Corruption in Sumo Wrestling

WinningIsn’t Everything: Corruption in Sumo Wrestling

By MARK DUGGAN AND STEVEN D. LEVITT*

Thereis agrowingappreciation among econ- (roughly5 feet2 inchesto 5feet3 inches)and omistsof theneed to betterunderstand the role anexcess number of men below 1.57 meters. thatcorruption plays in real-world economies. Notcoincidentally, the minimum height for Althoughsome have argued that it can be wel- conscriptioninto the Imperial army was 1.57 fare enhancing(Nathaniel Leff, 1964),most meters(Stephen Stigler, 1986). More recent em- commentatorsbelieve that a willingnessto ac- piricalwork on corruption includes Robert H. ceptbribes (or similarforms ofcorruption) in Porterand J. DouglasZona (1993), which nds eitherthe public or the private sector reduces evidencethat construction companies collude economicef ciency (Andrei Shleifer and whenbidding for statehighway contracts by RobertW. Vishny,1993). As aresult,govern- meetingbefore the auction, designating a seri- mentsand rms oftencreate incentives to mo- ousbidder, and having other cartel members tivatetheir employees to be honest (Gary S. submitcorrespondingly higher bids. R. Preston Beckerand George J. Stigler,1974). McAfee(1992) details a widevariety of bid- Whileit is generally agreed that corruption is riggingschemes. Paulo Mauro (1995) uses sub- widespread,there is little rigorous empirical jectiveindices of corruptionacross countries to researchon thesubject. Because of corruption’ s demonstratea correlationbetween corrupt gov- illicitnature, those who engage in corruption ernmentsand lower rates of economic growth, attemptnot to leave a trail.As aconsequence, althoughthe relationship may not be causal. muchof the existing evidence on corruption is RayFisman (2001) analyzes how stock prices anecdotalin nature. More systematic empirical ofIndonesian rms uctuatewith changes in substantiationof corruptpractices is unlikely to former Prime MinisterSuharto’ s healthstatus. appearin typicaldata sources. Rather, research- Firms withclose connections to Suharto,which ers mustadopt nonstandard approaches in an presumablybene t from corruptionwithin the attemptto ferret outindirect evidence of regime,decline substantially more than other corruption. Indonesian rms whenSuharto’ s healthweak- Todate, there have been only a handfulof ens.Whether the rents accruing to thoseclose to studiesthat attempt to systematically document Suhartoare due to corruption or simply bad theimpact of corruption on economic out- policy,however, is hard to determine. Rafael Di comes.The rst empiricalstudy of corruption Tellaand Ernesto Schargrodsky (2000) docu- datesto 1846 when Quetelet documented that mentthat the prices paid for basicinputs at theheight distribution among French males publichospitals in Buenos Aires fallby 10 –20 basedon measurements taken at conscription percentafter a corruptioncrackdown. was normallydistributed except for apuzzling Inthis paper we lookfor corruptionamong shortageof men measuring 1.57– 1.597 meters Japan’s elitesumo wrestlers. While acknowl- edgingthat sumo wrestling is not itself a subject ofdirectinterest to economists, we believethat *Duggan:Department ofEconomics, University of Chi- thiscase study nonetheless provides potentially cago,1126 East 59thStreet, Chicago, IL 60637, and National valuableinsights. First, if corrupt practices Bureauof EconomicResearch (e-mail: mduggan@midway thrivehere, one might suspect that no institution .uchicago.edu);Levitt: American Bar Foundationand De- issafe. Sumo wrestling is the national sport of partmentof Economics, University of Chicago, 1126 East 59thStreet, Chicago, IL 60637(e-mail: slevitt@midway Japan,with a 2,000-yeartradition and a focus .uchicago.edu).We wouldlike to thank Gary Becker, Casey onhonor,ritual, and history that may be unpar- Mulligan,Andrei Shleifer, Stephen Stigler, Mark West, two alleledin athletics. 1 Moreover,Japan is generally anonymousreferees, seminar participants,and especially SergueyBraguinsky for helpful comments. Kyung-Hong Parkprovided truly outstanding research assistance. Levitt gratefullyacknowledges the research supportof the Na- 1 See MarkWest (1997)for an examination of the legal tionalScience Foundationand Sloan Foundation. rulesand informal norms that govern sumo wrestling in Japan. 1594 VOL. 92 NO. 5 DUGGAN ANDLEVITT:CORRUPTION IN SUMOWRESTLING 1595 foundto have relatively low rates of corruption incross-countrycomparisons (Transparency In- ternational,2000). 2 Second,because of the sim- plicityof theinstitutional framework, it is easy tounderstand and model the incentives facing participants.Third, data to test for matchrig- gingare readily available. While the exact tech- niqueswe utilizefor studyingcorrupt behavior insumowrestling will require modi cation before beingapplied to more substantive applica- tions,our analysis may nonetheless aid future researchersin that task. Thekey institutional feature of sumo wres- tlingthat makes it ripe for corruptionis the FIGURE 1. PAYOFF TO TOURNAMENT WINS existenceof a sharpnonlinearity in the payoff functionfor competitors.A sumotournament (basho)involves66 wrestlers ( rikishi) partici- typicalvictory. Consequently, a wrestlerenter- patingin 15 bouts each. A wrestlerwho ingthe nalmatch of a tournamentwith a 7-7 achievesa winningrecord (eight wins or more, recordhas far moreto gainfrom avictorythan known as kachi-koshi )isguaranteed to rise up anopponent with a recordof, say, 8-6 has to theof cial ranking ( banzuke);awrestlerwith a lose.There will also be incentivesfor forward- losingrecord ( make-koshi)fallsin therankings. lookingwrestlers torig matches on earlierdays Awrestler’s rankis a sourceof prestige, the ofthe tournament. 4 Accordingto our rough basisfor salarydetermination, and also in u- calculations,moving up a singlespot in the encesthe perks that he enjoys. 3 rankingsis worth on average approximately Figure1 demonstratesempirically the impor- $3,000a yearto a wrestler,so the potential tanceof an eighth win to a wrestler.The hori- gainsto trademay be substantialif the wrestlers zontalaxis of the gureis thenumber of winsa x a match.5 Of course,no legally binding wrestler achievesin a tournament;the vertical contractcan be written. axisis the average change in rank as a conse- Inthis paper, we examinemore than a decade quenceof thetournament. The change in rankis ofdata for Japan’s sumoelite in search of apositivefunction of thenumber of wins. With evidencedemonstrating or refuting claims of theexception of theeighth win, the relationship matchrigging. We uncoveroverwhelming evi- isnearlylinear: each additional victory is worth dencethat match rigging occurs in the naldays approximatelythree spots in the rankings. The ofsumotournaments. Wrestlers who are on the criticaleighth win— which results in asubstan- marginfor attainingtheir eighth victory win far tialpromotion in rankrather than a demotion— moreoften than would be expected. High win- garnersa wrestler approximately11 spotsin the ningpercentages by themselves, however, are ranking,or roughly four times the value of the

