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    Winning Isn't Everything: Corruption in Sumo WrestlingBy M A R K D U G G A N AN D S T EV E N P . L E V I T T *

    There is a growing appreciation among econ-omists of the need to belter understand the rolethat corruption plays in real-world economies.Although some have argued that it can be wel-fare enhancing (Nathaniel Leff, 1964), mostcommentators believe that a willingness to ac-cept bribes (or similar forms of corruption) ineither the public or the private sector reduceseconomic efficiency (Andrei Shleifer andRobert W. Vishny, 1993). As a result, govern-ments and firms often create incentives to mo-tivate their employees to be honest (Gary S,Becker and George J. Stigler, 1974).While it is generally agreed that corruption iswidespread, there is little rigorous empiricalresearch on the subject. Because of corruption'sillicit nature, those who engage in corruptionattempt not to leave a trail. As a consequence,much of the existing evidence on corruption isanecdotal in nature. More systematic empiricalsubstantiation of corrupt practices is unlikely toappear in typical data sources. Rather, research-ers must adopt nonstandard approaches in anattempt to ferret out indirect evidence ofcorruption.To date, there have been only a handful ofstudies that attempt to systematically documentthe impact of corruption on economic out-comes. The first empirical study of corruptiondates to 1846 when Quetelet documented thatthe height distribution among French malesbased on measurements taken at conscriptionwas normally distributed except for a puzzlingshortage of men measuring 1.57-1.597 meters

    * Duggan: Department of Economics. University of Chi-cago, 1 !26 East 59th Street. Chicago, R. 60637. and NationalBureau of Economic Research (e-mail: mduggant*midway.uchicago.edu); Levitt: American Bar Foundation and De-panmeni of Economics, University of Chicago. 1126 East59th Street. Chicago. IL 60637 (e-mail: sievittmidway.uchicago.edu). We w ould like to thank G ary Becker, Casey

    (roughly 5 feet 2 inches to 5 feet 3 inches) andan excess number of men below 1.57 meters.Not coincidentally, the minimum height forconscription into the Imperial army was 1.57meters (Stephen Stigler, 1986). More recent em-pirical work on corruption includes Robert H.Porter and J. Douglas Zona (1993), which findsevidence that construction companies colludewhen bidding for state highway contracts bymeeting before the auction, designating a seri-ous bidder, and having other cartel memberssubmit correspondingly higher bids. R. PrestonMcAfee (1992) details a wide variety of bid-rigging schemes. Paulo Mauro (1995) uses sub-jective indices of corruption across countries todemonstrate a correlation between corrupt gov-ernments and lower rates of economic growth,although the relationship may not be causal.Ray Fisman (2001) analyzes how stock pricesof Indonesian firms fluctuate with changes informer Prime Minister Suharto's health status.Firms with close connections to Suharto, whiehpresumably benefit from corruption within theregime, decline substantially more than otherIndonesian firms when Suharto's health weak-ens. Whether the rents accruing to those close toSuharto are due to corruption or simply badpolicy, however, is hard to determine. Rafael DiTelia and Ernesto Schargrodsky (2000) docu-ment that the prices paid for basic inputs atpublic hospitals in Buenos Aires fall by 10-20percent after a corruption crackdown.

    In this paper we look for corruption amongJapan's elite sumo wrestlers. While acknowl-edging that sumo wrestling is not itself a subjectof direct interest to economists, we befieve thatthis case study nonetheless provides potentiallyvaluable insights. First, if corrupt practicesthrive here, one might suspect that no institutionis safe. Sumo wrestling is the national sport ofJapan, with a 2,000-year tradition and a focuson honor, ritual, and history that may be unpar-

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    92 NO. 5 DUGGAN AND LEVITT: CORRUPTION IN SUMO WRESTUNG 1595

    our analysis may nonetheless aid futureThe key institutional feature of sumo wres-

    involves 66 wrestlers (rikishi) partici-kachi-koshi) is guaranteed to rise up(banzukey, a wrestler with a{make-ko.shi) falls in the rankings.

