School of Economics and Management
TECHNICAL UNIVERSITY OF LISBON
Department of Economics
Carlos Pestana Barros & Nicolas Peypoch
Carlos Pestana Barros , Albert Assaf and Fabio Sá-Earp
A Comparative Analysis of Productivity Change in Italian and
Portuguese
Airports
Brazilian Football
League Technical
Efficiency: A
Bootstrap Approach
WP 27/2009/DE/UECE
WP 006/2007/DE
_________________________________________________________
_________________________________________________________
WORKING PAPERS
ISSN Nº 0874-4548
Brazilian Football League Technical Efficiency: A Bootstrap Approach
Carlos Pestana Barros1 , Albert Assaf2 and Fabio Sá-Earp 3
1. Instituto Superior de Economia e Gestão; Technical University of Lisbon Rua
Miguel Lupi, 20; 1249-078 - Lisbon, Portugal and UECE (Research Unit on
Complexity and Economics). Phone: +351 - 213 016115; fax: +351 - 213 925 912.
Email: [email protected]
2
Centre for Tourism and Services Research, Victoria University, Australia.
albert.assaf @ vu.edu.au.
3. Department of Economics , University of Rio de Janeiro, Brazil. Email:
[email protected]
Abstract: This paper introduces a two stage bootstrapped DEA-Data Envelopment
analysis model to analyze the technical efficiency of Brazilian first league football
clubs, using recent input and output data over the period 2006-2007. In the first stage
a bootstrapped DEA model is used to derive the efficiency scores and in the second
stage, the determinants of technical efficiency are identified using a bootstrapped
truncated regression. Results from the model estimation show that the efficiency
ranking is mixed with some clubs of similar characteristics showing different
performance. Factors which contributed to these results as well as other policy
implications are provided.
Keywords: Football, Brazil, Bootstrap, DEA, Technical Efficiency.
1
UECE (Research Unit on Complexity and Economics) is financially supported by FCT (Fundação
para a Ciência e a Tecnologia), Portugal. This article is part of the Multi-annual Funding Project
(POCI/U0436/2006).
1. Introduction
Research on technical efficiency of football clubs is common in Europe
(Dawson, Dobson and Gerrard, 2000A; Carmichael, Thomas and Ward, 2001; Barros
and Leach; 2006A; 2006B; Haas, 2003A; Espitia-Escuer and García-Cebrian, 2004;
Kern and Süssmuth, 2005) USA (Hofler and Payne, 1996; Hadley et al., 2000; Einolf,
2004), but generally uncommon in other football leagues. The growing importance of
this topic is related to the fact that there is a direct relationship between the success of
sports clubs on the pitch and their financial wealth in the long run. In the past,
contradictory claims have been made regarding the main objectives of a sports club.
For example, Sloane (1971) suggests that sport results are the objective of a sport
club. A different focus was later taken by El Hodiri and Quirk (1971), Neale (1964),
and Quirk and Fort (1992) who suggest that the financial profit is the objective of a
sport club. These two concepts were then consolidated by Vrooman (2000) who
suggests that sport results and financial results are the simultaneous objective of sport
clubs.
The current literature therefore acknowledges the importance of combining
sport and financial results. At the club level, these two dimensions are also parts of
management objectives. It is therefore not surprising that many recent studies have
focused on the efficiency of sports clubs, given that the financial results and
operational performance are strongly related (Coelli et al., 1998). Indirectly,
efficiency is also related to sport results as club success drives financial and
operational performance. In contrast to simple financial indicators, the importance of
efficiency is that it provides a more comprehensive measure of performance, enabling
2
therefore an accurate identification of areas of potential improvements. Efficiency
also sets the stage for a direct benchmarking between competing sport clubs.
In the present study, the aim is to extend the performance modelling of sport
clubs to Brazil, a country with a long standing reputation in football performance.
Despite the fact that Brazilian football is the biggest exporter of international players,
no studies have so far addressed the performance of this league. In estimating the
efficiency of Brazilian clubs, this study also aims to introduce a methodological
innovation. Previous studies in the area have mainly relied on the simple Data
Envelopment Analysis (DEA) or Stochastic frontier models to analyse efficiency.
While both methods offer comprehensive measures of performance they suffer from
several limitations. One of the major limitations of DEA, for example, is that it is a
deterministic technique and thus does not account for measurement error in deriving
the efficiency measures. SFA is again subject to criticism, as it requires a prespecification of the functional form in the estimation of cost or production frontier
technologies. SFA also requires larger sample size than DEA.
To account for these limitations we use in this paper the DEA bootstrapping
methodology recently developed by Simar and Wilson (1999,2000, 2007), in which it
is possible to keep the advantages of DEA, and also performs statistical hypothesis
