Institute for Economic Studies, Keio University
Keio-IES Discussion Paper SeriesPeer Learning in Teams and Work Performance: Evidence from a
Randomized Field Experiment
Kenju Kamei、John Ashworth

5 April, 2022
DP2022-005
https://ies.keio.ac.jp/en/publications/18310/

Institute for Economic Studies, Keio University
2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan
ies-office@adst.keio.ac.jp
5 April, 2022

Peer Learning in Teams and Work Performance: Evidence from a Randomized Field
Experiment
Kenju Kamei、John Ashworth
Keio-IES DP2022-005
5 April, 2022
JEL Classification: C93, J24, I23
Keywords: peer effects;dilemma;field experiment;teamwork;knowledge sharing

Abstract
A novel field experiment shows that learning activities in pairs with a greater spread in
abilities lead to better individual work performance, relative to those in pairs withsimilar abilities. The positive effect of the former is not limited to their performance inpeer learning material, but it also spills over to their performance in other areas. The
underlying improvement comes from the stronger increased performance of those
whose achievements were weak prior to peer learning. This implies that exogenously
determining learning partners with different abilities helps improve productivity
through knowledge sharing and potential peer effects.

Kenju Kamei
Faculty of Economics, Keio University
2-15-45 Mita, Minato-ku, Tokyo
kenju.kamei@keio.jp
John Ashworth
Department of Economics and Finance, Durham University
Durham University Business School, Mill Hill Lane, Durham DH1 3LB, United Kingdom

Peer Learning in Teams and Work Performance:
Evidence from a Randomized Field Experiment

Kenju Kamei,1,* and John Ashworth2
1
2

Faculty of Economics, Keio University

Department of Economics and Finance, Durham University

April 2022

Abstract: A novel field experiment shows that learning activities in pairs with a greater
spread in abilities lead to better individual work performance, relative to those in pairs
with similar abilities. The positive effect of the former is not limited to theirperformance in peer learning material, but it also spills over to their performance inother areas. The underlying improvement comes from the stronger increased
performance of those whose achievements were weak prior to peer learning. Thisimplies that exogenously determining learning partners with different abilities helps
improve productivity through knowledge sharing and potential peer effects.
JEL classification codes: C93, J24, M53, M54, I23
Keywords: peer effects, dilemma, knowledge sharing, field experiment, teamwork

Acknowledgement: The authors thank all the staff in the undergraduate office in Durham
University for facilitating the peer review assessment activities in the 2019/20 academic year,
and also Ashlee Bennett for organizing background data of the students. The authors thank Pedro
Dal Bó and Katy Tabero for their helpful comments.
*

Correspondence Author: Faculty of Economics, Keio University, 2-15-45, Mita, Minato-ku,

Tokyo 108-8345, Japan. Email: kenju.kamei@gmail.com, kenju.kamei@keio.jp.

11. Introduction
Situations in which peers interact with each other to improve performance, while aiming
to achieve individual goals, are ubiquitous whether in schools, daily lives, or the workplace. A
key to achieving a Pareto optimal outcome is successful collaboration among peers. Benefits
from peer interactions may be strong when they have heterogeneous abilities and skills if the lessendowed interact with and learn from the highly endowed, because the former has larger room
for improvement. A dilemma, nevertheless, exists since peer learning interactions may not becost-free and benefits may be small for the highly endowed individuals.
Prior research suggests that people’s individual performances, whether work-related oracademic, are affected by other members in their peer groups due to peer pressure and learning
through social interactions (e.g., Katz et al., 2001; Sacerdote, 2001; Falk and Ichino, 2006; Mas
and Moretti, 2009). For example, peer interactions and learning are powerful practices in firms
and organizations (e.g., Ichniowski et al., 1997; Hamilton et al., 2003). However, how peergroups should be formed is not straightforward. First, peer interactions are known to lead tobetter overall work performance in a group with heterogeneous rather than homogeneous
abilities and skills1 under individual-based remunerations (i.e., each member is evaluated basedon their own individual performance), even though the average abilities and skills are similar forthe two types of groups (e.g., Carrell et al., 2009; Lyle, 2009; Duflo et al., 2011; Feld and Zölitz,2017). The superiority of group heterogeneity is driven by high-ability (-achieving) members.
They are able to and tend to form subgroups with like-minded high achievers, thereby leading toa further improvement of their performances. In contrast, low-ability (-achieving) members
suffer, although, on average, overall performance is better thanks to the strong improvement ofhigh types. It is therefore difficult to judge the efficacy of heterogeneity normatively. Second,groups with a greater spread in abilities are likewise known to have an advantage under group
incentives, that is, when members are evaluated based on their group performance. The
underlying mechanism is, however, different, and is the so-called mutual learning hypothesis:
under group incentives, more able workers not only impose norms for the sake of othermembers, but they also teach less able workers (e.g., Ichniowski et al., 1997; Hamilton et al.,2003). Hence, the finding from the second branch of the literature implies that a way to form asocially-desirable peer group under individual-based remunerations may be to have a sufficiently
small peer group with a greater spread in abilities, thereby preventing sub-groups fromendogenously emerging and, at the same time ensuring a pairing between more able and less able

1

The former (latter) group is also called a “heterogeneous” (“homogeneous”) group, hereafter, in the paper.

2

workers. Such pairing may result in a Pareto improvement through effective mutual learninginteractions. This paper experimentally manipulates interim achievement differences in pairs andthen studies how the intervention affects individual work performance.
While it is unclear how the mutual learning hypothesis extends to the case of a small
group under individual incentives, pairing a more able worker with a less able worker for peer
learning has an advantage at least from a theoretical perspective. For example, experimental
literature suggests that people have social image concerns and other-regarding preferences (e.g.,
Ariely et al., 2009; Shang and Croson, 2009). Pairing with a high-ability worker may give thelow-ability worker a particular incentive to work hard to avoid incurring disutility from social
effects, such as shame and harming their social image (e.g., Bénabou and Tirole, 2006 and 2011;
Bowles and Gintis, 2015). Such a pairing may also change reference points of the less able
workers if they have poor work attitudes and are over-optimistic about their own performances(e.g., Abeler et al., 2011; Svenson, 1981). High-ability workers may also try helping low-ability
ones from inequality aversion if they are required to interact with each other (e.g., Fehr andSchmidt, 1999). A possible concern is, however, a perverse reaction by high-ability workers:
those who are forcibly matched with low-ability ones contrary to their preferences may notcontribute their best efforts in peer learning activities (e.g., Kamei and Markussen, 2020).
This paper provides clean evidence from a randomized field experiment in a classroomthat pairing individuals with a large achievement difference, rather than with similarachievement levels, leads to better overall performance on average. All first-year undergraduate
students in accounting and finance took a compulsory first-year introductory course ineconomics in Durham University during the 2019/20 academic year. This was a full-year course
which began in the first term of the academic year. Students learned microeconomics in the firstterm, and macroeconomics in the second term. The students’ performances were evaluated solely
based on their own marks in a written examination which took place at the end of the academicyear.
The students’ learning activities were composed of attendance in lectures, engagement inbi-weekly mandatory seminars (whose size was 15 to 20 students), two formal written
assignments (one for each term), and two peer review assessment activities (one for each team).
In the peer review assessment activities, each student was paired with another in their respective
seminar group. They independently attempted a problem set, after which they critically assessed
their partner’s solutions and then discussed the problem set in pairs by holding a meeting. Pairpartners were changed between terms 1 and 2. An intervention was made for the peer review
activities in term 2: while each student was randomly assigned their pair partner in half of the3seminar groups (treatment condition), pairs were formed so that their interim class performanceswere similar to each other in the other half of the seminar groups (control condition). Thus, pairs
in the treatment condition had a greater variation in interim achievement levels between pairmates, relative to those in the control treatment. Partner assignment was random in all seminargroups for term 1.
The exam performance data show that students were higher-achieving on average in thetreatment than in the control condition. This underscores the effectiveness of having a pair with agreater spread in prior performances for peer learning in organizations. A close look at the data
reveals that the worse performers improved academic performance significantly more than theirmatched better performers in pairs belonging to the treatment condition. This suggests thatconsistent with the mutual learning theory, exogenously determining learning partners withdifferent abilities helps improve productivity through knowledge sharing and positive peer
effects. Further, interestingly, the students in the treatment groups showed better understandingof even the term 1 material in the examination, suggesting that their peer learning experiences inmacroeconomics spilled over to their understanding of microeconomics. This may mean thatworse performers improved study habits when revisiting the term 1 material for the exam. Suchproductivity spillovers within individuals further imply the importance of devising an effective
pairing procedure.
The rest of the paper proceeds as follows: Section 2 describes the related literature, andthen Section 3 discusses the background, the experimental design, and the procedure. Section 4
provides hypotheses based on behavioral models and 5 presents the results. Section 6 provides
discussions and concludes.
2. Related LiteratureThis study is closely related to three branches of the literature in labor, organizational andpersonnel economics, experimental economics, and economic education: (a) peer interactions inheterogeneous teams, (b) peer pressure and productivity, and (c) mutual learning theory. Whilethe literature in (a) seem to suggest that teams with homogeneous rather than heterogeneous
abilities and skills lead to better performance, the literature in (b) and (c) suggests the opposite.
However, prior research, on balance, suggests the superiority of heterogeneous teams.
2.1. Peer Interactions in Heterogeneous Setups
A key aspect of teamwork in teams is how students share knowledge and skills with theirteammates. Such a peer interaction structure can be described by an asymmetric public goods
game as students’ knowledge and abilities differ according to their backgrounds and unobserved4characteristics, and knowledge sharing is a typical example of a social dilemma. A richlaboratory experiment literature suggests that collaboration would be less successful in aheterogeneous rather than a homogeneous setup, because the tension between highly and lessendowed members is usually intense. For example, in a team where endowments are unequallydistributed, members’ endowment sizes are known to be negatively correlated with their levels ofcooperativeness in the voluntary provision of a public good (e.g., Chan et al., 1996; Kamei,
2018; Maurice et al., 2013). For example, in Kamei (2018), while the average contribution of thehighly endowed was less than 10% of their endowment, that of the least endowed was more than
50% of the endowment on average.
Further, a negative effect of productivity heterogeneity in teams among team members
was also reported. For example, Fischbacher et al. (2014) experimentally showed thatheterogeneity in returns, i.e., Marginal per capita return (MPCR), from contributing to a public
good undermines cooperation, perhaps driven by members’ pessimistic beliefs about others’
contribution behaviors.2
In sum, this line of the literature suggests higher academic performances through more
successful collaboration in homogeneous rather than heterogeneous teams. Having said that, theprevious experiments listed above were conducted under anonymous conditions in a laboratory(where subjects’ identities, such as faces and names, were not revealed to each other) and also
subjects’ individual contribution decisions were not verifiable since the experiments were
designed based on public goods games with group sizes of at least three. Hence, the earlier
findings may not apply to the setup of the present study since students’ interactions within pairs
in the peer review assessment activities are made with full transparency here. Literature in (b) infact suggests the positive impact of observability – see Section 2.2. Most of the empiricalresearch or randomized field experiments in literature (b) and (c) used non-anonymous setups,
finding the superiority of team heterogeneity – see Sections 2.2 and 2.3.
2.2. Peer Pressure and Productivity
There is a substantial literature, both theoretically and empirically/experimentally, for therole of peer pressure on influencing behaviors. Much theoretical research suggests that having
detailed information about members’ behaviors per se, such as through peer review assessment
2

The positive impact of homogeneity is not limited to the distribution of resources or productivity. Prior
experimental research on sorting in public goods games found a higher level of cooperation when like-minded
individuals (in terms of cooperative dispositions) are grouped together rather than otherwise, although whether
cooperation norms prevail in a group depends on the group’s cooperativeness – for example, see, Gunnthorsdottir etal. (2007) and Gӓchter and Thöni (2005). In Page et al. (2005), even the average contribution of groups where lesscooperative subjects were grouped together were not that low under sorting.

