Unversty of Freburg Department of Internatonal Economc Polcy Dscusson Paper Seres Nr. 1 What does t take to be a star? The role of performance and the meda for German soccer players Erk E. Lehmann and Günther G. Schulze December 2007 ISSN 1866 4113
Unversty of Freburg Department of Internatonal Economc Polcy Dscusson Paper Seres The Dscusson Papers are edted by: Department of Internatonal Economc Polcy Insttute for Economc Research Unversty of Freburg D 79085 Freburg, Germany Platz der Alten Synagoge 1 Tel: +49 761 203 2342 Fax: +49 761 203 2414 Emal: ep@vwl.un freburg.de Edtor: Prof. Dr. Günther G. Schulze ISSN: 1866 4113 Electroncally publshed: 5.3.2008 Autor(s) and Department of Internatonal Economc Polcy, Unversty of Freburg
What Does t Take to be a Star? The Role of Performance and the Meda for German Soccer Players Erk E. Lehmann Günther G. Schulze Abstract We test exstng superstar theores for the German soccer league. We use varous measures for ndvdual players performance and meda presence to analyze whether performance and popularty can explan salares and superstars n soccer. Moreover, we argue that quantle regresson technque should be appled to analyze superstar phenomena nstead of OLS used htherto. Key words: Superstars, soccer, quantle regressons, Rosen, Adler JEL classfcaton: J3, J4, L83, Z1 Dept. of Economcs and Management, Unversty of Augsburg. Correspondng author. Dept. of Economcs, Unversty of Freburg, D 79085 Freburg.Br., Germany, Emal: Guenther.Schulze@vwl.un freburg.de We are grateful to Egon Franck, Bernd Schauenberg, and semnar partcpants at the Unversty of Hedelberg and Unversty of Zurch for helpful comments. Danel Werner provded excellent research assstance. The usual dsclamer apples.
1. Introducton In the season 1998/99 the top fve per cent of the players n the German soccer league earned 5.5 tmes as much as the medan player. How s ths skewness n ncome dstrbuton explaned snce performances of professonal soccer players n the frst league seem not to dffer so vastly? What does t take to be a superstar? In hs semnal paper on The Economcs of Superstars Rosen (1981) explans how small dfferences n talent translate nto large dfferences n earnngs. Spectators prefer hgh qualty performances (of artsts, athletes etc.) to lower qualty performances of the otherwse same servce; at the same tme strong scale economes n consumpton allow better performng artsts or athletes to draw large audences n soccer stadums, concert halls or va TV. Therefore, only slght dfferences n qualty and thus n ndvduals wllngness to pay are leveraged nto large dfferences n earnngs. To derve hs result, Rosen assumes not only scale economes n consumpton and mperfect substtutablty of dfferent qualtes, but also perfect knowledge on the qualty of the athletes. Adler (1985) offers a dfferent explanaton: In order to value the performance of artsts or athletes, people need to buld up knowledge about them and they do so through communcatng wth others. Stars may thus be born because ntally (slghtly) more people happen to know one artst/athlete than any other artst/athlete of possbly equal talent and communcate about hm or her more wth others. Artst/athlete specfc knowledge s bult up more rapdly through ths postve network externalty: ths artst/athlete wll snowball nto a star. Followng Adler s logc, the meda have a decsve role n creatng stars as they mpart knowledge about ndvdual artsts or athletes that makes the publc value ther performances. 1 In ths short paper we analyze whether these two competng although not mutually exclusve superstar theores can explan the superstar salares n German soccer. We use a unque dataset that combnes the salares for all players n the frst dvson wth a host of ndvdual performance parameters. Furthermore, we nclude a measure for meda coverage 1 For the lterature on superstars cf. Schulze (2003) and Adler (2006), for smlartes of artsts and athletes see Seaman (2003). Frck (2007) surveys the lterature on labor markets for soccer players. 2
