Evaluatng Rent Dsspaton n the Spansh Football Industry * Gudo Ascar Dp. d Economa Poltca e Metod Quanttatv Va S. Felce 5 27100 Pava, Italy Tel: (+39) 0382 506211 Fax: (+39) 0382 304226 gascar@eco.unpv.t Phlppe Gagnepan Departamento de Economa Unversdad Carlos III de Madrd C/ Madrd, 126; 28903 Getafe, Span Tel: (+34) 91 624 5732 Fax: (+34) 91 624 9875 phlppe@eco.uc3m.es January 2004 Abstract The economc lterature has suggested that the competton among teams n a football league can be modeled through the wndow of the contests theory. Ths paper proposes to evaluate emprcally the consequences of the rent-seekng behavor of clubs on ther budget. The emprcal work entals estmatng a football budget, objectve, and demand system wth data on clubs competng n the frst and second Spansh leagues over the 1996-2003 seasons. The estmaton suggests that the average budget dsspaton n the ndustry les between 45% and 52% n the perod consdered. Ths provdes an nterestng llustraton of the fnancal dffcultes faced recently by most European football clubs. * Marca s gratefully acknowledged for provdng the data. Ascar thanks the Department of Economcs at Unversty Carlos III Madrd for the hosptalty whle startng the research on ths paper. The authors wsh to thank Stefan Szymansk for very helpful comments, as well as partcpants of the Industral organzaton workshop of Carlos III and at the EARIE 2003 conference n Helsnk. All errors are ours.
1. Introducton The recent theoretcal lterature descrbes sportng contests by the means of tournament/contest theory (see Szymansky, 2002). In such framework, sport clubs compete for a prze, whch has both fnancal and non-fnancal dmensons. To wn the prze, they nvest n players and dsspate part of the rent that can be obtaned from that prze, damagng thus ther own proftablty. In Tullock (1980), where a symmetrc rent-seekng model of a wnner-take-all contest wth a sngle prze s consdered, the ndvdual effort (or rent-seekng expendture) ncreases wth the value of the prze, and decreases wth the number of contestants. It s shown moreover that the total rent-seekng expendture made by all compettors s never greater than the value of the prze tself. Thus, even f there s only one player wnng the prze and makng profts whle the others are makng losses, the total proft of the ndustry s always postve. On the other hand, t s as f the players were caught n a prsoner dlemma type of equlbrum. Indeed, n a symmetrc contest, the probablty of wnnng s the same for each player and s therefore ndependent from the level of effort provded at the equlbrum. From the pont of vew of the contestants, the least costly stuaton to be obtaned s then the one were they are able to coordnate on a symmetrc equlbrum wth the lowest possble level of effort. Such equlbrum s not feasble snce the strategc nteracton among the players leads to a hgher level of expendture wth no relatve gan n performance. The smple Tullock s model has then been extended n varous ways. It has been suggested for nstance that contestants may have dfferent valuatons on the prze (Hllman and Rley, 1989; Nt, 1999; and Sten, 2002). Asymmetrc valuatons tend to generate a bas towards under-dsspaton of the rent, makng the total rent dsspaton smaller than what could be obtaned n a symmetrc context. Lkewse, compettors may be offered several prces smultaneously. Clark and Rs (1996, 1998) show that n a multple prze and symmetrc players settng, the amount of rent seekng s reduced compared to a stuaton where there s a unque prce. 1 Fnally, the value of the prze may tself be endogenous. Chung (1996) for nstance proposes a framework where the value of the prze ncreases wth the effort spent by all the partcpants. It s shown that, at the equlbrum, rent-seekng contests generate excessve effort f the prze s ncreasng n aggregate effort. Wth respect to the Tullock s (1980) contest, we may then conclude that some features restran the amount of rent-seekng expendtures, whle some others are lkely to boost t. The lterature deals manly wth one ssue at a tme and t s not clear-cut how they nterrelate (Szymansk and Vallett, 2003). Our objectve n ths paper s to focus on clubs competng n the 1 Szymansk and Vallett (2003) suggest that ths may not hold f players have asymmetrc valuatons. They analyze a mult-prze model wth players of dfferent abltes. Sten (2002) shows that there s a sort of equvalence between dfferent valuatons of the prze and dfferent abltes. 1
Spansh football ndustry and provde an emprcal evaluaton of rent seekng expendtures as fnancal dstorton above a theoretcal fronter supported by these clubs. Our motvaton regardng the choce of the football ndustry to conduct our emprcal test s twofold: Frst, the football ndustry s an nterestng canddate to consder f one s wllng to deal wth the theory of contests. Football leagues are naton wde contests where several clubs compete aganst each other over a certan perod. Clubs spend costly effort to enroll the best players and ncrease ther probablty to reach a partcular objectve. Snce they are producton unts of dfferent sze and they face dfferent types of audence, t s well accepted that these clubs have asymmetrc valuatons of the prce they run after. Moreover, a football league may offer dfferent przes,.e., the best ones compete to wn the league whle others seek the qualfcaton to the European cup. In European football Leagues there are also heavy negatve przes due to relegaton to second league of the teams at the bottom of the table, and ths s lkely to boost the ncentve to rent-seekng (see Rosen and Sanderson, 2001). Fnally, the value of the przes s very lkely to be endogenous. Indeed, the European Leagues are competng among themselves on the nternatonal market and the value of the Italan Sere A, the Spansh Lga or the Englsh Premershp, n terms of nternatonal TV rghts, for examples, certanly depend on the total amount of expendtures made by the varous teams. The more proflgate League wll be featurng the hghest number of nternatonal star players and wll have the hghest value on the nternatonal market. Second, experence has shown that European football clubs have ncreased ther expenses over the last two decades up to a pont where most of them are not even capable of balancng ther budget. The European football ndustry s thus gong through one of the most mportant crss of ts hstory. Its clubs are very often forced to reduce ther budget sgnfcantly, or some of them go bankrupt. 