distribution , which would occur if these players acted like non-intelligent particles in a closed system following the laws of statistical physics.
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

Credit risk

.The Gini coefficient is also commonly used for the measurement of the discriminatory power of rating systems in credit risk management.^ Income distribution was measured by the Gini coefficient, a commonly used indicator of income inequality.
  • The Relationship Between Primary Care, Income Inequality, and Mortality in US States, 1980-1995 -- Shi et al. 16 (5): 412 -- The Journal of the American Board of Family Medicine 10 January 2010 3:15 UTC www.jabfm.org [Source type: Academic]

^ The Gini coefficient can also be used to measure wealth inequality .
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

^ The Lorenz curve and Gini coefficient are typically used to measure inequality.
  • http://www.foldvary.net/works/ineq.html 10 January 2010 3:15 UTC www.foldvary.net [Source type: Academic]

.The discriminatory power refers to a credit risk model's ability to differentiate between defaulting and non-defaulting clients.^ It is also commonly used for the measurement of discriminatory power of rating systems in the credit risk management.
  • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

.The above formula G1 may be used for the final model and also at individual model factor level, to quantify the discriminatory power of individual factors.^ The above formula G 1 may be used for the final model and also at individual model factor level, to quantify the discriminatory power of individual factors.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ In other words, what factors predict the degree of behavioural concentration at the individual level?
  • Concentration of Web users' online information behaviour 10 January 2010 3:15 UTC informationr.net [Source type: Academic]

^ Explanatory variables were selected for the final models only if they had a P value < 0.05 after adjustment for variables from the same or prior levels of determinants.
  • PAHO Revista/Journal 10 January 2010 3:15 UTC journal.paho.org [Source type: Academic]

.This is as a result of too many non defaulting clients falling into the lower points scale e.g.^ This is as a result of too many non defaulting clients falling into the lower points scale e.g.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ The discriminatory power refers to a credit risk model's ability to differentiate between defaulting and non-defaulting clients.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

factor has a .10 point scale and 30% of non defaulting clients are being assigned the lowest points available e.g.^ This is as a result of too many non defaulting clients falling into the lower points scale e.g.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ The discriminatory power refers to a credit risk model's ability to differentiate between defaulting and non-defaulting clients.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

0 or negative points. .This indicates that the factor is behaving in a counter-intuitive manner and would require further investigation at the model development stage.^ This indicates that the factor is behaving in a counter-intuitive manner and would require further investigation at the model development stage.
  • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

^ Recall the discussion above, in which we explain why multi-stage samples for this investigation would require initial selection of low-SES census tracts, or other comparable area units.

^ Our findings of higher indices of caries in towns with poorer figures of socioeconomic development indicate differential levels of exposure to risk factors for dental caries.
  • PAHO Revista/Journal 10 January 2010 3:15 UTC journal.paho.org [Source type: Academic]

References: The Analytics of risk model validation

See also

References

  1. ^ Wittebolle, Lieven; et al (2009). "Initial community evenness favours functionality under selective stress". Nature 458: pp. 623–626. 
  2. ^ Asada, Yukiko (2005). "Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups". Population Health Metrics 3: pp. 7. doi:10.1186/1478-7954-3-7. 
  3. ^ Graczyk, Piotr (2007). "Gini Coefficient: A New Way To Express Selectivity of Kinase Inhibitors against a Family of Kinases". Journal of Medicinal Chemistry 50: pp. 5773–5779. doi:10.1021/jm070562u. 
  4. ^ Bob Sutcliffe (April 2007), Postscript to the article ‘World inequality and globalization’ (Oxford Review of Economic Policy, Spring 2004), http://siteresources.worldbank.org/INTDECINEQ/Resources/PSBSutcliffe.pdf, retrieved 2007-12-13 
  5. ^ United Nations Development Programme
  6. ^ "Gini Ratios for Households, by Race and Hispanic Origin of Householder: 1967 to 2007". Historical Income Tables - Households. United States Census Bureau. http://www.census.gov/hhes/www/income/histinc/h04.html. 
  7. ^ "Table 3. Income Distribution Measures Using Money Income and Equivalence-Adjusted Income: 2007 and 2008". Income, Poverty, and Health Insurance Coverage in the United States: 2008. United States Census Bureau. p. 17. http://www.census.gov/prod/2009pubs/p60-236.pdf. 
  8. ^ Note that the calculation of the index for the United States was changed in 1992, resulting in an upwards shift of about 2.
  9. ^ http://www.eurofound.europa.eu/areas/qualityoflife/eurlife/index.php?template=3&radioindic=158&idDomain=3
  10. ^ Ray, Debraj. Development Economics. Princeton University Press, 1998. page 188].
  11. ^ Friedman, David D.
  12. ^ (Data from the Statistics Sweden.)
  13. ^ N. Blomquist, "A comparison of distributions of annual and lifetime income: Sweden around 1970", Review of Income and Wealth, Volume 27 Issue 3, Pages 243 - 264, [1]
  14. ^ "Politics, work, and daily life in the USSR", James R. Millar, 1987, p.193

