Class-size effects in secondary school

Abstract

We analyze class-size effects on academic achievement in secondary school in Denmark exploiting an institutional setting where pupils cannot predict class size prior to enrollment, and where post-enrollment responses aimed at affecting realized class size are unlikely. We identify class-size effects combining a regression discontinuity design with control for lagged achievement and school fixed effects. Using administrative registry data, we find statistically significant negative effects of class size on academic achievement.

Keywords:

• school quality
• human capital investment
• regression discontinuity design
• value-added models
• school fixed effects
• maximum-class-size rule

JEL codes:

• C23
• I2
• I21

Acknowledgements

We would like to thank seminar participants at the 2012 ‘III Workshop on Economics of Education: Improving Quality in Education’ at University of Barcelona, participants at the 2013 ‘Fourth International Workshop on Applied Economics of Education’ organized by Universita’ Magna Graecia and Lancaster University, seminar participants at Aarhus University, and especially two anonymous referees and the editor Colin Green for very helpful comments and suggestions.

Funding

This work was supported by The Danish Council for Strategic Research [grant 09-070295].

Notes

1 Positive effects of reducing class size on years of schooling and other long-term outcomes are found in Krueger (2003) and Chetty et al. (2011) based on the STAR experiment, and in Browning and Heinesen (2007) and Fredriksson, Öckert, and Oosterbeek (2013) based on analyses using maximum class-size rules and Danish and Swedish administrative data, respectively.

2 This optional tenth grade is a rather unique feature of the Danish school system. To our knowledge, only Finland has a similar optional tenth grade, but enrollment is only around 2% (own calculation on data from Statistics Finland).

3 This hypothesis is somewhat supported by the findings that the correlation between class size in tenth grade and class size in ninth grade the year before is only 0.20 while the within-school correlation between class sizes in tenth grade across years is 0.40.

4 In the case of a school change during the school year of tenth grade, we use data on class size at the school where the exit exam is taken.

5 Hence we exclude boarding schools and public tenth grade schools. The reason for this is that they only to some extend use the traditional class structure. The average class size is not a meaningful measure for these schools and in addition the reported number of classes is imprecise (typically much too low) for these institutions.

6 We drop observations with class size above 35. In total, we drop 1746 observations corresponding to 3.6% of the sample. Our estimation results are robust to this restriction; see Section 5.2.

7 The ordinary exams which we include in the analysis are in Danish (written and oral), spelling (Danish, written), math (written and oral), and English (oral). The advanced exams included in the analysis are in the mandatory subjects: Danish (written and oral), math (written and oral), and English (written and oral).

8 It is beyond the scope of this paper to analyze dropout, but regressions using data at school by year level of the number of pupils who are at the schools at the end of the school year according to the exam register on class size and enrollment at the beginning of the school year (and year dummies) result in marginally significant negative coefficients of class size, indicating that a reduction in class size will tend to reduce dropout. This is in line with the indications of a positive effect of reducing class size on the probability of taking advanced exams in Table 4.