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Class size and sorting in market equilibrium: Theory and evidence

  • Miguel Urquiola

    ()

    (Columbia University - Department of Economics)

  • Eric A. Verhoogen

    ()

    (Columbia University)

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 Columbia University, Department of Economics in its series Discussion Papers with number 0607-14.

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Length: 28 pages
Date of creation: 2007
Date of revision:
Handle: RePEc:clu:wpaper:0607-14
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  1. 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.
  2. Banerjee, Abhijit & Cole, Shawn & Duflo, Esther & Linden, Leigh, 2006. "Remedying Education: Evidence from Two Randomized Experiments in India," CEPR Discussion Papers 5446, C.E.P.R. Discussion Papers.
  3. 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.
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  5. Simon P. Anderson & André de Palma, 2000. "Product Diversity in Asymmetric Oligopoly: Is the Quality of Consumer Goods too Low?," Virginia Economics Online Papers 349, University of Virginia, Department of Economics.
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  8. Alan Krueger, 2000. "Economic Considerations and Class Size," Working Papers 826, Princeton University, Department of Economics, Industrial Relations Section..
  9. 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.
  10. 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.
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  12. Lee, David S. & Card, David, 2008. "Regression discontinuity inference with specification error," Journal of Econometrics, Elsevier, vol. 142(2), pages 655-674, February.
  13. Epple, Dennis & Figlio, David & Romano, Richard, 2004. "Competition between private and public schools: testing stratification and pricing predictions," Journal of Public Economics, Elsevier, vol. 88(7-8), pages 1215-1245, July.
  14. Shaked, Avner & Sutton, John, 1982. "Relaxing Price Competition through Product Differentiation," Review of Economic Studies, Wiley Blackwell, vol. 49(1), pages 3-13, January.
  15. 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.
  16. 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.
  17. 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.
  18. Edward P. Lazear, 1999. "Educational Production," NBER Working Papers 7349, National Bureau of Economic Research, Inc.
  19. Eric Verhoogen, 2007. "Trade, quality upgrading and wage inequality in the Mexican manufacturing sector," Discussion Papers 0607-08, Columbia University, Department of Economics.
  20. 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.
  21. Charles T. Clotfelter, 1999. "Public School Segregation in Metropolitan Areas," Land Economics, University of Wisconsin Press, vol. 75(4), pages 487-504.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. Joseph G. Altonji & Ching-I Huang & Christopher R. Taber, 2010. "Estimating the Cream Skimming Effect of School Choice," NBER Working Papers 16579, National Bureau of Economic Research, Inc.
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  1. Class-Size Caps, Sorting, and the Regression-Discontinuity Design (AER 2009) in ReplicationWiki
  2. Economic Logic blog

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