Journal of Quantitative Economics

, Volume 17, Issue 1, pp 41–56 | Cite as

Economic Properties of Statistical Indices: The Case of a Multidimensional Gini Index

  • Asis Kumar BanerjeeEmail author
Original Article


This paper seeks to construct a Gini index of the distribution of standard of living. Since standard of living has various dimensions, we need a multidimensional Gini index (MGI). The literature on index numbers contains two distinct approaches: the statistical and the economic. In the context of MGIs the statistical approach (which obtains the indices from conditions based on statistical or data-related considerations) seems to be open to the criticism that it sometimes yields indices that violate economic norms. However, the economic approach (where the indices are derived from norms based on economic theory) also does not seem to have succeeded so far in obtaining an MGI satisfying the various normative requirements that have been proposed in the literature. This paper shows that it is possible to obtain an MGI from the statistical approach ensuring, at the same time, that the economic norms are satisfied. In this sense it is an attempt to bring the two disparate traditions in index construction referred to above closer to each other. The index that is developed here does not appear in the existing literature. Moreover, the literature does not seem to contain any other MGI satisfying all of the proposed economic norms.


Multidimensional inequality Gini index Transfer principle Uniform majorisation 

JEL Classification

D60 D63 


  1. Aaberge, R., and A. Brandolini. 2015. Multidimensional poverty and inequality. In Handbook of income distribution, vol. 2A, ed. A.B. Atkinson, and F. Bourguignon. Amsterdem: North-Holland.Google Scholar
  2. Atkinson, A.B., and F. Bourguignon. 1982. The comparison of multi-dimensioned distributions of economic status. Review of Economic Studies 49: 183–201.CrossRefGoogle Scholar
  3. Banerjee, A.K. 2010. A multidimensional Gini index. Mathematical Social Sciences 60: 87–93.CrossRefGoogle Scholar
  4. Boland, D.J., and F. Proschan. 1988. Multidimensional arrangement increasing function with applications in probability and statistics. Journal of Multivariate Analysis 25: 286–298.CrossRefGoogle Scholar
  5. Brandolini, A. 2009. On applying synthetic indices of multidimensional well-being: Health and income inequalities in France, Germany, Italy and the United Kingdom. In Against injustice: The new economics of amartya sen, ed. R. Gotoh, and P. Dumouchel. Cambridge: Cambridge University Press.Google Scholar
  6. Bourguignon, F. 1999. Comment on Maasoumi (1999). In Handbook of income inequality measurement, ed. J. Silber. Boston: Kluwer Academic Publishers.Google Scholar
  7. Dardanoni, V. 1996. On multidimensional inequality measurement. Research on Economic Inequality 6: 202–207.Google Scholar
  8. Decancq, K., and M.A. Lugo. 2012. Inequality of well-being: A multidimensional approach. Economica 79: 721–746.Google Scholar
  9. Epstein, L.G., and S.M. Tanny. 1980. Increasing generalized correlation: A definition and some economic concepts. Canadian Journal of Econimics 13: 16–34.CrossRefGoogle Scholar
  10. Gajdos, T., and J.A. Weymark. 2005. Multidimensional generalized Gini indices. Economic Theory 26: 471–496.CrossRefGoogle Scholar
  11. Hardy, G.H., J.E. Littlewood, and G. Poliya. 1934. Inequalities. Cambridge: Cambridge University Press.Google Scholar
  12. Herrero, C., R. Martinez, and A. Villar. 2010. Multidimensional social evaluation. An application to the measurement of human development. Review of Income and Wealth 56: 483–497.CrossRefGoogle Scholar
  13. Herrero, C., R. Martinez, and A. Villar. 2012. A newer human development index. Journal of Human Development and Capabilities 13: 247–268.CrossRefGoogle Scholar
  14. Hotelling, H. 1933. Analysis of complex statistical variables into principal components. Journal of Educational Psychology 24: 417–441 and 498–520.CrossRefGoogle Scholar
  15. Huntington, E.V. 1927. Sets of independent postulates for the arithmetic mean, the geometric mean, the harmonic mean and the root-mean-square. Transactions of the American Mathematical Society 29: 1–22.CrossRefGoogle Scholar
  16. Klasen, S. 2000. Measuring poverty and deprivation in South Africa. Review of Income and Wealth 46: 33–58.CrossRefGoogle Scholar
  17. Kolm, S.-C. 1977. Multidimensional egalitarianisms. Quarterly Journal of Economics 91: 1–13.CrossRefGoogle Scholar
  18. Koshevoy, G.A., and K. Mosler. 1997. Multivariate Gini indices. Journal of Multivariate Analysis 60: 252–276.CrossRefGoogle Scholar
  19. Marshall, A.W., and I. Olkin. 1979. Inequalities: theories of majorization and its applications. New York: Academic Press.Google Scholar
  20. Ram, R. 1982. Composite indices of physical quality of life, basic needs fulfilment and income. Journal of Development Economics 11: 227–247.CrossRefGoogle Scholar
  21. Tintner, G. 1946. Some applications of multivariate analysis to economic data. Journal of American Statistical Association 41: 472–500.CrossRefGoogle Scholar
  22. Tsui, K.-Y. 1999. Multidimensional inequality and multidimensional generalized entropy measures: An axiomatic derivation. Social Choice and Welfare 16: 145–157.CrossRefGoogle Scholar
  23. Weymark, J.A. 2006. The normative approach to the measurement of multidimensional Inequality. In Inequality and economic integration, ed. F. Farina, and E. Savaglio. New York: Routledge.Google Scholar

Copyright information

© The Indian Econometric Society 2018

Authors and Affiliations

  1. 1.Honorary Visiting Professor of EconomicsInstitute of Development Studies KolkataSalt LakeIndia

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