Random-growth urban model with geographical fitness
AbstractThis paper formulates a random-growth urban model with a notion of geographical fitness. Using techniques of complex-network theory, we study our system as a type of preferential-attachment model with fitness, and we analyze its macro behavior to clarify the properties of the city-size distributions it predicts. First, restricting the geographical fitness to take positive values and using a continuum approach, we show that the city-size distributions predicted by our model asymptotically approach Pareto distributions with coefficients greater than unity. Then, allowing the geographical fitness to take negative values, we perform local coefficient analysis to show that the predicted city-size distributions can deviate from Pareto distributions, as is often observed in actual city-size distributions. As a result, the model we propose can generate a generic class of city-size distributions, including but not limited to Pareto distributions. For applications to city-population projections, our simple model requires randomness only when new cities are created, not during their subsequent growth. This property leads to smooth trajectories of city population growth, in contrast to other models using Gibrat’s law. In addition, a discrete form of our dynamical equations can be used to estimate past city populations based on present-day data; this fact allows quantitative assessment of the performance of our model. Further study is needed to determine appropriate formulas for the geographical fitness.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 391 (2012)
Issue (Month): 23 ()
Contact details of provider:
Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
Urban population; Pareto distribution; Complex network; Geographical fitness; Zipf’s law;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Esteban Rossi-Hansberg & Mark L. J. Wright, 2003.
"Urban structure and growth,"
Discussion Paper / Institute for Empirical Macroeconomics
141, Federal Reserve Bank of Minneapolis.
- Mark Wright & Esteban Rossi-Hansberg, 2004. "Urban Structure and Growth," 2004 Meeting Papers 33, Society for Economic Dynamics.
- Esteban Rossi-Hansberg & Mark L.J. Wright, 2005. "Urban Structure and Growth," NBER Working Papers 11262, National Bureau of Economic Research, Inc.
- Esteban Rossi-Hansberg & Mark L. J. Wright, 2006. "Urban structure and growth," Staff Report 381, Federal Reserve Bank of Minneapolis.
- Masahisa Fujita & Paul Krugman & Anthony J. Venables, 2001. "The Spatial Economy: Cities, Regions, and International Trade," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262561476, December.
- Henderson, J V, 1974.
"The Sizes and Types of Cities,"
American Economic Review,
American Economic Association, vol. 64(4), pages 640-56, September.
- Maarten Bosker & Steven Brakman & Harry Garretsen & Marc Schramm, 2006.
"A Century of Shocks: The Evolution of the German City Size Distribution 1925 – 1999,"
CESifo Working Paper Series
1728, CESifo Group Munich.
- Bosker, Maarten & Brakman, Steven & Garretsen, Harry & Schramm, Marc, 2008. "A century of shocks: The evolution of the German city size distribution 1925-1999," Regional Science and Urban Economics, Elsevier, vol. 38(4), pages 330-347, July.
- Nitsch, Volker, 2005.
Journal of Urban Economics,
Elsevier, vol. 57(1), pages 86-100, January.
- Donald R. Davis & David E. Weinstein, 2002.
"Bones, Bombs, and Break Points: The Geography of Economic Activity,"
American Economic Review,
American Economic Association, vol. 92(5), pages 1269-1289, December.
- Donald R. Davis & David E. Weinstein, 2001. "Bones, Bombs and Break Points: The Geography of Economic Activity," NBER Working Papers 8517, National Bureau of Economic Research, Inc.
- Donald R. Davis & David E. Weinstein, 2002. "Bones, bombs and break points: The geography of economic activity," Discussion Papers 0102-02, Columbia University, Department of Economics.
- Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
- Kwok Tong Soo, 2004.
"Zipf's law for cities: a cross country investigation,"
LSE Research Online Documents on Economics
19947, London School of Economics and Political Science, LSE Library.
- Soo, Kwok Tong, 2005. "Zipf's Law for cities: a cross-country investigation," Regional Science and Urban Economics, Elsevier, vol. 35(3), pages 239-263, May.
- Kwok Tong Soo, 2004. "Zipfs Law for Cities: A Cross Country Investigation," CEP Discussion Papers dp0641, Centre for Economic Performance, LSE.
- Moura, Newton J. & Ribeiro, Marcelo B., 2006. "Zipf law for Brazilian cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 441-448.
- Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
- Sarabia, José María & Prieto, Faustino, 2009. "The Pareto-positive stable distribution: A new descriptive model for city size data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4179-4191.
- Ergün, G. & Rodgers, G.J., 2002. "Growing random networks with fitness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(1), pages 261-272.
- Benguigui, Lucien & Blumenfeld-Lieberthal, Efrat, 2009. "The temporal evolution of the city size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1187-1195.
- Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
- Rosen, Kenneth T. & Resnick, Mitchel, 1980. "The size distribution of cities: An examination of the Pareto law and primacy," Journal of Urban Economics, Elsevier, vol. 8(2), pages 165-186, September.
- Malcolm Asadoorian, 2008. "Simulating the spatial distribution of population and emissions to 2100," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 39(3), pages 199-221, March.
- Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
- Gabaix, Xavier & Ioannides, Yannis M., 2004.
"The evolution of city size distributions,"
Handbook of Regional and Urban Economics,
in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378
- Xavier Gabaix & Yannis M. Ioannides, 2003. "The Evolution of City Size Distributions," Discussion Papers Series, Department of Economics, Tufts University 0310, Department of Economics, Tufts University.
- Li, Xiang & Ying Jin, Yu & Chen, Guanrong, 2003. "Complexity and synchronization of the World trade Web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 287-296.
- Young, D.S., 2013. "Approximate tolerance limits for Zipf–Mandelbrot distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1702-1711.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.