5

activities in the present study, may trigger positive effects on work performance. For example,
working in teams could trigger social image concerns among members, thereby encouraging
hard work to be recognized by others (e.g., Bénabou and Tirole, 2006 and 2011). Because highobservability makes it possible to compare self with others, teamwork could also trigger social
effects, such as guilt, shame and pride, among members in teams (e.g., Bowles and Gintis, 2015),
hence inducing them to study harder to achieve better academic performance.
Laboratory experiments support the idea that high visibility encourages socially-desirable
behaviors under certain conditions: e.g., voluntary contributions to a public good (e.g., Samekand Sheremeta, 2014), direct punishment of norm violators (e.g., Kamei and Putterman, 2015),
third party enforcement of social norms (e.g., Kamei, 2018), and charitable-giving (e.g., Ariely etal., 2009; Soetevent, 2005). For example, in a real-effort experiment where no material
incentives were associated with effort provision, Ariely et al. (2009) demonstrated that worker
subjects exert stronger efforts for charity when they have to tell others about their own donation
amounts than when their identities and acts remain anonymous. In the context of this study,
students can realize their partners’ achievement levels in the peer review assessment activities,
which would give the less able student in a pair an incentive to work hard in and after the peer
review activities so that she can avoid incurring disutility due to such information effects frombeing seen her weaker performances by her pair mate or other students outside the peer review
activities. This kind of behavioral effect would be larger, the larger ability difference a pair has.
Hence, it can be predicted that the learning effects of peer review activities would be on averagelarger in pairs with heterogeneous than with homogeneous abilities.
The information effect in pairs is not limited to the social effects. For example, information
about peers’ strong efforts and/or performance may change the reference points of the less able
students (e.g., Abeler et al., 2011). For example, Shang and Croson (2009) found that people
donate larger amounts when they are informed of others’ active charitable-giving behaviors, evenif own donation amounts are kept private (also see Croson and Shang [2008]). This line of theliterature again suggests that students’ learning outcomes in the present paper would on average behigher in pairs with a greater spread in abilities and skills, since the less able students can becomeaware of their academic positions through the peer review assessment activities, thereby updating
their expected study behaviors. This prediction may be reinforced by the fact that workers are on
average known to have overconfident and biased beliefs about own ability (e.g., Langer, 1975;
Svenson, 1981; Larkin et al., 2012).
During the last two decades, economists have devoted considerable efforts into identifying
peer pressure and interactions in realistic setups using randomized field experiments. Prior
6research can be broken into either (i) peer effects with (possible) social interactions – simply “peereffects,” hereafter (e.g., Katz et al., 2001; Sacerdote, 2001; Carrell et al., 2009; De Grip andSauermann, 2012)3 or (ii) peer effects without direct interactions – “pure peer effects,” hereafter(e.g., Falk and Ichino, 2006; Guryan et al., 2009; Brune et al., forthcoming).
The research area of (i), the closest to the present experiment, suggests positive peer
effects. For example, based on random assignment of university students to dorms and roommates,
Sacerdote (2001) found that assigned peers have a strong impact on own academic achievement
measured by grade point average – see also Carrell et al. (2009) who showed similar academic
peer effects for random assignment of students to large peer groups called squadrons. In thecontext of residential neighborhoods, Katz et al. (2001) likewise found positive peer effects, basedon a research design with random assignment of housing vouchers to poor families. In the context
of the workplace, De Grip and Sauermann (2012) studied peer effects among call agents (whowork individually) in call centers. They found that work-related training not only improves theworker productivity, but it also leads to an increase in the productivity of coworkers that did notparticipate in the training program. These positive peer effects can be thought of as having two
components: (a) the mere effects from high visibility and the presence of peers, and (b) local
social interaction effects.
While these studies successfully provide insights into the role of peers, suggesting thatpeer effects lead to similar behavioral outcomes among peer mates, the recent literature further
advances the mechanisms behind peer effects by exploring how it is affected by teamheterogeneity. Its main finding is on the superiority of heterogeneous teams in terms of abilities,
and peer effects differ largely by the ability and achievement level. The research discusses thathigh-ability (-achieving) individuals gain more than low-ability (-achieving) ones in aheterogeneous team (e.g., Lyle, 2009; Duflo et al., 2011; Carrell et al., 2013; Feld and Zölitz,
2017; Booij et al., 2017). This is because the former tend to benefit more from like-minded hightypes in social interactions within a heterogeneous team, as they selectively form sub-teams withlike-minded high types, while low-ability (-achieving) individuals are hurt in peer interactions.
Such sorting is not possible in homogeneous teams. The proportion of females in a peer group isalso known to enhance positive peer effects (e.g., Black et al., 2013; Lavy and Schlosser, 2011; Lu
and Anderson, 2015).
Albeit quite convincing, one issue for some randomized field experiments with a large
scale, such as Sacerdote (2001), is its internal validity of the research in that there are no controls

3

Roughly speaking, this can also be called social effects in the term used by Charles Manski (e.g., Manski, 1993).

7

for the ways in which individuals interact with each other locally. This means that one is unable
to underpin what kinds of social interactions exactly triggered the positive peer effects in thesestudies. The present paper uses a microenvironment that clearly specifies who interacts withwhom, and in what way. As discussed in Section 3, each student, divided into either treatment orcontrol groups, has the same learning activities with their assigned partner using a predetermined pair activity. The intervention may create positive peer interactions locallyafterwards to achieve their individual goals.
Another common feature of the prior research is that peer groups are large in mostpapers: for example, the peer group size is a squadron consisting of 30 students in Carrell et al.
(2009), 35 cadets per company in Lyle (2007, 2009), and 10-15 students per classroom section in
Feld and Zölitz (2017). While a large peer group size is ubiquitous in our real lives, a smaller
peer group is also equally common (e.g., pair work in an academic environment such as aclassroom, police officers patrolling in pairs). The present paper uses the minimum peer groupsize – a two-person pair. The use of the smallest size has a methodological advantage as a better
control: its setup makes it possible to specify who interacts with whom, while classifying a betteror worse performer in each pair, and excluding possible formation of sub-teams. This setup maylead to a result different from the earlier established finding on the heterogeneous treatment
effects. For example, the worse performer may benefit more through peer learning since herpaired better performer has no choice but to interact with him in the activity. This paper
supplements a large body of the prior research with randomized field experiments by providing
clean evidence on the role of team heterogeneity in peer interactions when the peer group size issufficiently small.
It is not possible to identify how large the pure peer effects would be according toliterature (i). This question was investigated by using clever setups with high internal validity byvarious sets of authors, for example, in the context of part-time jobs by Falk and Ichino (2006),
pluckers working in an agricultural firm by Brune et al. (forthcoming), and professional sports
tournaments by Guryan et al. (2009). Most studies, such as Falk and Ichino (2006) and Brune etal. (forthcoming), found positive pure peer effects, although some studies (e.g., Guryan et al.,2009) did not find such effects. While the sizes of pure peer effects vary largely across the labormarkets and different contexts, a meta-analysis in fact showed that pure peer effects would be on
average positive (Herbst and Mas, 2015).
2.3. Mutual Learning Theory
A rich body of the empirical literature in labor and personnel economics discussed thatsocial interactions (e.g., communication) among peers and training help improve individual
8

productivity. For example, Ichniowski et al. (1997) documented that innovative human resource
management practices used in steel finishing lines improved productivity. The practices include
enhanced communication practices among workers and skills training, combined with manyother aspects such as high involvement in teams and employment security. Using data from a
garment plant, Hamilton et al. (2003) found that, while given a choice workers sorted into
teamwork, rather than individual work, teams with a greater spread in abilities were moreproductive under team-based remuneration. They discussed that this phenomenon can be
explained by an intra-team bargaining model (i.e., high-ability workers impose strong norms)
and the mutual learning theory (i.e., high-ability workers teach less-ability ones).
While the prior research was successful in showing the importance of incentives, peer
learning and team heterogeneity, it is not possible to measure the effects of peer learning in
isolation, since the practices contain at least several dimensions at the same time. It is also not
clear how more able workers teach less able workers if each worker is compensated based only
on their individual performance.
The impact of productivity spillovers was also empirically identified in specific sectors,
suggesting that it may be positive. For example, Arcidiacono et al. (2017) showed that
productivity spillovers among professional players play an important role in the team outcomesin the National Basketball Association. Mas and Moretti (2009), using high-frequency scanner
data, showed that introducing a high-skilled cashier to a shift would improve other cashiers’
productivity in supermarket chain stores. See also Azoulay et al. (2010) for research productivity
spillovers among academics and Jackson and Bruegmann (2009) for the case of teachingeffectiveness in elementary schools. Nevertheless, it is unclear exactly what kinds of social
interactions or learning (if any) triggered positive effects on those involved in the prior studies.
3. Background, Experimental Design and Procedure
The Introduction to Economics module (ECON1101) is a core compulsory module that
all the first-year undergraduate students in finance and accounting (a total of 250 to 350 students
dependent on the year) must take at Durham University. A “module” is a term used in the United
Kingdom to refer to a course. Teaching in a module is organized and implemented by a teachingteam. As the very first economics module, students learn the basic principles of economics, andthe module serves as a foundation for upper-year core modules in micro- and macroeconomics.
Even though it is the first introductory course, because Durham University is highly ranked in
the United Kingdom with high quality entrants, students learn some technical aspects, such as
mathematical calculations for Cournot competition, the Solow growth model and the IS-LM

