GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.236

Peer effects of swimmers

Shoko Yamane and Ryohei Hayashi

January 2012GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Peer effects of swimmers

Shoko Yamane†
Ryohei Hayashi‡
January 2012

Abstract

In this study, we purely and directly revealed peer effects by using a large dataset from the official
Internet site of the Japanese Swimming Federation. First, we completely excluded the endogeneityof peer assignment and found that the performance of adjacent peers positively influencesswimmers’ performance; swimmers can swim faster with fast, high-ability peers. We also found thatswimmers are aware of their peer who has a lower best record than theirs. Being chased improves
swimmers’ performance. Second, using absent-peer data, we directly compared the performance ofindividual swimmers with and without an adjacent peer. We found that the existence of adjacentpeers enhances swimmers’ performance. Furthermore, when we compared the records for freestyleand backstroke competitors, we found that the ability to observe peers affects the emergence of peer
effects.

Keywords: Peer effects, Swimming, Online data
JEL classification: J44, L83† Graduate School of Economics, Osaka University, Research Fellow of the Japan

Society for the Promotion of Science, E-mail: evidence8money@gmail.com
Address: 1-7-504 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
‡ Graduate School of Economics, Osaka University, Email: pey@ryohei.info
We thank Fumio Ohtake, Takahiro Ito, Yoshihiro Miyai, Masaru Sasaki, Richard
Freeman, Takao Kato, Ken Ariga, and Daiji Kawaguchi for their valuable comments.
We also thank the participants of the Ohtake and Sasaki Seminar in ISER,
Trans-Pacific Labor Seminar 2011, Summer Workshop Economic Theory 2011, andAnnual Conference of Applied Micro Econometrics 2011.
1

1. Introduction
Do employees work hard when their coworkers are working hard? In a workplace, this is a very
important question because the workplace is a social place where workers must share and cooperate.
This question is related to designing the optimal workplace environment and incentives. Guryan et al.
(2009) suggested three pathways of social effects that influence us in the workplace. The first iscalled the “learning effect,” which describes the process that the workers learn from their coworkers
about how to perform a given task in the best way. The second is the “motivation effect,” whereby
workers are motivated when they see their coworkers working hard and performing well. The third is
the “mechanical effect.” In some production processes such as assembly lines in automobile
factories, coworkers’ productivity mechanically influences a worker’s productivity. Guryan et al.
(2009) defined learning effects and motivation effects as “peer effects.” Peer effects have beenthoroughly studied in economics, and also in many psychological studies under a different label.
In psychology, researchers seem to have reached consensus on the existence of peer effects. Theirmain issue is the direction of peer effects, that is, whether a person is facilitated or inhibited byothers. The earliest study Tripllet (1898) found positive peer effects among cyclists, whereas Pessin(1993) found negative effects. Zajonc (1965) suggested that the direction of peer effects depends onthe characteristics of tasks, indicating that there are positive peer effects in well-learned tasks andnegative peer effects in complicated tasks.
In contrast, economics has focused on the existence of peer effects. Economics research has
assumed that peer effect implicitly means a positive effect, and no regard is given to negative peer
effects. Peer effects in economics were first studied in crime rates and education. Falk and Ichino(2006) studied peer effects in the workplace with a laboratory experiment, whereas Mas and Moretti(2009) and Bandiera, Barankay, and Rasul (2010) measured peer effects using actual workplace data.
Mas and Moretti (2009) investigated the productivity of cashiers in supermarkets and suggested theiroptimal placement. Bandiera, Barankay, and Rasul (2010) focused on social ties, indicating theimportance of the presence of friends. Most economic studies conclude that peer effects exist, but
Guryan et al. (2009) by using golf tournament data found no peer influence. The golf tournament
data are well suited to random assignment, which are always important in avoiding the statisticalproblem of common shock inherent in estimating peer effects. They found that in golf tournaments,
performance arises from strong financial incentives, but they did not consider the nonlinearity ofpeer effects. If negative peer effects are balanced by positive peer effects, the result can be no peer
effects. Such mutual cancellation may explain their inability to observe peer effects among golfers.
The purpose of the present paper is to examine peer effects using swimming data. Swimming dataoffer many advantages for testing peer effects so as to reveal the peer effect purely and directly. The
primary advantage of swimming data is that the rule for peer assignment is completely observable,
and we can eliminate endogeneity in peer assignment. Previous studies found the optimal condition2

