Equilibrium sorting of heterogeneous consumers across locations: theory and empirical implications
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.
|Date of creation:||01 Mar 2002|
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- 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.
- David Card & Alan Krueger, 1990. "Does School Quality Matter? Returns to Education and the Characteristics of Public Schools in the United States," NBER Working Papers 3358, National Bureau of Economic Research, Inc.
- Brown, James N & Rosen, Harvey S, 1982.
"On the Estimation of Structural Hedonic Price Models,"
Econometric Society, vol. 50(3), pages 765-68, May.
- James N. Brown & Harvey S. Rosen, 1982. "On the Estimation of Structural Hedonic Price Models," NBER Technical Working Papers 0018, National Bureau of Economic Research, Inc.
- Eric A. Hanushek, 1996. "Measuring Investment in Education," Journal of Economic Perspectives, American Economic Association, vol. 10(4), pages 9-30, Fall.
- 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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- 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..
- 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.
- 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.
- 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.
- 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.
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