9

model. ECON1101 consists of ten weeks to study microeconomics (term 1) and nine weeks tostudy macroeconomics (term 2) – see Figure 1. The students’ performances are evaluated solely
based on one written examination (summative assessment, hereafter) which takes place at theend of the academic year (at the end of May). The maximum (minimum) mark given is 100 (0).
Each student will be given an academic grade based on their own mark. The grade is: first class(≥ 70), second class (below 70 but ≥ 50), third class (below 50 but ≥ 40), or fail (below 40). Boththe raw mark and grade will be written in the student’s official transcript.
The summative assessment consists of three parts: Parts A, B, and C. Part A consists of
two short-answer questions, each of which accounts for 10% of the assessment mark. Part B (C)consists of two questions from microeconomics (macroeconomics), and each student must selectone of the two questions. Parts B and C each account for 40% of the assessment mark. Most
questions are essay-type (the summative assessment can be found in Supplementary materials
Section A.7). The examination is held online and students need to complete the problem set in a
48 hours window when the problem set is distributed.4 There is a rigorous word limit: themaximum word count is 3,750 words (markers will stop reading once the maximum word countis reached).5 Students are instructed not to copy and paste from textbooks or lecture notes (copies
and pastes are not given marks). A plagiarism check is also performed for each script by theundergraduate office and also by the Turnitin software. Kamei was the module leader for
ECON1101 for the 2019/20 academic year and Ashworth was the department head when the
randomized field experiment was planned before the academic year started (he was thedepartment head from 2016 to 2019). The experiment was designed and implemented using thestudents of this module for the 2019/20 academic year.
Students have four key learning activities. The first one is weekly two-hour lectures.
Kamei delivers lectures in term 2, while another faculty member does so in term 1.6 The lectures
are held in a large lecture hall, and all students take the same sessions. The lectures are designed
to introduce the key economic concepts and methods, and to present the technical analysis inaction. They are always accompanied by presentation slides (and sometimes also mathematical4

The summative assessment is released on May 25, 2020 at 9 am, with the deadline being May 27 at 9 am.
Marking is operated through a rigorous double-marking procedure. The university appoints first markers and second
markers in this module. When each first marker finishes marking their assigned set of scripts, second markers
independently determine marks on randomly selected scripts (see the University’s Learning and Teaching handbook).
6
Lecturing of macroeconomics is the only teaching duty of Kamei. Kamei is responsible for the management of themodule (e.g., coordinating with the other lecturer in term 1, monitoring the teaching work of seminar tutors duringterms 1 and 2). The allocation of teaching and the make-up of teaching teams and duties within the teams are
determined by the department with the members of staff informed of the team and responsibilities for the modelprior to the start of the 2019/20 academic year.
510

handouts) whose electronic files are distributed to every student through a Blackboard (DUO)
prior to the lectures. The lecture time is not designed as interactive (rather one-way delivering of
key concepts), although students have some opportunities to raise issues and confirm theirunderstanding of the analysis. Other than lectures in terms 1 and 2, there are two additional
lectures (one for microeconomics, and the other for macroeconomics) in term 3, i.e., revisionperiods, as reviews before the summative assessment.
Second, students have one-hour mandatory seminars in every other week (a total of four
seminars for microeconomics in term 1 and another four for macroeconomics in term 2). The
students in accounting and finance are allocated to one of the 16 seminar groups by theundergraduate office.7 Each seminar group has around 15 to 20 students. There are three tutors in
the module. One tutor is responsible for seven seminar groups in term 1, while another tutor is
responsible for the other nine groups in term 1.8 The third tutor is responsible for all 16 seminargroups and uses the same instruction across the 16 groups in term 2. This would minimize thepossible effects of common shocks (e.g., Lyle, 2007). Students’ learning could, nevertheless, beaffected by their assigned seminar group since they have social interactions there. Hence, seminargroup clustering is included for all data analyses such as regression analyses in Section 5.
A problem set is distributed to students one week prior to a given seminar session, andstudents are expected to attempt those questions before the class. Seminars are designed to beinteractive. While a seminar tutor explains the answer, students are also invited to discuss theiranswers in their seminar group. This means that the unit of independent observation is seminars.
Students’ attempts before the seminar are not checked (nor are these activities subject tostudents’ final marks). However, attendance at seminars is mandatory and registers are taken inall sessions as an important academic commitment.9
Third, students have one formative assessment – simply “formative” hereafter – in eachterm (two pieces in total). Students must answer a problem set and submit their answers
officially to the university. The term 1 formative asks questions on the producer theory, while theterm 2 assessment asks those on the short-run macroeconomics – see the problem set in
Supplementary materials Section A.3 and A.5. The seminar tutors mark the scripts online, and7

The undergraduate office (using a University algorithm) is fully responsible for the allocation. Anyone in theteaching team, including the module leader (Kamei), is not at all involved in the allocation process.
8
As students’ performances might be affected by the difference in the seminar tutor in term 1, term 1 tutor
assignment is controlled by having a dummy variable when estimating treatment effects in data analysis (Section 5).
9Students were also informed: “Failure to attend without a prior arrangement will be noted and any student who
misses a seminar without having made a prior arrangement should attend their tutor’s next consultation hour.
Persistent absences will result in our instigating formal monitoring processes.”11

provide individual feedback to each student. While the marks are not be counted towards their
final marks, they are recorded in the students’ information sheet in the university. The formative
aims to help students understand the material and its applications in a structured way, as well as
help them prepare for the summative assessment. An intervention was made in term 2 utilizing
the students’ performances in the term 1 formative (further details below).
The fourth activity is a peer review assessment (PRA), for which a randomized control
trial is implemented (the above three learning activities are identical to all students). This activity
starts earlier than the formative assessment in each term. In the PRA activity, students are first
distributed a problem set whose format is the same as the formative (e.g., on October 28, 2019
for term 1), attempt the problems independently, and then submit their scripts officially to theuniversity (e.g., the submission deadline is November 8, 2019 for term 1). The term 1 peer
review assessment asks questions on the consumer theory, while the term 2 assessment asks
those on long-run macroeconomics. Notice that the topic of the PRA is different from that of theformative. The problem set can be found in Supplementary materials Section A.2 and A.4. Oncethe submission deadline passes, students are informed of their pair partner (e.g., on November
11, 2019 for term 1). The seminar tutors collect students’ scripts of the respective seminar groups
from the undergraduate office and give students their partners’ scripts during the following
seminars. Each pair works together to discuss the problem set and their scripts. The procedureuses a proforma prepared by the authors – see Supplementary materials Section A.6 for the
proforma in term 2 as an example. Specifically, each student critically assesses their partner’s
script by completing Part A of the proforma for each question, has a meeting in their pair, gives
their partner the proforma so that the partner can write afterwards what they learned from theactivity, and also jointly decide on an agreed mark for the script. Students must submit the
proforma officially to the undergraduate office. The students go through the whole process
without seeing answer sheets of the PRA problem set: a solution to the problem set is distributed
to students in each term after the deadline of proforma submission passes. Each pair is
encouraged to study and find answers by themselves if both the students in the pair did not solve
the problem set. The timeline of the assessment, along with other module activities, can be foundin Figure 1 (also in Supplementary materials Section A.1).
In term 1, in the PRA activities, all students are randomly broken into pairs in theirrespective seminar groups. When the number of students in a given seminar is odd, there is one
team consisting of three students. In term 2, by contrast, seminar groups are randomly assigned
either the random matching condition (“treatment condition”) or the sorting condition (“control
condition”) so that the number of seminar groups in each condition is 8 out of 16. On the one
12hand, students in a group with the treatment condition are randomly broken into pairs as in term
1. The pairing is completely random, implemented through computer random number
generation.10 On the other hand, students in the control condition are sorted in descending orderaccording to their term 1 formative assessment marks, and pairs (teams) are formed so that theirmarks are adjacent to each other.11 Any student is not aware of this paring process.
In order to study how the PRA activities affect their focus on preparing for thesummative assessment, one question comes from the consumer theory (long-run
macroeconomics) and the other comes from the producer theory (short-run macroeconomics) inPart B (Part C) in the summative assessment. In other words, the topics of the four questions
appearing in Parts B and C are covered by the two formatives and two PRA in the module. The
students were not given any information regarding which topics would be tested in thesummative assessment.
To maximize the external and internal validity of the project, it is essential for students toengage in the learning activities without knowing the presence of on-going experiments or thematching differences by seminar group. The institutional review board (IRB) at Durham
University, however, asked the authors to seek consent from the students and explain a possible
research activity. As a compromise, the research team simply includes a generic consent
statement in the proforma of the term 1 peer review assessment without writing any substance ofthe research as follows:
Consent:
Your assessment marks may be used for the purpose of further research and to enhance
the learning experience for the programme. I consent this possibility.
Your Signature: _______________________________________The performances of only those who gave us consent are used for the study (this procedure has
been approved by the IRB).12 Hence, students in the module are not aware of any experimental
aspects. Students are simply explained the learning objective of the PRA activities using thematerials in Supplementary materials Section A.1.
To further enhance the internal validity of the experiment, all module teaching teammembers perform lecturing, tutoring and consultation following the module outline and the10

There is an exception in which the same four pairs as in term 1 were formed by chance and hence the pairing was
further randomly changed to ensure that all students had different partners for terms 1 and 2.
11
The same eight pairs as in term 1 was formed by sorting. Their pairing was adjusted by the authors, swapping thepartners among similar interim marks so that all students had different partners.
12
Another condition in obtaining the IRB approval is for us not to make any student’s proforma publicly available.

13requirement set by Kamei, without being informed of the on-going experiment. Moreover, alladministrative staff members in the undergraduate office are likewise uninformed of the presenceof the experiment. Note that Kamei does not serve as a tutor of any student in the module. Seminartutors deal with all aspects of the peer review assessment activities as well as direct interactions
with students in seminars. Kamei’s minimum interactions with the students help minimize apossible unconscious bias that might have occurred had he tutored any of the students.
4. Hypothesis
Either a behavioral model that incorporates social effects, such as shame and pride(Section 4.1), or a behavioral model with interdependent motives (Section 4.2), predicts that (i)students perform better on the summative assessment in pairs with a greater spread in interim
performances, and (ii) the worse performers in the treatment condition improve performances
through working with their matched better performers, in the setup of this study. Both the
motives would be plausible ones. This section mathematically illustrates the mechanism of eachmotive in isolation to derive the hypothesis of the paper based on behavioral effects.
4.1. Social Effects among Peer Mates
Assume first the following payoff functional forms to describe the situation prior to
engaging in the peer review assessment activities for high type (h) and low type (l):𝐺ℎ (𝑦ℎ ) = 𝑔(𝑦ℎ ) − γℎ 𝑦ℎ 2 .

(1)𝐺𝑙 (𝑦𝑙 ) = 𝑔(𝑦𝑙 ) − γ𝑙 𝑦𝑙 2 .

(2)Here, 𝑔(𝑦𝑖 ) is the student’s interim performance gauged by the formative in the module, 𝑦𝑖∈{ℎ,𝑙}is the effort put so far by type i to learn class materials, and γ𝑖 𝑦𝑖 2 is the cost associated with theeffort provision, and the cost function is assumed to be quadratic. For simplicity, further assumethat:𝑔(𝑦𝑖 ) = 𝛼𝑖 + 𝛽𝑖 𝑦𝑖 .