in which the assignment of peers is considered to be random (e.g., cashiers or golf tournament). In
swimming, however, the adjacent peer is assigned mechanically using each player’s best record
according to the International Rules. Because we have each swimmer’s best record in our dataset, we
can perfectly control the endogeneity of peer assignment using the lane assignment rule. Thus, we
can extract the pure peer effect.
The second advantage is that, with absent-peer data, we can also test the effect of peer existence bycomparing the performance of individual swimmers with and without an adjacent competitor.
Swimmers are aware only of competitors in adjacent lanes, and hence, if both adjacent competitors
are absent, swimmers perceive themselves to be swimming alone. Using this absent-peer data, we
can obtain and compare an individual’s records both with and without adjacent peers, allowing us to
identify the effects of peer existence. Third, we can use the differences between stroke styles. There
are four styles in swimming: freestyle, breaststroke, backstroke, and butterfly. As noted below indetail, we test the existence of peer observability using the differences between freestyle andbackstroke. Because swimmers cannot see adjacent peers in backstroke, we can assume that thedifference between freestyle and backstroke results from the ability to observe peers.
The other advantage of swimming data is that they are free from common shocks that hamper theestimation of peer effects, such as the weather condition in Guryan et al. (2009). In addition, because
our data are extracted from an Internet site, the large dataset of swimming records is sufficient toinclude swimmers with low to high performance levels. This allows us to examine the relationshipbetween peer effects and skill levels. On the other hand, Mas and Moretti (2009) investigated peer
effects only in low-skilled workers, and Guryan, Kroft, and Notowidigdo (2009) studied professional,
highly skilled workers.
There is no need to consider learning in swimming because the very brief time (only about one
minute) during which swimmers swim is too short for learning to occur. Therefore, our definition ofpeer effects is limited to the effect of being motivated by the performance of their adjacentswimmers. Our first contribution is revealing purely the peer effect and showing the nonlinearity of
its influence by excluding peer assignment endogeneity. Our secondary contribution is showing
directly the effect of peer existence.
Although swimming data have many advantages in testing peer effect, they may also seem to havesome weakness, but are not. There is no direct monetary reward in swimming data, but there are thequalifying standard and the qualification rank provided by Japanese Swimming Federation1 (JSF),
which motivate swimmers to achieve better scores. If a swimmer obtains a higher qualifying
standard and qualification rank, he can participate in more numerous and higher rank meets. They
To be exact, the qualifying standards are provided by the organizer of each meet.
Some meets are organized by the Japanese Swimming Federation, while others areorganized by the Japan Sports Association, the swimming federation of each prefecture,
the All Japan High School Athletic Federation, and so on.
13also gain fame and subsidies for national meets or training camps if they achieve a very highstandard or rank. Thus, we might say that the rewards that motivate swimmers include primarily
honor (nonmonetary), in addition to a few monetary rewards. Furthermore, there seem to bemechanical effects from waves. It is possible that the waves caused by peers affect swimmers’
performance. As noted below in detail, we reject this doubt in representing the results of backstroke.
The rest of this paper is organized as follows. Section 2 describes the international rules ofswimming. Section 3 explains the estimation model and dataset. Section 4 describes the results, andSection 5 presents the conclusion and discussion.

2. RulesThe International Rules specify how swimmers are assigned their lanes. Our explanation focuses oneight-lane pools because most competitions have eight lanes 2 . Each swimmer applies to acompetition by submitting his best records to date. Swimmers are classified into groups of eight. As
shown in Figure 1, lane 1 is on the right extremity of the pool as seen when facing the pool from thestarting line. The swimmer with the fastest record is placed in lane 4, and the next fastest is assigned
to his immediate left (lane 5). The assignment of the other swimmers alternates to the right and left
in accordance with their submitted records.

Pool
Lane number

lane 8lane 7lane 6lane 5lane 4lane 3lane 2lane 1

Order of best record

8th

6th

4th

2nd

1st

3rd

5th

7th

Figure 1: Lane numbers and order

3. Data and Model
3.1 Data Detail
We

used

two

onlinedatasets,

both

from

“Swim-Record

dot

com”

(http://www.swim-record.com/index.html), the official Internet search site of the Japanese
Swimming Federation (JSF). The site includes approximately 1,500 official competition records per
year from competitions held by each JSF member organization (mainly in each prefecture).

The method of assignment in a pool with more or fewer lanes than eight is provided inAppendix 1, the International Rules.
2

4

Members are obliged to reveal all records of official JSF competitions to the public. The official
record contains only JSF-registered swimmers in competitions governed by International Rules.
Therefore, unofficial records (for example, of citizen’s competitions) are excluded from our data.
The number of these unofficial records is insufficient to affect our results.
The athletic events comprising our data from both datasets were 100 meter freestyle short course
competitions for men from 2007 to 2010 for the following reasons: (1) Short course competition isheld year-round, providing extensive and easily mined data. (2) The 100 meter freestyle is a general
event, whereas the 200 meter freestyle is a specialty event. The general event includes competitorswith a range of skills and therefore provides the necessary range of skill-level data. (3) The timespan of a 50 meter freestyle event is approximately 30 seconds, and the competitor’s success often
depends on the quality of his entry into water. Therefore, it provides less suitable data for testing
peer effects. (4) Swimmers customarily breathe with their heads turned consistently to the left or
right. Since the 50 meter event involves swimming one length of the pool, competitors can see only
the competitor on their left or right side during the competition. On the other hand, the 100 meter
event involves swimming two lengths, enabling athletes to see both adjacent competitors during therace if he breathes only with right or left side. We used data only from an event’s qualifying heats,
not its final competition. With the slower competitors eliminated, only the fastest swimmers compete
in the final match, which would have skewed our statistical results.
There are two types of races. One is finals; only swimmers who survive the heats swim in the final
match. The Olympic Games adopt this system. In the final match, all the fastest competitors swim
simultaneously. Therefore, we cannot distinguish the peer effects and order effect using finals data
because it is natural for the swimmers to swim faster with fast peers, all of whom want to win thecup. The other type is timed finals, which has no final match. Swimmers are classified into groups of
approximately eight, and each swimmer’s time in the heats determines the final rank. Here aswimmer cannot necessarily win the cup if he swims faster than adjacent swimmers, because evenfaster swimmers may be competing in different heats. Thus, each swimmer’s optimal strategy is to
give his best performance regardless of his peers’ performance. We use timed finals data to examine
peer effects.

