Explaining the size distribution of cities: x-treme economies

Berliant, Marcus and Watanabe, Hiroki (2011): Explaining the size distribution of cities: x-treme economies.

Abstract

We criticize the theories used to explain the size distribution of cities. They take an empirical fact and work backward to obtain assumptions on primitives. The induced theoretical assumptions on consumer behavior, particularly about their inability to insure against the city-level productivity shocks in the model, are untenable. With either self insurance or insurance markets, and either an arbitrarily small cost of moving or the assumption that consumers do not perfectly observe the shocks to firms' technologies, the agents will never move. Even without these frictions, our analysis yields another equilibrium with insurance where consumers never move. Thus, insurance is a substitute for movement. We propose an alternative class of models, involving extreme risk against which consumers will not insure. Instead, they will move, generating a Fréchet distribution of city sizes that is empirically competitive with other models.

• Item Type: MPRA Paper
• Language: English
• Keywords: Zipf's Law; Gibrat's Law; Size Distribution of Cities; Extreme Value Theory
• Subjects: R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity

References

Axtell, R.L., 2001. "Zipf Distribution of U.S. Firm Sizes." Science 293, 1818-1820.

Behrens, K., Duranton, G. and F. Robert-Nicoud, 2010. "Productive Cities: Sorting, Selection, and Agglomeration." mimeo.

Berliant, M., and F.-c. Kung, 2010. "Can Information Asymmetry Cause Stratification?" Regional Science and Urban Economics 40, 196-209.

Cabrera, M.O., and A.I. Volodin, 2005. "Mean Convergence Theorems and Weak Laws of Large Numbers for Weighted Sums of Random Variables under a Condition of Weighted Integrability." Journal of Mathematical Analysis and Applications 305, 644-658.

Coles, S., 2001. An Introduction to Statistical Modelling of Extreme Values. Springer-Verlag.

Duranton, Gilles, 2006. "Some Foundations for Zipf's Law: Product Proliferation and Local Spillovers." Regional Science and Urban Economics 36(4), 542-563.

Duranton, Gilles, 2007. "Urban Evolutions: The Fast, The Slow, and the Still." American Economic Review 97(1), 197-221.

Eaton, J., and S. Kortum, 2002. "Technology, Geography, and Trade." Econometrica 70(5), 1741-1779.

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.

Embrechts, P., Kluppelberg, C. and T. Mikosch, 1997. Modelling Extremal Events. Springer-Verlag.

Fisher, R.A. and L.H.C. Tippett, 1928. "Limiting Forms of the Frequency by Distribution of the Largest or Smallest Members of a Sample." Proceedings of the Cambridge Philosophical Society, 180-190.

Fujita, M., 1986. "Urban Land Use Theory," in Location Theory. Edited by J. Lesourne and H. Sonnenschein. New York: Harwood Academic Publishers.

Fujita, M. and T. Mori, 1997. "Structural Stability and Evolution of Urban Systems." Regional Science and Urban Economics 27, 399-442.

Fujita, M. and J.-F. Thisse, 2002, Economics of Agglomeration. Cambridge: Cambridge University Press.

Gabaix, X., 1999a. "Zipf's Law for Cities: An Explanation." Quarterly Journal of Economics 114(3), 739-767.

Gabaix, X., 1999b. "Zipf's Law and the Growth of Cities." American Economic Review Papers and Proceedings 89(2), 129-132.

Gabaix, X., 2011. "The Granular Origins of Aggregate Fluctuations." Econometrica 79(3), 733-772.

Gabaix, X., Gopikrishnan, P., Plerou, V. and H. E. Stanley, 2003. "A Theory of Power Law Distributions in Financial Market Fluctuations." Nature 423, 267-70.

Gabaix, X. and Y. Ioannides, 2004. "Evolution of City Size Distributions." Chapter 53, 2341-2378, in J. Vernon Henderson and Jacques-Francois Thisse, eds., Handbook of Regional and Urban Economics IV: Cities and Geography, North-Holland, Amsterdam.

Goldstein, M.L., Morris, S.A. and G.G. Yen, 2004. "Problems with Fitting to the Power-Law Distribution." The European Physical Journal B - Condensed Matter Physics 41(2), 255-258.

Halloy, Stephan R.P., 1999. "The Dynamic Contribution of New Crops to the Agricultural Economy: Is it Predictable?" Perspectives on New Crops and New Uses, J. Janick (ed.), ASHS Press, Alexandria, VA.

Mills, E.S., 1967. "An Aggregative Model of Resource Allocation in a Metropolitan Area." American Economic Review 57(2), 197-210.

Rossi-Hansberg, E. and M.L.J. Wright, 2007. "Urban Structure and Growth." The Review of Economic Studies 74(2), 597-624.

Soo, K.T., 2005. "Zipf's Law for Cities: A Cross-Country Investigation." Regional Science and Urban Economics 35(3), 239-263.

Starrett, D., 1978. "Market Allocations of Location Choice in a Model with Free Mobility." Journal of Economic Theory 17, 21-37.