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Using Maimonides' Rule to Estimate the Effect of Class Size on Student Achievement

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Joshua D. Angrist
Victor Lavy

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Abstract

The effect of class size on student achievement has long been of concern to educators, parents, and scholars. In Israeli public schools today, class size is partly determined using a rule proposed by Maimonides in the 12th century. This rule induces a nonlinear and non-monotonic relationship between enroll- ment size and class size. We use this relationship to construct instrumental variables estimates of the effect of class size on the test scores of Israeli 4th and 5th graders in 1991 and 3rd graders in 1992. Because the up-and-down pattern in class size induced by Maimonides' rule matches a similar pattern in test scores, the rule provides a credible source of exogenous variation for investigation of the causal effect of class size on student achievement. Our use of Maimonides' rule can be viewed as an application of Campbell's (1969) regression-discontinuity design to the class size question. The results of this application show that reductions in class size induce a significant increase in reading and math scores for 5th graders and a smaller increase in reading scores for 4th graders. In contrast, there is little evidence of any association between class size and the test scores of 3rd graders, although this finding may result from problems with the 1992 wave of the testing program. The estimates also suggest that the gains from small classes are largest for students from disadvantaged backgrounds. Besides being of metho- dological interest and providing new evidence on the class size question, these findings are of immediate policy interest in Israel where legislation to reduce the maximum class size is pending.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 5888.

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Date of creation: Jan 1997
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Handle: RePEc:nbr:nberwo:5888

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Find related papers by JEL classification:
I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity

References listed on IDEAS
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  1. Card, David & Krueger Alan B, 1996. "School Resources and Student Outcomes: An Overview of the Literature and New Evidence from North and South Carolina," Journal of Economic Perspectives, American Economic Association, vol. 10(4), pages 31-50, Fall. [Downloadable!] (restricted)
    Other versions:
  2. Hanushek, Eric A., 2006. "School Resources," Handbook of the Economics of Education, Elsevier. [Downloadable!] (restricted)
  3. Michael Boozer & Cecilia Rouse, 1995. "Intraschool Variation in Class Size: Patterns and Implications," Working Papers 723, Princeton University, Department of Economics, Industrial Relations Section.. [Downloadable!]
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  6. Hanushek, Eric A, 1995. "Interpreting Recent Research on Schooling in Developing Countries," World Bank Research Observer, Oxford University Press, vol. 10(2), pages 227-46, August.
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  7. Card, David & Krueger, Alan B, 1992. "School Quality and Black-White Relative Earnings: A Direct Assessment," The Quarterly Journal of Economics, MIT Press, vol. 107(1), pages 151-200, February. [Downloadable!] (restricted)
    Other versions:
  8. 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. [Downloadable!] (restricted)
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  9. Caroline M. Hoxby, 1998. "The Effects of Class Size and Composition on Student Achievement: New Evidence from Natural Population Variation," NBER Working Papers 6869, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  10. James Heckman & Anne Layne-Farrar & Petra Todd, 1995. "Does Measured School Quality Really Matter? An Examination of the Earnings-Quality Relationship," NBER Working Papers 5274, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  14. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August. [Downloadable!] (restricted)
  15. Akerhielm, Karen, 1995. "Does class size matter?," Economics of Education Review, Elsevier, vol. 14(3), pages 229-241, September. [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. Susan Chen & Wilbert van der Klaauw, 2006. "The Work Disincentive Effects of the Disability Insurance Program in the 1990s," Working Papers 06-05, Center for Economic Studies, U.S. Census Bureau. [Downloadable!]
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  2. Joshua D. Angrist & Kevin Lang, 2004. "Does School Integration Generate Peer Effects? Evidence from Boston's Metco Program," American Economic Review, American Economic Association, vol. 94(5), pages 1613-1634, December. [Downloadable!]
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  3. Do, Quy-Toan & Phung, Tung Duc, 2006. "Superstition, family planning, and human development," Policy Research Working Paper Series 4001, The World Bank. [Downloadable!]
  4. Thomas Dee & Martin West, 2008. "The Non-Cognitive Returns to Class Size," NBER Working Papers 13994, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. Joshua Angrist & Victor Lavy, 1999. "New Evidence on Classroom Computers and Pupil Learning," NBER Working Papers 7424, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  6. Michael Fertig, 2004. "What Can We Learn From International Student Performance Studies? Some Methodological Remarks," RWI Discussion Papers 0023, Rheinisch-Westfälisches Institut für Wirtschaftsforschung. [Downloadable!]
  7. Joshua D. Angrist & Kevin Lang, 2002. "How Important are Classroom Peer Effects? Evidence from Boston's Metco Program," Staff Working Papers 02-85, W.E. Upjohn Institute for Employment Research. [Downloadable!] (restricted)
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  8. Weili Ding & Steven F. Lehrer, 2006. "Do Peers Affect Student Achievement in China's Secondary Schools?," NBER Working Papers 12305, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  9. Das, Jishnu & Dercon, Stefan & Habyarimana, James & Krishnan, Pramila, 2004. "When can school inputs improve test scores?," Policy Research Working Paper Series 3217, The World Bank. [Downloadable!]
    Other versions:
  10. Jeff Borland & Yi-Ping Tseng & Roger Wilkins, 2005. "Experimental and Quasi-Experimental Methods of Microeconomic Program and Policy Evaluation," Melbourne Institute Working Paper Series wp2005n08, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne. [Downloadable!]
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