The organisation of university education is increasingly in the spotlight, both in academic and policy circles. Recent research has stressed the importance of higher education in providing positive externalities within firms (Moretti 2004), within local labour markets (Glaeser et al. 1992), and in fostering economy wide growth (Aghion et al. 2007). Concurrently, most OECD countries have adopted policies that have led to dramatic increases in university enrolment during the last decade. The average annual increase in university enrolment in OECD countries during the period 1995-2005 was above 4%. In the UK, this growth has occurred at both the undergraduate and graduate level, as shown in Figure 1, and across a wide range of universities. The UK is actually at the low end of enrolment growth within the OECD. Between 1998 and 2005, the US experienced a 30% increase in student enrolment, for example.
Figure 1. Aggregate UK enrolment in higher education (1995=100)
Such breathtaking increases in enrolment inevitably lead to university students facing larger class sizes. The effect of increasing class size in tertiary education is not well understood.
The established literature on class size effects in primary and secondary schools provides useful guidance (Krueger 1999, Angrist and Lavy 1999, Hoxby 2000), in universities the range of class sizes is typically larger than at other tiers of the education system, and different mechanisms driving class size effects might operate. Although tertiary education may involve more self-learning than primary or secondary education, class size remains solidly at the top of the policy agenda and concerns of both faculty and students.1
Identifying class-size effects from within-student variation
To address this policy question, we estimate the impact of class size on the final exam marks of graduate students in a leading UK university between 1999 and 2004 (Bandiera et al. 2010). As we observe the same student being exposed to very different class sizes, we estimate the effects of class size on students’ exam performance by comparing the same student’s performance to her own performance in courses with small and large class sizes.2 It is important to stress that, on average, most of the variation in marks is due to fixed students’ characteristics and not university inputs.3 On average the performance of a given students only varies by around 7% of the average mark across her courses. We shed light on how much of this within-student difference is attributable to differing class sizes the student faces.
The effect of class size on students’ performance is – as expected – negative; students do worse in big classes. Namely, a given student receives lower marks in courses with larger classes, everything else equal.
To get a sense of the magnitude of this effect, our estimates imply that a one standard deviation increase in class size from the mean (that is going from the average class of 56 to a class size of 89) would decrease the mark by 9% of the observed variation in marks within a given student. These estimates, however, mask two important forms of heterogeneity: (i) the impact of class size varies across the range of class sizes; (ii) the effect of class size varies across students.
On the first form of heterogeneity, the negative effect of class size on student exam performance is large and negative only in the smallest and the largest classes. There is no class size effect across a wide range of intermediate class sizes. The magnitudes imply that moving the average student from a class of 10 to a class of 25 leads to a drop in exam performance of around 12.5% of within-student standard deviation. Increasing the class size from 25 to 45 determines a further 12.5% drop. In contrast, there is no impact in a wide intermediate range, while moving from 80 to 150 determines a further drop of 25% in the within-student standard deviation. If moved from a very small class (of size 10) to a very large class (of size 150), the average student can be expected to suffer a loss corresponding to about 50% of the overall variation in exam marks the average student experiences across all of her courses.
The second form of heterogeneity concerns students’ ability. Students at the top of the mark distribution are those most affected by class size. The effect is almost four times larger for students in the top 10% of the distribution of exam marks than for students at the bottom 10%, and about 50% larger than the average student. This heterogeneity is most apparent in the largest classes and virtually non-existent for a range of intermediate class sizes. This implies the highest-ability students would benefit the most, in terms of academic achievement, from any reduction in class sizes, when class sizes are initially very large.
To shed light on the underlying mechanisms for the class-size effect, our analysis uses information on teachers' assignments to classes and on students' characteristics. We find no evidence that departments purposefully assign faculty of differing quality to different class sizes, and we find no evidence that faculty members alter their behaviour when exposed to different class sizes. It appears that the preparation and delivery of lectures is independent of the number of students taught.
On student characteristics, the class-size effect does not vary with proxies for students' wealth. Hence if larger classes resulted in lower grades because students had more limited access to library books or computer laboratories, the effect should have been smaller for students who can purchase these inputs privately. Moreover, the class-size effect does not vary with student's familiarity with this particular university as an undergraduate or with the UK system generally. This casts doubts on the relevance of mechanisms that work through the information students have, such as their awareness of other local resources (for example other libraries in the area), or their knowledge of the characteristics of faculty, courses, or departments.
Discussion and policy implications
Against a backdrop of rapidly increasing enrolment rates in tertiary education, our analysis has important policy implications. Class size matters for student performance and particularly for the most able students.
However, reducing class size is not always an effective strategy and is certainly not effective for all students in the same way. Reducing the size of very large modules (above 100) could be a cost-effective way to improve students’ performance. For modules in the range 30-100 reducing class size could be a rather ineffective strategy, while for classes below 30 it could be a valid but not necessarily cost-effective strategy. Attention should be devoted to other inputs in such cases, and more refined and cost-effective solutions than pure number counting should be identified. To this end, it is important to have a better understanding of the mechanisms that link class size and performance.
Although student-to-staff ratio is a commonly used indicator of quality both in national and international comparisons, this might be a noisy measure of quality over this intermediate range of class sizes.4 Given the mechanisms our data rule outs, there appear to be at least two ways that larger classes reduce students' performance. First, changes in student behaviour such as their attentiveness or participation. Second, reduced resource availability, such as library books or faculty time during office hours.
As the best students are the most affected, that could imply that large classes induce a reduction in tutoring activity rather than a substantial deterioration in classroom conditions. It is reasonable to expect that the best students are able to compensate classroom deterioration at least as well as other students. However, the best students are also those that benefit the most (in terms of both learning and motivation) from contact with teachers. They, therefore, suffer the most in terms of reduced performance when such contacts or tailored feedback is less frequent.
1 This is particularly evident in the UK, where concerns on the increasing student-to-staff ratios in higher education institutions have recently been expressed in a report of the Department for Innovation, Universities, and Skills and by the most important unions of university teachers.
2 Our estimates are therefore purged from confounding effects that arise because students choose which modules to take. For instance, if more able students were to choose smaller classes, a cross-student comparison would capture both the effect of class size and the effect of student ability. The within-student comparison only captures the former.
3 Characteristics like ability and motivation are certainly affected by previous experiences and schooling, but they can be taken as given for what concerns university policy.
4 This choice is somehow justified by the fact that, in order to evaluate teaching quality, the student to staff ratio probably remains the only globally available and comparable indicator.
Aghion, P., L. Boustan, C. Hoxby, and J. Vandenbussche (2007), “Exploiting States' Mistakes to Identify the Causal Impact of Higher Education on Growth”, mimeo, Harvard University.
Angrist, J. and V. Lavy (1999), "Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement", Quarterly Journal of Economics 114: 533-75.
Bandiera, O., V. Larcinese and I. Rasul (2010), “Heterogeneous Class Size Effects: New Evidence from a Panel of University Students”, forthcoming, Economic Journal.
Glaeser, E. L., H. D. Kallal, J. Scheinkman, and A.Shleifer (1992), "Growth in Cities", Journal of Political Economy 100: 1126-51.
Hoxby, C. (2000), "The Effects of Class Size on Student Achievement: New Evidence from Natural Population Variation", Quarterly Journal of Economics 116: 1239-86.
Krueger, A. (1999), "Experimental Estimates of Education Production Functions", Quarterly Journal of Economics 114: 497-532.
Moretti, E. (2004), "Workers' Education, Spillovers and Productivity: Evidence from Plant-Level Production Functions", American Economic Review 94: 656-90.