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Equilibrium Sorting of Heterogeneous Consumers Across Locations

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  • Lars Nesheim

Abstract

This paper develops a model in which a continuum of consumers choose from a continuum of locations indexed by school quality. It computes equilibria that are sustained by an equilibrium price function that matches consumers to different locations based on their willingness to pay for school quality. In equilibrium each location is inhabited by a set of people with varying levels of education, ability, intensity of preference for education, and income. The distributions of characteristics within each location are determined by the structural elements of the model. This paper also demonstrates how the equilibrium implications of a structural economic matching model can be used to solve two important econometric identification problems. First, it is likely that regressions that seek to estimate the effects of school quality on educational outcomes are biased because people choose where their children go to school. The model in the paper solves this problem by using a consumer location choice equation and an equilibrium pricing relation to create a valid instrument for the school quality variable. Second, hedonic estimation problems in a single market are unidentified because the marginal price function is unknown or collinear with the level of the product demanded. This paper solves this problem by exploiting the restrictions that equilibrium in the sorting economy imposes on the equilibrium price function. The equilibrium price equation introduces a non-linearity into the system that is sufficient for identification

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 337.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:337

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Keywords: school quality; location choice; sorting; peer effects;

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References

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  1. Eric A. Hanushek, 1996. "Measuring Investment in Education," Journal of Economic Perspectives, American Economic Association, vol. 10(4), pages 9-30, Fall.
  2. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2004. "Identification and Estimation of Hedonic Models," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages S60-S109, February.
  3. Epple, Dennis, 1987. "Hedonic Prices and Implicit Markets: Estimating Demand and Supply Functions for Differentiated Products," Journal of Political Economy, University of Chicago Press, vol. 95(1), pages 59-80, February.
  4. David Card & Alan Krueger, 1990. "Does School Quality Matter? Returns to Education and the Characteristics of Public Schools in the United States," Working Papers 645, Princeton University, Department of Economics, Industrial Relations Section..
  5. Robert Haveman & Barbara Wolfe, 1995. "The Determinants of Children's Attainments: A Review of Methods and Findings," Journal of Economic Literature, American Economic Association, vol. 33(4), pages 1829-1878, December.
  6. Epple, Dennis & Platt, Glenn J., 1998. "Equilibrium and Local Redistribution in an Urban Economy when Households Differ in both Preferences and Incomes," Journal of Urban Economics, Elsevier, vol. 43(1), pages 23-51, January.
  7. Brown, James N & Rosen, Harvey S, 1982. "On the Estimation of Structural Hedonic Price Models," Econometrica, Econometric Society, vol. 50(3), pages 765-68, May.
  8. Betts, Julian R, 1995. "Does School Quality Matter? Evidence from the National Longitudinal Survey of Youth," The Review of Economics and Statistics, MIT Press, vol. 77(2), pages 231-50, May.
  9. Kahn, Shulamit & Lang, Kevin, 1988. "Efficient Estimation of Structural Hedonic Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 157-66, February.
  10. 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.
  11. Rosen, Sherwin, 1974. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 34-55, Jan.-Feb..
  12. Bartik, Timothy J, 1987. "Estimating Hedonic Demand Parameters with Single Market Data: The Problems Caused by Unobserved Tastes," The Review of Economics and Statistics, MIT Press, vol. 69(1), pages 178-80, February.
  13. Teulings, Coen N, 1995. "The Wage Distribution in a Model of the Assignment of Skills to Jobs," Journal of Political Economy, University of Chicago Press, vol. 103(2), pages 280-315, April.
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Citations

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Cited by:
  1. Yannis M. Ioannides, 2010. "Neighborhood Effects and Housing," Discussion Papers Series, Department of Economics, Tufts University 0747, Department of Economics, Tufts University.
  2. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2003. "Identification and Estimation of Hedonic Models," CESifo Working Paper Series 1031, CESifo Group Munich.
  3. James J. Heckman & Rosa Matzkin & Lars Nesheim, 2003. "Simulation and Estimation of Nonaddative Hedonic Models," NBER Working Papers 9895, National Bureau of Economic Research, Inc.
  4. Yannis M. Ioannides, 2008. "Full Solution of an Endogenous Sorting Model with Contextual and Income Effects," Discussion Papers Series, Department of Economics, Tufts University 0724, Department of Economics, Tufts University.
  5. Patrick Bayer & Fernando Ferreira & Robert McMillan, 2003. "A Unified Framework for Estimating Preferences for Schools and Neighborhoods," Working Papers 872, Economic Growth Center, Yale University.
  6. Blume,L.E. & Durlauf,S.N., 2005. "Identifying social interactions : a review," Working papers 12, Wisconsin Madison - Social Systems.
  7. Rosa L. Matzkin & James Heckman & Lars Nesheim, 2002. "Nonparametric Estimation and Nonadditive Hedonic Models," Working Papers 51, Universidad de San Andres, Departamento de Economia, revised Jun 2002.
  8. Patrick Bayer & Fernando Ferreira & Robert McMillan, 2007. "A Unified Framework for Measuring Preferences for Schools and Neighborhoods," Working Papers 07-27, Center for Economic Studies, U.S. Census Bureau.
  9. Helen Tauchen & Ann Dryden Witte, 2001. "Estimating Hedonic Models: Implications of the Theory," NBER Technical Working Papers 0271, National Bureau of Economic Research, Inc.
  10. James J. Heckman, 2003. "Simulation and Estimation of Hedonic Models," CESifo Working Paper Series 1014, CESifo Group Munich.
  11. Brett Day & Ian Bateman & Iain Lake, 2007. "Beyond implicit prices: recovering theoretically consistent and transferable values for noise avoidance from a hedonic property price model," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 37(1), pages 211-232, May.
  12. Steve Gibbons, 2002. "Neighbourhood Effects on Educational Achievement," CEE Discussion Papers 0018, Centre for the Economics of Education, LSE.
  13. Brock,W.A. & Durlauf,S.N., 2005. "Social interactions and macroeconomics," Working papers 5, Wisconsin Madison - Social Systems.
  14. Rebecca Allen & Simon Burgess & Tomas Key, 2010. "Choosing secondary school by moving house: school quality and the formation of neighbourhoods," The Centre for Market and Public Organisation 10/238, Department of Economics, University of Bristol, UK.

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