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Making Inferences About Rich Country - Poor Country Convergence: The Polarization Trapezoid and Overlap measures

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  • Gordon Anderson
  • Teng Wah Leo
  • Oliver Linton

Abstract

Underlying the unresolved debate over whether the gap between rich and poor country GNP per capita has narrowed is a concern for wellbeing. The issue is really about the changing shapes of distributions of wellbeing indicators. As limiting cases con- vergence between rich and poor country groups can be brought about by countries within groups becoming less alike without any diminution of growth rate differentials between them or it can be brought about by reductions in these differentials without any diminution of within group identity. In essence the debate is about the extent to which rich and poor countries are polarizing, a subject first theoretically explored by Esteban and Ray (1994). The empirical issue is about whether separate groups can be identified in the overall distribution and whether they are tending toward common or distinct equilibria. This paper proposes two simple statistics for the problem, the Overlap measure and the Trapezoidal measure, changes in which reflect a combination of increasing (decreasing) subgroup location differences and decreasing (increasing) subgroup spreads which are the characteristics of polarization (convergence). The former statistic is of use when the sub-distributions are identified, while the latter can be used whether or not the subgroups are identified. These techniques are applied to the examination of convergence in GDP per capita between rich and poor nations when growth is viewed either as a wellbeing index or a technology index (i.e. the data are, or are not, population weighted). It turns out that such a distinction matters, viewed technologically there is divergence, viewed in a wellbeing sense there is convergence. As a collection of countries Africa is diverging from the rest of the world whatever the perspective of growth.

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Bibliographic Info

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number tecipa-387.

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Length: 27 pages
Date of creation: 14 Jan 2010
Date of revision:
Handle: RePEc:tor:tecipa:tecipa-387

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Keywords: Convergence; Polarization; Trapezoid Measure; Overlap measure;

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References

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  1. Gordon Anderson & Oliver Linton & Yoon-Jae Wang, 2009. "Non Parametric Estimation of a Polarization Measure," Working Papers tecipa-363, University of Toronto, Department of Economics.
  2. Gary S. Becker & Tomas J. Philipson & Rodrigo R. Soares, 2003. "The Quantity and Quality of Life and the Evolution of World Inequality," NBER Working Papers 9765, National Bureau of Economic Research, Inc.
  3. Quah, Danny, 1997. "Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs," CEPR Discussion Papers 1586, C.E.P.R. Discussion Papers.
  4. Roberto Zelli & Maria Grazia Pittau, 2006. "Empirical evidence of income dynamics across EU regions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 605-628.
  5. DECANCK, Koen & DECOSTER, André & SCHOOKAERT, Erik, . "The evolution of world inequality in well-being," CORE Discussion Papers RP -2140, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Johnson, Paul A., 2000. "A nonparametric analysis of income convergence across the US states," Economics Letters, Elsevier, vol. 69(2), pages 219-223, November.
  7. Nazrul Islam, 2003. "What have We Learnt from the Convergence Debate?," Journal of Economic Surveys, Wiley Blackwell, vol. 17(3), pages 309-362, 07.
  8. Charles I. Jones, 1997. "On the Evolution of the World Income Distribution," Journal of Economic Perspectives, American Economic Association, vol. 11(3), pages 19-36, Summer.
  9. Esteban, J. & Ray, D., 1993. "On the Measurement of Polarization," UFAE and IAE Working Papers 221.93, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  10. Duclos, Jean-Yves & Esteban, Joan & Ray, Debraj, 2003. "Polarization: Concepts, Measurement, Estimation," Cahiers de recherche 0301, CIRPEE.
  11. James Foster & Michael Wolfson, 2010. "Polarization and the decline of the middle class: Canada and the U.S," Journal of Economic Inequality, Springer, vol. 8(2), pages 247-273, June.
  12. Sudhir Anand & Paul Segal, 2008. "What Do We Know about Global Income Inequality?," Journal of Economic Literature, American Economic Association, vol. 46(1), pages 57-94, March.
  13. Xavier Sala-i-Martin, 2006. "The World Distribution of Income: Falling Poverty and ... Convergence, Period," The Quarterly Journal of Economics, MIT Press, vol. 121(2), pages 351-397, May.
  14. Quah, Danny T, 1997. " Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs," Journal of Economic Growth, Springer, vol. 2(1), pages 27-59, March.
  15. Bianchi, Marco, 1997. "Testing for Convergence: Evidence from Non-parametric Multimodality Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(4), pages 393-409, July-Aug..
  16. Paapaa, Richard & van Dijk, Herman K., 1998. "Distribution and mobility of wealth of nations," European Economic Review, Elsevier, vol. 42(7), pages 1269-1293, July.
  17. Paul Beaudry & Fabrice Collard & David A. Green, 2005. "Changes in the World Distribution of Output Per Worker, 1960-1998: How a Standard Decomposition Tells an Unorthodox Story," The Review of Economics and Statistics, MIT Press, vol. 87(4), pages 741-753, November.
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