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Class Size and Sorting in Market Equilibrium: Theory and Evidence

  • Urquiola, Miguel
  • Verhoogen, Eric A

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 C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 6425.

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Date of creation: Aug 2007
Date of revision:
Handle: RePEc:cpr:ceprdp:6425
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  1. Charles T. Clotfelter, 1998. "Public School Segregation in Metropolitan Areas," NBER Working Papers 6779, National Bureau of Economic Research, Inc.
  2. 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.
  3. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366 Elsevier.
  4. 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.
  5. Anderson, Simon P & de Palma, Andre, 2001. "Product Diversity in Asymmetric Oligopoly: Is the Quality of Consumer Goods Too Low?," Journal of Industrial Economics, Wiley Blackwell, vol. 49(2), pages 113-35, June.
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  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Charles T. Clotfelter, 1999. "Public School Segregation in Metropolitan Areas," Land Economics, University of Wisconsin Press, vol. 75(4), pages 487-504.
  13. Verhoogen, Eric A, 2007. "Trade, Quality Upgrading and Wage Inequality in the Mexican Manufacturing Sector," CEPR Discussion Papers 6385, C.E.P.R. Discussion Papers.
  14. 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.
  15. Abhijit Banerjee & Shawn Cole & Esther Duflo & Leigh Linden, 2005. "Remedying Education: Evidence from Two Randomized Experiments in India," NBER Working Papers 11904, National Bureau of Economic Research, Inc.
  16. Kremer, Michael R, 1995. "Research on Schooling: What We Know and What We Don't: A Comment," World Bank Research Observer, World Bank Group, vol. 10(2), pages 247-54, August.
  17. McCrary, Justin, 2008. "Manipulation of the running variable in the regression discontinuity design: A density test," Journal of Econometrics, Elsevier, vol. 142(2), pages 698-714, February.
  18. 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.
  19. Lee, David S. & Card, David, 2008. "Regression discontinuity inference with specification error," Journal of Econometrics, Elsevier, vol. 142(2), pages 655-674, February.
  20. 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.
  21. 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.
  22. 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.
  23. Shaked, Avner & Sutton, John, 1982. "Relaxing Price Competition through Product Differentiation," Review of Economic Studies, Wiley Blackwell, vol. 49(1), pages 3-13, January.
  24. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
  25. 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.
  26. M. Niaz Asadullah, 2005. "The effect of class size on student achievement: evidence from Bangladesh," Applied Economics Letters, Taylor & Francis Journals, vol. 12(4), pages 217-221.
  27. Maria Marta Ferreyra, 2007. "Estimating the Effects of Private School Vouchers in Multidistrict Economies," American Economic Review, American Economic Association, vol. 97(3), pages 789-817, June.
  28. Joseph G. Altonji & Ching-I Huang & Christopher R. Taber, 2015. "Estimating the Cream Skimming Effect of School Choice," Journal of Political Economy, University of Chicago Press, vol. 123(2), pages 266 - 324.
  29. 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.
  30. 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.
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  1. Class-Size Caps, Sorting, and the Regression-Discontinuity Design (AER 2009) in ReplicationWiki
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