Random-growth urban model with geographical fitness
This 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.
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Volume (Year): 391 (2012)
Issue (Month): 23 ()
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- 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.
- J.V. Henderson, 1972.
"The Sizes and Types of Cities,"
75, Queen's University, Department of Economics.
- 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.
- Esteban Rossi-Hansberg & Mark L. J. Wright, 2007.
"Urban Structure and Growth,"
Review of Economic Studies,
Oxford University Press, vol. 74(2), pages 597-624.
- Esteban Rossi-Hansberg & Mark L. J. Wright, 2003. "Urban structure and growth," Discussion Paper / Institute for Empirical Macroeconomics 141, Federal Reserve Bank of Minneapolis.
- Esteban Rossi-Hansberg & Mark L.J. Wright, 2005. "Urban Structure and Growth," NBER Working Papers 11262, National Bureau of Economic Research, Inc.
- 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, 2006. "Urban structure and growth," Staff Report 381, Federal Reserve Bank of Minneapolis.
- 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.
- 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, March.
- 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.
- 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.
- 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.
- 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.
- 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.
- Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
- Kwok Tong Soo, 2004.
"Zipfs Law for Cities: A Cross Country Investigation,"
CEP Discussion Papers
dp0641, Centre for Economic Performance, LSE.
- 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. "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.
- 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.
- Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
- 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.
- Malcolm Asadoorian, 2008. "Simulating the spatial distribution of population and emissions to 2100," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 39(3), pages 199-221, March.
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