(3)Parameter values are set so that 𝛼ℎ > 𝛼𝑙 > 0, 𝛽ℎ > 𝛽𝑙 > 0, and 0 < γℎ < γ𝑙 (i.e., the high typehas higher returns from study effort and lower unit effort costs than the low type).
Each type’s optimal interim effort provision can then be derived by using the first-orderconditions for (1) and (2):𝛽𝑦ℎ ∗ = 2γℎ .
ℎ𝛽𝑦𝑙 ∗ = 2γ𝑙 .
𝑙

14

(4)
(5)

𝛽

𝛽

Note that 2γℎ > 2γ𝑙 and the second-order conditions are satisfied. Hence, it can be predicted thatℎ𝑙

the high type exerts stronger effort and has a better interim achievement level than the low type.
As the PRA activities help improve each other’s performance through mutual learning,
the payoff function after the activities can be re-written for each type as below:
𝜋ℎ (𝑦ℎ , 𝑒ℎ |𝑒𝑙 ) = 𝐺ℎ (𝑦ℎ ) + 𝑎𝑙 𝑒𝑙 + 𝑏ℎ 𝑒ℎ − 𝑐ℎ 𝑒ℎ 2 .

(6)𝜋𝑙 (𝑦𝑙 , 𝑒𝑙 |𝑒ℎ ) = 𝐺𝑙 (𝑦𝑙 ) + 𝑎ℎ 𝑒ℎ + 𝑏𝑙 𝑒𝑙 − 𝑐𝑙 𝑒𝑙 2 .

(7)

In these equations, 𝑒𝑖∈{ℎ,𝑙} is the effort level provided by i to teach his/her partner through criticalassessment of the partner’s script and discussions. The cost function is assumed to be quadratic
for peer learning as well, i.e., 𝑐𝑖 𝑒𝑖 2 , such that 𝑐𝑙 > 𝑐ℎ (the unit effort costs in the PRA activities
are higher for the low than for the high type). The term 𝑏𝑖 𝑒𝑖 refers to student i’s own benefit fromengaging in the PRA activities. By contrast, 𝑎𝑙 𝑒𝑙 (𝑎ℎ 𝑒ℎ ) is the benefit that the high (low) typereceives from her (his) matched low (high) type in the pair, and 𝑎ℎ > 𝑎𝑙 .
Equations (6) and (7) suggest that the PRA activities do not change each type’s optimal
effort choice decision regarding yi, because𝜕𝜋𝑖 (𝑦𝑖 ,𝑒𝑖 |𝑒𝑗 )𝜕𝑦𝑖=𝜕𝐺𝑖 (𝑦𝑖 )𝜕𝑦𝑖

for i = h, l. However, the optimal

choice would change if it is additionally assumed that each type receives a positive (negative)
utility when their own class performance is better (worse) than their pair partner’s. For an
illustrative purpose, consider the following utility function:
𝜃ℎ (𝑦ℎ , 𝑒ℎ |𝑒𝑙 ) = 𝜋ℎ (𝑦ℎ , 𝑒ℎ |𝑒𝑙 )+𝜇ℎ [{𝑔(𝑦ℎ ) + 𝑎𝑙 𝑒𝑙 + 𝑏ℎ 𝑒ℎ } − {𝑔(𝑦𝑙 ) + 𝑎ℎ 𝑒ℎ + 𝑏𝑙 𝑒𝑙 }]2 .

(8)𝜃𝑙 (𝑦𝑙 , 𝑒𝑙 |𝑒ℎ ) = 𝜋𝑙 (𝑦𝑙 , 𝑒𝑙 |𝑒ℎ )−𝜇𝑙 [{𝑔(𝑦ℎ ) + 𝑎𝑙 𝑒𝑙 + 𝑏ℎ 𝑒ℎ } − {𝑔(𝑦𝑙 ) + 𝑎ℎ 𝑒ℎ + 𝑏𝑙 𝑒𝑙 }]2 .

(9)The equation in the squared bracket (= {𝑔(𝑦ℎ ) + 𝑎𝑙 𝑒𝑙 + 𝑏ℎ 𝑒ℎ } − {𝑔(𝑦𝑙 ) + 𝑎ℎ 𝑒ℎ + 𝑏𝑙 𝑒𝑙 }) is theintra-pair difference in the achievement level after the PRA activities. The assumption here isthat the high (low) type has feelings of pride (shame), which leads to a positive (negative) utility.
𝜇 indicates each type’s utility weight on the social effects. 𝜇ℎ and 𝜇𝑙 are both positive, such that𝜇ℎ < 𝜇𝑙 . This condition means that the impact of shame is stronger than that of pride. The
presence of such social effects does influence their self-study efforts. This can be seen by using
the first-order conditions for utilities (8) and (9) as follows:
𝜕𝜃ℎ
𝜕𝑦ℎ
𝜕𝜃𝑙
𝜕𝑦𝑙

= 𝛽ℎ − 2γℎ 𝑦ℎ + 2𝜇ℎ 𝛽ℎ [{𝑔(𝑦ℎ ) + 𝑎𝑙 𝑒𝑙 + 𝑏ℎ 𝑒ℎ } − {𝑔(𝑦𝑙 ) + 𝑎ℎ 𝑒ℎ + 𝑏𝑙 𝑒𝑙 }] = 0.

(10)

= 𝛽𝑙 − 2γ𝑙 𝑦𝑙 + 2𝜇𝑙 𝛽𝑙 [{𝑔(𝑦ℎ ) + 𝑎𝑙 𝑒𝑙 + 𝑏ℎ 𝑒ℎ } − {𝑔(𝑦𝑙 ) + 𝑎ℎ 𝑒ℎ + 𝑏𝑙 𝑒𝑙 }] = 0.

(11)

15

Notice that
𝜕𝜃ℎ

𝛽 2

𝛽2

ℎ

𝑙

|
𝜕𝑦

= 2𝜇ℎ 𝛽ℎ [𝛼ℎ − 𝛼𝑙 + 2γℎ − 2γ𝑙 + 𝑎𝑙 𝑒𝑙 + 𝑏ℎ 𝑒ℎ − 𝑎ℎ 𝑒ℎ − 𝑏𝑙 𝑒𝑙 ].

𝜕𝜃𝑙= 2𝜇𝑙 𝛽𝑙 [𝛼ℎ − 𝛼𝑙 + 2γℎ − 2γ𝑙 + 𝑎𝑙 𝑒𝑙 + 𝑏ℎ 𝑒ℎ − 𝑎ℎ 𝑒ℎ − 𝑏𝑙 𝑒𝑙 ].

∗ 𝛽ℎ
∗ 𝛽𝑙
ℎ 𝑦ℎ =2γ ,𝑦𝑙 =2γ
ℎ
𝑙

|
𝜕𝑦

∗ 𝛽ℎ
∗ 𝛽𝑙
𝑙 𝑦ℎ =2γ ,𝑦𝑙 =2γ
ℎ
𝑙

𝛽 2

𝛽2

ℎ

𝑙

Here, the squared bracket (the difference in achievement level between the high and low types
𝛽 2

𝛽2

ℎ

𝑙

after the PRA activities) is considered as still positive because 𝛼ℎ > 𝛼𝑙 , 2γℎ > 2γ𝑙 and 0 < 𝜇ℎ <𝜇𝑙 . This suggests that the optimal self-study effort exerted by type i (denoted as 𝑦𝑖 ∗∗ ) is greater𝛽than 𝑦𝑖 ∗ = 2γ𝑖 . This means that both the high and low types work harder driven by the social𝑖effects. Conditions (10) and (11) can also be simplified to:𝛽𝑦ℎ − ℎ2γℎ𝛽𝑦𝑙 − 𝑙
2γ𝑙

=

𝜇ℎ 𝛽ℎ
γℎ
𝜇𝑙 𝛽𝑙
γ𝑙

𝜇 γ𝛽

= 𝜇ℎ γ𝑙 𝛽ℎ.
𝑙

ℎ 𝑙

γ𝛽

By the assumptions on 𝛽 and γ, γ𝑙 𝛽ℎ > 1. Thus, the above condition implies that the lowℎ 𝑙type shows a stronger improvement than the high type if the effect of shame is large enough thatγ𝛽𝜇𝑙 > γ𝑙 𝛽ℎ 𝜇ℎ .
ℎ 𝑙These analytical implications can be summarized as Proposition 1 below. Proposition 1
suggests that peer review activities with a greater spread in interim performances lead to an
stronger effect than those with similar performances, as the social effects operate strongly in theformer than in the latter.
Proposition 1: Suppose that the high (low) type receives a positive (negative) utility due tofeelings of pride (shame) through the PRA activities. Then, the PRA activities encourage both thehigh and low types to study harder to improve own understanding of class materials, accordingly
resulting in performance improvements. The positive effect on the low type is stronger than onγ𝛽

the high type if the low type is concerned about shame large enough that 𝜇𝑙 > γ𝑙 𝛽ℎ 𝜇ℎ .
ℎ 𝑙4.2. Interdependent Motives
The mutual learning hypothesis states that high-ability workers teach less-ability ones,
thereby improving the performances of especially the latter. To see this, for tractability, let us
simplify the payoff functions (6) and (7) as follows:𝜋ℎ (𝑒ℎ |𝑒𝑙 ) = 𝑘ℎ + 𝑎𝑙 𝑒𝑙 + 𝑏ℎ 𝑒ℎ − 𝑐ℎ 𝑒ℎ 2.
16

(12)

𝜋𝑙 (𝑒𝑙 |𝑒ℎ ) = 𝑘𝑙 + 𝑎ℎ 𝑒ℎ + 𝑏𝑙 𝑒𝑙 − 𝑐𝑙 𝑒𝑙 2 .

(13)Here, 𝑘ℎ and 𝑘𝑙 are the students’ interim performances before engaging in the PRA activities,
such that 𝑘ℎ > 𝑘𝑙 > 0. Each type’s optimal effort provision in the PRA activities can be derived
by using the first-order conditions for (12) and (13):𝑏𝑒ℎ ∗ = 2𝑐ℎ .
ℎ𝑏𝑒𝑙 ∗ = 2𝑐𝑙 .
𝑙

(14)
(15)

Notice that 𝑒ℎ ∗ and 𝑒𝑙 ∗ are each dependent only on their own payoff parameters. This means thatwithout considering interdependent concerns, each type’s effort provision in peer learning would
not be affected by their partner’s ability or payoff parameters.
In order to show how the prediction may change by the inclusion of interdependent motives,
as an illustration, assume now that each type’s utility function can be expressed as follows:𝑢ℎ (𝑒ℎ |𝑒𝑙 ) = 𝜋ℎ − 𝑥ℎ ∙ (𝜋ℎ − 𝜋𝑙 )2.

(16)

𝑢𝑙 (𝑒𝑙 |𝑒ℎ ) = 𝜋𝑙 − 𝑥𝑙 ∙ (𝜋𝑙 − 𝜋ℎ )2 .

(17)

This means that a student prefers to have similar academic performances between pair mates. 𝑥𝑖
is the utility weight on the interdependent preferences. Each type’s optimal effort provision canagain be derived by differentiating utilities (16) and (17) with respect to 𝑒𝑖 :𝜕𝑢ℎ𝜕𝑒ℎ

= [1 − 2𝑥ℎ ∙ (𝜋ℎ − 𝜋𝑙 )](𝑏ℎ − 2𝑐ℎ 𝑒ℎ ) + 2𝑎ℎ 𝑥ℎ (𝜋ℎ − 𝜋𝑙 ) = 0.

