Peer Effects: Evidence from Secondary School Transition in England^†

1 Introduction

Schools seem often to be judged on the kind of children they enrol, rather than on the quality of their teaching or the other facilities they offer. This observation has led many to argue that the background and abilities of a child's schoolmates must have an important influence on his/her own achievements at school. Motivated by this argument, a rich international literature has evolved to try to model and measure the consequences of social interactions between students – so called ‘peer-group effects’ – spanning the economics, education, sociological and psychological fields.

The issue is a critical one in respect to current educational policy which favours expansion of school choice because choice based on school group composition can lead to a high degree of sorting across schools along lines of prior ability (e.g. Epple and Romano, 2000). An understanding of the prevalence of peer effects is also important because they imply that educational interventions that appear beneficial when tested on the individual student may be even more effective (or less effective) when rolled out to the population (Glaeser, Sacerdote and Scheinkman, 2003). It is also well known that peer group effects have efficiency implications when the effects are non-linear, or if there are complementarities between group and individual characteristics.

Our aim in this paper is to contribute to the evidence on the benefits of being educated in schools alongside high-ability peers. The investigation is carried out by looking at student achievement in national standardized tests in secondary school age 14 (Key Stage 3 tests, ks3)1 and their prior achievement in national standardized tests in primary school age 11 (Key Stage 2 tests, ks2). We use a detailed administrative data set on the population of students in England's state schools, between 2004/5 and 2007/8. Specifically, our empirical work investigates whether children progress faster academically during their secondary school years up to ks3, if their secondary schoolmates performed well in their primary school at ks2. Students' secondary school peer quality is defined here as the mean of secondary schoolmates' prior achievement (ks2 primary school scores) upon enrolment in secondary school. On average, we find that peers do have a positive impact on student secondary school achievement: 1 SD increase in the mean ks2 scores on intake to secondary school is associated with a 2% of 1 SD increase in student achievement in ks3. This effect is small relative to the variation in achievement across students, lending weight to the existing international evidence that finds that the causal effect of peer group quality is low down the rankings of factors determining students' academic outcomes. However, scaled relative to other educational interventions, these effects are not so trivial. For instance, the recent literature on teacher effects (Hanushek and Rivkin, 2010) finds that a 1 SD increase in teacher quality raises student achievement by only 10–15% of 1 SD. We further show that these peer effects on age 14 achievement are also evident when we measure prior achievement using even earlier age 7 (Key Stage 1, ks1) tests. This implies that students benefit from attributes of their peers, perhaps motivation, innate ability, or aspects of family background, that were evident very early on in their schooling. We find no evidence for heterogeneity in the effects of peers across students of different types, or complementarities between students with different prior achievements.

In common with other work on peer effects (and other group and spatial effects), the main threats to identification of a causal influence of peer group prior achievement on individual student academic outcomes are: (i) non-random sorting of individuals into groups, implying that unobservable characteristics of individuals tend to be correlated with the characteristics of the group; (ii) unobservable factors affecting the group simultaneously which, coupled with sorting, can lead individual outcomes and group characteristics to become correlated;2 (iii) reverse causality running from individuals to the group which will tend to inflate the magnitude of the estimated effects;3 and (iv) insufficiently large variation in peer group quality across students, once steps are taken to mitigate the effects of (i)–(iii).Our paper offers several contributions to the field in the way it deals with these problems.

Firstly, the fact that we observe multiple cohorts of the population of state-school children in an administrative census allows us to transform the data in ways that eliminate salient fixed and trending factors. We control for individual effects using student's prior achievement in an educational value-added specification (as, e.g. in Ding and Lehrer, 2007). At the same time, we control for fixed effects and trends for current and previous school in a variant of the classic within-school, cohort-to-cohort differencing approach popularized by Hoxby (2000) and employed in a number of peer group papers (e.g. Hanushek et al., 2003; Lavy, Paserman and Schlosser, 2011). The resulting design implies that we identify peer effects on individual test score gains, from shocks to peer group quality, that are likely to be unanticipated, conditional on primary and secondary school fixed effects and trends. The design is only feasible because we look at the transition between primary and secondary schooling, and, as we will demonstrate, eliminates potential sorting and selection effects and controls for unobservable factors affecting students who make the same schooling choices. A particular novelty of our set-up is that this analysis is carried out on student data aggregated to primary school-by-secondary school-by-cohort cells. Aggregating the data in this way has an advantage over working with the individual-level data as they make it feasible to eliminate fixed effects and trends using first-differences and second-differences between cohorts, without any loss of information on peer group changes. Aggregation of test scores across groups of students also mitigates some of the problems inherent in individual-level value-added models, when test scores are noisy measures of prior achievement (Todd and Wolpin, 2003).