3.2

Estimation Models and Data Setting

In this paper, we examine peer effects and their attributes from three viewpoints. We test peer
effects by creating three datasets, one suitable for each effect.
First, we test the peer effect that has been thoroughly examined in previous studies. We examine
this effect more purely than have previous studies by using the rules of5lane assignment. Let Ritdenote the records of an individual i in competition t , andRsi denote the records of anindividual i in competition s . We denote peer status by a dummy variable Pi , which has value 1
with R1i and 0 with R0i . We use this notation to distinguish it from the other peer effect noted
below, and can describe this effect as a conditional expectation of Ri given Pi . The peer effect isexpressed as follows:

ERti  Rsi | Pi  1(1)

By this estimator, we can observe how the performance of the peers improves one’s performance.
We test this effect by using our first dataset, the “Peer Dataset,” which consists of the panel data of
the same individual in the same lane; the panel identifier consists of the individual and lane number.
Thus, when the swimmer is assigned the same lane, the peers assigned on his left and right areconsidered random. For each swimmer and his competitors on the left and right, we compute the bestrecords from all past competitions in our data. We created this elaborate dataset because we faced
two problems in estimating the peer effect. One is the reflection problem (Manski 1993). A swimmer
influenced by his adjacent peer also influences that peer, so we cannot use the peer records for thecurrent competition as peer productivity. The other is the assignment problem. As shown in Section 2,
lane assignment occurs according to the rule and each lane has its unique characteristics. Therefore,
we cannot use the panel data of only swimmers’ names as the panel identifier. To control for thischaracteristic of the lane, we estimate the fixed effects on the panel identifier consisting of individualand lane number. For the Peer Dataset, we specify the estimation model as follows:

Rilt  il   1Bit   2 B jt   3 X it   ilt(2)

Rilt denotes the record of swimmer i in lane l of competition t . Bit is swimmer i ’s bestrecord at t . In this model, subscript j implies i ’s peer, so  2 captures the peer effect. X i is

i ’s personal variable such as school age. We estimate these parameters with fixed effects on i andl . Each swimmer’s optimal strategy is to give his best performance regardless of his peers’
performance, whether faster or slower. Then, the coefficient of the peer’s performance equals 0.
Thus, we can say that there is a positive peer effect if swimmers swim faster when adjacent peers
swim fast and a negative peer effect if swimmers swim slower when adjacent peers swim fast.
We use the records of only swimmers who swim more than three times and have better records thanboth their left and right swimmers. We also exclude the records of the endmost lanes, such as lanes 1
and 8, in the eight-lane pool. The Peer Dataset contains 11486 records of 5373 swimmers.
Second, we examine the peer existence effect directly. Let R1i denote the records of an individual

i if he had peers and R0i denote the records of an individual i if he had no peer by theabstention of peers. The peer existence effects are expressed as follows:6

ER1i  R0i (3)In the previous test, it is impossible to obtain both records R1i and R0i for the same individual.
However, we can observe both records R1 and R0 for each individual in swimming data becauseof the abstention of peers. We have the data of individual swimmers’ performances with and without
a competitor in the adjacent lane. Swimmers can watch only the peer competitor swimming in theimmediately adjacent lanes of the pool; hence, if no peer swimmer is present, there is no peer effect.
We directly compare the performance in both situations. Since the absence of an adjacent swimmer
is an exogenous shock for a swimmer, we can consider the data as resulting from a naturalexperiment. Using the estimator of equation (3), we investigate whether the existence of adjacentpeers enhances or diminishes performance.
In our second dataset to test the effect of peer existence, the “Abstention Dataset,” we have tworecords: R0i denotes the records when the swimmer has no peer and R1i denotes the existence ofa peer in both his right and left adjacent lanes (i.e., two peers). We choose R1i from all records foreach swimmer i as follows:

R1i  arg min{D1i  D0i }(4)

D0i is the date of a competition in which i had no peer. The nearest data of all competitions for
i are chosen as a target for comparison so that the progressive athletic development of i would
not distort the results. To estimate the peer existence effects, we specify the model as follows:Ri   i  1 Pi   2 Di   i
Ri  R0i , R1i , Di  D0i , D1i(5)

Pi is a dummy variable that has value 1 with R1i and 0 with R0i . Hence,  1 captures the peer
existence effects. Swimmers’ performance is enhanced by adjacent peers if  1 is positive andinhibited if negative. This dataset contains R1i that are older than R0i ; other data have more
recent R1i . Swimmers become faster as they develop. To take that into account when comparing
data with and without peers, we use the date of record as an independent variable. Thus  2
captures the effect of swimmers’ development.
We primarily use the records when both-sided peers are present as R1i , but also have records when
only a one-sided peer is present for some individuals. To examine whether the number of peers
influences the impact of the peer existence, we also compare these one-sided presence records with

R0i . If the number of peers linearly influences the impact of peer existence, the presence of aone-sided peer has half the impact of the presence of both-sided peers. However, there might besome nonlinearity between the number of peers and the impact of the peer existence.
We count the swimmers who did not participate in the race at all for the abstentions. We do notregard abstention players who swam until the middle of the race. Similarly, we exclude disqualified
7

players from the Abstention Dataset because we do not know when a competitor left the race. We
also exclude the records of the endmost lanes. The Abstention Dataset contains 21954 records of
5187 unique swimmers and 3924 one-sided abstention records of 1267 unique swimmers.
Finally, we examine the influence of observable peers by comparing the records of backstroke andfreestyle swimmers. In backstroke, swimmers cannot see adjacent peers because they swim on theirback. Hence, the difference between freestyle and backstroke results from the observability of peers.
To reveal the existence of observable peers, we created a third dataset, the “Backstroke Dataset,”
structured the same as the Peer Dataset, with the panel data of the same swimmer in the same lane.
We can thus reveal how the existence of observable peers influences swimmers’ performance. We
perform the estimation with model (2) using backstroke records, and compare two  2 , one fromfreestyle estimation and the other from backstroke estimation. The difference between these two  2
represents the effect of observability. The Backstroke Dataset contains 1096 backstroke (100 meterin short course) records of 602 swimmers3.
Now we can examine all three effects: the pure peer effect, the peer existence effect, and theobservability effect. This examination demonstrates the influence of peers and its attributes moreclearly and minutely.