of each ndvdual player to test for the role of the meda for the makng of superstars. That allows us to assess the relatve mportance of both lnes of arguments: We are able to determne whether performance dfferences translate nto more than proportonal dfferences n earnngs (the Rosen superstar explanaton ) or whether dfferences n popularty measured by meda presence s able to explan the strong earnngs dfferentals ( Adler s explanaton for superstars ), and f so, what the relatve contrbutons of both theores are. Tests on superstar theores for the arts are plagued by the nablty to measure the relevant performance parameters accurately, 2 drect tests on superstar theores n soccer, the largest spectator sport world wde, have been almost mpossble up to now due to the lack of data on ndvdual salares (Dobson and Goddard 2001:221). 3 Lucfora and Smmons (2003) are the frst to analyze superstar effects n soccer. They fnd superstar effects (n the Rosen sense) for the Italan Soccer League for some performance measures for forwards (assst and strke rate, but not goals) and mdfelders (goals, but not asssts). Unfortunately, ther data set does not have a full set of performance measures that covers relevant performance measures for defense players and they do not test for the nfluence of popularty on players remuneratons. 4 Garca del Barro and Pujol (2007), whch was publshed after our paper had been wrtten, defne superstars as those players wth the hghest nternet exposure. They show n a log log wage regresson on a sem subjectve performance ndex by journalsts, Google hts, and usual control varables that the superstars so defned earn a premum above what s explaned by ther performance, popularty, and other control varables. 2 For example Hamlen (1991) tests the nfluence of harmonc content of voce as relevant performance measure of pop musc stars on ther record sales and thus ther superstar status. It s however by no means clear that ths s the only or the most mportant superstar factor as sex appeal, stage performance, vdeo clps, or lyrcs may play an equally mportant role. (Otherwse the success of Brtney Spears or Bob Dylan could not be explaned.) In sports, however, performance parameters are more easly dentfed and measured, makng t more sutable for tests of superstar theores. 3 The emprcal lterature on superstars s surveyed by Schulze (2003) and Adler (2006) for the arts and by Dobson and Goddard (2001) for sports. 4 In a second equaton they defne superstars as those players that score more than 0.4 goals per match n the frst dvson; the superstar dummy n the wage equaton turns out sgnfcant. It s not clear that ths defnton s approprate as a number of superstars n the past or presence have not been top scorers: For nstance, Franz Beckenbauer has been defender (Lbero) for most of hs career and Mchael Ballack has been a playmaker, but not the top scorer. They specfy loglnear wage equatons so that they can capture only convex nfluences on earnngs accordng to the superstar theores; t s not clear whether nsgnfcant varables turn out nsgnfcant, because they do not exert any nfluence on salares or whether ths nfluence s sgnfcant, but non convex. 3
We have a slghtly dfferent approach: In our readng of the lterature superstars n the Rosen and the Adler sense are defned by ther top ncome (not performance or popularty) whch s very substantally hgher than that of the followng percentle of compettors and they are explaned by a hghly convex performance ncome gradent (Rosen) or substantally hgher popularty (Adler) at the top end of the ncome dstrbuton. Thus, n order to dentfy superstar effects we need to gve specal consderaton to the top end of the ncome dstrbuton. Because the earnngs performance gradent ncreases sharply only at the top end of the earnngs dstrbuton an estmator such as the OLS procedure that regresses on the mean value wll not be able to capture the phenomenon correctly. To fnd convexty (or a lack thereof) n performance measures through least squares regressons does not establsh superstar effects (or ther absence) as ths result can be drven by the lower part of the dstrbuton. Instead, the approprate technque s a set of quantle regressons that uses a sutable set of measures on performance and meda exposure and looks for a convex mpact of those at hgh percentles. Our paper thus makes the followng contrbutons. Frst, we are the frst to test the superstar phenomenon for the German soccer league; thanks to our data set we are able to lnk ndvdual players salares to a wde range of performance parameters. Second, we are the frst to nclude the role of meda for the emergence of superstars. That allows us to assess the relatve mportance of Rosens s and Adler s superstar theores. Thrd we make a methodologcal pont: We argue that the superstar phenomenon has been tested wth an napproprate estmaton technque. Instead, we use quantle regresson technque to test for a convex gradent at the top end of the dstrbuton. 