2 Examples llustratng ths general tendency are numerous: n Span, clubs 2 Experts usually argue that one of the man reasons for such a declne s that televson channels, whch have consttuted the man source of clubs revenues over the last ten years, are facng fnancal dffcultes. Va Dgtal n Span, as well as RAI n Italy have decded to reduce by 50% ther nvestment n football broadcastng. Two major groups, ITV Dgtal n England, and Krch n Germany went bankrupted. In France, Canal Plus s wllng to reduce sgnfcantly ts partcpaton n the football ndustry. It may also be mportant to note that the ntroducton of the Bosman law n 1995 dramatcally changed the European football labor market regulatons. Before 1995, any club wllng to hre a player had to pay a compensaton fee to the former club even f the contract had expred. Hence, even out-ofcontract players were not completely free to leave ther employer. Moreover, the clubs were not allowed to employ more than three players comng from abroad. The clubs had strong barganng power snce they could prevent a player from changng team f the compensaton fee dd not satsfy them. The stuaton was very much alke the case of clubs monopsony power descrbed by Rottenberg (1956) n the baseball ndustry. Snce 1995, an out-of-contract player can freely negotate wth a team and does not have to pay any compensaton fee to hs former club. The clubs now antcpate ths new ngredent and provde the players wth ncentves to sgn long-term contracts. Any player wllng to breach the contract n order to change club has to pay the compensaton fee mentoned above. The man consequence has been that the compensaton fees and players wages have greatly ncreased snce 1995. Snce clubs are loosng ther most lucratve source of revenue, they are not capable of handlng the exploson of ther budgets and the growng ncrease of players wages. 2
spent only 92.3 Mllons Euros to enroll new players n the natonal champonshp n 2002, whch represents a cut of 211 Mllons Euros (358 Mllons respectvely) wth respect to what had been nvested the year before (two years before respectvely). In Italy, three of the most famous clubs of the champonshp faced mportant fnancal dffcultes. Two of them, Roma and Lazo, found t dffcult to reduce ther defct and to meet the requrements to be allowed to regster n the champonshp, whle a thrd one, Forentna, went bankrupt. In addton, several players of the other teams accepted to reduce ther earnngs and some club drectors advocated some correctve measures. 3 In England, one of the rchest clubs of the country, Chelsea, before beng bought by a Russan tycoon n 2003, was not allowed to hre any new player because of a too hgh level of debt. Moreover, several clubs competng n the second league went close to bankruptcy (Bradford and Lecester among others). In Germany n 2002, the clubs nvested 102.2 Mllons Euros n hrng, whch represents a 35% cut wth respect to the prevous year. The total amount of debt n 2003 n the Spansh Lga and n the Italan Sere A amounts to 1.625 and 1.800 Bllons Euros, respectvely. 4 We argue that these fnancal dffcultes are the drect consequence of the compettve nteracton between clubs. Therefore, consderng the European league s approprate for our study. Our am s thus to evaluate the total amount of expendtures n the football ndustry that produces no relatve gan n performance, but s supported n equlbrum n the contest. In the standard Tullock s (1980) symmetrc contest, for example, the ndustry as a whole could have obtaned the same relatve performances among teams by spendng zero effort n rent-seekng. As we argued, a football league s a much more complex phenomenon. Clubs valuatons of the przes are not observable. Moreover, a non neglgble part of the values of the przes for presdents of football clubs s not pecunary and mpossble to quantfy. 5 Fnally, also the contest success functon s unknown. There are therefore unobservable elements of the contest that determne the amount of expendtures that sngle teams are supportng n the attempt to wn 3 See for nstance the ntervew of Gallan (vce presdent of A.C. Mlan and presdent of the Italan Football League) who advocates salary caps n the Correre della Sera, 18 th of May 2002. Moreover, on 5th November 2002, the so-called G-14, a group of western Europe s bggest clubs, met n Brussels to draw up new rules and proposed that from 2005 ts members restrct ther salary blls to 70% of the club s turnover. 4 These data have been collected n El País, 28 th of August 2002, L Equpe, 23 rd of October 2002 and Repubblca 8 th of June 2003. 5 It s usually suggested that European football clubs depart from sport professonal clubs n the U.S. n the sense that they care more about ther rankng n the natonal champonshp than ther proft. Professonal teams n the U.S. are usually thought as proft maxmzers, whle European clubs may only be performance seekers n sport competton. Ths dea goes back to the semnal contrbutons of Rottenberg (1956), Neale (1964) and Sloane (1971) and has been more recently advocated by Szymansk and Smth (1997). Prestge and vsblty are prceless contrbutons for the persons n charge of the organzaton of the club. The general rule s that the owners of European football clubs are at the same tme the holders of one or several prvate companes. Besdes prestge and vsblty, the management of a football club can also be seen as a way to advertse ther core busness or mplement vertcal ntegraton. Extreme cases may be the ones of those who started a poltcal career through sport competton. 3
