González-Val, Rafael and Ramos, Arturo and Sanz-Gracia, Fernando (2010): Size Distributions for All Cities: Lognormal and q-exponential functions.
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This paper analyses in detail the features offered by a function which is practically new to Urban Economics, the q-exponential, in describing city size distributions. We highlight two contributions. First, we propose a new and simple procedure for estimating their parameters. Second, and more importantly, we explain the characteristics associated with two traditional graphic methods (Zipf plots and cumulative density functions) for discriminating between functions. We apply them to the lognormal and q-exponential, justifying them as the best functions for explaining the entire distribution, and that the relationship between them is of complementarity. The empirical evidence relies on the analysis of urban data of three countries (USA, Spain and Italy) over all of the 20th century.
|Item Type:||MPRA Paper|
|Original Title:||Size Distributions for All Cities: Lognormal and q-exponential functions|
|Keywords:||city size distribution; q-exponential; lognormal|
|Subjects:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C16 - Specific Distributions
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General
R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R0 - General > R00 - General
|Depositing User:||Rafael González-Val|
|Date Deposited:||10. Sep 2010 17:27|
|Last Modified:||15. Feb 2013 15:43|
Anderson, G. and Y. Ge (2005). “The size distribution of Chinese cities,” Regional Science and Urban Economics 35, 756-776.
Bates, D. M. and D. G. Watts (1988). “Nonlinear regression analysis and its applications,” New York: Wiley.
Black, D. and J. V. Henderson (2003). “Urban evolution in the USA,” Journal of Economic Geography 3, 343-372.
Bosker, M., S. Brakman, H. Garretsen and M. Schramm (2008). “A century of shocks: the evolution of the German city size distribution 1925-1999,” Regional Science and Urban Economics 38, 330-347.
Cameron, T. A. (1990). “One-stage structural models to explain city size,” Journal of Urban Economics, 27(3): 294-207.
Cheshire, P. (1999). “Trends in sizes and structure of urban areas,” in Handbook of Regional and Urban Economics, Vol. 3, P. Cheshire and E. S. Mills, (eds.) Amsterdam: Elsevier Science, Chapter 35, 1339-1373.
Cheshire, P. C. and S. Magrini (2006). “Population growth in European cities: weather matters-but only nationally,” Regional Studies 40(1), 23-37.
Choulakian, V. and M. A. Stephens (2001). “Goodness-of-fit tests for the generalized Pareto distribution,” Technometrics 43, 478-484.
Eeckhout, J. (2004). “Gibrat’s Law for (all) cities,” American Economic Review 94(5), 1429-1451.
Eeckhout, J. (2009). “Gibrat’s Law for (all) cities: reply,” American Economic Review 99(4), 1676-1683.
Gabaix, X. (1999). “Zipf’s law for cities: An explanation,” Quarterly Journal of Economics, 114(3):739-767.
Gabaix, X. and Y. M. Ioannides (2004). “The evolution of city size distributions,” in Handbook of urban and regional economics, Vol. 4, J. V. Henderson and J. F. Thisse, (eds.) Amsterdam: Elsevier Science, North-Holland.
Garmestani, A. S., C. R. Allen and C. M. Gallagher (2008). “Power laws, discontinuities and regional city size distributions,” Journal of Economic Behavior & Organization, 68: 209–216.
Garmestani, A. S., C. R. Allen, C. M. Gallagher and J. D. Mittelstaedt (2007). “Departures from Gibrat's law, discontinuities and city size distributions,” Urban Studies, 44(10): 1997–2007.
Gibrat, R. (1931). “Les inégalités économiques,” Paris: Librairie du recueil Sirey.
Giesen, K., A. Zimmermann and J. Suedekum (2010). “The size distribution across all cities – double Pareto lognormal strikes,” Journal of Urban Economics, 68: 129-137.
González-Val, R. (2010a). “Deviations from Zipf’s law for American cities: an empirical examination,” Urban Studies, forthcoming. DOI: 10.1177/0042098010371394
González-Val, R. (2010b). “The evolution of US city size distribution from a long term perspective (1900-2000),” Journal of Regional Science, forthcoming. DOI 10.1111/j.1467-9787.2010.00685.x
González-Val, R., L. Lanaspa and F. Sanz (2010). “Gibrat’s Law for cities revisited,” Mimeo, Universidad de Zaragoza.
Grimshaw, S. D. (1993). “Computing maximum likelihood estimates for the generalized Pareto distribution,” Technometrics 35, 185-191.
Hosking, J. R. M. and J. R. Wallis (1987). “Parameter and quantile estimation for the generalized Pareto distribution,” Technometrics 29, 339-349.
Hsing, Y. (1990). “A note on functional forms and the urban size distribution,” Journal of Urban Economics, 27(1): 73-79.
Ioannides, Y. M. and H. G. Overman (2003). “Zipf’s law for cities: an empirical examination,” Regional Science and Urban Economics 33, 127-137.
Ioannides, Y. M. and S. Skouras (2009). “Gibrat’s Law for (all) cities: a rejoinder,” Economics Department Working Paper, Tufts University.
Kalecki, M. (1945). “On the Gibrat distribution,” Econometrica 13(2), 161-170.
Kamecke, U. (1990). “Testing the rank size rule hypothesis with an efficient estimator,” Journal of Urban Economics, 27(2): 222-231.
Krugman, P. R. (1996a). “Confronting the mystery of urban hierarchy,” Journal of the Japanese and the International Economies 10, 399-418.
Krugman, P. R. (1996b). “The self-organizing economy,” Oxford: Blackwell.
Levy, M. (2009). “Gibrat’s Law for (all) cities: a comment,” American Economic Review 99(4), 1672-1675.
Malacarne, L. C., R. S. Mendes and E. K. Lenzi (2001). “ -exponential distribution in urban agglomeration,” Physical Review E 65, (017106) 1-3.
Michaels, G., F. Rauch and S. J. Redding (2010). “Urbanization and Structural Transformation,” unpublished manuscript, London School of Economics.
Reed, W. (2002). “On the rank-size distribution for human settlements,” Journal of Regional Science 42, 1-17.
Rosen, K. and M. Resnick (1980). “The size distribution of cities: an examination of the Pareto law and primacy,” Journal of Urban Economics 8, 165-186.
Rozenfeld, H. D., D. Rybski, J. S. Andrade, Jr., M. Batty, H. E. Stanley and H. A. Maksea (2008). “Laws of population growth,” Proceedings of the National Academy of Sciences, 105(48): 18702–18707.
Sharma, S. (2003). “Persistence and stability in city growth,” Journal of Urban Economics 53, 300-320.
Soo, K. T. (2005). “Zipf’s Law for cities: a cross-country investigation,” Regional Science and Urban Economics 35, 239-263.
Soo, K. T. (2007). “Zipf's Law and urban growth in Malaysia,” Urban Studies 44(1), 1-14.
Tsallis, C. (1988). “Possible generalization of Boltzmann-Gibbs statistics,” Journal of Statistical Physics 52, 479-487.
Zipf, G. K. (1949). “Human Behaviour and the Principle of Least Effort,” Cambridge, MA:Addison-Wesley.
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On the best functions to describe city size distributions. (deposited 07. Apr 2010 17:36)
- Size Distributions for All Cities: Lognormal and q-exponential functions. (deposited 10. Sep 2010 17:27) [Currently Displayed]