Further reading

.
  • Amiel, Y.; Cowell, F.A. (1999).^ Amiel, Y.; Cowell, F.A. (1999).
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .Thinking about Inequality.^ Thinking about Inequality .
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .Cambridge. 
  • Anand, Sudhir (1983).^ Anand, Sudhir (1983).
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .Inequality and Poverty in Malaysia.^ Inequality and Poverty in Malaysia .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    .New York: Oxford University Press. 
  • Brown, Malcolm (1994).^ New York: The New Press, 1999: 99–104 Judge K. Income distribution and life expectancy: a critical appraisal.
    • The Relationship Between Primary Care, Income Inequality, and Mortality in US States, 1980-1995 -- Shi et al. 16 (5): 412 -- The Journal of the American Board of Family Medicine 10 January 2010 3:15 UTC www.jabfm.org [Source type: Academic]

    ^ New York: The New Press.
    • Eastern Economic Journal - Socialism vs Social Democracy as Income-Equalizing Institutions 10 January 2010 3:15 UTC www.palgrave-journals.com [Source type: Academic]

    ^ New York: Oxford University Press; 1996.
    • Population Health Metrics | Full text | Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups 10 January 2010 3:15 UTC www.pophealthmetrics.com [Source type: Academic]

    ."Using Gini-Style Indices to Evaluate the Spatial Patterns of Health Practitioners: Theoretical Considerations and an Application Based on Alberta Data". Social Science Medicine 38: 1243–1256. doi:10.1016/0277-9536(94)90189-9. 
  • Chakravarty, S. R. (1990).^ Social Science & Medicine 1994; 38: 1243-1256.
    • Rural and Remote Health Journal - View Article 10 January 2010 3:15 UTC www.rrh.org.au [Source type: Academic]

    ^ Social Science and Medicine 47: 7-17.

    ^ Social Science Medicine 38 : 1243-1256.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    .Ethical Social Index Numbers.^ Ethical Social Index Numbers .
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .New York: Springer-Verlag. 
  • Deaton, Angus (1997).^ Princeton development economist Angus Deaton (1997, 139) simplified the Gini calculation to one easy formula: .
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ New York: Springer-Verlag.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Deaton, Angus (1997).
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .Analysis of Household Surveys.^ Analysis of Household Surveys .
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .Baltimore MD: Johns Hopkins University Press. 
  • Dixon, PM, Weiner J., Mitchell-Olds T, Woodley R. (1987).^ [Web of Science] Dixon PM, Weiner J, Mitchell-Olds T, Woodley R. 1987.
    • Assessment of Inequality of Root Hair Density in Arabidopsis thaliana using the Gini Coefficient: a Close Look at the Effect of Phosphorus and its Interaction with Ethylene -- HE et al. 95 (2): 287 -- Annals of Botany 10 January 2010 3:15 UTC aob.oxfordjournals.org [Source type: Academic]

    ^ Dixon, PM, Weiner J., Mitchell-Olds T, Woodley R. (1987).
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ [CrossRef] [Web of Science] Dixon PM, Weiner J, Mitchell-Olds T, Woodley R. 1988.
    • Assessment of Inequality of Root Hair Density in Arabidopsis thaliana using the Gini Coefficient: a Close Look at the Effect of Phosphorus and its Interaction with Ethylene -- HE et al. 95 (2): 287 -- Annals of Botany 10 January 2010 3:15 UTC aob.oxfordjournals.org [Source type: Academic]

    ."Bootstrapping the Gini coefficient of inequality". Ecology 68: 1548–1551. doi:10.2307/1939238. 
  • Dorfman, Robert (1979).^ A low Gini coefficient indicates a more equal distribution, with 0 corresponding to complete equality, while higher Gini coefficients indicate more unequal distribution, with 1 corresponding to complete inequality.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Inequality in this diagram is measured using the Gini coefficient, although in principle one could use some other measure of inequality as well.
    • AG EC 450 - Inequality and Corruption in Developing Countries 10 January 2010 3:15 UTC 450.aers.psu.edu [Source type: Original source]

    ^ Comparison of skewness coefficient, coefficient of variation, and Gini coefficient as inequality measures within populations.
    • Assessment of Inequality of Root Hair Density in Arabidopsis thaliana using the Gini Coefficient: a Close Look at the Effect of Phosphorus and its Interaction with Ethylene -- HE et al. 95 (2): 287 -- Annals of Botany 10 January 2010 3:15 UTC aob.oxfordjournals.org [Source type: Academic]

    ."A Formula for the Gini Coefficient". The Review of Economics and Statistics 61: 146–149. doi:10.2307/1924845. 
  • Gastwirth, Joseph L. (1972).^ GDP statistics are often criticised as they do not represent changes for the whole population; the Gini coefficient demonstrates how income has changed for poor and rich.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ The Review of Economics and Statistics 61 : 146-149.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ (The Gini coefficient is a measurement used to gauge the concentration of different variables, mainly income, mortality, and the distribution of health services (10, 11).
    • PAHO Revista/Journal 10 January 2010 3:15 UTC journal.paho.org [Source type: Academic]