2. Data Our dataset ncludes all players who were employed by the 18 soccer clubs n the frst dvson durng the seasons 1998/1999 and 1999/2000. For those players we collected nformaton about ndvdual salares, performance, and meda presence. The endogenous varable WAGE contans the entre pay earned by each player n the season 1999/2000. Ths 4
ncludes bonuses etc. but excludes advertsng money. 5 Data were provded by magazne Sportbld. 6 We use the followng explanatory varables: the poston of the players as dummy varables (FORWARD, MIDFIELD, DEFENSE, and KEEPER). For all outfeld players we ncluded the number of goals scored (GOALS), the number of asssts for a goal (ASSISTS), the number of shots on the goal (SHOTS), and the percentage of successful tackles (TACKLES) as performance measures, all for the season 1998/99. 7 All ndvdual performance data were provded by Kcker sport magazne, the world s largest magazne n soccer. We also used nteracton terms of the performance measures wth the dummes for the postons as some performance measures may be more mportant for certan postons than others. For nstance FGOAL denotes the number of goals scored by a forward, MGOAL those by a mdfelder etc. In addton we ncluded the varable AGE to account for senorty payment schedules or remuneraton for experence as s typcally found n normal wage regressons as well as n baseball (MacDonald and Reynolds 1994). We controlled for the orgn of players and used dummes for Germany, EU, Eastern Europe, and overseas (OVERSEAS). To capture the effects of meda presence we collected the number of hts of a player s name n the onlne verson of Kcker sport magazne durng ths season (HITS). 8 All performance ndcators (except for TACKLES as a percentage value) and the HITS were ncluded as quadratc terms as well to see whether dfferences n performance and popularty translate nto 5 Bonus payments were rather low at that tme and counted for less then one percent of the monthly or annual salares pad (Lehmann and Wegand 1997). Bonus payments ncluded are on average 1500 DM (767 or 818 US$ at that tme) for every game won at that tme. 6 Germany s stll the only country where salary nformaton s avalable for every sngle player snce the md 1990s (Frck 2007). Sportbld was the frst magazne whch publshed ndvdual player salares. In the more recent past, the natonwde Sunday newspaper Welt am Sonntag and the hghly respected soccer magazne Kcker started to collect and publsh the same data. 7 We do not have 1998/99 performance data for those players whose clubs played n the second dvson n 1998/99 and rose to the frst dvson n 1999/2000. These players, however, are not the superstars. Cf. Szymansk (2003) for the desgn of soccer contests. 8 Alternatvely, we could have used ctatons n newspapers such as Frankfurter Allgemene Zetung, Süddeutsche Zetung or Tagesspegel, but even though these newspapers have natonal coverage they tend to favor the local sports clubs such as Entracht Frankfurt, FC Bayern München or Herta BSC respectvely, thereby creatng a based pcture. Kcker clearly has unbased natonal coverage. We also decded aganst Internet hts such as Google hts (as used by Garca del barro and Pujol 2007) due to the nherent bases. Google hts cannot dstngush between older and newer webstes and thus favour players wth longer tenure whle Kcker hts only report entres made n a certan tme span. Popularty however s best measured by the frequency of reports wthn a gven season. In addton, players mgratng from a dfferent league to the Bundeslga may be very popular n that league thus creatng a lot of nternet hts, but may be relatvely unfamlar for the German audence. What s more, we started workng on ths paper n 2004, but our data on ndvdual soccer players refer to 1998 2000; thus Google hts measured n 2004 would clearly have been napproprate. We preferred to use the Kcker database from that tme perod to guarantee that we only count entres for the tme perod for whch we have performance data. 5