    Figure I demonstrates empirically the impor-

    ly linear: each additional victory is worth

    ers a wrestler approximately 11 spots in the

    ^ Nevertheless, in recent years, sumo wrestling has been

    ' For instance, the lowesl-ranked wrestlers in the hevti

    1510

    o-5

    -10-15 1

    >

    /

    /[

    1

    3 4 5 6 7 8 9 10Tournament wins

    FIGURE 1. PAYOFF TO TOURNAME.NT W INS

    typical victory. Consequently, a wrestler enter-ing the final match of a tournament with a 7-7record has far more to gain IVotii a victory thanan opponent with a record of, say, 8-6 has tolose. There will also be incentives for forward-looking wrestlers to rig matches on earlier daysof the tournament."* According to our roughcalculations, moving up a single spot in therankings is worth on average approximately$3,000 a year to a wrestler, so the potentialgains to trade may be substantial if the w restlersfix a match,^ Of course, no legally bindingcontract can be written.In this paper, we examine more than a decadeof data for Japan's sumo elite in search ofevidence demonstrating or refuting claims ofmatch rigging. We uncover overwhelming evi-dence that m atch rigging occurs in the final daysof sumo tournaments. Wrestlers who are on themargin for attaining their eighth victory win farmore often than would be expected. High win-ning percentages by themselves, however, ai'e

    " An earlier version of this paper, Duggan and Leviu(20()l), derive a formal mode! of the incenlives facing partic-ipants. For wrestlers on the bubble, the incentive to rig matchesincreases monotonically over the course of a tournament.^ Wrestlers ranked between lifth and tenth earn an annualincomeincluding only official wages, bonuses, and prizemoney of roughly $230,000 per year. The fortieth-rankedwrestler earns approximately $170,000, The seventieth-ranked wrestler receives only about SL^i.OOO per year (noofficial salary, just a small stipend to cover tournamentexpenses, some prize money, and room and board). Allinformation on annual salaries are based on the authors'

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    THE AMERICAN ECONOMIC REVIEW DECEMBER 200far from conclusive proof of match rigging.Those wrestlers who are on the margin forachieving the eighth win may exert greater ef-fort because their reward for winning is larger.W e offer a number of pieces of evidence againstthis altemative hypothesis. First, whereas thewrestler who is on the margin for an eighth winis victorious with a surprisingly high frequency,the next time that those same two wrestlers faceeach other, it is the opponent who has an un-usually high win percentage.*^ This result sug-gests that at least part of the currency used inmatch rigging is promises of throwing futurematches in return for taking a fall today. Sec-ond, win rates for wrestlers on the bubble varyin accordance with factors predicted by theoryto support implicit collusion. For example, suc-cess rates for wrestlers on the bubble risethroughout the career (consistent with the de-velopment of reputation), but fall in the last yearof a wrestler's career. Third, match rigging dis-appears during times of increased media scru-tiny. Fourth, some wrestling stables (known asheya) appear to have worked out reciprocityagreements with other stables such that wres-tlers from either stable do exceptionally well onthe bubble against one another.^ Finally, wres-tlers identified as "'not corrupt" by two formersumo wrestlers who have alleged match riggingdo no better in matches on the bubble than intypical m atches, whereas those accused of beingcorrupt are extremely successful on the bubble.I( is difficult to reconcile any of these findingswith effort as the primary explanation.

    The remainder of this paper is organized asfollows. Section I introduces the data used inthe analysis and presents the empirical evidencedocumenting the strong performance of wres-tlers on the bubble. Section II attempts to dis-tinguish between increased effort and matchrigging as an explanation for the observed pat-terns in the data and also considers the way inwhich the market for rigged matches operates,e.g., how contracts are enforced, the use of cashpayments versus promises of future thrownmatches, and individuals versus stabies as thelevel at which deals are brokered. Section III

    concludes with a discussion of the broader economic implications of our analysis.1. Evidence of Strong Performance

    on the BubbleOur data set consists of almost every officiasumo match that took place in the top rank(Sekitori) of Japanese sumo wrestling betweenJanuary 1989 and January 2000. Six tournaments are held a year, with nearly 70 wrestlerper tournament, and 15 bouts per wrestlerThus, our initial data set consists of over 64,000wrestler-matches representing over 32,000 tota

    bouts (since there are two wrestlers per bout). AsmaJl number of observations (less than 5 per-cent of the total data set) are discarded due tomissing data, coding e rrors, or early withdrawafrom the tournament due to injuiy. A total of281 wrestlers appear in our data, with the aver-age number of observations per wrestler in arandomly selected match equal to 554, and amaximum of 990. The average number of totamatches between the same two wrestlers com-peting in a randomly selected match is 10; thuswe often have many observations involving thesame two wrestlers at different points in time.