    ."The Estimation of the Lorenz Curve and Gini Index". The Review of Economics and Statistics 54: 306–316. doi:10.2307/1937992. 
  • Giles, David (2004).^ The Review of Economics and Statistics 54 : 306-316.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ The Review of Economics and Statistics 54 : 306–316.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ The Gini index is defined as a ratio of the areas on the Lorenz curve diagram.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ."Calculating a Standard Error for the Gini Coefficient: Some Further Results". Oxford Bulletin of Economics and Statistics 66: 425–433. doi:10.1111/j.1468-0084.2004.00086.x. 
  • Gini, Corrado (1912).^ Oxford Bulletin of Economics and Statistics 62 : 119–122.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ The Gini coefficient calculated from a sample is a statistic and its standard error, or confidence intervals for the population Gini coefficient, should be reported.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Oxford Bulletin of Economics and Statistics 62 : 123–129.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ."Variabilità e mutabilità" Reprinted in Memorie di metodologica statistica (Ed.^ "Variabilità e mutabilità" Reprinted in Memorie di metodologica statistica (Ed.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ 'Variabilità e mutabilità' Reprinted in Memorie di metodologica statistica (Ed.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    Pizetti E, Salvemini, T). Rome: Libreria Eredi Virgilio Veschi (1955).
  • Gini, Corrado (1921). ."Measurement of Inequality of Incomes". The Economic Journal 31: 124–126. doi:10.2307/2223319. 
  • Karagiannis, E. and Kovacevic, M. (2000).^ Income distribution was measured by the Gini coefficient, a commonly used indicator of income inequality.
    • The Relationship Between Primary Care, Income Inequality, and Mortality in US States, 1980-1995 -- Shi et al. 16 (5): 412 -- The Journal of the American Board of Family Medicine 10 January 2010 3:15 UTC www.jabfm.org [Source type: Academic]

    ^ The Gini coefficient is a measure of statistical dispersion most prominently used as a measure of inequality of income distribution or inequality of wealth distribution.
    • Down the O-Hole: why the present administration's plans lead to catastrophe (and there isn't anything you can do about it.) | The Agonist 10 January 2010 3:15 UTC agonist.org [Source type: FILTERED WITH BAYES]

    ^ Using a 20 years time series on population health and inequalities in economic, pre-tax, and disposable incomes in Israel, none of the three income inequality measures by itself had an effect over time on population health.
    • Population health and income inequality: new evidence from Israeli time-series analysis -- Shmueli 33 (2): 311 -- International Journal of Epidemiology 10 January 2010 3:15 UTC ije.oxfordjournals.org [Source type: Academic]

    ."A Method to Calculate the Jackknife Variance Estimator for the Gini Coefficient". Oxford Bulletin of Economics and Statistics 62: 119–122. doi:10.1111/1468-0084.00163. 
  • Mills, Jeffrey A.; Zandvakili, Sourushe (1997).^ Oxford Bulletin of Economics and Statistics 68 : 385–390.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Oxford Bulletin of Economics and Statistics 62 : 119–122.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Oxford Bulletin of Economics and Statistics 62 : 123–129.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ."Statistical Inference via Bootstrapping for Measures of Inequality". Journal of Applied Econometrics 12: 133–150. doi:10.1002/(SICI)1099-1255(199703)12:2<133::AID-JAE433>3.0.CO;2-H. 
  • Modarres, Reza and Gastwirth, Joseph L. (2006).^ Journal of Applied Econometrics 12 : 133-150.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ The Gini coefficient is a measure of statistical dispersion most prominently used as a measure of inequality of income distribution or inequality of wealth distribution.
    • Down the O-Hole: why the present administration's plans lead to catastrophe (and there isn't anything you can do about it.) | The Agonist 10 January 2010 3:15 UTC agonist.org [Source type: FILTERED WITH BAYES]

    ^ (SICI)1099-1255(199703)12:2 <133::AID-JAE433> 3.0.CO;2-H .
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ."A Cautionary Note on Estimating the Standard Error of the Gini Index of Inequality". Oxford Bulletin of Economics and Statistics 68: 385–390. doi:10.1111/j.1468-0084.2006.00167.x. 
  • Morgan, James (1962).^ With a few assumptions, it can estimate the standard error for any statistic.
    • Population Health Metrics | Full text | Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups 10 January 2010 3:15 UTC www.pophealthmetrics.com [Source type: Academic]

    ^ Oxford Bulletin of Economics and Statistics 68 : 385–390.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ The Gini index is a statistical measure of income inequality.
    • EastSouthWestNorth: Gini Index in Hong Kong 10 January 2010 3:15 UTC www.zonaeuropa.com [Source type: Original source]

    ."The Anatomy of Income Distribution". The Review of Economics and Statistics 44: 270–283. doi:10.2307/1926398. 
  • Ogwang, Tomson (2000).^ The Review of Economics and Statistics 61 : 146-149.
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]

    ^ Income Inequality Decomposition by Income Source and the Breakdown of Inequality Differences Between Two Population Subgroups ," Swiss Journal of Economics and Statistics (SJES) , Swiss Society of Economics and Statistics (SSES), vol.
    • Jacques Silber at IDEAS 11 September 2009 5:58 UTC ideas.repec.org [Source type: Academic]

