Berliant, Marcus and Watanabe, Hiroki (2007): Explaining the size distribution of cities: X-treme economies.
Download (226kB) | Preview
The methodology used by theories to explain the size distribution of cities is contrived in that it takes an empirical fact and works backward to first obtain a reduced form of a model, then pushes this reduced form back to assumptions on primitives. The induced assumptions on consumer behavior, particularly about their ability 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. Equilibrium implies a uniform distribution of agents. Even without these frictions, our analysis yields another equilibrium with insurance that gives exactly the same utility level to consumers as the equilibrium studied in the literature, but where consumers never move. Thus, insurance is a substitute for movement. Even aggregate shocks are insufficent to generate consumer movement, since consumers can borrow and save. We propose an alternative class of models, involving extreme risk against which consumers will not insure. Instead, they will move.
|Item Type:||MPRA Paper|
|Institution:||Washington University in St. Louis|
|Original Title:||Explaining the size distribution of cities: X-treme economies|
|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|
|Depositing User:||Marcus Berliant|
|Date Deposited:||25. Oct 2007|
|Last Modified:||18. Feb 2013 06:51|
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. Eeckhout, J., 2004. "Gibrat's Law for (All) Cities." American Economic Review 94(5), 1429-1451. 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., and T. Mori, 1997. "Structural Stability and Evolution of Urban Systems." Regional Science and Urban Economics 27, 399--442. Gabaix, Xavier, 1999a. "Zipf's Law for Cities: An Explanation." Quarterly Journal of Economics 114(3), 739-767. Gabaix, Xavier, 1999b. "Zipf's Law and the Growth of Cities." American Economic Review Papers and Proceedings 89(2), 129-132. 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. Janowicz, J.R.; Gray, D.M. and Pomeroy, J.W., 2003. "Spatial Variability of Fall Soil Moisture and Spring Snow Water Equivalent Within a Mountainous Sub-Arctic Watershed." 60th Eastern Snow Conference, Sherbrooke, Québec, Canada. Limpert, Eckhard; Staehl, Werner A. and Abbt, Markus, 2001. "Log-normal Distributions across the Sciences: Keys and Clues." Bioscience 51(5), 341-352. Meneghini, R.; Jones, J.A.; Iguchi, T.; Okamoto, K.; and Kwiatkowski, J., 2001. "Statistical Methods of Estimating Average Rainfall over Large Space-Timescales Using Data from the TRMM Precipitation Radar." Journal of Applied Meteorology 40(3), 568-585. Rossi-Hansberg, E. and M.L.J. Wright, 2007. "Urban Structure and Growth." The Review of Economic Studies 74(2), 597-624.