This study analyzes the technical efficiency of Serie A Italian football clubs during the

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1 A Bayesian stochastic frontier of Italian football C. P. Barros a and G. Rossi b,* a Instuto Superior de Economia e Gestão; Technical Universy of Lisbon, Lisbon, Portugal b Royal Docks Business School, Universy of East London, London This study analyzes the technical efficiency of Serie A Italian football clubs during the seasons wh a Bayesian stochastic frontier model using unique data extracted from clubs annual reports. Specifically, the focus of the study is on assessing the impact effects on clubs' efficiency whether they are big clubs, they employ several foreign player, they compete in European competions, and their involvement wh football scandals in the Italian football. The empirical results reveal that efficiency varies among the clubs analyzed and policy implications are derived. I. Introduction In the economic lerature, efficiency analysis of sport leagues is a well-established research field that use a variety of tools to assess their efficiency from different points of view (Espia-Escuer and García-Cebrian, 004; Kahane, 005; Barros and Leach, 006a, 006b, 007; Ascari and Gagnepain, 007). Wh the introduction of UEFA Financial Fair Play, efficiency in football is becoming more and more relevant. As a result, a major transparency of information and a large availabily of data will increase the populary of football clubs' efficiency as a convenient research topic in the near future. Clubs make their investments in players, coaching teams and management in order to increase the chance of winning and thereby attract addional money from ticket sales, marketing and sponsorship. Although players and clubs consider victory on the pch as their ultimate achievement, financial stabily is also a main driver for long term success. Club shareholders and credors also watch closely the returns on investment, and cash flow movements and interest coverage, according to the amount of money they frequently lose. * Address: g.rossi@uel.ac.uk 1

2 The motivation for the present research is the following: First, to focus on Italian leagues, which have not yet attracted much research attention. Most of the researches analyzes efficiency looking mainly at English leagues and, then, other European leagues except for Italian football (Kulikova and Goshunova, 013). Second, to adopt the Bayesian stochastic frontier model, which, although well known, is still rare in applied research (Tsionas, 00; Griffin and Steel, 008). The Bayesian SF-stochastic frontier is generally more suable for panel data since replications can overcome a small data span sample. Furthermore, in contrast to DEA-data envelopment analysis, SF accounts for measurement error in the data. Third, to explore how the Bayesian frontier model differs from standard frontier models. Ultimately, this research aims to include in the analysis the role of the big club effect, the effect of foreign players' presence in the team roster, UEFA competions effect and Calciopoli scandal effect on Italian football clubs' costs. However, the role of big clubs, the presence of foreign players in the team roster, the participation in UEFA competions and the impact of scandal in the football industry on the cost function of football clubs have not yet been analyzed. All these elements are important in sports since big clubs and foreign players signal the leading clubs in a country. UEFA competions are the main international cups that the best European clubs compete for, serving as a funding advantage for the national teams. Finally, scandal in the football industry characterizes the corrupted sport practices that have recently affected the Italian league Serie A. After this introduction, this paper is organized as follows: the contextual setting is introduced, succeed by a review of previous lerature. Then, the adopted methodology is described, and the specific hypotheses are presented. Finally, the sections of data and results are illustrated and conclusions and discussions are commented. II. Contextual Setting From being the best football tournament in the world during the 1990s, Serie A, the top Italian football league, has been facing a slow and constant decline since the mid 000s.

