Association for Public Policy Analysis & Management

Class size reduction (CSR) policies have been widely implemented around the world in the past decades. However, only a few studies have focused on the differential class size effects across the student achievement distribution, and their findings have been mixed. Our study was designed to explore the differential class size effects for students with different levels of achievement. In particular, we examined the effects of class size across the student achievement distribution (i.e., middle and upper or lower tails), in an attempt to address the question of whether CSR closes the achievement gap between high- and low-achievers.

We used the data from the 2011 fourth-grade sample of the Trends in International Mathematics and Science Study (TIMSS) in 14 European countries. The European countries we selected had maximum class size rules, which allowed us to use an instrumental variable (IV) approach to explore the causal effects of class size on student achievement across the achievement distribution.

In particular, we employed quantile regression to estimate class size effects on student achievement in the middle as well as in the lower and upper tails of the achievement distribution. To deal with the potential endogeneity of class size, we computed the average class size in a school based on the maximum class size rule in each country, which was used as an instrumental variable (IV) for class size. We used the control function approach (see Lee, 2007) to estimate the differential causal effects of class size effect on fourth graders’ mathematics achievement.

Our IV approach can also be seen as a regression discontinuity design, because the maximum class size rule generates discontinuities in terms of the actual and the computed average class size as school enrollment increases. We checked whether covariates are locally balanced near the cut off points, in an attempt to validate both the RD design and the instrument. We also examined the correlation between the instrument and teacher reported class size through OLS regression to exclude the countries with weak instrument.

Generally, the findings from the quantile regression indicated no systematic patterns of association between class size and achievement. In two of the nine European countries with strong and valid IV, we found insignificant class size effects. The exceptions were Romania and the Slovak Republic, where significant class size effects were detected in some quantiles. These significant class size effects were quite substantial in magnitude compared to prior studies (e.g., Angrist & Lavy, 1999). Nonetheless, our findings are in congruence with the findings of previous work that used prior cycles of TIMSS and have indicated generally insignificant relationships between class size and achievement (Pong & Palls, 2001; Wossmann, 2005; Wossmann & West, 2006). We also compared class size coefficients at the lower and upper tails of the achievement distribution and found no differential class size effects across the achievement distribution. In sum, our findings suggest that smaller classes did not reduce the achievement gap between low- and high-achieving students.