Secondly, a strength of our administrative data is that they have information on the family background and test score histories of each student, with test scores measured at age 7 (ks1). This test score history allows us to examine to what extent peers' early achievements, determined well before secondary peer group formation, drive peer effects in secondary school. We can also use this information to control for the individual student specific trends in achievement.

Thirdly, and crucially, we have large changes in peer group quality, because we look at peer group reformation during the transition between primary and secondary school, occurring immediately after students take their standard ks2 tests in primary. At this point of transition, students are reassigned from their old school groups to new school groups and this transition generates large changes in peer group characteristics (on average 88% of a student's peers are new to them in secondary school). This rearrangement of peer groups ensures that we observe large changes in peer group quality, and allows us to identify the causal influence of peers from contribution of new members to a student's peer group, thus eliminating the potential biases induced by student and peer prior achievements being determined by shared past factors and reverse causality. In addition, we reduce biases from re-sorting of students after entry to secondary school, in response to revealed secondary school quality by basing our peer group measure on the peer group composition in the first year in secondary school. This ensures that our peer measure is not affected by the students selecting into or out of secondary schools in response to what they learn about schools and peers after entry.

Taken together, these elements of our design ensure that: (i) student and peer characteristics are not correlated by sorting of similar students into similar schools; (ii) the pre-existing characteristics of students and their new peers are not determined jointly by the past events that students and their peers shared, or by reverse causality; but (iii) we are still left with substantial variation in peer group quality. Ultimately, our identification comes from cohort-to-cohort changes in the secondary school peer group experienced by students making a given primary–secondary school transition, conditional on primary-by-cohort fixed effects, the prior (ks2) achievements and other characteristics of students making this primary–secondary school transition in each year.

The rest of the paper is structured as follows: section 2 provides an overview of recent relevant literature on the influence of peers on student achievement, outlining relevant methodological issues. Section 3 explains our empirical approach. Section 4 describes the data and how they relate to the school system in England. Section 5 presents and discusses the results, and section 6 concludes.

2 Background and literature

The role of social interaction in modifying individual behaviour is central in many fields in social science and social psychologists have been conducting related experiments for half a century. Economists too have a long-standing theoretical interest (Becker, 1974), and the past two decades have seen rapid growth in applied work that has attempted to investigate both the existence and functional structure of peer group influence. The range of outcomes that have interested researchers is diverse, including smoking (Alexander et al., 2001; Ellickson et al., 2003), joke-telling (Angelone et al., 2005), purchase of a retirement plan (Duflo and Saez, 2000), fruit picking (Bandiera, Barankay and Rasul 2005, 2010), academic cheating (Carrell, Malmstrom and West, 2008), check-out throughput (Moretti and Mas, 2009), routine tasks (Falk and Ichino, 2006), obesity (Trogdon, Nonnemaker and Pais, 2008; Carrell, Hoekstra and West, 2010), performance in professional golf tournaments (Guryan, Kroft and Notowidigo, 2007), to give a few examples. Introspection does suggest that many decisions are linked to similar decisions by a friend or associate, and many consumption decisions rely on other consumers participating (e.g. Facebook). However, the more interesting possibility is that group behaviour or attributes can modify individual actions in relation to important social and economic decisions that will affect their life chances – especially achievement in education.

Some very bold claims have been made about the potency of peers in child development (Rich Harris, 1999), yet the results of numerous studies are very mixed, finding strong, weak or non-existent effects across a wide range of outcomes. This reflects the difficulty in defining the peer-group, isolating causal peer-group effects from other influences, lack of appropriate data and different identification methodologies adopted by researchers. Most empirical work in economics refers to Manski's (1993) framework which distinguishes between three channels of peer influence: endogenous effects from group behaviour; exogenous or contextual effects from group characteristics, and correlated effects from unobservables that influence members of the group in common. In practical applications with linear specifications, these channels are difficult to disentangle, because mean group behaviour is determined by mean group observable characteristics, so endogenous and contextual effects are not separately identified from the reduced form parameters (the reflection problem). A related challenge is individual self-selection into peer groups. Individuals generally choose the groups to which they belong, so peer group characteristics and unobserved individual characteristics are likely to be correlated through sorting, making the distinction between peer effects or selection effects even more difficult.