3 Although in the new millennium Italy is still considered as one of the most successful football nations, having won the World Cup in 006 and having played the European Cup finals in 000 and 01, Italian clubs are struggling to compete in international competions due to their operational defics and huge debts. The main result of this competive decline has been the loss of one place available to Italian clubs to compete in the UEFA Champions League since the 011/1 season. During the 011/1 season, professional football in Italy is estimated to have generated an aggregate turnover equal to approximately.5bn for all teams participating in professional football tournaments, i.e. 0.15% of GDP (Arel et al., 01). Together the professional football teams contributed a total of 1.3bn in tax revenues. Nevertheless, Italian professional football has been facing a constant and slow decline since the last decade due to clubs rising payrolls, which have been needed to attract worldwide football stars in a highly competive transfer market, combined wh sluggish growth in revenues compared to the other four major European football leagues (Baroncelli and Lago, 006; Bof et al., 008; Boeri and Severgnini, 01). Nevertheless, the wage cost per point in Serie A varies considerably across clubs according to the presence of superstars, wh top teams spending significantly more per point than the other clubs (Boeri and Severgnini, 01). In particular, AC Milan, FC Inter Milan, AS Roma and FC Juventus on average spent between 1.3m and 3.3m per point in the last five years, while the second layer teams (Fiorentina, Napoli, Lazio and Udinese) spent between 0.5m and 1.5m per point. As Boeri and Severgnini (01) report, Italian clubs are perhaps unsurprisingly subject to a high mortaly rate; 9 out of 37 teams participating in Serie A, 5% of the total, declared bankruptcy in the period from 001 to 011. In the same period, accounting data reveals an upward trend in net losses, wh an average of 50m in losses per year, and a compound annual growth rate in operational losses of 7%. The total debt of Serie A clubs has been increasing at a compound growth rate of about 9% per year, i.e. by over 60% since 006/07. On the revenue side, while TV and new media rights revenues are stable and represented about 56% of total revenues in 3

4 010/11, gate revenues are declining: from , Italian stadia had an average of less than 5,000 spectators per Serie A match, the lowest among the top European leagues. Notwhstanding the fact that the financial problems and debts are also common in the other top European football leagues, Italian football has been involved in several major scandals in s modern history because of poor practice in corporate governance and administration linked variously to doping, false passports, bribery and match-fixing (Agnew, 007; Foot, 007; Jones, 007; Di Meo and Ferraris, 01). Amongst these scandals, arguably the most damaging was the Calciopoli scandal which emerged shortly before the World Cup in Germany in 006. The Italian police discovered a network of close relationships between team managers, referees, agents and club executives wh the intention of affecting the final results of a number of league matches (Hamil et al., 010). The Serie A clubs, FC Juventus, AC Milan, ACF Fiorentina, SS Lazio and Reggina Calcio, and the Serie B club, Arezzo, were involved in the scandal through some of their club officials. The final punishments awarded points deductions to all clubs involved in the scandal and several club officials were also banned from taking part at any level of Italian football for specific periods (Hamil et al., 010). As Caruso and Di Domizio (01) argue, the declining attendance trend cannot be explained by the high price of tickets or by excess exposure of football on TV. Several episodes of violence and hooliganism occurring in the proximy, if not whin, Italian stadiums have negatively characterised the image of Italian football. As Babatunde et al. (01) show, the falls in stadium attendance may also be related to the corruption highlighted by the Calciopoli investigation in 006. The scandal exacerbated the declining trends in gate attendances and revenues leading to deteriorating balance sheets for many clubs. Revenues from match attendance declined strongly for all the teams involved and there was a negative spill-over on attendance for the other teams. This was only partially offset by rising income from sales of television broadcast rights. 4

