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The median as watershed

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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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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. Aaberge, Rolf & Mogstad, Magne, 2010. "On the Measurement of Long-Term Income Inequality and Income Mobility," IZA Discussion Papers 4699, Institute for the Study of Labor (IZA).
  2. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-30, September.
  3. Joan-Maria Esteban & Debraj Ray, 1991. "On the Measurement of Polarization," Boston University - Institute for Economic Development 18, Boston University, Institute for Economic Development.
  4. Rolf Aaberge, 2000. "Ranking Intersecting Lorenz Curves," Discussion Papers 271, Research Department of Statistics Norway.
  5. Jean-Yves Duclos & Joan Esteban & Debraj Ray, 2003. "Polarization: Concepts, Measurement, Estimation," Working Papers 46, Barcelona Graduate School of Economics.
  6. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer, vol. 17(4), pages 639-653.
  7. BOSSERT, Walter & SCHWORM, William, 2007. "A Class of Two-Group Polarization Measures," Cahiers de recherche 10-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Esteban, Joan & Ray, Debraj, 1999. "Conflict and Distribution," Journal of Economic Theory, Elsevier, vol. 87(2), pages 379-415, August.
  9. Garfinkel, Michelle R. & Skaperdas, Stergios (ed.), 2012. "The Oxford Handbook of the Economics of Peace and Conflict," OUP Catalogue, Oxford University Press, number 9780195392777.
  10. Sen, Pranab Kumar, 1988. "The harmonic Gini coefficient and affluence indexes," Mathematical Social Sciences, Elsevier, vol. 16(1), pages 65-76, August.
  11. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  12. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-64, July.
  13. Andreas Peichl & Thilo Schaefer & Christoph Scheicher, 2010. "Measuring Richness And Poverty: A Micro Data Application To Europe And Germany," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(3), pages 597-619, 09.
  14. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  15. Jullien Bruno & Green Jerry G, 1988. "Ordinal independence in non-linear utility theory," CEPREMAP Working Papers (Couverture Orange) 8818, CEPREMAP.
  16. 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.
  17. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  18. Wolfson, Michael C, 1994. "When Inequalities Diverge," American Economic Review, American Economic Association, vol. 84(2), pages 353-58, May.
  19. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  20. 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.
  21. Michal Brzezinski, 2010. "Income Affluence in Poland," Social Indicators Research, Springer, vol. 99(2), pages 285-299, November.
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Cited by:
  1. Aaberge, Rolf & Atkinson, Anthony B. & Modalsli, Jorgen Heibo, 2013. "The Ins and Outs of Top Income Mobility," IZA Discussion Papers 7729, Institute for the Study of Labor (IZA).

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