Peer effects studies related to student achievements in schools and college have employed various strategies to address these problems. The earliest studies on peer effects in educational attainment (Hanushek, 1971; Summers and Wolfe, 1977; Henderson, Mieszkowski and Sauvageau, 1978) took relatively few steps towards overcoming problems of peer-group endogeneity. However, more recent studies have applied the standard set of modern econometric tools. Some have tried instrumental variables approaches, although it is very hard to find instruments that are plausibly uncorrelated with unobserved individual attributes or do not have direct effects (Gaviria and Raphael, 2001; Robertson and Symons, 2003; Goux and Maurin, 2007; Kang, 2007). Several papers have sought identification from random year-to-year variation in mean peer group quality, occurring through ‘sampling’ variation as new cohorts are drawn from the population into schools, or as students move from one school to another. Variants of this approach appear in Hoxby (2000), Hanushek et al. (2003), Arcidiacono and Nicholson (2005), Gould, Lavy and Paserman (2009). Other papers rely on a cross-sectional school-specific fixed effects strategy, where variation in peer groups is between class groups, for example McEwan (2003), Vigdor and Nechyba (2007), Ammermueller and Pischke (2009) and Kang (2007). Calvo-Armengol, Pattachini and Zenou (2009) use detailed data on friendship networks, using fixed effects for groups of friends and exogenous variation in peer group achievement arising from the intransitive nature of the friendship network structure. Others have incorporated regression discontinuity designs based on class size rules (Angrist and Lang, 2004) or entrance exams (Ding and Lehrer, 2007). Occasionally, opportunities arise for analysis based on explicit randomization, or assignment that is plausibly random, given the institutional arrangements (e.g. Sacerdote, 2001; Cullen, Jacob and Levitt, 2003; Zimmerman, 2003; Angrist and Lang, 2004; Sanbonmatsu et al., 2004; Hoxby and Weingarth, 2005; Lyle, 2007; Carrell, Fullerton and West, 2009; Imberman, Kugler and Sacerdote, 2009; Duflo, Dupas and Kremer, 2011). Some designs included individual student fixed effects, relying on variation in differences in peer group quality for students moving schools (Burke and Sass, 2013), or for students taking different subjects Lavy, Silva and Weinhardt (2012). This last study is close to ours in that it studies the same school system and builds on our previous work and data. In their cross-sectional analysis, Lavy et al. (2012) find that students in school peer groups that have a comparative prior achievement dis-advantage in, say, maths, do slightly worse in maths than in other subjects. The drawback of their approach is that it is not based on any variation in peer group membership, but only on variation in the relative abilities in different subjects of a fixed group of students. Their approach thus, eliminates any influences from peer group background or motivation that is common across different subjects, and it is impossible to generalize the results to the case where a student moves into a peer group that performs better in all subject areas. Epple and Romano (2011) provide a more detailed recent review of theory and evidence on peer effects, highlighting the differences in the identification strategies adopted and the findings.

Even empowered with all these more sophisticated estimation methods and richer data than earlier studies, researchers are still divided on the importance of peer effects. However, it is worth emphasizing that even those studies that find statistically significant effects, tend to find relatively small effects: student achievement rises by <10%, of 1 SD for a 1 SD rise in peer group quality (measured in terms of the between-peer group variance). The outliers tend to be the studies based on IV approaches and/or single cross-sections. Our research design is the closest to the papers that use temporal variation in peer group quality over time. In the next section, we outline and justify this empirical strategy for assessing whether students derive any benefit from the prior academic achievement of their cohort schoolmates in England's secondary schools.

