Time evolution of city distributions in Germany

Ikeda, Kiyohiro and Osawa, Minoru and Takayama, Yuki (2021): Time evolution of city distributions in Germany.

Abstract

This paper aims to capture characteristic agglomeration patterns in population data in Germany from 1987 to 2011, encompassing pre- and post-unification periods. We utilize a group-theoretic double Fourier spectrum analysis procedure (Ikeda et al., 2018) as a systematic means to capture characteristic agglomeration patterns in population data. Among a plethora of patterns to be self-organized from a uniform state, we focus on a megalopolis pattern, a rhombic pattern, and a core--satellite pattern (a downtown surrounded by hexagonal satellite cities). As the technical contribution of this paper, we newly introduce a principal vector as a superposition of these patterns in order to grasp the multi-scale nature of agglomerations. Benchmark spectra for these patterns are advanced and are found in the population data of Germany in 2011. An incremental population is investigated using this principal vector to successfully detect a shift of predominant population increase/decrease patterns in the pre- and post-unification periods.

• Item Type: MPRA Paper
• Language: English
• Keywords: Central place theory City distribution Core--satellite pattern German reunification Hexagons Megalopolis Spectrum analysis
• Subjects: R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R0 - General

References

Banaszak, M., Dziecielski, M., Nijkamp, P., Ratajczak, W., 2015. Self-organisation in spatial systems: From fractal chaos to regular patterns and vice versa. PLOS ONE 10 (9): e0136248.

Barbero and Zofio, 2016. The multiregional core-periphery model: The role of the spatial topology. Networks and Spatial Economics 16, 469-496.

Bosker, M., Brakman, S., Garretsen, H., Schramm, M., 2008. A century of shocks: The evolution of the German city size distribution 1925-1999. Regional Science and Urban Economics 38 (4), 330-347.

Bosker, M., Brakman, S., Garretsen, H., Schramm, M., 2010. Adding geography to the new economic geography: bridging the gap between theory and empirics. Journal of Economic Geography 10 (6), 793-823.

Christaller, W., 1933. Die zentralen Orte in Suddeutschland. Gustav Fischer. English translation: 1966. Central Places in Southern Germany. Prentice Hall.

Clarke, M., Wilson, A. G., 1983. The dynamics of urban spatial structure: Progress and problems. Journal of Regional Science 23 (1), 1-18.

Dray, S., Legendre, P., Peres-Neto, P. R., 2006. Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbour matrices (PCNM). Ecological Modelling 196, 483-493.

Ducruet, C., Beauguitte, L., 2014. Spatial science and network science: Review and outcomes of a complex relationship. Networks and Spatial Economics 14, 297-316.

Eaton, B. C., Lipsey, R. G., 1975. The principle of minimum differentiation reconsidered: Some new developments in the theory of spatial competition. The Review of Economic Studies 42 (1), 27-49.

Findeisena, S., Sudekum, J., 2008. Industry churning and the evolution of cities: Evidence for Germany. Journal of Urban Economics 64 (2), 326-339.

Fujita, M., Krugman, P., Mori, T., 1999. On the evolution of hierarchical urban systems. European Economic Review 43 (2), 209-251.

Golubitsky, M., Stewart, I., Schaeffer, D. G., 1988. Singularities and Groups in Bifurcation Theory, Vol. 2, Springer-Verlag.

Ikeda, K., Murota, K., 2014. Bifurcation Theory for Hexagonal Agglomeration in Economic Geography, Springer-Verlag.

Ikeda, K., Murota, K., Akamatsu, T., Kono, T., Takayama, Y., 2014. Self-organization of hexagonal agglomeration patterns in new economic geography models. Journal of Economic Behavior \& Organization 99, 32-52.

keda, K., Murota, K., Takayama, Y., 2017. Stable economic agglomeration patterns in two dimensions: Beyond the scope of central place theory. Journal of Regional Science 57 (1), 132-172.

Ikeda, K., Takayama, Y., Onda, M., Murakami, D., 2018. Group-theoretic spectrum analysis of population distribution in Southern Germany and Eastern USA. International Journal of Bifurcation and Chaos 28 (14),18300458.

Losch, A., 1940 Die raumliche Ordnung der Wirtschaft, Gustav Fischer.

Mulligan, G. F., Partridge, M. D., Carruthers, J. I., 2012. Central place theory and its reemergence in regional science. The Annals of Regional Science 48 (2), 405-431.

Munz, M., Weidlich. W., 1990. Settlement formation, Part II: Numerical simulation. The Annals of Regional Science 24, 177-196.

Murakami, D., Griffith, D. A., 2015. Random effects specifications in eigenvector spatial filtering: a simulation study, J. Geographical Systems 17, 311-331.

Redding, S. J., Sturm, D. M., 2008. The costs of remoteness: Evidence from German division and reunification. The American Economic Review 98 (5), 1766-1797.

Sanglier, M., Allen, P., 1989. Evolutionary models of urban systems: An application to the Belgian provinces. Environment and Planning A 21, 477-498.

Stelder, D., 2005. Where do cities form? A geographical agglomeration model for Europe. Journal of Regional Science 45, 657-679.

Tabuchi, T., Thisse, J. F., 2011. A new economic geography model of central places. Journal of Urban Economics 69, 240--252.

Tiefelsdorf, M., Griffith, D. A., 2007. Semiparametric filtering of spatial autocorrelation: the eigenvector approach, Environment Planning A 39, 1193-1221.