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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
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    References listed on IDEAS

    as
    1. Villasenor, JoseA. & Arnold, Barry C., 1989. "Elliptical Lorenz curves," Journal of Econometrics, Elsevier, vol. 40(2), pages 327-338, February.
    2. 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.
    3. 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.
    4. 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.
    5. Blyde, Juan S., 2006. "Convergence Dynamics in Mercosur," Journal of Economic Integration, Center for Economic Integration, Sejong University, vol. 21, pages 784-815.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053.
    11. 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.
    12. 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.
    13. 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.
    14. Fuller, Mike, 1979. "The estimation of Gini coefficients from grouped data : Upper and Lower Bounds," Economics Letters, Elsevier, vol. 3(2), pages 187-192.
    15. 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.
    16. Murray, David, 1978. "Extreme values for Gini coefficients calculated from grouped data," Economics Letters, Elsevier, vol. 1(4), pages 389-393.
    17. 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.
    18. 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.
    19. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. Le Grand, Julian, 1987. "Inequalities in health : Some international comparisons," European Economic Review, Elsevier, vol. 31(1-2), pages 182-191.
    26. 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.
    27. 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.
    28. 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.
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    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.

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    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

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