Do class size effects differ across grades?

Abstract

This paper contributes to the class size literature by analysing whether short-run class size effects are constant across grade levels in compulsory school. Results are based on administrative data on all pupils enrolled in Danish public schools. Identification is based on a government-imposed class size cap that creates exogenous variation in class sizes. Significant (albeit modest) negative effects of class size increases are found for children at primary school levels. The effects on math achievement are statistically different across grade levels. Larger classes do not affect girls, non-Western immigrants and socioeconomically disadvantaged pupils more adversely than other pupils.

Keywords:

• Class size
• regression discontinuity
• LATE
• compulsory school
• literacy
• test scores

Acknowledgements

The author thanks Helena Skyt Nielsen, Nina Smith, Maria Knoth Humlum, seminar participants at Aarhus University, the 2014 IWAEE, Catanzaro, and the 2014 EALE conference, Ljubljana, and especially the editor Colin Green and two anonymous referees for very helpful discussions and comments.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. To accommodate potential classroom divisions outside of the summer break caused by late school transfers, up to 30 pupils are allowed per classroom during the school year.

2. Further tests include reading (grade 4), English (grade 7), biology and geography (grade 8).

3. Sixty two percent of the missing test results occur in 2010 where the test system suffered a nationwide, technical breakdown that unexpectedly cancelled two weeks of testing. These tests are unidentifiable but likely missing at random. In terms of parental characteristics, pupils with missing test results are slightly negatively selected, but they represent a relatively small fraction of the sample.

4. The pattern is largely consistent across grades with a somewhat poorer fit for the eighth grade.

5. Each segment consists of pupil intervals around threshold : , where . The first segment also includes enrolments below 15 pupils: . Where the narrower bandwidths around the lower thresholds are used, segment consists of , where .

6. Results are driven by smaller schools. Firstly, because only observations around the three lower thresholds are included in the pupil sample. Secondly, even when all thresholds are included, the instruments cause a much greater difference in class size around the first threshold (13.5 pupils) compared to the second and third (9 and 6.75, respectively), and the weighted average causal treatment effect places larger weight on observations that are more affected by the instruments (Angrist and Imbens 1995; Angrist and Lavy 1999).

7. For simplicity, -values are from regressions on a pooled binary indicator for being above any threshold. Results carry through for regressions on each -indicator separately (available on request).

8. Clustering by grade enrolment is suggested by Lee and Card (2008) and performed in Fredriksson, Öckert and Oosterbeek (2013). This yields 136 clusters in the full estimation sample, which is considerably less than when clustering on the school grade by year level where the instrument varies. Thus, standard errors are slightly larger, but the difference is modest.

9. Columns of Table A.2 (see online supplemental data at http://dx.doi.org/10.1080/09645292.2015.1099616) summarise a specification analysis. Column presents the results from the OLS regression. Columns (2) and (3) present the results of 2SLS regressions with only a smooth second order polynomial in enrolment, and where class size is instrumented by and the -dummies, respectively.

10. To accommodate a serious threat to identification caused by potential measurement error in the enrolment variable, analyses excluding observations at the cutoffs (i.e. 28, 29, 56, 57 etc.) are also conducted. Results and conclusions are robust to this exclusion (available on request).

11. The ‘highest earnings’ variable is defined as the highest earnings of the pupil's mother and father. When parents are divorced, the income of the mother is used.

Additional information

Funding

Financial support from the Danish Council for Strategic Research [CSER, 09-070295] is gratefully acknowledged.