IDEAS home Printed from https://ideas.repec.org/p/qld/uq2004/398.html
   My bibliography  Save this paper

A Symmetric Information-Theoretic Index For The Measurement of Inequality

Author

Abstract

The application of information theory to the measurement of income inequality has yielded an impressive array of measurement techniques known as Generalized Entropy (GE) measures. Special cases of this class of index include Theil's T and L measures which are considered axiomatically superior to other types of metrics including the popular Gini coefficient. In this paper we show that the parallel between information theory and inequality measurement has not yet been fully explored and propose a new inequality measure based upon this concept. The proposed measure is already established as a tool for use in statistical classification and signal processing problems and is known in these fields as the J-Divergence or Symmetric Kullback-Leibler Divergence. As an inequality metric the measure is shown to be axiomatically complete and is in possession of an additional property allowing for an alternate type of decomposition analysis. The new type of decomposition makes the contribution of any individual or subgroup to the inequality metric directly observable such that the overall index may be reconciled with a weighted sum of each group contribution. We illustrate with an example using income micro-data from the United States where we evaluate the contributions of various racial groups to overall inequality. We also provide a standard decomposition of the inequalities between and within the racial groups to contrast the techniques. and within the racial groups to contrast the techniques.

Suggested Citation

  • Nicholas Rohde, 2009. "A Symmetric Information-Theoretic Index For The Measurement of Inequality," Discussion Papers Series 398, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uq2004:398
    as

    Download full text from publisher

    File URL: https://economics.uq.edu.au/files/44717/398.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Branko Milanovic, 2002. "True World Income Distribution, 1988 and 1993: First Calculation Based on Household Surveys Alone," Economic Journal, Royal Economic Society, vol. 112(476), pages 51-92, January.
    2. Rothschild, Michael & Stiglitz, Joseph E., 1973. "Some further results on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 188-204, April.
    3. Chotikapanich, Duangkamon & Valenzuela, Rebecca & Rao, D S Prasada, 1997. "Global and Regional Inequality in the Distribution of Income: Estimation with Limited and Incomplete Data," Empirical Economics, Springer, vol. 22(4), pages 533-546.
    4. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-316, March.
    5. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    6. 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.
    7. Xavier Sala-i-Martin, 2001. "The disturbing 'rise' of global income inequality," Economics Working Papers 616, Department of Economics and Business, Universitat Pompeu Fabra, revised Apr 2002.
    8. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    9. Cowell, Frank A. & Kuga, Kiyoshi, 1981. "Additivity and the entropy concept: An axiomatic approach to inequality measurement," Journal of Economic Theory, Elsevier, vol. 25(1), pages 131-143, August.
    10. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    11. Foster, James E., 1983. "An axiomatic characterization of the Theil measure of income inequality," Journal of Economic Theory, Elsevier, vol. 31(1), pages 105-121, October.
    12. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    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. Bart Capéau & Andre Decoster, 2004. "The Rise or Fall of World Inequality: A Spurious Controversy?," WIDER Working Paper Series DP2004-02, World Institute for Development Economic Research (UNU-WIDER).
    2. Satya R. Chakravarty & Pietro Muliere, 2003. "Welfare indicators: A review and new perspectives. 1. Measurement of inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 457-497.
    3. B. Capéau & A. Decoster, 2003. "The Rise or Fall of World Inequality Big Issue or Apparent Controversy?," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(4), pages 547-572.
    4. Stéphane Mussard & Françoise Seyte & Michel Terraza, 2006. "La décomposition de l’indicateur de Gini en sous-groupes : une revue de la littérature," Cahiers de recherche 06-11, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    5. David Warner & Prasada Rao & William E. Griffiths & Duangkamon Chotikapanich, 2011. "Global Inequality: Levels and Trends, 1993-2005," Discussion Papers Series 436, School of Economics, University of Queensland, Australia.
    6. Frank A Cowell, 2003. "Theil, Inequality and the Structure of Income Distribution," STICERD - Distributional Analysis Research Programme Papers 67, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Rodolfo Hoffmann & Diego Camargo Botassio, 2020. "Sensitivity of inequality measures considering regressive transfers with fixed relative income distance," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 279-296, December.
    8. Nicholas Rohde, 2008. "A comparison of inequality measurement techniques," Discussion Papers Series 377, School of Economics, University of Queensland, Australia.
    9. Casilda Lasso de la Vega & Ana Urrutia & Oscar Volij, 2011. "An Axiomatic Characterization Of The Theil Inequality Order," Working Papers 1103, Ben-Gurion University of the Negev, Department of Economics.
    10. Lorena Remuzgo & Jose Maria Sarabia, 2015. "A general factorial decomposition of the second Theil index of inequality with applications in environmental economics," Economics Bulletin, AccessEcon, vol. 35(2), pages 1369-1378.
    11. Ferreira,Francisco H. G., 2022. "The Analysis of Inequality in the Bretton Woods Institutions," Policy Research Working Paper Series 10149, The World Bank.
    12. Casilda Lasso de la Vega & Ana Urrutia & Oscar Volij, 2013. "An axiomatic characterization of the Theil inequality ordering," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 757-776, November.
    13. Anthony B. Atkinson & Andrea Brandolini, 2010. "On Analyzing the World Distribution of Income," The World Bank Economic Review, World Bank, vol. 24(1), pages 1-37, January.
    14. 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.
    15. Maxim Pinkovskiy & Xavier Sala-i-Martin, 2009. "Parametric Estimations of the World Distribution of Income," NBER Working Papers 15433, National Bureau of Economic Research, Inc.
    16. Frank Cowell, 2005. "Theil, Inequality Indices and Decomposition," Working Papers 01, ECINEQ, Society for the Study of Economic Inequality.
    17. Andonie, Costel & Kuzmics, Christoph & Rogers, Brian W., 2019. "Efficiency-based measures of inequality," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 60-69.
    18. Miguel Niño‐Zarazúa & Laurence Roope & Finn Tarp, 2017. "Global Inequality: Relatively Lower, Absolutely Higher," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 63(4), pages 661-684, December.
    19. Antonio Villar Notario, 2001. "Multidimensional Inequality And Social Welfare," Working Papers. Serie AD 2001-30, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    20. Frankel, David M. & Volij, Oscar, 2011. "Measuring school segregation," Journal of Economic Theory, Elsevier, vol. 146(1), pages 1-38, January.

    More about this item

    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:qld:uq2004:398. 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: SOE IT (email available below). General contact details of provider: https://edirc.repec.org/data/decuqau.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.