An Estimation of the Effects of Class Size using a Fixed Effect Model:

An Empirical Study with School Panel Data from the “National Assessment of Academic Ability” in Japan

Abstract

The purpose of this paper is to clarify the effects of class size on a student’s academic achievement with school panel data from the “National Assessment of Academic Ability” of Japan that was collected between 2013 and 2017.

Whether a reduction in class size improves a child’s academic ability or not is focused in educational policy. Findings on the effects of class size are often inconsistent, because of unobserved heterogeneity. Although recent studies have revealed class size’s causal effects by eliminating endogeneity, most of the studies analyzed cross sectional data. Therefore, in this paper, we used a fixed effect model with panel data to analyze the relation between class size and academic achievement.

The tasks of analysis in this paper are as follows.

First, we verify the effects of class size by eliminating unobserved heterogeneity with a fixed effect model using school panel data. The inconsistency in class size studies may be due to data analyses with cross sectional data. In other words, since the “quality” of the members that make up the group change every year, it is possible that “a grade with high academic ability with a smaller class size” has happened “by chance”.

Second, we verify whether class size has positive effects in schools with many school-aid recipients.

Third, we analyze whether or not class size has the same effect for all subjects or not.

In this paper, to clarify the effects of class size on students’ academic achievement, we analyzed panel data from the “National Assessment of Academic Ability” tracked by school between 2012 and 2017 for 5 years. The survey has been conducted almost exclusively since 2007. The panel data from the schools has few dropouts and extremely valuable data is collected. The number of cases for analysis in this paper is 16,798 primary schools and 8,740 middle schools. The connection rates are 81.4% (primary schools) and 84.7% (middle schools).

The results in this paper are as follows.

First, the overall effects of class size are statistically significant for all subjects for both primary schools ( 6 th grade) and middle schools ( 3 rd grade), and estimates in this paper indicate that the academic score increases when the class size decreases at the same school after eliminating unobservable heterogeneity. Second, we discovered the positive effects of class size for primary schools where the enrollment rate of school-aid recipients is 30% or more for 5 consecutive years. This finding may be meaningful for decisions on what kind of school to concentrate on when allocating teachers in a situation of limited financial resources.