a prze. Arguably, however, the same dstrbuton of probablty of wnnng, and hence expected relatve performance, could be attaned by a lower level of aggregate spendng by the ndustry as a whole. In other words, the run for the contest mples a rent-seekng dstorton n teams expendtures smply due to strategc nteracton, whch depends on some unobservable components, and wth no relatve gan n expected performance at the ndustry level. Ths paper proposes an emprcal evaluaton of these dstortons and entals measurng a global dstorton for the whole ndustry, but also dervng ndvdual assessments for each club. Ths can be done n a satsfactory way f a smultaneous system of three budget - objectve - demand equatons s consdered. Such a procedure allows accountng for the constrants mpngng on the actvty of each club. We choose moreover to approach the defnton of the budget equaton through the wndow of the stochastc fronters lterature. 6 Ths mples consderng a football club as a producton unt nvolved n a producton process whose ngredents such as the producton tself and the nputs have to be dentfed. Ths s an nterestng task n the partcular context of the sport ndustry. Once the producton process s dentfed, a budget fronter defnng a relatonshp between a producton level and the mnmal budget that allows the producer to reach the requred producton level can be determned. The fronter thus provdes us wth a one to one relatonshp between a specfc objectve made by a club under certan condtons, and a theoretcal budget. Consderng all the producton unts competng nsde a specfc league allows us to dentfy ths fronter. We argue then that the dstance between such fronter and the ndvdual and observable budget of a club provdes a drect measure of the amount of expendtures of ths club that produces no relatve gan n performance, but s supported at the equlbrum. We call such expendture the ndvdual budget dstorton above the ndustry s fronter. Thus, n the context of the football ndustry, estmatng a budget fronter entals dsentanglng the mnmum budget that allows the football clubs to reach ther producton levels relatve to the other compettor n the ndustry (.e., ther relatve performances), from the part of the budget due to the rent-seekng behavor of clubs n the van attempt to enhance ther relatve poston n the competton. A possble drawback of ths study s the hghly aggregated nature of the data avalable. Ths s partcularly true for fnancal data. The sources of revenue of a football club, as well as the dfferent parts consttutng ts global budget are dffcult to observe. Ths constrants the structure of the economc model under consderaton and reduces the nformaton that could be obtaned from t. However, consderng a smultaneous system of budget, performance, and demand mght be helpful n order to treat part of the endogenety that affects the varables under the control of each producton unt. Ths s the methodology that we consder here. 6 For a survey of the lterature usng stochastc producton fronter analyss n sport, see chapter 5 n Dobson and Goddard (2000). 4
The Spansh ndustry serves as a support for our study. Its organzaton as well as the behavor of ts clubs has been partcularly appealng over the last decade, as argued n detal n what follows. The database ncludes observatons for the forty clubs playng n frst and second league over the perod 1996-2002. The next secton presents the model to be estmated. Secton 3 descrbes the Spansh football ndustry n more detals. Secton 4 presents the data as well as the estmaton procedure and the results. Secton 5 proposes a dscusson and Secton 6 concludes. 2. The model Our am n ths secton s to construct a football budget, objectve, and demand system that can be appled to the Spansh ndustry. The estmaton of the model wll allow us to explore the structure of the ndustry and provde an ndvdual measure of the rent-seekng dstorton that affects the budget of each club partcpatng to the contest. Producton and Costs Each football club s a producton unt. The drector of the producton process s the presdent of the club. In a frst step, the presdent sets an objectve Y to be reached by hs team durng the season. He defnes then n a second step the mnmum budget B requred n order to acheve the objectve. We need frst to defne the nputs that enter the producton process. It s assumed that the objectve Y depends on the average qualty of each player. Followng Hoen and Szymansk (1999) and Szymansk (2000), we suppose that the average qualty and the average cost of the player are closely related. Consderng that the cost of labor w nstead of the usual quantty of labor L enters the producton functon s far n the partcular context of the football ndustry. The usual studes on producton consder that frms are prce takers and control for the quantty of labor n order to attan a partcular producton level. Such an approach does not ft the football ndustry. Frst, the frms may have suffcent power to affect the costs proposed at the equlbrum on the labor market. Second, gven that the amount of players on the playground s restrcted, t s well admtted that a hgher number of players does not allow the teams to obtan better result. 7 We therefore assume that what matters s the qualty of the group of players and not ts sze. Besde the costs, the experence K may be another good canddate to help settng the objectve of a team. It s supposed to be fxed n the short run. We also ntroduce a thrd term, namely ψ, to account for the unpredctable events, that are beyond the control of the club, and 7 Ideally, the producton process should account for the number of unts of talent that enters each club. Each player enrolled n the team would be worth a partcular amount of unts. Ths would allow defnng a prce for each unt of talent. Ths approach, far to subjectve, s dffcult to put nto practce. 5
