IDEAS home Printed from https://ideas.repec.org/a/zbw/ifweej/201111.html
   My bibliography  Save this article

Polarization measurement and inference in many dimensions when subgroups can not be identified

Author

Listed:
  • Anderson, Gordon

Abstract

The most popular general univariate polarization indexes for discrete and continuous variables are extended and combined to describe the extent of polarization between agents in a distribution defined over a collection of many discrete and continuous agent characteristics. A formula for the asymptotic variance of the index is also provided. The implementation of the index is illustrated with an application to Chinese urban household data drawn from six provinces in the years 1987 and 2001 (years spanning the growth and urbanization period subsequent to the economic reforms). The data relates to household adult equivalent log income, adult equivalent living space, which are both continuous variables and the education of the head of household which is a discrete variable. For this data set combining the characteristics changes the view of polarization that would be inferred from considering the indices individually.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:ifweej:201111
    DOI: 10.5018/economics-ejournal.ja.2011-11
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.5018/economics-ejournal.ja.2011-11
    Download Restriction: no
    File URL: https://www.econstor.eu/bitstream/10419/49713/1/66798416X.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.5018/economics-ejournal.ja.2011-11?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Alberto Alesina & Enrico Spolaore, 1997. "On the Number and Size of Nations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(4), pages 1027-1056.
    2. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-851, July.
    3. Joan Esteban & Debraj Ray, 2005. "A Comparison of Polarization Measures," Working Papers 310, Barcelona School of Economics.
    4. Jean-Yves Duclos & Joan Esteban & Debraj Ray, 2004. "Polarization: Concepts, Measurement, Estimation," Econometrica, Econometric Society, vol. 72(6), pages 1737-1772, November.
    5. Anderson, Gordon & Crawford, Ian & Leicester, Andrew, 2011. "Welfare rankings from multivariate data, a nonparametric approach," Journal of Public Economics, Elsevier, vol. 95(3), pages 247-252.
    6. Chiara Gigliarano & Karl Mosler, 2009. "Constructing indices of multivariate polarization," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(4), pages 435-460, December.
    7. Gordon Anderson, 2008. "The empirical assessment of multidimensional welfare, inequality and poverty: Sample weighted multivariate generalizations of the Kolmogorov–Smirnov two sample tests for stochastic dominance," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(1), pages 73-87, March.
    8. Gordon Anderson & Maria Grazia Pittau & Roberto Zelli, 2011. "Partially Identified Poverty Status: A New Approach to Measuring Poverty and the Progress of the Poor," Working Papers tecipa-421, University of Toronto, Department of Economics.
    9. Koshevoy, G. A. & Mosler, K., 1997. "Multivariate Gini Indices," Journal of Multivariate Analysis, Elsevier, vol. 60(2), pages 252-276, February.
    10. Anderson, Gordon, 2004. "Toward an empirical analysis of polarization," Journal of Econometrics, Elsevier, vol. 122(1), pages 1-26, September.
    11. Jean-Yves Duclos & David E. Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons," Economic Journal, Royal Economic Society, vol. 116(514), pages 943-968, October.
    12. 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.
    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. Tanzhe Tang & Amineh Ghorbani & Flaminio Squazzoni & Caspar G. Chorus, 2022. "Together alone: a group-based polarization measurement," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(5), pages 3587-3619, October.
    2. Stelios Rozakis & Athanasios Kampas, 2022. "An interactive multi-criteria approach to admit new members in international environmental agreements," Operational Research, Springer, vol. 22(4), pages 3461-3487, September.
    3. Gordon Anderson & Oliver Linton & Jasmin Thomas, 2017. "Similarity, dissimilarity and exceptionality: generalizing Gini’s transvariation to measure “differentness” in many distributions," METRON, Springer;Sapienza Università di Roma, vol. 75(2), pages 161-180, August.

    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. 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.
    2. 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.
    3. Hodler, Roland & Srisuma, Sorawoot & Vesperoni, Alberto & Zurlinden, Noémie, 2020. "Measuring ethnic stratification and its effect on trust in Africa," Journal of Development Economics, Elsevier, vol. 146(C).
    4. Héctor Galindo Silva, 2007. "Polarización económica y emergencia de confilctos violentos internos un estudio empírico," Documentos de Economía 4449, Universidad Javeriana - Bogotá.
    5. 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.
    6. 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.
    7. 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.
    8. Iñaki Permanyer, 2012. "The conceptualization and measurement of social polarization," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(1), pages 45-74, March.
    9. 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).
    10. 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.
    11. 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.
    12. 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.
    13. Fabio Clementi & Francesco Schettino, 2013. "Income polarization in Brazil, 2001-2011: A distributional analysis using PNAD data," Economics Bulletin, AccessEcon, vol. 33(3), pages 1796-1815.
    14. Ori Haimanko & Michel Breton & Shlomo Weber, 2007. "The stability threshold and two facets of polarization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(3), pages 415-430, March.
    15. Gornig, Martin & Goebel, Jan, 2018. "Deindustrialisation and the polarisation of household incomes: The example of urban agglomerations in Germany," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 55(4), pages 790-806.
    16. Chiara Assunta Ricci & Sergio Scicchitano, 2021. "Decomposing changes in income polarization by population group: what happened during the crisis?," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 38(1), pages 235-259, April.
    17. Joan Esteban & Debraj Ray, 2005. "A Comparison of Polarization Measures," Working Papers 310, Barcelona School of Economics.
    18. 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.
    19. F. Clementi & A. L. Dabalen & V. Molini & F. Schettino, 2017. "When the Centre Cannot Hold: Patterns of Polarization in Nigeria," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 63(4), pages 608-632, December.
    20. Iñaki Permanyer, 2008. "Social Polarization: Introducing distances between and within groups," UFAE and IAE Working Papers 751.08, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

    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:zbw:ifweej:201111. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/iwkiede.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.