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A Note on the Equilibrium Properties of Locational Sorting Models

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  • Patrick Bayer

    ()
    (Economic Growth Center, Yale University)

  • Christopher Timmins

Abstract

A central feature of many models of location choice -- whether of firms or households, within or across cities -- is the role of local interactions or spillovers, whereby the payoffs from choosing a location depend in part on the number or attributes of other individuals or firms that choose the same or nearby locations in equilibrium. The main goal of this paper is to develop the equilibrium properties of a broadly applicable and readily estimable class of sorting models that allow the location decision to depend on both fixed local attributes (including unobserved attributes) and such local interactions. In particular, we prove uniqueness in the case of congestion effects and use a series of simulations to demonstrate that a unique equilibrium is more likely to obtain (i) the smaller are any agglomeration effects, (ii) the larger are the set of choices available to the agents, (iii) the more "meaningful variation" there is in those choices, and (iv) the more heterogeneous are the agents themselves. This is encouraging for the use of our model to describe the sorting of individuals and firms over geographic space, where the number of choices is usually large and variation in exogenous fixed attributes can be important. Moreover, these results conveniently coincide with the conditions required for econometric identification of our model.

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Bibliographic Info

Paper provided by Economic Growth Center, Yale University in its series Working Papers with number 861.

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Length: 20 pages
Date of creation: Jul 2003
Date of revision:
Handle: RePEc:egc:wpaper:861

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Keywords: Local Spillovers; Social Interactions; Economic Geography; Natural Advantage; Endogenous Sorting; Discrete Choice Models; Agglomeration; Congestion; Random Utility;

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  1. Brock,W.A. & Durlauf,S.N., 2000. "Discrete choice with social interactions," Working papers 7, Wisconsin Madison - Social Systems.
  2. Patrick Bayer & Robert McMillan & Kim Rueben, 2004. "Residential Segregation in General Equilibrium," Working Papers 885, Economic Growth Center, Yale University.
  3. Glaeser, Edward L & Sacerdote, Bruce & Scheinkman, Jose A, 1996. "Crime and Social Interactions," The Quarterly Journal of Economics, MIT Press, vol. 111(2), pages 507-48, May.
  4. Bertrand, M. & Luttmer, E.F.P. & Mullainathan, S., 1998. "Network Effects and Welfare Cultures," Papers 201, Princeton, Woodrow Wilson School - Public and International Affairs.
  5. Edward L. Glaeser & Jose A. Scheinkman, 2001. "Non-Market Interactions," Harvard Institute of Economic Research Working Papers 1914, Harvard - Institute of Economic Research.
  6. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-93, May.
  7. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
  8. Patrick Bayer & Christopher Timmins, 2007. "Estimating Equilibrium Models Of Sorting Across Locations," Economic Journal, Royal Economic Society, vol. 117(518), pages 353-374, 03.
  9. Holger Sieg & V. Kerry Smith & H. Spencer Banzhaf & Randy Walsh, 2004. "Estimating The General Equilibrium Benefits Of Large Changes In Spatially Delineated Public Goods," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1047-1077, November.
  10. Michael L. Katz & Carl Shapiro, 1994. "Systems Competition and Network Effects," Journal of Economic Perspectives, American Economic Association, vol. 8(2), pages 93-115, Spring.
  11. Deichmann, Uwe & Fay, Marianne & Jun Koo & Lall, Somik V., 2002. "Economic structure, productivity, and infrastructure quality in southern Mexico," Policy Research Working Paper Series 2900, The World Bank.
  12. Vernon Henderson, 1999. "Marshall's Economies," NBER Working Papers 7358, National Bureau of Economic Research, Inc.
  13. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416.
  14. Dennis Epple & Holger Sieg, 1999. "Estimating Equilibrium Models of Local Jurisdictions," Journal of Political Economy, University of Chicago Press, vol. 107(4), pages 645-681, August.
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