4. Results
4.1 Descriptive Statistics
We begin with the descriptive statistics of key variables, as shown in Table 1. Panels A, B, and C
show descriptive statistics of the Peer Dataset, Abstention Dataset, and Backstroke Dataset,
respectively. A smaller value of “record” indicates higher performance. We represent the date by aserial value in which January 1, 1900 takes numeric value 1; January 2, 1900 takes 2; and so on.
Definitions of all variables appear in Appendix 2. In the Peer Dataset, the average of a swimmer’s
own record, the swimmer’s own best record, and peers’ best records are approximately 62 seconds
and 70 seconds, respectively, in the Backstroke Dataset. The mean records are approximately 64 s
regardless of the existence or the number of peers in the Abstention Dataset. There is no difference
between the average record of the competition with and without peer (t(21964) = −1.64, n.s.). The
quality of competitions is same regardless the existence of abstention swimmers.

The sample size is too small compared with the above two datasets. It is obtained fromthe number of swimmers because backstroke is a specialized event compared with 100
meter free style, in which the most swimmers participate. Later, we create the Freestyle
Dataset, which has the same sample size as the Backstroke Dataset, and denote its
results as well.
3

8

Table 1 Descriptive statistics
Panel A: Peer Dataset

Variable

N

Mean

SD

Min

Max

record

11486

62.00

6.27

48.10

104.99bestrecord

11486

62.42

6.64

48.88

106.49bestrecord_side

11486

62.65

6.73

49.06

116.90

bestrecord_left

11486

62.67

6.88

48.88

116.67

bestrecord_right

11486

62.64

6.94

48.88

126.41schoolage

11486

7.58

2.16

1

16

SD

Min

Max

Panel B: Abstention Dataset

Databoth-sided
abstention
data
one-sided
abstention
data

Records type

VariableN

Meanwith peer

record

10977

64.52

7.97

49.52

121.58

records

date

10977

17809.88

353.51

17257

18342

without peer

record

10977

64.34

7.91

49.63

121.67

records

date

10977

17848.10

347.99

17257

18343

with peer

record

1962

64.88

8.69

50.13

118.85records

date

1962

17840.95

304.27

17257

18342

without peer

record

1962

64.75

8.21

50.18

118.13

records

date

1962

17842.34

352.53

17264

18343

Panel C: Backstroke Dataset

Variable

N

Mean

SD

Min

Max

record

2534

68.45

6.61

53.34

95.58

bestrecord

2534

68.93

6.97

52.63

109.33

bestrecord _side

2534

69.55

6.89

53.37597.28

bestrecord _left

2534

69.61

7.42

52.63

102.64

bestrecord _right

2534

69.49

7.21

52.63

98.88

schoolage

2534

7.53

2.11

2

17

9

4.2 Pure Peer Effect
In this section, we identify the peer speed effect using the Peer Dataset. We examine the estimatedresults shown in Table 2. In column 1, the coefficient of the average of left and right peers’ bestrecords is highly significant and the signs are positive. Thus, the faster the peers swim, the faster theswimmer swims. In average neighborhood, the performance of a swimmer improves by 0.18 seconds
when his peer swims faster by 1 second. Column 2 represents the result of regression testing using
each of the right and left best records regardless of the average of best records. Both left and right
best records are highly significant, with both-sided peers equally influencing the swimmers.
In column 3, we present the estimation results considering the land characteristics. As shown insection 3.1, some swimmers have the peer with the faster best records than theirs in their left lane,
and others have the faster peer in their right lane. For example, in an eight-lane pool, the swimmers
in lane numbers 1, 2, and 3 have the faster peer in their left lane and the slower peer in their rightlane. In contrast, the swimmers in lanes 5, 6, 7, and 8 have the faster peer in their right lane and theslower peer in their left lane. In the regression of column 3, we omit the fastest lane (lane 4 in aneight-lane pool) because they have only slower peers. Column 3 of Table 2 shows that the coefficientof the slower lane is positively significant but that of faster lane is not. We found that the faster theslower lane peer swims, the faster the swimmer can swim. Thus, the performance of a swimmer isimproved by the slow-lane peer. This result shows that there is a “chased effect,” with a swimmer
aware only of his peer in the slower lane who has the slower best records4. We obtain the same result
using the swimmers who swam more than five times or ten times.
We can also use the current as well as best records of peers. Then, we perform the three-stage
estimation. The first and second stages consist of OLS estimation of the peer record at the current
competition; the records of the right or left peer are treated as endogenous variables and his bestrecord and school age are used as instrumental variables. In the third stage, we conduct OLS
estimation with estimation model (2) using peers’ current records instead of their best records. Table
3 represents the estimation result with instrumental variables. The coefficients of the records of theright and left peers remain positively significant. The coefficient of the slow lane peer’s record isalso positively significant; however, the fast lane peer’s record is also positively significant, unlikethat shown in Table 25.

We divide the sample by the relative position in the current competition as in Section
4.3, and obtain the same result as shown in Table 2 in all divisions.
5 We cannot, however, control the individual fixed effect in IV regression because of
insufficient sample.
4

10

Table 2: Regression result of peer effects
The dependent variable is the swimmer’s own record, with individual and course fixed effects.

