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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 16256.

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Date of creation: 2009
Date of revision: 2009
Publication status: Published in Journal of Income Distribution 1.18(2009): pp. 20-41
Handle: RePEc:pra:mprapa:16256

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Keywords: inequality measurement; Atkinson indices;

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  1. Peter Lambert & Giuseppe Lanza, 2006. "The effect on inequality of changing one or two incomes," Journal of Economic Inequality, Springer, vol. 4(3), pages 253-277, December.
  2. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 485-97, July.
  3. Theil, Henri & Sorooshian, Cyrus, 1979. "Components of the change in regional inequality," Economics Letters, Elsevier, vol. 4(2), pages 191-193.
  4. Foster, James E. & Shneyerov, Artyom A., 2000. "Path Independent Inequality Measures," Journal of Economic Theory, Elsevier, vol. 91(2), pages 199-222, April.
  5. Davies, James & Hoy, Michael, 1995. "Making Inequality Comparisons When Lorenz Curves Intersect," American Economic Review, American Economic Association, vol. 85(4), pages 980-86, September.
  6. 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.
  7. 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.
  8. 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).
  9. Deaton, A. & Zaidi, S., 1999. "Guidelines for Constructing Consumption Aggregates for Welfare Analysis," Papers 192, Princeton, Woodrow Wilson School - Development Studies.
  10. 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," Journal of Economic Inequality, Springer, vol. 6(2), pages 211-225, June.
  11. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  12. James E. Foster & Artyom A. Shneyerov, 1999. "A general class of additively decomposable inequality measures," Economic Theory, Springer, vol. 14(1), pages 89-111.
  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. 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.
  15. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
  16. repec:ebl:ecbull:v:4:y:2003:i:29:p:1-12 is not listed on IDEAS
  17. Cowell, Frank A, 1980. "On the Structure of Additive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 47(3), pages 521-31, April.
  18. 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 665-85, November.
  19. Russell, R Robert, 1985. "A Note on Decomposable Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 52(2), pages 347-52, April.
  20. 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.
  21. 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.
  22. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
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