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Inequality Foundations of Concentration Measures: An Application to the Hannah-Kay Indices



In this paper we provide a connection between concentration and inequality by showing that the inequality measures consistent with the whole class of Hannah-Kay concentration indices are the general entropy inequality indices. We isolate the inequality component underlying the concentration measures, obtaining an explicit additive decomposition of the change in concentration into the change in its two components: inequality and the number of firms. This relationship proves to be valid for the whole class of Hannah-Kay concentration indices, and embodies as particular cases other previously found in the literature. Finally, our proposed decomposition is shown by means of an empirical example, which illustrates the sources of a change in sectoral concentration between two points in time.

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  • Oscar Bajo & Rafael Salas, 1999. "Inequality Foundations of Concentration Measures: An Application to the Hannah-Kay Indices," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 9901, Departamento de Economía - Universidad Pública de Navarra.
  • Handle: RePEc:nav:ecupna:9901

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    References listed on IDEAS

    1. Encaoua, David & Jacquemin, Alexis, 1980. "Degree of Monopoly, Indices of Concentration and Threat of Entry," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 87-105, February.
    2. Marfels, Christian, 1971. "Absolute and Relative Measures of Concentration Reconsidered," Kyklos, Wiley Blackwell, vol. 24(4), pages 753-766.
    3. Salas, Rafael, 1998. "Welfare-consistent inequality indices in changing populations:: The marginal population replication axiomA Note," Journal of Public Economics, Elsevier, vol. 67(1), pages 145-150, January.
    4. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
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    Cited by:

    1. Dorian Owen, 2014. "Measurement of competitive balance and uncertainty of outcome," Chapters,in: Handbook on the Economics of Professional Football, chapter 3, pages 41-59 Edward Elgar Publishing.
    2. Owen, P. Dorian, 2010. "Limitations of the relative standard deviation of win percentages for measuring competitive balance in sports leagues," Economics Letters, Elsevier, vol. 109(1), pages 38-41, October.
    3. I. Brezina & J. Pekár & Z. Čičková & M. Reiff, 2016. "Herfindahl–Hirschman index level of concentration values modification and analysis of their change," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(1), pages 49-72, March.
    4. Irving Fisher Committee, 2013. "Proceedings of the Sixth IFC Conference on "Statistical issues and activities in a changing environment", Basel, 28-29 August 2012," IFC Bulletins, Bank for International Settlements, number 36.
    5. P. Dorian Owen & Nicholas King, 2015. "Competitive Balance Measures In Sports Leagues: The Effects Of Variation In Season Length," Economic Inquiry, Western Economic Association International, vol. 53(1), pages 731-744, January.
    6. repec:qut:auncer:2013_04 is not listed on IDEAS
    7. P. Owen & Michael Ryan & Clayton Weatherston, 2007. "Measuring Competitive Balance in Professional Team Sports Using the Herfindahl-Hirschman Index," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 31(4), pages 289-302, December.
    8. Frederico Rocha & Sálua Bueno & Luiza Nassif Pires, 2007. "Dinâmica Da Concentração De Mercado Na Indústria Brasileira, 1996-2003," Anais do XXXV Encontro Nacional de Economia [Proceedings of the 35th Brazilian Economics Meeting] 141, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
    9. Fernando Ávila & Emilio Flores & Fabrizio López-Gallo & Javier Márquez, 2013. "Concentration indicators: assessing the gap between aggregate and detailed data," IFC Bulletins chapters,in: Bank for International Settlements (ed.), Proceedings of the Sixth IFC Conference on "Statistical issues and activities in a changing environment", Basel, 28-29 August 2012., volume 36, pages 542-559 Bank for International Settlements.

    More about this item


    Concentration; inequality;

    JEL classification:

    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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