5 <<Insert Table 1>> Empirical research on the Italian league Serie A has focused on superstar effects (Lucifora and Simmons, 003; Bryson et al., 014), team stabily and longevy of team relationships (Montanari et al., 008), coach dismissal (De Paola and Scoppa, 01) and corruption (Boeri and Servegnini, 011; Babatunde et al., 01). The Italian football clubs analyzed in the present paper comprise those listed in Table 1 for the nine Serie A seasons between 003/04 and 011/1. Some operational characteristics for the year 01 are displayed. Firstly, the presence of persistent operational defics and cumulative debts highly characterizes Italian Serie A football. Wh a net loss of 8m in 01, Italian clubs had the second highest wages levels of the European leagues but only the fourth highest revenues. The wages to revenue ratio has been more than 90% since 004/05 and only eight Serie A clubs were profable at the end of the season 011/1 (Boeri and Severgnini, 01; Arel et al., 013). Secondly, Serie A reported a revenue increase of 4% in the last five years from 1.8bn in 007/08 to.3bn in 011/1 (Arel et al., 013). While Serie A average attendance remained around 3,000 in 011/1, the forth league in European football attendance ranking, broadcasting revenue has been the largest single contributor to growth, reflecting the new collective selling broadcast rights (Arel et al., 013). Then, the presence of qualy players in local competion is characterized by importing high profile players from foreign leagues. Following the CIES indicators (CIES, 01), since the season 008/09 the percentage of foreign players has constantly increased from 40% to 48% in 01.Similarly, an increasing trend was registered for international players, whose presence in Serie A moved from 46% in 008 to 56% in 01 Finally, is the domination of ticket sales by few large clubs from main cies while other small clubs struggle in small towns. AC Milan, Internazionale FC and Juventus FC accounted for 45% of the Serie A revenue (Delote, 011). III. Lerature Review 5

6 From an economic perspective, the lerature on football efficiency takes into consideration clubs eher as revenue maximisers or as share market value maximisers. In line wh this research, scholars have used different financial indicators to represent the revenue maximising approach adopted by clubs (Kulikova and Goshunova, 013): total revenue, sales, TV rights revenues, operating prof before depreciation and amortization, gross wages, and operational costs. Regarding the several approaches to measure and analyse efficiency, few ones are observed in sports. The index numbers approaches (e.g. Tornquist and Malmquist total factor productivy indices), for example, measure productivy and efficiency changes over time. Such indices can also be extended using the endogenous-weight total factor productivy approach (Yoshida and Fujimoto, 004). Other key popular methodologies include the econometric approach, such as Stochastic Frontier Analysis (SFA), or the non-parametric approach, such as Data Envelopment Analysis (DEA). While the DEA focuses primarily on the overall assessment of clubs' efficiency based on the analysis of sets of inputs and outputs that characterize the production function, the SFA use tools of deterministic correlation and regression analysis to determine the functional dependence of the variable considered in the model. In total, seven papers adopted the SFA to analyze the efficiency of football clubs as revenue maximizes. While the cost specification is adopted by Barros and Garcia-del- Barrio (008) and Barros and Leach (006b), other scholars such the Hofler and Payne (1996; 1997) Dawson et al. (000), Hadley et al. (000) and Scully (1994) prefer the production specification. The cost function adopted in all SFA papers recognizes the multiple output nature of the technology of the football club. The variables used in the cost function always include the standard microeconomics cost function variables (Varian, 1987). There are some differences in the output variables adopted in the cost function due to data availabily. In the present research the receipts are spl between marketing, sponsorship and other receipts. 6

7 What is clear from the existing lerature is that none of the existing papers has adopted the Bayesian stochastic frontier to analyse football efficiency. The Bayesian frontier is distinguished from standard frontier models due the marginal prior independence of the effects. The structure of prior information enables to estimate the models using Monte Carlo integration or Gibbs sampling (Koop et al. 1997). However, the final creria between two competing models is that the estimated frontier to be consistent wh economic regulary condions, enabling accurate results. The marginal prior independence of the effects, Monte Carlo integration or Gibbs sampling, enables an accurate estimation of the model consistent wh economic regulary condions. IV. Methodology The Bayesian stochastic random frontier model was introduced by Tsionas (00), and assumes that each firm is allowed different intercepts as well as slope coefficients. The main purpose of the model is to improve the accuracy in the efficiency estimation by separating the cost-efficiency estimates from heterogeney among football clubs. This model is different from the Bayesian fixed frontier model, introduced by Koop et al. (1997), which assumes that all football clubs share exactly the same production possibilies; i.e. no heterogeney between firms. To illustrate the Tsionas model, we consider the following cost equation: C X i v ; i 1,, N, t 1,, T [1] where C is a vector of the dependent variable for the h observation of year t, x is vector of explanatory variables, v is a random error identically and independently distributed as N(0,σ n ) and u is a non-negative random error which captures the level of cost inefficiency and ensures that each football club s cost-efficiency lies on or below the frontier model, β i is a vector of random coefficients, and a is a non-random intercept. In the Bayesian context, is common to assume that the inefficiency term u is 7

