Abstract

Zipf’s law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than S is proportional to 1/S. Suppose that, at least in the upper tail, all cities follow some proportional growth process (this appears to be verified empirically). This automatically leads their distribution to converge to Zipf’s law. I.

Citations

1343	Economic Growth - Barro, Sala-i-Martin - 1995
1186	Investment under Uncertainty - Dixit, Pindyck - 1994
391	How nature works: The science of self-organized criticality - Bak - 1997
306	The Spatial Economy - Fujita, Krugman, et al. - 1999
269	Brownian Motion and Stochastic Flow Systems - Harrison - 1985
248	On a class of skew distribution functions - Simon - 1955
236	Brownian Motion and Stochastic Calculus, 2nd Edition - Karatzas, Shreve - 1991
232	Self-organized criticality: An explanation of 1/f noise - Bak, Tang, et al. - 1987
204	Gibrat’s Legacy - Sutton - 1997
175	The Quark and the Jaguar - Gell-Mann - 1994
98	The Sizes and Types of Cities - Henderson - 1974
87	Urban Development: Theory, Fact, and Illusion - Henderson - 1988
80	Economic Growth in a Cross-Section of Cities - Glaeser, Scheinkman, et al. - 1995
72	Deterministic chaos - Schuster - 1988
65	Les Inégalités économiques - Gibrat - 1931
61	A model of income distribution - Champernowne - 1953
53	Cities and Growth: Theory and Evidence from France and - Eaton, Eckstein - 1997
53	Approximate Distributions of Order Statistics - Reiss - 1989
47	Trade and Circuses: Explaining Urban Giants.” The Quarterly - Ades, Glaeser - 1995
47	Convergent multiplicative processes repelled from zero: power laws and truncated power laws - Sornette, Cont - 1997
45	The Pareto-Lévy law and the distribution of income - Mandelbrot - 1960
44	Income Inequality and the Incomes of Very High Income Taxpayers: Evidence from Tax Returns," NBER Working Papers 4229, National Bureau of Economic Research - Feenberg, Poterba - 1993
31	Finite Horizons - Blanchard, “Debt - 1985
30	The Size Distribution of Cities: An Examination of the Pareto Law and Primacy - Rosen, Resnick - 1980
26	Das Gesetz der Bevölkerungskonzentration.” Petermanns Geographische Mitteilungen - Auerbach - 1913
19	Zipf’s Law and the growth of cities - Gabaix - 1999
19	Linear stochastic dynamics with nonlinear fractal properties, Physica A 250 - Sornette - 1998
14	European Urbanization, 1500–1800 - Vries - 1984
14	Dynamical explanation for the emergence of power law in a stock market model - Levy, Solomon - 1996
13	Interacting individuals leading to Zipf’s Law - Marsili, Zhang - 1998
12	Random Difference Equations and Renewal Theory for - Kesten - 1973
10	Urban concentration, agglomeration economies and the level of economic development", Economic Development and Cultural Change 30 - Wheaton, Shishido - 1981
9	Interacting individuals leading to Zipf ’s - Marsili, Zhang - 1998
8	National city-size distributions: what do we know after 67 years of research - Carroll - 1982
8	A note on the size distribution of cities over time - Parr - 1985
6	The rank-frequency form of Zipf’s law - Hill - 1974
4	The Random Spatial Economy: An Exploration in Settlement Theory - Curry - 1964
4	The Economics of Location, translated by - Lösch - 1944
4	Urban growth, an approach - Robson - 1973
4	Income Distribution: A - Rutherford - 1955
3	East Asian urbanization in the nineteenth century: Comparisons with Europe - Rozman - 1990
3	Finite Horizons," Journal of Political Economy - Blanchard, Debt - 1985
2	Theory of the Distribution of City Sizes - Richardson - 1973
2	Types of City-Size Distribution: A Comparative Analysis - Smith - 1990
1	Scale Economies and Diseconomies in the Determination of City Size Distribution - Alperovitch - 1982
1	The Population of European Cities: 800–1850 - Bairoch, Batou, et al. - 1988
1	City Hierarchies and the Distribution of City Size - Beckman - 1958
1	Dynamic Evolution of the U - Dobkins, Ioannides - 1998
1	Spatial Interactions among U - Dobkins, Ioannides - 1998
1	Introduction to Mathematical Statistics (New - Hoel - 1974