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Non Parametric Estimation of a Polarization Measure

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  • Gordon Anderson
  • Oliver Linton
  • Yoon-Jae Wang

Abstract

This paper develops a methodology for nonparametric estimation of a polarization measure due to Anderson Ge and Leo (2006) based on kernel estimation techniques. We give the asymptotic theory of our estimator, which in some cases is non standard due to boundary value problems. We also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider. We investigate finite sample proerties of our estimator by simulation methods. We give an application to the study of polarization in China in recent years.

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Bibliographic Info

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number tecipa-363.

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Length: 50 pages
Date of creation: 30 Jul 2009
Date of revision:
Handle: RePEc:tor:tecipa:tecipa-363

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Keywords: kernel estimation; Inequality; Overlap Coefficient; Poissonization.;

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References

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  1. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-51, July.
  2. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  3. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
  4. Schmid, Friedrich & Schmidt, Axel, 2006. "Nonparametric estimation of the coefficient of overlapping--theory and empirical application," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1583-1596, March.
  5. Clemons, Traci E. & Jr., Edwin L. Bradley, 2000. "A nonparametric measure of the overlapping coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 34(1), pages 51-61, July.
  6. Anderson, Gordon & Ge, Ying, 2005. "The size distribution of Chinese cities," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 756-776, November.
  7. Anderson, Gordon, 2004. "Toward an empirical analysis of polarization," Journal of Econometrics, Elsevier, vol. 122(1), pages 1-26, September.
  8. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  9. Knight, J. & Shi, L. & Renwei, Z., 1999. "A Spatial Analysis of Wages and Incomes in Urban China: Divergent Means, Convergent Inequality," Economics Series Working Papers 99209, University of Oxford, Department of Economics.
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Citations

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Cited by:
  1. Gordon Anderson & Kinda Hachem, 2009. "Institutions and Economic Outcomes: A Dominance Based Analysis of Causality and Multivariate Welfare With Discrete and Continuous Variables," Working Papers tecipa-378, University of Toronto, Department of Economics.
  2. Gordon Anderson & Teng Wah Leo & Oliver Linton, 2010. "Making Inferences About Rich Country - Poor Country Convergence: The Polarization Trapezoid and Overlap measures," Working Papers tecipa-387, University of Toronto, Department of Economics.
  3. Gordon Anderson & Oliver Linton & Teng Leo, 2012. "A polarization-cohesion perspective on cross-country convergence," Journal of Economic Growth, Springer, vol. 17(1), pages 49-69, March.

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