𝜕𝑢𝑙
𝜕𝑒𝑙

= [1 − 2𝑥𝑙 ∙ (𝜋𝑙 − 𝜋ℎ )](𝑏𝑙 − 2𝑐𝑙 𝑒𝑙 ) + 2𝑎𝑙 𝑥𝑙 (𝜋𝑙 − 𝜋ℎ ) = 0.

(18)
(19)

For simplicity, further assume that 𝑥ℎ and 𝑥𝑙 are small enough that the interdependent
preferences do not reverse the intra-pair relative payoff standing, i.e., 𝜋ℎ > 𝜋𝑙 , in equilibrium.
Condition (18) suggests that the optimal effort level of high type h (𝑒ℎ ∗∗ ) is greater than 𝑒ℎ ∗ if 𝑥ℎ
is sufficiently large. By contrast, Condition (19) suggests that the optimal effort level of low typel (𝑒𝑙 ∗∗ ) is always lower than 𝑒𝑙 ∗ . Hence, the students’ interdependent motives help shrink the
intra-pair performance difference through the PRA activities under certain conditions.
The size of intra-pair interim performance difference (i.e., 𝑘ℎ − 𝑘𝑙 ) and peer learning outcome:With this framework, it can be shown that a larger intra-pair difference in the interim
performance induces the high type h to put more efforts in improving her matched low type. To
show this, for simplicity, assume the following:
Assumption 1: 𝑏ℎ = 𝑏𝑙 = 0.
17

Assumption 2: 𝑐ℎ = 𝑐𝑙 = 𝑐, but 𝑎ℎ > 𝑎𝑙 .
Assumption 1 means that effort provision by the high type in the PRA activities is purely
costly without resulting in her own private benefits. Assumption 2 is merely a normalization:
while the unit effort cost is the same for the high and low types, the impact of the PRA activities(𝑎ℎ , 𝑎𝑙 in Equations (12) and (13)) differs by the type.
Proposition 2: Consider Assumptions 1 and 2. Then, the larger interim performance difference apair has (i.e., the higher 𝑘ℎ , relative to 𝑘𝑙 , the high type has), the greater effort the high typeexerts in improving the performance of her matched low type.
Proof: Assumption 1 implies that 𝑒ℎ ∗ = 𝑒𝑙 ∗ = 0 from Equations (14) and (15), and therefore
𝜋ℎ (𝑒ℎ ∗ |𝑒𝑙 ∗ ) = 𝑘ℎ > 𝑘𝑙 = 𝜋𝑙 (𝑒𝑙 ∗ |𝑒ℎ ∗ ).
Under these two assumptions, Condition (18) reduces to the following:𝑓(𝑒ℎ |𝑘ℎ , 𝑘𝑙 , 𝑎ℎ , 𝑐) ≔ −c𝑒ℎ + [2c𝑒ℎ 𝑥ℎ + 𝑎ℎ 𝑥ℎ ](𝑘ℎ − c𝑒ℎ 2 − 𝑘𝑙 − 𝑎ℎ 𝑒ℎ ) = 0(20)

Appling the Implicit Function Theorem to (20), it can be found that the larger 𝑘ℎ the high type hhas, the greater effort level h exerts in improving the performance of the low type:𝜕𝑒ℎ𝜕𝑓/𝜕𝑘ℎ2c𝑒ℎ 𝑥ℎ + 𝑎ℎ 𝑥ℎ
=−
=−
2
𝜕𝑘ℎ
𝜕𝑓𝜕𝑒ℎ
−𝑐 + 2c𝑥ℎ (𝑘ℎ − c𝑒ℎ − 𝑘𝑙 − 𝑎ℎ 𝑒ℎ ) − (2c𝑒ℎ 𝑥ℎ + 𝑎ℎ 𝑥ℎ )(2c𝑒ℎ + 𝑎ℎ )=−2c𝑒ℎ 𝑥ℎ + 𝑎ℎ 𝑥ℎ2c 2 𝑒ℎ−𝑐 + 2c𝑒 + 𝑎 − (2c𝑒ℎ 𝑥ℎ + 𝑎ℎ 𝑥ℎ )(2c𝑒ℎ + 𝑎ℎ )ℎℎ(Note: the above equality is obtained by using Condition (20))=

2c𝑒ℎ 𝑥ℎ + 𝑎ℎ 𝑥ℎ𝑐𝑎ℎ+ (2c𝑒ℎ 𝑥ℎ + 𝑎ℎ 𝑥ℎ )(2c𝑒ℎ + 𝑎ℎ )2c𝑒ℎ + 𝑎ℎ> 0. □

5. Results
284 students enrolled in the module at the beginning of the academic year. Almost all thestudents remained in the module when final module registrations emerge after the student review
period.13 The total number of students was 279 at the beginning of term 2. 92.8% of them gaveconsent for their data to be used for possible research. As a result, the subject pool includes 129
and 130 students in the treatment and control conditions, respectively. Table 1 summarizes
students’ performances in term 1 formative assessments. It indicates that almost all the students

13This is as expected since ECON1101 is a compulsory module.

18submitted the formative assessments. This is not a surprise since the submission of the formative
assessment was compulsory. The average mark of the formative assessment was 70.38 in thetreatment condition, somewhat lower than that in the control condition (72.05). However, thedifference is not statistically significant according to a Somers’ D test with seminar groupclustering (two-sided p = 0.721).14 This means that the random allocation of matching conditions
was successful. In the subject pool, 123 and 127 students in the treatment and control conditions,
respectively, completed summative assessments by the deadline.
Table 1 also includes information on the proportions of female students and those of
British students. It shows that the proportion of female students is somewhat smaller in thetreatment than in the control condition. The proportion of British students is somewhat larger inthe former than in the latter. Prior research suggests that having a higher proportion of female
peers helps improves performance (e.g., Black et al., 2013; Lavy and Schlosser, 2011; Lu andAnderson, 2015). If this is applicable for the student pool of this study, students may tend toachieve better academic performances in the control than in the treatment condition in the end.15
However, the differences in these proportions are not significantly different. Thus, thesedemographics are sufficiently balanced between the two conditions.
As explained in Section 3, students’ attendance in bi-weekly seminar activities were set
mandatory in the module. Some students missed the seminars, nevertheless (Figure 2). The
average attendance rates show similar trends for the treatment and control conditions. The rates
were high at the beginning of each term, and then gradually declined from seminar to seminar.
The attendance rates were around 70% (somewhat over 60%) in the fourth seminar in term 1(term 2). A Somers’ D test with seminar group clustering found that the difference in the averageseminar attendance rate was not significant between the treatment and control conditions at twosided p = 0.470. This means that students’ exposure to the seminar activities were also balanced.
The learning outcome in this module can be measured based on students’ performancesin the summative assessment at the end of the academic year. The data show that despite theslightly weaker interim (term 1 formative) performance in the treatment than in the control
condition (Table 1), students in the treatment condition achieved stronger performance in thesummative assessment. As shown in panel A of Figure 3, the difference in the average markbetween the two matching conditions was around three points and is significant at two-sided p =0.031 according to a Somers’ D test with seminar group clustering. In particular, while students
Testing based on Somers’ D is identical to the Mann-Whitney test if clustering is not included.
As will be explained in this section, students performed significantly better in the treatment than in the control
condition despite the somewhat lower percentage of female students in the former.
14
15

19

in the bottom 10% showed similar achievements in the two conditions, the rest (90% of students)
showed higher achievements in the treatment than in the control condition.
In term 2, a small fraction of students did not submit peer review assessments.16 Even if
students did not submit the PRAs, they were still encouraged to meet with their partners anddiscuss the problem set within the pairs as an academic commitment, meaning that there might
have still been some effect. However, having an effective discussion could be difficult without
having their partners’ scripts. Hence, it would be useful to study a possible treatment effect while
limiting data to pairs in which both pair mates submitted the PRAs. Panel B of Figure 3 reports
the cumulative distributions for the restricted dataset. It shows an almost similar pattern to panel
A and the performance difference is significant at two-sided p = 0.034 according to a Somers’ D
test with seminar group clustering. This suggests that the size of the treatment effect was notaffected by the omission of those who were not able to complete the PRA activities.
Care needs to be exercised when formally studying the treatment effect of intervention,
especially because not all students completed the summative assessments (i.e., submitted by thedeadline). The data indicate that among the 259 students who gave consent, nine students (3.47%of the subject pool) did not complete the assessment. No submission for “good cause” is treatedas different from zero marks in the exam with the university.17 As their marks were unobserved,a Heckman two-stage selection model was used to control for a possible impact of the selection
bias although the effect of selection bias seems to be very small. Considering that students’ effort
levels put in the module may explain their decisions to complete the exam, their attendance rates
in seminar activities and submission records of formative assessments are included as
independent variables in the first-stage selection equation.18 As shown in Table 2, the model was
estimated when using all data (columns I.i and I.ii) or using students who submitted the term 2
PRAs (columns II.i and II.ii). The t2 (term 2) random matching dummy is included in all the
specifications to estimate the effect of treatment intervention.
The estimation first reveals that, as expected, students’ efforts exerted in the module aregood predictors for their completion of the summative assessment: the number of formative
16

11 students (4.23% of the students in the subject pool) did not submit the assessments in term 2.
For example, if a student had a valid reason, such as illness, for not attending, there would be a blank in theirtranscript; they can take a resit exam as their first attempt. The authors do not have accessible data regarding reasonsfor not attending the exam or resit marks.
18
A given student’s seminar attendance rate was calculated based on the eight seminar activities in the module. It
should be acknowledged that in one seminar group, the seminar tutor failed to take attendance in the eighth seminar;
thus, the attendance rates of students in that group were calculated based on the records in the other seven seminars.
Results reported in this paper do not change qualitatively even if students’ attendance rates are calculated based on
the seven seminar activities for all seminar groups.
17

20

assessments not submitted has a significantly negative coefficient in the first-stage selection
equation. In addition, as shown in columns I.i and I.ii, the seminar attendance rate variable has asignificantly positive coefficient when all eligible subjects are considered.
Second, and most important, regardless of whether the students’ term 1 formative marks
are controlled for, the t2 random matching dummy consistently has a significantly positivecoefficient in the second stage regression. This suggests that working in pairs with different
abilities leads to a higher performance than pairing students whose achievement levels weresimilar to each other, in support of the view from the peer-effect hypothesis and the mutual
learning theory.19
Result 1: Students in pairs with a great spread in interim achievement levels performed better on
the summative assessment compared with those in pairs whose interim performances weresimilar to each other.
What drove the positive impact of the PRA activities in term 2? The only difference
between the two conditions is the use of random matching or sorting in the pairing process.
Students in the control (sorting) condition were divided into pairs so that their term 1 formative
assessment marks were similar to each other. By contrast, pairing was randomly formed forstudents in the treatment (random matching) condition. With this difference in the matching
protocol, the average intra-pair absolute difference in the formative mark was more than fourtimes in the treatment than in the control condition: it was 25.16 (5.81) marks with clustered
standard errors of 3.28 (1.07) marks in the former (latter). Panel A of Supplementary materials
Figure B.2 reports the histogram of absolute individual performance differences by the matchingcondition. It clearly indicates that the differences spread widely to the right in the treatment
condition, while they are concentrated around 0 in the control condition. Hence, these patterns
confirm that, as intended, pairs in the treatment condition had a greater variation in interim
achievement levels between pair mates, compared with those in the control treatment.
In order to study how the treatment effect differs by the intra-pair relative term 1
performance standing in the treatment condition, the data in the treatment condition was split

19

The gender composition in pairs may affect the size of peer effects (e.g., Black et al., 2013; Lavy and Schlosser,
2011; Lu and Anderson, 2015). However, in principle, individual characteristics do not need to be controlled in thisstudy since matching conditions were randomly assigned to groups and the proportion of female students was not
significantly different between the treatment and control conditions (Table 1). Nevertheless, an additional regression
was conducted as a robustness check while controlling for available demographic variables (own gender, pairpartner’s gender, and the interaction between the two gender variables, students’ nationality). The estimation foundqualitatively similar results, i.e., positive effects of having a greater spread in abilities in a pair – see Supplementarymaterials Table B.1 for the detail.

