Some comparative economics of the organization of sports: Competition and regulation in north American vs. European professional team sports leagues

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1 Some comparatve economcs of the organzaton of sports: Competton and regulaton n north Amercan vs. European professonal team sports leagues Wladmr Andreff To cte ths verson: Wladmr Andreff. Some comparatve economcs of the organzaton of sports: Competton and regulaton n north Amercan vs. European professonal team sports leagues. European Journal of Comparatve Economcs, 20, 8 (), pp <halshs > HAL Id: halshs Submtted on 8 Mar 202 HAL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. L archve ouverte plurdscplnare HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés.

2 Revsed verson for publcaton n the European Journal of Comparatve Economcs: SOME COMPARATIVE ECONOMICS OF THE ORGANIZATION OF SPORTS: COMPETITION AND REGULATION IN NORTH AMERICAN vs. EUROPEAN PROFESSIONAL TEAM SPORTS LEAGUES Wladmr Andreff What s the future of comparatve economcs? Ths queston has been wth us snce the collapse of the former communst regmes assocated wth socalst centrally planned economes. Varous responses have been suggested n the lterature durng the postcommunst perod of economc transformaton and I wll brefly sketch a few of them below (see secton ). But no one could magne that a possble dvdng lne between a quassocalst system and a deregulated market economy were to persst n some area untl today, 200. Had t been so, would not all those nvolved nto comparatve economcs have taken ths opportunty to prolong the use of ther usual economc and nsttutonal tools of comparatve analyss n that area? Amazng as t may seem, such an area does exst and my contrbuton s devoted to brefly present t as an avenue for new comparatve economc research. There s a dvdng lne between the North Amercan closed league system n professonal team sports a sort of sland of regulated quas-socalst economy n the mddle of a lberal Amercan market captalsm and the European open league system whch has rapdly been almost completely deregulated, startng from European football (soccer) n 995 and spreadng throughout other European sports and all open professonal team sport leagues. There are four dmensons along whch closed and open team sports leagues can be compared: organzatonal (secton 2), n a Walrasan model (secton 3), usng a Nash-equlbrum conjecture (secton 4), and through emprcal testng (secton 5). I wll brefly screen all four. The emprcal evdence wll show that European open leagues dffer from North Amercan Professsor Emertus at the Unversty of Pars Panthéon Sorbonne, Honorary Presdent of the Internatonal Assocaton of Sport Economsts, former Presdent of the EACES (997-98) and of the French Economc Assocaton ( ).

3 closed leagues n that teams' budget constrants n the former are soft whle they are hard n the latter. We thus meet Kornaï s nsght n unexpected places. A dsequlbrum model would ft open leagues better.. Whch future for comparatve economc studes? Jan Tnbergen (96) was the frst economst and Nobel Prze wnner who stated and predcted that the core object of comparatve economcs, captalsm versus socalsm, would vansh, snce the two opposte nsttutonal and economc systems may be replaced by a sngle system. Ths hypothess s known as one of convergence between economc systems (Andreff, 992). The collapse of the Sovet-type systems between 989 and 99 followed by two decades of post-communst transformaton dd not exactly confrm Tnbergen s (and others') convergence prognoss. The two former systems dd not merge because one of them the Sovet system was defntely submerged by the other wth a restoraton of a captalst market economy n former Sovet economes. Dd the total collapse of the communst system and the assocated globalsaton of captalsm put an end to comparatve economcs and turn the latter nto a branch of economc hstory? Nut (999) has contented that nothng could be further from the truth. Let me offer an elaboraton on Nut s seven arguments:. Some Sovet-type economes are survvng n countres lke Turkmenstan, Tajkstan, North Korea and even Cuba. 2. There are countres, namely Vetnam and Chna, whch are nether tradtonal Sovet-type systems, nor post-transtonal economes such as Central and Eastern European countres whch have joned the EU; sooner or later, ther systemc transformaton wll become a specal case, as Kornaï (2006), who adds the Muslm countres to the lst, suggested. He concludes that transtology (a varant of comparatve economcs when a system changes or collapses) s not over. 3. As long as we have dfferent systems, the queston of actual or possble transton from one to the other remans a topc for comparatve economcs, snce dfferent transton paths have been observed n the 990s. Even wthn captalsm, nsttutons evolved n varous countres at varous speeds (Kornaï, 2006). 4. Wthn the captalst system tself, there exst several prototypes of a market economy whch dstngush the Anglo-Amercan model from a Japanese and South Korean networked verson, German Mtbestmmung, and even more so (the former French) state captalsm n varous developng countres (see also Boyer, 993). On the other hand, t s the way whch s now used by manstream economcs to re-ntegrate a lberal analyss of 2