4 Anearlier versionof this paper, Duggan and Levitt (2001),derive a formal modelof the incentives facing partic- 2 Nevertheless, inrecent years, sumowrestling has been ipants.For wrestlers onthe bubble, the incentive to rig matches doggedby allegations of rigged matches, noneof which increases monotonicallyover the course of a tournament. havebeen substantiated. Of cials fromthe Japanese Sumo 5 Wrestlers rankedbetween fthand tenth earn anannual Associationdismiss these complaintsas fabricationson the income—including only of cial wages, bonuses,and prize partof disgracedformer wrestlers. Ultimately,despite years money—of roughly$250,000 per year. The fortieth-ranked ofallegations, no formal disciplinaryactions have been wrestler earns approximately$170,000. The seventieth- takentowards any wrestler. rankedwrestler receives onlyabout $15,000 per year (no 3 Forinstance, the lowest-ranked wrestlers inthe heya ofcial salary,just a small stipendto cover tournament mustrise early each morningto clean thebuilding and expenses,some prize money,and room and board). All prepare thefood for the main meal ofthe day. When a informationon annual salaries are basedon the authors’ wrestler reaches therank of juryo, placinghim among the calculationsand information provided in MinaHall (1997). top66 sumowrestlers inJapan, he nolongeris required to Unofcial sources ofincome such as endorsementswould dochoresfor other rikishi. Thosein the top 40 withranks of likelyincrease thedisparity between thetop and bottom maegashira orbetterhave their own servants. wrestlers. 1596 THEAMERICANECONOMIC REVIEW DECEMBER2002 far from conclusiveproof of match rigging. concludeswith a discussionof thebroader eco- Thosewrestlers whoare on the margin for nomicimplications of our analysis. achievingthe eighth win may exert greater ef- fortbecause their reward for winningis larger. I.Evidenceof Strong Performance Weoffer anumberof piecesof evidence against ontheBubble thisalternative hypothesis. First, whereas the wrestlerwho is on themargin for aneighth win Our dataset consists of almostevery of cial isvictoriouswith a surprisinglyhigh frequency, sumomatch that took place in the top rank thenext time that those same two wrestlers face (Sekitori)ofJapanese sumo wrestling between eachother, it is the opponent whohas an un- January1989 and January 2000. Six tourna- usuallyhigh win percentage. 6 Thisresult sug- mentsare held a year,with nearly 70 wrestlers geststhat at least part of the currency used in pertournament, and 15 bouts per wrestler. matchrigging is promises of throwing future Thus,our initial data set consists of over 64,000 matchesin return for takinga falltoday. Sec- wrestler-matchesrepresenting over 32,000 total ond,win rates for wrestlers onthe bubble vary bouts(since there are two wrestlers perbout). A inaccordance with factors predicted by theory smallnumber of observations (less than 5 per- tosupportimplicit collusion. For example,suc- centof the total data set) are discarded due to cessrates for wrestlers onthe bubble rise missingdata, coding errors, orearly withdrawal throughoutthe career (consistent with the de- from thetournament due to injury. A totalof velopmentof reputation), but fall in the last year 281wrestlers appearin ourdata, with the aver- ofawrestler’s career.Third, match rigging dis- agenumber of observations per wrestler in a appearsduring times of increased media scru- randomlyselected match equal to 554, and a tiny.Fourth, some wrestling stables (known as maximumof 990.The average number of total heya)appearto have worked out reciprocity matchesbetween the same two wrestlers com- agreementswith other stables such that wres- petingin arandomlyselected match is 10;thus tlersfrom eitherstable do exceptionallywell on we oftenhave many observations involving the thebubble against one another. 7 Finally,wres- sametwo wrestlers atdifferent points in time. tlersidenti ed as “ notcorrupt” by two former For eachobservation, we knowthe identity of sumowrestlers whohave alleged match rigging thetwo competitors, who wins, the month and dono better in matches on the bubble than in yearof thetournament, and the day of thematch typicalmatches, whereas those accused of being (tournamentslast 15 days with one match per corruptare extremely successful on thebubble. wrestlerper day). For roughly98 percentof the Itis dif cult to reconcile any of these ndings sample,we alsoknow what wrestling stable the witheffort as the primary explanation. wrestlers belongto; information is missing for Theremainder of this paper is organized as somewrestlers inthe early part of our sample follows.Section I introducesthe data used in whohad only a shortstint in the top ranks. theanalysis and presents the empirical evidence We beginby looking at the distribution of documentingthe strong performance of wres- winsacross wrestlers atthe end of tournaments. tlerson the bubble. Section II attemptsto dis- We expectthat a disproportionatenumber of tinguishbetween increased effort and match wrestlers should nishwith eight wins because riggingas an explanation for theobserved pat- ofthe high payoff associated with the eighth ternsin the data and also considers the way in win(see Figure1). To the extent that wrestlers whichthe market for riggedmatches operates, arerigging matches not only on the nalday, e.g.,how contracts are enforced, the use of cash butalso in the days immediately preceding the paymentsversus promises of future thrown endof thetournament, extra weight should also matches,and individuals versus stables as the beobservedon ninewins, as wrestlers whoare levelat which deals are brokered. Section III closeto the margin on days 13 or 14 may buy winsthat ultimately were notneeded to reach eightwins due to subsequent victories. Figure 2presentsa histogramof nalwins for the 6 Bythe second subsequent meeting, the winning percentages revert backto the expected levels, suggesting that 60,000wrestler-tournament observations in deals between individualwrestlers spanonly two matches. whicha wrestlercompletes exactly 15 matches. 7 Wrestlers inthesame stable donot wrestle each other. For purposesof comparison,we alsopresent the VOL. 92 NO. 5 DUGGAN ANDLEVITT:CORRUPTION IN SUMOWRESTLING 1597

