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Non Parametric Estimation of a Polarization Measure

  • Gordon Anderson
  • Oliver Linton
  • Yoon-Jae Wang

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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File URL: http://www.economics.utoronto.ca/public/workingPapers/tecipa-363.pdf
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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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  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. 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.
  3. Linton, Oliver & Maasoumi, Esfandiar & Whang, Yoon-Jae, 2003. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," SFB 373 Discussion Papers 2003,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  4. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
  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. 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. Jean-Yves Duclos & Joan Esteban & Debraj Ray, 2003. "Polarization: Concepts, Measurement, Estimation," Working Papers 46, Barcelona Graduate School of Economics.
  8. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  9. Anderson, Gordon & Ge, Ying, 2005. "The size distribution of Chinese cities," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 756-776, November.
  10. Anderson, Gordon, 2004. "Toward an empirical analysis of polarization," Journal of Econometrics, Elsevier, vol. 122(1), pages 1-26, September.
  11. 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.
  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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