that mght affect ts objectve. Let X be a vector of addtonal explanatory varables that wll be emphaszed at the moment of the estmaton. We defne then producton functon of each unt as the followng: ( w, K, X, t, ψ b) Y = f, (1) where b s a vector of parameters descrbng the technology and t s a trend. From equaton (1), we know that, to reach the expected objectve Y, the manager must pay the relevant average cost (that s, buy the relevant average qualty) w ( Y, K, X, t, b,ψ ) 1 = f. (2) Moreover, we argue that an unobservable ndvdual dstorton θ affect the prmal average cost w of each club. Ths dstorton results from the compettve nteracton between clubs, whch s taken as exogenous here; t does not mprove ther relatve performance and entals an upward budget dstorton. As ths term s unobservable, t needs to be evaluated through the estmaton process. Hence, the budget B can be expressed as: ( θ ) B( L, Y, K, X, t, θ, ε β ) B = wl exp =, (3) Note then that the budget (.e., the rent-seekng dstorton) depends also on L, the number of players enrolled n the team, ε, an error term and β, a vector of parameters to be estmated. Note that ε depends on ψ and b whle β s a functon of b. The budget equaton gven n (3) s a stochastc fronter that needs to be estmated. The objectve Y set by the club may tself depend on factors such as the characterstcs of ths club and the envronment where the producton process takes place,.e., Y may tself be endogenous. In order to account for such constrants, t s proposed to estmate smultaneously an objectve and a demand equaton. Objectve and demand The relaton between objectve Y and demand D n the football ndustry results from two effects that need to be consdered. On one hand, demand depends on the objectve of the team (see Szymansk and Smth, 1997, Hoen and Szymansk, 1999, and Dobson and Goddard, 2001). We expect the audence to be attracted by teams that are performng better durng the season and/or that set hgher objectves. Whether the players are foregners or not, whether they play n natonal teams, the arrval of a new traner, the number of the ttles won by the club n the past, whether the team plays n frst or second dvson are also features that are worth takng nto account. It s mportant as well to 6
consder the attractveness of the team, whch mples takng nto account the fact that the team presents an offensve or defensve confguraton. Ths effect can be captured through several varables lke for nstance the poston of the players on the feld, the number of goals scored or the number of vctory obtaned. Fnally, we expect the sze of the potental market faced by each club to be another mportant ngredent to determne demand. Note that our demand expresson does not nclude a prce varable. Ths should however not affect the estmaton sgnfcantly snce most emprcal studes n football fal to fnd a sgnfcant relatonshp between prces and attendance, especally n samples wth a short tme dmenson. 8 The demand functon s of the form (, A, Z, S, t,η γ ) D = D Y, (4) where A and Z denote attractveness and characterstcs of the team, S s the sze of the market, t s a trend, η s an error term and γ s a vector of parameters. On the other hand, the objectve Y must be adjusted to the level of demand D, so the former s endogenous to the latter. We therefore assume that the objectve of a team s constraned by the sze of ts audence. The man motvaton for such an assumpton s that a larger audence generates larger revenues and more ambtous objectves. Here we smply ntroduce a reduced form of a dynamc and techncal adjustment process between objectve Y and demand D that we specfy as follows ( D,t ρ δ ) Y = φ,, (5) where t s a trend, ρ s an error term and δ s a vector of parameters. Note that the demand functon n equaton (4) s nterpreted as a short-run demand snce t takes the objectve Y as gven. By replacng Y n ths demand functon by ts expresson n equaton (5), we obtan a reduced form nterpreted as the long run demand functon, defned as ( A, Z, S, t ξ d ) D = ϕ,, (6) where ξ s an error term, whch depends on ρ and η, and d s the fnal vector of parameters to be estmated. Estmatng equatons (5) and (6) avods the smultanety problem that exsts between D and Y. The next step conssts n estmatng equatons (3), (5) and (6). Note that the whole model under consderaton s sequental. Frst, attractveness and characterstcs of the team, as well as 8 In general, match-attendance models tend to have dffculty n dentfyng a relatonshp between varables such as admsson prces [ ] and attendances. (Dobson and Gerrard, 2001, p. 326). 7
market sze determne the magntude of demand. Second, demand establshes the attanable objectve. Thrd, the drector of the producton process determnes the average cost that allows her to reach the objectve, and thus the budget s determned. Snce the system gves rse to a block-recursve structure, each equaton can be estmated separately. We turn now to the descrpton of the Spansh ndustry and the data avalable. 3. The Spansh ndustry The Spansh Professonal league s a natural canddate for our purpose. Note frst that the Spansh clubs have been among the most proflgate ones regardng expendtures on wages and compensaton fees. Table 1 shows two rankngs of the hghest wages gven n Europe n 1999 and of the bggest compensaton fees that have been pad ever. Table 1: Wages and compensaton fees Wages, 1999 (per week, n Euros) Compensaton fees (up to 2002 n Euros) 1. Del Pero (Italy) 2. McManaman (Span) 3. Kluvert (Span) 4. Anelka (Span) 5. Ver (Italy) 6. Ronaldo (Italy) 7. Effenberg (Germany) 8. Balakov (Germany) 9. Elber (Germany) 10. Shearer (England) 11. Owen (England) 114,922 108,537 95,769 92,576 92,576 83,000 79,806 79,806 54,269 46,480 39,840 1. Zdane (Span) 2. Fgo (Span) 3. Crespo (Italy) 4. Ver (Italy) 5. Mendeta (Italy) 6. Ferdnand (England) 7. Overmars (Span) 8. Anelka (Span) Source: Dobson and Gerrad (2001) and El País, 28 th of August 2002. 75,100,000 61,400,000 59,760,000 51,460,000 48,000,000 46,800,000 41,500,000 39,000,000 Second, Spansh clubs are not present on the stock market yet, contrary to Englsh clubs for nstance, and ths mght have a sgnfcant mpact on clubs polces. Apart from beng a source of fnance, the stock market also acts as a constrant on expendtures and losses, because clubs are responsble towards ther shareholders. In Span, an assembly composed of fellows supportng the team generally elects the presdent of the club. As the fellows care about sportve results rather than profts, t seems that non-pecunary objectves are partcularly mportant n the valuaton of the przes for Spansh clubs, exacerbatng the rent-seekng. Indeed, clubs presdents are pressed to rase expendtures levels n order to enroll the best players. Ths specfc context s therefore partcularly approprated to our study. Another nterestng characterstc of the Spansh ndustry may le n the fact that the ethncal and cultural prde of some of ts clubs strengthens compettve and even aggressve behavors on the labor demand sde. The performance of the team assumes therefore a pecular mportance, as 8
