IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20080095.html
   My bibliography  Save this paper

The Bias of the Gini Coefficient due to Grouping

Author

Listed:
  • Tom Van Ourti

    (Erasmus University Rotterdam, the Netherlands)

  • Philip Clarke

    (University of Sydney, Australia)

Abstract

Read also the publication in the 'Review of Economics and Statistics' , 2010, 93(3), 982-994. We propose a first order bias correction term for the Gini index to reduce the bias due to grouping. The first order correction term is obtained from studying the estimator of the Gini index within a measurement error framework. In addition, it reveals an intuitive formula for the remaining second order bias which is useful in empirical analyses. We analyze the empirical performance of our first order correction term using income data for 15 European countries and the US, and show that it reduces a considerable share of the bias due to grouping.

Suggested Citation

  • Tom Van Ourti & Philip Clarke, 2008. "The Bias of the Gini Coefficient due to Grouping," Tinbergen Institute Discussion Papers 08-095/3, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20080095
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/08095.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ryu, Hang K. & Slottje, Daniel J., 1996. "Two flexible functional form approaches for approximating the Lorenz curve," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 251-274.
    2. Schader, Martin & Schmid, Friedrich, 1994. "Fitting Parametric Lorenz Curves to Grouped Income Distributions--A Critical Note," Empirical Economics, Springer, vol. 19(3), pages 361-370.
    3. Lambert, Peter J & Aronson, J Richard, 1993. "Inequality Decomposition Analysis and the Gini Coefficient Revisited," Economic Journal, Royal Economic Society, vol. 103(420), pages 1221-1227, September.
    4. Chen, Chau-Nan & Tsaur, Tien-Wang & Rhai, Tong-Shieng, 1982. "The Gini Coefficient and Negative Income," Oxford Economic Papers, Oxford University Press, vol. 34(3), pages 473-478, November.
    5. Buzzacchi, Luigi & Valletti, Tommaso M., 2006. "Firm size distribution: Testing the "independent submarkets model" in the Italian motor insurance industry," International Journal of Industrial Organization, Elsevier, vol. 24(4), pages 809-834, July.
    6. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    7. Murray, David, 1978. "Extreme values for Gini coefficients calculated from grouped data," Economics Letters, Elsevier, vol. 1(4), pages 389-393.
    8. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    9. Xavier Sala-i-Martin, 2006. "The World Distribution of Income: Falling Poverty and … Convergence, Period," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(2), pages 351-397.
    10. Pradhan, Menno & Sahn, David E. & Younger, Stephen D., 2003. "Decomposing world health inequality," Journal of Health Economics, Elsevier, vol. 22(2), pages 271-293, March.
    11. Chun-Hung Lin, 2007. "Education Expansion, Educational Inequality, and Income Inequality: Evidence from Taiwan, 1976–2003," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 80(3), pages 601-615, February.
    12. Lerman, Robert I. & Yitzhaki, Shlomo, 1989. "Improving the accuracy of estimates of Gini coefficients," Journal of Econometrics, Elsevier, vol. 42(1), pages 43-47, September.
    13. Mills, Jeffrey A & Zandvakili, Sourushe, 1997. "Statistical Inference via Bootstrapping for Measures of Inequality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 133-150, March-Apr.
    14. Datt, Gaurav & Ravallion, Martin, 1992. "Growth and redistribution components of changes in poverty measures : A decomposition with applications to Brazil and India in the 1980s," Journal of Development Economics, Elsevier, vol. 38(2), pages 275-295, April.
    15. Villasenor, JoseA. & Arnold, Barry C., 1989. "Elliptical Lorenz curves," Journal of Econometrics, Elsevier, vol. 40(2), pages 327-338, February.
    16. Wagstaff, Adam & Paci, Pierella & van Doorslaer, Eddy, 1991. "On the measurement of inequalities in health," Social Science & Medicine, Elsevier, vol. 33(5), pages 545-557, January.
    17. Blyde, Juan S., 2006. "Convergence Dynamics in Mercosur," Journal of Economic Integration, Center for Economic Integration, Sejong University, vol. 21, pages 784-815.
    18. Tomson Ogwang, 2003. "Bounds of the Gini Index Using Sparse Information on Mean Incomes," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 49(3), pages 415-423, September.
    19. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053, September.
    20. Aronson, J Richard & Johnson, Paul & Lambert, Peter J, 1994. "Redistributive Effects and Unequal Income Tax Treatment," Economic Journal, Royal Economic Society, vol. 104(423), pages 262-270, March.
    21. Aisling Reynolds-Feighan, 2007. "Competing Networks, Spatial and Industrial Concentration in the US Airline Industry," Spatial Economic Analysis, Taylor & Francis Journals, vol. 2(3), pages 237-257.
    22. Fuller, Mike, 1979. "The estimation of Gini coefficients from grouped data : Upper and Lower Bounds," Economics Letters, Elsevier, vol. 3(2), pages 187-192.
    23. Graham Pyatt & Chau-nan Chen & John Fei, 1980. "The Distribution of Income by Factor Components," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(3), pages 451-473.
    24. 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.
    25. Tomson Ogwang, 2006. "An Upper Bound Of The Gini Index In The Absence Of Mean Income Information," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 52(4), pages 643-652, December.
    26. Le Grand, Julian, 1987. "Inequalities in health : Some international comparisons," European Economic Review, Elsevier, vol. 31(1-2), pages 182-191.
    27. van Praag, Bernard M S & Hagenaars, Aldi J M & van Eck, Wim, 1983. "The Influence of Classification and Observation Errors on the Measurement of Income Inequality," Econometrica, Econometric Society, vol. 51(4), pages 1093-1108, July.
    28. Kakwani, Nanak & Wagstaff, Adam & van Doorslaer, Eddy, 1997. "Socioeconomic inequalities in health: Measurement, computation, and statistical inference," Journal of Econometrics, Elsevier, vol. 77(1), pages 87-103, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sumudu Perera & Mahinda Siriwardana & Stuart Mounter, 2014. "Reducing poverty and income inequality in Sri Lanka: does trade liberalisation help?," Journal of the Asia Pacific Economy, Taylor & Francis Journals, vol. 19(4), pages 629-655, October.
    2. Clarke, Philip & Van Ourti, Tom, 2010. "Calculating the concentration index when income is grouped," Journal of Health Economics, Elsevier, vol. 29(1), pages 151-157, January.
    3. Philip Clarke & Tom Van Ourti, 2009. "Correcting the Bias in the Concentration Index when Income is Grouped," CEPR Discussion Papers 599, Centre for Economic Policy Research, Research School of Economics, Australian National University.

