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

  • Joshua D. Angrist
  • Victor Lavy

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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Publication status: published as Quarterly Journal of Economics (May 1999).
Handle: RePEc:nbr:nberwo:5888
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  10. 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.
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  12. David Card & Alan B. Krueger, 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.
  13. 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.
  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.
  15. 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.
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  17. Joshua D. Angrist & Guido W. Imbens, 1995. "Average Causal Response with Variable Treatment Intensity," NBER Technical Working Papers 0127, National Bureau of Economic Research, Inc.
  18. 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.
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