Principal investigator: Viviane Pires Ribeiro
Paper Title: Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement
Authors: Joshua D. Angrist and Victor Lavy
Location of the Intervention: Israel
Sample Size: 62.000 students
Main theme: Education
Main Variable of Interest: School quality
Type of InterventionMaimonides' Rule
Methodology: Instrumental Variables
Understanding the relationship between class size and academic achievement has motivated several studies that, until now, have reached inconclusive results. While some authors have found results indicating that smaller classes are associated with higher academic achievement, others have refuted these results. In this context, Angrist and Lavy (1999) use Maimonides' rule of 40 students per class to construct instrumental variable estimates of the effects of class size on test scores. The estimates show that reducing class size induces a significant and substantial increase in test scores for fourth- and fifth-grade students, although not for third-grade students.
Evaluation Context
Class size is a variable at the heart of political debates concerning the quality of education and the allocation of school resources. Parents and teachers typically prefer smaller classes because they believe this type of class offers a more conducive learning environment. Furthermore, this variable is considered easily manipulated by policymakers. It is observed that despite this widespread interest in the consequences of modifying class size, the causal effects of this variable on school performance have been a difficult parameter to measure.
Although the level of educational inputs differs substantially between and within schools, these differences are often associated with factors such as students' training or socioeconomic background. Possibly for this reason, much of the research on the relationship between class size and performance is inconclusive.
Intervention Details
According to Angrist and Lavy (1999), the 12th-century rabbinical scholar Maimonides proposed a maximum class size of 40 students. This maximum suggests a non-linear and non-monotonic relationship between grade enrollment and class size in Israeli public schools. Thus, the authors emphasize that this rule has been used since 1969 to determine the division of... cohorts Regarding class enrollment in Israeli public schools, the maximum of 40 classes is known to teachers and school principals and is distributed annually through a set of decrees from the Director General of the Ministry of Education. Furthermore, this rule generates a potentially exogenous source of variation in class size that can be used to estimate the effects of class size on the academic performance of Israeli students.
In this sense, Angrist and Lavy (1999) use the class size function induced by Maimonides' rule to construct instrumental variable estimates of class size effects. Although the class size function and the instruments derived from it are themselves a function of the size of the cohorts Regarding registration, these functions are non-linear and non-monotonic. Therefore, a wide range of smooth registration effects can be controlled when using the rule as a tool.
Furthermore, the authors emphasize that Maimonides' rule is not the only source of variation in Israeli class sizes, and the average class size is generally smaller than would be predicted by a strict application of that rule. But Israeli classes are large by United States standards, and the 40-student-per-class cap is a real limitation faced by many school principals.
Methodology Details
Maimonides' rule of 40 is used by Angrist and Lavy (1999) to construct instrumental variable estimates of the effects of class size on test scores. The resulting identification strategy can be seen, according to the authors, as an application of Donald Campbell's regression discontinuity design to the issue of class size.
The average class size in the study data is 31 students, with 25% of classes having more than 35 students and 10% having more than 38 students. A regression of the actual mid-year class size against the predicted class size using enrollment data from the beginning of the year and Maimonides' rule explains about half of the variation in class size in each grade (in a population of about 2.000 classes per grade).
The test score data used comes from a short-term national testing program in Israeli primary schools. In June 1991, near the end of the school year, all fourth- and fifth-grade students received achievement tests designed to measure reading and math skills. The scores used in the Angrist and Lavy (1999) study consist of a composite constructed from some of the basic questions and all of the more advanced questions on the test, divided by the number of questions in the composite score, so that the score was scaled from 1 to 100.
As part of the same program, similar tests were administered to third-grade students in June 1992. The achievement tests generated considerable public controversy due to lower-than-expected scores, especially in 1991, and due to the large regional differences in results. After 1992, the national testing program was abandoned.
Results
Angrist and Lavy (1999) present a variety of Ordinary Least Squares (OLS) and instrumental variable estimates of the effect of class size on reading and math scores of elementary school children in Israel. Instrumental variable estimates constructed using Maimonides' rule functions as instruments for class size, while controlling for enrollment and student history, consistently show a negative association between larger classes and student performance.
It is observed that these effects are larger for the math and reading scores of fifth-grade students, with smaller effects for the reading scores of fourth-grade students. The results for the math scores of fourth-grade students are not significant, although the pooled estimates for fourth- and fifth-grade students are significant and precise in both tests.
Lessons in Public Policy
Angrist and Lavy (1999) emphasize that even though the effects reported in the study are mostly smaller than those reported in the Tennessee STAR experiment, they may represent important gains in relation to the distribution of Israeli test results. The authors comment that the Israeli Parliament has initiated a debate on a bill that would reduce the maximum legal class size to 30 students. Thus, using the class size distributions of cohortThey estimated that the new law would reduce the average class size in elementary school from 31 to about 25 and reduce the top quartile from 35 to 27. These reductions would clearly be costly to implement, requiring something like 600 additional classes per grade. But the results reported in the study imply that the resulting change to Maimonides' rule could have an impact equivalent to moving two “deciles"in the 1991 distribution of class averages."
Finally, it is worth considering whether the results for Israel are likely to be relevant to the United States or other developed countries. Beyond cultural and political differences, Israel has a lower standard of living and spends less on education per student than the United States and some countries in the Organisation for Economic Co-operation and Development (OECD). Furthermore, Israel also has larger class sizes than the United States, the United Kingdom, and Canada. Therefore, the results presented may be showing evidence of a marginal return for reductions in class size within a range of sizes that is not characteristic of most American schools. On the other hand, while classes as large as those in Israel are not typical in the United States, in 1991 the average eighth-grade class size in California was 29 students, not dramatically below the corresponding Israeli average of 32 students.
References
ANGRIST, Joshua D.; LAVY, Victor. Using Maimonides' rule to estimate the effect of class size on scholastic achievement. The Quarterly journal of economics, v. 114, no. 2, p. 533-575, 1999.