a matter of natonalstc prde, addng up to ncrease the valuaton of the rent and the assocated rent-seekng expendture level. Fnally, the Spansh professonal league seems to have fully accomplshed the Bosman revoluton snce t s one of the most nternatonally open of the European Leagues: n 1999 only 61% of players were Spansh natonals. As a result, some of the best European and non- European players are partcpatng to the Spansh competton whch mght be the strongest one n Europe. 4. Estmaton and results We present n ths secton the estmaton of the system defned above and the results. The varables enterng the equatons are frst examned n more detal. The system The demand functon s specfed as ln D = d 0 + d 1 SYS + d 2 ln GOAL + d 3 SFOR + + d 4 SFORW + d 5 SNAT + d 6 TRAIN + d 7 ln POP + d 8 t + ξ (7) As sad above, the varables to be consdered n the demand functon should be the sze of the market, the attractveness and the characterstcs of the team. The strategc scheme elected (SYS) and the number of goals scored durng the season (GOAL) are used as proxes n order to evaluate the attractveness of the team. There are manly two types of strategc schemes mplemented by teams: three forwards and three mdfelders or two forwards and four mdfelders. The varable SYS takes value one f the former strategy s mplemented, and zero otherwse. We expect a more offensve strategy (.e., wth three forwards) to attract a larger audence. Lkewse, we expect the numbers of goals scored to have a postve effect on demand. There are several varables that can be vewed as good canddates to descrbe the characterstcs of the team. Frst, foregn players playng outsde ther own country are typcally hghly sklled and have a sgnfcant nfluence on the performance of the team. Thus, we nclude two varables n (7) to consder the effects of foregn players on demand: SFOR s the share of foregn players and SFORW s the share of foregn players from outsde Europe among the foregn players. These two varables should have a postve effect on demand. Second, Spansh players who are also members of the natonal team are also expected to have an ablty that s hgher than the average. Therefore, the share of such players (SNAT) s also accounted for. We 9
antcpate demand to be also postvely nfluenced n ths case. Thrd, we ntroduce a dummy varable (TRAIN) that takes value one f the traner of the team s new, and zero otherwse. The manager s responsble for the tranng and the organzaton of the team. The presdents of the clubs decde on changng traners when new (hgher) objectves are n order. The audence s usually hghly senstve to such a decson and TRAIN should have a postve effect on demand. The last explanatory varable s POP. It denotes the sze of the populaton of the cty to whch the club under consderaton belongs. Obvously, teams representng large urban areas attract a larger audence. Ths varable acts as a proxy for the market sze and thus we expect t to have a postve effect on demand. The characterzaton of the endogenous varable D s now requred. The audence s roughly defned as the set of ndvduals supportng the team. It ncludes spectators attendng the games n the stadum, those watchng the games on televson, but also people generally followng the performance of the club through the meda. To evaluate and measure the sze of such an audence s a dffcult task. However, a very useful proxy can be consdered for that matter. We use the average effectve attendance durng the season as a proxy for general audence. Note that ths allows us to take nto account two ndvdual effects. The frst effect, denoted as the sze effect, mples that a more popular team plays n a bgger stadum, whch s consstent wth a larger audence; t can be seen as a long-run effect. The second effect, denoted as the lkng effect, s a short-run effect. It mples that the nstantaneous attendance of the stadum gets close to full capacty when the team s performng well, whch should be a clear ndcator of how the general audence behaves along the season. Taken together, these two effects should be helpful for our purpose. We turn now to the objectve equaton. It s smply determned as ln = δ + δ ln Dˆ + δ t + ρ. (8) Y 0 1 2 Note that Dˆ s the predcted value of D obtaned from the estmaton of equaton (7). We need to defne a measure of the varable Y. As the objectve of the club s dffcult to measure, we choose to proxy t wth an ndex of actual performance of ths club along the season. A smple and far nstrument s the number of ponts obtaned by each team at the end of the season. Any vctory s worth three ponts whle a draw yelds one pont. All frst league teams are credted a surplus of ponts equal to the total amount obtaned by the best team of the second league at the end of the season. Dong so enables us to consder the forty teams smultaneously, as f they all belonged to one sngle league. The last equaton to be estmated s the budget functon. It s defned as 10