3 Empirical strategy

Linear in means regression estimates: methods

The aim of our empirical work is to estimate the effect of a secondary school students' peers' pre-existing achievements and characteristics, on his or her subsequent secondary school achievements. These are ‘contextual’ peer effects, to use the commonly applied terminology of Manski (1993, 2000). In what follows, we work with an aggregated panel design that allows us to estimate these effects on consecutive cohorts (c) of students making primary (p) to secondary (s) school transitions at age 11. Using this aggregated design allows us to exploit putatively exogenous, unanticipated year-on-year shocks to the peer group quality experienced by students making a given primary school to secondary school transition (ps) in different years. We refer to these groups, indexed by ps, as primary–secondary transition groups (or simply ‘transition groups’). As a result of this aggregation, there is one observation of each transition group in each cohort.4 As set out below, defining and aggregating to these groups allow us to control easily for transition group fixed effects and trends using first and second differences within transition groups, between cohorts. This aggregating and differencing help to eliminate similarities in unobservable school preferences and abilities.

Our design is based on a simple representation of peer group effects using the ‘linear-in-means’ formulation that is standard in the literature (i.e. we assume that mean peer group characteristics exert a linear effect on outcomes). The aggregating-and-differencing method we use is, however, generalizable to more elaborate types of heterogeneity and complementarity between groups with different characteristics and abilities (and non-linearities in peer group effects) as we discuss in section 3. The starting point for our empirical specification is a ‘value-added’ educational production function for groups of students in transition group ps in cohort c:

(1)

in which average secondary school achievements for each cohort of students in a given primary–secondary transition group () depends on student prior achievement and background characteristics that we can observe in our data (a); on mean peer group prior achievement and background characteristics in their secondary school cohort (ga); and on a composite error term. This error term includes unobservable components of secondary school quality (, excluding the peer effects represented by βga). The error term also includes unobservable characteristics of the students in the transition group (), that is unobservable student attributes, effects from primary school quality (including teaching, resources and primary school peer effects).

Our aim is to get consistent estimates of the parameter β in this specification, interpreted as the causal ‘contextual’ effect of secondary school peer characteristics, that is the expected difference in achievements between similar students who attend similar secondary schools with different peer group quality ga. It is well known that estimation of specifications of peer group effects models like 1 is problematic, because the unobservables are correlated with the group characteristics through self-selection of students into peer groups of different quality. In our case, this is because students are making choices over which secondary school to attend.5 Note that it is infeasible to control for secondary-school-by-cohort fixed effects to eliminate since this also eliminates variation in secondary school peer group quality. However, as set out below, we can use controls for primary-school-by cohort fixed effects and primary-by-secondary-school fixed effects to eliminate the main unobservables that are a source of concern in equation 1.

The first part of this strategy for mitigating the biases induced by these unobserved components is to control for fixed effects common to students making the same primary-school-to-secondary-school transition. We do this by first-differencing the variables across adjacent cohorts, within primary-school-by-secondary-school groups. This eliminates preferences and other unobservables that are common to students who make the same choices over primary and secondary schooling over the years in our data. This transformation also eliminates secondary school fixed effects and primary school fixed effects. As a second step, primary-school-by-cohort fixed effects components that are common to all students leaving primary school p in cohort c, can be controlled for in these first differenced models by using a within-group transformation (differencing the variables from primary-school-by-cohort means). The primary-by-secondary-school fixed effects control for cohort-to-cohort changes in primary school peer group and quality ( in equation 1), and which have a mechanical correlation with secondary school peer group (), given that the secondary and primary school peer group have common members. These transformations yield a final specification:

(2)

Here, the notation is defined to mean, for example for the peer group variable ga: where is the average of the secondary school peer group characteristics for students who were in the same primary school p in a given cohort c. The first component in brackets in this expression depends on the difference between the secondary school peer group of a group of students in a cohort from a given primary school, and the secondary school peer group experienced by their fellow students in the same primary school who went to different secondary schools.6 The second component in brackets is the same as the first, but for the previous cohort. Identification of β, thus, comes from the change between cohorts in the differences in secondary peer group quality experienced by groups of students making transitions to different secondary schools from the same primary school. This variation comes about due to between-cohort differences in observed achievements and characteristics (a) and from changes in the patterns of enrolment in secondary schools from year to year. The identifying assumption in our design, is that this shock to peer group quality upon moving to secondary school is unpredictable and unanticipated, uncorrelated with either primary or secondary school quality and, generally, uncorrelated with unobservable determinants of subsequent achievement at secondary school (i.e. it is ‘as good as random’). If the change in peer group is unanticipated, there is no potential for student sorting on secondary school peer groups. As discussed in section 3 below, there are good reasons to expect these changes in peer group to be unpredictable from the perspective of students making their school choices. This is because there is a random element in the school admissions process generated by fluctuations in the size of the age-cohort applying, and the preferences and constraints of this applicant pool.