marginin the match. Rankdiff isthe gap be- tweenthe of cial ranking of wrestlers i and j enteringtournament t.Insome regressions, we include xedeffects for eachwrestler and each opponent;in other speci cations we include wrestler-opponentinteractions. In all cases, we estimatelinear probability models, with standarderrors correctedto take into account the factthat a matchis included in the data set twice—once for wrestler i andonce for wrestler j. Table1 reportsthe excess win percentages for wrestlers onthemargin, by day,for thelast FIGURE 2. WINS IN A SUMO TOURNAMENT (ACTUAL VS. BINOMIAL) vedays of the tournament. On day 15, only wrestlers withexactly seven wins are on the margin;on day 14, wrestlers witheither six or sevenwins are on the margin, etc. The six expectedpattern of results assuming that all columnscorrespond to different regression wrestlers areidentical and that match outcomes specications. The even columns include the areindependently distributed. differencesin ranksfor thetwo wrestlers enter- Figure2 providesclear visual evidence in ingthis tournament. The rst twocolumns have supportof the model’ s prediction.Approxi- nowrestler xedeffects; columns (3) and(4) mately26.0 percent of all wrestlers nishwith includeboth wrestler and opponent xedeffects. exactlyeight wins, compared to only 12.2 per- The naltwo columns add wrestler-opponent centwith seven wins. The binomial distribution interactionsso that the identi cation comes predictsthat these two outcomes should occur onlyfrom deviationsin this match relative to withan equal frequency of 19.6 percent. The othermatches involving the same two wrestlers. nullhypothesis that the probability of sevenand Theresults in Table1 arequite similar across eightwins is equalcan be rejected at resounding specications. 8 Wrestlerson the bubble on day levelsof statistical signi cance. Nine victories 15arevictorious roughly 25 percentmore often alsoappears more often than would be ex- thanwould be expected. Win percentages are pected.Although this distortion is far lesspro- elevatedabout 15 percenton day14, 11 percent nouncedvisually, nine victories is signicantly onday13, and 5 percenton day12 for wrestlers morelikely than six (16.2 percent versus 13.9 onthe margin. There is no statistically signi - percent). cantevidence of elevated win rates for wrestlers Furtherevidence that wrestlers onthe bubble onthe bubble on day 11. The pattern of coef- winfar moreoften than would be expected cientsis consistent with the hypothesis that the comesfrom estimatingregressions of the gen- frequencyof match rigging will rise as the tour- eral form namentcomes to a close.If allof the excess winsare due to rigging, then the results imply

(1) Win ijtd 5 bBubbleijtd 1 gRankdiffijt thaton day 15 half of the bubble matches are crooked.For days14, 13, and 12 respectively, 1 lij 1 dit 1 eijtd theestimated percentage of rigged matches is roughly28, 22, and 10 percent respectively. where i and j representthe two wrestlers, t correspondsto a particulartournament, and d is theday of thetournament. The unit of observationis a wrestler-match. Bubble isa vectorof 8 Addingthe difference incurrent rank between wres- indicatorvariables capturing whether wrestler i tlers has littleimpact ontheother coef cients inthe regres- or j isonthe margin for reachingeight wins in sion.The difference inranks is animportant predictor of thebout in question. The Bubble variablesare match outcomeswhen wrestler xedeffects are excluded fromthe model. The top-ranked wrestler facingan average coded1 ifonly the wrestler is on the margin, wrestler wouldbe expectedto win about 70 percent of the 21ifonly the opponent is onthemargin, and 0 time. Once we controlfor wrestler xedeffects, however, ifneither or both of the combatants are on the theexplanatory power of thedifference inranksdisappears. 1598 THEAMERICANECONOMIC REVIEW DECEMBER2002

TABLE 1—EXCESS WIN PERCENTAGESFOR WRESTLERSON THE MARGIN FOR ACHIEVING AN EIGHTH WIN, BY DAY OF THE MATCH

Onthe Margin on: (1) (2) (3) (4) (5) (6) Day 15 0.244 0.249 0.249 0.255 0.260 0.264 (0.019)(0.019) (0.018) (0.019) (0.022) (0.022) Day 14 0.150 0.155 0.152 0.157 0.168 0.171 (0.016)(0.016) (0.016) (0.016) (0.019) (0.019) Day 13 0.096 0.107 0.110 0.118 0.116 0.125 (0.016)(0.016) (0.016) (0.016) (0.019) (0.019) Day 12 0.038 0.061 0.064 0.082 0.073 0.076 (0.017)(0.018) (0.017) (0.018) (0.020) (0.021) Day 11 0.000 0.018 0.015 0.025 0.010 0.012 (0.018)(0.018) (0.018) (0.018) (0.021) (0.021) Rankdifference — 0.0053 — 0.0020 — 20.0020 (0.0003) (0.0003) (0.0004) Constant 0.500 0.500 — — — — (0.000)(0.000) R2 0.008 0.018 0.030 0.031 0.0634 0.0653 Numberof observations 64,27262,708 64,272 62,708 64,272 62,708 Wrestler andopponent xedeffects No No Yes Yes Yes Yes Wrestler-opponentinteractions No No No No Yes Yes

