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The Extended Atkinson Family and Changes in the Expenditure Distribution: Spain 1973/74-2003

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  • Goerlich, Francisco José
  • Lasso de la Vega, Mª Casilda
  • Urrutia, Ana Marta

Abstract

This paper emphasizes the properties of a family of inequality measures which extends the Atkinson indices and is axiomatically characterized by a multiplicative decomposition property where the withingroup component is a generalized weighted mean with weights summing exactly to 1. This family contains canonical forms of all aggregative inequality measures, each bounded above by 1, has a useful and intuitive geometric interpretation and provides an alternative dominance criterion for ordering distributions in terms of inequality. Taking the Spanish Household Budget Surveys (HBS) for 1973/74, 1980/81, and 1990/91 and the more recent Continuous HBS for 2003, we show the advantages and possibilities of this extended family in regard to completing and detailing information in studies of inequality focussing on the tails of the distribution and on the changes in the distribution when the population is partitioned into population subgroups.

Suggested Citation

  • Goerlich, Francisco José & Lasso de la Vega, Mª Casilda & Urrutia, Ana Marta, 2009. "The Extended Atkinson Family and Changes in the Expenditure Distribution: Spain 1973/74-2003," MPRA Paper 16256, University Library of Munich, Germany, revised 2009.
    • Handle: RePEc:pra:mprapa:16256
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    References listed on IDEAS

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    1. Theil, Henri & Sorooshian, Cyrus, 1979. "Components of the change in regional inequality," Economics Letters, Elsevier, vol. 4(2), pages 191-193.
    2. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 521-531.
    3. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 485-497.
    4. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    5. Casilda Lasso de la Vega & Ana Urrutia, 2008. "The ‘Extended’ Atkinson family: The class of multiplicatively decomposable inequality measures, and some new graphical procedures for analysts," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(2), pages 211-225, June.
    6. repec:ebl:ecbull:v:4:y:2003:i:29:p:1-12 is not listed on IDEAS
    7. Foster, James E. & Shneyerov, Artyom A., 2000. "Path Independent Inequality Measures," Journal of Economic Theory, Elsevier, vol. 91(2), pages 199-222, April.
    8. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    9. Davies, James & Hoy, Michael, 1995. "Making Inequality Comparisons When Lorenz Curves Intersect," American Economic Review, American Economic Association, vol. 85(4), pages 980-986, September.
    10. Angus Deaton & Salman Zaidi, 1999. "Guidelines for Constructing Consumption Aggregates For Welfare Analysis," Working Papers 217, Princeton University, Woodrow Wilson School of Public and International Affairs, Research Program in Development Studies..
    11. A.B. Atkinson & F. Bourguignon (ed.), 2000. "Handbook of Income Distribution," Handbook of Income Distribution, Elsevier, edition 1, volume 1, number 1.
    12. Blackorby, Charles & Donaldson, David, 1978. "Measures of relative equality and their meaning in terms of social welfare," Journal of Economic Theory, Elsevier, vol. 18(1), pages 59-80, June.
    13. Mª Casilda Lasso de la Vega & Ana Marta Urrutia, 2003. "A new factorial decomposition for the atkinson measure," Economics Bulletin, AccessEcon, vol. 4(29), pages 1-12.
    14. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    15. Charles Blackorby & David Donaldson & Maria Auersperg, 1981. "A New Procedure for the Measurement of Inequality within and among Population Subgroups," Canadian Journal of Economics, Canadian Economics Association, vol. 14(4), pages 665-685, November.
    16. Peter Lambert & Giuseppe Lanza, 2006. "The effect on inequality of changing one or two incomes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 4(3), pages 253-277, December.
    17. Francisco Goerlich & Matilde Mas, 2002. "Intertemporal and interprovincial variations in income inequality: Spain, 1973-1991," Regional Studies, Taylor & Francis Journals, vol. 36(9), pages 1005-1015.
    18. Mª Casilda Lasso de la Vega & Ana Marta Urrutia, 2005. "Path independent multiplicatively decomposable inequality measures," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 379-387, May.
    19. R. Robert Russell, 1985. "A Note on Decomposable Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(2), pages 347-352.
    20. 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.
    21. Josep Oliver Alonso & Xavier Ramos & José Luis Raymond-Bara, 2001. "Recent trends in Spanish Income Distribution: A Robust Picture of Falling Income Inequality," Working Papers wp0107, Department of Applied Economics at Universitat Autonoma of Barcelona.
    22. Matilde Mas Ivars & Francisco José Goerlich Gisbert, 1999. "- Desigualdad Y Convergencia," Working Papers. Serie EC 1999-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    23. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    24. James E. Foster & Artyom A. Shneyerov, 1999. "A general class of additively decomposable inequality measures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 89-111.
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    More about this item

    Keywords

    inequality measurement; Atkinson indices;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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