    For each ob servation, we know the identity ofthe two competitors, who wins, the month andyear of the tournament, and the day of the match(tournaments last 15 days with one match perwrestler per day). For roughly 98 percent of thesample, we also know what wrestling stable thewrestlers belong to: information is missing forsome wrestlers in the early part of our samplewho had only a short stint in the top ranks.We begin by looking at the distribution ofwins across wrestlers at the end of tourna ments.We expect that a disproportionate number ofwrestlers should finish with eight wins becauseof the high payoff associated with the eighthwin (see Figure 1). To the extent that wrestlersare rigging matches not only on the final day,but also in the days immediately preceding theend of the tournament, extra weight should alsobe observed on nine wins, as wrestlers who areclose to the margin on days 13 or 14 may buywins that ultimately were not needed to reach

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    DUGGAN AND LEVITT: CORRUPTION IN SUMO WRESTLING 1597

    Actual data

    Binomial

    2 4 6 8 10 12 14Total WinsFIGURE 2, WtNs IN A SUMO TOURNAMENT

    (ACTUAL VS. BINOMIAL)

    Figure 2 provides clear visual evidence in

    cted at resounding

    Further evidence that wrestlers on the bubble

    Win.j,, = ^Bu bble , , , + jRankdiff,+ A,;, + 6,, + e^ ,,,

    d is

    j is on the margin for reaching eight wins in

    margin in the match. Rankdiff is the gap be-tween the official ranking of wrestlers / and jentering tournament t. ln some regressions, weinclude fixed effects for each wrestler and eachopponent; in other specifications we includewrestler-opponent interactions. In all cases, weestimate linear probability models, with stan-dard errors corrected to take into account thefact that a match is included in the data settwice once for w restler / and once for wrestler /.Table 1 reports the excess win percentagesfor wrestlers on the margin, by day, for the lastfive days of the tournament. On day 15, onlywrestlers with exactly seven wins are on themargin; on day 14, wrestlers with either six orseven wins are on the margin, etc. The sixcolumns correspond to different regressionspecifications. The even columns include thedifferences in ranks for the two wrestlers enter-ing this tournament. The first two columns haveno wrestler fixed effects; columns (3) and (4)include both wrestler and opponent fixed effects.The final two columns add wrestler-opponentinteractions so that the identification comesonly from deviations in this match relative toother matches involving the same two wrestlers.The results in Table 1 are quite similar acrossspecifications.** Wrestlers on the bubble on day15 are victorious roughly 25 percent more oftenthan would be expected. Win percentages areelevated about 15 percent on day 14. 11 percenton day 13, and 5 percent on day 12 for wrestlerson the margin. There is no statistically signifi-cant evidence of elevated win rates for w restlerson the bubble on day 11, The pattern of coeffi-cients is consistent with the hypothesis that thefrequency of match rigging will rise as the tour-nament comes to a close. If all of the excesswins are due to rigging, then the results implythat on day 15 half of the bubble matches arecrooked. For days 14. 13, and 12 respectively,the estimated percentage of rigged matches isroughly 28, 22, and 10 percent respectively.

    ^ Adding tbe difference in current rank between wres-tlers has little impact on the other coefficients in tbe regres-sion, Tbe difference in ranks is an important predictor ofmatch outcomes when wrestler fixed effects are excluded

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    THE AMERICAN ECONOMIC REVIEW DECEMBER 2002T A B L E 1EXCESS W I N PERCE f ACES F O R W R E S T L E R S O N T H E M A R G I N F O R A C H I E V I N G ANE I G H T H W I N .

