Gibrat’s law, Zipf’s law and Cointegration

Lalanne, Aurélie and Zumpe, Martin (2015): Gibrat’s law, Zipf’s law and Cointegration.

Abstract

This paper examines the methods to detect the nature of the urban growth processes. It seems that cointegration testing enables to disentangle two versions of Gibrat’s law: a first one with growth shocks that are iid across time and cities (implying convergence of the city-size distribution towards Zipf’s law), and an alternative one with growth shocks that are only iid over time (implying conservation of the initial structure of the city size distribution).

• Item Type: MPRA Paper
• Language: English
• Keywords: Zipf’s law, Gibrat’s law, Cointegration tests, unit root tests, urban growth, urban system
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C41 - Duration Analysis ; Optimal Timing Strategies; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O40 - General; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R0 - General > R00 - General; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R11 - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes

References

Chen Z., Fu S., and Zhang D., 2013, Searching for the parallel growth of cities in China. Urban Studies 50, 2118-2135

Clark, S., & Stabler, J., 1991. Gibrat's law and the growth of Canadian cities. Urban Studies 28, 635-639

Eeckhout, J., 2004. Gibrat's law for (all) cities. The American Economic Review 94, 1429-1451

Gabaix, X., 1999. Zipf's law for cities: an explanation. The Quaterly Journal of Economics 114, 739-767

Giesen, K., & Südekum, J., 2011. Zipf's law for cities in the regions and the country. Journal of Economic Geography 11, 667-686.

Gonzáles-Val, R., Lanaspa, L., & Sanz-Gracia, F., 2013. Gibrat's law for cities, growth regressions and sample size. Economics Letters 118, 367-369

Krugman, P. , 1996, Confronting the mystery of urban hierarchy. Journal of the Japanese and the International Economies 10, 399-418.

Kwiatkowski, D., Phillips, P., Schmidt, P. and Shin, Y., 1992. Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? Journal of Econometrics 54, 159-178.

Levin, A., Lin, C. F., and Chu, C. J., 2002, Unit root tests in panel data: asymptotic and finite properties. Journal of Econometrics 108, 1-24.

Im, K., Pesaran, M., and Shin, Y., 2003, Testing for unit roots in heterogeneous panels. Journal of Econometrics 115, 53-74.

Sharma, S., 2003. Persistence and stability in city growth. Journal of Urban Economics 53, 300-320.