Similarly, the (unobserved) secondary-school-by-cohort effects are transformed into that is the cohort-to-cohort change, in the difference in secondary school quality between one group of primary school students and their primary schoolmates who went to different secondary schools. Again if this change is unanticipated, there is no scope for biases due to selection on unobserved secondary school quality in this transformed specification.

We can further increase the likely validity of these assumptions of unpredictability in shocks to secondary school quality and secondary school peer groups by controlling for linear primary-school-by-secondary-school trends. This is easily done in our aggregated design by double-differencing the variables across adjacent cohorts, before applying the within group transformation, that is such that identification of peer group effects comes from:

(3)

7

Our aggregating-and-differencing design makes it feasible to control for these high dimensional time trends – for around 60,000 primary-by-secondary school groups in our empirical analysis below.

For estimation of equations 2 and 3, we measure secondary school achievement (y) by standardized ‘ks3’ national tests in maths, science and English taken at age 14. In our main estimates, prior achievement (a) on entry to secondary school in September at age 11 and the mean peer group prior achievements in secondary school (ga), are both measured by ‘ks2’ tests taken in primary school earlier in the same calendar year in May (the ks2 tests are comparable to the ks3 tests, but less advanced). We can further refine measurement of prior achievement and control for pre-existing student trends in achievement by controlling for tests at an even earlier stage in primary school, using data on the ‘ks1’ achievements of the same children at age 7. Our data provide additional information on student characteristics which we can use as control variables, and to provide alternative peer group measures, as discussed in section 3.

In summary, we use a data set of student ks3, ks2 and ks1 test scores and other student characteristics aggregated to primary-school-by-secondary-school-by-cohort cells. In our basic set-up, we regress mean ks3 test scores of this student group on the mean ks2 test scores of other students in same secondary school cohort, with controls for the student group's own mean ks2 test scores, primary-school-by-secondary-school fixed effects and trends (which, as explained above are eliminated by first or second differencing), and primary-school-by-cohort fixed effects (eliminated by the within-groups transformation).

There are several innovations here relative to previous peer group studies, which are feasible due to the fact that we study students changing schools between the primary and secondary phases. Firstly, aggregation to primary-school-by-secondary group cells allows us to eliminate high dimensional fixed effects and trends by simple differencing techniques. No equivalent aggregation is feasible in previous studies that do not exploit information on origin and destination schools for students moving between schools. Secondly, focussing on primary to secondary school transition means we have substantial changes in peer group composition between primary and secondary school. This implies that students from the same cohort in the same primary school end up going to many different secondary schools, generating wide variation in secondary peer group quality, conditional on primary school attended. Therefore, we can control for the initial conditions of students more effectively by including primary-by-cohort fixed effects. This is not feasible in studies which, for example simply track changes in peer group quality within the same school from one year to the next. Moreover, an important feature of the primary–secondary school transition process is that there are substantial changes between cohorts coming partly from cohort to cohort variation in student characteristics, but mainly due to random variations in the secondary admissions process. It is worth noting, finally, that there is no loss of salient information in this aggregated set-up, because any meaningful variation in peer group composition occurs at an even more aggregated, secondary-school-by-cohort level. Therefore, estimation at the individual level brings no particular advantages and makes eliminating multi-way high dimensional fixed effects and trends virtually impossible.

Extensions to the key results: background vs. primary schooling; heterogeneity

In the set-up above, peers' primary school test scores are just a marker for pre-secondary school achievement, which could embody: (i) peers' background characteristics and other ‘contextual’ factors (income, genetics, prior effort, parents etc.); (ii) teaching quality or other factors in peers' primary schools that are common to children attending those schools. Knowing which of these matters is important. Peer effects originating from prior schooling quality are potentially more interesting from a policy perspective, because they imply that teaching interventions feed through to others in later years through peer effect mechanisms implying long run ‘social multiplier’ effects (Glaeser et al., 2003). We assess the relative importance of these sources of influence, by partitioning peers' prior achievements into two components: the part due to family background and early-age achievements (age 7, ks1), and a part due to the test score gains they experienced during primary school (ks2 − ks1) scores.