4 nsttutons nto the so-called new comparatve economcs see for nstance Djankov et al. (2003), Glaeser et al. (200 & 2003), Glaeser & Shlefer (200, 2002 & 2003), and for a crtcsm Andreff (2006). 5. Even economc systems wth dentcal economc nsttutons may behave very dfferently f ther economc polces are systematcally (permanently and consstently) dfferent for nstance Thatcherte-Reagante polcy as aganst Scandnavan soldarty welfare polces. 6. There s some sort of study of economc engneerng,.e. of new or modfed economc nsttutons, ncludng yet untred sets of economc nsttutons ( utopas ) as well as hstorcal comparsons, e.g., wth ancent economc systems and ther great transformaton (Polany, 944). 7. Hstory never end up: both sngle nsttutons and the systems they form evolve contnually; n ths sense, Karl Marx was the frst notable practtoner of evolutonary economcs through hs theory of the development of modes of producton (.e., economc systems). To make Nut s lstng absolutely comprehensve, I would add another ssue whch also pertans to comparatve economcs: 8. Emergng captalsm exhbts dfferent features, nsttutons and n lne wth the evolutonst vew dfferent levels of and paths to economc development as compared to already developed fully-fledged captalst market economes; ths s exemplfed nowadays by the attractveness of BRICs or BRICS 2 to comparatve economc studes. Eleven years after Nut s artcle, many studes n comparatve economcs have drfted towards ether economc nsttutonalsm or development economcs whch has translated, snce 997, nto a rapd decrease n the number of Econlt-lsted publcatons belongng to comparatve economc systems, as notced by Dallago (2004). Wth Nut s arguments 2, 4 and 6, t may sound that the future of comparatve economcs les wth nsttutonal economcs, whle arguments 3 (ncludng path dependence) and 7 lead comparatve economcs to combne wth nsttutonal and development economcs nto an evolutonary approach. Comparatve economcs comes even closer to development economcs f (our) argument 8 s accepted. Although Nut was certanly rght sayng that post-communst transformaton has enrched 2 Brazl, Russa, Inda, Chna wth a small s, addng South Afrca wth a bg S. 3

5 the range of system morphology, and has greatly enhanced the mportance and sgnfcance of the study of comparatve economc systems, polces and nsttutons, and ther processes of transton and evoluton, n the long run, comparatve economsts mght well be left wth only four countres to study (argument ) or must become and specalse as nsttutonalsts, evolutonsts or development economsts. Comparatve economcs wll be all the more phased out for those who consder Russa (and other transton countres) as havng made remarkable economc and socal progress n order to become a normal country (Shlefer & Tresman, 2005). However, such concluson s hghly debatable and, for nstance, Rosefelde (2005) contends that a country lke Russa s an abnormal poltcal economy unlkely to democratze, westernze or embrace free enterprse any tme soon. In such a mood, t s crucal to fnd new avenues for comparatve economcs. I have dscovered one of them n studyng the economcs of sports (Andreff 98 to, among others, Andreff, 989, 996, 200 & 2008; Andreff & Staudohar, 2000; Andreff & Szymansk, 2006; Poupaux & Andreff, 2007), because professonal team sports leagues are not desgned, organzed, regulated and functonng wth the same basc characterstcs everywhere. On the one hand, closed North Amercan sports leagues are exempt from the bulk of legslaton that apples to any other U.S. ndustry, whle a quas-socalst monopolstc regulaton s used to make sports leagues proftable to ther owners. On the other hand, open European sports leagues operate n a more compettve envronment due to ther coverage by the European competton polcy. However, snce the major objectve of a European sport club s not proft maxmsaton and ts budget constrant s usually soft, some peces of the former economc analyss of planned (shortage) economes seem to be relevant there. Ths s the story I would tell you to convnce that the economcs of sports, n partcular the economcs of professonal team sports leagues, s a new promsng area for comparatve economcs. 2. An organzatonal comparson between closed and open team sports leagues Insttutonal rules that fx how a professonal team sports league s organzed, regulated and managed can be encapsulated n twelve stylzed facts (Andreff, 2007a; Szymansk, 2003).. A North Amercan professonal team sports league s an ndependent organzaton whch s closed by an entry barrer created by franchse sales; a European league, lke n soccer, s ntegrated n a herarchcal structure where the natonal soccer federaton supervsng the league s tself dependent on an nternatonal federaton. Entry n a closed league s only possble by the purchase of an expanson franchse, f there s any for sale, when the new 4

6 enterng team s market and ts assgned locaton are assessed proftable by a league commssoner. Moreover, entry n the league cartel must be approved by a qualfed majorty of ncumbent teams. Competton can only occur wth the creaton of a rval major league n the same professonal sport as another closed league. In open leagues, entry reles on a promoton/relegaton system, but the creaton of a second major league n the same professonal sport n a gven country s ruled out by the nternatonal federaton. 2. In a closed major league the number and the dentty of the teams are fxed, whereas a team's upward/downward moblty s ensured by promoton/relegaton n open leagues: best ranked teams of the second dvson are promoted n frst dvson whle last-ranked teams of the frst dvson are demoted to second dvson. Thus from one season to the next the dentty of some clubs, those demoted and promoted, changes n an open league. One team whch starts playng n the lowest amateur dvson can clmb step by step the whole ladder of the sportng herarchy, smply due to ts sportng performance, and end up n the frst dvson, and even qualfy for a European league. Such a bottom-up route does not exst n a closed league system, snce the major league s closed downwards. 3. In a closed league a team enjoys an absolute exclusvty over a urban area where t s the only one (n any gven professonal sport) allowed to organze a major league s games. Thus each team has a monopoly n the local market for ts sport shows. If the local market ceases to be proftable, a team can, wth the league s agreement, move to another urban area. From ther ncepton up to 2005, 48 team relocatons have occurred n the four North Amercan major leagues (7 n NFL, 9 n NHL, 2 n MLB, and 20 n NBA). In an open league there s no such geographcal team moblty; moblty s vertcal from lower to upper dvsons and the other way round. There s nether terrtoral exclusvty nor local monopoly of a team n a gven sport: n most European captals, more than one team play n the frst soccer dvson. 4. Compettve balance s looked for n both closed and open leagues. Labour market regulatons are the major tool for attemptng to reach t n closed leagues. Though they exst also n open leagues, labour market regulatons are supplemented wth other nstruments. In partcular, promoton/relegaton automatcally ensures a partal re-balancng of the sport contest at the end of each season by demotng the weakest and promotng the strongest. Moreover ths system acts as an ncentve mechansm: teams exert mportant efforts to avod the sancton (demoton) and gan the reward (promoton); the proporton of games hgh n contenton s bgger than n a closed league. On the other hand, promoton/relegaton s a selfunbalancng process from an economc vewpont and leads to deep economc and fnancal dspartes across the league. Beng qualfed for the Champons League, a team wll ncrease 5