    ^ On an absolute measure of distributional change ," European Economic Review , Elsevier, vol.
    • Jacques Silber at IDEAS 11 September 2009 5:58 UTC ideas.repec.org [Source type: Academic]

    ."A Convenient Method of Computing the Gini Index and its Standard Error". Oxford Bulletin of Economics and Statistics 62: 123–129. doi:10.1111/1468-0084.00164. 
  • Ogwang, Tomson (2004).^ Oxford Bulletin of Economics and Statistics 68 : 385–390.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Oxford Bulletin of Economics and Statistics 62 : 119–122.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Oxford Bulletin of Economics and Statistics 62 : 123–129.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ."Calculating a Standard Error for the Gini Coefficient: Some Further Results: Reply". Oxford Bulletin of Economics and Statistics 66: 435–437. doi:10.1111/j.1468-0084.2004.00087.x. 
  • Xu, Kuan (January 2004).^ Oxford Bulletin of Economics and Statistics 68 : 385–390.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ Oxford Bulletin of Economics and Statistics 62 : 119–122.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ The Gini coefficient calculated from a sample is a statistic and its standard error, or confidence intervals for the population Gini coefficient, should be reported.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .How Has the Literature on Gini's Index Evolved in the Past 80 Years?.^ How Has the Literature on Gini's Index Evolved in the Past 80 Years?
    • vivi_新浪博客 10 January 2010 3:15 UTC blog.sina.com.cn [Source type: FILTERED WITH BAYES]
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ "How Has the Literature on Gini's Index Evolved in the Past 80 Years?".
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ For statistics nerds, calculating Gini indices of weird stuff (like how many pairs of socks a person buys in a year) is a common dorky timewaster.
    • Matthew Yglesias » Social Spending and Inequality 10 January 2010 3:15 UTC yglesias.thinkprogress.org [Source type: Original source]

    .Department of Economics, Dalhousie University.^ Department of Community Health and Epidemiology, Faculty of Medicine, Dalhousie, University, 5790 University Avenue, Halifax, Nova Scotia, B3H 1V7, Canada .
    • Population Health Metrics | Full text | Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups 10 January 2010 3:15 UTC www.pophealthmetrics.com [Source type: Academic]

    ^ Dispersion, Asymmetry and the Gini Index of Inequality ," International Economic Review , Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol.
    • Jacques Silber at IDEAS 11 September 2009 5:58 UTC ideas.repec.org [Source type: Academic]

    ^ Department of Economics Bar Ilan University .
    • Jacques Silber at IDEAS 11 September 2009 5:58 UTC ideas.repec.org [Source type: Academic]

    .http://economics.dal.ca/RePEc/dal/wparch/howgini.pdf.^ The paper describing this method can be found here: http://web.uvic.ca/econ/ewp0202.pdf .
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ RePEc/dal/wparch/howgini.pdf .
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    .Retrieved 2006-06-01.
      The Chinese version of this paper appears in Xu, Kuan (2003).^ Retrieved 2006-06-01 .
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ The Chinese version of this paper appears in Xu, Kuan (2003).
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ."How Has the Literature on Gini's Index Evolved in the Past 80 Years?". China Economic Quarterly 2: 757–778. 
  • Yitzhaki, S. (1991).^ The measure that the stories in China have been using -- one beloved of academics the world over -- is the United Nations Development Program's so-called "Gini coefficient index."
    • Letting the Gini Out of the Bottle - WSJ.com 10 January 2010 3:15 UTC online.wsj.com [Source type: News]

    ^ China Economic Quarterly 2 : 757–778.
    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    ^ How Has the Literature on Gini's Index Evolved in the Past 80 Years?
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    • Boston University School of Theology Archives 10 January 2010 3:15 UTC sthweb.bu.edu [Source type: Academic]

    "Calculating Jackknife Variance Estimators for Parameters of the Gini Method". Journal of Business and Economic Statistics 9: 235–239. doi:10.2307/1391792. 

External links

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The Gini coefficient is a measure of statistical dispersion developed by the Italian statistician Corrado Gini and published in his 1912 paper "Variability and Mutability" (Italian: Variabilità e mutabilità).

The Gini coefficient is a measure of the inequality of a distribution, a value of 0 expressing total equality and a value of 1 maximal inequality. It has found application in the study of inequalities in disciplines as diverse as economics, health science, ecology, chemistry and engineering.

It is commonly used as a measure of inequality of income or wealth. Worldwide, Gini coefficients for income range from approximately 0.23 (Sweden) to 0.70 (Namibia) although not every country has been assessed.

Contents

Definition

The Gini coefficient is usually defined mathematically based on the Lorenz curve, which plots the proportion of the total income of the population (y axis) that is cumulatively earned by the bottom x% of the population (see diagram). The line at 45 degrees thus represents perfect equality of incomes. The Gini coefficient can then be thought of as the ratio of the area that lies between the line of equality and the Lorenz curve (marked 'A' in the diagram) over the total area under the line of equality (marked 'A' and 'B' in the diagram); i.e., G=A/(A+B).

