IDEAS home Printed from https://ideas.repec.org/a/spr/joecin/v22y2024i4d10.1007_s10888-024-09623-y.html
   My bibliography  Save this article

A note on Sen’s representation of the Gini coefficient: Revision and repercussions

Author

Listed:
  • Oded Stark

    (University of Bonn
    University of Warsaw)

Abstract

Sen (1973 and 1997) presents the Gini coefficient of income inequality in a population as follows. “In any pair-wise comparison the man with the lower income can be thought to be suffering from some depression on finding his income to be lower. Let this depression be proportional to the difference in income. The sum total of all such depressions in all possible pair-wise comparisons takes us to the Gini coefficient.” (This citation is from Sen 1973, p. 8.) Sen’s verbal account is accompanied by a formula (Sen 1997, p. 31, eq. 2.8.1), which is replicated in the text of this note as equation (1). The formula yields a coefficient bounded from above by a number smaller than 1. This creates a difficulty, because the “mission” of a measure of inequality defined on the unit interval is to accord 0 to perfect equality (maximal equality) and 1 to perfect inequality (maximal inequality). In this note we show that when the Gini coefficient is elicited from a neat measure of the aggregate income-related depression of the population that consists of the people who experience income-related depression, then the obtained Gini coefficient is “well behaved” in the sense that it is bounded from above by 1. We conjecture a reason for a drawback of Sen’s definition, and we present repercussions of the usage of the “well-behaved” Gini coefficient.

Suggested Citation

  • Oded Stark, 2024. "A note on Sen’s representation of the Gini coefficient: Revision and repercussions," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 22(4), pages 1061-1067, December.
    • Handle: RePEc:spr:joecin:v:22:y:2024:i:4:d:10.1007_s10888-024-09623-y
    DOI: 10.1007/s10888-024-09623-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10888-024-09623-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10888-024-09623-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Oded Stark, 2020. "An Economics-Based Rationale for the Rawlsian Social Welfare Program," Research on Economic Inequality, in: Inequality, Redistribution and Mobility, volume 28, pages 179-186, Emerald Group Publishing Limited.
    2. Lidia Ceriani & Paolo Verme, 2012. "The origins of the Gini index: extracts from Variabilità e Mutabilità (1912) by Corrado Gini," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(3), pages 421-443, September.
    3. Stark, Oded, 2023. "On a tendency in health economics to dwell on income inequality and underestimate social stress," Economics & Human Biology, Elsevier, vol. 49(C).
    4. Amartya Sen, 1976. "Real National Income," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(1), pages 19-39.
    5. Oded Stark & Wiktor Budzinski, 2021. "A social‐psychological reconstruction of Amartya Sen’s measures of inequality and social welfare," Kyklos, Wiley Blackwell, vol. 74(4), pages 552-566, November.
    6. George Deltas, 2003. "The Small-Sample Bias of the Gini Coefficient: Results and Implications for Empirical Research," The Review of Economics and Statistics, MIT Press, vol. 85(1), pages 226-234, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Oded Stark & Wiktor Budzinski, 2021. "A social‐psychological reconstruction of Amartya Sen’s measures of inequality and social welfare," Kyklos, Wiley Blackwell, vol. 74(4), pages 552-566, November.
    2. Ulrich Schmidt & Philipp C. Wichardt, 2019. "Inequity aversion, welfare measurement and the Gini index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 585-588, March.
    3. Jorge A. Bonilla & Claudia Aravena & Ricardo Morales-Betancourt, 2021. "Assessing Multiple Inequalities and Air Pollution Abatement Policies," Documentos CEDE 19465, Universidad de los Andes, Facultad de Economía, CEDE.
    4. Ogwang, Tomson, 2007. "Additional properties of a linear pen's parade for individual data using the stochastic approach to the Gini index," Economics Letters, Elsevier, vol. 96(3), pages 369-374, September.
    5. Anastasios Evgenidis & Apostolos Fasianos, 2019. "Monetary Policy and Wealth Inequalities in Great Britain: Assessing the role of unconventional policies for a decade of household data," Papers 1912.09702, arXiv.org.
    6. Jo Thori Lind & Karl Moene, 2011. "Miserly Developments," Journal of Development Studies, Taylor & Francis Journals, vol. 47(9), pages 1332-1352, June.
    7. He, Xi, 2018. "Bigger Farms and Bigger Food Firms-The Agricultural Origin of Industrial Concentration in the Food Sector," 2018 Annual Meeting, August 5-7, Washington, D.C. 274206, Agricultural and Applied Economics Association.
    8. Miguel A. Márquez & Elena Lasarte & Marcelo Lufin, 2019. "The Role of Neighborhood in the Analysis of Spatial Economic Inequality," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 141(1), pages 245-273, January.
    9. Xiaofeng Lv & Gupeng Zhang & Guangyu Ren, 2017. "Gini index estimation for lifetime data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 275-304, April.
    10. Zengzeng Fan & Wei Zou, 2023. "A Three-Component Decomposition of the Change in Relative Poverty: An Application to China," Land, MDPI, vol. 12(1), pages 1-15, January.
    11. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    12. David E. Giles, 2005. "The Bias of Inequality Measures in Very Small Samples: Some Analytic Results," Econometrics Working Papers 0514, Department of Economics, University of Victoria.
    13. Fotis Papadopoulos & Panos Tsakloglou, 2015. "Chronic material deprivation and long-term poverty in Europe in the pre-crisis period," ImPRovE Working Papers 15/16, Herman Deleeck Centre for Social Policy, University of Antwerp.
    14. Stefan Thewissen & Olaf Vliet & Chen Wang, 2018. "Taking the Sector Seriously: Data, Developments, and Drivers of Intrasectoral Earnings Inequality," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 138(3), pages 1023-1048, August.
    15. Juan Antonio Duro Moreno, 2001. "Cross-country inequalities in aggregate welfare: some evidence," Applied Economics Letters, Taylor & Francis Journals, vol. 8(6), pages 403-406.
    16. Silvia De Nicol`o & Maria Rosaria Ferrante & Silvia Pacei, 2021. "Mind the Income Gap: Bias Correction of Inequality Estimators in Small-Sized Samples," Papers 2107.08950, arXiv.org, revised May 2023.
    17. Tom Van Ourti & Philip Clarke, 2008. "The Bias of the Gini Coefficient due to Grouping," Tinbergen Institute Discussion Papers 08-095/3, Tinbergen Institute.
    18. Guillermo Durán, 2021. "Sports scheduling and other topics in sports analytics: a survey with special reference to Latin America," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 125-155, April.
    19. Schepelmann, Philipp & Goossens, Yanne & Makipaa, Arttu (ed.), 2009. "Towards sustainable development: Alternatives to GDP for measuring progress," Wuppertal Spezial, Wuppertal Institute for Climate, Environment and Energy, volume 42, number 42.
    20. R駩s Chenavaz & Octavio Escobar, 2015. "Population distribution, effective area and economic growth," Applied Economics, Taylor & Francis Journals, vol. 47(53), pages 5776-5790, November.

    More about this item

    Keywords

    Sen’s definition of the Gini coefficient of income inequality; Aggregate income-related depression of a population; A “well-behaved” Gini coefficient;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecin:v:22:y:2024:i:4:d:10.1007_s10888-024-09623-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.