7 ts revenues by 20% to 40%. Beng relegated n a lower dvson, a team may see ts revenues plunge by 75-80% n European soccer whle beng promoted should ncrease ts revenues fve tmes or so. 5. A closed league can restrct recrutment rules and players moblty snce t enjoys a monopsony power n the labour market for talent. Ths occurred frst n baseball as early as 879 when a reserve clause was ntroduced to prohbt any player's move from one team to another wthout the team owner s agreement. Snce the 970s, after several labour conflcts strkes and lockouts veterans have obtaned a free agent status that takes hold after a defned number of years of playng n a major league. However, newcomers (young and foregn players) n the league are pcked n rooke draft, ranked by experts accordng to ther prevous sportng performance. In European open leagues a reservaton system, based frst on a lfelong contract untl 968 and then on a system of transfer at the end of players' labour contract, had restrcted players' moblty and ther freedom to sgn a team. The Bosman case (995) has ruled out all restrctons to player free choce on the European labour market for talent. Ths rulng algned professonal sports wth Artcle 48 of the Rome Treaty that guarantees free worker moblty to all European Unon ctzens. The Bosman rulng also phased out quotas of natonal players (6 out of n 995) that a professonal soccer team had to feld at any game. 6. Rooke draft also functons as a reverse-order-of-fnsh draft (Kahane, 2006). Thus, professonal team sports s the only ndustry n North Amerca where frms, that s, teams, have a restrcted rght to choose whom they wll hre. Team owners n North Amercan major leagues argue that such restrcton s a must for balancng team sports contests. Hrng players s also quanttatvely restrcted by roster lmts. There s no such thng as rooke draft qualtatve lmtaton or quanttatve roster lmts n European open leagues. The Bosman deregulaton of the labour market has trggered hgh player moblty, n partcular wth regards to superstars. European open leagues have to comply wth EU competton polcy, though team managers have argued wthout success for a sports ndustry excepton, smlar to North Amercan leagues exempton of anttrust law, to escape t. 7. Player moblty n closed leagues s all the more lmted n that tradng for cash s restrcted or forbdden (snce 960 n NFL and 976 n MLB), especally for superstars. Inter-team player transfers are usually barters, so that team competton for hrng the same player s practcally nonexstent (Szymansk, 2004a). In European open leagues most player transfers are transactons n cash or monetary settlement, barters and loans of players to another team beng a rare excepton. 6

8 8. Player workng condtons and salares result from collectve barganng between club owners and player trade unons n closed leagues. Some leagues (NBA 983, NFL 994) have succeeded n barganng a salary cap whch has been advocated by club owners as a means to avod superstar concentraton n rch teams and mantan a compettve balance. But t s also a lever for keepng a league monopsony on the labour market snce the reserve clause has been abandoned. A luxury tax completes ths payroll regulaton n some leagues. In open leagues wth deregulated labour markets (post-bosman Europe), the degree of player unonsaton s much lower, collectve barganng s much less formalsed, and salary caps are rare. 9. Poolng TV rghts sales at the league level wth revenue dstrbuton across teams s common practce n closed leagues. A monopoly power s thus ensured to the league n the market for ts derved product,.e. televsed sport. Professonal team sports are the only U.S. ndustry where such cartel behavour s exempted from ant-trust law ever snce the Sports Broadcastng Act (96). Revenues obtaned from gate recepts, sponsorshp and merchandsng are also pooled and re-dstrbuted. Local TV revenues are the only excepton to poolng and re-dstrbuton. TV rghts poolng also prevals n open leagues wth a few exceptons for nstance, soccer TV rghts are sold by the teams themselves n Greece, Portugal, Span (and Italy untl 2007). There s no poolng for sponsorshp and merchandsng, and gate recepts dstrbuton between home and vstng teams has been gven up n the 980s. 0. Most Amercan sports teams are not stockholdng companes whose shares are floated on the stock exchange. In the NFL flotaton s even absolutely forbdden. Club owners do not want to be exposed to the rsk of beng merged or acqured by an outsder another entry barrer n the closed leagues. In European soccer open leagues flotaton of team shares has developed snce the 990s, even though varous teams have been de-lsted after ther shares have floated down (Agletta et al., 2008).. Beng a cartel of teams, a closed league maxmzes ts profts and shares them across teams. Thus t can be assumed that the objectve functon of North Amercan professonal sports teams s proft maxmzaton. When a team s no longer n the race for playoffs, ths fnancal objectve fnally gans over wnnng games. In an open league, a team strugglng for promoton or threatened by demoton usually adopts a wn maxmzaton objectve (Sloane, 97) possbly subject to t has often been assumed (Késenne, 996) a balanced budget constrant. 7

