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The Effectiveness of Spline Urban Density Functions: An Empirical Investigation

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  • Gershon Alperovich

    (Department of Economics, Bar-Ilan University, 52900 Ramat-Gan, Israel, Department of Economics, Hong Kong University of Science and Technology, Hong Kong)

Abstract

Recent studies of population distribution in urban settings suggest that cubic-spline functions may be preferable to the conventional exponential form. It is contemplated that this specification is more suitable for untangling, discovering and depicting the complex density patterns of today's relatively dispersed urban areas. This paper examines the usefulness as well as the amenability of the cubic-spline function for describing and testing hypotheses on the processes underlying the determination of population densities in Tel Aviv-Yafo. The principal findings of the analysis are threefold. First, from the theoretical and empirical points of view the cubic-spline function is unlikely to be useful for testing hypotheses. Multicollinearity among distance variables renders the cubic-spline function without much practical merit for this purpose. Secondly, an exponential spline form which does not utilise high-order terms of distance is better suited for this purpose and should therefore be preferred to the cubic-spline. Thirdly, an alternative approach which employs an improved exponential form obtained by incorporating pertinent information on actual patterns of land-use development into the theoretically derived exponential form was highly supported by the data. Utilisation of the latter approach led to an increase in the explanatory power of the model from a mere 0.24 to a respectable 0.83. Indeed, the general lesson to be learned from the analysis is that utilisation of general functional forms cannot by itself correct for possible biases in sample selection, model specification or, for that matter, replace thorough understanding of the processes one is trying to model.

Suggested Citation

  • Gershon Alperovich, 1995. "The Effectiveness of Spline Urban Density Functions: An Empirical Investigation," Urban Studies, Urban Studies Journal Limited, vol. 32(9), pages 1537-1548, November.
  • Handle: RePEc:sae:urbstu:v:32:y:1995:i:9:p:1537-1548
    DOI: 10.1080/00420989550012393
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    References listed on IDEAS

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    1. Gershon Alperovich & Joeseph Deutsch, 1992. "Population Density Gradients and Urbanisation Measurement," Urban Studies, Urban Studies Journal Limited, vol. 29(8), pages 1323-1328, December.
    2. Anderson, John E., 1982. "Cubic-spline urban-density functions," Journal of Urban Economics, Elsevier, vol. 12(2), pages 155-167, September.
    3. Suits, Daniel B & Mason, Andrew & Chan, Louis, 1978. "Spline Functions Fitted by Standard Regression Methods," The Review of Economics and Statistics, MIT Press, vol. 60(1), pages 132-139, February.
    4. McDonald, John F., 1989. "Econometric studies of urban population density: A survey," Journal of Urban Economics, Elsevier, vol. 26(3), pages 361-385, November.
    5. Alperovich Gershon & Deutsch Joseph, 1994. "Joint Estimation of Population Density Functions and the Location of the Central Business District," Journal of Urban Economics, Elsevier, vol. 36(3), pages 239-248, November.
    6. Brueckner, Jan K., 1986. "A switching regression analysis of urban population densities," Journal of Urban Economics, Elsevier, vol. 19(2), pages 174-189, March.
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