8 exponentially distributed (other distribution such as truncated and gamma are also possible) wh a parameter u, and which can be expressed as follows: f ( u ) exp( ) [] To complete the model assumptions, the parameters β i follows a multivariate normal distribution i ~ N (, ) [3] where β is a vector of parameter means, and Ω is a posive-define covariance matrix. This makes the model hierarchical wh two levels of latent variables, β i and u. Specifically, each football club under consideration has s own cost function wh parameters bi which account for heterogeney or technological differences between firms. The restriction of Ω=0 will make the model in Equation (1) converge to the tradional or fixed stochastic frontier model, which is commonly used in the lerature. Some addional assumptions of the model are that β i are independently distributed, and n as well as u are independent of x. For details about the likelihood and the condional posteriors of the model refer to the appendix. The final model to be estimated wh the dummy variables and that define the hypothesis and the errors term is the following: ln OC / PF T t 1 T tt ln TR 1 ln W 3 ln PL PF 4 ln PK PF ln TR 5 * ln W ln TR 6 * ln PL PF 7 ln TR * ln PK PF ln W 8 * n PL PF ln W 9 * ln PK PF 10 ln PL PF * ln PK PF BG 1 FP UCL 3 UEL 4 PD 5 SB 6 ln v ln [ 4 ] where T and T are time trend variables; OC is the total operational costs; TR is the total receipts; W is the number of match won during the football season t by club i; PL is the price of labour, measured by dividing total wages between the number of workers 8

9 including players; PK is the price of capal premises, measured by dividing the total amortization by the value of total assets; PF is the price of funding, measured by dividing the interest paid on total debt. Note that we divided the total cost, price of labour, price of capal-premise by the price of capal-funding, PF, to ensure homogeney in price for the cost function. Several characteristics are analyzed wh dummy variables that take the value of 1 for football clubs that have the specific characteristic and zero elsewhere: big clubs (BG), clubs qualified for the UEFA Champions League (UCL), clubs qualified for the UEFA Europa League (UEL), clubs relegated to Serie B (SB). Two other continuous variables take into consideration the percentage of foreign players whin the team roster (FP) and the point deductions inflicted toclubs involved in the Calciopoli scandal (PD). While v is a rand error identically and independently distributed as N(0,σ n ), u is a non-negative random error and captures the level of cost inefficiency. V. Hypotheses Based on the lerature survey and contextual setting, some hypotheses are defined. We aim here to test the relationship between football club technical efficiency and the following covariates defined in the hypotheses in the sections below. Big clubs It is often argued that large firms are possibly more efficient because they can use more specialized inputs, coordinate their resources better, and reap the advantages of economies of scale (Alvarez and Crespi, 003). In our present context, firm size might also take on an addional importance, since football clubs might thus be more profable if they increase their size, in order to achieve economies of scale and make up for the external market failures (Khanna and Palepu, 000; Ghemawat and Khanna, 000). Since related studies on sports also indicate that firm size contributes to higher efficiency due to 9