21

into two sets: the “better performers” and the “worse performers.” The better (worse) performer
is defined as a student whose term 1 formative mark is better (worse) than his/her matched
partner’.20 The average term 1 formative marks of the better and worse performers were 80.35
and 57.81, respectively, in the treatment condition (the average mark in the control condition wasin the middle between the two, and it was 72.05 as already discussed in Table 1) – see also panel
B of Supplementary materials Figure B.2. Intriguingly, the performance data in the summative
assessment by the relative standing reveal that the better and worse performers had similarachievements in the end, scoring 71.31 and 71.94 points, respectively, each of which was better
than the average summative performance under sorting (Table 1).21 This seems to suggest thatworking in a team with a greater spread in abilities strongly supports the learning of the worse
performer.
A regression was performed by including two indicator variables – the better performer
and the worse performer dummies – as independent variables, to formally study the role ofrelative performance standing in the treatment condition. Having the two dummies make itpossible to identify how the aggregate positive effect of term 2 random matching (Result 1)
differs by student’s interim achievement standing. The reference group is the students in thecontrol condition.
Table 3 reports the estimation results. The regression only uses the data from pairs inwhich both the pair mates submitted term 1 formative assessments, since otherwise it is notpossible to judge which student was the better or worse performer in the interim stage. A
Heckman selection model was again used in the analysis in order to deal with unobserved
summative marks of some students. As shown in columns I.i and II.i, when only the two
performance dummies are used as independent variables in the second stage equation, thedummies obtain weakly significantly or significantly positive coefficients. This implies that not
only the worse but also the better students might have similarly benefited from the PRA
activities in the treatment condition. However, this interpretation is misleading. As shown incolumns I.ii and II.ii, once students’ term 1 formative assessment marks are controlled for, only
the worse performer dummy obtains a significantly positive coefficient at the 5% level or better.
It follows that the significant coefficients for the better performer dummy in columns I.i and II.i

There was no student whose term 1 formative mark was exactly the same as his/her partner’s.
The absolute size of marks are not perfectly comparable between the formative and summative assessments
because the former has only one problem set while the latter has multiple problem sets.
20

21

22

are driven by the differences in the term 1 formative marks, and the worse performers in pairs
are the ones that mainly benefited from the PRA activities.22
It should be worth noting that the coefficient estimates for the better performer dummy
are not negative, but close to zero. This means that the better performers were not hurt by being
matched with the worse performers.
The empirical results from columns I.ii and II.ii of Table 3 can be rationalized by afrequently-used behavioral model that assumes that the utilities of students may be influenced bysome social effects, such as shame, guilt, and pride, or some interdependent preferences, such as
inequality aversion (see Section 4 for an illustrative theoretical analysis). This is because undersuch assumptions, the worse performer in a pair has more non-material incentives than the paired
better performer to improve performance due to feelings of shame under certain conditions. It
can also be predicted that consistent with the mutual learning hypothesis, the more able haveinterdependent motives to exert efforts in improving her matched student’s academic
performance in the PRA activities. Which motives matter more, social effects such as shame, or
the mutual learning motives, would depend according to the students’ characteristics andpreferences, and the contexts.
Result 2: The worse performers in the treatment condition improved performance throughworking with the better performers in the peer review assessment activities.
While the average treatment effect was quite strong on the worse performers, one may
wonder more precisely how their improvements depend on the sizes of intra-pair interim
achievement differences. For example, if the abilities are too different among pair mates,
improvements may be weak as they may not be able to effectively communicate with each otherdue to the lack of basic technical skills or fundamentally different work attitudes. Alternatively,
the weaker the interim performance they have compared with the better performers, the worse
performers may benefit more, considering that they have more room for improvement and also
even worse performers have certain competency being admitted to the university based on theadmission criteria.23 This question can be examined by looking at the relationship between (a)22With the same reason as written in footnote 198, an additional regression was conducted while controlling for
demographic information as a robustness check, finding almost the same as in Table 3 (see Supplementary materials
Table B.2).
23
The students’ pre-university data, such as A-level grades, were unavailable due to its confidentiality, making it
impossible to study possible effects of pre-university achievement levels. Having said this, these background data
were in any case not used in any aspect of the module. The unavailability of the data would also not affect thefindings of the paper since seminar group allocations of students were random (footnote 7) and the background data
were not required for pairing in the PRA activities.

23

student i’s performance relative to his/her pair partner j’ in the term 1 formative assessment (i.e.,
xi = fi – fj) and (b) i’s performance improvement gauged by the summative assessment relative to
i’s interim mark (i.e., yi = si – fi).24
Figure 4 reports the relationship by matching condition. Three interesting patterns
emerge. First, the more behind a student was in the interim stage, the larger improvement she
achieved in the end through the term 2 PRA activities in the treatment condition (see the region
where xi < 0 in panel A). This resonates with the idea that peer learning is an effective way to
improve the performance of poorer workers. This tendency is also seen for some small numberof pairs in the control condition where intra-pair interim performance difference happened to belarge despite the sorting process (see the region where xi < 0 in panel B). Second, the peerlearning benefit of better performers did not depend on the size of the interim performancedifferences they had compared with their matched weak performers. In the region where xi > 0 ofpanel A, the slope of the fitted curve becomes flatter as x becomes large. The small elasticity ofthe better performers’ marks may be driven by a ceiling effect (the maximum mark is bounded
above at 100). This also importantly means that forming pairs with larger ability differences
would not hurt the better performers. Third, and as anticipated, observations were moreconcentrated around xi = 0, and the variation in y was much smaller in the control than in thetreatment condition. Specifically, the standard errors (with seminar group clustering) were 2.414
and 1.568 marks in the treatment and control treatments, respectively. This suggests that thepeer-learning effects are more homogeneous in the control than in the treatment condition.
The impact of the PRA activities can also be seen in the students’ choices in thesummative assessment. Students selected one of the two questions in Part B, and likewise in Part
C. Among the two questions in each Part, one question came from the topics in the PRA, while
the other came from the topics in the formative. In Parts B and C of the summative assessment,
strikingly, 98.0% and 91.6% of the students, respectively, selected questions whose topics werecovered by the PRA (Figure 5.A). Hence, the PRA activities are more effective in deepening thelearning and/or enhancing their study motivations than the formatives that are simply marked bytutors.
A closer look at students’ performances by the Part reveals two further interesting
patterns (Figures 5.B and 5.C). First, the students in pairs with a great spread in abilities

24

As noted in footnote 21, the absolute size of the summative mark (si) is not fully comparable to that of the term 1
formative mark (fi), whose aspect makes the interpretation of the size of yi difficult. However, yi {= si – fi} is still anuanced measure of academic improvement for across-subject comparisons. For example, given the value of f, thehigher academic improvement a student has, the greater s and therefore the greater y a student has.

24(treatment condition) performed markedly better in the long-run macro question in Part C, thetopic of term 2 PRA, relative to those in pairs with similar interim performances (control
condition). It should be acknowledged that students’ marks for the short-run macro question
were not that different between the two conditions as seen in panel C, whose result might havebeen driven by its small sample size (panel A).
Second, and equally important, the positive effect of term 2 peer learning spills over totheir learning of term 1 materials. Those in the treatment condition performed much morestrongly in Part B than those in the control condition, whether they selected the consumer theory
question (the topic in term 1 PRA) or the producer theory question (the topic in term 1
formative). Notice that each student had two PRA partners – one for term 1 activities, and theother for term 2 activities. There were no differences in the partner assignment procedure for theterm 1 activities between the treatment and control conditions.
Lastly, students performed well in the short-answer questions in Part A of the summative
assessment regardless of the matching condition: their average mark in Part A does not
significantly differ by the matching condition (14.89 for the treatment condition; 14.61 for thecontrol condition). This means that students in both matching conditions likely put in sufficient
effort, being able to grasp the basic concepts and applying the concepts to economic questions.
In order to formally study treatment effects on students’ performances in Part B, and also
in Part C, a Heckman selection model was estimated (Table 4). The dependent variable is either
their performances in Part B (column I) or Part C (column II), and the independent variables are
the same as in Tables 2 and 3. The model was estimated without splitting the data further tothose who selected Question 3 or 4 (Question 5 or 6) because the attempt here is to study theoverall impact on their performance on the term 1 (term 2) materials. The estimation clearlyshows that students performed better in the treatment than in the control condition for both Parts
B and C – see the t2 random matching dummy variable. Consistent with Result 2, the positiveeffect under term 2 random matching was driven by an improved performance exhibited by theworse performer in the pairs – see columns I.iv and II.iv.
As a further robustness check, nevertheless, the same model was also estimated whenusing students’ marks in the PRA materials, namely Question 3 (Question 5), as the dependent
variable. It finds almost the same results as Table 4 – see Supplementary materials Table B.3.25
Hence, it can be concluded that the spill-over effects of term 2 peer learning on term 1 materials
Additional regressions were further performed to study the impact of term 2 random matching on the students’scores in the formative materials, i.e., Question 4 in Part B (Question 6 in Part C). However, the selection model was
not able to be estimated due to a small number of selected data.
25

