Using Maimonides' rule to estimate the effect of class size on scholastic achievement
Angrist and Lavy attempt to investigate what the causal impact is of an offer of a small class student achievement as measured by reading and math scores.
Most work in the past had been in the from of either randomized experiments like the Tennessee STAR experiment or in the form o observational studies where performance of students in small classes are compared to students in large classes and controls are added for alternative explanations (e.g., SES, etc). Of course, schools with smaller classes might have smaller classes because of unobserved factors of the society or community or administrators which are also driving the higher levels of educational performance.
Angrist and Lavy use data from Israeli National Censuses of Schools which includes beginning-of-year enrollment data and school characteristics. They also have data on actual class size collected during the year and average test within schools from National Center for Education Feedback in Hebrew reading and math.
The authors use "Maimonides’ rule" as an exogenous source of variation in class size that can be used to estimate the effects of class size on scholastic achievement of Israeli pupils. The rule comes from a Talmudic passage where a Babylonian Rabbi named Maimonides suggested that no class should have more than 40 students for a single teacher. This rule is adhered to closely within Israeli. Angrist and Lavy treat schools with 35-40 students as equal in expectation to schools with 40-45 -- although the former would have large classes and the former would have small classes.
In doing so, they assume that non-class-size effects on test scores do not depend on enrollment except through a smooth function of the control variables they have and that parents do not selectively exploit Maimonides rule. They present evidence and robustness checks to address each assumption.
They find different effects of class size at different grade levels:
- In 5th grade, the offer of a small class substantially increases math and reading scores.
- In 4th grade, smaller classes appear to increase reading scores moderately.
- In 3rd grade there is no apparently effect from an offer of a small class.
They suggest that the grade 3 finding is a result of different testing procedures during the year that the third grade data was collected.
Theoretical and practical relevance:
Angrist and Lavy's model of using absolute cutoffs in terms of class sizes has been replicated now in more than a dozen different studies across the world that exploit these policies of a way of finding opportunities to use regression discontinuitiy designs.