Finally, to address questions about heterogeneity in students' response to their peers, and complementarities between student and peer characteristics, we estimate equations 2 and 3 separately for different student groups. Estimation in this case requires that we re-aggregate the data into primary-by-secondary-by-student-type-by cohort (psgc) groups:

(4)

such that, for example for Boys, we are differencing over time within groups of Boys making the same primary–secondary school transition. Coefficient provides an estimate of the influence of secondary school peers ks2 on students of type g.

All the above methods are applied to administrative data on school children in England. In the following sections we describe the institutional setting for our analysis, and the data we use.

4 England's school context

Compulsory education in state schools in England is organized into five ‘Key Stages’. The primary phase, from ages 4–11, spans the Foundation Stage, ks1 and ks2. At the end of ks2, when students are 10–11, children leave the primary phase and go on to secondary school where they progress through to ks3 at age 14, and to final qualifications at 16 (GCSE). At the end of each Key Stage, prior to age 16, students are assessed on the basis of standard national tests, although the ks3 tests were abolished after 2009. Students do not repeat grades or retake these Key Stage tests. Our study uses these national tests as a basis for estimating the effects of school intake quality on student achievement.

An important institutional factor underlying our analysis is the school admissions process at secondary level in England, since this governs the way students are allocated to schools. Our sample focuses on Comprehensive state schools, which do not systematically select students on the basis of prior achievement or entrance exams and represent over 90% of state school students. For the period of our study, there were about 2,700 secondary schools of this type England and about 14,500 primary schools.8 For most of these schools, the admissions process was one that might be called 'geographically constrained choice'. Applications were handled centrally by the relevant Local Authority (LA), and in London admissions across LAs were coordinated by a pan-London admissions body. Applicants list schools in order of preference, and in principle could choose any school. In practice, however, the choice is severely constrained by the rules that apply when schools are over-subscribed. These rules depend in part on the type of school in question.

During the years to which our analysis refers, the large majority of students attended ‘Community Schools’ (64% at secondary level). In this case, the LA employs the school's staff, owns the school's land and buildings and has primary responsibility for deciding the arrangements for admitting students. In the case of over-subscription, the LA applied a standard set of criteria for deciding admissions, typically prioritizing children with siblings in the school, children with special needs and children who live closest. Most other schools were faith 'Voluntary Aided' schools (15%), or were governed by some other charitable foundation (17%). Usually, these schools have greater autonomy from the LA than Community schools, and their oversubscription criteria may prioritize children who are practising in the religious denomination of the school. Other school types in our data include faith schools under Local Authority control ('Voluntary Controlled', 3%), City Technology Colleges (0.3%) and Academies (0.76%). The Academies are something like US Charter schools and have greater autonomy in admissions procedures, but are still constrained by a national Schools Admissions Code,9 and do not admit students systematically on the basis of test scores or other measures of achievements. Some Voluntary Aided, Foundation, CTC and Academy schools admit a minority (<10%) of students on the basis of aptitude in special skills such music. Since 2010, after the period covered by analysis, Coalition government policies have changed the school institutional, funding and admissions landscape considerably, with the emergence of many more ‘Academies’ and ‘Free Schools’ which have much greater degrees of autonomy and are free of Local Authority control.

The implication of these admissions' arrangements is that there is a lot of cross-sectional variation between schools in terms of the average achievements and characteristics of their intake. This variation exists because of the geographical location of the school and the characteristics of the residential neighbourhoods from which it recruits, and because of its reputation and ethos, and hence the types of families it attracts. Gibbons and Telhaj (2007) document some of these secondary school intake differences in ks2 achievements. Clearly, this cross-sectional variation is of limited use as a source of variation for estimating causal peer group effects, because it is the result of selection and sorting of students into schools on the basis of long-run and easily observed school characteristics, which will lead to spurious correlation between individual and group achievements. However, there is also considerable variation within schools, from year to year. This variation occurs because demographic changes and changing patterns of demand interact with the LA and school admissions criteria, to generate changes in the types of students admitted. One principle reason for this is that the geographical catchment areas of schools tend to expand and contract according to demand. This variation in demand is, in turn, driven by the size of the age cohort in the population, the preferences and constraints of the applicant pool, the number of applicants with siblings already at the school and the number of children with special needs. For example, a child who hoped to attend a particular local school may, unexpectedly, find they are outside the catchment area due to a high number of children in their birth cohort in a given year, or a high proportion of high-priority applicants with siblings already in the school. Similarly, a child entering a school which previously had high average intake ability from a narrow catchment area, could find lower than expected peer group quality because their age cohort is small, causing the school's catchment area to expand to encompass a more diverse student pool. Therefore, in any year, families may have to compromise on the schools they apply for, may not be awarded their first choice of school, and the peer group quality in the school may change in ways that they had not anticipated. Although the data on school admissions indicate that nationally, some 84% of families get their first choice school (DfE Secondary School Applications and Offers in England data 2011), this figure is potentially misleading about fulfilment of preferences, because families are unlikely to request schools for which they have no chance of admission. For instance, LAs typically publish the maximum geographical radius to which offers were made from each school in the previous year, which is likely to deter families from listing preferred schools that lie beyond this distance. In short, there is always some compromise and an element of uncertainty involved in choice of school, meaning not all choices are optimal. Our empirical analysis exploits the putatively random components of this variation over time as a source of exogenous variation in intake and peer group quality.