10 the big club effect (El-Hodiri and Quirk, 1971), we thus assume that firm size has a posive impact on the efficiency of Italian football clubs. H1: Big clubs have a posive impact on the Italian football clubs reducing clubs costs. Foreign players In Italy, most renowned and successful clubs rely more on foreign players than others. Bryson et al. (014) find consistent evidence of superstar status for foreign players. Changes in the proportion of foreign players in the team roster are posively associated wh club points. In other words, foreign players help clubs to achieve better results than if Italian players replace them. In our model, we assume that a higher presence of foreign players might have an impact on costs by contributing to the transfer of knowledge and economies of scale between football clubs. H: Higher presence of foreign players have a posive influence in increasing football clubs' operative costs. UEFA Champions League The presence of Italian football clubs in the UEFA Champions League, UCL, perms the clubs to display their qualy at European level and enables the club to achieve higher income from the prizes. In Serie A, the loss of a place available for Italian clubs to compete for the UEFA Champions League since the 011/1 season has put big clubs under pressure if they fail to qualify for the major European competion for clubs. For instance, a detailed analysis of AS Roma annual report reveals that club's total revenues decrease by 7.6 million due to Italian absence from the UEFA Champions League (Delote, 013). In detail, broadcast and match day revenues decreased by 6.3 million and.9 million respectively. AS Roma drop four place to the 19th posions in the Delote Football Money League ranking of the highest earning football clubs in the world. This evidence suggests that club competing for qualifying for the UEFA Champions League have high incentive to invest in players' talent in order to remain 10

11 competive whin their national league. In our model, we argue that competing for qualifying for a posion in the UEFA Champions League might have an impact on operative costs by increasing clubs' investment in football talent wh increasing teams' payrolls. H3: The presence of football clubs competing for qualifying to the UEFA Champions League has a posive influence on the efficiency of Italian football clubs increasing the impact of the operative costs. UEFA Europa League Although is not so financially attractive as the UEFA Champions League, competing for the UEFA Europe League also provides perms Serie A football clubs the opportuny to display their qualy at European level and to increase their commercial revenues and income from the prizes. H4: The presence of football clubs competing for qualifying to the UEFA Europa League has a posive influence on the efficiency of Italian football clubs increasing their operative costs Calciopoli scandal As highlighted by Buiramo et al. (01), Calciopoli scandal resulted in a relevant loss of supporters that were used to follow their clubs' matches at the stadia. This effect is particular significant for the clubs involved in the scandal and saw a non-trivial decline of their gate-revenue. This evidence might suggest that clubs forecast this negative effects of the scandal and, consequently, they restructured their investment according to their revised football ambions according to the award of their respective point deductions. In our model, we assume that Calciopoli scandal might have a significant impact on operative costs by affecting clubs' investment strategy in function of their respective decrease of revenue. 11

12 H5: The involvement of football clubs in corruptive scandals has a negative influence on the efficiency of Italian football clubs decreasing s cost. Serie B According to Arel et al. (011), along the period the relegation from Serie A to Serie B determined a average decrease of 19m per each club relegated. This result would have been more negative whout the parachute system that support finally relegated clubs. Similarly, operative costs also diminished wh an average reduction of 10m. Overall, relegated clubs' EBITDA registered an average decrease of 6.1m. Serie A football clubs competing to avoid the relegation tend to marginal increase the team payrolls at decreasing marginal level in relation to the other clubs Arel et al. (011). In our model, we argue that competing for avoiding the relegation might have a significant impact on operative costs by increasing clubs' total payrolls. H6: The presence of football clubs competing for avoiding the relegation to Serie B has a posive influence on the efficiency of Italian football clubs increasing their operative costs. VI. Data Our analysis includes 6 Italian football clubs over the period (16 observations). Table presents some descriptive statistics of the variables. <<Insert table around here >> While clubs' performance data and the composion of team roster were collected from the digal archive of Soccerassociation.com, the financial data, such operational costs and total receipts, were obtained from the annual reports of the football clubs available at the Italian Companies House. VII. Results 1