ln B = β 0 + ln L + β 1 ln Ŷ + β 2 DIV+ β 3 ln UEFA + β 4 ln K 1 + + β 5 ln K 2 + β 6 ln CAPS + β 7 t +θ + ε (9) The total budget ncludes wage and fee expendtures that must be pad n order to purchase players from other clubs. Several explanatory varables are requred to dentfy ndvdual dstortons above the budget fronter. The rght hand sde of Equaton (9) ncludes the number of players L, the objectve Y, and the experence K. Note that we use the predcted performance Yˆ obtaned from the estmaton of equaton (8). The experence K s decomposed nto two varables. The frst one, K 1, denotes the number of years spent n frst league whle K 2 ndcates the number of years spent n second league. We expect these two varables to have opposte effects on clubs expendtures. Indeed, the valuaton of the prze by teams presdents, and thus, ther behavor regardng expendtures should depend on the hstory of the performance of the club. For nstance, a club wth a long hstory n the frst league s expected to have hgher valuatons, thus, hgher long run objectves and larger budgets. Lkewse, a club, whch spent most of hs hstory n second league, may not be able and/or wllng to afford hgh expenses. Besdes objectve and experence, we ntroduce addtonal varables n order to capture part of the heterogenety among producton unts. The frst one (UEFA) s a dummy varable that takes value one f the team smultaneously competes n the European league, and zero otherwse. Ths varable should have a postve nfluence on expendtures snce beng commtted on two fronts needs addtonal unts of talents. Another varable of nterest s CAPS, whch measures the number of tmes the players of the team have been enrolled n ther respectve natonal squad. Ths varable enables us to control for the qualty of the players enrolled n the team and t should also have a postve effect on the budgets. Besdes, we use a dummy varable (DIV) that takes value one f the team s competng n frst dvson, and zero otherwse. Ths varable should most certanly have a postve effect on the budget. Fnally a trend t s ntroduced. Data In order to test the economc model, we need data on the fnancal performance of the clubs as well as data on the supply and demand of the ndustry. The database s constructed usng the annual data collecton edted by the Spansh sport newspaper Marca. The collecton dates back to the begnnng of the nnetes but relevant nformaton regardng clubs competng n the Second league could only been obtaned from 1996. Therefore, our sample ncludes nformaton on all clubs of Frst and Second league startng wth the 1996-1997 season up to the 2002-2003 season, whch represents seven years of observaton. Marca s a rch source of data regardng 11
clubs budgets as well as players and teams characterstcs and performances, stadums affluences, clubs hstorcal course etc. The Frst league embraces twenty clubs whle the Second League may nclude twenty or twenty-two clubs. At the end of each season, the three clubs ranked at the bottom of Frst League go down to Second League. Lkewse, the four worst clubs of Second League are relegated to Thrd League and the three best clubs are promoted to Frst League. Note that two samples wll be consdered: The frst one s an unbalanced panel, whch ncludes 281 observatons. Some clubs may dsappear from one year to the other,.e., may go down to Thrd League and hence may dsappear from the sample whle new ones may appear snce some Thrd League clubs are promoted and ascend to Second League. The result s a database of ffty dfferent clubs that are not necessarly observed seven tmes over the perod. The second sample that wll be consdered s a balanced panel. Consderng smultaneously a balanced panel allows us to drop all the clubs that compete n Thrd League at least once durng the perod of observaton and thus reduce the heterogenety among the economc agents. The balanced panel ncludes observatons on 28 clubs observed seven tmes over the perod. In order to complete the database, the data on urban areas populaton (varable POP n equaton 7) has been collected from the webste of the Insttuto Naconal de Estatstcas (INE). 9 Summary statstcs regardng the varables are provded n Table 2. Estmaton The system to be estmated s made of equatons (7), (8) and (9). Snce t s sequental, the three expressons can be estmated separately. The three error terms ξ, ρ and ε are supposed to be ndependent and to have a normal densty functon (wth mean 0 and respectve varances 2 σ ξ, 2 σ ρ and σ 2 ε.) Maxmum lkelhood appled to equatons (7) and (8) does not requre addtonal specfcatons. However, when estmatng the cost functon expressed n (9), a dffculty arses due to the fact that the term θ s unobservable. We wll assume that θ s characterzed by a densty functon f (θ ) defned over an nterval [0, ). The error structure u = θ + ε adopted n (9) follows a Panel Data specfcaton 10 where ε are 2 assumed to be..d. N ( 0, σ ε ) and θ s a non-negatve term accountng for dstortons above the theoretcal budget B ~ ( L, Yˆ, K1, K 2, CAPS, EUR, t,ε β ) where β s the vector of parameters to be estmated. We need now to say somethng about the densty f (θ ) and the way the estmaton s performed. Denotng as t = 1,..., T and = 1,..., N, the subscrpts for tme and clubs respectvely, fve dfferent procedures of estmaton are consdered: 9 www.ne.es. 10 A survey of references on ths ssue can be found n Kumbhakar and Lovell (2000). All models were estmated usng the FRONTIER41 software, wrtten by Tm Coell. 12
() The frst procedure consders that the θ s are constant over tme but vary across clubs. + 2 Moreover, the densty f (θ ) s half normal,.e., the θ are..d N ( 0, σ θ ). () The second procedure s smlar to the prevous one except that the densty f (θ ) s + 2 Truncated normal,.e., the θ are..d N ( µ, σ θ ). Ths allows the dstrbuton to have a nonzero mode and provdes a somewhat more flexble representaton of the pattern of the dstorton θ n the data. Note that an addtonal parameter µ needs then to be estmated. () The thrd procedure assumes that the θ s dffer from one club to the other and vary systematcally wth tme. They are of the form = θ ( η( t T )) + 2..d as truncatons at 0 of the (, σ ) θ exp and are assumed to be N 0 θ dstrbuton. Note that ths specfcaton requres an addtonal parameter η, dentcal for all clubs, to be estmated. (v) The next procedure s smlar to the prevous one except that the densty f (θ ) s Truncated + 2 normal,.e., the θ are..d N ( µ, σ θ ). (v) Note that the four prevous specfcatons requre the ε t and the θ to be dstrbuted ndependently of each other, and of the regressors. Moreover, specfc dstrbutonal forms are necessary for θ. These two constrants can be relaxed f the θ are consdered as fxed effects. Ths procedure can be performed through the estmaton of a dfferent constant β 0 for each club. Ths approach s nterestng n the sense that the assumpton that the dstorton θ may not be ndependent from the performance Y should not be dscarded. Moreover, ths s an addtonal mean to provde more evdence on the robustness of the results snce the chosen dstrbutonal form for θ may nfluence the ndvdual estmates θˆ. The results of the dfferent estmatons are presented below. Two types of comments are worth emphaszng. Frst, snce two databases are consdered, we specfy ten dfferent sets of results for the estmaton of the budget functon. 