Our peer group quality measure is school-by-cohort mean prior achievement (and other characteristics in some specifications). Using school-by-cohort peer group definitions rather than class-based definitions avoids biases induced by within-school sorting and selection, and provides a consistent estimate of linear in means of peer effects in class groups if the assignment to classes within schools is random. Under these conditions, if individuals are influenced by peers in multiple classes within their school cohort, then measuring the peer group in just one of these classes would introduce a measurement error and lead to downward biased estimates. However, a common counter-contention is that the school-wide peer group definitions mask the causal effect of class peer groups, because setting (streaming) within schools implies that a given student does not experience the peer group implied by the school-mean peer characteristics. In practice, for marginal changes in school peer group mean achievement, setting/streaming into classes that are stratified by prior achievement is unlikely to undo the relationship between improvement in school-mean prior achievement and class-mean prior achievement. Any rightward shift in the distribution at school level will cause a rightward shift in the mean in each stratified class group, so raising the peer group mean for students in the middle of the distribution in each class group. However, for large non-marginal changes in school intake, students with achievement at the bottom of each class in a stratified class structure would find themselves in a lower set, so would experience a deterioration in peer group quality within their class as a consequence of a school-mean increase in intake quality. Similarly, students who would have been at the top of a class could find themselves at the bottom of a higher class if there was a deterioration in school-mean intake achievement. The exact consequences clearly depend on the specific institutional context.

Generally, in England's Comprehensive schools, students are not taught in the same groups for all lessons but mix with students from throughout their age-cohort, which motivates our school level peer effects approach. Although there are no recent comprehensive surveys of practice in England's secondary schools, what evidence there is (Ireson, Hallam and Plewis, 2010), combined with anecdotal evidence and personal knowledge of the system, indicates that ability setting is prevalent, but was not pervasive during the years in our data. It is more likely to occur in maths, and in science where the ks3 tests were organized into 'tiers', two in science and four in maths. In these subjects, students were entered into the tests in a specific tier which tested across their ability levels, and students could only achieve a result on the test that was within the range of the tier into which they were allocated. The ideal design might involve instrumenting a measure of class (or other sub-school peer group) quality with the school-level variables, but in the absence of information on classes, or subject specific streaming practice, we maintain school-wide measures of peer quality as the best indicator of peer group exposure available to us. In section 3, we will present evidence based on subject specific effects and school sizes that supports this approach.

5 Data sources

The UK's Department for Education (DfE) collects a variety of data on state-school students centrally, because the student assessment system is used to publish school performance tables and because information on student numbers and characteristics is necessary for administrative purposes – in particular to determine funding. A National Student Database (NPD) holds information on each student's academic assessment record in the Key Stage Assessments throughout their school career, starting in 1996. For our period of study, assessments at ks1, ks2 and ks3 (ages 7, 11 and 14) included a test-based component and teacher assessment component for core curriculum areas. At ks2 and ks3, these core subjects were maths, science and English, with reading, writing and maths tested at ks1. We work with the overall test score in these subjects at ks2 and ks3, and with a points-based grading system at ks1. All scores are converted into percentiles of the student distribution within our estimation sample and so the results are scaled as effects on student rankings within the national distribution of school achievement.10 Using these data, we create own-achievement measures at ks1, ks2 and ks3 and calculate peer group mean ks1 and ks2 achievement at the point of entry into secondary school.