overproportonal dfferences n pay as the superstar theores suggest. They are ndcated by the endng SQD. Descrptve statstcs are provded n the appendx. 3. Results We ran OLS regressons on the entre sample (651 players) and on the subsample of the 359 players who played at all n the season. As results do not dffer sgnfcantly, we report only the latter. 9 Moreover we ran a quantle regresson for the 95 percentle for the same sample to see whether performance and meda presence have a dfferent mpact for the top earners than on average. 10 Ths s the approprate regresson technque because a strongly convex gradent may show up only at the top end of the ncome dstrbuton the superstars and not for average players. Regresson on the mean, as OLS does, or on the medan may smply blur the underlyng relatonshp. Moreover, OLS s napproprate because of the skewness and excess kurtoss of the dependent varable (see appendx). Ths semparametrc technque provdes a general class of models n whch the condtonal quantles have a lnear form. In ts smplest form, the least absolute devaton estmator fts medans to a lnear functon of covarates; n more general form quantle regressons mnmze the asymmetrcally weghted sum of absolute resduals wth the weghts ndcatng the percentle. The method of quantle regresson s potentally attractve for the same reason that the medan or other quantles are a better measure of locaton than the mean. Other useful features are the robustness aganst outlers and that the lkelhood estmators are n general more effcent than least square estmators. Besdes these techncal features, quantle regressons allow that potentally dfferent solutons at dstnct quantles may be nterpreted as dfferences n the response of the dependent varable to changes n the regressors at varous ponts n the condtonal dstncton of the dependent varable. Thus, (a 9 We do not have performance measures for the prevous season for those teams that played n the second dvson and only rose to the frst dvson n 1999, and for other players who dd not play n the German frst dvson n the last season (rookes and those comng from dfferent leagues). We are mssng salary data for 160 players; but 157 of those dd not play at all n the season under consderaton (1999/2000) and are thus n all lkelhood at the lower end of the skll and salary dstrbuton. In any case, snce we analyze only players that have played at all, our results are unaffected by ths. As a consequence, our sample reduces to 264 players who have played n season 1999/2000 and for whom we have prevous performance and current salares. 10 The 95 % quantle starts at an ncome of 7.5 mllon DM per annum whch equaled US$4.1 mllon n 1991. (It would have been roughly equal to 3.8 mllon Euro.) 6
set of) quantle regressons reveal asymmetres n the data, whch could not be detected by smple OLS estmatons. 11 Let y, x ), =1,...,n, be a sample of observatons (here players pay), where x s a Kx1 ( vector of regressors. Assume that Quant θ ( y, x ) devotes the condtonal quantle of y, condtonal on the regressor vector. The dstrbuton of the error term satsfes the x quantle restrcton Quantθ ( uθ, x ) = 0. Thus, we estmate y = Quantθ ( y, x ) + μθ, or, wth Quant : y = x θ ( y, x ) = x ' β θ ' β + μ, θ θ The estmator thus solves the followng mnmzaton problem (Buchnsky 1998: 95): u θ 1 mn β n θ y x ' β + : y x ' β : y < x ' β (1 θ ) y x ' β, where θ denotes the quantle. We analyze the 0.95 quantle whch weghs most strongly the players wth the hghest salares [ θ = 0.95]. As one ncreases θ from 0 to 1, one traces the entre condtonal dstrbuton of the endogenous varable y, the salares, condtonal on x. The quantle regresson s coeffcent could be nterpreted usng the partal dervatve of the quantle of y wth respect to one of the regressors, say j. Ths dervatve can be nterpreted as the margnal change n the θth condtonal quantle due to margnal change n the jth element of x. As performance measures we used the nteracton terms whch descrbe the relevant performance ndcator for the poston: goals by forwards (FGOAL), asssts by mdfelders (MASSISTS), and share of successful tackles for defenders (DTACKLES). 