The Gini coefficient can range from 0 to 1; it is sometimes multiplied by 100 to range between 0 and 100. A low Gini coefficient indicates a more equal distribution, with 0 corresponding to complete equality, while higher Gini coefficients indicate more unequal distribution, with 1 corresponding to complete inequality. To be validly computed, no negative goods can be distributed. Thus, if the Gini coefficient is being used to describe household income inequality, then no household can have a negative income. When used as a measure of income inequality, the most unequal society will be one in which a single person receives 100% of the total income and the remaining people receive none (G=1); and the most equal society will be one in which every person receives the same income (G=0).

Some find it more intuitive (and it is mathematically equivalent) to think of the Gini coefficient as half of the relative mean difference. The mean difference is the average absolute difference between two items selected randomly from a population, and the relative mean difference is the mean difference divided by the average, to normalize for scale.

Calculation

The Gini index is defined as a ratio of the areas on the Lorenz curve diagram. If the area between the line of perfect equality and the Lorenz curve is A, and the area under the Lorenz curve is B, then the Gini index is A/(A+B). Since A+B = 0.5, the Gini index, G = A/(0.5) = 2A = 1-2B. If the Lorenz curve is represented by the function Y = L(X), the value of B can be found with integration and:

G = 1 - 2\,\int_0^1 L(X) dX.

In some cases, this equation can be applied to calculate the Gini coefficient without direct reference to the Lorenz curve. For example:

  • For a population uniform on the values yi, i = 1 to n, indexed in non-decreasing order ( yiyi+1):
G = \frac{1}{n}\left ( n+1 - 2 \left ( \frac{\Sigma_{i=1}^n \; (n+1-i)y_i}{\Sigma_{i=1}^n y_i} \right ) \right )
This may be simplified to:
G = \frac{2 \Sigma_{i=1}^n \; i y_i}{n \Sigma_{i=1}^n y_i} -\frac{n+1}{n}
  • For a discrete probability function f(y), where yi, i = 1 to n, are the points with nonzero probabilities and which are indexed in increasing order ( yi < yi+1):
G = 1 - \frac{\Sigma_{i=1}^n \; f(y_i)(S_{i-1}+S_i)}{S_n}
where
S_i = \Sigma_{j=1}^i \; f(y_j)\,y_j\, and S_0 = 0\,
G = 1 - \frac{1}{\mu}\int_0^\infty (1-F(y))^2dy = \frac{1}{\mu}\int_0^\infty F(y)(1-F(y))dy
  • Since the Gini coefficient is half the relative mean difference, it can also be calculated using formulas for the relative mean difference. For a random sample S consisting of values yi, i = 1 to n, that are indexed in non-decreasing order ( yiyi+1), the statistic:
G(S) = \frac{1}{n-1}\left (n+1 - 2 \left ( \frac{\Sigma_{i=1}^n \; (n+1-i)y_i}{\Sigma_{i=1}^n y_i}\right ) \right )
is a consistent estimator of the population Gini coefficient, but is not, in general, unbiased. Like, G, G(S) has a simpler form:
G(S) = 1 - \frac{2}{n-1}\left ( n - \frac{\Sigma_{i=1}^n \; iy_i}{\Sigma_{i=1}^n y_i}\right ) .

There does not exist a sample statistic that is in general an unbiased estimator of the population Gini coefficient, like the relative mean difference.

Sometimes the entire Lorenz curve is not known, and only values at certain intervals are given. In that case, the Gini coefficient can be approximated by using various techniques for interpolating the missing values of the Lorenz curve. If ( X k , Yk ) are the known points on the Lorenz curve, with the X k indexed in increasing order ( X k - 1 < X k ), so that:

  • Xk is the cumulated proportion of the population variable, for k = 0,...,n, with X0 = 0, Xn = 1.
  • Yk is the cumulated proportion of the income variable, for k = 0,...,n, with Y0 = 0, Yn = 1.
  • Yk should be indexed in non-decreasing order (Yk>Yk-1)

If the Lorenz curve is approximated on each interval as a line between consecutive points, then the area B can be approximated with trapezoids and:

G_1 = 1 - \sum_{k=1}^{n} (X_{k} - X_{k-1}) (Y_{k} + Y_{k-1})

is the resulting approximation for G. More accurate results can be obtained using other methods to approximate the area B, such as approximating the Lorenz curve with a quadratic function across pairs of intervals, or building an appropriately smooth approximation to the underlying distribution function that matches the known data. If the population mean and boundary values for each interval are also known, these can also often be used to improve the accuracy of the approximation.