9 2. Due to proft maxmzaton n closed leagues, nvestment n sportng talent s only undertaken f t ncreases revenues more than costs. Unlke bg-market teams, small-market teams lack proft ncentves to buld up compettve teams that wll maxmze league revenues; ths s another manner n whch bg market-teams subsdze small-market teams n the closed leagues (Fort & Qurk, 995). Promoton-relegaton and wn-maxmzaton drve teams nto an arms race or a rat race à la Akerlof (976) n whch each team attempts to recrut the best players to mprove ts relatve strength compared wth opponent teams; the latter, n turn, are led to overbd. The problem s that such nvestments n talent are socally effcent only f they upgrade the absolute (and not only relatve) qualty of teams (Lazear & Rosen, 98), whch cannot be taken for granted. Snce there s only one (or a few) wnner(s) n the arms race who can recoup ther nvestment costs, an open league s always under the threat of generalsed cost nflaton of salary and transfer fees, all the more so because the latter s not slowed down by a proft maxmzaton objectve. Most bg teams are doomed to be n the red n a deregulated open league. 3. Can a Walrasan equlbrum model explan the stylzed facts? Snce El Hodr and Qurk (97) a Walrasan equlbrum model has been used to represent a two-team closed league wth proft-maxmzng and wage-taker teams n a compettve labour market for talents. Each team n market of sze m maxmzes ts proft through varatons n the quantty of talent t : Max Max ( R C ), () R R R R R R R m, t, 0, 0 or 0, 0, 0, (2) m t t t t m 0 C s t c (3) It s assumed that a number of unts of homogenous talent are emboded n each player, more n superstars than n other players. Then Fort and Qurk (995, p. 27) assume that talent s measured n unts such that an addtonal unt of talent ncreases wn percent by one unt. w Under ths conventon: (4) t Yes, t deserves a number snce t s refered to several tmes n the followng text WA 8

10 Such assumpton allows to substtute wn percent by the quantty of recruted talent n the revenue functon R of team. The supply of talent s assumed to be fxed ( t = ) snce the labour market s closed by league regulaton. Wth a fxed supply of talent, team owners nternalze the followng externalty: recrutng an addtonal unt of talent wll deprve the other team of ths unt, whch wll deterorate the league compettve balance. Team revenue R s a functon of local market sze m, tcket prce 3 and the number of wns or wn percent w (therefore of t ). The revenue functon s concave n wn percent and thus wns have a decreasng margnal effect on revenues. The margnal revenue of a wn, assumng the revenue functon s quadratc, b R a w w k 2 s: dr a b w, b 0 dw, (5) and t. (6) Team revenue s ncreasng n wns untl a maxmum after whch t decreases, namely when the team wns the champonshp. Talent has an ncreasng then a decreasng return. In the team cost functon, s s the salary per unt of talent and c 0 represents a fxed cost (stadum, management). The equlbrum wage s provded by the nvsble hand or a Walrasan auctoneer. Team augments ts talent recrutment untl margnal revenue of talent s equal to ts margnal cost, the exogenous equlbrum unt wage: R m, t M R s for. (7) t Graph : Compettve balance wth proft maxmzaton 3 Tcket prce s assumed to be formed n a compettve market and t s gven as a parameter n the team economc calculaton (lke n the standard Walrasan model). The product market of a team (sport show sales) s not focused on n ths standard model. 9

11 bg team small team 2 MR MR 2 E* s* t 2 0,5 t* t Graph shows a bg-market team (bg team) competng over talent wth a small-market team 2 (small team) wth m > m 2. Snce market s bgger than market 2, ths creates a revenue dsparty between the two teams. For any gven wage, team 's demand for talent s bgger than team 2's demand. In equlbrum (E*), the sum of the two teams' demand for talent s equal to the supply of talent of unt, at equlbrum wage s*. Then the bg team recruts more unts of talent than the small team, t > t 2, and the league does not reach the best compettve balance (t = 0,5). The league's economc equlbrum s assocated wth dspartes n team payrolls. Wn lkelhoods are uneven, w > w 2, and the league s unbalanced. Economc equlbrum generates compettve mbalance n a closed league. The standard model has long been consdered the benchmark to assess actual North Amercan leagues and, often, to crtcze ther monopolstc regulaton as not beng able to mprove compettve balance and guarantee an effcent resource allocaton. In partcular: A. The model valdates the nvarance prncple (Rottenberg, 956), snce restrcton (reserve clause) of player moblty does not change the dstrbuton of talent across teams. Assume that restrctons generate a talent dstrbuton t a t* (Graph 2). Then the margnal revenue of talent s hgher n the bg than the small team: mr > mr 2. Despte the reserve clause, the two teams can ncrease ther proft by tradng players, the small team sellng talents to the bg team untl the dfference n margnal revenues wll vansh, n E*. We are back to the same equlbrum as wth a free (unrestrcted) labour market. From ths derves a polcy recommendaton: phase out restrctons on player moblty snce they have no effect on the compettve balance. 0

