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Inequality foundations of concentration measures: an application to the hannah-kay indices

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  • Bajo, Oscar
  • Salas, Rafael

Abstract

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 and 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 ilustrates the sources of a change in sectoral concentration between two points in time.

Suggested Citation

  • Bajo, Oscar & Salas, Rafael, 1999. "Inequality foundations of concentration measures: an application to the hannah-kay indices," UC3M Working papers. Economics 6137, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:6137
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    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.
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    4. 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.
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    6. 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.
    7. Leslie Hannah & J. A. Kay, 1977. "Concentration in Modern Industry," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-02773-6, October.
    8. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    9. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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    Cited by:

    1. Bukvić, Rajko, 2022. "Концентрация И Конкуренция В Современном Банковском Секторе Сербии: Перемены И Декомпозиция Индекса Херфиндаля – Хиршмана [Concentration and Competition in Modern Banking Sector of Serbia: Changes ," MPRA Paper 112928, University Library of Munich, Germany, revised 2022.
    2. Dorian Owen, 2014. "Measurement of competitive balance and uncertainty of outcome," Chapters, in: John Goddard & Peter Sloane (ed.), Handbook on the Economics of Professional Football, chapter 3, pages 41-59, Edward Elgar Publishing.
    3. Najahi, Akbar & Mousavi Jahromi, Yeghaneh & Khodadadkashi, Farhad & Haji, Golam Ali, 2016. "Relationship between Structure and Performance in the Banking Industry of Iran," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 11(4), pages 443-466, October.
    4. 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.
    5. Guglielmo D’Amico & Giuseppe Di Biase & Raimondo Manca, 2011. "Immigration Effects On Economic Systems Through Dynamic Inequality Indices," Global Journal of Business Research, The Institute for Business and Finance Research, vol. 5(5), pages 11-25.
    6. 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.
    7. 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.
    8. Bukvić, Rajko, 2022. "Koncentracija u sektoru osiguranja u Srbiji: promene u periodu 2011–2020. i njihova dekompozicija [Concentration in Serbian Insurance Sector: 2011–2020 Changes and Their Decomposition]," MPRA Paper 113347, University Library of Munich, Germany, revised 2022.
    9. 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.
    10. Bukvić, Rajko, 2022. "Типови Промена Концентрације У Банковном Сектору Србије: Декомпозиција Индекса Хиршмана-Херфиндала [Types of the Changes in Banking Sector of Serbia Concentration: Decomposition of the Hirschman-He," MPRA Paper 114612, University Library of Munich, Germany, revised 2022.
    11. repec:qut:auncer:2013_04 is not listed on IDEAS
    12. 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.
    13. Ivan Brezina & Juraj Pekár, 2013. "Analýza citlivosti hodnot Herfidalovho-Hirschmanovho indexu slovenského bankového sektora [Sensitivity Analysis of Herfindahl-Hirschman Index on the Slovak Banking Sector]," Politická ekonomie, Prague University of Economics and Business, vol. 2013(6), pages 735-751.
    14. 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 Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    15. 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.
    16. Bukvić, Rajko, 2022. "Concentration in Serbian Insurance Sector: 2011–2020 Changes and Their Decomposition," MPRA Paper 113386, University Library of Munich, Germany, revised 2022.
    17. Guglielmo D’Amico & Giuseppe Di Biase & Raimondo Manca, 2015. "Measuring Income Inequality: An Application Of The Population Dynamic Theil'S Entropy," Accounting & Taxation, The Institute for Business and Finance Research, vol. 7(1), pages 103-114.
    18. Bukvić, Rajko, 2023. "Market Concentration in banking sector of Serbia: decomposition of the Changes in 2016–2021," MPRA Paper 120970, University Library of Munich, Germany, revised 2023.

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    More about this item

    Keywords

    Concentrations;

    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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