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

Ivan Muñiz (), Anna Galindo () and Miquel-Àngel Garcia-López
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Ivan Muñiz: Departament d'Economia Aplicada, Universitat Autonoma de Barcelona
Anna Galindo: Departament d'Economia Aplicada, Universitat Autonoma de Barcelona

Working Papers from Department of Applied Economics at Universitat Autonoma of Barcelona

Abstract: 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.

Keywords: polycentrism; cubic spline functions (search for similar items in EconPapers)
JEL-codes: R14 R40 (search for similar items in EconPapers)
Pages: 33 pages
Date: 2002-05
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Citations: View citations in EconPapers (1)

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