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The median as watershed

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Abstract

This paper is concerned with concepts – poverty, inequality, affluence, and polarization – that are typically treated in different literatures. Our aim here is to place them within a common framework and to identify the way in which different classes of income transfers contribute to different objectives. In particular, we examine the role of transfers that preserve both the mean and the median, and the importance of distinguishing between transfers across the median and transfers on one side of the median. The aim of the paper is to bring out some of the implications of adopting the median as a dividing line for these measurement purposes, particularly with respect to the robustness of the conclusions reached. In doing so, we develop the two alternative approaches – primal and dual – applied to Lorenz curves in Aaberge (2001). Our focus is on “well-off” countries where poverty is a minority, rather than a majority, phenomenon. At the other end of the scale, rich people are found in all countries, but less attention has been paid to the definition of cut-offs for affluence. The measurement of “affluence” can proceed along similar lines to the measurement of poverty. The threshold may be set, relatively, as a percentage of the median, and we can ask similar questions about the sensitivity and seek similar dominance results. Moreover, we focus on societies that have a middle class in the sense that the median person is never defined as “rich”. The motivation of Foster and Wolfson’s paper “Polarization and the decline of the middle class” (1992/2010) was the sensitivity of conclusions to the – essentially arbitrary – definition of the middle class. They proposed “a range-free approach to measuring the middle class and polarization based on partial orderings” (2010, page 247). We introduce an alternative partial ordering defined in terms of a bi-polarization curve capturing the distance from the median.

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Bibliographic Info

Paper provided by Research Department of Statistics Norway in its series Discussion Papers with number 749.

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Date of creation: Aug 2013
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Handle: RePEc:ssb:dispap:749

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Keywords: Poverty; Affluence; Polarization; Dispersion; Tail-heaviness; Stochastic dominance; Transfer principles;

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References

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  1. Esteban, J.M. & Ray, D., 1992. "On the Measurement of Polarization," UFAE and IAE Working Papers 171.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  3. Aaberge, Rolf, 2008. "Ranking Intersecting Lorenz Curves," IZA Discussion Papers 3852, Institute for the Study of Labor (IZA).
  4. Jean-Yves Duclos & Joan Esteban & Debraj Ray, 2003. "Polarization: Concepts, Measurement, Estimation," Working Papers 46, Barcelona Graduate School of Economics.
  5. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  6. Wolfson, Michael C, 1994. "When Inequalities Diverge," American Economic Review, American Economic Association, vol. 84(2), pages 353-58, May.
  7. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
  8. Walter Bossert & William Schworm, 2008. "A Class of Two-Group Polarization Measures," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(6), pages 1169-1187, December.
  9. Rolf Aaberge & Magne Mogstad, 2009. "On the Measurement of Long-Term Income Inequality and Income Mobility," ICER Working Papers 09-2009, ICER - International Centre for Economic Research.
  10. Peichl, Andreas & Schaefer, Thilo & Scheicher, Christoph, 2008. "Measuring Richness and Poverty: A Micro Data Application to Europe and Germany," IZA Discussion Papers 3790, Institute for the Study of Labor (IZA).
  11. Garfinkel, Michelle R. & Skaperdas, Stergios (ed.), 2012. "The Oxford Handbook of the Economics of Peace and Conflict," OUP Catalogue, Oxford University Press, number 9780195392777.
  12. Michal Brzezinski, 2010. "Income Affluence in Poland," Social Indicators Research, Springer, vol. 99(2), pages 285-299, November.
  13. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer, vol. 17(4), pages 639-653.
  14. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-64, July.
  15. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  16. Jullien Bruno & Green Jerry G, 1988. "Ordinal independence in non-linear utility theory," CEPREMAP Working Papers (Couverture Orange) 8818, CEPREMAP.
  17. Esteban, Joan & Ray, Debraj, 1999. "Conflict and Distribution," Journal of Economic Theory, Elsevier, vol. 87(2), pages 379-415, August.
  18. Sen, Pranab Kumar, 1988. "The harmonic Gini coefficient and affluence indexes," Mathematical Social Sciences, Elsevier, vol. 16(1), pages 65-76, August.
  19. Aaberge, Rolf, 2001. "Axiomatic Characterization of the Gini Coefficient and Lorenz Curve Orderings," Journal of Economic Theory, Elsevier, vol. 101(1), pages 115-132, November.
  20. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-30, September.
  21. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
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Cited by:
  1. Rolf Aaberge & Anthony B. Atkinson & Jørgen Modalsli, 2013. "The ins and outs of top income mobility," Discussion Papers 762, Research Department of Statistics Norway.

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