(1) with average of left(2) with each of left

and right bestand right bestlane

records

records

characteristics

Coef.

p valueCoef.

p value(3) with adjacentCoef.

p valueConstant

20.535 [0.000]**

20.515 [0.000]**

18.997 [0.000]**

best record

0.553 [0.000]**

0.553 [0.000]**

0.554 [0.000]**

schoolage-0.548 [0.000]**-0.547 [0.000]**-0.476 [0.000]**

best record _side

0.177 [0.000]**

best record _right0.093 [0.000]**

best record _left

0.084 [0.000]**

best record _fastlane

0.036 [0.070]

best record _slowlane

0.156 [0.000]**

Obs

11486

11486

7541

R squared

0.834

0.834

0.832

Note: ** 1%, * 5% significance.

11

Table 3: IV result of peer effects

Model

Dependent var.
recprd_rightrecord_left(1) with each of left andright best records

recordrecord_fastlane

record_slowlane(2) with adjacent lane
characteristics

recordIndependent var.

Coef.

p valueConstant

4.985 [0.000]***besttime_right

0.915 [0.000]***schoolage_right-0.013 [0.000]***Constant

4.758 [0.000]***besttime_left

0.918 [0.000]***schoolage_left-0.011 [0.000]***Constant

4.039 [0.000]***besttime

0.665 [0.000]***

time_right0.134 [0.000]***

time_left

0.136 [0.000]***schoolage-0.043 [0.000]***Constant

5.428 [0.000]***besttime_fastlane

0.907 [0.000]***schoolage_fastlane-0.012 [0.000]***Constant

5.365 [0.000]***besttime_slowlane

0.910 [0.000]***schoolage_slowlane-0.015 [0.000]***Constant

5.083 [0.000]***besttime

0.668 [0.000]***

time_fastlane

0.090 [0.000]***

time_slowlane

0.161 [0.000]***schoolage-0.063 [0.000]***Note: ** 1%, * 5% significance.

12

Next, we examine whether the impact of peer effect is influenced by skill level. Because skill level
and age can be highly correlated, we use quantile regression by school level: elementary school,
junior high school, senior high school and adult. We have five quantiles: 0.1 quantile (very low skill),
0.25 quantile (low skill), 0.5 quantile (medium skill), 0.75 quantile (high skill), and 0.9 quantile(very high skill). Table 4 reports the regression result at each school level. Panel A of Table 4 showsthe elementary school students (sample size 4036), Panel B shows the junior high school (sample
size 5192), and Panel C shows high school and older (sample size 2258). Figure 2 shows the size ofthe coefficient of “besttime_side” in each quantile and each school level. The results show that therelationship of the size of the peer effect and skill level is nonlinear. Among the elementary school
swimmers, low-skilled swimmers feel the strongest peer effects and the impact of the peer effectdecreases with rising skill level. However, the highest-skilled swimmers are more influenced bypeers. Although the junior high school swimmers exhibit almost same results as the elementary
school swimmers, the coefficients of peers’ records are smaller than those for elementary school
swimmers in all quantiles. In contrast, the high school and adult swimmers seem to have a very
different pattern. That is, the 0.25 quantile is least affected and the highest-skilled swimmers aremost affected. However, we found that the coefficient of peer speed effect for the 0.25 quantile ofhigh school is similar to that for the 0.75 quantile of junior high school, and that of the 0.5 quantile
for high school is as large as the 0.9 quantile for junior high school, as shown in Figure 2. We canconsider that the 0.25 quantile of high school overlaps with the 0.75 quantile of junior high school,
and the 0.5 quantile of high school overlaps with the 0.9 quantile of junior high school. Therefore,
we can draw a U-shaped line whose lowest point is approximately the median6. On the whole, thelowest-skilled swimmers (beginners) are most affected and the second-most affected are the top
swimmers.

We think this idea is feasible because the average records of the two resemble eachother; the 0.25 quantile of high school is 57.52 seonds, and 0.75 quantile of junior highschool is 57.77 seconds. Similarly, the average record of the 0.5 quantile of high school is
55.35 seconds, and that of the 0.9 quantile of junior high school is 55.81 seconds.
6

13

Table 4: Result of quantile regression for peer speed effect in school
The dependent variable is the swimmer’s own record.

Panel A: Elementary school students
0.1 quantile
Coef.

p value

0.25 quantile
Coef.

p value

0.5 quantile
Coef.

p value

0.75 quantile
Coef.

p value

0.9 quantile
Coef.

p valueConstant

11.98 [0.000]**

8.481 [0.000]**

6.26 [0.000]**

3.924 [0.000]**

0.707 [0.264]

bestrecord

0.584 [0.000]**

0.705 [0.000]**

0.789 [0.000]**

0.840 [0.000]**

0.861 [0.000]**

bestrecord_side

0.232 [0.000]**

0.170 [0.000]**

0.129 [0.000]**

0.122 [0.000]**

0.156 [0.000]**

schoolage−0.382 [0.000]**−0.283 [0.000]**−0.259 [0.000]**−0.223 [0.000]**−0.169 [0.001]**

0.25 quantile

0.5 quantile

0.75 quantile

0.9 quantile

Panel B: Junior high school students
0.1 quantile
Coef.

p valueCoef.

p valueCoef.

p valueCoef.

p valueCoef.

p valueConstant

10.988 [0.000]**

7.228 [0.000]**

5.097 [0.000]**

2.98 [0.000]**

1.427 [0.031]*

best record

0.645 [0.000]**

0.724 [0.000]**

0.793 [0.000]**

0.847 [0.000]**

0.850 [0.000]**

bestrecord_side

0.170 [0.000]**

0.146 [0.000]**

0.121 [0.000]**

0.109 [0.000]**

0.132 [0.000]**

schoolage−0.197 [0.000]**−0.052 [0.070]−0.027 [0.284]−0.006 [0.836]

