Peer Effects and Individual Performance: Evidence From Swimming Competitions

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  • of Sports Economics online version of this article can be found at:

    DOI: 10.1177/1527002514521429

    published online 30 January 2014Journal of Sports EconomicsWen-Jhan JaneCompetitions

    Peer Effects and Individual Performance: Evidence From Swimming

    Published by:

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    EconomistsThe North American Association of Sports EconomistsThe North American Association of Sports

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  • Article

    Peer Effects andIndividual Performance:Evidence FromSwimming Competitions

    Wen-Jhan Jane1

    AbstractThis article addresses the issue of peer effects on a swimmers performance. TheNational Database of Student Athletes in Taiwan from 2008 to 2010 is employed.The results show that a swimmer performs better when his or her competitors arefaster. The evidence shows that peer effects are positive. As to the relative quality ofswimmers in a competition, dispersed-quality competitors make a swimmer faster.The evidence also shows that older and taller boys swim faster. The regressions ofthe Heckman selection model support these conclusions.

    KeywordsHeckman selection model, National Database of Student Athletes, peer effects onindividual performance


    There is growing literature that stresses the importance of the environment in deter-

    mining the outcomes of individuals. Most of this literature is concerned with exam-

    ining how peers and environmental factors affect youth behavior with regard to their

    educational achievements, health, criminal involvement, work status, and other

    1Department of Economics, Shih Hsin University, Taipei, Taiwan

    Corresponding Author:

    Wen-Jhan Jane, Department of Economics, Shih Hsin University, No. 111, Sec.1, Mujha Rd., Wunshan

    District, Taipei 116, Taiwan.


    Journal of Sports Economics1-9

    The Author(s) 2014Reprints and permission: 10.1177/1527002514521429

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  • economic variables. This article differs from previous studies by looking at the inter-

    action of individual performance in swimming competitions.

    It has long been recognized by psychologists that an individuals performance

    might be influenced by his peers. The first study to show evidence of such peer

    effects was that of Triplett (1898), who noted that cyclists raced faster when they

    were pitted against one another and slower when they raced only against a clock.

    While Tripletts study showed that the presence of others could facilitate perfor-

    mance, others found that the presence of others inhibited performance. In particular,

    Allport (1920) found that people in a group setting wrote more refutations of a logi-

    cal argument, but that the quality of the work was lower than when they worked

    alone. Zajonc (1965) resolved these paradoxical findings by pointing out that the

    task in these experimental setups varied in a way that confounded the results. In par-

    ticular, he argued that for well-learned or innate tasks, the presence of others

    improves performance. For complex tasks, however, he argued that the presence

    of others worsens performance.

    The growing body of empirical studies on peer effects consistently find the pos-

    itive impact of high-ability workers on their peers.1 Mas and Moretti (2009), for

    example, showed that under hourly wages, high-ability grocery checkers increase

    coworker efforts through social processes. Ichino and Maggi (2000) found that

    absenteeism and episodes of misconduct are considerably more frequent in the

    southern branches of the bank. They showed the impact of peers on negative produc-

    tivity (absenteeism) in Italian bank workers and that an individuals shirking level

    increased with his coworkers average shirking level. However, their study was

    based on cultural norms rather than ability. Azoulay, Zivin, and Wang (2010) found

    that deaths of academic superstars lead to declines in coauthors publication rates.

    Depken and Haglund (2011) found that team member quality improves team per-

    formance, but at a decreasing rate in the National Collegiate Athletic Association

    4 400 m mens relay teams.This article investigates whether positive or negative peer effects exist for swim-

    mers in the National High School Athletic (NHSA) Games in Taiwan. To assess

    whether swimmers experience peer effects, we estimated various empirical models

    that relate an absolute and relative performance to the average quality of their com-

    petitors in a race. The results suggest that as the average competitor quality

    increases, that is, competitors average time decreases, individual performance

    improves. However, as the standard deviation of the competitors quality increases,

    that is, competitors standard deviation of time increases, individual performance

    decreases. The former supports the positive peer effects. The latter indicates that a

    disparity of quality in a competition reduces a swimmers performance.