testing on the DEA efficiency scores. In this way it is also possible to overcome the
large sample requirement of the SFA method. The study does not stop on the
estimation of efficiency, but also uses a second stage regression to explain the
variations in the efficiency results. In doing so, the paper uses an innovative double
bootstrapping methodology to account for the dependency problem of DEA efficiency
3
scores which violates the model assumption of regression analysis. The main idea is
to substitute the incorrect estimators of the standard error of the regression with the
bootstrapped estimates of these standard errors. More details are given in later in the
paper.
The remainder of the paper is organized as follows: Section 2 briefly describes
the contextual settings of the Brazilian first football leagues. Section 3 reviews
previous studies on efficiency in the sport literature. Section 4 outlines the procedure
used to carry out the empirical analysis. Sections 5 and 6 present the data and
empirical results. Section 7 discusses the economic implications of the results as well
as conclusions of the main findings.
2. Contextual Setting
Brazilian football clubs analysed in the present paper comprise those listed in
Table 1. Some operational characteristics for the year 2007 are displayed.
<<Insert Table 1>>
The financial variables are in thousand real, the Brazilian money. The table
displays 20 main old renowned Brazilian football clubs such as Botafogo, Flamengo
and Vasco da Gama. From the table emerges that the leading clubs in terms of
attendance are Flamengo (745207), Santos (685672), São Paulo (515204) and
Cruzeiro (446568), which compare with the smaller club in terms of attendance, São
Caetano (18280).
4
All Brazilian Premier League clubs had operational deficits and huge debts. In
2007, the 20 biggest clubs received 560 million euros (the same amount Real Madrid
plus Manchester United received the same year) and had 900 million euros as debts
with government, other clubs and ancient players. These clubs are the bigger
exporters of players for the European and Asian football leagues, which is the main
source of income that balances the financial accounts.
Brazilian clubs receipts are very much smaller than Europeans. The population is
poorer so tickets and marketing receipts are relatively minor.
<<Insert Table 2>>
The planned realization of “Football World Cup” in 2014 has improved the
expectations that some public investments in stadiums will appear and improve the
economic conditions of main football clubs. Additional contextual characteristic of
this sport market is the shallow income available for sport attendance. This
shallowness is revealed in the above table as well as in the failure of Timemania, a
sport lottery aiming to help football clubs to pay their debts. In the 39th round,
Timemania has only achieved 27% of its expected value. Moreover, the football clubs
TV receipts has been almost constant in the last 10 years (Casual Report, 2008).
Timemania is not competitive in the lottery market – these prizes are no more than
30% of those of the best important Brazilian lottery.
3. Literature Survey
5
There are three main approaches to measure efficiency, two of which are
observed in sports: First, the index numbers approaches, such as the Tornquist and
Malmquist total factor productivity index, (Coelli, Estache, Perelman and Trujillo
2003, p. 27) which measure the productivity and efficiency changes over time. Such
indexes can also be extended using the endogenous-weight total factor productivity
approach (Yoshida 2004). Such approach has not yet been used in sports. A second
popular methodology is the econometric or parametric approach such as the stochastic
frontier approach, adopted by Dawson, Dobson and Gerrard (2000A), Dawson,
Dobson and Gerrard (2000B), Carmichael, Thomas and Ward (2001), Kahane (2005),
Barros and Leach (2006B, 2007), Ascari and Gagnepain (2007); Barros, Garcia-delBarrio and Leach (2008) , Barros, del Corral and Garcia-del-Barrio (2008) and
Barros, Garcia-del-Barrio and Leach (2009). As mentioned before, a main
disadvantage of the stochastic frontier is that it requires a pre-specification of the
functional form in the estimation of cost or production frontier technologies, and also
requires larger sample size than DEA.
The DEA approach has also been quite common, recently adopted by EspitiaEscuer, García-Cebrian (2004), Fizel and D’Itri (1997), Haas (2003B), and Barros
and Leach (2006). For a more extended literature revision see Barros, Garcia-delBarrio and Leach (2009). What is clear from the existing literature is that none of the
existing papers has adopted the bootstrapped DEA procedure, despite its advantage
over the traditional DEA or stochastic frontier approaches. The focus on Brazilian
football has also been ignored in the literature. Therefore the present research is
innovative in this context.
6
4. Methodology
4.1. Data Envelopment Analysis (DEA)
In this paper we employ DEA, a non-parametric linear programming method
that estimates “best practice” frontiers relative to producers’ measured efficiency
scores. The method is well-known in the literature, and can simply derive efficiency
measures, using the following linear programming formulation:

n
n

i =1
i =1
λˆ ( x, y ) = max λ λ y ≤ ∑ γ i yi ; x ≥ ∑ γ i xi for (γ 1 ,..., γ n )

such that ∑ γ i = 1;γ i ≥ 0, i = 1,..., n 
i =1

n
(1)
where yi is vector of outputs , xi is a vector of inputs, γ is a I ×1 vector of constants.
The value of λˆi obtained is the technical efficiency score for the i-th football club. A
measure of λˆi =1 indicates that a club is technically efficient, and inefficient if λˆi >1.
The value 1 / λi defines a technical efficiency (TE) score which varies between zero and one.
This linear programming problem must be solved n times, once for each club in the
sample. For more detailed literature on the method refer to Fried et al. (2008).
4.2. Bootstrapping DEA
7
As mentioned before, DEA is a linear programming methodology and thus has
no statistical properties or account for measurement error. Simar and Wilson (1998,
1999, and 2000) have recently addressed this problem and showed that it is possible
to obtain statistical properties via the use of the “bootstrap” approach. In a simple
definition, bootstrapping efficiency scores involve replicating the data generating
process (DGP), generating an appropriately large number of pseudo-samples and then
applying the original estimator to these pseudo-samples. In the case of DEA, the
general aim of the bootstrap approach is to simulate the original sample B times, each
time recalculating the parameter of interest which is the DEA efficiency score. This
will allow B estimates of the parameter, and thus makes it possible to generate an
empirical distribution for the parameter of interest. The empirical distribution can then
be used to be used to construct confidence interval for the DEA efficiency scores, and
also obtain other statistical properties. Simar and Wilson (1998) also suggested an
improvement to their bootstrapping approach by adopting a smoothing procedure
which accounts for the fact that the DEA efficiency score is bounded between zero
and one. The complete bootstrap algorithm can be illustrated as follows:
1. Compute the efficiency scores λ̂ for each club i = 1,..., n , by solving the linear
programming model in (1)
2. Use the kernel density estimation and the reflection method to generate a
{
}
{
*
random sample of size n from λˆi ; i = 1,..., n , providing λˆ1*b ,.., λˆnb
}
3. Compute a pseudo data set {( x, yib* ), i = 1,..., n} to form the reference bootstrap
technology
8
*
of
4. Using this pseudo data, compute the bootstrap estimate of efficiency λˆnb
λˆi for each i = 1,..., n
5. Repeat steps 2-4 a large number B of times in order to obtain a set of estimates
{λˆ ; b = 1,..., B}
*
ib
4.3. Accounting for Environmental Variables
The bootstrap approach used in this paper is also extended to account for the
impact of environmental variables on efficiency. These variables are viewed as
possibly affecting the production process, but not under the control of managers.
Determining how these variables influence on efficiency is essential for determining
performance improvement strategies.
One of most common approaches in testing the impact of environmental
variables on efficiency involve the use of two-stage Tobit regression approach
wherein DEA efficiency estimates are obtained in the first stage and then regression
on environmental variables in a parametric, second-stage analysis. Simar and Wilson