Since 2002, a Student Level Annual Census (PLASC) records information on students school, gender, age, ethnicity, language skills, any special educational needs or disabilities, entitlement to free school meals and various other pieces of information including postcode of residence (a postcode is typically 10–12 neighbouring addresses). PLASC is integrated with the student's assessment record in the NPD, giving a large and detailed data set on students along with their test histories.

From these sources, we derive an extract that follows four cohorts of children from their ks1 primary school test score results at age 7, through to their ks2 tests at age 11, and on to their ks3 secondary school results at age 14. These four age-cohorts took their ks3 tests in 2004/5–2007/8. Various other data sources can be merged in, either at school level (school types and other characteristics) or at students' residential neighbourhood using postcodes and Census area codes. In our empirical analysis, we will use various Census 2001 residential neighbourhood characteristics (including unemployment rates, adult qualifications, proportion of socially rented homes and ethnicity) as control variables, and for balancing tests. Our data cover students in all comprehensive state schools (non-selective) of the types discussed in section 3.11

This large and complex combined data set provides us with information on around 1.6 million children aged 14 for the period 2004/5–2007/8.

6 Results

7 Discussion and conclusions

The results in the paper suggest that student academic achievement at age 14 in England is influenced by the prior, age 11 achievements of their secondary school peers. In England, students re-sort themselves into new school groups when they move from primary to secondary schools at the age of 11. Part of this re-assignment is through preference, and part will be random because of failure to secure schools of choice or because of unanticipated variation in peer group quality within schools of choice. We have used this re-allocation at age 11 as a source of variation in peer group quality within primary–secondary school pairs over time and employed a unique, aggregated, cohort-differenced research design that controls for primary-by-cohort fixed effects and primary-by-secondary fixed effects and trends. The design controls for sorting and selection into schools and for unobservable factors affecting students who make similar schooling choices. Given the richness of our student record data set, we have – unlike any previous study – also been able to control for student's achievement at a much earlier stage in a student's school career using data on test scores at age 7. A range of balancing tests supports our identification strategy, showing that our peer quality measure is not correlated with individual student, school and neighbourhood characteristics once we control appropriately for primary-by-secondary and primary-by-cohort fixed effects.

Our general finding is that school-level peer effects exist, but they are small in magnitude: a 1 SD increase in the mean ks2 primary school scores of secondary schoolmates is associated with a 0.02 SD increase in student achievement in secondary school ks3 achievement. These peer effects originate in characteristics of secondary school peers that were already evident in their achievements at age 7. Direct effects from family background, conditional on early achievement and progression during the later years of primary schooling preceding secondary school entry take a backseat role. This finding suggests a rather limited role for peer effects in amplifying the effects of educational interventions (e.g. social multiplier effects as in Glaeser et al., 2003), unless these interventions occur very early on in life. Our results show no heterogeneity across student demographic types or ability groups.

The magnitude of our estimates is in line with, or lower than previous quasi-experimental and experimental studies. This finding adds weight to the argument that group composition matters little, relative to other factors (such as student background) that drive differences in achievements between students. However, scaled relative to other school-level factors that influence student achievement, peer effects of this magnitude are not inconsequential, because schools overall contribute relatively little to differences in achievement between students. For example, Kramarz, Machin and Ouazad (2009) estimate school fixed effects on student achievement from a panel of primary school students in England, and find that the correlation of school fixed effects with student achievement is around 0.12–0.16, that is a 1 SD improvement in school quality overall raises student achievement by 0.12–0.16 SD. Some of the biggest effects claimed in the economics of education literature are general teacher quality impacts, estimated from teacher fixed effects in student value-added models on multiple cohorts of students. Typically, in this literature (Hanushek and Rivkin, 2010), a 1 SD increase in teacher quality also leads to a 0.10–0.15 SD improvement in student achievement. Benchmarked against this, peer group effects of the order of magnitude we find here are not inconsequential. Of course, test scores are not everything, and better peer-groups might also provide other immediate and long-run benefits which we are not measuring – physical safety, emotional security, familiarity, lifetime friendship networks or simply exclusivity – which make schools with good peer groups desirable commodities, regardless of whether they offer any short-run educational advantages. These issues remain open for future investigation.