    The goal of this article is to employ the data of swimming competitions from

    NHSA Games to investigate peer effects in a race. The remainder of this article is

    organized as follows: The data and the empirical methodology are presented in the

    second section. The results are discussed in the third section, and the article ends

    with a summary of the main conclusions.

    2 Journal of Sports Economics

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  • Empirical Methodology and Data Description

    In Taiwan, the National Database of Student Athletes has accumulated approximately

    1,582,000 athletes demographic data and performance records from 2007 to 2013,

    forming a rare set of micro data that we use as the basis for this study. The database

    includes all swimming, track and field, gymnastic, table tennis, badminton, tennis,

    kickboxing, judo, archery, karate, and soft tennis athletes in the NHSA Games.2

    For the NHSA swimming, individual races consist of freestyle, breaststroke,

    backstroke, and butterfly races. Races cover 50, 100, 200, 400, 800, and 1,500 m.

    The 800 m is for females and the 1,500 m is for males only. The butterfly, back-

    stroke, and breaststroke races each cover 100 and 200 m. All four strokes are used

    in the 200 m and 400 m individual medley events. The data cover 14 types of races

    and were provided by the Ministry of Education for research purposes. Our data con-

    tain extensive personal characteristics and yearly performance information on com-

    petitors from 2008 to 2010. Demographic data include age, gender, height, and

    weight. Competition dates and locations, as well as athletes schools, are also

    included in the data set.

    In order to consider peer effect on performance in a traditional labor market, two

    challenges need to be overcome. One is the measure of individual performance and the

    other is the definition of peers. This is the main reason why there are still few articles

    discussing this issue. Swimming races present an ideal case where the performance of

    each player, that is, the time, is easily measured in a uniform way. In addition, peers

    for a player are easily defined in a game, that is, the rest of the competitors.

    To test for a positive or negative peer effect, we control for both the average and

    the standard deviation of participant quality in a race. The swimmers production

    function estimated model can be specified as:

    Timejt b0 b1AvgTimejt1 b1SDTimejt1 FXit e; 1

    where Timejt represents jth players seconds in a race. bs and F are estimated para-meters, and e is an error term. The explanatory variables include the average secondsof competitors which excluded player j in the previous race (AvgTimejt1); and thestandard deviation of competitors seconds which excluded player j in the previous

    game (SDTimejt1).3 Control variables (Xjt) are the swimmers characteristics and

    environmental factors. The former consists of swimmers height (Height), weight

    (Weight), age (Age), and gender (Gender). The latter are dummies for the race types

    (GameType), year dummy (Year), dummies for whether the race was a preliminary

    (PRELIMS, yes 1, otherwise 0), and a final against a clock (CFINALSyes 1, otherwise 0). Table 1 presents the descriptive statistics of the data.

    The variable AvgTimejt1 is expected to have a positive relationship withTimejt, if there exists a positive peer externality on a swimmer. Conversely, if the

    peer externality on a swimmers performance is negative, the variable AvgTimejt1is expected to be negative.

    Jane 3

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  • The parameter of SDTimejt1, on the other hand, could be either positive or neg-ative since the dispersion degree of time for the competitors can result from any com-

    bination of swimmers. For example, the participants in a race could consist of eight

    average swimmers, or of three above-average swimmers, three below-average swim-

    mers, and two average swimmers. However, when comparing two races with the same

    potential (i.e., participants average time in a race), the sign of the parameter on

    SDTimejt1 provides evidence as to whether the average member in a race suffersfrom positive peer effects, ceteris paribus. If the coefficient is positive, it means that

    a dispersed human capital race induces more seconds. Therefore, a race with averagely

    talented members has better individual performance. This represents that an average

    human capital race suffers positive peer effects. Conversely, if the coefficient is neg-

    ative, an average human capital race suffers negative peer effects.

    Table 1. Descriptive Statistics of the Data.

