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

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  • 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.

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  • 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
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    5. 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.
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    9. 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.
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    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.

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    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

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