    BY D A Y O F T H E M A T C H

    O n theMar gin on: (1) (2) (3) (4) (5) (6)Day 15D a y 14 : ,]

    Day 13Day 12Day 11Rank differenceConstant

    Number of observationsWrestler and opponent fixed effectsWrestler-opponent interactions

    0.244(0.019)0.150(0.016)0,096(0,016)0,038(0,017)0,000(0,018)

    0.500(0,000)0,00864,272

    NoNo

    0.249(0.019)0.155(0,016)0,107(0,016)0,061(0.018)0.018(0,018)0,0053(0,0003)0.500(0,0(X))0,01862.708

    NoNo

    0.249(0,018)0,152(0.016)0,110(0,016)0,064(0,017)0.015(0,018)

    0,03064.272

    YesNo

    0,255(0.019)0.157(0.016)0.118(0.016)0.082(0.018)0.025(0.01 S)0.0020(0.0003)

    0.03162,708

    YesNo

    0,260(0.022)0.168(0.019)0.116(0.019)0.073(0.020)0.010(0.021)

    0.063464,272

    YesYes

    0,264(0,022)0,171(0.019)0,125(0,019)0,076(0,021)0.012(0.021)

    - 0 , 0 0 2 0(0,0004)

    0.065362,708

    YesYes

    Notea: The dependent variable in all regressions is an indicator variable corresponding to w hether or not awrestler wins thematch. The unit of observation is awrestler-match. Values reported in the table are coefficients associated with an indicatorvariable taking the value I if only the wrestler is on the margin for achieving eight wins, -1 if only the opponent is on themargin for achieving eighi wins, and 0otherwise. On day 15, only wrestlers with seven w ins are on the margin. On day 14,wrestlers with six or seven wins are on the margin. On day 13, wrestlers with five, six. or seven wins are on the margin, andso on. The omitted category inall regressions is all wrestlers who are not on the margin for achieving eighi wins, as well aswrestlers in matches in which both panicipants are on the margin for eight wins. When a full set of wrestler and opponentfixed effects are included, the constant is omilted. In all cases, standiu^d errors are corrected to account for ihe fact thai thereare two observation s per bout (one for each w restler). The differences in the wrestler rank variable is the numerical rank orde rof the wrestler minus that of his opponen t, based on official rankings pub lished prior to each tournam ent. This variable ismissing for pan of our sample.

    n. Distinguishing Between Match Riggingand Effort

    The empirical results presented thus far areconsistent with a model in which opponentsthrow matches to allow wrestlers on the marginto achieve an eighth victory. The results, how-ever, are also consistent with a scenario inwhich effort is an important determinant of thematch outcome, andwrestlers on the bubble,having more togain from a win, exert greatereffort.^ ln this section, we present a wide variety

    of analyses that appear to confirm the corruptionstory and rule out effort as the explanation.A. What Characteristics Infiuence theLikelihood ofWinning When on the Bubble?

    We begin by analyzing the personal and sit-uational characteristics that influence the suc-cess rate of the wrestler on the bubble. Onepotentially important determinant of the frequency of match rigging is the probability thatthe collusive behavior will be detected. During

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    92 NO. 5 DUGGAN AND LEVITT: CORRUPTION IN SUMO WRESTUNG 1599

    The literature on repeated-play games (e.g..

    the better he will do when he is on the

    Because there are a series of monetary prizes

    '" In order to m inimize endoge neity, we e.xclude the very

    given tournament, wrestlers in the running forsuch prizes are unlikely to be willing to throwmatches." The overall tournament championwins $ 100,000; the jiirvo champion wins$20,000. In addition, $20,000 awards for "fight-ing spirit" and "outstanding technique," In orderto win those prizes, wrestlers must compile verystrong records. The potential value of a victoryfor a wrestler in the running for such prizes islikely lo be at least as great as the value to awrestler on the margin for an eighth win.A final determinant of match rigging that weconsider is the possibility of coordinated matchrigging among stables of wrestlers. The lives ofsumo wrestlers center around the stable withwhich they are associated. Stable-masters exerta tremendous influence over both the wrestlingcareer of wrestlers and their lives more gener-ally. ~ Given the important role of the stable,and the fact that stable-masters benefit fromhaving highly ranked wrestlers, it would not besuiprising if corruption were coordinated at thestable level. For example, stables might havecollective reputations, with stable-masters en-forcing punishments on wrestlers who pursuetheir individual best interests at the expense ofthe stable. Some stable-masters, on the otherhand, may not condone match rigging becauseof ethical concerns or risk aversion.We empirically examine one particular formof stahle-level collusion: the presence of reci-procity agreements across stables. If such dealsexisted, one would expect both that wrestlersfrom stable A will have very high win rateswhen on the bubble facing wrestlers from stableB, and vice versa,'* It is difficult to tell analternative story that would account for such apattern in the data. For instance, if effort is the