    Variable Description M SD Min. Max.

    Time Players seconds in a game 163.8458 177.6139 24.43 1,220.95Proxies of peer effects

    AvgTime Average seconds ofcompetitors

    161.2749 174.0081 25.2075 1,126.244

    SDTime Standard deviation ofcompetitors seconds

    18.6576 27.3796 .3707 257.8379

    AvgTimeP Average seconds ofcompetitors inpreliminaries

    124.7666 75.8428 25.2475 333.0688

    SDTimeP Standard deviation ofcompetitors seconds inpreliminaries

    5.8531 4.2992 .3500 21.5017

    AvgTime(t 1)

    Average seconds ofcompetitors last year

    181.9861 234.1711 27.3015 1,119.079

    SDTime(t 1)

    Standard deviation ofcompetitors seconds lastyear

    139.3349 767.0914 1.40498 4,678.039

    Control variablesAge Swimmers age 19.8242 1.8767 16 24Height (cm) Swimmers height 167.9784 8.4398 116 201Weight (kg) Swimmers weight 60.4344 9.9606 33 100Gender Swimmers gender (male

    1, otherwise 0).5366 .4987 0 1

    CFINALS Dummy of final raced onlyagainst a clock (yes 1,otherwise 0)

    .0701 .2553 0 1

    PRELIMS Dummy of preliminary(yes 1, otherwise 0)

    .6580 .4745 0 1

    Note. n 4,210.

    4 Journal of Sports Economics

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  • According to the literature concerning the relationship between a swimmers soma-

    totype and performance, the coefficients of Height and Gender are expected to be neg-

    ative, the coefficient of Age is expected to be negative, and the coefficient of Weight is

    insignificant.4 Cyclists raced faster when they were pitted against one another and

    slower when they raced only against a clock (Triplett, 1898). The comparison base for

    PRELIMS and CFINALS is the finals, so both coefficients are expected to be positive.

    Empirical Results

    The empirical results of Equation 1 for pooled ordinary least squares (OLS) regressions

    are regressed. The w2 values of the BreuschPagan (B-P) test (9303.39) rejects the nullhypothesis of homoscedasticity. Therefore, a robust regression using iteratively

    reweighted least squares is employed in the following estimations. Moreover, unob-

    served individual-specific heterogeneity and sample selection biases induced by the non-

    random process for competitors in a race are considered in the regressions. The Breusch

    and Pagan Lagrangian multiplier test (622.92) rejects the null hypothesis of the absenceof an unobserved effect, and the Hausman (1978) test cannot reject the null hypothesis

    that the difference in coefficients is not systematic. The random effects (RE) model is

    supported. In a test of the selectivity effect, however, Mills ratio (l) does not support theresults in the Heckman selection model. The results are presented in Table 2.

    The parameters on the measures of peer effects are of most interest in this article.

    Both coefficients of AvgTimet1 and SDTimet1 are significant. The former is con-sistently and positively related to a swimmers seconds, and the latter is consistently

    and negatively related to a swimmers seconds in OLS, weighted least squares

    (WLS), and Heckman selection regressions.

    The evidence here indicates that a swimmers speed is influenced by the compet-

    itors average and relative quality. The evidence of AvgTimet1 supports a positivepeer effect on individual performance. A one-unit decrease in the average time of

    the participants represents better competitors in a game and it will result in shorter

    seconds (e.g., 0.31 s in the Heckman selection model with clustering race) for a

    swimmer in a race. This part of the results corresponds to Depken and Haglund

    (2011). Moreover, the evidence of SDTime indicates that a dispersed human capital

    race induces a shorter time. A race with average quality members leads to a swim-

    mer achieving longer seconds. A one-unit decrease in SDTime increases a swim-

    mers time by 0.056 s in the Heckman selection model with clustering race,

    ceteris paribus. This is in contrast to Browns (2011) findings that large ability dif-

    ferences in golfers is associated with lower performance.

    As for the control variables, the coefficients of age, height, and gender are nega-



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