13 To proceed wh the Bayesian estimation, we estimate a SF model wh WinBUGS software, applying the Gibbs sampling wh data augmentation for the above data using 80,000 erations (first 10,000 erations are dropped to avoid sensivy of starting values). The value r i was set at following other studies in the lerature (van den Broeck et al., 1994; Tsionas, 00). The posterior estimates and posterior standard deviations are reported in Table 3. <<Insert table 3: Results around here>> From the results, is verified that operational costs (OC) increase wh the time trend (T) but the square term (T ) reveals that increases at decreasing marginal rates. The operational costs increase as theoretically expected wh the input prices (PL, PK) and wh the outputs, signifying that is costly to produce football matches. Relative to the equation square terms, the costs increase wh some and decrease wh others. Concerning the six tested hypotheses, hypothesis 1 is accepted since the parameter of foreign players has a posive influence in increasing the Italian football clubs' costs. Hypothesis is also validated since the presence of big clubs have a negative influence in increasing a football club cost. Addionally, both hypothesis 3 and hypothesis 4 are also accepted because clubs competing for the UEFA Champions League and UEFA Europa League tles have posive influence on the efficiency of Italian football clubs and the specific variables are posive and statistical significant in explaining Italian football clubs' costs. Finally, hypothesis 5 is confirmed since points deductions decreases the cost of the Italian football. Finally, hypothesis 6 is rejected since competing for avoiding the relegation to Serie B have a posive impact on football clubs' operative costs but is significant at 5% level. 13

14 Relative to the SF parameters, both the error term and the non-negative random error are statistically significant, meaning that this data is adequately described by a SF model. Table 4 present the Italian football clubs efficient scores. <<Insert table 4: Efficient scores around here>> From the scores is verified that the mean efficiency is 0.960, signifying that the average waste is of =0.04. This small waste varies among the clubs analyzed, wh Ascoli Calcio, which reaches 0.973, being the most efficient football club in the period followed by Atalanta and Empoli. US Lecce is the least efficient club, wh an average value of Therefore the differences are small, signifying that football clubs adopt a similar behavior in the Italian context. VIII. Conclusions and Discussions This study is the first to compare the efficiency of Italian football clubs from wh a Bayesian SF frontier model. This aspect represents an essential contribution, since the lerature lacks evidence on whether football clubs in the Italian Serie A are relatively efficient. The results reveal that efficiency varies among Serie A football clubs. However, this variabily is small, signifying that football clubs have a homogenous efficiency behavior in the Italian Serie A. This result is obtained wh the Tsionas (00) Bayesian stochastic random frontier model that allows for heterogeney in the sample. Therefore, the result are robust and they are also based on a sound theoretical grounding. In relation to the hypotheses tested, only one hypothesis is rejected and the remaining five are accepted revealing the importance of foreign players and cy location in Italian football context and. While an higher presence of foreign players have a posive influence in increasing the club s cost, the big club effect has a negative influence in decreasing a football club s cost, validating previous research in sports (El Hodiri and Quirk, 1971). Furthermore, the qualification to compete to the UEFA Champions League has a posive influence on the efficiency of Italian football clubs, increasing costs. Similarly, the same 14

15 empirical trend at a lower impact applies to clubs qualified to compete for the UEFA Europa League participation. Finally, points deductions inflicted to football clubs involved in Calciopoli scandal decreases has a negative impact on their operative costs. Therefore, the general conclusion is that Italian football clubs are relatively efficient and relatively homogenous and football is costly wh most of the descriptive covariates increasing costs. The policy implication of this study is that common policies are suable for these relatively homogenous football clubs and that benchmarking studies should be conducted on a regular basis to observe the evolution of Italian football clubs. The study is useful for the Italian football league, since most of the available industry reports rely on simple methodologies based on sport results and neglect the contribution of financial results and other contextual covariates in the analysis of football club performance. Relative to other research, the results are similar to papers that found homogeney in sports league but found heterogeney in wide studies (Barros et al., 008; Montanari et al., 008). However, more research is needed to confirm the present results. 15

