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Equilibrium sorting of heterogeneous consumers across locations: theory and empirical implications

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  • Lars Nesheim

    () (Institute for Fiscal Studies and cemmap and UCL)

Abstract

This paper develops a model in which a continuum of consumers choose froma continuum of locations indexed by school quality. It computes equilibria that are sustained by a 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. The paper also develops a set of computational algorithms that solve several complex numerical problems. These problems include the calculation of a number of diffcult integrals, the calculation of asymptotic approximations to those integrals, the solution of an implicitly defined differential equation that depends on the integrals previously calculated, and the maximization of a likelihood function that depends on the solution of the differential equation. Finally, this paper 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 produce biased and inconsistent estimates 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 suffcient for identification.

Suggested Citation

  • Lars Nesheim, 2002. "Equilibrium sorting of heterogeneous consumers across locations: theory and empirical implications," CeMMAP working papers CWP08/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:08/02
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    File URL: http://cemmap.ifs.org.uk/wps/cwp0208.pdf
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    References listed on IDEAS

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    1. Dennis Epple & Thomas Romer & Holger Sieg, 1999. "The Tiebout Hypothesis and Majority Rule: An Empirical Analysis," NBER Working Papers 6977, National Bureau of Economic Research, Inc.
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    3. Card, David & Krueger, Alan B, 1992. "Does School Quality Matter? Returns to Education and the Characteristics of Public Schools in the United States," Journal of Political Economy, University of Chicago Press, vol. 100(1), pages 1-40, February.
    4. 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.
    5. 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.
    6. Eric A. Hanushek, 1996. "Measuring Investment in Education," Journal of Economic Perspectives, American Economic Association, vol. 10(4), pages 9-30, Fall.
    7. 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..
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    9. 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 231-250, May.
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    Cited by:

    1. Miguel Urquiola & Eric Verhoogen, 2009. "Class-Size Caps, Sorting, and the Regression-Discontinuity Design," American Economic Review, American Economic Association, vol. 99(1), pages 179-215, March.
    2. Philip Kostov & Myles Patton & Seamus McErlean, 2008. "Nonparametric analysis of the influence of buyers' characteristics and personal relationships on agricultural land prices," Agribusiness, John Wiley & Sons, Ltd., vol. 24(2), pages 161-176.
    3. Brock, William A. & Durlauf, Steven N., 2007. "Identification of binary choice models with social interactions," Journal of Econometrics, Elsevier, vol. 140(1), pages 52-75, September.
    4. Steven N. Durlauf & Yannis M. Ioannides, 2010. "Social Interactions," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 451-478, September.
    5. Pedro Carneiro & Jishnu Das & Hugo Reis, 2016. "The value of private schools: evidence from Pakistan," CeMMAP working papers CWP22/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. O'Donoghue, Cathal & Lopez, Jeremey & O’Neill, Stephen & Ryan, Mary, 2015. "AHedonic Price Model of Self-Assessed Agricultural Land Values," 150th Seminar, October 22-23, 2015, Edinburgh, Scotland 212639, European Association of Agricultural Economists.
    7. Yannis M. Ioannides, 2010. "Neighborhood Effects and Housing," Discussion Papers Series, Department of Economics, Tufts University 0747, Department of Economics, Tufts University.
    8. 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, Springer;European Association of Environmental and Resource Economists, vol. 37(1), pages 211-232, May.
    9. 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.
    10. Binner, Amy & Day, Brett, 2015. "Exploring mortgage interest deduction reforms: An equilibrium sorting model with endogenous tenure choice," Journal of Public Economics, Elsevier, vol. 122(C), pages 40-54.

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