25

are significant. The spill-over effects can be thought of as being driven indirectly by the worse
performers’ improved learning in the PRA discussions, and/or by their study habits reformed
through the PRA experiences.
Result 3: The students in the treatment condition performed better than those in the control
condition not only for Part C but also for Part B of the summative assessment. This suggests thatthe positive treatment effects of pair heterogeneity through the term 2 PRA activities spillover totheir learning of the term 1 materials.
5. Conclusion
Using a randomized field experiment in a classroom, this paper found that exogenously
pairing two individuals with different interim achievement levels leads to better overall
performance through peer learning, compared with pairing together those whose achievements
are similar to each other, even though average achievement levels at the interim stage weresimilar for the two kinds of peer groups. The positive impact of pair heterogeneity was driven bya strong performance improvement of the less able, rather than of the more able, in a pair. The
more able was also not hurt by being matched with the less able. This result is consistent with thebargaining and mutual learning hypotheses: more able workers can not only impose productive
norms for the sake of their teams, but they also teach less able workers (e.g., Ichniowski et al.,
1997; Hamilton et al., 2003). An important aspect here is that the prediction from these theories
holds even if each student is evaluated based on their individual performance. A detailed look at
the data further revealed that the positive effect of peer learning activities in term 2 was not
limited to their understanding of term 2 materials (macroeconomics), but it also spilled over totheir understanding of term 1 materials (microeconomics). This underlines great importance indevising effective pairing when implementing human resource management practices such ascommunication, peer learning, and skill training in organizations.
The role of team heterogeneity is an active research agenda in the recent literature. Basedon randomized field experiments, it suggests that while peer effects are stronger in teams with agreater spread in abilities, the positive effects tend to be limited to high-ability individuals in alarge team since they endogenously choose to interact with like-minded high types (e.g., Carrell
et al., 2009; Carrell et al., 2013; Lyle, 2009; Duflo et al., 2011; Feld and Zölitz, 2017). The lowability individuals are therefore hurt in such teams. This matching situation was modeled in thesorting condition of the present study. The random matching condition of this paper showedstronger work performance than the sorting condition, and the worst performer in the former
benefited more than the better performer. With the smallest peer group size, each student had nochoice but to interact with their assigned peer in a mandatory peer learning activity. In addition,
26

each pair was given a pre-determined task for learning activities. This setup effectively prevented
the less able from being excluded from the more able students in the module.
This finding has a policy implication regarding effective learning practices. As alreadydiscussed, sub-groups tend to endogenously emerge among like-minded peers when the peergroup size is large and their skills and abilities are heterogeneous. While the present study
suggests a simple solution, namely, forcedly pairing more able with less able individuals, the socalled “tracking” has been proposed to help enhance productivity in the literature to date. For
example, using a clear field experiment in primary schools, Duflo et al. (2011) demonstrated thatwhen students are divided into sections based on prior achievement levels, even those assigned
to low-achievement peer groups can improve academic performance. They argue that teachers
can better tailor their instruction levels and methods if students are sorted based on theiracademic skills. The finding of the present paper, nevertheless, suggests that the effect of suchtracking may not be strong under certain conditions if peer learning is an important element toachieve a given goal.26 The field experiment in this study suggests that the more able would
effectively teach the less able if they are forced to be paired through a fair process, which results
in a performance improvement of the latter. This kind of pairing can be nested and implemented
in multiple activities in organizations. Such positive effects of heterogeneity cannot be obtained
if low-achieving individuals are simply grouped together.
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30

Figure 1: Timeline of Peer Review Activities
A. Term 1 (Microeconomics)#2
Lecture(Mon.):

week 1week 2week 3week 4week 5week 6week 7week 8week 9week 10

Oct. 7

Oct. 14

Oct. 21Oct. 28

Nov. 4

Nov. 11

Nov. 18

Nov. 25

Dec. 2

Dec. 9Kamei explained PRA at the
beginning of the lecture#4

seminar 2#1

seminar 1#1

Peer review assessment (PRA) will
be distributed to students on
October 28 (Mon.)

seminar 3#1

seminar 4#1
Submission deadline offormative assessment
is December 12 (Thr.).

Students receive PRA
partners' scripts during
the seminar time.

Submission deadline of
PRA scripts: noon
November 8 (Fri.)

Partner assignment announced on
November 11 (Mon.): pair partner
is randomly assigned in both
treatment and control conditions

Submission deadline of
PRA proforma:
December 3 (Tues.)

Each student critically assesses PRA partner’s work,
meets with the partner, discusses the problem
set, and then completes proforma together.

B. Term 2 (Macroeconomics)#3
Lecture(Mon.):

week 1week 2week 3week 4week 5week 6week 7week 8week 9Jan. 13Jan. 20

Jan. 27

Feb. 3Feb. 10

Feb. 17

Feb. 24

Mar. 2Mar. 9seminar 1#1

Peer review assessment (PRA) will
be distributed to students on
February 3 (Mon.), 2020.

seminar 2#1

Submission deadline of
PRA scripts: noon
February 14 (Fri.)seminar 3#1

Students receive PRA
partners' scripts during
the seminar time.

Partner assignment announced on
Febraury 17 (Mon.): pair partner israndomly assigned in the treatment
condition, while partner is assigned
based on sorting in the control
condition. (students are not informedof the matching process)seminar 4#1
Submission deadline offormative assessment
is March 16 (Thr.).
Submission deadline of
PRA proforma:
March 10 (Tues.)

Each student critically assesses PRA partner’s work,
meets with the partner, discusses the problem
set, and then completes proforma together.

Notes: #1 Each seminar is scheduled during a two weeks window. The date of biweekly seminars (Monday, Tuesday or Thursday)
differs by the seminar group, set by the undergraduate office. #2 Students’ conditions are identical for the treatment and control
seminar groups in term 1. #3 There is only one difference between the treatment and control groups in term 2. In a control seminargroup, students are sorted in descending order according to term 1 formative marks; two students with the closest marks are
paired. By contrast, in a treatment group, students are randomly broken into pairs for the peer review activities irrespective of
their term 1 formative mark. #4 As discussed, another faculty member was responsible for the lecturing in term 1. PRA was
explained by Kamei using the materials in Supplementary materials A.1 at the onset of the second lecture in term 1.

31

Figure 2: Trends of Average Seminar Attendance Rates
100%
90%
80%
70%
60%
50%
40%
30%

Treatment (random matching)

20%

Control (sorting)

10%
0%
1st
seminar

2nd
seminar

3rd
seminar4th
seminarTerm 1

1st
seminar

2nd
seminar

3rd
seminar4th
seminarTerm 2

Note: The attendance rates were calculated based on eligible students (those who gave consent).

32

Figure 3: Distribution of Students’ Summative Assessment Marks

Avg. = 69.29 [0.70]
Avg. = 71.69 [0.93]
Avg. = 72.38 [0.95]

Avg. = 68.77 [0.72](B) Students who submitted term 2 PRA and whose
partner also submitted the assessment(A) All eligible students in the subject pool

Notes: The numbers in squared brackets are standard errors clustered by seminar group ID. The number of eligible
observations in panel A is not the same as the size of the subject pool since a small number of students did notcomplete the summative assessments (Table 1).

33

Figure 4: Interim Achievement Differences and Improvement of Performancesy = -0.0000x3 + 0.0043x2 - 0.4226x - 2.5682 100(0.0000) (0.0006) (0.0456) (2.2982)
R² = 0.5151

Summative markminus term 1
formative mark (y)y = -0.0002x3 + 0.0300x2 - 0.2656x - 6.5468(0.0001) (0.0104) (0.1631) (2.2859)
R² = 0.2990

80

80

60

60

40

40

20

20

0

0

-20

-20

intra-pair difference in term 1 formative mark (x)
-40
-100
-80
-60
-40
-20
0

Summative markminus term 1
formative mark (y)100intra-pair difference in term 1 formative mark (x)
-40

20

40

60

80

100

-60

-100

-80

-60

-40

-20

0

20

40

60

80

100

-60

(A) Treatment condition (random matching)(B) Control condition (sorting)Notes: The size of each point indicates its frequency. Almost all points have the frequency of one (i.e., one student). The
numbers in parentheses in the polynomial equations in the figures are robust standard errors clustered by seminar group ID.

34

Figure 5: Students’ Decisions to Select Questions and Performancesin the Summative Assessment
Topics in PRA

Treatment (random matching)

Topics in formative

100%

30

80%

29

Control (Sorting)Treatment (random matching)34

Control (sorting)

32
30
60%

28

40%

27

20%

26

28
26

24
22
20

0%

25
Part B (Micro)

Part C (Macro)(A) Distribution of students’ selection

18

Consumer Theory

Long-run Macro(B) Avg. marks for topics in PRAs

Producer Theory

Short-run Macro(C) Avg. marks for topics in formatives

Notes: The maximum mark in each part is 40. The topics in the PRA are the consumer theory (term 1) and long-run
macroeconomics (term 2). The topics in the formatives are the producer theory (term 1) and short-run
macroeconomics (term 2). As in other analyses, those who gave consent and completed the summative assessment
were used to calculate the distributions of problem selection and average marks.

35

Table 1: Summary of Conditions
Treatment

A. Treatment condition B. Control condition(Random matching)(Sorting)

C. TotalTwo-sided p for
H0: A = B#5

a. Number of seminar groups

8

8

16

---

b. Total number of students#2

139#1

139

278

---

129
(92.8%)

130(93.5%)

259(93.2%)---

c.ii. Number of female students out of c.i

59

72

131

0.1365c.iii. Number of British students out of c.i44
122(87.8%)

33
121(87.1%)

77243(87.5%)

0.136370.38
123(95.4%)

72.05
127(97.7%)

71.21
250(96.5%)

0.721

116(83.5%)

118(84.9%)

234(84.2%)

---

70.84

71.71

71.28

0.867

c. Students who gave consent (subject pool)c.i. Number of the students

c.iv. Number of those who submitted term 1
formatives out of c.ic.v. Avg. term 1 formative mark (out of 100) #3,#4
c.vi. Number of those who submitted summative
assessments out of c.ic.vii. Number of those who submitted summative
assessments out of c.iv
c.viii. Avg. term 1 formative mark for c.vii#3

---

---

Notes: #1 The number of the students was 142 at the beginning of term 2 when treatment allocations were made. Three
students in the treatment condition were, however, were not assigned any pair partners because one student requested
exemption from the activity due to disability, another was found to have been suspended from the university (this student
was not able to attend any academic activities in term 2), and the other withdrew from the module at the beginning of term
2. #2 When the number of students in a given seminar group was odd, one interaction unit was a three-student team where
PRA scripts were swapped among them. #3 The cumulative distributions of formative assessment marks can be found in
Supplementary material Section B.1. #4 The average term 2 formative marks were similar for the two conditions (60.4 in
the treatment condition; and 59.6 in the control condition). It should be worth noting that students were distributed, andstarted to work on, the term 2 formative assessment on February 24, 2020, which was before the peer review assessment
activities were completed. Hence, it is not surprising to see no effects of the treatment interventions on term 2 formative
performances. #5 Fisher’s exact tests for rows c.ii and c.iii, and Somers’ D with seminar group clustering for rows c.v andc.viii.

