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A nonparametric estimation of the local Zipf exponent for all US cities

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  • Rafael González-Val

Abstract

The methodology proposed by Ioannides and Overman (2003 Regional Science and Urban Economics 33 127–137) is applied to estimate a local Zipf exponent using data for the entire 20th century of the complete distribution of cities (incorporated places) without any size restrictions in the US. First, kernel regressions are run using the Nadaraya–Watson estimator, excluding some atypical observations (5.66% of the sample). The results reject Zipf’s law from a long-term perspective, but the evidence supports Gibrat’s law. In the short term, decade by decade, the evidence in favour of Zipf’s law is stronger. Second, to consider the whole sample the LOcally WEighted Scatter plot Smoothing (LOWESS) algorithm is applied. From a long-term perspective the evidence supporting Zipf’s law increases, but the evidence supporting Gibrat’s law is weaker, as small cities exhibit higher variance than the other cities. Finally, the estimated values by decade are again closer to Zipf’s law. Keywords: Zipf’s law, Gibrat’s law, urban growth

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Bibliographic Info

Article provided by Pion Ltd, London in its journal Environment and Planning B: Planning and Design.

Volume (Year): 39 (2012)
Issue (Month): 6 (November)
Pages: 1119-1130

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Handle: RePEc:pio:envirb:v:39:y:2012:i:6:p:1119-1130

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  1. Kwok Tong Soo, 2004. "Zipfs Law for Cities: A Cross Country Investigation," CEP Discussion Papers dp0641, Centre for Economic Performance, LSE.
  2. Y Ioannides & Henry Overman, 2000. "Zipfs Law for Cities: An Empirical Examination," CEP Discussion Papers dp0484, Centre for Economic Performance, LSE.
  3. 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.
  4. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
  5. Yannis M. Ioannides & Henry G. Overman, 1999. "Cross-Sectional Evolution of the U.S. City Size Distribution," Discussion Papers Series, Department of Economics, Tufts University 9926, Department of Economics, Tufts University.
  6. Yoshihiko Nishiyama & Susumu Osada & Yasuhiro Sato, 2008. "OLS ESTIMATION AND THE "t" TEST REVISITED IN RANK-SIZE RULE REGRESSION," Journal of Regional Science, Wiley Blackwell, vol. 48(4), pages 691-716.
  7. Cheshire, Paul, 1999. "Trends in sizes and structures of urban areas," Handbook of Regional and Urban Economics, in: P. C. Cheshire & E. S. Mills (ed.), Handbook of Regional and Urban Economics, edition 1, volume 3, chapter 35, pages 1339-1373 Elsevier.
  8. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
  9. Xavier Gabaix & Rustam Ibragimov, 2007. "Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents," NBER Technical Working Papers 0342, National Bureau of Economic Research, Inc.
  10. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 41(2), pages 255-258, 09.
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Cited by:
  1. Peter G. Backus, 2012. "Gibrat’s law and legacy for non-profit organisations: a non-parametric analysis," Working Papers 2012/8, Institut d'Economia de Barcelona (IEB).

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