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20 Appendix A The likelihood of the model in Equation (1) can be expressed as L (,,, ; C, X ) NT ln ( ) T t 1 N i 1 W T t 1 N i 1 ln W ( 1 / W [A1] Where - C X ; w X X ; φ( ) denotes the standard normal distribution function, and X is a matrix of explanatory variables. Along wh this likelihood, the Bayesian estimation of the model requires prior information about the parameters. The general priors for the model can follows: be summarized as ( N 1) (,, ) 1 exp(- exp(- q 1 N 1 ( K v - q ) - 1 ) / exp( - 1 tr where N 1, N, q1 and q are small posive numbers, and S is a posive define matrix ) S [A] A common practice is to choose the priors for α and β as flat (i.e. imposing no prior information about the parameter mean). A gamma prior is selected for θ, an inverted gamma prior is selected for σ. Having information about the likelihood, and the priors, the condional posterior of each of the model parameters can then be estimated. The condional posteriors of the model parameters can be summarized as follows: for σ. q1 N t 1 N i 1 ( C u X ) ~ X (NT, N 1 ) A3 For - - p(,,,,, C, i X) exp 1 N i 1 ( ) i 1 ( ) i A4 for u :,,,,, C, X) ~ N(C - - X - W ) i - A5 0

21 and the condional posterior for θ is gamma,.,,,,, C, X) ~ G(NT N, ln r *) A6 i T T t 1 i 1 where r i * is a measure of cost-efficiency of the h football club. Using these condional densies the Gibbs sampler follows. When the erations approach to infiny, the Gibbs sampling methods converges to the actual joint posterior densy function. In this paper, we generate 100,000 parameter vectors and drop the first 10,000 to avoid sensivy of starting values 1

22 Table 1: Characteristics of the Italian Football clubs Analyzed in 01 N. obs. Football clubs Points Wins Operational costs ( ) TV receipts ( ) 1 A.C. Milan A.S. Roma Cagliari C F.C. Int. Milano Fiorentina V Juventus F.C S.S. Lazio U. S. Sampdoria U.S.C. Palermo Udinese C A.C. Siena Parma FC AC Bologna US Lecce Ascoli Calcio AS Livorno Atalanta AC Chievo Brescia Calcio FC Empoli Reggina Calcio SSC Napoli Catania Calcio Genoa Mean Median Std. Dev Source: Financial Accounts of the clubs

23 Table. Descriptive statistics of the data Variable Description Min. Max. Mean St. De. Ln OC Logarhm of operational cost of Italian football clubs in Euros, 008= T Trend variable from 1=004 to 9= Tsq Squared value of the trend variable Ln PL Logarhm of price of workers, measured by dividing total wages by the number of workers Ln PK Logarhm of price of capal premises, measured by amortizations divided by total assets Ln PF Logarhm of price of capal-funding, measured by financial cost divided by total liabilies Ln TR Logarhm of total receipts including TV receipts and sponsoring, 008= W Club's games won during the period BC Dummy variable which is one for a club of a big club and zero elsewhere FP Proportion of foreign clubs in each club UCL Dummy variable which is one for a club participating in the UEFA Champions League and zero elsewhere UEL Dummy variable which is one for a club participating in the UEFA Europa League and zero elsewhere PD Points deduction due to corrupted practices adopted by some clubs SB Dummy variable which is one for a club in the second division, Serie B, during the period and zero elsewhere

24 Table 3. Posterior mean parameters estimates Variables Parameter Coefficient SE Constant Cons T β * T β * PL β3 0.30* PK β4 0.90* TR β * W β ½ (PL) β ½(PK) β ½(TR) β * ½ (W) β PL*PK β * PL*TR β * PL*W β PK*TR β PK*W β * TR*W β * BC ρ1-0.8* FP ρ 0.081* UCL ρ * UEL ρ * PD ρ5-0.00* SB ρ Error term v 0.55* non-negative random error μ 0.017* Number of observations Nobs 17 Number of erations Iterations Note: * significant parameter at 1% level. 4

25 Table 4. Efficient scores N. obs. Italian Clubs Mean Efficiency ranks 1 A.C. Milan A.S. Roma Cagliari C F.C. Int. Milano Fiorentina V Juventus F.C S.S. Lazio U. S. Sampdoria U.S.C. Palermo Udinese C A.C. Siena Parma FC AC Bologna US Lecce Ascoli Calcio AS Livorno Atalanta AC Chievo Brescia Calcio FC Empoli Reggina Calcio 0.96 SSC Napoli Catania Calcio Genoa Mean Median 0.96 Std. Dev