Notes: Thedependent variable in all regressionsis an indicator variable corresponding to whether or nota wrestler winsthe match. Theunit of observationis awrestler-match. Values reportedin the table are coefcients associated withan indicator variabletaking the value 1 ifonly the wrestler is onthe margin for achieving eight wins, 21ifonlythe opponent is on the marginfor achieving eight wins, and 0 otherwise.On day 15, only wrestlers withseven wins are onthemargin. On day 14, wrestlers withsix or sevenwins are onthe margin. On day 13, wrestlers with ve,six, or seven wins are onthemargin, and soon. The omitted category in all regressionsis all wrestlers whoare noton themargin for achieving eight wins, as well as wrestlers inmatches inwhich both participants are onthemargin for eight wins. When a fullset ofwrestler andopponent xedeffects are included,the constant is omitted. In all cases, standarderrors are corrected toaccountfor the fact thatthere are twoobservations per bout (one for each wrestler). Thedifferences inthewrestler rankvariable is thenumerical rankorder ofthe wrestler minusthat of his opponent, based on of cial rankingspublished prior to each tournament.This variable is missingfor part of oursample.

II.DistinguishingBetween Match Rigging ofanalysesthat appear to conrm thecorruption and Effort storyand rule out effort as the explanation.

Theempirical results presented thus far are A. WhatCharacteristics In uence the consistentwith a modelin which opponents Likelihoodof Winning When on the Bubble? throwmatches to allowwrestlers onthemargin toachieve an eighth victory. The results, how- We beginby analyzing the personal and sit- ever,are also consistent with a scenarioin uationalcharacteristics that in uence the suc- whicheffort is animportant determinant of the cessrate of the wrestler on the bubble. One matchoutcome, and wrestlers onthe bubble, potentiallyimportant determinant of the fre- havingmore to gain from awin,exert greater quencyof match rigging is the probability that effort.9 Inthis section, we presenta widevariety thecollusive behavior will be detected. During oursample, there have been two periods in

