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|
|Contact details of provider:|| Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE|
Phone: (+44) 020 7291 4800
Fax: (+44) 020 7323 4780
Web page: http://cemmap.ifs.org.uk
More information through EDIRC
|Order Information:|| Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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 157-166, February.
- 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..
- 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.
- David Card & Alan B. 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..
- Brown, James N & Rosen, Harvey S, 1982. "On the Estimation of Structural Hedonic Price Models," Econometrica, Econometric Society, vol. 50(3), pages 765-768, 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.
- 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.
- 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.
- 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.
- Eric A. Hanushek, 1996. "Measuring Investment in Education," Journal of Economic Perspectives, American Economic Association, vol. 10(4), pages 9-30, Fall.
- 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 178-180, February. Full references (including those not matched with items on IDEAS)