0.071 [0.090]

0.25 quantile

0.5 quantile

0.75 quantile

0.9 quantile

Panel C: High school student and adults
0.1 quantile
Coef.

p valueCoef.

p valueCoef.

p valueCoef.

p valueCoef.

p valueConstant

6.308 [0.000]**

4.791 [0.000]**

2.423 [0.000]**

0.926 [0.127]

0.387 [0.598]

bestrecord

0.725 [0.000]**

0.793 [0.000]**

0.810 [0.000]**

0.807 [0.000]**

0.820 [0.000]**

bestrecord_side

0.152 [0.000]**

0.122 [0.000]**

0.151 [0.000]**

0.186 [0.000]**

0.194 [0.000]**

schoolage−0.051 [0.096]

0.048 [0.020]*−0.021 [0.170]

0.004 [0.858]−0.005 [0.860]

Note: ** 1%, * 5% significance.
14

.25
.2
.15
.1

0.1

0.25

0.5

0.75

0.9

quantile
Elementary school
High school & Adult

Jr. high school

Figure 2: Coefficient of peer’s best records

4.3 Peer Existence Effects
In this section, we test the peer existence effects by the regression of the dummy variable forhaving peers using the Abstention Dataset. Table 5 represents the results of the regression using theboth-sided abstention and presence records. In the first column, which shows the results of all
samples, the coefficient of the peer dummy is highly significant, and its sign is negative; swimmers
swim faster against competitors than alone. Then, we divide the sample by the relative position withthe peers, and regression (2) in Table 5 shows the result of swimmers who swim faster than bothpeers. Here we find that the coefficient of the peer dummy is also negatively significant. However, inregression (3), the result of the swimmers who swim slower than peers, the coefficient of the peer
dummy is positively significant. Thus, we find that the relative position to peers changes the
direction of the peer existence effect. Because the swimmer who is behind both adjacent peers is atleast rank 3, he might lose his motivation.
Regressions (4) and (5) show the results of the swimmers who swim faster or slower than at least
one of two peers. The coefficient of the peer dummy is also negatively significant in swimmers
faster than at least one peer, but the size of its coefficient is smaller than regression (2). In the groupslower than at least one peer, the coefficient of the peer dummy is not significant.
Next, to confirm whether the number of peers influences the impact of peer existence, we compare15

the records when the one-sided peer is present and the other-sided peer is absent with those when
both-sided peers are absent. Column 1 of Table 6 shows the results of all samples, and the peer
dummy is not significant. However, if we consider the relative position to peers, we obtain the same
results as those in Table 2: a swimmer can swim faster with a slower peer than alone, but he swims
slower with a faster peer than alone.
From Tables 5 and 6, we found that a swimmer can swim faster than alone when he is pursued frombehind, but slower when his peer swims ahead of him. Thus, the existence of a pursuer improves
swimmers’ performance. This is similar to the chased effect noted in Section 4.2. On average, peer
existence improves a swimmer’s performance by 0.64 seconds when the peers are slower than him
and diminishes it by 0.48 seconds when the peers are faster than him7. In all regressions of Tables 5
and 6, the coefficient of date is negatively significant, which appropriately captures the effects ofdevelopment.
The performance of swimmers far from peers might be same as that of the swimmers swimmingalone, and there could be stronger peer effects in a close match. Therefore, we divide the samples by
the difference between the swimmer’s own and peers’ records and perform the same regression foreach group. Our first group is within 0.5 seconds faster or slower than the peers. The 0.5 seconds
difference is nearly equal to half the body-length’s distance, so this case is considered a close match.
The other group has 2 seconds difference, representing approximately a 3 meter difference, which ismore than a two-body-lengths’ distance. Table 7 shows the regression results. We found nodifference between a swimmer’s own and peers’ speeds (lead/lag distance).Thus, Swimmers are
more influenced by peers’ relative position.

Naturally, a 1-s improvement from 45 s and 70 s should be considered to be different.
Therefore, we can interpret the coefficient of peer existence “in average neighborhood”.
7

16

Table 5: Result of regression with fixed effects of swimmers’ names(both-sided peer existence)
Dependent variables: swimmers’ own records(1) Default
Coef.

(2) Faster than both peers

p value

Coef.

(3) Slower than both peers

p valueCoef.

p valueConstant

221.365 [0.000]**

226.14 [0.000]**

221.878 [0.000]**

peer−0.151 [0.000]**−0.641 [0.000]**

0.475 [0.000]**

date−0.009 [0.000]**−0.009 [0.000]**−0.009 [0.000]**

Obs

21954

6878

5746

R squared

0.589

0.611

0.566

(4) Faster than one peer(5) Slower than one peer

at least

at least

Coef.

p valueCoef.

p valueConstant

222.028 [0.000]**

220.269 [0.000]**

peer−0.375 [0.000]**

0.067 [0.077]

date−0.009 [0.000]**−0.009 [0.000]**

Obs

16208

15076

R squared

0.598

0.578

Note: “Peer” is a dummy variable that equals 1 if the record includes data when both adjacent swimmers
are present and 0 otherwise. ** 1%, * 5% significance.

Table 6: Result of regression with fixed effects of swimmers’ names(one-sided peer existence)
Dependent variables: swimmers’ own records(1) Default
Coef.
Constant

p value(2) Faster than peer(3) Slower than peer

Coef.

