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Nonparametric estimation of a polarization measure

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  • Gordon Anderson

    (Institute for Fiscal Studies and University of Toronto)

  • Oliver Linton

    ()
    (Institute for Fiscal Studies and London School of Economics)

  • Yoon-Jae Whang

    (Institute for Fiscal Studies and Seoul National University)

Abstract

This paper develops methodology for nonparametric estimation of a polarization measure due to Anderson (2004) and Anderson, Ge, and Leo (2006) based on kernel estimation techniques. We give the asymptotic distribution theory of our estimator, which in some cases is nonstandard due to a boundary value problem. 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 the finite sample properties of our methods by simulation methods. We give an application to the study of polarization within China in recent years.

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File URL: http://cemmap.ifs.org.uk/wps/cwp1409.pdf
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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP14/09.

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Date of creation: Jun 2009
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Handle: RePEc:ifs:cemmap:14/09

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Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
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Web page: http://cemmap.ifs.org.uk
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References

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  1. 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).
  2. 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.
  3. Anderson, Gordon, 2004. "Toward an empirical analysis of polarization," Journal of Econometrics, Elsevier, vol. 122(1), pages 1-26, September.
  4. 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.
  5. Jean-Yves Duclos & Joan Esteban & Debraj Ray, 2003. "Polarization: Concepts, Measurement, Estimation," Working Papers 46, Barcelona Graduate School of Economics.
  6. Holmström, Lasse & Klemelä, Jussi, 1992. "Asymptotic bounds for the expected L1 error of a multivariate kernel density estimator," Journal of Multivariate Analysis, Elsevier, vol. 42(2), pages 245-266, August.
  7. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2003. "Consistent testing for stochastic dominance under general sampling schemes," LSE Research Online Documents on Economics 2208, London School of Economics and Political Science, LSE Library.
  8. 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.
  9. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  10. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
  11. Anderson, Gordon & Ge, Ying, 2005. "The size distribution of Chinese cities," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 756-776, November.
  12. 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.
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Cited by:
  1. 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.
  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 & 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.

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