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Random Walk-Based Segregation Measures

Author

Listed:
  • Coralio Ballester

    (Universidad de Alicante)

  • Marc Vorsatz

    (Universidad Nacional de Educación a Distancia and Fundación de Estudios de Economía Aplicada)

Abstract

We propose an intuitive way of how to measure segregation in social and spatial networks. Using random walks, we define the segregation index as the probability that an individual meets an individual from the same social group. The segregation index is a generalization of the isolation index and a homophily index introduced in Currarini, Jackson, and Pin (2009), and it has a closed-form relation to PageRank that facilitates its computation. We also show that the Spectral Segregation Index proposed by Echenique and Fryer (2007) is not continuous with respect to the network structure. Finally, we apply the measure to Spanish census data and to citations data from economics, and rationalize the index as the equilibrium outcome of a game. © 2014 The President and Fellows of Harvard College and the Massachusetts Institute of Technology

Suggested Citation

  • Coralio Ballester & Marc Vorsatz, 2014. "Random Walk-Based Segregation Measures," The Review of Economics and Statistics, MIT Press, vol. 96(3), pages 383-401, July.
    • Handle: RePEc:tpr:restat:v:96:y:2014:i:3:p:383-401
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    File URL: http://www.mitpressjournals.org/doi/pdf/10.1162/REST_a_00399
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    References listed on IDEAS

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    1. 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..
    2. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(2), pages 441-485.
    3. David M. Cutler & Edward L. Glaeser, 1997. "Are Ghettos Good or Bad?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(3), pages 827-872.
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    Cited by:

    1. Sandro Sousa & Vincenzo Nicosia, 2022. "Quantifying ethnic segregation in cities through random walks," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    2. Sergio Currarini, & Elena Fumagalli & Fabrizio Panebianco, 2012. "Games on Networks: Direct Complements and Indirect Substitutes," Discussion Papers in Economics 13/04, Division of Economics, School of Business, University of Leicester.
    3. Casilda Vega & Oscar Volij, 2014. "Segregation, informativeness and Lorenz dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 547-564, October.
    4. Hannu Salonen, 2016. "Equilibria and centrality in link formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1133-1151, November.
    5. Michael D. König & Dominic Rohner & Mathias Thoenig & Fabrizio Zilibotti, 2017. "Networks in Conflict: Theory and Evidence From the Great War of Africa," Econometrica, Econometric Society, vol. 85, pages 1093-1132, July.
    6. Gordon Anderson, 2018. "Measuring Aspects of Mobility, Polarization and Convergence in the Absence of Cardinality: Indices Based Upon Transitional Typology," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 139(3), pages 887-907, October.
    7. Oscar Volij, 2018. "Segregation: theoretical approaches," Chapters, in: Conchita D’Ambrosio (ed.), Handbook of Research on Economic and Social Well-Being, chapter 21, pages 480-503, Edward Elgar Publishing.
    8. Herings, P. Jean-Jacques & Peeters, Ronald & Tenev, Anastas P. & Thuijsman, Frank, 2021. "Naïve imitation and partial cooperation in a local public goods model," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 162-185.
    9. Abhimanyu Khan & Ronald Peeters & Frank Thuijsman & Philippe Uyttendaele, 2016. "Network Characteristics Enabling Efficient Coordination: A Simulation Study," Dynamic Games and Applications, Springer, vol. 6(4), pages 495-519, December.
    10. José M. Casado-Díaz & Raquel Simón-Albert & Hipólito Simón, 2022. "Reassessing the commuting penalty for immigrants: new evidence from Spain," Transportation, Springer, vol. 49(4), pages 1099-1132, August.
    11. Matthew Gentzkow & Jesse M. Shapiro & Matt Taddy, 2019. "Measuring Group Differences in High‐Dimensional Choices: Method and Application to Congressional Speech," Econometrica, Econometric Society, vol. 87(4), pages 1307-1340, July.
    12. Mariano Bosch & M. Carnero & Lídia Farré, 2015. "Rental housing discrimination and the persistence of ethnic enclaves," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 6(2), pages 129-152, June.
    13. 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.
    14. Fernández-Huertas Moraga, Jesús & Ferrer-i-Carbonell, Ada & Saiz, Albert, 2019. "Immigrant locations and native residential preferences: Emerging ghettos or new communities?," Journal of Urban Economics, Elsevier, vol. 112(C), pages 133-151.
    15. Gauvin, Laetitia & Vignes, Annick & Nadal, Jean-Pierre, 2013. "Modeling urban housing market dynamics: Can the socio-spatial segregation preserve some social diversity?," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1300-1321.

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    More about this item

    Keywords

    Isolation; Homophily; Network; PageRank; Markov Chain; Segregation.;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification

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