36

Table 2: Treatment Effects of Term 2 Random Matching(A) Second Stage Regression (Treatment effect)
Dependent variable: Summative assessment mark of student i
Data:(I) All data

Independent variable:(a) t2 random matching dummy {=1(0) for thetreatment (control) condition}(b) A dummy that equals 1 if i did not submit term
1 formative assessment(c) Interaction term: (1 – variable (b)) × term 1
formative assessment markA three-student team dummy {= 1(0) if a student
was assigned to a three(two)-student team}Constant# observations# selected
Log pseudolikelihood(II) Both i and i’s partner
submitted term 2 PRA
(i)
(ii)

(i)

(ii)

3.10***(1.19)-6.13*(3.45)
70.15***(1.62)

3.30***(1.03)
4.26(5.80)
0.16***(.040)-0.89(3.47)
59.54***(3.00)-4.50(4.00)
70.39***(1.09)

2.50**(1.02)
6.20(6.55)
0.16***(.05)
0.30(4.03)
59.51***(3.35)

259
250-1005.01259
250-995.13236
228-906.96236
229-902.24-----

2.43**(1.16)-----(B) Selection equation that explains whether student i submits the summative assessment (i.e., thesubmission is observed)
Data:(I) All data

Independent variable:

(i)

(ii)

(a) t2 random matching dummy {=1(0) for thetreatment (control) condition}(b) A dummy that equals 1 if i did not submit term
1 formative assessment(c) Interaction term: (1 – variable (b)) × term 1
formative assessment mark(d) The number of formative assessments not
submitted {= 0, 1, 2}(e) Seminar attendance rate  [0, 1]

0.04
(.09)

0.17**(0.08)
5.09(n.a.)
0.002(0.003)-0.36***(0.02)
0.50***(0.02)
4.15(n.a.)
1.16***(0.26)

A three-student team dummy {= 1(0) if a student
was assigned to a three(two)-student team}Constant-----0.61***(0.03)
0.23***(0.01)
0.09(0.27)
1.80***(0.14)(II) Both i and i’s partner
submitted term 2 PRA
(i)
(ii)

-0.21
(.33)
-----0.60**(0.29)
0.18(0.68)
4.70***(.86)
2.28***(0.62)-0.15(0.29)
4.87(3.15)
0.005(0.01)-0.86*(0.47)
0.28(0.71)
4.14**(1.86)
1.93***(0.65)

Notes: Estimations of the Heckman two-stage selection model with robust standard errors clustered by seminar group ID.
The numbers in parentheses are standard errors. In addition to the independent variables listed in the table, a term 1 tutor
dummy was controlled in both stages of regressions since there were two seminar tutors in term 1. A three-student teamdummy was also added as a control since there was one such team in a session whose number of students was odd. In
columns II.i and II.ii, only observations in which a student submitted term 2 peer review assessment and his/her partner
also submitted it were used as data. Equations I.i, I.ii, II.i, and II.ii of panel B are the selection equations of columns I.i,
I.ii, II.i, and II.ii, respectively, of panel A. *, **, and *** indicate significance at the .10 level, at the .05 level and at
the .01 level, respectively.

37

Table 3: Mechanism behind the Positive Impact of Term 2 Random Matching(A) Second Stage Regression
Dependent variable: Summative assessment mark of student i
Data:(I) All data

Independent variable:

(i)

(ii)

(a) Better performer dummy: 1{xi > xj, random matching}#1

1.67*
(.89)
2.78*
(1.54)

0.08(0.97)
5.34***(1.65)
0.20***(0.05)
0.42(3.76)
57.53***(3.58)
243
234-926.36(b) Worse performer dummy: 1{xi < xj, random matching }#2(c) Term 1 formative assessment mark (xi)---A three-student team dummy {= 1(0) if a student was
assigned to a three(two)-student team}Constant# observations# selected
Log pseudolikelihood-6.67(4.70)
71.06***(1.18)
243
234-935.95(II) Both i and i’s partner
submitted term 2 PRA
(i)
(ii)

2.48**(1.05)
2.56(1.57)---5.94(5.19)
71.36***(1.15)
226
218-858.79

0.27(1.22)
3.64**(1.72)
0.19***(0.06)
0.89(4.54)
57.83***(3.90)
226
218-859.79(B) Selection equation that explains whether student i submits the summative assessment (i.e., thesubmission is observed)
Data:
Independent variable:(a) Better performer dummy: 1{xi > xj, random matching}#1(b) Worse performer dummy: 1{xi < xj, random matching}#2(c) Term 1 formative assessment mark (xi)(I) All data
(i)

(ii)

-0.38***(0.08)
0.12(0.12)-0.24*(0.13)-0.08(0.17)-0.006(0.006)-0.51***(0.14)
0.41***(0.09)---(d) The number of formative assessments not
submitted {= 0, 1, 2}(e) Seminar attendance rate  [0, 1]
A three-student team dummy {= 1(0) if a student was
assigned to a three(two)-student team}Constant-0.57***(0.03)
0.24***(0.01)
0.13(0.37)
1.71***(0.14)

n.a.#3
1.95***(0.65)(II) Both i and i’s partner
submitted term 2 PRA
(i)
(ii)

-0.44***(0.10)
0.12(0.13)---.69***(0.04)
0.81***(0.05)
3.81(n.a.)
1.42***(0.15)-0.42(0.53)
0.14(0.40)
0.010(0.014)-1.02**(0.50)
0.31(0.65)
3.25(3.39)
1.69***(0.95)

Notes: Estimations of the Heckman two-stage selection model with robust standard errors clustered by seminar group ID.
The numbers in parentheses are standard errors. In addition to the independent variables listed in the table, a term 1 tutor
dummy was controlled in both stages of regressions since there were two seminar tutors in term 1. Only observations inwhich a student submitted term 1 formative and his/her partner also submitted it were used as data. A three-student teamdummy was also added as a control since there was one such team in a session whose number of students was odd. #1 1{xi >xj, random matching} is an indicator variable which equals 1 if xi > xj and i is in the treatment condition; 0 otherwise. Here, xi(xj) is i’s (i’s partner j’s) term 1 formative assessment mark #2 1{xi < xj, random matching} is an indicator variable whichequals 1 if xi < xj and i is in the treatment condition; 0 otherwise. The reference group is observations in the control
condition. Equations I.i, I.ii, II.i, and II.ii of panel B are the selection equations of columns I.i, I.ii, II.i, and II.ii, respectively,of panel A. #3 The three-student team dummy was not included in the selection equation since otherwise the model was notconverged. *, **, and *** indicate significance at the .10 level, at the .05 level and at the .01 level, respectively.

38

Table 4: The Impact of Term 2 Random Matching by Part in the Summative Assessment(A) Second Stage Regression
Dependent variable:
Independent variable:(I) Mark of student i in Part B (Micro)
(i)
(ii)
(iii)
(iv)

(a) t2 random matching dummy {=1(0)1.49**
for the treatment (control) condition} (0.75)(b) A dummy that equals 1 if i did not--submit term 1 formative assessment(c) Interaction term: (1 – variable (b)) ×--term 1 formative assessment mark(d) Better performer dummy: 1{xi > xj,--random matching}#1(e) Worse performer dummy: 1{xi < xj,--random matching}#2(f) Term 1 formative assessment mark--(xi)
A three-student team dummy {= 1(0) if-0.35
a student was assigned to a
(2.12)
three(two)-student team}
28.72***
Constant(0.73)# observations# selected
Log pseudolikelihood

259
250-870.62

1.62**(0.65)
3.77(2.84)
0.08***(0.02)-----(II) Mark of student i in Part C (Macro)
(i)
(ii)
(iii)
(iv)

---

---

1.35**(0.55)

---

---

---

---

---

---

1.14**(0.49)
1.20(1.07)

0.32(0.47)
2.27**(1.02)
0.09***(0.03)

---

---

1.98
(1.92)-0.96(2.54)

1.71(2.15)

1.01*(0.57)-.20(3.55)
0.05**(0.02)

---

---

---

---

---

---

0.01
(0.65)
0.95(0.82)-0.21(0.66)
2.19***(0.85)
0.06***(0.02)

---

---

---

---

---

---

---

-4.03***(1.10)-1.58(1.65)-3.37(2.19)-2.24(2.21)

23.14*** 28.94*** 22.59***(1.64)(0.48)(1.98)

26.98*** 23.68***(0.53)(1.52)

27.53*** 23.79***(0.62)(1.74)

259
250-863.83259
250-827.49243
234-777.63

243
243
234
234
-815.16 -807.72

259
250-835.17243234-761.32(B) Selection equation that explains whether i submits the summative assessment (i.e., the submission is observed)
Dependent variable:
Independent variable:(I) Mark of student i in Part B (Micro)
(i)
(ii)
(iii)
(iv)

(a) t2 random matching dummy {=1(0)-0.20*(0.11)
for the treatment (control) condition}(b) A dummy that equals 1 if i did not--submit term 1 formative assessment(c) Interaction term: (1 – variable (b)) ×--term 1 formative assessment mark(d) Better performer dummy: 1{xi > xj,,--random matching}#1(e) Worse performer dummy: 1{xi < xj,--random matching}#2(f) Term 1 formative assessment mark--(xi)(g) The number of formative assessments -0.27***(0.01)
not submitted {= 0, 1, 2}
0.00(h) Seminar attendance rate  [0, 1](0.00)
A three-student team dummy {= 1(0) if a
-0.086
student was assigned to a three(two)(0.28)
student team}
1.76***
Constant(0.12)

0.001(0.09)
0.26(0.39)
0.001(0.003)(II) Mark of student i in Part C (Macro)
(i)
(ii)
(iii)
(iv)

---

---

0.26***(0.08)

---

---

---

---

---

---

-0.17***(0.06)-0.05(0.14)

0.32(0.27)
6.32***(0.88)
0.004(0.01)

---

---

---

---

---

---

-0.38
(0.35)-0.37(0.41)-------0.28***(0.01)-0.26***(0.010)-0.40***(0.02)-0.13***(0.01)-0.24(1.15)-0.23(0.48)
0.00(0.02)-0.47(0.96)-0.08(0.09)-0.036(0.26)

2.70(n.a.)

3.85(n.a.)

4.45(n.a.)

6.04***(0.35)

4.78***(0.47)

6.52(n.a.)

1.76***(0.22)

1.85***(0.10)

1.99***(0.29)

1.26***(0.10)

2.00***(0.52)

2.25***(0.52).83***(0.29)

-----

---

---

---

---

---

---

---

-0.16***(0.01)
0.00(0.00)-0.55*(0.29)
0.05(0.65)-0.54**(0.27)
0.09(0.59)-0.03(0.11)-0.46(0.14)
0.003(0.004)-0.58***(0.04)
0.61***(0.04)

Notes: Estimations of the Heckman two-stage selection model with robust standard errors clustered by seminar group ID. The
numbers in parentheses are standard errors. All data are used. In addition to the independent variables listed in the table, a term 1
tutor dummy was controlled in both stages of regressions since there were two seminar tutors in term 1. For columns I.iii, I.iv,
II.iii, and II.iv, only observations in which a student submitted term 1 formative and his/her partner also submitted it were used asdata. #1 1{xi > xj, random matching} is an indicator variable which equals 1 if xi > xj and i is in the treatment condition; 0
otherwise. Here, xi (xj) is i’s (i’s partner j’s) term 1 formative assessment mark #2 1{xi < xj, random matching} is an indicator39

variable which equals 1 if xi < xj and i is in the treatment condition; 0 otherwise. Equations I.i, I.ii, I.iii, I.iv, II.i, II.ii, II.iii andII.iv of panel B are the selection equations of columns I.i, I.ii, I.iii, I.iv, II.i, II.ii, II.iii and II.iv, respectively, of panel A. Resultschange little when the demographic information is added as controls. *, **, and *** indicate significance at the .10 level, at
the .05 level and at the .01 level, respectively.

40