11 Our am s to show that the estmaton results regardng the dstortons θ s are robust to the nature of the dataset and the type of estmaton consdered. Second, note that wth panel data, the estmator s able to dstngush each club s ndvdual persstence from statstcal nose. Therefore, the realzaton of θ for a partcular frm can be dentfed, thus overcomng the lmtaton of a cross-secton from whch one can only dentfy the expectaton of θ condtonal on statstcal nose (see Sckles, 2003 for a dscusson of ths ssue). We turn now to the presentaton of the estmaton results. t Results The results are reproduced n Tables 3 and 4. We present frst the ones on the demand and performance equatons. 11 Note that whle presentng the results, t wll be suggested that µ s never statstcally dfferent from 0. The models consderng truncated normal dstrbutons wll then be dscarded and only sx sets of results wll be presented. 13
Consder the performance equaton. The R-squared s equal to 0.559 (0.549 respectvely) f the unbalanced panel (balanced respectvely) s taken nto consderaton. All the parameters are strongly sgnfcant. The result suggests that performance s affected by the sze of the audence. Moreover, the nature of the dataset consdered does not affect the demand elastcty of performance n a sgnfcant manner. Consder now the demand equaton. The R-squared (0.940 f the panel s unbalanced and 0.878 f the panel s balanced) suggests that the varables selected strongly explan the sze of the audence. A frst set of results goes along wth the ntal ntuton. Thus, demand sgnfcantly ncreases wth the number of goals scored (GOAL). 12 Moreover, t s postvely affected f the club strategy responds to a more offensve profle (SYS takes value one). 13 Ths suggests that the audence ncreases f the team consdered presents a hgher offensve profle. Unsurprsngly, the characterstcs of the squad enrolled n the club are essental to explan demand. The audence responds postvely and sgnfcantly to a hgher share of players wth experence n the natonal team of ther country of orgn (SNAT). Ths latter varable s a good canddate to account for qualty n the team. A strkng result also comes from the varables related to the natonal dentty of players. The estmaton sheds lght on the fact that the share of players (SFOR) from outsde Span sways negatvely demand. It should be noted however that the parameter for SFOR s only sgnfcant at 10% n the balanced panel, whle t s not sgnfcant n the unbalanced one. Moreover, f the share of players from outsde Europe among foregn players (SFORW) s hgher, then demand s postvely and sgnfcantly affected. These two results may suggest the followng: Frst, the audence may have a preference for Spansh players. Second, most non-european players of the Spansh league come from South Amerca, and, n the vew of the audence, such players may be culturally smlar to Spansh players and may not alter the natonal dentty of the club. Another possble explanaton reles on the supposed comparatve advantage of the dfferent types of players. Agan, n the vew of the audence, South Amercan players convey the dea of an entertanng and attractve way of playng, whch s not necessarly assocated wth contnental European players. The populaton sze of the cty (POP) from whch the club orgnates has a postve and sgnfcant effect on demand. Lkewse, demand ncreases over tme, as ndcated by the postve parameter of the trend t. Fnally, note that the coeffcent of TRAIN s not sgnfcant n any of the estmatons. Contrary to what has been predcted, the latter suggests that our databases do not provde any emprcal evdence regardng the way demand s affected by the hrng of a new traner. 12 The addtonal varable VIC, namely the number of vctores obtaned durng the season, also had a postve effect on demand. However t presented strong evdence of correlaton wth the number of goals scored and has therefore been dscarded. 13 The latter effect s not sgnfcant however f the unbalanced panel s consdered. 14
We focus now on the cost expresson. Table 4 presents sx dfferent sets of results where the followng dstnctons are made: (1) The panel s unbalanced, the θ s are constant over tme but vary across clubs, and the densty f (θ ) s half normal. (2) The panel s unbalanced, the θ s dffer from one club to the other and vary systematcally wth tme, and the densty f (θ ) s half normal. (3) The panel s unbalanced and the θ s are treated as fxed effects. (4) The panel s balanced, the θ s are constant over tme but vary across clubs, and the densty f (θ ) s half normal. (5) The panel s balanced, the θ s dffer from one club to the other and vary systematcally wth tme, and the densty f (θ ) s half normal. (6) The panel s balanced and the θ s are treated as fxed effects. In the course of the estmaton t appeared that the parameter µ was never statstcally dfferent from 0. We therefore dscarded the truncated normal dstrbutons and rather focus on half normal ones. We observe only small devatons of the parameters values across the dfferent sets of results. As expected, the coeffcent of Yˆ s always postve and sgnfcant, whch mples that a hgher performance requres a greater budget. Note that a 1% ncrease n performance requres a less than 1% ncrease n costs, meanng that the ndustry s characterzed by economes of scale. The parameters of K 1 and K 2 are always postve and negatve, respectvely, and sgnfcant. Ths confrms that the hstory of the club performance matters when defnng the budget. As explaned prevously, the drector of the producton process s more nclned to set up a large budget f the club performed well n the past. On the other hand, weak performances n the past act as a break upon objectves. The parameters of UEFA are all postve and sgnfcant. Ths suggests that the