The Gini coefficient calculated from a sample is a statistic and its standard error, or confidence intervals for the population Gini coefficient, should be reported. These can be calculated using bootstrap techniques but those proposed have been mathematically complicated and computationally onerous even in an era of fast computers. Ogwang (2000) made the process more efficient by setting up a “trick regression model” in which the incomes in the sample are ranked with the lowest income being allocated rank 1. The model then expresses the rank (dependent variable) as the sum of a constant A and a normal error term whose variance is inversely proportional to yk;

k = A + \ N(0, s^{2}/y_k)

Ogwang showed that G can be expressed as a function of the weighted least squares estimate of the constant A and that this can be used to speed up the calculation of the jackknife estimate for the standard error. Giles (2004) argued that the standard error of the estimate of A can be used to derive that of the estimate of G directly without using a jackknife at all. This method only requires the use of ordinary least squares regression after ordering the sample data. The results compare favorably with the estimates from the jackknife with agreement improving with increasing sample size. The paper describing this method can be found here: http://web.uvic.ca/econ/ewp0202.pdf

However it has since been argued that this is dependent on the model’s assumptions about the error distributions (Ogwang 2004) and the independence of error terms (Reza & Gastwirth 2006) and that these assumptions are often not valid for real data sets. It may therefore be better to stick with jackknife methods such as those proposed by Yitzhaki (1991) and Karagiannis and Kovacevic (2000). The debate continues.

The Gini coefficient can be calculated if you know the mean of a distribution, the number of people (or percentiles), and the income of each person (or percentile). Princeton development economist Angus Deaton (1997, 139) simplified the Gini calculation to one easy formula:

G = \frac{N+1}{N-1}-\frac{2}{N(N-1)u}(\Sigma_{i=1}^n \; P_iX_i)

where u is mean income of the population, Pi is the income rank P of person i, with income X, such that the richest person receives a rank of 1 and the poorest a rank of N. This effectively gives higher weight to poorer people in the income distribution, which allows the Gini to meet the Transfer Principle.

Generalised inequality index

The Gini coefficient and other standard inequality indices reduce to a common form. Perfect equality—the absence of inequality—exists when and only when the inequality ratio, r_j = x_j / \overline{x}, equals 1 for all j units in some population; for example, there is perfect income equality when everyone’s income x_j equals the mean income \overline{x}, so that r_j=1 for everyone). Measures of inequality, then, are measures of the average deviations of the r_j=1 from 1; the greater the average deviation, the greater the inequality. Based on these observations the inequality indices have this common form:[1]

Inequality = \Sigma_j \, p_j \, f(r_j)\, ,

where pj weights the units by their population share, and f(rj) is a function of the deviation of each unit’s rj from 1, the point of equality. The insight of this generalised inequality index is that inequality indices differ because they employ different functions of the distance of the inequality ratios (the rj) from 1.

Gini coefficient of income distributions

While developed European nations and Canada tend to have Gini indices between 24 and 36, the United States' and Mexico's Gini indices are both above 40, indicating that the United States and Mexico have greater inequality. Using the Gini can help quantify differences in welfare and compensation policies and philosophies. However it should be borne in mind that the Gini coefficient can be misleading when used to make political comparisons between large and small countries (see criticisms section).

The Gini index for the entire world has been estimated by various parties to be between 56 and 66.[2][3]

US income Gini indices over time

Gini indices for the United States at various times, according to the US Census Bureau:[4][5][6]

  • 1929: 45.0 (estimated)
  • 1947: 37.6 (estimated)
  • 1967: 39.7 (first year reported)
  • 1968: 38.6 (lowest index reported)
  • 1970: 39.4
  • 1980: 40.3
  • 1990: 42.8
  • 2000: 46.2 [7]
  • 2005: 46.9
  • 2006: 47.0 (highest index reported)
  • 2007: 46.3
  • 2008: 46.69
  • 2009: 46.8

EU Gini index

In 2005 the AVERAGE Gini index for the EU was estimated at 31.[8]

Advantages of Gini coefficient as a measure of inequality

  • It can be used to compare income distributions across different population sectors as well as countries, for example the Gini coefficient for urban areas differs from that of rural areas in many countries (though the United States' urban and rural Gini coefficients are nearly identical).
  • It is sufficiently simple that it can be compared across countries and be easily interpreted. GDP statistics are often criticized as they do not represent changes for the whole population; the Gini coefficient demonstrates how income has changed for poor and rich. If the Gini coefficient is rising as well as GDP, poverty may not be improving for the majority of the population.
  • The Gini coefficient can be used to indicate how the distribution of income has changed within a country over a period of time, thus it is possible to see if inequality is increasing or decreasing.
  • The Gini coefficient satisfies four important principles[9]:
    • Anonymity: it does not matter who the high and low earners are.
    • Scale independence: the Gini coefficient does not consider the size of the economy, the way it is measured, or whether it is a rich or poor country on average.
    • Population independence: it does not matter how large the population of the country is.
    • Transfer principle: if income (less than half of the difference), is transferred from a rich person to a poor person the resulting distribution is more equal.