12 We also added team dummes as salares may not only be nfluenced by ndvdual performance (whch n part s a functon of team performance), but also by team characterstcs not captured otherwse (such as team sze or clubs budget constrants). 11 See Buchnsky (1998) or Koenker/Hallock (2001) for a survey of the method and applcatons to labor markets. 12 When we ncluded all performance ndcators for all postons,.e. goal, asssts, tackles, results were not as sgnfcant blurrng the underlyng relatonshps. 7
Results are summarzed n Table 1 whch allows comparng OLS results wth those of the 95% quantle regresson. For quantle regressons standard errors have been bootstrapped (1000 replcatons). Table 1 about here In the OLS regressons, performance parameters are hghly sgnfcant and have the expected sgn. Ths ndcates that performance s a major determnant of players salares. However, better performance does not lead to a more than proportonal ncrease n pay; f anythng we observe dmnshng returns to performance. Ths fndng s n stark contrast to Rosen s theory on superstars whch cannot explan the exstence of German soccer stars. Lkewse we do not fnd support for Adler s hypothess n a strct sense. Meda coverage does exert an mportant nfluence on players salares the parameter s hghly sgnfcant and postve and the explanatory power of the regresson ncreases very substantally. Yet, there are also dmnshng returns to meda presence as ndcated by the sgnfcantly negatve sgn of the number of hts squared. Meda presence s thus mportant, but does not lead to superstar status (n terms of pay). If we look at the.95 quantle regresson we fnd smlar results performance and meda presence matter, but not more than proportonal as mpled by Rosen s and Adler s theory of superstars. Thus there s no evdence for the exstence of superstars n the Rosen or Adler sense, but salary dfferences can be explaned by dfferent performance and popularty. There are other nterestng fndngs: The mpact of age on salary follows an nverted U shape peakng at 25.4 years (other thngs beng equal, model (2)). We also observe a postve dscrmnaton of foregners from overseas. Whle European foregners, both from the EU and Eastern Europe, are pad no dfferent than ther German counterparts, players from overseas most of whom stem from South Amerca are pad a premum whch s not reflected n better performance. We carred out a number of robustness checks. In partcular ndvdual meda presence may tself only be a functon of performance as those players who perform well tend to be mentoned more often. The sgnfcant ncrease n R 2 after the ncluson of the meda parameter, however, ndcates that meda presence cannot be explaned by performance alone. Indeed the regresson of meda presence on performance and the other control varables resulted only n an R 2 of.22 n a regresson wthout club dummes and.42 n a 8
regresson wth club dummes. Only FGOAL and MASSIST turned out sgnfcant as the news, of course, reported the goals ncludng the scorng and assstng players. In order to address ths endogenety of the varable HITS we appled a two stage regresson procedure: We ran an OLS regresson of HITS on all explanatory varables n the second stage,.e. all performance parameters, age, and ther squared terms (except for DTACKLES as a share value), the dummy varable OVERSEAS, club dummes and a constant. We then used the resduals of ths equaton as the part of meda presence whch s not explaned by actual performance, age, club, or orgn, but rather by ndvdual reputaton or popularty and thus s able to portray the Adler effect. Results are gven n Table 2. Table 2 about here. It turns out that the results of the OLS regresson s largely unaffected by ths procedure. We stll fnd postve but dmnshng returns on performance varables and meda presence n the OLS regresson and a relatvely smlar pattern n the 95 % quantle regresson. Table 2 also provdes some ndcaton on the behavor of quantle regressons. We report the medan regresson and the 90 and 95 percent quantles. The nfluence of performance parameters s largely unaffected by the percentle θ chosen for the quantle regresson. AGE loses ts sgnfcance. The more weght we gve to the superstar bracket, the less meda presence s able to explan ncome dfferences. For no quantle regresson do we fnd a convex earnngsperformance or earnngs popularty gradent. We do not fnd superstar effects as descrbed by Rosen or Adler. 