12 Graph 2: Compettve balance wth proft maxmzaton and player moblty restrctons s MR MR2 E* mr s* mr2 t 2 t a t* B. Revenue dstrbuton across teams, through the redstrbuton of gate recepts and TV rghts, does not affect the compettve balance and lower equlbrum wage. Assume that revenue sharng s such as each team keeps a share of ts revenue and dstrbutes a ( ) share to the other team. Then team revenue s: R + ( ) R j (8) Margnal revenue of team wns s: RM ( ) RM j (9) whch, by (5) substtutng t for w (by 4) becomes: (a b t ) ( ) (a j b j t j ) (0) that corresponds to MRd and MRd 2 n Graph 3. t Graph 3: Compettve balance wth proft maxmzaton and revenue sharng

13 s MR MR 2 s* s d MRd A E* MRd 2 E d t 2 t Thus, n a two-team model, revenue sharng dmnshes both margnal revenues n the same proporton and margnal cost must also decrease n the same proporton to mantan equal to margnal revenue. Equlbrum wage s down by the same proporton. In Ed, the dstrbuton of talent s the same as n E*, and the nvarance prncple s confrmed. Both teams lower ther demand for talent because they would have to share the revenue from an addtonal recrutment wth the other team; lower recrutment s detrmental to game qualty n the league. A polcy recommendaton ensues: snce revenue sharng does not mprove compettve balance and snce t lowers qualty, t should be avoded. Note however that f the small team whch benefts from revenue redstrbuton would keep ths redstrbuted share to ncrease ts proft nstead of nvestng n talent (pont A, Graph 3), revenue sharng would alter the compettve balance. On the other hand, f the demand for talent decreases more n the bg team, revenue sharng would mprove the compettve balance (Késenne, 2000a). C. A salary cap n such model produces a more even talent dstrbuton across teams, lowers the wage and nflates owners proft, but the wage loss s more sgnfcant than proft ncrease because the new market equlbrum dverges from the one that maxmzes proft (Késenne, 2007). Thus, a salary cap lowers overall league revenues. Talent dstrbuton s more even but ther allocaton s not effcent, some players operatng below ther margnal revenue (Késenne, 2000b). A salary cap s not recommended n a closed league though t sustans small team fnancal vablty. The Walrasan model has been adapted to open leagues by Késenne (996 & 2000a) through alterng three assumptons: a. teams are wn maxmzers; b. therefore they recrut as much 2

14 talent as possble wthn ther budget constrant; c. n a globalzed labour market, free entry of players renders the assumpton of a fxed supply of talent rrelevant. Teams reman wage takers n ths market so that: Max t () R (m, t ) s. t c 0 = 0 (2). Usng the Lagrangan, frst order condtons are: hence R s 0 3, t RM = s / < s (4) R s. t = 0 (5). From (4), the margnal revenue of talent s shown to be lower than ts margnal cost. For a gven unt of talent cost, the team demand for talent that maxmzes ts wns s bgger than f the team were proft maxmzng; thus the team spends more to recrut more talent (Graph 4). Equaton (5) shows that a team's demand for talent s no longer gven by ts margnal revenue curve but by ts average revenue curve (revenue per unt of talent): R = R / t = s. Equlbrum s no longer located n E* (as wth proft maxmzaton) but n E v. The equlbrum wage s hgher wth wn maxmzaton (s v > s*) and talent dstrbuton s even more uneven,.e. the league s more unbalanced than n a closed league wth proft maxmzng teams. Overall league revenue s lower than n the latter case snce all talents between t* and t v play n the bg team where ther margnal revenue s lower than what t would have been n the small team. Graph 4: Compettve balance wth wn maxmzaton (compared to proft maxmzaton) 3

15 s mr MR E v mr 2 s v MR 2 E* s* t 2 t* t v t In European open leagues, regulaton bascally reles on TV revenue sharng. Assume that n accordance wth the sharng agreement team keeps an share of TV revenues and leaves a ( ) share to the other team, wth 0,5 <. For wn maxmsng teams, the demand for talent s gven by the average revenue curve, that s: R r R R c 6 0 t where R s team average revenue whose partal dervatve wth respect to s: r R R 7 R t. The rght-hand sde of (7) s postve for a bg team, ts demand curve for talent moves downwards when the degree of revenue sharng ncreases. It s negatve for the small team whose demand curve for talent moves upwards. If the small team's budget s short of funds and t s less endowed wth talent, then the revenue sharng agreement s compettve balance mprovng. The nvarance prncple does not hold. Revenue sharng enhances equlbrum wage compared wth a no revenue sharng stuaton: players beneft from t n an open league. Table Compettve balance (Noll-Scully rato) n Amercan major sports leagues 4

