Education curriculum and student achievement: theory and evidence

ABSTRACT

We propose a theory of education curricula as horizontally differentiated by their paces. The pace of a curriculum and the preparedness of a student jointly determine the match quality of the curriculum for this student, so different students derive different benefits from learning under the same curriculum. Furthermore, a change in the curricular pace has distributional effects across students, benefiting some while hurting others. We test the model prediction using a quasi-natural experiment we call the G8 reform in Germany, which introduced a faster-paced curriculum for academic-track students. We find evidence consistent with our theory: While the reform improves students' test scores on average, such benefits are more pronounced for well-prepared students. In contrast, less-prepared students do not seem to benefit from the reform.

KEYWORDS:

• Education curriculum
• horizontal differentiation
• distributional effects
• PISA

JEL CLASSIFICATION:

• I21
• D20
• I28

Acknowledgements

We are grateful to Nicole Fortin for sharing her STATA codes with us. We thank seminar participants at University of Alberta, Canadian Economic Association conference, European Economic Association conference, and International Workshop of Applied Economics of Education for helpful comments. All remaining errors are our own.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. We have borrowed the terminology of horizontal versus vertical differentiation from the industrial organization literature, see Tirole (1988) for example.

2. The paper is also related to the ‘peer effects’ literature pioneered by Epple and Romano (1998), where any student would benefit from having better-ability peers. In contrast, our curriculum model suggests that a less-prepared (low-ability) student may actually suffer from having well-prepared (high-ability) peers, if the curriculum is geared toward her peers and consequently too fast-paced for her own learning.

3. Two recent studies, Homuth (2017) and Huebener, Kuger, and Marcus (2017), perform empirical analysis similar to that in Andrietti and Su (forthcoming) (whose first version appeared as Andrietti 2015), and find similar results.

4. In a related context, Morin (2013) and Krashinsky (2014) examine the impact of an Ontarian high school reform on students' university outcomes. Similar to the G8 reform, the Ontario reform reduces the high school duration for most students from five to four years. Unlike the G8 reform, instead of keeping the total amount of academic content required for high school graduation fixed, the Ontario reform also reduces the number of course credits and the academic content typically associated with the fifth and last year. As a result, the Ontario reform has no impact on the pace of the curriculum per se, but rather delivers less content in a shorter period. Both studies find that, on average, the four-year graduates perform significantly worse than their five-year counterparts.

5. The current one-stage curriculum model can be easily extended to a multi-stage framework, where the human capital output from a given stage s determines the student preparation for a subsequent stage s+1, with the initial level being the innate ability. This is in line with the literature on human capital accumulation pioneered by Ben-Porath (1967) and more recently Cunha and Heckman (2007).

6. Note that since (1(1) ) represents only a local approximation, the results may not hold globally, in particular at the far end of the preparedness distribution.

7. In contrast, such an interpretation would be invalid in an alternative framework, e.g. Duflo, Dupas, and Kremer (2011), where education benefits are hump-shaped (instead of strictly increasing) across student ability levels. In that framework, the same test score may be obtained by students on either side of the hump shape, i.e. different ability levels.

8. Given its flexibility, the RIF method has recently been applied to analyze a range of issues such as cigarette taxes (Maclean, Webber, and Marti 2014) and child care (Havnes and Mogstad 2015).

9. See Firpo, Fortin, and Lemieux (2009), Borah and Basu (2013).

10. We implement the RIF-DiD estimation procedure using the STATA ado file rifreg – downloaded from http://faculty.arts.ubc.ca/nfortin/datahead.html (last accessed December, 2015). The RIF is computed using a Gaussian kernel with an optimal bandwidth.

11. Baumert (2009), Prenzel (2007), Prenzel (2010), Klieme (2013), Prenzel (2015)

12. Using item response theory, PISA maps student performance in each subject on a scale with an international mean of 500 and a standard deviation of 100 across the OECD countries. The scores are averages of plausible values, which are drawn from a distribution of values that a student with the given amount of correct answers could achieve as a test score (OECD 2012).

13. Two states, Berlin and Brandenburg, have tracking start in grade 7.

14. For our sample period (2000–2012), Saxony and Thuringia are thus always ‘treated’ with the G8 status.

15. For example, in earlier policy discussions, then-federal secretary of education Jürgen Mölleman strongly argued for the reform because ‘[German] graduates are two to three years older than their peers against whom they compete for jobs in the European labor market…. German pension systems and demographics (characterized by a significant fraction of senior, retired citizens) cannot support such a late start of employment by young adults…. Students reach the age of majority at 18 and should have completed secondary schooling by then. (Translation by author)’ (Wiater 1996). When the reform was actually implemented, its was implemented for similar reasons: ‘As mentioned earlier, reducing the number of years of education is one of several measures aimed at lowering the age at which academically qualified workers enter the labor force, which is regarded as too high when compared internationally and, in light of the rising demand for highly educated workers in a globalizing world, is expected to result in a competitive disadvantage for German university graduates, and hence for Germany itself…. In order to protect social insurance systems, the palpable aging of the population, coupled with the simultaneous decline in births and population, necessitates an earlier entry of young adults into a longer phase of gainful employment. (Translation by author)’ See Kühn et al. (2013) for more discussions.

16. As a comparison between the quantile regression and RIF-regression, Firpo, Fortin, and Lemieux (2009) examine the union status on male wages. What they find is that while the union status compresses within-group wage inequality among unionized workers, it increases between-group wage inequality of unionized workers relative to non-unionized workers. As a result, the conditional treatment effect (given by the quantile regression) is monotonically decreasing, while the unconditional treatment effect (given by RIF regression) exhibits an inverted-U shape.