4. Concluson Indvdual performance and and ndependently thereof meda presence explan a large part of German soccer players pay. The strong nfluence of popularty s partcularly noteworthy n soccer, for whch the contrbuton to team success could be expected to be the domnant determnant of ndvdual pay. Our results ndcate that clubs proft also from the part of players popularty that s not lnked to measurable performance on the feld, presumably through hgher gate recepts, merchandse sales, sponsors contrbutons, commercals, and broadcast revenues. However, we do not fnd superstar effects descrbed by Adler s or Rosen s theores: nether dfferences n performance nor n meda presence translate nto more than proportonal dfferences n the earnngs of soccer stars. 9
Two lnes of arguments may be put forward for ths non exstence result: Frst, we capture only ex ante salares of players from ther clubs. As data are unavalable we do not nclude ncome from commercals whch are concentrated wth only a few players and thus the real ncome dstrbuton s much more skewed. However, ths should not prevent superstar effects n the salares unless clubs antcpate ths effect n ther salary offers and are able to prce ths n whch should be very dffcult gven nternatonal competton for stars. Second, because the Italan, Englsh and Spansh top clubs are rcher than ther German counterparts due to the dfferent marketng rghts for TV transmsson, real superstars have an ncentve to seek employment wth them. 13 That mght explan why Lucfora and Smmons (2003) and Garca del barro and Pujol (2007) fnd superstar effects for the Italan and Spansh premer leagues and we do not for the Bundeslga. Yet, t could also be that they fnd superstar effects because of ther dfferent methodologcal approach. Obvously there s a need for more research n ths area. Unlke prevous contrbutons to the superstar lterature, future research should use quantle regresson technques n order to seek to dentfy the determnants of the superstar phenomenon. Only ths technque s able to measure approprately the nfluence of talent and popularty for the top ncome earners the superstars. 13 Ths nterpretaton s n lne wth the recent development that n the past two years especally after the World Champonshp n Germany n 2006 more German players have been playng abroad. Mchael Ballack and Jens Lehmann are the prme examples. 10
Lterature Adler, M. (1985) Stardom and Talent, Amercan Economc Revew, 75, 208 212. Adler, M. (2006) The Economcs of Superstars: Theores and ther Applcaton, n V. Gnsburgh and D. Throsby (eds.), Handbook of the Economcs of Art and Culture, Elsever Scence, North Holland, Amsterdam. Buchnsky, M. (1998), Recent Advantages n Quantle Regresson Models, n: Journal of Human Resources, Vol. 33(1), pp. 88 126. Dobson, S. and J. Goddard (2001) The Economcs of Football, Cambrdge Unversty Press, Cambrdge/ UK. Frck, B. (2007) The Football Players Labor Market: Emprcal Evdence from the Major European Leagues, Scottsh Journal of Poltcal Economy, 54: 422 446. Garca del Barro, P. and F. Pujol (2007) Hdden Monopsy Rents n Wnner take all Markets_sport and Economc Contrbuton of Spansh Soccer Players, Manageral and Decson Economcs, 28: 57 70. Hamlen, W. (1991) Superstardon n Popular Musc: Emprcal Evdence, Revew of Economcs and Statstcs, 73: 729 33. Koenker, R. and K. Hallock (2001): Quantle Regresson: An Introducton, Journal of Economc Perspectves 15, 143 156. Lehmann, E. and J. Wegand (1997): Money makes the Ball go round: Fußball als ökonomsches Phänomen, Ifo Studen, 43: 381 409. Lucfora, C. and R. Smmons (2003): Superstar Effects n Sports: Evdence from Italan Soccer, Journal of Sports Economcs 4, 35 55. MacDonald, N. and M. R. Reynolds (1994) Are Baseball Players Pad by ther Margnal Products? Manageral and Decson Economcs, 15, 443 457. Rosen, S. (1981) The Economcs of Superstars, Amercan Economc Revew, 71: 845 858. Schulze, G. (2003) Superstars, n The Handbook of Cultural Economcs, edted by R. Towse, Edward Elgar, Cheltenham/UK, 431 436. Seaman, B. (2003) Cultural and Sport Economcs: Conceptual Twns?, Journal of Cultural Economcs, 27: 81 126. Szymansk, S. (2003) The Economc Desgn of Sportng Contests, Journal of Economc Lterature, 41, 1137 1187. 11