Coef.

p valuep value

248.933 [0.000]**

242.011 [0.000]**

248.889 [0.000]**

peer

0.124 [0.111]−0.258 [0.011]*

0.489 [0.000]**

date−0.01 [0.000]**−0.01 [0.000]**−0.01 [0.000]**

Obs

3924

1980

1944

R squared

0.575

0.602

0.555

Note: “Peer” is a dummy variable that equals 1 if the record includes data when an adjacent swimmer ispresent and 0 otherwise. ** 1%, * 5% significance.

17

Table 7: Close match or not, with fixed effects of swimmers’ names

Faster by more than

Slower by more than

Faster within 0.5 s

Slower within 0.5 s

2 s than both peers

2 s than both peers

than both peers

than both peers

Constant

281.294 [0.000]**

297.781 [0.000]**

216.928 [0.000]**

174.583 [0.000]**peer-0.671 [0.000]**

1.695 [0.000]**-0.827 [0.003]**-0.288 [0.210]

date-0.012 [0.000]**-0.013 [0.000]**-0.009 [0.000]**-0.006 [0.000]**

Obs

1714

1154

282

268

R squared

0.663

0.623

0.574

0.515

Faster by more than

Slower by more than

Faster within 0.5 s

Slower within 0.5 s

2 s than one peer

2 s than one peer

than one peer

than one peerConstant

207.597 [0.000]**

247.343 [0.000]**

155.933 [0.000]**

154.47 [0.000]**

peer-0.389 [0.013]*

1.006 [0.000]**-0.329 [0.045]*-0.309 [0.044]*

date-0.008 [0.000]**-0.01 [0.000]**-0.005 [0.000]**-0.005 [0.000]**

Obs

820

802

386

416

R squared

0.49

0.47

0.43

0.447

Note: ** 1%, * 5% significance.

4.4 Peer Observability
Finally, we examine the effect of peer observability using the Backstroke Dataset. Columns 1 and 2of Table 8 show the estimated results. The coefficient of peers’ performance is not significant. We
know that the observability of peers is important; however, unlike freestyle, backstroke swimmers
are not aware of the existence of the adjacent peer8. This result also shows that there is no wave
effect. If the wave effect existed, peer performance would be also significant in the backstroke.
To examine the effect of peer observability again, we estimate using the next two lanes. The result
is presented in columns 3 and 4 of Table 8. Although we might assume that swimmers are actuallyaware only of swimmers in adjacent lanes, we test this assumption. If swimmers are aware of not
only their adjacent peers but also those to the right and left past the next lane peers, the coefficient ofpeers’ best records is significant in this estimation. We have 3757 short course freestyle records (100To exclude the doubt that this result comes from a small sample, we choose randomly
a freestyle sample equaling the backstroke sample (about 1000). We repeat this choice
10 times, and the coefficient of peer performance is positively significant in all trials,
two at 10% significance, one at 5% significance, and the rest at 1% significance.
818m) of 2485 swimmers with the best records of their two adjacent peers. The coefficients of the next
two peers’ best records are not significant. Thus, we find that swimmers are aware of only their
immediately adjacent peers.

Table 8: Regression result using backstroke and two adjacent peers
The dependent variable is the swimmer’s own record, with individual and course fixed effects.

Backstroke(1) with average of

Two adjacent peers(2) with each of left(3) with average of(4) with each of left

left and right bestand right bestleft and rightand right bestrecords

records

best records

records

Coef.

p valueCoef.

p valueCoef.

p valueCoef.

p valueConstant

29.481 [0.000]**

30.129 [0.000]**

22.165 [0.000]**

22.21 [0.000]**

bestrecord

0.632 [0.000]**

0.629 [0.000]**

0.649 [0.000]**

0.651 [0.000]**

schoolage−1.100 [0.000]**−1.116 [0.000]**−0.551 [0.000]**−0.554 [0.000]**

bestrecord_side

0.054 [0.414]

bestrecord_left

0.061 [0.256]

bestrecord_right−0.012 [0.840]

bestrecord_2side

0.055 [0.088]

bestrecord_2left

0.042 [0.106]

bestrecord_2right0.011 [0.713]

Obs

1094

1094

3757

3757

R squared

0.814

0.815

0.827

0.828

Note: ** 1%, * 5% significance.

5. Conclusion
In this study, we investigated peer effects on swimmers. First, we found that the performance ofadjacent peers positively influences swimmers’ performance. In particular, swimmers are aware ofand influenced by their slower-lane peer with the lower best record than theirs. Second, we revealed
a peer’s existence effect using abstention data. These data are nearly natural experiment data thatenable us to observe the pure impact of peer existence. We found that swimmers swim faster thanwhen alone if their peer is behind them, but they swim slower if their peer swims ahead. Ourfindings showed that being chased by others enhances individual performance. There are similar
situations to our findings in daily life. For example, the existence of a brilliant senior member does
not improve one’s performance, but that of excellent younger members increases it. We also foundthat the relationship between the skill level and the impact of peer speed effect is nonlinear and takes
19

a U shape. The lowest-skilled swimmers and top-level swimmers are more influenced than medium
level swimmers. This result might be related to their development stage. It is considered that thelow-skill swimmers are sensitive to the exogenous environment including peer effects. Thissensitivity fades with experience, and higher-level swimmers become aware of competitors because
they want to obtain the relative information about their ability. Additional research is, however,needed.
Our study is the first empirical economic study to purely and directly reveal the effects of peer
existence and their nonlinear aspects. The result of this study suggests that competition improves
performance. To construct the optimal environment or incentive design in a workplace, we shouldtake into account the existence and nonlinearity of peer effects.