    '' Although we do not directly obsei-ve which wrestlersmighl be under consideration for these prizes, having one ofthe five best records (plus lies) up until that point in thetournament is an excellent predictor. Wrestlers with one ofthe live best records in the tournament entering days 13. 14,or 15 win a prize 50 percent of the time. Less than fivepercent of wrestlers with records outside the top five ondays 13-15 eventually win a prize.^ For instance, it is expected that the foremost siiino wres-

    tler in a slable will marry tiie daughter of the stable-master." T h e variable we use to test Ihis empirically is theoverall win rate for wrestlers on the bubble in matches

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    1600 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

    story, then stables with wrestlers capable ofexerting particularly high effort when they needa win might also be expected to have wrestlerswho rise to the occasion when faced with theopportunity to beat a very motivated opponent,leading to a zero or negative correlation. Simi-larly, if one stable has developed specific tech-niques that provide it with an advantage over aparticular stable, success rates on the bubblewill again be negatively related.These various hypotheses are tested in Table 2.Because our interest is in how these factorsinfluence success on the bubble, the table re-ports only the coefficients on the interactionsbetween these various factors and the outcomeof bubble matches, i.e., any incremental impactthat these factors have on bubble matches aboveand beyond their impact in nonbubble matches.Also included in the specifications, but notshown in the table, are the main effects. Column(1) is the baseline specification. Column (2)adds both wrestler and opponent fixed effects.Column (3) also includes wrestler-opponent in-teractions. The results are generally quite simi-lar across the three columns of the table.

    The top row of the table is the main effect ofa wrestler being on the bubble, which leads toan excess win likelihood of roughly 12-16 per-centage points, in those tournam ents with a highlevel of media scrutiny, however, these excesswins completely disappe ar.'^ In two of the threespecifications, the performance of wrestlers onthe bubble in high and low media scrutiny tour-naments is statistically significant at the 0.05level. In none of the three columns can onereject the null hypothesis that wrestlers on thebubble in high-scrutiny tournaments do any bet-ter than chance. In the words of Supreme CourtJustice Lxjuis D. Brandeis, "Sunlight is said tobe the best disinfectant."'^

    When the opponent is In the running forwinning one of the special prizes awarded, anybenefit of being on the bubble also disappears.This result is consistent with opponents in therunning for prizes being unwilling to throw amatch.The variables designed to capture factors in-

    TAHLE 2DETERMINANTS OF EXCESS WIN LIKFJ-IHOODSFOR WRE-.VRLI-RS ON THE BUBBLE

    VariableWrestler on bubbleWrestler on bubbleinteracted with:

    High mediascrutinyOpponent intunning for aprize thislournamentNumber ofmeetingsbetween twoopponents inIhe last yearWrestler onbuhblein his last yearof competingYears in sumo forwrestler on

    bubbleWinningpercentage inother bubblematchesbetween thesetwo stablesR'Wrestler andopponent fixedeffects?Wrestler-opponentinteractions?

    (1)0.126(0.026)

    1

    - 0 . 1 8 8(0.071)- 0 . 1 4 9(0.047)

    - 0 . 0 0 4 8(0.0082)

    -0 .0361(0.0398)

    0.0077(0.0036)

    0.272(0,059)

    0.016No

    1 :

    No

    (2)0.117(0.026)

    - 0 . 1 7 7(0.071)- 0 , 1 2 9(0.046)

    - 0 . 0 0 3 1(0.0081)

    -0-0195(0.0395)

    0.0077(0.0036)

    0.293(0.058)

    0,074Yes

    No

    (3)0.155(0.029)

    - 0 . 1 4 6(0.080)- 0 , 1 5 6(0,052)

    - 0 . 0 0 2 4(0,0096)

    - 0 . 0 3 4 6(0.0493)0.0O91

    (0.0043)