16 and the fve most sgnfcant European soccer leagues, 966/ /06 League 966/67 to 976/77 to 986/87 to 996/97 to Average 975/76 985/86 995/ /06 966/2006 North Amercan leagues NFL.70,5,48,54,56 MLB,78,8,62.90,78 NBA 2,7 2,43 2,96 2,77 2,72 NHL 2,42 2,32,82,74 2,08 European soccer leagues Premer League (England),44,46,44,6,49 Lgue (France),22, ,32 Bundeslga (Germany),26,45,35,46,38 Lega Calco (Italy),46,39,54,67,5 Lga de Futbol (Span),2,33,47,38,35 Source : Krngstad & Gerrard (2007). In summary, a Walrasan model often passed successfully the econometrc testng of ts assumptons n the case of closed leagues n the past decades. However, n more recent years, the results are blurred. Econometrc studes of the NFL have shown a weak proft ncentve to wn (Zmbalst, 2002). Lavoe (2005) has stressed fnancal defcts and team bankruptces, nstead of compettve balance, n North Amercan leagues. Downward and Dawson (2000) conclude ther analyss sayng that the standard model has pad too much attenton to compettve balance. The most strkng emprcal observaton s that compettve balance s worse n closed than n open leagues (Buzzach et al., 2003 & Table ), contrary to the expectatons of the theoretcal model. Emprcal testng of the standard model for open leagues s at ts begnnng, but t appears that revenue concentraton on a few bg teams nether deterorates league compettve balance nor game attendance (Szymansk, 200). Those European soccer leagues whch have abandoned TV revenue poolng wth revenue dstrbuton are the most unbalanced (Andreff & Bourg, 2006). 4. A comparson wthn a Nash-equlbrum model The Walrasan model has recently been called nto queston as the relevant bass for analysng and comparng closed and open leagues, snce the assumpton of a fxed supply of talent does not hold any longer wth labour market globalsaton after Bosman n open leagues but also n closed leagues (Osborne, 2006). Szymansk's assumpton (2003), that an ncrease of one talent unt augments the wn percent by one unt (relaton 4 above), for any wn percent, s not unaffected by ths change. Gven ths assumpton, the margnal revenue of a wn s equal for 5

17 all teams. When n realty teams of nearly all natonal leagues recrut n a global market, an addtonal talent hred by one team s no longer lost for another team of the same league, f the player s transferred from a foregn or lower league. Fxed supply s no longer nternalzed by teams n ther strateges. The Walrasan model must be substtuted by a non cooperatve Nash game, where each team's strategy s to fx ts quantty of talent wthout knowng the effect of the recrutment choce made by ts opponent team (n a two-team game). Not f the supply s not fxed,.e. unknown WA. On the other hand, Szymansk (2004b) stresses that n a league of 20 to 30 teams t s not sensble to assume that teams are wage takers snce some teams (ex: Manchester Unted, Chelsea) are much more nfluental n the market for talent: a pure competton model s not relevant. In a game whose payoff s wnnng a prze, the relatonshp between effort and success percent defnes a contest success functon. A smple representaton of the latter s a functon n whch wn probablty probable wn percent s a rato between effort (nvestment n talent) of a team partcpatng to the game and overall effort by all teams. In a two-player model, such rato s: Dfferentatng (8): w t t w t 2 t t t t t dt t dt Assumpton (4) of Walrasan model w t 2 mples snce, wth a fxed supply t t of talent, such model s a zero-sum game, one unt of talent recruted by team s subtracted w to team 2. If so, then (9) becomes : 20. t t t 2 Team 2 has only one response (loosng one unt of talent) to team s recrutment strategy n the Walrasan model. The rato between wns and nvestment n talent (20) s equal to when t + t 2 =,.e. wth a fxed supply of talent. Now, f supply s flexble, one unt of talent 2 9. t 2 recruted by one team s not subtracted from the other team, so that 0 t (and t t 2 0 ). In a non cooperatve game, team 2 has varous responses to any possble change n team recrutment strategy. 6

18 For a comparson between the mplcatons of both Walrasan and Nash models (Szymansk, 2004b), let us consder the dervatve of a quadratc revenue functon (6) on the quantty of recruted talent. Ths dervatve s equal to : a b w 2 w. t t 2 Assumng that and normalzng total talent to one, (2) becomes equal to (5),.e., t margnal revenue s a lnear functon of wns. If, on the contrary, we assume a noncooperatve game, (2) becomes (a b w ) w j and margnal revenue s no longer a lnear t functon of talent. Wth two teams, and gven that 2 0, when overall supply of talent s t normalzed to one, Why? Demonstrate! WA (9) smplfes to be equal to v 2 and margnal revenue of talent s: (a b w ) w 2. Graph 5 exhbts the dfference between the margnal revenue functon of a team wn, wth the Nash conjecture, that s MR Nash = (a b w ) w 2, and the margnal revenue functon of talent (whch s also the margnal revenue functon of a wn) n the Walrasan model, that s MR W = a b w. A smlar dfference shows up for team 2. 7

19 Graph 5 Nash conjecture and Walrasan equlbrum wth proft maxmzaton and a fxed supply of talent R n % of w R n % of w 2 MR W MR Nash E* MR 2W s* MR 2Nash E N w * w w N Nash equlbrum s n E N, to the left of Walrasan equlbrum E*. If a bg team recruts more than a small team (t > t 2 ), the bg team wll obtan a lower wn percent n the non-cooperatve game than under the Walrasan model (w N < w *), and the small team wll obtan a hgher wn percent. The small team mposes a stronger externalty than the bg team because the latter generates more sgnfcant addtonal revenue than the small team for any ncrease n wn percent. In E N, the margnal revenue of one talent unt s equal n the two teams, but margnal revenue of a wn s not equal between teams; t s hgher n the bg team than n the small one. Késenne (2007) nfers that the Nash equlbrum s not effcent because the league's overall revenue could be ncreased by movng talents from the small to the bg team but. Yet ths wll worsen league compettve mbalance. From ths Nash equlbrum model a number of results have been derved n the recent contbutons: A. The nvarance prncple does not hold n the non-cooperatve game (Szymansk, 2003) and gate revenue sharng deterorates the compettve balance wth proft maxmzng teams (Szymansk & Késenne, 2004). However, f the teams are wn maxmzers, revenue sharng mproves compettve balance (Késenne, 2005). 8

