Skip to main content

An (almost) unbiased estimator for the S-Gini index


This note provides an unbiased estimator for the absolute S-Gini and an almost unbiased estimator for the relative S-Gini for integer parameter values. Simulations indicate that these estimators perform considerably better then the usual estimators, especially for small sample sizes.

This is a preview of subscription content, access via your institution.


  1. 1.

    Barrett, G., Donald, G.: Statistical inference with generalized Gini indices of inequality, poverty and welfare. J. Bus. Econ. Stat. 27, 1–17 (2009)

    Article  Google Scholar 

  2. 2.

    Barrett, G.F., Pendakur, K.: The asymptotic distribution of the generalized Gini indices of inequality. Can. J. Econ. 28, 1042–1055 (1995)

    Article  Google Scholar 

  3. 3.

    Bossert, W.: An axiomatization of the single-series Ginis. J. Econ. Theory 50, 82–92 (1990)

    Article  Google Scholar 

  4. 4.

    Cowell, F.A.: Sampling variance and decomposable inequality measures. J. Econom. 42, 27–41 (1989)

    Article  Google Scholar 

  5. 5.

    Davidson, R.: Reliable inference for the Gini index. J. Econom. 150, 30–40 (2009)

    Article  Google Scholar 

  6. 6.

    Deaton, A.S.: The Analysis of Household Surveys: A Microeconometric Approach to Development Policy. John Hopkins University Press for the World Bank, Baltimore (1997)

    Google Scholar 

  7. 7.

    Deltas, G.: The small-sample bias of the Gini coefficient: results and implications for empirical research. Rev. Econ. Stat. 85, 226–234 (2003)

    Article  Google Scholar 

  8. 8.

    Donaldson, D., Weymark, J.A.: A single-parameter generalization of the Gini indices of inequality. J. Econ. Theory 22, 67–86 (1980)

    Article  Google Scholar 

  9. 9.

    Fisher, M.: Household welfare and forest dependence in southern Malawi. Environ. Dev. Econ. 9, 135–154 (2004)

    Article  Google Scholar 

  10. 10.

    Gini, C.: On the measurement of concentration and variability of characters. Metron 63, 3–38 (2005)

    Google Scholar 

  11. 11.

    Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics. Addison-Wesley, Reading (1989)

    Google Scholar 

  12. 12.

    Lall, S.V., Shalizi, Z., Deichmann, U.: Agglomeration economies and productivity in Indian industry. J. Dev. Econ. 73, 643–673 (2001)

    Article  Google Scholar 

  13. 13.

    Liu, H.: Changing regional rural inequality in China: 1980–2002. Area 38, 377–389 (2006)

    Article  Google Scholar 

  14. 14.

    Milanovic, B.: Half a world: regional inequality in five great federations. J. Asia Pac. Econ. 10, 408–445 (2005)

    Article  Google Scholar 

  15. 15.

    Ostby, G., Nordas, R., Ketil Rod, J.: Regional inequalities and civil conflict in 21 sub-saharan African countries, 1986–2004. Mimeo (2006)

  16. 16.

    Reynolds-Feighan, A.J.: Competing networks, spatial and industrial concentration in the US airline industry. Spatial Econ. Anal. 2, 237–257 (2007)

    Article  Google Scholar 

  17. 17.

    Salimonu, K.K., Atoyebi, J.O., Sanusi, W.A.: Income inequality, poverty and social welfare among gonvernment and private employees in Lagos and Osum state of Nigeria. Agric. J. 1, 315–319 (2006)

    Google Scholar 

  18. 18.

    Tsui, K.: Economic reform and interprovincial inequalities in China. J. Dev. Econ. 50, 353–368 (1996)

    Article  Google Scholar 

  19. 19.

    Wei, H., Yi, J., Zhang, J.: Inequality and internal migration in China: evidence from village panel data. United Nations Development Programme Human Development Reports Research Paper 2009/27 (2009)

  20. 20.

    Wei, Y.D., Kim, S.: Widening inter-country inequality in Jiangsu province, China, 1950–95. J. Dev. Stud. 38, 142–164 (2002)

    Article  Google Scholar 

  21. 21.

    Wen, M.: Relocation and agglomeration of Chinese industry. J. Dev. Econ. 73, 329–347 (2004)

    Article  Google Scholar 

  22. 22.

    Xu, K.: Inference for generalized Gini indices using the iteratied-bootstrap method. J. Bus. Econ. Stat. 18, 223–227 (2000)

    Article  Google Scholar 

  23. 23.

    Xu, K.: U-statistics and their asymptotic results for some inequality and poverty measures. Econom. Rev. 26, 567–577 (2007)

    Article  Google Scholar 

  24. 24.

    Yao, Y.: Village election, accountability and income distribution in rural China. China World Econ. 14, 20–38 (2006)

    Article  Google Scholar 

  25. 25.

    Yingying, Z., Hua, H., Harrel, S.: Inequality in rural China, 1988–2006. Chin. Q. 195, 515–534 (2008)

    Google Scholar 

  26. 26.

    Yitzhaki, S.: On an extension of the Gini inequality index. Int. Econ. Rev. 24, 617–628 (1983)

    Article  Google Scholar 

  27. 27.

    Yitzhaki, S.: Calculating jackknife variance estimators for parameters of the gini method. J. Bus. Econ. Stat. 9, 235–39 (1991)

    Article  Google Scholar 

  28. 28.

    Zitikis, R., Gastwirth, J.: The asymptotic distribution of the S-Gini index. Aust. N. Z. J. Stat. 44, 439–446 (2002)

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Thomas Demuynck.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Demuynck, T. An (almost) unbiased estimator for the S-Gini index. J Econ Inequal 10, 109–126 (2012).

Download citation


  • S-Gini
  • Unbiased estimators
  • Combinatorics

JEL Classification

  • D63
  • C10