9 Theresults are alsoconsistent with a modelin which wrestlers showaltruism for one another, sacri cing their ownoutcomes to help an opponent who has more togain. wrestler oflosingthe match (roughly$10,000), the altruism Giventhe nature of athletics andthe nontrivial cost to the storystrikes us as anunlikely explanation. VOL. 92 NO. 5 DUGGAN ANDLEVITT:CORRUPTION IN SUMOWRESTLING 1599 whichmedia attention has focused on match giventournament, wrestlers inthe running for rigging.The rst ofthesewas inApriland May suchprizes are unlikely to be willing to throw of1996. A former sumowrestler whohad be- matches.11 Theoverall tournament champion comea stable-mastercame forward withalle- wins$100,000; the juryo championwins gationsof match rigging. At thesame time, $20,000.In addition, $20,000 awards for “ght- anotherformer wrestleralso came forward to ingspirit” and “ outstandingtechnique.” In order decryrigged matches. Ironically, both of these towinthose prizes, wrestlers mustcompile very mendied a few weekslater, just hours apart, in strongrecords. The potential value of avictory thesame hospital. This fueled speculation for awrestler inthe running for suchprizes is amongthe media of foul play, although a sub- likelyto be at least as great as the value to a sequentpolice investigation revealed no evi- wrestleron the margin for aneighth win. dencefor this.The second period of media Analdeterminant of match rigging that we scrutinytook place in late1999 –early2000. A consideris the possibility of coordinatedmatch former sumowrestler named Itai raised allega- riggingamong stables of wrestlers. The lives of tionsof matchrigging that were widelycovered sumowrestlers centeraround the stable with bythe media, even in the United States. The whichthey are associated. Stable-masters exert threetournaments in our sample that are most atremendousin uence over both the wrestling likelyto be affected by the media attention are careerof wrestlers andtheir lives more gener- thoseheld in May 1996, November 1999, and ally.12 Giventhe important role of the stable, January2000. andthe fact that stable-masters bene t from Theliterature on repeated-play games (e.g., havinghighly ranked wrestlers, it would not be Drew Fudenbergand Jean Tirole, 1991) sug- surprisingif corruption were coordinatedat the geststhat the ability to sustaincollusion should stablelevel. For example,stables might have bepositively related to the frequency with collectivereputations, with stable-masters en- whichtwo wrestlers expectto meetin the future forcingpunishments on wrestlers whopursue sincemore future meetings imply the availabil- theirindividual best interests at the expense of ityof more severe punishments for wrestlers thestable. Some stable-masters, on the other whodo not cooperate. Empirically, we proxy hand,may not condone match rigging because theexpected frequency of futurematches using ofethical concerns or riskaversion. twovariables: (1) thenumber of meetings be- We empiricallyexamine one particular form tweenthe two wrestlers thattook place in the ofstable-level collusion: the presence of reci- precedingyear, and (2) whetherthe wrestler is procityagreements across stables. If suchdeals inthe last year of his career. Although the existed,one would expect both that wrestlers preciseending of a wrestler’s careeris not from stable A willhave very high win rates knownin advanceto theparticipants, it is likely whenon thebubble facing wrestlers from stable thatsignals of retirement are available (e.g., B,andvice versa. 13 Itis dif cult to tell an decliningperformance, injuries, etc.). 10 If it alternativestory that would account for sucha takestime to establisha reputationas awrestler patternin the data. For instance,if effort is the whois willing to collude and who can be trusted,then one might predict that the longer a 11 wrestlerhas been active in the top ranks of Althoughwe donot directly observe which wrestlers mightbe underconsideration for these prizes,having one of sumo,the better he will do when he is on the the vebest records (plus ties) upuntil that point in the bubble,and also, the worse hewill perform tournamentis an excellent predictor. Wrestlers withone of whenthe opponent is on the bubble. the vebestrecords in the tournament entering days 13, 14, Becausethere are a seriesof monetaryprizes or15 win a prize 50percent of the time. Less than ve givento wrestlers whohave good records in a percentof wrestlers withrecords outside the top veon days13– 15 eventually win a prize. 12 Forinstance, it is expectedthat the foremost sumo wrestler ina stable willmarry thedaughter of the stable-master. 10 Inorderto minimize endogeneity,we excludethe very 13 Thevariable we use totest thisempirically is the last tournamentof a wrestler’s career. Itis possiblethat a overallwin rate forwrestlers onthe bubble in matches losson thebubble may dropthe wrestler outofthetop level involvingboth a wrestler fromstable A anda wrestler from ofwrestlers, inducingretirement. Includingthe last tourna- stable B (excludingthe current match). Thisvariable re ects ment ofawrestler’s career slightlyincreased themagnitude both stable A’ssuccess onthe bubble against stable B and andstatistical signicance ofthecoef cient. stable B’ssuccess againststable A. 1600 THEAMERICANECONOMIC REVIEW DECEMBER2002 story,then stables with wrestlers capableof TABLE 2—DETERMINANTSOF EXCESS WIN LIKELIHOODS exertingparticularly high effort when they need FOR WRESTLERSON THE BUBBLE awinmight also be expected to have wrestlers Variable (1) (2) (3) whorise to the occasion when faced with the opportunityto beat a verymotivated opponent, Wrestler onbubble 0.126 0.117 0.155 leadingto a zeroor negative correlation. Simi- (0.026)(0.026) (0.029) larly,if onestable has developed speci c tech- Wrestler onbubble niquesthat provide it with an advantage over a interactedwith: particularstable, success rates on the bubble High media 20.188 20.177 20.146 willagain be negatively related. scrutiny (0.071)(0.071) (0.080) Thesevarious hypotheses are tested in Table 2. Opponent in 20.149 20.129 20.156 Becauseour interest is in how these factors runningfor a (0.047)(0.046) (0.052) inuence success on the bubble, the table re- prize this portsonly the coef cients on the interactions tournament betweenthese various factors and the outcome Number of 20.0048 20.0031 20.0024 ofbubblematches, i.e., any incremental impact meetings (0.0082)(0.0081) (0.0096) thatthese factors have on bubblematches above between two andbeyond their impact in nonbubblematches. opponentsin thelast year Alsoincluded in the speci cations, but not shownin the table, are the maineffects. Column Wrestler on 20.0361 20.0195 20.0346 (1) isthe baseline speci cation. Column (2) bubble inhis last year (0.0398)(0.0395) (0.0493) addsboth wrestler and opponent xedeffects. ofcompeting Column(3) alsoincludes wrestler-opponent interactions.The results are generally quite simi- Years insumo for 0.0077 0.0077 0.0091 wrestler on (0.0036)(0.0036) (0.0043) laracross the three columns of the table. bubble Thetop row ofthetable is the main effect of awrestler beingon the bubble, which leads to Winning 0.272 0.293 — percentage in (0.059)(0.058) anexcesswin likelihood of roughly12– 16 per- otherbubble centagepoints. In those tournaments with a high matches levelof media scrutiny, however, these excess between these winscompletely disappear. 14 Intwo of thethree two stables specications, the performance of wrestlers on R2 0.0160.074 0.246 thebubble in highand low media scrutiny tour- Wrestler and No Yes Yes namentsis statistically signi cant at the 0.05 opponent xed level.In none of the three columns can one effects? rejectthe null hypothesis that wrestlers onthe Wrestler-opponent No No Yes bubblein high-scrutiny tournaments do anybet- interactions? terthan chance. In the words of SupremeCourt JusticeLouis D. Brandeis,“ Sunlightis said to Notes: Thedependent variable in all three regressionsis an bethe best disinfectant.” 15 indicatorvariable corresponding to whether or nota wrestler winsthe match. Inaddition to the listed interaction Whenthe opponent is in the running for terms, all main effects are alsoincluded in the speci ca- winningone of thespecial prizes awarded, any tions.Wrestler onbubble is anindicator variable that equals benet ofbeing on the bubble also disappears. 1 (21)ifthe wrestler (opponent)is onthe bubble on days Thisresult is consistent with opponents in the 13,14, or 15 (recordof 7-7, 7-6, 6-7, 7-5, 6-6, or 5-7) but runningfor prizesbeing unwilling to throw a theopponent (wrestler) isnot, and 0 otherwise.Matches from1989, the rst year ofour sample, are excludedbe- match. cause thevariable for the number of matches between the Thevariables designed to capture factors in- twowrestlers inthe previous year cannotbe computed. Observationswhere stables are unknownor no two wrestlers fromthe stables ever meet onthebubble in ourdata set 14 Tocalculate theoverall excess winpercent for a are alsoexcluded from the sample. Thenumber of obser- wrestler onthe bubble in a periodof highmedia scrutiny, vationsis consequently 42,788. Standard errors are cor- thecoef cients inrows 1 and2 are addedtogether. rected toaccount for the fact thatthere are twoobservations 15 Wethankan anonymous referee forbringing this very perbout (one for each wrestler). appropriatequote to ourattention. VOL. 92 NO. 5 DUGGAN ANDLEVITT:CORRUPTION IN SUMOWRESTLING 1601