    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. Philip Clarke & Tom Van Ourti, 2009. "Correcting the Bias in the Concentration Index when Income is Grouped," CEPR Discussion Papers 599, Centre for Economic Policy Research, Research School of Economics, Australian National University.
    2. Mohammad Hajizadeh & Luke Brian Connelly & James Robert Gerard Butler, 2014. "Health Policy and Equity of Health Care Financing in Australia: 1973–2010," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(2), pages 298-322, June.
    3. Adam Wagstaff & Eddy van Doorslaer, 2004. "Overall versus socioeconomic health inequality: a measurement framework and two empirical illustrations," Health Economics, John Wiley & Sons, Ltd., vol. 13(3), pages 297-301, March.
    4. Heshmati, Almas, 2004. "Inequalities and Their Measurement," IZA Discussion Papers 1219, Institute of Labor Economics (IZA).
    5. Martin Ravallion & Shaohua Chen, 2022. "Is that really a Kuznets curve? Turning points for income inequality in China," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(4), pages 749-776, December.
    6. David E. Sahn & Stephen D. Younger, 2006. "Changes in Inequality and Poverty in Latin America: Looking Beyond Income to Health and Education," Journal of Applied Economics, Taylor & Francis Journals, vol. 9(2), pages 215-233, November.
    7. Hai Zhong, 2010. "On decomposing the inequality and inequity change in health care utilization: change in means, or change in the distributions?," International Journal of Health Economics and Management, Springer, vol. 10(4), pages 369-386, December.
    8. Clarke, Philip & Van Ourti, Tom, 2010. "Calculating the concentration index when income is grouped," Journal of Health Economics, Elsevier, vol. 29(1), pages 151-157, January.
    9. Chiang, Yen-Sheng, 2015. "Inequality measures perform differently in global and local assessments: An exploratory computational experiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 1-11.
    10. Van Ourti, Tom & van Doorslaer, Eddy & Koolman, Xander, 2009. "The effect of income growth and inequality on health inequality: Theory and empirical evidence from the European Panel," Journal of Health Economics, Elsevier, vol. 28(3), pages 525-539, May.
    11. Saloua Sehili & Elamin H. Elbasha & David G. Moriarty & Matthew M. Zack, 2005. "Inequalities in self‐reported physical health in the United States, 1993‐1999," Health Economics, John Wiley & Sons, Ltd., vol. 14(4), pages 377-389, April.
    12. David Cantarero & Marta Pascual & Jose Maria Sarabia, 2004. "Can income inequality contribute to understand inequalities in health? An empirical approach based on the European Community Household Panel," ERSA conference papers ersa04p230, European Regional Science Association.
    13. I. Josa & A. Aguado, 2020. "Measuring Unidimensional Inequality: Practical Framework for the Choice of an Appropriate Measure," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(2), pages 541-570, June.
    14. Juan Luis Londoño & Miguel Székely, 2000. "Persistent Poverty and Excess Inequality: Latin America, 1970-1995," Journal of Applied Economics, Universidad del CEMA, vol. 3, pages 93-134, May.
    15. Londoño, Juan Luis & Székely, Miguel, 1997. "Persistent Poverty and Excess Inequality: Latin America, 1970-1995," IDB Publications (Working Papers) 6092, Inter-American Development Bank.
    16. Guido Erreygers & Roselinde Kessels & Linkun Chen & Philip Clarke, 2016. "Decomposing Socioeconomic Inequality of Health," EcoMod2016 9574, EcoMod.
    17. 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.
    18. Kenya Valeria M. S. Noronha & M™nica Viegas Andrade, 2002. "Desigualdades sociais em saúde: evidências empíricas sobre o caso brasileiro," Textos para Discussão Cedeplar-UFMG td171, Cedeplar, Universidade Federal de Minas Gerais.
    19. Hai Zhong, 2010. "The impact of missing data in the estimation of concentration index: a potential source of bias," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 11(3), pages 255-266, June.
    20. Tatjana Miljkovic & Ying-Ju Chen, 2021. "A new computational approach for estimation of the Gini index based on grouped data," Computational Statistics, Springer, vol. 36(3), pages 2289-2311, September.

    More about this item

    Keywords

    Gini index; grouped data; measurement error; first-order correction;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • I30 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General

    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:tin:wpaper:20080095. 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: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    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.