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Measuring Dissimilarity

Author

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  • Francesco Andreoli

    (Department of Economics (University of Verona))

  • Claudio Zoli

    (Department of Economics (University of Verona))

Abstract

The analysis of many social phenomena requires to compare distributions of outcomes achieved by individuals belonging to different social groups, defined for instance by their gender, ethnicity, birthplace, education, age or parental background. When the groups are similarly distributed across classes of realizations, their members have equal chances to achieve any of the attainable outcomes. Otherwise, a form of dissimilarity prevails. We frame dissimilarity comparisons of sets of groups distributions by showing the equivalence between axioms underpinning information criteria, majorization conditions, agreement between dissimilarity indicators and new empirical tests based on Zonotopes and Path Polytopes inclusion. Multi-group comparisons of segregation, discrimination and mobility, as well as inequality evaluations, are embedded within the dissimilarity model.

Suggested Citation

  • Francesco Andreoli & Claudio Zoli, 2014. "Measuring Dissimilarity," Working Papers 23/2014, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:23/2014
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    References listed on IDEAS

    as
    1. Frankel, David M. & Volij, Oscar, 2011. "Measuring school segregation," Journal of Economic Theory, Elsevier, vol. 146(1), pages 1-38, January.
    2. Yalonetzky, Gaston, 2012. "Measuring group disadvantage with inter-distributional inequality indices: A critical review and some amendments to existing indices," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 6, pages 1-32.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1998. "Intrinsic Preference for Information," Journal of Economic Theory, Elsevier, vol. 83(2), pages 233-259, December.
    5. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-316, March.
    6. George J. Borjas, 2021. "Ethnicity, Neighborhoods, and Human-Capital Externalities," World Scientific Book Chapters, in: Foundational Essays in Immigration Economics, chapter 7, pages 135-160, World Scientific Publishing Co. Pte. Ltd..
    7. Dardanoni Valentino, 1993. "Measuring Social Mobility," Journal of Economic Theory, Elsevier, vol. 61(2), pages 372-394, December.
    8. Valentino Dardanoni & Mario Fiorini & Antonio Forcina, 2012. "Stochastic monotonicity in intergenerational mobility tables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(1), pages 85-107, January.
    9. Udo Ebert & Patrick Moyes, 2003. "Equivalence Scales Reconsidered," Econometrica, Econometric Society, vol. 71(1), pages 319-343, January.
    10. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    11. Lefranc, Arnaud & Pistolesi, Nicolas & Trannoy, Alain, 2009. "Equality of opportunity and luck: Definitions and testable conditions, with an application to income in France," Journal of Public Economics, Elsevier, vol. 93(11-12), pages 1189-1207, December.
    12. Jenkins, Stephen P., 1994. "Earnings discrimination measurement : A distributional approach," Journal of Econometrics, Elsevier, vol. 61(1), pages 81-102, March.
    13. Alonso-Villar, Olga & del Río, Coral, 2010. "Local versus overall segregation measures," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 30-38, July.
    14. Roemer, John E., 2012. "On Several Approaches To Equality Of Opportunity," Economics and Philosophy, Cambridge University Press, vol. 28(2), pages 165-200, July.
    15. Van de Gaer, Dirk & Schokkaert, Erik & Martinez, Michel, 2001. "Three Meanings of Intergenerational Mobility," Economica, London School of Economics and Political Science, vol. 68(272), pages 519-537, November.
    16. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 183-201.
    17. Gleb Koshevoy, 1997. "The Lorenz zonotope and multivariate majorizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 1-14.
    18. Alessio Fusco & Jacques Silber, 2014. "On social polarization and ordinal variables: the case of self-assessed health," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 15(8), pages 841-851, November.
    19. Donaldson, David & Weymark, John A., 1998. "A Quasiordering Is the Intersection of Orderings," Journal of Economic Theory, Elsevier, vol. 78(2), pages 382-387, February.
    20. Federico Echenique & Roland G. Fryer Jr & Alex Kaufman, 2006. "Is School Segregation Good or Bad?," American Economic Review, American Economic Association, vol. 96(2), pages 265-269, May.
    21. Le Breton, Michel & Michelangeli, Alessandra & Peluso, Eugenio, 2012. "A stochastic dominance approach to the measurement of discrimination," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1342-1350.
    22. Hutchens, Robert M., 1991. "Segregation curves, Lorenz curves, and inequality in the distribution of people across occupations," Mathematical Social Sciences, Elsevier, vol. 21(1), pages 31-51, February.
    23. Butler, Richard J & McDonald, James B, 1987. "Interdistributional Income Inequality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 13-18, January.
    24. Dirk Van De Gaer & Erik Schokkaert & Michel Martinez, 2001. "Three Meanings of Intergenerational Mobility," Economica, London School of Economics and Political Science, vol. 68(272), pages 519-538, November.
    25. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 1-13.
    26. Ebert, Udo, 1984. "Measures of distance between income distributions," Journal of Economic Theory, Elsevier, vol. 32(2), pages 266-274, April.
    27. Chakravarty, Satya R. & Silber, Jacques, 2007. "A generalized index of employment segregation," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 185-195, March.
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    Cited by:

    1. Francesco Andreoli & Eugenio Peluso, 2016. "So close yet so unequal: Reconsidering spatial inequality in U.S. cities," Working Papers 21/2016, University of Verona, Department of Economics.
    2. Francesco Andreoli & Mauro Mussini & Vincenzo Prete, 2019. "Urban poverty: Theory and evidence from American cities," Working Papers 08/2019, University of Verona, Department of Economics.
    3. José María Sarabia & Vanesa Jorda, 2020. "Lorenz Surfaces Based on the Sarmanov–Lee Distribution with Applications to Multidimensional Inequality in Well-Being," Mathematics, MDPI, vol. 8(11), pages 1-17, November.
    4. Francesco Andreoli & Claudio Zoli, 2015. "Measuring the interaction dimension of segregation: the Gini-Exposure index," Working Papers 30/2015, University of Verona, Department of Economics.
    5. Francesco Andreoli & Mauro Mussini & Vincenzo Prete & Claudio Zoli, 2021. "Urban poverty: Measurement theory and evidence from American cities," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(4), pages 599-642, December.
    6. Martyna Kobus & Olga Półchłopek & Gaston Yalonetzky, 2019. "Inequality and Welfare in Quality of Life Among OECD Countries: Non-parametric Treatment of Ordinal Data," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 143(1), pages 201-232, May.

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    More about this item

    Keywords

    Dissimilarity; informativeness; majorization; Zonotopes.;
    All these keywords.

    JEL classification:

    • J71 - Labor and Demographic Economics - - Labor Discrimination - - - Hiring and Firing
    • D30 - Microeconomics - - Distribution - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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