uencingimplicit collusion achieve mixed re- Table3 exploresthe pattern of match out- sults.The number of matches between two comesover time for wrestlers whomeet when wrestlers inthe preceding year has an unex- oneis onthemargin. The even columns include pectednegative impact on a wrestler’s likeli- wrestler-opponentinteractions so identi cation hoodof winning a matchon the bubble, oftheparameters comes only from variationin althoughthe coef cient is substantively small outcomesinvolving the same two opponents; andcarries a t-statisticof far lessthan 1 inall of theodd columns do not. The regression speci- thespeci cations. Wrestlers in the last year of cationsinclude indicator variables categoriz- theircareer do slightly worse thanexpected on ingthe timing of the meetings between two thebubble, although again the result is not wrestlers relativeto thematch where one wres- statisticallysigni cant. With the exception of tleris on the bubble. The omitted category is thelast year, however, success on the bubble matchespreceding a bubblemeeting by atleast increasesover the career. A ve-yearveteran is threematches. 17 about4 percentagepoints (off abaselineof 13 Focusing rst oncolumns(1) and(2), which percentagepoints) more likely to win on the correspondto all meetings on thebubble, there bubblethan a rookie.This last result is consis- areno systematicdifferences in outcomes in the tentwith the importance of developing a twomatches preceding the match on thebubble, reputation. asre ected in the statistically insigni cant co- Finally,the bottom row ofcoef cients in efcients in the top row. Whenthe wrestler is Table2 measuresthe extent to which a wres- onthe bubble (second row), heis much more tler’s successon the bubble today is inuenced likelyto win, consistent with the earlier tables. byoverall success rates (excluding this match) Theparameter of greatest interest is the nega- whenwrestlers from thatstable meet wrestlers tivecoef cient for the rst meetingbetween the from theopponent’ s stableand one of thewres- twowrestlers afterthe match in which the wres- tlersis on the bubble. 16 Thecoef cient is tleris on the bubble. The wrestler who was on stronglypositive and statistically signi cant. As themargin in thelast meeting is approximately notedabove, that result that is dif cult to rec- sevenpercent less likelyto win than would oncilewith any hypothesis other than stable- otherwisebe predicted. This ndingis consis- coordinatedcollusion. Moreover, the size of the tentwith part of thecompensation for throwing coefcient is large: for each10-percentage- amatchbeing the promise of the opponent pointincrease in success in other bubble returningthe favor in thenext meeting. There is matchesbetween these two stables, the wrestler noevidence that any return of favors extends onthebubble is 3percentagepoints more likely beyondthe next match, as two and three towin today, controlling for otherfactors. matchesout the winning percentages return to normal. B. WhatHappens When Wrestlers Meet The nalfour columns of Table 3 replicate Againin the Future? the rst twocolumns, except that the sample is dividedinto cases where the wrestler winswhen If collusionis the reason that wrestlers onthe onthe margin versus instances when the wres- bubbleperform well, then the opponent must be tlerloses when on themargin. 18 Onewould not compensatedin someway for losingthe match. expecta wrestlerto intentionally lose in future Itis possible that such payments are made in meetingsto anopponent who does not throw the cash,or in promises to return the favor in the matchon the margin. Thus, breaking down the future.The likelihood that two wrestlers will meetagain soon is high: in our data 74 percent 17 ofthe wrestlers whomeet when one is on the We haveexperimented with other groupings of matches, forinstance allowing a differentcoef cient for marginfor eightwins will face one another matches preceding/followingthe bubble match bymore againwithin a year. thanthree meetings.The parameters ofinterest are not sensitiveto alternative speci cations. 18 Incolumns(3)– (6), the actual matches takingplace on 16 Because wrestlers donot change stables overthe thebubble are excludedfrom the regression since there isno courseof their careers, there is nousable variation in this variation.In columns (3) and (4), all bubblematches are variablewhen wrestler-opponent interactions are included wonby thewrestler onthe bubble; in columns (5) and (6), incolumn(3). nomatches are wonby the wrestler onthe bubble. 1602 THEAMERICANECONOMIC REVIEW DECEMBER2002

TABLE 3—WIN PERCENTAGESIN PRECEDINGAND SUBSEQUENT MATCHES (ForTwo Wrestlers WhoMeet WhenOne is onthe Margin in the Final Three Days ofa Tournament)

OnlyMatches in OnlyMatches in AllMatches onthe Whichthe Wrestler on Whichthe Wrestler on Margin theMargin Wins theMargin Loses Variable (1) (2) (3) (4) (5) (6) One ortwomatches priorto the 20.002 0.005 0.020 0.019 20.041 20.035 bubblematch (0.009)(0.012) (0.011) (0.017) (0.016) (0.022) Bubblematch 0.151 0.164 — — — — (0.010)(0.014) Firstmeeting after bubblematch 20.073 20.062 20.082 20.079 20.056 20.040 (0.011)(0.015) (0.015) (0.020) (0.020) (0.027) Secondmeeting after bubblematch 20.002 0.005 0.031 0.028 20.061 20.039 (0.013)(0.016) (0.017) (0.022) (0.023) (0.030) Three ormore meetingsafter 20.010 0.012 0.013 0.022 20.045 20.013 bubblematch (0.006)(0.011) (0.007) (0.014) (0.008) (0.017) Constant 0.500 — 0.500 — 0.500 — (0.000) (0.000) (0.000) Wrestler-opponentinteractions? No Yes No Yes No Yes R2 0.008 0.271 0.002 0.279 0.002 0.279

