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Cubic spline population density functions and subcentre delimitation. The case of Barcelona

  • Ivan Muñiz

    ()

    (Departament d'Economia Aplicada, Universitat Autonoma de Barcelona)

  • Anna Galindo

    ()

    (Departament d'Economia Aplicada, Universitat Autonoma de Barcelona)

  • Miguel Ángel García

    ()

    (Departament d'Economia Aplicada, Universitat Autonoma de Barcelona)

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    The presence of subcentres cannot be captured by an exponential function. Cubic spline functions seem more appropriate to depict the polycentricity pattern of modern urban systems. Using data from Barcelona Metropolitan Region, two possible population subcentre delimitation procedures are discussed. One, taking an estimated derivative equal to zero, the other, a density gradient equal to zero. It is argued that, in using a cubic spline function, a delimitation strategy based on derivatives is more appropriate than one based on gradients because the estimated density can be negative in sections with very low densities and few observations, leading to sudden changes in estimated gradients. It is also argued that using as a criteria for subcentre delimitation a second derivative with value zero allow us to capture a more restricted subcentre area than using as a criteria a first derivative zero. This methodology can also be used for intermediate ring delimitation.

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    File URL: http://www.ecap.uab.es/RePEc/doc/wpdea0209.pdf
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    Paper provided by Department of Applied Economics at Universitat Autonoma of Barcelona in its series Working Papers with number wpdea0209.

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    Length: 33 pages
    Date of creation: May 2002
    Date of revision:
    Handle: RePEc:uab:wprdea:wpdea0209
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    1. Daniel P. McMillen & John F. McDonald, 1998. "Population Density in Suburban Chicago: A Bid-rent Approach," Urban Studies, Urban Studies Journal Limited, vol. 35(7), pages 1119-1130, June.
    2. Small Kenneth A. & Song Shunfeng, 1994. "Population and Employment Densities: Structure and Change," Journal of Urban Economics, Elsevier, vol. 36(3), pages 292-313, November.
    3. GOFFETTE-NAGOT, Florence & SCHMITT, Bertrand, 1997. "Agglomération economies and spatial configuration in rural areas," LATEC - Document de travail - Economie (1991-2003) 1997-16, LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS UMR 5118, Université de Bourgogne.
    4. Steen, Robert C., 1986. "Nonubiquitous transportation and urban population density gradients," Journal of Urban Economics, Elsevier, vol. 20(1), pages 97-106, July.
    5. Craig, Steven G. & Ng, Pin T., 2001. "Using Quantile Smoothing Splines to Identify Employment Subcenters in a Multicentric Urban Area," Journal of Urban Economics, Elsevier, vol. 49(1), pages 100-120, January.
    6. Anderson, John E., 1982. "Cubic-spline urban-density functions," Journal of Urban Economics, Elsevier, vol. 12(2), pages 155-167, September.
    7. McMillen, Daniel P., 2001. "Nonparametric Employment Subcenter Identification," Journal of Urban Economics, Elsevier, vol. 50(3), pages 448-473, November.
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