    0.246Yes

    Yes

    Notes: The dependent variable in all three regressions is anindicator variable corresponding to whether or not a wres-tler wins the match. In addition to the listed interactionterms, all main effects are also included in the specifica-tions. Wrestler on bubble is an indicator variable that equalsI (- 1 ) if the wrestler (opponent) is on the bubble on day13. 14, or 15 (record of 7-7. 7-6, 6-7. 7-5. 6-6, or 5-7) buthe opponent (wrestler) is not. and 0 otherwise. Matchesfrom 1989, the first year of our sam ple, are excluded be-cause the variable for the number of matches between thetwo wrestlers in the previous year cannot be computedObservations where stables are unknown or no two wres-

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    OL 92 NO. 5 DUGGAN AND LEVITT: CORRUPTION IN SUMO WRESTUNG 1601

    The number of matches between two

    1 in all of

    Finally, the bottom row of coefficients in

    B. What Happens When Wrestlers MeetAgain in the Future?If collusion is the reason that wrestlers on the

    '" Because w restlers do not chang e stables over the

    Table 3 explores the pattern of match out-comes over time for wrestlers who meet whenone is on the margin. The even columns includewrestler-opponent interactions so identificationof the parameters comes only from variation inoutcomes involving the same two opponents;the odd columns do not. The regression speci-fications include indicator variables categoriz-ing the timing of the meetings between twowrestlers relative to the match where one wres-tler is on the bubble. The omitted category ismatches preceding a bubble meeting by at leastthree matches.'^Focusing first on columns (I) and (2), whichcorrespond to all tneetings on the bubble, thereare no systematic differences in outcomes in thetwo matches preceding the match on the bubble,as reflected in the statistically insignificant co-efficients in the top row. When the wrestler ison the bubble (second row), he is much morelikely to win, consistent with the earlier tables.The parameter of greatest interest is the nega-tive coefficient for the first meeting between thetwo wrestlers after the match in which the wres-tler is on the bubble. The wrestler who was onthe margin in the last meeting is approximatelyseven percent le.ss likely to win than wouldotherwise be predicted. This finding is consis-tent with part of the compensation for throwinga match being the promise of the opponentreturning the favor in the next meeting. There isno evidence that any return of favors extendsbeyond the next match, as two and threematches out the winning percentages return tonormal.The final four columns of Table 3 replicatethe first two columjis, except that the sample isdivided into cases where the wrestler wins whenon the margin versus instances when the wres-tler loses when on the margin.'** One would notexpect a wrestler to intentionally lose in futuremeetings to an opponent who does not throw thematch on the margin. Thus, breaking down the

    '^ We have experim ented with other g rouping s ofma tches, for instance allowing a different coefficient formatches preceding/following the bubble match by morethan three meetings. The parameters of interest are notsensitive to alternative specifications,'^ In columns (3)-(6). the actual matches taking place on

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    1602 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

    TABLE 3WIN PERCENTAGES tN PRECEDING AND StrasEQUENT MATCHES(For Two Wrestlers Who Meet When One ison the Margin in the Final Three Days of a T ournament)

    VariableOne or two matches prior to thebubble matchBubble mateh ,

    First meeting after bubble match

    Seeond meeting after bubble match

    Three or more meetings afterbubble matchConstiint .^ 1

    Wrestler-opponent interaetions?R-

    All Matches on theMaj'gin

    (1)- 0 , 0 0 2(0,009)

    0.151(0,010)- 0 . 0 7 3(0,011)- 0 , 0 0 2(0.013)- 0 , 0 1 0(0,006)

    0.500(0,000)No

    0,008

    (2)0.005(0,012)0,164(0,014)

    - 0 , 0 6 2(0.015)0.005(0,016)0,012(0,011)

    Yes0.271

    Only Matches inWhich the Wrestler onthe Margin Wins(3)

    0.020(0.011)

    - 0 . 0 8 2(0,015)0,031(0.017)0.013(0.007)0.500(0,000)No

    0.002

    (4)0.019(0.017)

    - 0 , 0 7 9(0,020)0.028(0.022)0.022(0.014)

    Yes0.279

    Only Matches inWhich the Wrestler onthe Margin Loses(5)

    -0 ,041(0.016)