20 B. The demand for talent s hgher wth wn maxmzng than for proft maxmzng teams, the sport contest s more unbalanced and the equlbrum wage s hgher (Késenne, 2006). C. Wth wn maxmzng teams, talent dstrbuton s the same under a non-cooperatve game and Walrasan equlbrum (Késenne, 2007). A team whch ntends to wn as many games as possble wthn ts budget constrant wll spend all ts revenues on talent recrutment wthout consderng other teams recrutment strateges. A hot debate has followed up the emergence of a Nash model of sports leagues. Some economsts have contended that the Walrasan model can no longer co-exst snce only a sngle general theory of professonal sports leagues can preval (Szymansk, 2004b; Késenne, 2006). Others advocate that the assumpton of a fxed talent supply and Walrasan model are stll vald (Eckard, 2006) and stll others clam that the Walrasan model remans relevant for closed leagues wth proft maxmzaton whle the non-cooperatve game apples to open leagues n whch team owners have non cooperatve strateges (Fort, 2006). The queston s stll open whether any equlbrum model fts wth European open leagues. 5. European open leagues wth a soft budget constrant Snce open leagues are now essentally deregulated 4 and teams bascally do not am at proft maxmzaton, an ncreasng number of professonal (soccer) teams are runnng heavy defcts, season after season, and are snkng nto very deep ndebtedness 5. However, repeated defcts and ncreasng debt have not drven any of them to bankruptcy snce they have been baled out by banks (Span), occasonally by the State (Italy, 2006), often by TV channels, and they are not lqudated even after heavy arrears of payments, No, bascally to supplers even though there may be some wage arrears, but few WA of socal contrbuton and of taxes (as n France and other European countres). In such a case, economc theory says that frms (teams) enjoy a soft budget constrant but also that the whole economy functons all the tme n dsequlbrum. Ths stuaton, typcal of shortage economes (Kornaï, 980),.e., former centrally planned economes, can also emerge n a number of ndustres n market economes to whch the model has been extended (Kornaï et al., 2003). 4.. Soft budget constrant: a dsequlbrum model of a sports league 4 At least much less regulated than North Amercan leagues. 5 See Journal of Sports Economcs 7 () 2006 specal ssue on the fnancal crss of European soccer and a part of the 8 (6) 2007 ssue, ncludng my own (Andreff, 2007b). 9

21 If team can survve after years of defct, a soft budget constrant (22) s to replace (2): R (m, t, e ) s. t c 0 0 (22). M.U. s well known as one of the (nearly the only one) exceptons that confrm the rule WA Then the model swtches from equlbrum to a dsequlbrum regme (Andreff, 2009), that s common n a model of excess demand n the labour market. Teams attempt to maxmze ther wns and purchase as much talent as they can snce they are not effectvely constraned by ther budget (n all cases when the relatonshp 22 s strctly negatve). Of course, ths explans the arms race to recrut players as well as a tendency to fuel all the more wage nflaton and transfer fees when superstars have a monopoly on ther specfc (non substtutable) talents. Then, teams develop an excess aggregated demand for talents n the labour market, such that demand grows beyond the pont where margnal revenue of talent s equal to ts equlbrum wage s, so that n dsequlbrum (23) prevals: R m, t s (23). Wth an excess recrutment of talent, most teams except the wnners wll not be able to reach the wn percent that they would have obtaned n an equlbrum model. Thus teams wll not be able to recoup ther recrutment expendtures at the end of the season because they wll earn less (attendance and TV) revenues than expected and less than f they had been the contest wnners. Ths wll, agan and agan, fuel excess expendtures s.t compared to revenues R. Then, the easest way for many clubs n the red s to fnd someone to bal them out. A league barganng TV rghts wth TV channels and re-dstrbutng TV rghts revenues across teams s the most usual means to pour more money nto the defct team budgets. The most crucal ssue for European open leagues s to sustan or recover fnancal balance much more than compettve balance n teams drven to excess demand for talent n a deregulated global market. A further consequence of a soft budget constrant n a market economy s bad governance of the frm (team) as long as teams fnd a way to be baled out (Andreff, 2007c) TV rghts revenues / salares vcous crcle that softens team budget constrant Studes of sport and TV have not yet establshed a relatonshp between the arms race for superstars and TV rghts that ease team revenues n a league wth wn maxmzng teams operatng under a soft budget constrant. Yet nearly all European soccer leagues rely bascally on TV rghts revenues for ther fnance whle an ncreasng number of teams are n the red (Ascar & Gagnepan, 2006). All studes wtness a correlaton between the rse n TV rghts 20