Notes: Entriesin the table are regressionestimates ofthe outcomes of matches between,after, andcontemporaneous with these twowrestlers meetingwhen one wrestler ison the margin for achieving eight wins on the last three daysof the tournament.The dependent variable in all regressionsis anindicator variable for whether the wrestler winsa match. Theunit ofobservationis awrestler match. The rst twocolumns correspond to all wrestlers whomeet whenone is onthe margin. Incolumns(3) and (4), the coef cients reportedcorrespond only to those cases where thewrestler onthe bubble wins the match. Columns(5) and (6) report coef cients onlyfor those wrestlers onthebubble who lose the match. Columns(3) and (5)are estimated jointly,as are columns(4) and (6). Except for columns (1) and (2), bubble matches are excludedfrom the regressions.The excluded category in all regressionsare matches occurringmore thantwo matches priorto a bubblematch andnot falling into any of theother categories named.When a fullset ofwrestler andopponent xedeffects are included, theconstant is omitted.In all cases, standarderrors are corrected toaccount for the fact thatthere are twoobservations per bout(one for each wrestler). Numberof observationsis equalto 64,273. datain this way provides a naturaltest of the (4),there is no downward spike in wins following hypothesisthat the poor performance in thenext thebubble match. The ndingthat winners on the matchis due toadeferredpayoff to an opponent bubblefare badlythe next time they face the same whothrew a match.The data provide clear opponent,but losers do not, is consistent with the supportfor thecollusion hypothesis. Wrestlers match-rigginghypothesis, but not with an effort whowin on the bubble tend to doslightlybetter story.If increasedeffort is responsible for strong thanexpected leading up to the bubble match, performancesin matches on the margin, there is thendo much worse inthe next meeting with noreason to expect systematic underperformance thesame opponent. Relative to thesurrounding thenext time the two wrestlers meet, and certainly matches,the rst post-bubblematch sees the wrestler losingapproximately 10 percentage pointsmore frequently than would be expected 19 Whentwo wrestlers meet andboth are onthe bubble, (i.e.,row 3minusrow 1). there is similarlyno evidence that the wrestler whowins Thepattern for wrestlerswho lose to the oppo- fares more poorlythe next time thetwo wrestlers meet. This nentwhen on the margin for achievingeight wins is consistentwith no match riggingoccurring when both isvery different. In the matches just prior to the wrestlers are onthe bubble, as predictedby themodel. Moregenerally, there is noevidence of negative serial bubblematch, the wrestler is slightly underper- correlationin match outcomes.When multiple lags of past forming.This continues unaffected through the match outcomesbetween thetwo wrestlers are addedto the post-bubblematches as well. Unlike columns (1)– specications, the coef cients are positive. VOL. 92 NO. 5 DUGGAN ANDLEVITT:CORRUPTION IN SUMOWRESTLING 1603 notexclusively among those who won on the Table4 reportsthe results of the estimation. bubble.19 Allof thecoef cients in the table come from a Thepayment-in-kind story suggested by the singleregression. The values in the table repre- resultsabove is unlikelyto betheonly form of sentexcess win percentages on thebubble, i.e., compensationfor wrestlers whothrow matches. howmuch better a wrestlerdoes when on the Basedon Table 3, roughly two-thirds of the bubblerelative to matches in which neither excesswins garnered on thebubble are returned wrestleris on the bubble. The columns of the thenext time the two wrestlers meet.This tableidentify the status of the wrestler on the price—two-thirds of a matchdown the road in bubble—the wrestler who wants to buy a vic- returnfor throwinga matchtoday— istoo low tory.The rows correspondto the status of the torepresent the only form ofpayment. When opponentof the wrestler on the bubble— the rumorscirculate about match rigging in sumo, wrestlerwho might want to sell a win.When theyoften suggest the presence of cash trans- twowrestlers identied as corrupt meet on the fers, althoughwe areable to provide no evi- bubble,the one who needs the victory is 26 denceabout this channel. percentagepoints more likely to win the match thanif those two wrestlers metwith neither on C. Dothe Data Con rm PublicAllegations of thebubble. This excess win percentage is highly Cheatingby Sumo Insiders? statisticallysigni cant. When a corruptwrestler meetsa wrestlerclassi ed as “statusunknown,” Twoformer sumowrestlers havemade pub- theresults are very similar. Win percentages for licthe names of 29wrestlers whothey allege to thewrestler needingthe victory when both becorrupt and 14 wrestlers whothey claim wrestlers areclassi ed as“statusunknown” are refuseto rig matches (Keisuke Itai, 2000; Ona- alsohighly elevated (18.1 percentage points ruto, 2000; Shukan Post, 2000).20 In this sec- higher),but not quite as extreme. In stark con- tion,we investigatewhether the performance on trast,none of the vecoef cients involving thebubble of these two groups of wrestlers wrestlers identied as cleanare statistically sig- systematicallydiffers. If strongperformance on nicant from zero.This implies that the out- thebubble is due to match rigging and the comesof bubble matches involving a clean allegationsare true, then one would expect the wrestler areno different than the results when corruptwrestlers todo extremely well on the thesame two wrestlers meet,but neither is on bubble,whereas the honest wrestlers woulddo thebubble. This result holds true regardless of nobetter in bubble matches than on any other whetherthe clean wrestler is himself on the match. bubbleor facing a wrestler whois on the bub- Totest this hypothe sis,we estimatea re- ble.Thus, Table 4 providesstrong con rmation gressionidentica ltoequatio n(1), butinclud- notonly of theclaim that elevated win percent- inga fullset of interactionsbetween whether ageson the bubble are due to matchrigging, but amatchis onthebubble and the classi cation alsothat the allegations made by the two sumo ofeach wrestler andhis opponen taseither insidersappear to be truthful. Moreover, it ap- “corrupt,”“ clean,”or “statusunknown .”Only pearsthat most of thewrestlers notspeci cally 43of the 281 wrestlers (15percent) in our namedby thewhistle-blowers are corrupt, since sampleare speci cally identi ed as either theiroutcomes differ only slightly from those corruptor clean.The remainder are classi ed wrestlers namedas corrupt. asstatusunknown .Thewhistle-b lowerswere morelikely to identify prominen twrestlers III.Conclusion withlong careers, however, so over 60 percentof thematches in our sample involve at Thispaper provides strong statistical analysis leastone wrestler identied bynameas either documentingmatch rigging in sumo wrestling. cleanor corrupt. Theincentive structure of promotion leads to gainsfrom tradebetween wrestlers onthemar- ginfor achievinga winningrecord and their 20 Thebooks that we cite are publishedonly in Japanese. We thankSerguey Braguinsky both for bringing the exis- opponents.We showthat wrestlers wina dis- tence ofthis information to ourattention and for translating proportionateshare of the matches when they therelevant material forus. areon the margin. Increased effort cannot 1604 THEAMERICANECONOMIC REVIEW DECEMBER2002