6. References
Bandiera, O., Barankay, I. and Rasul, I. 2010 Social Incentives in the Workplace. Review of
Economic Studies, 77, pp. 417–458.
Falk, A. and Ichino, A. 2006 Clean Evidence on Peer Effects. Journal of Labor Economics, 24(1), pp.
39–57.
Guryan, J., Kroft, K. and Notowidigdo, M. J. 2009 Peer Effects in the Workplace: Evidence from
Random Groupings in Professional Golf Tournaments. American Economic Journal: Applied
Economics, 1(4), pp. 34–68.
Manski, C. 1993 Identification of Endogenous Social Effects: The Reflection Problem. Review of
Economic Studies, 60 (3), pp. 531–542.
Mas, A. and Moretti, E. 2009 Peers at Work. American Economic Review, 99(1), pp. 112–145.
Pessin, J. 1933 The Comparative Effects of Social and Mechanical Stimulation on memorizing.
American Journal of Psychology, 45(2), pp. 263–270.
Prendergast, C. 1992 Career Development and Specific Human Capital Collection. Journal of theJapanese and International Economics, 6, pp. 207–227.
Triplett, N. 1898 The Dynamogenic Factors in Pacemaking and Competition. American Journal of
Psychology, 9(4), pp. 507–33.
Zajonc, R. B. 1965 Social Facilitation. Science, 149(3681), pp. 269–274.

20Appendix 1: International Swimming Rules about heats by Federation Internationale de Natation(FINA).

SW 3.1 Heats
SW 3.1.1 The best competitive times of all entrants for the preceding twelve (12) months prior to theentry deadline of the competition, shall be submitted on entry forms and listed in order oftime by the Management Committee. Swimmers who do not submit official recorded
times shall be considered the slowest and shall be placed at the end of the list with a notime. Placement of swimmers with identical times or of more than one swimmer without
times shall be determined by draw. Swimmers shall be placed in lanes according to theprocedures set forth in SW 3.1.2. below. Swimmers shall be placed in trial heats
according to submitted times in the following manner.

SW 3.1.1.1 If one heat, it shall be seeded as a final and swum only during the final session.
SW 3.1.1.2 If two heats, the fastest swimmer shall be seeded in the second heat, next fastest in
the first heat, next fastest in the second heat, next in the first heat, etc.
SW 3.1.1.3 If three heats, the fastest swimmer shall be placed in the third heat, next fastest in
the second, next fastest in the first. The fourth fastest swimmer shall be placed in
the third heat, the fifth in the second heat, and the sixth fastest in the first heat, theseventh fastest in the third heat,etc.
SW 3.1.1.4 If four or more heats, the last three heats of the event shall be seeded in accordancewith SW 3.1.1.3 above. The heat preceding the last three heats shall consist of thenext fastest swimmers; the heat preceding the last four heats shall consist of thenext fastest swimmers, etc. Lanes shall be assigned in descending order ofsubmitted times within each heat, in accordance with the pattern outlined in SW
3.1.2 below.
SW 3.1.1.5 Exception: When there are two or more heats in an event, there shall be a minimumof three swimmers seeded into any one preliminary heat, but subsequent scratches
may reduce the number of swimmers in such heat to less than three.
SW 3.1.1.6 Where a 10 lane pool is available and equal times are established for the 8th placein the heats of 800m and 1500m Freestyle events, lane 9 will be used with a draw
for lane 8 and lane 9. In case of three (3) equal times for 8th place, lane 9 and 0
will be used with a draw for lane 8, 9 and 0.
SW 3.1.1.7 Where a 10 lane pool is not available SW 3.2.3 will apply.

SW 3.1.2 Except for 50 metre events in 50 metre pools, assignment of lanes shall be (number 1 lane
21

being on the right side of the pool when facing the course from the starting end) byplacing the fastest swimmer or team in the centre lane in pool with an odd number oflanes, or in lane 3 or 4 respectively in pools having 6 or 8 lanes. The swimmer having thenext fastest time is to be placed on his left, then alternating the others to right and left inaccordance with the submitted times. Swimmers with identical times shall be assigned
their lane positions by draw within the aforesaid pattern.

SW 3.1.3 When 50 metre events are contested in 50 metre pools, the races may be swum, at thediscretion of the Management Committee, either from the regular starting end to theturning end or from the turning end to the starting end, depending up suchfactors asexistence of adequate Automatic Equipment, starter's position, etc. The Management
Committee should advise swimmers of their determination well before the start of thecompetition. Regardless of which way the race is swum, the swimmers shall be seeded in
the same lanes in which they would be seeded if they were both starting and finishing at
the starting end.

22

Appendix 2: Definition of the variables

Table A1: Definition of the variables

Variables

Explanation

recordOwn record

peer
date
bestrecord

Dummy variable: 1 if the record includes data when both adjacent swimmers arepresent and 0 otherwise
Date by serial value in which January 1, 1900 takes 1; January 2, 1900 takes 2;
and so on
Own fastest records at that point

bestrecord_side

Average of right and left swimmers’ best record

bestrecord_left

Record of left swimmer

bestrecord_right

Record of right swimmer

bestrecord_fastlane

Record of peer who is assigned fast lane

bestrecord_slowlane

Record of peer who is assigned slow lane

bestrecord_2side

Average of right and left after the next swimmers’ best record

bestrecord_2left

Record of left after the next swimmer

bestrecord_2right

Record of right after the next swimmer

schoolage

School age; 7 corresponds to the first year of junior high school, 10 to the firstyear of high school, and 13 to the first year of college.

23