    - 0 . 0 5 6(0.020)- 0 , 0 6 1(0,023)- 0 . 0 4 5(0.008)

    0,500(0.000)No

    0.002

    (6)- 0 , 0 3 5(0,022)

    - 0 , 0 4 0(0,027)- 0 , 0 3 9(0,030)- 0 . 0 1 3(0,017)

    Yes0.279

    Notes: Entries in the table are regression estimates of the outcomes of matches between, after, and contemporaneous withthese two wrestlers meeting when one wrestler is on the margin for achieving eight wins on the last three days of thetournament. The dependent variable in all regressions is an indicator variable for whether the wrestler wins amatch. The unitof observation is a wrestler match. The first two columns correspond to all wrestlers who meet when one is on the margin.In columns (3) and (4), the coefficients reported correspond only tothose cases where the wrestler on the bubble wins tbematch. Colum ns (5) and (6) report coefficients only for those w restlers on the bubble w ho lose the match. Colum ns (3) and(5) are estimated jointly, as are columns (4) and (6), Except for columns (I) and (2), bubble matches are excluded from theregressions. The excluded category in all regressions are matches occurring more than two matches prior to a bubble matchand not falling into any of the other categories named. When a full set of wrestler and opponent fixed effects are included,the constant is omitted. Inall eases, standard errors are corrected to account for the fact that there are two observations perbout (one for each wrestler). Number of observations is equal to 64,273.

    data in this way provides a natural test of thehypothesis that the poor performance in the nextmatch is due to a deferred payoff to an opponentwho threw a match. The data provide clearsupport for the collusion hypothesis. Wrestlerswho win on the bubble tend to do slightly betterthan expected leading up tothe bubble match,then do much worse in the next meeting withthe same opponent. Relative to the surroundingmatches, the first post-bubble match .sees thewrestler losing approximately 10 percentagepoints more frequently than would be expected(i.e,, row 3 minus row 1).The pattern for wrestlers who lose to the oppo-

    (4), there is no downward spike in wins followingthe bubble match. The finding that w inners on thebubble fare badly the next time they face die sameopponent, but losers do not, is consistent with thematch-rigging hypothesis, but not with an effortstory. If increased effort is responsible for strongperformances in matches on the miirgin. there isno reason to expect systematic underperformancethe next time the two wrestlers meet, and certainly

    ' ' ' When two wrestlers meet and both are on the bubble,there is similarly no evidence that thewrestler who winsfares more poorly the next lime the two wrestlers meet. This

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    92 NO. 5 DUGGAN AND LEVITT: CORRUPTION IN SUMO WRESTLING 1603

    The payment-in-kind story suggested by the

    although we are able to provide no evi-

    . Do the Data Confirm Public Allegations ofCheating by Sumo Insiders?Two former sumo wrestlers have made pub-

    Shukan Post, 2000).^" In this sec-

    To test this hypothesis, we estimate a re-

    ~" The bo oks that we cite are published only in Japanese.

    Table 4 reports the results of the estimation.All of the coefficients in the table come from asingle regression. The values in the table repre-sent excess win percentages on the bubble, i.e.,how much better a wrestler does when on thebubble relative to matches in which neitherwrestler is on the bubble. The columns of thetable identify the status of the wrestler on thebubblethe wrestler who wants to buy a vic-tory. The rows correspond to the status of theopponent of the wrestler on the bubblethewrestler who might want to sell a win. Whentwo wrestlers identified as corrupt meet on thebubble, the one who needs the victory is 26percentage points more likely to win the matchthan if those two wrestlers met with neither onthe bubble. This excess win pe rcentage is highlystatistically significant. When a corrupt wrestlermeets a wrestler classified as "status unknown,"the results are very similar. Win percentages forthe wrestler needing the victory when bothwrestlers are classified as "status unknown" areaiso highly elevated (18.1 percentage pointshigher), but not quite as extreme. In stark con-trast, none of the five coefficients involv ingwrestlers identified as clean are statistically sig-nificant from zero. This implies that the out-comes of bubble matches involving a cleanwrestler are no different than the results whenthe same two wrestlers meet, but neither is onthe bubble. This result holds true regardless ofwhether the clean wrestler is himself on thebubble or facing a wrestler who is on the bub-ble. Thus. Table 4 provides strong confirmationnot only of the claim that elevated win percent-ages on the bubble are due to match rigging, butalso that the allegations made by the two sumoinsiders appear to be truthful. Moreover, it ap-pears that most of the wrestlers not specificallynamed by the whistle-blowers are corrupt, sincetheir outcomes differ only slightly from thosewrestlers named as corrupt.

