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Class Size and Sorting in Market Equilibrium: Theory and Evidence

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Author Info
Miguel Urquiola
Eric Verhoogen

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Abstract

This paper examines how schools choose class size and how households sort in response to those choices. Focusing on the highly liberalized Chilean education market, we develop a model in which schools are heterogeneous in an underlying productivity parameter, class size is a component of school quality, households are heterogeneous in income and hence willingness to pay for school quality, and schools are subject to a class-size cap. The model offers an explanation for two distinct empirical patterns observed among private schools that accept government vouchers: (i) There is an inverted-U relationship between class size and household income in equilibrium, which will tend to bias cross-sectional estimates of the effect of class size on student performance. (ii) Some schools at the class size cap adjust prices (or enrollments) to avoid adding another classroom, which produces stacking at enrollments that are multiples of the class size cap. This generates discontinuities in the relationship between enrollment and household characteristics at those points, violating the assumptions underlying regression-discontinuity (RD) research designs. This result suggests that caution is warranted in applying the RD approach in settings in which parents have substantial school choice and schools are free to set prices and influence their enrollments.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 13303.

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Date of creation: Aug 2007
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Handle: RePEc:nbr:nberwo:13303

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Find related papers by JEL classification:
C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
I2 - Health, Education, and Welfare - - Education
L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
O1 - Economic Development, Technological Change, and Growth - - Economic Development

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References listed on IDEAS
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  1. Joshua D. Angrist & Victor Lavy, 1999. "Using Maimonides' Rule To Estimate The Effect Of Class Size On Scholastic Achievement," The Quarterly Journal of Economics, MIT Press, vol. 114(2), pages 533-575, May. [Downloadable!] (restricted)
  2. Eric A. Verhoogen, 2007. "Trade, Quality Upgrading and Wage Inequality in the Mexican Manufacturing Sector," IZA Discussion Papers 2913, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  3. Hsieh, Chang-Tai & Urquiola, Miguel, 2006. "The effects of generalized school choice on achievement and stratification: Evidence from Chile's voucher program," Journal of Public Economics, Elsevier, vol. 90(8-9), pages 1477-1503, September. [Downloadable!] (restricted)
  4. Miguel Urquiola, 2005. "Does School Choice Lead to Sorting? Evidence from Tiebout Variation," American Economic Review, American Economic Association, vol. 95(4), pages 1310-1326, September. [Downloadable!] (restricted)
  5. 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. [Downloadable!]
  6. Dennis Epple & Richard Romano & Holger Sieg, 2006. "Admission, Tuition, and Financial Aid Policies in the Market for Higher Education," Econometrica, Econometric Society, vol. 74(4), pages 885-928, 07. [Downloadable!] (restricted)
    Other versions:
  7. Anderson, Simon P & de Palma, Andre, 2001. "Product Diversity in Asymmetric Oligopoly: Is the Quality of Consumer Goods Too Low?," Journal of Industrial Economics, Blackwell Publishing, vol. 49(2), pages 113-35, June. [Downloadable!] (restricted)
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  8. M. Niaz Asadullah, 2005. "The effect of class size on student achievement: evidence from Bangladesh," Applied Economics Letters, Taylor and Francis Journals, vol. 12(4), pages 217-221, March. [Downloadable!] (restricted)
  9. Dobbelsteen, Simone & Levin, Jesse & Oosterbeek, Hessel, 2002. " The Causal Effect of Class Size on Scholastic Achievement: Distinguishing the Pure Class Size Effect from the Effect of Changes in Class Composition," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 64(1), pages 17-38, February. [Downloadable!] (restricted)
  10. Jakubowski, Maciej & Sakowski, Pawel, 2006. "Quasi-Experimental Estimates of Class Size Effect in Primary Schools in Poland," MPRA Paper 4958, University Library of Munich, Germany. [Downloadable!]
  11. Wilbert van der Klaauw, 2002. "Estimating the Effect of Financial Aid Offers on College Enrollment: A Regression-Discontinuity Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1249-1287, November. [Downloadable!] (restricted)
  12. Edward P. Lazear, 2001. "Educational Production," The Quarterly Journal of Economics, MIT Press, vol. 116(3), pages 777-803, August. [Downloadable!] (restricted)
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  13. Dennis Epple & David Figlio & Richard Romano, 2000. "Competition Between Private and Public Schools: Testing Stratification and Pricing Predictions," NBER Working Papers 7956, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  14. Jesse Rothstein, 2004. "Good Principals or Good Peers? Parental Valuation of School Characteristics, Tiebout Equilibrium, and the Effects of Inter-district Competition," NBER Working Papers 10666, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  15. Patrick Bayer & Robert McMillan & Kim Rueben, 2004. "An Equilibrium Model of Sorting in an Urban Housing Market," NBER Working Papers 10865, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  16. Thomas J. Nechyba, 2003. "Centralization, Fiscal Federalism, and Private School Attendance," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(1), pages 179-204, February. [Downloadable!] (restricted)
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  17. Epple, Dennis & Romano, Richard E, 1998. "Competition between Private and Public Schools, Vouchers, and Peer-Group Effects," American Economic Review, American Economic Association, vol. 88(1), pages 33-62, March. [Downloadable!] (restricted)
  18. Clotfelter, Charles T., 1998. "Public School Segregation in Metropolitan Areas," Working Papers 98-12, Duke University, Department of Economics.
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  19. Guido Imbens & Thomas Lemieux, 2007. "Regression Discontinuity Designs: A Guide to Practice," NBER Technical Working Papers 0337, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  20. Eric Verhoogen, 2007. "Trade, quality upgrading and wage inequality in the Mexican manufacturing sector," Discussion Papers 0607-08, Columbia University, Department of Economics. [Downloadable!]
  21. Shaked, Avner & Sutton, John, 1982. "Relaxing Price Competition through Product Differentiation," Review of Economic Studies, Blackwell Publishing, vol. 49(1), pages 3-13, January. [Downloadable!] (restricted)
  22. Alan B. Krueger, 2003. "Economic Considerations and Class Size," Economic Journal, Royal Economic Society, vol. 113(485), pages F34-F63, February. [Downloadable!] (restricted)
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  23. Kremer, Michael R, 1995. "Research on Schooling: What We Know and What We Don't: A Comment," World Bank Research Observer, Oxford University Press, vol. 10(2), pages 247-54, August.
  24. Caroline M. Hoxby, 2000. "The Effects Of Class Size On Student Achievement: New Evidence From Population Variation," The Quarterly Journal of Economics, MIT Press, vol. 115(4), pages 1239-1285, November. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Alejandra Mizala & Miguel Urquiola, 2007. "School Markets: The Impact of Information Approximating Schools' Effectiveness," NBER Working Papers 13676, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  2. Alejandra Mizala & Miguel Urquiola, 2007. "Parental choice and school markets: The impact of information approximating school effectiveness," Documentos de Trabajo 239, Centro de Economía Aplicada, Universidad de Chile. [Downloadable!]
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