The estimation of peer effects at school has received intense attention in recent years. Several studies have presented convincing evidence about race, gender, and immigrants’ peer effects. Recent examples include Angrist and Lang (2004) on peer effects through racial integration; Hoxby (2000) and Lavy and Schlosser (2007) on gender peer effects; and Gould, Lavy and Paserman (2009) on the effect of immigrants on native students. But important questions about ability peer effects in education remain open, with little conclusive evidence. One well-known exception is Sacerdote (2001), who presents evidence on ability peer effects in college based on randomly paired roommates in university housing.
In recent research (Lavy et al. 2009), we study ability peer effects in educational outcomes between schoolmates in secondary schools in England with the goal of exploring which segments of the ability distribution of peers drive the impact of peer quality on pupils’ achievements. In particular, we study whether the extreme tails of the ability distribution of peers – namely the exceptionally low- and high-achievers – as opposed to the average peer quality, drive any significant peer effect on the outcomes of students.
To do so, we use data for all secondary schools in England for four cohorts of age-14 (9th grade) pupils entering secondary school in the academic years 2001/2002 to 2004/2005 and taking their age-14 national tests in 2003/2004 to 2006/2007. We link this information to data on pupils’ prior achievement at age 11, when they took their end-of-primary education national tests. We use this information to obtain pre-determined proxies of peer ability in secondary schools. In particular, we construct measures of average peer quality based on pupils’ age-11 achievements and proxies for the very high- and very low-achievers, obtained by identifying pupils in the highest 5% or lowest 5% of the national distribution of cognitive achievement at age 11.
This way of measuring peer ability presents a major improvement over previous studies which do not directly measure the academic ability of students’ peers, but rely on socio-economic characteristics as proxies for this.
Identifying peer effects: A complex issue
Our analysis also presents a new approach to estimating the causal impact of peers’ ability. The identification of these effects in non-experimental settings is fraught with difficulties because of the reflection problem (Manski, 1993). As Manski explains, it is called “the reflection problem because it is similar to an inferential problem that occurs when one observe the almost simultaneous movements of a person and of his image in a mirror. Does the mirror image cause the person's movements, does the image reflect the person’s movements, or do the person and image move together in response to a common external stimulus? Empirical observations alone cannot answer this question.” Sorting of pupils across schools based on their ability and characteristics and those of their peers poses additional problems as do other unobserved factors.
To by-pass the reflection problem we exploit the fact that, as a consequence of the large reshuffling of pupils in England during the primary-to-secondary school transition, students in our sample on average meet 87% new peers at secondary schools, i.e. students that do not come from the same primary school. In our analysis, we single out new peers from old peers, and focus on the effect of new peers’ ability on pupil achievement, thus by-passing reflection issues.
Regarding sorting, there is indeed significant evidence that the average ability of peers – as measured by their age-11 test scores – and pupil’s own ability in English secondary school are highly correlated. More surprisingly, this correlation survives even when we look at the within-secondary-school variation over time of pupils’ and their peers’ ability, i.e. conditional on secondary school fixed-effects. This suggests that sorting is taking place, with pupils and schools possibly being affected by and responding to cohort-specific unobserved shocks.
In order to overcome this problem, we rely on within-pupil regressions. These exploit variation in achievements across the three compulsory subjects – English, Mathematics and Science – tested at age 14. We further exploit the fact that students were tested on the same three subjects at the end of primary schools, so that we can measure peers’ ability separately by subject. We then study whether subject-to-subject variation in outcomes for the same student is systematically associated with the subject-to-subject variation in peers’ ability.
One significant advantage of this approach is that we are able to control for a pupil’s own unobservable average ability across the three subjects, as well as for unmeasured family background characteristics. Additionally, we can control for school-by-cohort and other cohort-specific unobservables that might affect pupils’ and peers’ quality similarly across the three subjects.
So are there any peer effects? New evidence
We show that a large fraction of ”bad” peers at school – as identified by students in the bottom 5% of the ability distribution – negatively and significantly affects the cognitive performance of other schoolmates. Importantly, as we show in our work, it is only the very bottom 5% students that (negatively) matter, and not ‘bad’ peers in other parts of the ability distribution (e.g. the 5-to-10% worst students).
Using the variation in the data, we can also assess how sizeable these effects are. To do so, we consider the peer effect for a pupil who experiences a change in the fraction of bad peers from 20% (the maximum in our data) to 0% (the minimum). She would experience an improvement in her age-14 test score of about 2 percentiles, which amounts to 0.17 of the within-pupil standard deviation in the age-14 test distribution. A more modest 10 percentage point decline would imply an improvement of around 0.08 of the standard deviation. Relative to other studies that focus on school inputs and interventions, our estimates of the effect of academically weak peers capture a small-sized, but non-negligible effect.
