IDEAS home Printed from https://ideas.repec.org/a/dem/demres/v44y2021i49.html

Measuring the concentration of urban population in the negative exponential model using the Lorenz curve, Gini coefficient, Hoover dissimilarity index, and relative entropy

Author

Listed:
  • Joel E. Cohen

    (Rockefeller University)

Abstract

Background: Stewart (1947) and Clark (1951) proposed that urban population density is a negative exponential function of the distance from a city’s center. This model of the spatial distribution of urban population density has been influential in urban economics, transportation planning, and urban demography. Duncan (1957) suggested characterizing the inequality in the distribution of urban population density in this model by using standard economic measures of concentration or unevenness: the Lorenz curve, the Gini coefficient, and the Hoover dissimilarity index. Batty (1974) advocated measuring concentration using relative entropy. Objective: We execute Duncan’s (1957) and Batty’s (1974) suggestions using mathematical analysis, not simulations. Methods: We modify the negative exponential model to recognize that any city has a finite radius. Results: Mathematical analysis reveals that all four measures of concentration depend sensitively on the finite radius of the city in the negative exponential model. We give a numerical example of the sensitivity of the concentration measures to the boundary radius. Contribution: In empirical applications of the negative exponential model of urban population density, it is important to have clear, consistent standards for defining urban boundaries. Otherwise, differences between cities or over time within the same city in these four and perhaps other measures of concentration could be due at least in part to differences in defining the radius or other boundaries of the city.

Suggested Citation

  • Joel E. Cohen, 2021. "Measuring the concentration of urban population in the negative exponential model using the Lorenz curve, Gini coefficient, Hoover dissimilarity index, and relative entropy," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 44(49), pages 1165-1184.
    • Handle: RePEc:dem:demres:v:44:y:2021:i:49
    DOI: 10.4054/DemRes.2021.44.49
    as

    Download full text from publisher

    File URL: https://www.demographic-research.org/volumes/vol44/49/44-49.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.4054/DemRes.2021.44.49?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. Douglas Massey & Jonathan Tannen, 2015. "A Research Note on Trends in Black Hypersegregation," Demography, Springer;Population Association of America (PAA), vol. 52(3), pages 1025-1034, June.
    2. McDonald, John F., 1989. "Econometric studies of urban population density: A survey," Journal of Urban Economics, Elsevier, vol. 26(3), pages 361-385, November.
    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. Ruiz Reina, Miguel Ángel, 2025. "Robust analysis of spatio-temporal inequality with Inverse entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 666(C).

    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. Florence Gofette-Nagot & Bertrand Schmitt, 1997. "Agglomeration economies and spatial configurations in rural areas," Working Papers hal-01526882, HAL.
    2. Carozzi, Felipe & Roth, Sefi, 2023. "Dirty density: Air quality and the density of American cities," Journal of Environmental Economics and Management, Elsevier, vol. 118(C).
    3. Mun, Se-il & Konishi, Ko-ji & Yoshikawa, Kazuhiro, 2005. "Optimal cordon pricing in a non-monocentric city," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 723-736.
    4. Ilenia Epifani & Rosella Nicolini, 2013. "On The Population Density Distribution Across Space: A Probabilistic Approach," Journal of Regional Science, Wiley Blackwell, vol. 53(3), pages 481-510, August.
    5. Ahlfeldt, Gabriel M. & Barr, Jason, 2022. "The economics of skyscrapers: A synthesis," Journal of Urban Economics, Elsevier, vol. 129(C).
    6. Kopits, Elizabeth & McConnell, Virginia & Miles, Daniel, 2009. "Lot Size, Zoning, and Household Preferences: Impediments to Smart Growth?," RFF Working Paper Series dp-09-15, Resources for the Future.
    7. Daniel P. McMillen, 2003. "Employment subcenters in Chicago: past, present, and future," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 27(Q II), pages 2-14.
    8. Ahlfeldt, Gabriel M. & Wendland, Nicolai, 2011. "Fifty years of urban accessibility: The impact of the urban railway network on the land gradient in Berlin 1890-1936," Regional Science and Urban Economics, Elsevier, vol. 41(2), pages 77-88, March.
    9. Gershon Alperovich & Joeseph Deutsch, 1992. "Population Density Gradients and Urbanisation Measurement," Urban Studies, Urban Studies Journal Limited, vol. 29(8), pages 1323-1328, December.
    10. Li, Mingxi, 2024. "Transportation, decentralization, and path dependence: How did the old tramway shape Shanghai, China?," Explorations in Economic History, Elsevier, vol. 94(C).
    11. Craig Olwert & Jean-Michel Guldmann, 2012. "A Computable General Equilibrium Model of the City: Impacts of Technology, Zoning, and Trade," Environment and Planning A, , vol. 44(1), pages 237-253, January.
    12. McConnell, Virginia & Walls, Margaret & Kopits, Elizabeth, 2006. "Zoning, TDRs and the density of development," Journal of Urban Economics, Elsevier, vol. 59(3), pages 440-457, May.
    13. Voith, Laura A. & Russell, Katie N. & Lee, Hyunjune & Atwell, Meghan Salas & McKinney, Sherise J. & Thomas, Tito & Barksdale, Edward M., 2023. "Using grounded theory to develop a theory of change for a violence intervention program," Evaluation and Program Planning, Elsevier, vol. 99(C).
    14. Samantha Friedman & Tabassum Z. Insaf & Temilayo Adeyeye & Jin-Wook Lee, 2023. "Spatial Variation in COVID-19 Mortality in New York City and Its Association with Neighborhood Race, Ethnicity, and Nativity Status," IJERPH, MDPI, vol. 20(17), pages 1-14, September.
    15. Ivan Muñiz & Ana Galindo & Miguel Angel García, 2002. "Urban spatial structure and suburbanisation. The case of the Barcelona Metropolitan," Working Papers wp0202, Department of Applied Economics at Universitat Autonoma of Barcelona.
    16. Kang, Sanggyun, 2020. "Why do warehouses decentralize more in certain metropolitan areas?," Journal of Transport Geography, Elsevier, vol. 88(C).
    17. Heather A. Moody & Sue C. Grady, 2021. "Lead Emissions and Population Vulnerability in the Detroit Metropolitan Area, 2006–2013: Impact of Pollution, Housing Age and Neighborhood Racial Isolation and Poverty on Blood Lead in Children," IJERPH, MDPI, vol. 18(5), pages 1-20, March.
    18. John F. McDonald & Paul J. Prather, 1994. "Suburban Employment Centres: The Case of Chicago," Urban Studies, Urban Studies Journal Limited, vol. 31(2), pages 201-218, March.
    19. Joan Carles Martori & Rafa Madariaga & Ramon Oller, 2016. "Real estate bubble and urban population density: six Spanish metropolitan areas 2001–2011," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 56(2), pages 369-392, March.
    20. Sukkoo Kim, 2007. "Changes In The Nature Of Urban Spatial Structure In The United States, 1890–2000," Journal of Regional Science, Wiley Blackwell, vol. 47(2), pages 273-287, May.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

    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:dem:demres:v:44:y:2021:i:49. 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: Editorial Office (email available below). General contact details of provider: https://www.demogr.mpg.de/ .

    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.