22 revenues and payroll nflaton. In an optmstc nterpretaton of such correlaton the followng vrtuous crcle s assumed: TV revenues enable teams to pay hgh salares n order to feld hghly performng squads whose frequent wns support ncreased TV revenues, and so on and so forth (Baroncell & Lago, 2006). Italan Calco, to whch Baroncell and Lago refer, s n the deepest fnancal crss and hardly confrms the dea of such a vrtuous crcle. It s more realstc to assume a vcous crcle n whch the league, as a monopoly n ts sport market, bargans for the hghest possble TV rghts n vew of gatherng ex post suffcent resources to cover uncurbed payroll nflaton (and superstar recrutment). If barganng s successful as s usual ths wll sustan the league's fnances and bal out teams n the red. However, n many soccer leagues, lke the French Lgue, the recrutment strategy fnanced by TV revenues does not translate nto suffcent team productvty ncreases n terms of wnnng European contests 6 to earn bg enough revenues. Then teams are not able to recoup ther recrutment expendtures and the league has to come back to TV channels for barganng even hgher TV rghts. TV rghts barganng Increased team budgets Payroll nflaton Insuffcent productvty ncrease (n terms of wns) Insgnfcant revenue ncrease Back to TV rghts barganng Now, the causalty of the relatonshp between TV rghts revenues and payroll has to be tested n order to valdate the vcous crcle assumpton. The test s confned to the two French professonal soccer leagues 7, due to the paucty of data about TV rghts revenues whch hnders an extenson of econometrc verfcaton to other European leagues. Our sample encompasses 23 observatons from up to seasons. If the vcous crcle s to be confrmed, TV rghts revenues are the endogenous varable, and we use a double OLS methodology wth nstrumental varables. The dependent varable TV t s defned as the amount of TV rghts revenues of club n year t. We test whether t s explaned wth three exogenous nstrumental varables: POP 2005, 2005 populaton of the cty where the team s located; 6 At least qualfyng for the quarter fnals n the Champons League and UEFA Cup. 7 All French professonal soccer teams are compelled by law to publsh ther fnancal accounts every year snce the season. 2

23 NOT s a varable representng the meda notorety of a team,.e., the team rankng by LFP (the French football league) accordng to ts broadcastng performance (LFP utlses ths rankng to re-dstrbute 20% of TV rghts revenues across teams); DIST s a proxy for the dstance that TV channels have to cover n order to reach the stadum of dfferent teams n vew of broadcastng all league games. DIST s measured as team transportaton costs (taken from team budgets) whch s an acceptable proxy snce t measures the costs ncurred for a team to travel to all other stadums n the league (and nearly the same costs fall on a TV channel whch moves to all stadums for broadcast purpose). The followng model s tested usng our 23 observaton sample: TV t = k + a.pop + b.dist + c.not t + u t In three other specfcatons we control for the possble nfluence of each season, the dvson level (takng Lgue as the reference category) and the seasons n three other specfcatons. Results are avalable n Table 2. Table 2: OLS regresson of TV rghts revenues on nstrumental varables TV rghts revenues (I) (II) (III) (IV) Coeffcent P > t Coeffcent P > t Coeffcent P > t Coeffcent P > t POP ** * ** ** DIST ** * ** * *** *** NOT ** *** LEAGUE ** * *** Year Year Year *** Year * *** Year *** Constant ** * *** R F-stat *** Sgnfcant at a % threshold; ** at a 5% threshold; * at a 0% threshold. 22

24 We then test the relatonshp between payroll (salares and compulsory socal contrbutons) and the endogenous regressor TV as t s explaned n the four above mentoned models. Stager and Stock (997) have demonstrated that, when nstrumental varables I would not argue, refer to Stager & Stock WA happen to be weak, conventonal asymptotc results do not hold wth bg samples. If the F-statstc s smaller than 0 wth a sngle endogenous regressor, there s a potental ssue of weak nstrumental varable. To be relevant, our test must exhbt F > 0, whch s the case. Table 3: OLS regresson of payroll on predcted TV rghts revenues Payroll (I) (II) (III) (IV) Coeffcent P > t Coeffcent P > t Coeffcent P > t Coeffcent P > t Predcted TV *** *** *** *** LEAGUE ** Year Year Year Year *** *** Year ** *** Constant R F-stat *** Sgnfcant at a % threshold; ** at a 5% threshold; * at a 0% threshold. The relatonshp between the TV varable and the nstrumental varables s sgnfcant n all four models (Table 3). Playng n hgher league s also sgnfcant. The observaton year s not sgnfcant, except n 2007 and 2008 when a very harsh bargan faught by LFP wth competng TV channels, led to a new agreement n February 2008 whch ncreased TV rghts. The relatonshp between payroll and TV rghts revenues s sgnfcant n all models, and the assumpton of a vcous crcle n whch TV rghts revenues determne salares s valdated. Concluson Closed and open sports leagues can be compared as regards ther organsaton, ther uncertanty of outcome (compettve balance) whch results from league (de-)regulaton n the framework of a standard Walrasan model and a non-cooperatve game. However, open leagues cannot compare to closed leagues wth regards to fnancal varables, and the team recrutment strateges that they trgger, because teams budget constrant s n effect soft n the 23

25 former and hard n the latter. Furthermore, ncreased TV rghts revenues are barganed by the league, whch enable teams to nflate ther payrolls. All ths shows that sports economcs promses to be a promsng area for comparatve economcs. Our conclusons could probably be extended, by further research, beyond professonal team sports leagues to amateur sports organsaton, the commercal sports sector, sports and economc development and, of course, to comparsons of the sports economy and ts nsttutonal dmensons n post-communst countres wth ts features n developed market economes. 24

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