Table 1: Regresson results, endogenous varable: WAGE VARIABLES AGE 792438.5** (1) (2) (3) (2.45) AGESQD 15405.94** ( 2.56) KEEPER 1099645** (2.09) MIDFIELD 204850.7 FORWARD ( 0.41) 904439 b ( 1.62) FGOAL 449946*** (3.61) FGOALSQD 4440.098 ( 0.66) MASSIST 747041.9 *** (4.39) MASSISTSQD 43393.81*** ( 2.61) DTACKLES 18673.23** (2.42) OVERSEAS 489454.2* (1.35) OLS 598928.5** (2.19) 11773.68** ( 2.31) 565798.7 (1.30) 303938.2 ( 0.75) 665347.7 ( 1.45) 226102.2** (2.16) 3862.711 ( 0.70) 540681.1*** (3.84) 41970.72*** ( 3.07) 9287.729 (1.45) 850207.1 *** (2.84) HITS 60621.71 *** (9.40) HITSSQD 162.9496*** ( 6.02) quantle regresson, a 95% quantle 1683468* (1.67) 33070.15* ( 1.74) 1674404 (1.56) 328759.5 (0.34) 1057635 ( 1.15) 596558** (2.17) 17195.81 ( 0.97) 1233679*** (2.47) 93176.13** ( 2.08) 37712.7** (2.04) 1310638 (0.78) 44477.61** ( 1.82) 120.3744 ( 0.97) Team dummes yes yes yes constant 8504594* ( 1.95) 6693148* ( 1.83) 1.87e+07 ( 1.39) R 2 / Pseudo R 2 0.51 0.68 0.53 F(29,234) = 8.46*** F( 31, 232) = 15.59*** a quantle regresson wth bootstrapped standard errors (1000 replcatons), b sgnfcant at the 11 percent level, t values n parentheses, ***/**/* ndcates sgnfcance at the 1%/5%/10%/ level, no. obs.:264 12
Table 2: Regresson results, endogenous varable: WAGE (4) (5) (6) (7) VARIABLES OLS quantle regresson AGE 613230.5** (1.09) AGESQD 11862.73** ( 2.17) KEEPER 1261176 *** (2.72) MIDFIELD 153423.2 ( 0.36) FORWARD 873530.5* ( 1.80) FGOAL 442148.5*** (4.08) FGOALSQD 4188.419 ( 0.71) MASSIST 728706.9*** (4.93) MASSISTSQD 40782.67*** ( 2.82) DTACKLES 20243.07*** OVERSEAS HITS (EXOGENOUS) HITSSQD (EXOGENOUS) (3.00) 504998.5 b (1.60) 31447.71 *** (8.17) 104.5877** ( 2.37) 50% quantle 90% quantle 95% quantle 233793.9 (0.45) 4334.354 ( 0.45) 1105528* (1.73) 71960.51 (0.12) 662194.9 ( 1.06) 426621.8*** (3.01) 2411.079 ( 0.25) 488205.7** (2.01) 14234.63 ( 0.50) 23134.71*** (2.53) 415438.8 (0.93) 38556.5*** (4.25) 49.89813 ( 0.30) 1145832 (1.32) 22354.88 ( 1.36) 1305183 (1.11) 97474.02 ( 0.09) 1189450 ( 1.21) 564792.5* (1.92) 9169.255 ( 0.49) 1187399** (2.38) 71666.57 ( 1.46) 30329.97 (1.48) 211320.1 (0.18) 28796.09* (1.71) 128.1668 ( 0.42) 929858.8 (0.89) 17966.05 ( 0.90) 947850.5 (0.83) 322082.1 ( 0.27) 1390813 ( 1.57) 535747.6 ** (2.11) 8345.439 ( 0.56) 1427821 *** (2.74) 91569.94* ( 1.88) 32808.67* (1.77) 246914.7 (0.20) 18111.48 (1.18) 284.843 Teamdummes yes yes yes Yes constant 6189992 ( 1.57) 1844163 ( 0.27) 1.09e+07 ( 0.94) (1.11) 7792228 ( 0.57) R 2 / Pseudo R 2 0.63 0.47 0.52 0.54 F( 31, 232)=12.96*** a quantle regresson wth bootstrapped standard errors (1000 replcatons); b sgnfcant at the 11 percent level t values n parentheses, ***/**/* ndcates sgnfcance at the 1%/5%/10%/ level, no. obs.:268 13
Appendx: Descrptve statstcs 1. Endogenous varable: Wage n season 1999/2000 PERCENTILES WAGE IN DM 1% 100,000 5% 250,000 10% 500,000 25% 800,000 50% 1,500,000 75% 3,000,000 90% 5,500,000 95% 7,000,000 99% 10,000,000 Obs. 493 Mean 2,350,507 Std.Dev. 2,107,301 Varance 4.44e+12 Skewness 1.597043 Kurtoss 5.366672 1 DM = 0.51130 Euros In 1999 1 DM equalled 0.54543 US Dollars (annual average) 14
2. Explanatory varables Varable Obs. Mean Std. Dev. Mn Max KEEPER 651.1059908.3080625 0 1 DEFENSE 651.2519201.4344494 0 1 MIDFIELD 651.4254992.4947987 0 1 FORWARD 651.2165899.4122375 0 1 GOALS 651 1.416283 2.885024 0 28 FGOAL 651.6989247 2.63672 0 28 ASSIST 651 1.066052 2.099875 0 12 MASSIST 651.6390169 1.809449 0 12 TACKLES 651 15.72219 23.97067 0 69.3 DTACKLES 651 5.49616 17.01095 0 69.3 HITS 648 23.35185 31.72442 0 315 Out of 651 players 292 players (or 45 %) dd not play at all n the season 1998/99; the medan s at 216 mnutes out of 3060 possble mnutes. The mean s at 894 mnutes; standard devaton s 1040 mnutes. 15