Question

Explain why Maimonides’ rule is a good instrumental variable for class size. Without such an instrumental variable, if we regress pupil performance on class size with ordinary least squares, give one reason why the effect of class size may be underestimated and one reason why it may be overestimated. Can you think of another good instrumental variable for class size?

Answer 1

Maimonides' rule identifies a correlation between class size and students' achievements. It states that a class size may rise to an upper limit of 40 students. Once this quota is reached the class is cut in half, so instead of one class with forty-one students there are now two classes: one with twenty students and one with twenty-one students.

Maimonides’ rule is a good instrument for the discontinuity sample. Maimonides’ rule is extremely effective with schools with a high PD index. The rule can be used as an identification method as it “induces a discontinuity in the relationship between enrolment and class size at enrolment multiples of 40” (pp. 540). It means that class size varies “abruptly and predictably” or is variable, every time enrolment exceeds a multiple of 40, when a new class needs to be formed. Put another way, at the points of discontinuity the school average class size drops from 40 (when grade enrolment is 40, 80, 120 etc) to 20.5 (when the 41st, 81st, 121st etc student is enrolled), reflecting an exogenous variation created by the institutional rule.

The econometric identification of class-size effects is difficult, because class-size is a highly endogenous variable. Naive, ordinary least squares estimations of the impact of class-size on test scores usually yield positive coefficients: it seems that increasing class 2 size helps students.

Least squares estimates with no control variables show a strong positive correlation between class size and achievement.The positive correlation between achievement and class size is clearly an artifact of the association between smaller classes and the proportion of pupils from disadvantaged backgrounds. Instrumental variables estimates constructed by using functions of Maimonides’ rule as instruments for class size while controlling for enrollment and pupil background consistently show a negative association between larger classes and student achievement.

A substantial amount of unobserved remedial education by means of smaller classes takes place and ordinary least squares estimates of class-size coefficients are biased upwards.