On the other hand, we uncover little evidence that the average peer quality and the share of very ‘good’ peers – as identified by students in the top 5% of the ability distribution affect the educational outcomes of other pupils. But these findings mask a significant degree of heterogeneity along the gender dimension.
By separating our sample into boys and girls, our results also show that girls significantly benefit from interactions with very bright peers, whereas boys are negatively affected by a larger proportion of academically outstanding peers at school. We also find that the positive effect stemming from interactions with ”good” peers is more pronounced for female in the bottom part of the ability distribution. On the other hand, while not strongly significant, our results suggest that more able boys suffer from interacting with a larger fraction of outstanding schoolmates.
Although it is impossible given our data to convincingly rationalise this pattern of results, some possible explanations can be found in the educational and psychological literature. Research in these areas has highlighted marked gender differences in behavioural responses to settings that should lead to reciprocity, suggesting that female are more positively influenced by peers and social interactions (Cross and Madson 1997, Eagly 1978). Additionally, perverse "big-fish-small-pond" mechanisms have been shown to be more pronounced for males (Marsh 2005). In a very recent piece from the economics field, Jackson (2009) finds gender heterogeneity in peer effects along the same lines as discussed here.
The gender and ability differences that we document allow us to perform some interesting policy simulations. To begin with, suppose that our students were exposed to the following two treatments simultaneously: a reduction in the percentage of top 5% and bottom 5% new peers from 20% to 0%. This change can be viewed as a move towards a class of closer ability. This shift would unambiguously improve male students’ age-14 achievements by about 0.22 of a within-pupil standard deviation. This effect is not dissimilar for the most and least able boys, and is only slightly larger than the findings in Duflo et al. (2008) on Kenyan primary schools. On the other hand, our experiment would give more heterogeneous results for girls. On average, the shift would improve female students’ age-14 achievements by about 0.06 of a within-pupil standard deviation. But this overall effect would turn negative for girls in the bottom part of the ability distribution, who could lose out as much as 0.10 of a standard deviation. At the other extreme, the most talented girls could gain more than 0.20 of a standard deviation from being educated in homogeneous environments.
Another policy-relevant experiment is to simulate the effects of tracking by grouping all students – including the bottom 5% and top 5% – into two classes perfectly segregated along the lines of student’s ability. The first group would include pupils who are above the median of the ability distribution, and the second those below the median. This shift would unambiguously worsens students’ age-14 achievements in the low ability class, with a negative impact of about -0.03 of a standard deviation for boys, and -0.06 for girls. On the other hand, the changes experienced in the high ability group would improve boys’ age-14 achievements by at most 0.01, while girls would benefit by up to 0.06.
Do our results lend overall support to tracking of students by ability? Besides any equity consideration, there is no simple answer to this question from an efficiency-of-learning point of view. As we have just shown, our results are clearly heterogeneous in relation to a pupil’s ability and gender, and vary according to the exact details of the tracking-experiment being carried out.
Despite not giving a one-size-fit-all policy recommendation, we believe our findings are rich enough to provide a solid ground for insightful interventions targeting students’ ability mix as a means to improve learning standards.
Angrist, Joshua D and Kevin Lang (2004), “Does School Integration Generate Peer Effects? Evidence from Boston’s Metco Program”, American Economic Review, 94(5):1613-1634.
Cross, Susan and Laura Madson (1997), “Models of the Self: Self-Construals and Gender”, Psychological Bulletin, 12:5-37.
Eagly, Alice (1978), “Sex Differences in Influenceability,” Pshycological Bulletin, 85: 86-116.
Gould, Eric D, Victor Lavy and Daniele M Paserman (2009), “Does Immigration Affect the Long-Term Educational Outcomes of Natives? Quasi-Experimental Evidence”, Economic Journal, 119:1243-1269.
Hoxby, Carloine M (2000), “Peer Effects in the Classroom: Learning from Gender and Race Variation”, NBER Working Paper 7867.
Jackson, C Kirabo (2009), “Peer Quality or Input Quality? Evidence from Trinidad and Tobago”, mimeo, Cornell University.
Lavy, Victor, Olmo Silva and Felix Weinhardt (2009), “The Good, The Bad and The Average: Evidence on the Scale and Nature of Ability Peer Effects in School”, NBER Working Paper 15600.
Lavy, Victor and Analia Schlosser (2008), “Mechanisms and Impacts of Gender Peer Effects at School”, NBER Working Paper 13292.
Manski, Charles F (1993), “Identification of Endogenous Social Effects: The Reflection Problem”, Review of Economic Studies, 60(3):531-542.
Marsh, Herbert W (2005), “Big Fish Little Pond Effect on Academic Self-concept: Cross-cultural and Cross-Disciplinary Generalizability”, paper presented at the AARE Conference.
Sacerdote, Bruce (2001), “Peer Effects with Random Assignment: Results for Dartmouth Roommates”, Quarterly Journal of Economics, 116(2): 681-704.