Did Zipf Anticipate Socio-Economic Spatial Networks?
An avalanche of empirical studies has addressed the validity of the rank-size rule (or Zipf’s law) in a multi-city context in many countries. City size in most countries seems to obey Zipf’s law, but the question under which conditions (e.g. sample size, spatial scale) this ‘law’ holds remained largely underinvestigated. Another complementary question is whether socio-economic networks in space also show a similar hierarchical pattern. Against this background, the present paper investigates – from a methodological viewpoint – the relationship between network connectivity and the rank-size rule (or Zipf’s law) in an urban-economic network constellation. After a review of the literature, we address in particular the following methodological issues: (i) the (aggregate) behavioural foundation underlying the rank-size rule/Zipf’s law in the light of spatial-economic network theories (e.g. entropy maximization, spatial interaction theory, etc.); (ii) the nature of the analytical relationship between social-spatial network analysis and the rank-size rule/Zipf’s law. We argue that the rank size rule is compatible with conventional economic foundations of spatial network models. Consequently, a spatial-economic interpretation – as well as a network connectivity interpretation – of the rank-size rule coefficient is provided. Our methodological contribution forms the foundation for the subsequent empirical analysis applied to spatial networks in a socio-economic context. The aim here is to test the sensitivity of empirical findings for changes in scale, functional forms, time periods, and network structures. Our application is concerned with an extensive spatio-temporal panel database related to the evolution of urban population in Germany. We test the relevance of the rank-size rule/Zipf’s law, and its evolution over the years, and – in parallel – the related ‘socio-economic’ connectivity in these urban networks. In particular, we will show that Zipf’s law (i.e., with the rank-size coefficient equal to 1) is only valid under particular conditions of the sample size. The paper concludes with some retrospective and prospective remarks.
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- Glaeser, E.L. & Scheinkman, J.A., 1993.
"Economic Growth in a Cross-Section of Cities,"
Harvard Institute of Economic Research Working Papers
1645, Harvard - Institute of Economic Research.
- Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
- Francesca Lotti & Enrico Santarelli & Marco Vivarelli, 2009.
"Defending Gibrat’s Law as a long-run regularity,"
Small Business Economics,
Springer, vol. 32(1), pages 31-44, January.
- Giesen, Kristian & Suedekum, Jens, 2009.
"Zipf's Law for Cities in the Regions and the Country,"
IZA Discussion Papers
3928, Institute for the Study of Labor (IZA).
- Kristian Giesen & Jens Südekum, 2011. "Zipf's law for cities in the regions and the country," Journal of Economic Geography, Oxford University Press, vol. 11(4), pages 667-686, July.
- Gan, Li & Li, Dong & Song, Shunfeng, 2006. "Is the Zipf law spurious in explaining city-size distributions?," Economics Letters, Elsevier, vol. 92(2), pages 256-262, August.
- Nijkamp, Peter, 1975. "Reflections on gravity and entropy models," Regional Science and Urban Economics, Elsevier, vol. 5(2), pages 203-225, May.
- 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.
- Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
- Nitsch, Volker, 2005.
Journal of Urban Economics,
Elsevier, vol. 57(1), pages 86-100, January.
- Valente J. Matlaba & Mark Holmes & Philip McCann & Jacques Poot, 2011.
"A Century of the Evolution of the Urban System in Brazil,"
Working Papers in Economics
11/12, University of Waikato, Department of Economics.
- Valente J. Matlaba & Mark J. Holmes & Philip McCann & Jacques Poot, 2013. "A Century Of The Evolution Of The Urban System In Brazil," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 25(3), pages 129-151, November.
- J W Weibull, 1980.
"On the Numerical Measurement of Accessibility,"
Environment and Planning A,
, vol. 12(1), pages 53-67, January.
- repec:hoo:wpaper:e-95-4 is not listed on IDEAS
- Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521857406, June.
- Aura Reggiani & Peter Nijkamp (ed.), 2006. "Spatial Dynamics, Networks and Modelling," Books, Edward Elgar Publishing, number 3887.
- Sebastien TERRA, 2009. "Zipf's Law for Cities: On a New Testing Procedure," Working Papers 200920, CERDI.
- Berliant, Marcus & Watanabe, Hiroki, 2014.
"A scale-free transportation network explains the city-size distribution,"
59448, University Library of Munich, Germany.
- Berliant, Marcus & Watanabe, Hiroki, 2011. "A scale-free transportation network explains the city-size distribution," MPRA Paper 34820, University Library of Munich, Germany.
- Berliant, Marcus & Watanabe, Hiroki, 2015. "A scale-free transportation network explains the city-size distribution," MPRA Paper 66802, University Library of Munich, Germany.
- Marcus Berliant & Hiroki Watanabe, 2012. "A Scale-Free Transportation Network Explains the City-Size Distribution," ERSA conference papers ersa12p601, European Regional Science Association.
- Fungisai Nota & Shunfeng Song, 2008.
"Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist?,"
08-005, University of Nevada, Reno, Department of Economics;University of Nevada, Reno , Department of Resource Economics.
- Fungisai Nota & Shunfeng Song, 2007. "Further Analysis of the Zipf's Law: Does the Rank-Size Rule Really Exist?," Working Papers 07-006, University of Nevada, Reno, Department of Economics;University of Nevada, Reno , Department of Resource Economics.
- 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.
- Aura Reggiani & Pietro Bucci & Giovanni Russo, 2011. "Accessibility and Impedance Forms: Empirical Applications to the German Commuting Network," International Regional Science Review, , vol. 34(2), pages 230-252, April.
- Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
- Parr, John B., 1985. "A note on the size distribution of cities over time," Journal of Urban Economics, Elsevier, vol. 18(2), pages 199-212, September.
- Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
- Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521674096, June.
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