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The median as watershed

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This paper is concerned with concepts - poverty, inequality, affluence, and polarization - that are typically treated in different literatures. Our aim here is to place them within a common framework and to identify the way in which different classes of income transfers contribute to different objectives. In particular, we examine the role of transfers that preserve both the mean and the median, and the importance of distinguishing between transfers across the median and transfers on one side of the median. The aim of the paper is to bring out some of the implications of adopting the median as a dividing line for these measurement purposes, particularly with respect to the robustness of the conclusions reached. In doing so, we develop the two alternative approaches - primal and dual - applied to Lorenz curves in Aaberge (2001). Our focus is on "well-off" countries where poverty is a minority, rather than a majority, phenomenon. At the other end of the scale, rich people are found in all countries, but less attention has been paid to the definition of cut-offs for affluence. The measurement of "affluence" can proceed along similar lines to the measurement of poverty. The threshold may be set, relatively, as a percentage of the median, and we can ask similar questions about the sensitivity and seek similar dominance results. Moreover, we focus on societies that have a middle class in the sense that the median person is never defined as "rich". The motivation of Foster and Wolfson's paper "Polarization and the decline of the middle class" (1992/2010) was the sensitivity of conclusions to the - essentially arbitrary - definition of the middle class. They proposed "a range-free approach to measuring the middle class and polarization based on partial orderings" (2010, page 247). We introduce an alternative partial ordering defined in terms of a bi-polarization curve capturing the distance from the median.

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  • Rolf Aaberge & A B Atkinson, 2013. "The median as watershed," Discussion Papers 749, Statistics Norway, Research Department.
  • Handle: RePEc:ssb:dispap:749
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    File URL: https://www.ssb.no/en/forskning/discussion-papers/_attachment/130759
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    1. Andreas Peichl & Thilo Schaefer & Christoph Scheicher, 2010. "Measuring Richness And Poverty: A Micro Data Application To Europe And Germany," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(3), pages 597-619, September.
    2. Michael Sattinger (ed.), 2001. "Income Distribution," Books, Edward Elgar Publishing, volume 0, number 2018, April.
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    4. Walter Bossert & William Schworm, 2008. "A Class of Two-Group Polarization Measures," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(6), pages 1169-1187, December.
    5. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-851, July.
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    1. repec:eme:ceapzz:s0573-855520140000293006 is not listed on IDEAS
    2. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
    3. Vincenzo Prete & Alessandro Sommacal & Claudio Zoli, 2016. "Optimal Non-Welfarist Income Taxation for Inequality and Polarization Reduction," Working Papers 23/2016, University of Verona, Department of Economics.
    4. Bea Cantillon & Diego Collado & Natascha Van Mechelen, 2015. "The end of decent social protection for the poor? The dynamics of low wages, minimum income packages and median household incomes," Working Papers 1501, Herman Deleeck Centre for Social Policy, University of Antwerp.
    5. Bea Cantillon & Diego Collado & Natascha Van Mechelen, 2015. "The end of decent social protection for the poor? The dynamics of low wages, minimum income packages and median household incomes," ImPRovE Working Papers 15/03, Herman Deleeck Centre for Social Policy, University of Antwerp.
    6. Nancy Birdsall & Christian J. Meyer, 2015. "The Median is the Message: A Good Enough Measure of Material Wellbeing and Shared Development Progress," Global Policy, London School of Economics and Political Science, vol. 6(4), pages 343-357, November.
    7. Rolf Aaberge & Anthony B. Atkinson & Jørgen Modalsli, 2013. "The ins and outs of top income mobility," Discussion Papers 762, Statistics Norway, Research Department.
    8. Rolf Aaberge & Ugo Colombino, 2014. "Labour Supply Models," Contributions to Economic Analysis,in: Handbook of Microsimulation Modelling, volume 127, pages 167-221 Emerald Publishing Ltd.

    More about this item

    Keywords

    Poverty; Affluence; Polarization; Dispersion; Tail-heaviness; Stochastic dominance; Transfer principles;

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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