Cumulative instructional time and student achievement

ABSTRACT

This study uses a newly compiled data set of instructional time and student performance by subject across German federal states for student cohorts enrolled at the primary level in the 1990s and tested at the secondary level in the 2000s. It finds evidence for the school inputs-student achievement relationship, taking nonlinearity, cross-discipline and cross-academic progress effects into account, on the basis of regression models with state fixed effects. We find that high school ninth graders benefit from lifetime instructional time, in particular at the pre-secondary level. The results accommodate self-productivity, dynamic complementarity, and depreciation.

KEYWORDS:

• Education production function
• student performance
• school resources

JEL CLASSIFICATION:

• I21
• I28
• L38

Acknowledgments

We would like to thank the editor, Colin Green, and two anonymous referees for many helpful comments and suggestions that markedly improved our paper. We also thank Stefano DellaVigna, Guido Heineck, Hans Fricke, Andreas Hauffler, Ludger Wössmann, and participants of seminars and conferences at the University of Göttingen, the University of Munich, and the RWI Leibniz Institute Berlin for many remarks and fruitful discussions. Carolin Amann, Fabian Feierabend, Constantin Tabor, Stepahnie Najort, Marcus Strobel, and Annika Backes greatly assisted us in assembling the data.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Differences in school options parallel to the high school track and the variation (not only across states but also over time) in the share of students attending high school may raise concerns about systematic variation in the ability distribution. Therefore, we use the share of students on the high school track as a control variable in the analysis.

2. Pooling is a common practice in the literature. An example for pooling subjects is Eren and Millimet (2007). Pooling German states and merging in data on aggregate countries is done in Wössmann (2010). It is frequently claimed that studies relying on data at the level of states or districts suffer from an aggregation bias. Coates (2003) argues that the profession has not yet reached a consensus on whether such bias tends to produce spurious resource effects or not. According to Wössmann (2010) aggregation bias is not an issue in the case of marginal effects estimated using German state-level data.

3. We use the term ‘hour’ even though a school hour takes only 45 minutes. To be sure, the actual hours of instruction may fall short of the scheduled number of hours, in particular due to sickness of students and teachers. In addition, our analysis abstracts away from the implications of repeating (or skipping) a grade-level and the issue that a small fraction of students may have moved across state borders. Our analysis therefore relies on the assumption that the incidence of the issues did not vary systematically.

4. Abbreviations for states: Brandenburg (BB), Berlin (BE), Baden-Württemberg (BW), Bavaria (BY), Bremen (HB), Hesse (HE), Hamburg (HH), Mecklenburg-West Pomerania (MV), Lower Saxony (NI), North Rhine-Westphalia (NW), Rhineland-Palatinate (RP), Schleswig-Holstein (SH), Saarland (SL), Saxony (SN), Saxony-Anhalt (ST), Thuringia (TH).

5. While not statistically significant, a negative elasticity is implied for instruction at the high school level. It is worth noting that in value added specifications (as opposed to levels-type specifications) by Figlio (1999) elasticities of instructional hours similarly turn out negative and statistically indistinguishable from zero. As his study is based on a U.S. nation-wide standardized test of eighth-graders (National Education Longitudinal Survey) and a follow-up examination when tested students were tenth-graders, the author interprets this finding as suggesting that much of the benefit from instructional hours found in levels specifications ‘must accrue in the grades prior to eighth grade’ (Figlio 1999, p. 247).

6. More results are available from the authors upon request.