TABLE 4—EXCESS WIN PERCENTAGESON THE BUBBLE FOR WRESTLERS LABELED BY SUMO INSIDERS AS “CORRUPT” OR “CLEAN”

Wrestler onthe Bubble Is Identied as: CorruptStatus Unknown Clean Corrupt 0.260 0.270 20.010 Opponent of (0.037) (0.021) (0.038) wrestler onthe Status 0.271 0.181 0.041 bubble is unknown (0.021) (0.019) (0.031) identied as: Clean 0.036 20.033 0.022 (0.027) (0.035) (0.074)

Notes: Entriesin the table are coefcients froma regressionwith full set ofinteractions between whethera match is onthe bubble and the classi cation of awrestler andhis opponent as clean, corrupt,or status unknown by twosumo insiders (Itai, 2000; Onaruto, 2000; Shukan Post,2000).The regression is identicalto equation(1) in the text, except for the inclusion of theaforementioned interactions. Twenty-nine wrestlers are categorizedas corrupt,14 are classied as clean. Theremainder ofwrestlers are notspeci cally named andare categorized as statusunknown. Standard errors are corrected totake intoaccount that there are two observationsper bout (one for each wrestler). Numberof observationsis equal to 64,273. explainthe ndings.Match rigging disappears articially imposed nonlinearity in incentives intimes of increased media scrutiny. Wrestlers for wrestlers whoachieve a winningrecord. 21 whoare victorious when on the bubble lose more Removingthis distortion to incentives would frequentlythan would be expected the next time eliminatethe bene ts of corruption. Second, theymeet that opponent, suggesting that part of matchrigging appears to be sensitive to the thepayment for throwinga matchis future pay- costsof detection. Increased media scrutiny mentin-kind. Reciprocity agreements between aloneis suf cient to eliminate the collusive stablesof wrestlers appear to exist, suggesting that behavior.Presumably, other approaches to rais- collusivebehavior is not carried out solely by ingthe expected punishment would likewise be individualactors. Allegations by sumo insiders are effective.Third, at least in the sumo context, demonstratedto be veri ed in our data. insidersappear to havegood information about Whilesumo wrestling per se is not of direct whois corrupt. Providing strong incentives for interestto economists, the case study that it whistle-blowers,particularly when such accusa- providesis potentiallyof usefulnessto the eco- tionscan be corroborated by objective data nomicanalysis of corruption.Anecdotal allega- analysis,may prove effective in restrainingcor- tionsof corruptpractices among sumo wrestlers ruptbehavior. haveoccasionally surfaced, but have been dis- Whileperhaps beyond the scope of this pa- missedas impossible to substantiate. In this per,a questionof interestis whythose in charge paper,we demonstratethat the combination of a ofthe sumo wrestling have not attempted to clearunderstanding of the incentives facing par- eliminatecorruption, either by eliminating the ticipantscombined with creative uses of data nonlinearityor by increasing expected punish- canreveal overwhelming statistical evidence of ments.A partialanswer is that there are barriers corruption.Details of thecorrupt practices, the toentry for asecondsumo league, so the com- datasources, and the telltale patterns in thedata petitivepressure exerted on the current sumo willall vary from oneapplication to the next. associationis limited. 22 Asecondpossibility is Nonetheless,the success of our study in documentingthe predicted patterns of corruption in onecontext raises the hope that parallel studies 21 Nonlinearitiesof thissort have been shown to distort withmore substantive economic focus may behaviorin many other contexts as well,including Robert yieldsimilar results. Topel(1983) and Judith Chevalier and Glenn Ellison (1997). Moreover,our analysis provides insight into 22 Itisworthnoting that the popularity of sumowrestling howto combatcorruption. First, the match rig- has declinedsubstantially over the last twodecades, sug- gingwe identifycan be directly linked to the gestingthat other forms ofrecreation are substitutes. VOL. 92 NO. 5 DUGGAN ANDLEVITT:CORRUPTION IN SUMOWRESTLING 1605 thatthe nonlinear payoff structure generates Leff,Nathaniel. “EconomicDevelopment through interestin otherwise unimportant matches on the BureaucraticCorruption.” AmericanBehav- naldays of thetournament. For thesame rea- ioralScientist ,November1964, 8(3), pp. sonthat wrestlers wantto rigthe matches on the 8 –14. bubble,the fans are interested in the outcome. Mauro,Paulo. “Corruptionand Growth.” Quar- terlyJournal of Economics ,August1995, REFERENCES 110(2),pp. 681– 711. McAfee,R. 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