Disadvantages of Gini coefficient as a measure of inequality

  • While the Gini coefficient measures inequality of income, it does not measure inequality of opportunity. For example, some countries may have a social class structure that may present barriers to upward mobility; this is not reflected in their Gini coefficients.
  • The Gini coefficient of different sets of people cannot be averaged to obtain the Gini coefficient of all the people in the sets: if a Gini coefficient were to be calculated for each person it would always be zero. For a large, economically diverse country, a much higher coefficient will be calculated for the country as a whole than will be calculated for each of its regions. (The coefficient is usually applied to measurable nominal income rather than local purchasing power, tending to increase the calculated coefficient across larger areas.)
  • The Lorenz curve may understate the actual amount of inequality if richer households are able to use income more efficiently than lower income households or vice versa. From another point of view, measured inequality may be the result of more or less efficient use of household incomes.
  • Economies with similar incomes and Gini coefficients can still have very different income distributions. (This is true for any single measure of a distribution.) This is because the Lorenz curves can have different shapes and yet still yield the same Gini coefficient. For example, consider a society where half of individuals had no income and the other half shared all the income equally (i.e. whose Lorenz curve is linear from (0,0) to (0.5,0) and then linear to (1,1)). As is easily calculated, this society has Gini coefficient 0.5 -- the same as that of a society in which 75% of people equally shared 25% of income while the remaining 25% equally shared 75% (i.e. whose Lorenz curve is linear from (0,0) to (0.75,0.25) and then linear to (1,1)).
  • It measures current income rather than lifetime income. A society in which everyone earned the same over a lifetime would appear unequal because of people at different stages in their life; a society in which students study rather than save can never have a coefficient of 0. However, Gini coefficient can also be calculated for any kind of single-variable distribution, e.g. for wealth.[10]
  • Gini coefficients do include investment income; however, the Gini coefficient based on net income does not accurately reflect differences in wealth—a possible source of misinterpretation. For example, Sweden has a low Gini coefficient for income distribution but a significantly higher Gini coefficient for wealth (for instance 77% of the share value owned by households is held by just 5% of Swedish shareholding households ).[11] In other words, the Gini income coefficient should not be interpreted as measuring effective egalitarianism.
  • Too often only the Gini coefficient is quoted without describing the proportions of the quantiles used for measurement. As with other inequality coefficients, the Gini coefficient is influenced by the granularity of the measurements. For example, five 20% quantiles (low granularity) will usually yield a lower Gini coefficient than twenty 5% quantiles (high granularity) taken from the same distribution. This is an often encountered problem with measurements.
  • Care should be taken in using the Gini coefficient as a measure of egalitarianism, as it is properly a measure of income dispersion. For example, if two equally egalitarian countries pursue different immigration policies, the country accepting higher proportion of low-income or impoverished migrants will be assessed as less equal (gain a higher Gini coefficient).
  • The Gini coefficient is a point-estimate of equality at a certain time, hence it ignores life-span changes in income. Typically, increases in the proportion of young or old members of a society will drive apparent changes in equality. Because of this, factors such as age distribution within a population and mobility within income classes can create the appearance of differential equality when none exist taking into account demographic effects. Thus a given economy may have a higher Gini coefficient at any one point in time compared to another, while the Gini coefficient calculated over individuals' lifetime income is actually lower than the apparently more equal (at a given point in time) economy's.[12] Essentially, what matters is not just inequality in any particular year, but the composition of the distribution over time.

General problems of measurement

  • Comparing income distributions among countries may be difficult because benefits systems may differ. For example, some countries give benefits in the form of money while others give food stamps, which might not be counted by some economists and researchers as income in the Lorenz curve and therefore not taken into account in the Gini coefficient. Income in the United States is counted before benefits, while in France it is counted after benefits, which may lead the United States to appear somewhat more unequal vis-a-vis France. In another example, the Soviet Union was measured to have relatively high income inequality: by some estimates, in the late 1970s, Gini coefficient of its urban population was as high as 0.38,[13] which is higher than many Western countries today. This number would not reflect those benefits received by Soviet citizens that were not monetized for measurement, which may include child care for children as young as two months, elementary, secondary and higher education, cradle-to-grave medical care, and heavily subsidized or provided housing. In this example, a more accurate comparison between the 1970s Soviet Union and Western countries may require one to assign monetary values to all benefits – a difficult task in the absence of free markets. Similar problems arise whenever a comparison between pure free-market economies and partially socialist economies is attempted. Benefits may take various and unexpected forms: for example, major oil producers such as Venezuela and Iran provide indirect benefits to its citizens by subsidizing the retail price of gasoline.
  • Similarly, in some societies people may have significant income in other forms than money, for example through subsistence farming or bartering. Like non-monetary benefits, the value of these incomes is difficult to quantify. Different quantifications of these incomes will yield different Gini coefficients.
  • The measure will give different results when applied to individuals instead of households. When different populations are not measured with consistent definitions, comparison is not meaningful.
  • As for all statistics, there may be systematic and random errors in the data. The meaning of the Gini coefficient decreases as the data become less accurate. Also, countries may collect data differently, making it difficult to compare statistics between countries.

As one result of this criticism, in addition to or in competition with the Gini coefficient entropy measures are frequently used (e.g. the Theil Index and the Atkinson index). These measures attempt to compare the distribution of resources by intelligent agents in the market with a maximum entropy random distribution, which would occur if these agents acted like non-intelligent particles in a closed system following the laws of statistical physics.

Credit risk

The Gini coefficient is also commonly used for the measurement of the discriminatory power of rating systems in credit risk management.

