IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1714.html
   My bibliography  Save this paper

Nonparametric Estimation of a Polarization Measure

Author

Listed:
  • Gordon Anderson

    (University of Toronto)

  • Oliver Linton

    (London School of Economics)

  • Yoon-Jae Whang

    (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.

Suggested Citation

  • Gordon Anderson & Oliver Linton & Yoon-Jae Whang, 2009. "Nonparametric Estimation of a Polarization Measure," Cowles Foundation Discussion Papers 1714, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1714
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d17/d1714.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jean-Yves Duclos & Joan Esteban & Debraj Ray, 2004. "Polarization: Concepts, Measurement, Estimation," Econometrica, Econometric Society, vol. 72(6), pages 1737-1772, November.
    2. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 735-765.
    3. 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.
    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. Anderson, Gordon & Ge, Ying, 2005. "The size distribution of Chinese cities," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 756-776, November.
    6. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-851, July.
    7. Anderson, Gordon, 2004. "Toward an empirical analysis of polarization," Journal of Econometrics, Elsevier, vol. 122(1), pages 1-26, September.
    8. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(3), pages 560-586, June.
    9. 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, September.
    10. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sokbae (Simon) Lee & Yoon-Jae Whang, 2009. "Nonparametric tests of conditional treatment effects," CeMMAP working papers CWP36/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. 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.
    3. Gordon Anderson, 2010. "Polarization Of The Poor: Multivariate Relative Poverty Measurement Sans Frontiers," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(1), pages 84-101, March.
    4. 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.
    5. Maria Grazia Pittau & Roberto Zelli & Paul A. Johnson, 2010. "Mixture Models, Convergence Clubs, And Polarization," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(1), pages 102-122, March.
    6. 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.
    7. Amal Helu & Hani Samawi & Robert Vogel, 2011. "Nonparametric overlap coefficient estimation using ranked set sampling," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 385-397.
    8. Hani M. Samawi & Amal Helu & Robert Vogel, 2011. "A nonparametric test of symmetry based on the overlapping coefficient," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 885-898, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Anderson, Gordon & Linton, Oliver & Whang, Yoon-Jae, 2012. "Nonparametric estimation and inference about the overlap of two distributions," Journal of Econometrics, Elsevier, vol. 171(1), pages 1-23.
    2. Liu, Shen & Maharaj, Elizabeth Ann & Inder, Brett, 2014. "Polarization of forecast densities: A new approach to time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 345-361.
    3. Daniel J. Henderson & Christopher F. Parmeter & R. Robert Russell, 2008. "Modes, weighted modes, and calibrated modes: evidence of clustering using modality tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 607-638.
    4. Mariateresa Ciommi & Chiara Gigliarano & Giovanni Maria Giorgi, 2019. "Bonferroni And De Vergottini Are Back: New Subgroup Decompositions And Bipolarization Measures," Working Papers 439, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    5. 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.
    6. Jose G. Montalvo & Marta Reynal‐Querol, 2008. "Discrete Polarisation with an Application to the Determinants of Genocides," Economic Journal, Royal Economic Society, vol. 118(533), pages 1835-1865, November.
    7. Gordon Anderson & Jasmin Thomas, 2019. "Measuring Multi-group Polarization, Segmentation and Ambiguity: Increasingly Unequal Yet Similar Constituent Canadian Income Distributions," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 145(3), pages 1001-1032, October.
    8. Chiara Gigliarano & Daniel Nowak & Karl Mosler, 2019. "A Polarization Index for Overlapping Groups," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 65(4), pages 712-735, December.
    9. Jayadev, Arjun & Reddy, Sanjay G., 2011. "Inequalities between Groups: Theory and Empirics," World Development, Elsevier, vol. 39(2), pages 159-173, February.
    10. Azomahou, Théophile T. & Diene, Mbaye, 2012. "Polarization patterns in economic development and innovation," Structural Change and Economic Dynamics, Elsevier, vol. 23(4), pages 421-436.
    11. Michal Brzezinski, 2013. "Income polarization and economic growth," Working Papers 296, ECINEQ, Society for the Study of Economic Inequality.
    12. Azomahou, Theophile & Diene, Mbaye, 2012. "Income polarization and innovation: Evidence from African economies," MERIT Working Papers 2012-048, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    13. Anderson, Gordon, 2011. "Polarization measurement and inference in many dimensions when subgroups can not be identified," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 5, pages 1-19.
    14. Jo Thori Lind & Karl Moene, 2011. "Miserly Developments," Journal of Development Studies, Taylor & Francis Journals, vol. 47(9), pages 1332-1352, June.
    15. Teixidó-Figueras, J. & Duro, J.A., 2014. "Spatial Polarization of the Ecological Footprint Distribution," Ecological Economics, Elsevier, vol. 104(C), pages 93-106.
    16. Alesina, Alberto & Devleeschauwer, Arnaud & Easterly, William & Kurlat, Sergio & Wacziarg, Romain, 2003. "Fractionalization," Journal of Economic Growth, Springer, vol. 8(2), pages 155-194, June.
    17. Joan Esteban & Laura Mayoral & Debraj Ray, 2012. "Ethnicity and Conflict: An Empirical Study," American Economic Review, American Economic Association, vol. 102(4), pages 1310-1342, June.
    18. Sommarat Chantarat & Christopher Barrett, 2012. "Social network capital, economic mobility and poverty traps," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(3), pages 299-342, September.
    19. Hodler, Roland & Valsecchi, Michele & Vesperoni, Alberto, 2021. "Ethnic geography: Measurement and evidence," Journal of Public Economics, Elsevier, vol. 200(C).
    20. Koki Oikawa & Minoru Kitahara, 2017. "Technology Polarization," Working Papers e113, Tokyo Center for Economic Research.

    More about this item

    Keywords

    Kernel estimation; Inequality; Overlap coefficient; Poissonization;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1714. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.