budget s hgher f the club s nvolved smultaneously n the European champonshp. Surprsngly, the coeffcent of CAPS turned out to be non-sgnfcant and faled to act as a varable that accounts for qualty n the team. Note however that the coeffcents of CAPS are postve as expected. The varable DIV that takes value 1 f the club competes n Frst League and 0 otherwse presents a postve and sgnfcant parameter n all the models. Ths entals that budgets are hgher when the clubs compete n frst dvson. Note also that the parameter of the trend t s postve mplyng that the costs of the whole ndustry are ncreasng over tme. Fnally, the parameter η s negatve and sgnfcant. Ths s an nterestng result, whch shows that the clubs budget dstortons over the theoretcal fronter follow a systematc and sgnfcant ncrease over tme. Ths suggests that the overall value of the Spansh football league as well as the valuaton of the przes by clubs have ncreased, snce theory predcts that n ths case rent-seekng and rent-dsspaton augment. The average ncrease from one year to the other s estmated to be close to 6%, regardless of whch database s consdered. A smple lkelhood rato test allows testng model (2) aganst model (1) and model (5) aganst model (4). The LR test statstc s equal to 4 (3.2 respectvely) f the panel s unbalanced (balanced respectvely), 15
whch confrms that the model that allows θ to ncrease over tme s preferred to a model where θ remans constant over tme. 14 5. Evaluatng ndvdual cost dstortons From the estmaton of the three equatons system, predctons of ndvdual budget dstorton parameters θ can be recovered usng the procedures ntated by Hausman and Taylor (1981) and Battese and Coell (1988). The budget dstorton over the theoretcal fronter s smply defned as exp ( θ ). Table 5 provdes estmates of the ndvdual exp ( θ ). Fve sets of results are presented; they are assocated to the models (1)-(5) defned above. Note that specfcaton (6) has been dscarded snce the constant and the output parameter are not sgnfcant and ths may alter the valdty of our estmates. 15 Several results are worth emphaszng. Frst, note that the estmaton results are usually robust to the nature of the estmaton procedure or the dataset under consderaton. They show lttle dfferences wth respect to the rankng of the clubs and the evaluaton of ther ndvdual dstorton. Second, 10 to 16% of clubs n the unbalanced sample (18% to 21.4% n the balanced one) have a dstorton greater than 2,.e., ther observed budget s more than twce hgher than the theoretcal budget predcted by ther performance. Ths suggests a strong dscrepancy between a few frms that can support heavy dstortons of ther expenses and the others that suffer from hgher fnancal constrants. Unsurprsngly, the most famous clubs n the hstory of the Spansh league belong to ths frst group wth the hghest dstorton, sgnalng a more actve rent-seekng actvty. Thrd, notce that Frst League and Second League clubs can be ndfferently found along the dfferent postons of the fve dfferent rankng, suggestng that there s no clear persstence n the relatonshp between each league and the relatve budget dstortons of the clubs. Fnally, consder the unbalanced panel. 16 The means for the average club of the sample range from 1.452 to 1.525,.e., the dstorton of the average frm then les from 45.2 to 52.5% above the fronter. The average club supports a budget of 19.8 mllons Euros over the perod. Ths mples that such a club bears an absolute dstorton of 6.1 to 6.8 mllons Euros above the theoretcal fronter. Note that ths club would have reached the same performance f no dstorton had been dsspated,.e., wth a budget that ranges from 13 to 13.7 mllons Euros. A smlar remark can be provded for the whole Spansh football ndustry. Consder for nstance the last year of observaton,.e., the 2002-2003 season. The whole ndustry supported durng 14 The levels of sgnfcance are 5% and 10% (unbalanced and balanced panel respectvely). 15 The fxed-effect specfcaton uses the constant as the reference to evaluate frms ndvdual effects. 16 Results on the balanced sample are avalable upon request. 16
ths perod a total budget of 1.182 Bllon Euros, whle the total dstorton above the theoretcal fronter ranged from 368 to 407 mllons Euros, dependng on whether estmaton procedures (1), (2) or (3) are consdered. Agan, all the clubs of both Frst and Second League would have reached the same performance f these dstortons had not been dsspated. 6. Concluson Consderng smultaneously the demand, the performance, and the budget of football clubs performng n the Spansh league has allowed us to obtan nterestng results regardng the structure of the ndustry and the fnancal results of these clubs. Frst, the parameters of the varables of nterest are usually sgnfcant and have the expected sgns; ndvdual estmates of budgets dstortons go well wth basc ntutons. Ths suggests that the methodology chosen n ths paper presents some emprcal relevance. Second, the emprcal results have shed lght on mportant budget dstortons faced by clubs competng n the ndustry to seek the dfferent przes. The estmated cost dstorton n nomnal terms durng the 2002-2003 season amounts to a stunnng fgure of 368 to 407 mllons Euros. It seems that rent-dsspaton s partcularly hgh for the Spansh football ndustry, n accordance wth casual observaton of losses and debts of football teams. The results n ths paper well llustrate the mportance of the fnancal crss faced by the Spansh ndustry and other European countres at the end of 2003. One could be dsapponted by the hghly aggregated nature of the fnancal data and would expect a more dsaggregated model to perform better. It would be nterestng to take nto account other effects such as the openng of the European fronters or the superstar effect mentoned by Rosen (1981). Modelng these effects calls for data ncludng observatons on wages and compensaton fees, as well as nformaton regardng ndvdual revenues comng form advertsng. Once these data are avalable, a more structural approach can be mplemented. Thus, the research agenda wll be complete. 17
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