    m . ConclusionThis paper provides strong statistical analysisdocumenting match rigging in sumo wrestling.The incentive structure of promotion leads to

    gains from trade between wrestlers on the mar-gin for achieving a winning record and their

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    1604 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

    TABLE AEXCESS W IN PERCENTAGES ON THE BUBBLE FOR WRESTLERS LABELED BY SUMOINSIDERS AS "CORRUPT" OR " C L E A N "

    Opponent ofwrestler on thebubble isidentified as:

    CorruptStatusunknownClean

    Wrestler on the Bubble Is IdentifietCorrupt

    0.260(0,037)0,271(0,021)0,036(0,027)

    Status Unknown0.270(0.021)0.181(0.019)

    - 0 . 0 3 3(0.035)

    as :Clean

    - 0 . 0 1 0(0.038)0.041(0.031)0.022(0.074)

    Notes: Entries in the table are coefficients from a regression with full set of interactionsbetween whether a match is on the bubble and ihe classification of a wrestler and his opponentas clean, corrupt, or status unknown by two sumo insiders (Itai, 2000: Onaruto, 20 00; SbukanPost. 2000). The regression is identical to equation (1) in the text, except for the inclusion ofthe aforementioned interactions. Twenty-nine wrestlers are categorized as corrupt, 14 areclassified as clean. The remainder of wrestlers are not specifically named and are categori/xdas status unknown. Standard errors are corrected to take into account that there are twoobservations per bout (one for each wrestler). Number of observations is eqtial to 64,273,

    explain the findings. Match rigging disappearsin times of increased media scrutiny. Wrestlerswho are victorious when on the bubble lose morefrequently than would be expected the next timethey meet that opponent, suggesting that part ofthe payment for throwing a match is future pay-ment in-kind. Reciprocity agreements betweenstables of w restlers appear to exist, suggesting thatcollusive behavior is not carried out solely byindividual actors. Allegations by sumo insiders aredemonstrated to be verified in our data.

    While sumo wrestling per se is not of directinterest to economists, the case study that itprovides is potentially of usefulness to the eco-nomic analysis of corruption. Anecdotal allega-tions of corrupt practices among sumo wrestlershave occasionally surfaced, but have been dis-missed as impossible to substantiate. In thispaper, we demonstrate that the com bination of aclear understanding of the incentives facing par-ticipants combined with creative uses of datacan reveal overwhelming statistical evidence ofcorruption. Details of the corrupt practices, thedata sources, and the telltale patterns in the datawill all vary from one application to the next.Nonetheless, the success of our study in docu-menting die predicted patterns of corruption inone context raises the hope that parallel studieswith more substantive economic focus may

    artificially imposed nonlinearity in incentivesfor wrestlers who achieve a winning record.^'Removing this distortion to incentives wouldeliminate the benefits of corruption. Seeond,match rigging appears to be sensitive to thecosts of detection. Increased media scrutinyalone is sufficient to eliminate the collusivebehavior. Presumably, other approaches to rais-ing the expected punishment would likewise beeffective. Third, at least in the sumo context,insiders appear to have good information aboutwho is corrupt. Providing strong incentives forwhistle-blowers, particularly when such accusa-tions can be corroborated by objective dataanalysis, may prove effective in restraining cor-rupt behavior.

    While perhaps beyond the scope of this pa-per, a question of interest is why those in chargeof the sumo wrestling have not attempted toeliminate corruption, either by eliminating thenonlinearity or by increasing expected punish-ments. A partial answer is that there are barriersto entry for a second sumo league, so the com-petitive pressure exerted on the current sumoassociation is limited.^^ A second possibility is

    -' Nonlinearities of this sort have been shown to distort

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    DUGGAN AND LEVITT: CORRUPTION IN SUMO WRESTLING 1605

    ant to rig the m atches on the

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