The discriminatory power refers to a credit risk model's ability to differentiate between defaulting and non-defaulting clients. The above formula G_1 may be used for the final model and also at individual model factor level, to quantify the discriminatory power of individual factors. This is as a result of too many non defaulting clients falling into the lower points scale e.g. factor has a 10 point scale and 30% of non defaulting clients are being assigned the lowest points available e.g. 0 or negative points. This indicates that the factor is behaving in a counter-intuitive manner and would require further investigation at the model development stage. [14]

Other uses

Although the Gini coefficient is most popular in economics, it can in theory be applied in any field of science that studies a distribution. For example, in ecology the Gini coefficient has been used as a measure of biodiversity, where the cumulative proportion of species is plotted against cumulative proportion of individuals.[15] In health, it has been used as a measure of the inequality of health related quality of life in a population.[16] In education, it has been used as a measure of the inequality of universities.[17] In chemistry it has been used to express the selectivity of protein kinase inhibitors against a panel of kinases.[18] In engineering, it has been used to evaluate the fairness achieved by Internet routers in scheduling packet transmissions from different flows of traffic.[19] In statistics, building decision trees, it is used to measure the purity of possible child nodes, with the aim of maximising the average purity of two child nodes when splitting.

See also

References

  1. ^ Firebaugh, Glenn (1999). [Expression error: Unexpected < operator "Empirics of World Income Inequality"]. American Journal of Sociology 104 (6): 1597–1630. doi:10.1086/210218 . See also     (2003). "Inequality: What it is and how it is measured". The New Geography of Global Income Inequality. Cambridge, MA: Harvard University Press. ISBN 0674010671 .
  2. ^ Bob Sutcliffe (April 2007). "Postscript to the article ‘World inequality and globalization’ (Oxford Review of Economic Policy, Spring 2004)". http://siteresources.worldbank.org/INTDECINEQ/Resources/PSBSutcliffe.pdf. Retrieved 2007-12-13 
  3. ^ United Nations Development Programme
  4. ^ "Gini Ratios for Households, by Race and Hispanic Origin of Householder: 1967 to 2007". Historical Income Tables - Households. United States Census Bureau. http://www.census.gov/hhes/www/income/histinc/h04.html. 
  5. ^ "Table 3. Income Distribution Measures Using Money Income and Equivalence-Adjusted Income: 2007 and 2008". Income, Poverty, and Health Insurance Coverage in the United States: 2008. United States Census Bureau. p. 17. http://www.census.gov/prod/2009pubs/p60-236.pdf. 
  6. ^ "Income, Poverty and Health Insurance Coverage in the United States: 2009". Newsroom. United States Census Bureau. http://www.census.gov/newsroom/releases/archives/income_wealth/cb10-144.html. 
  7. ^ Note that the calculation of the index for the United States was changed in 1992, resulting in an upwards shift of about 2.
  8. ^ "Monitoring quality of life in Europe - Gini index". Eurofound. 26 August 2009. http://www.eurofound.europa.eu/areas/qualityoflife/eurlife/index.php?template=3&radioindic=158&idDomain=3 .
  9. ^ Ray, Debraj (1998). Development Economics. Princeton, NJ: Princeton University Press. p. 188. ISBN 0691017069 .
  10. ^ Friedman, David D.
  11. ^ (Data from the Statistics Sweden.)
  12. ^ Blomquist, N. (1981). [Expression error: Unexpected < operator "A comparison of distributions of annual and lifetime income: Sweden around 1970"]. Review of Income and Wealth 27 (3): 243–264. doi:10.1111/j.1475-4991.1981.tb00227.x .
  13. ^ Millar, James R. (1987). Politics, work, and daily life in the USSR. New York: Cambridge University Press. p. 193. ISBN 0521348900 .
  14. ^ The Analytics of risk model validation[specify]
  15. ^ Wittebolle, Lieven; et al. (2009). [Expression error: Unexpected < operator "Initial community evenness favours functionality under selective stress"]. Nature 458 (7238): 623–626. doi:10.1038/nature07840. PMID 19270679. 
  16. ^ Asada, Yukiko (2005). [Expression error: Unexpected < operator "Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups"]. Population Health Metrics 3: 7. doi:10.1186/1478-7954-3-7. PMID 16014174. 
  17. ^ Halffman, Willem; Leydesdorff, L (2010). [Expression error: Unexpected < operator "Is Inequality Among Universities Increasing? Gini Coefficients and the Elusive Rise of Elite Universities"]. Minerva 48 (1): 55–72. doi:10.1007/s11024-010-9141-3. PMID 20401157. 
  18. ^ Graczyk, Piotr (2007). [Expression error: Unexpected < operator "Gini Coefficient: A New Way To Express Selectivity of Kinase Inhibitors against a Family of Kinases"]. Journal of Medicinal Chemistry 50 (23): 5773–5779. doi:10.1021/jm070562u. PMID 17948979. 
  19. ^ Shi, Hongyuan; Sethu, Harish (2003). "Greedy Fair Queueing: A Goal-Oriented Strategy for Fair Real-Time Packet Scheduling". Proceedings of the 24th IEEE Real-Time Systems Symposium. IEEE Computer Society. pp. 345–356. ISBN 0-7695-2044-8 

Further reading

External links


Citable sentences

Up to date as of December 22, 2010

Here are sentences from other pages on Gini coefficient, which are similar to those in the above article.








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