(2007) have however recently criticised this approach, and suggested instead a double
bootstrap approach in which it is possible to improve the accuracy of the regression
estimates. Before illustrating their procedure we first present the following model:
λˆi = zi β + ε i
(2)
9
where zi is a vector of environmental variables which is expected to affect the
efficiency of clubs under consideration and β refers to a vector of parameters with
some statistical noise ε i . A popular procedure in the literature is to use the Ordinarily
Least Square (OLS) regression to estimate this relationship. However, as described in
Simar and Wilson (2007), this might lead to estimation problems mainly related to the
correlation and dependency problems of the efficiency scores which violate the
regression assumption that ε i are independent of zi . The importance of the Simar and
Wilson (2007) procedure is that it produces with bias corrected estimates for the
parameters in the regression model. We describe their bootstrap algorithm in the
following steps:
1. Use the original data to compute λˆi = λˆ ( xi , yi ) , i = 1,..., n , by the DEA
method in (1).
2. Compute the parameter estimates β̂ and σˆ ε from the truncated regression in
(2), using the maximum likelihood method.
3. Loop over the next four steps (3.1-3.4) B1 times to obtain a set of bootstrap
estimates {λi*,b , b = 1,...B1} .
(
3.1.For i = 1,..., L , draw ε i* from N ( 0, σˆ ε ) with left truncation 1− βˆ ' zi
)
3.2.Compute λi* = βˆ ' zi + ε i* , i = 1,..., n .
3.3.Set xi* = xi , yi* = yi λˆi / λi* , for all i = 1,..., n .
3.4.Compute λˆi* = λ ( xi , yi ) , i = 1,..., n , by replacing ( xi , yi ) by ( xi* , yi* ) .
10
4. Compute the bias-corrected estimator using the bootstrap estimates and the
ˆ
ˆ (λˆi ) .
original estimates and the original estimates ( λˆi = λˆi − bias
ˆ
ˆ
5. Estimate the truncated regression of λˆi on zi , yielding ( βˆ , σˆˆ ) .
6. Loop over the next three steps (6.1-6.3) B2 times to obtain a set of bootstrap
 ˆ

estimates  βˆb* , σˆˆ b* , b = 1,.....B2 


( )
6.1. For i = 1,,,,,, n , ε i is drawn from N 0, σˆˆ with left truncation at
1− βˆˆ ' z  .

i


ˆ
6.2. For i = 1,,,,,, n , compute λi** = βˆ ' zi + ε i** , i = 1,..., n .
6.3. Use the maximum likelihood method again to estimate the truncated
ˆ
regression of λi** on zi , providing estimates ( βˆ * , σˆˆ * )
7. Construct confidence intervals for the efficiency scores.
4. Data
The estimation of the bootstrapped DEA model in this study involves a balanced
panel data of 20 Brazilian football clubs over the period 2006-2007 (2 × 20=40
observations). The data were obtained from the Causal Report (2008) on Brazilian
Football Finance, published for the first time in December 2008.
The selection of input/output variables for this study follows primarily previous
studies in the literature. Data availability was also a factor in determining the list of
inputs/outputs variables. On the outputs side we use: (i) number of attendance; (ii)
total receipts in thousand real and (iii) points in a league, while inputs are: (iv)
operational cost (excluding labour costs) in thousand reals (v) total assets in thousand
11
reals and (vi) team payroll in thousand reals. In this way sport and financial variables
are combined in estimating technical efficiency, allowing therefore a more
comprehensive performance measure. The football clubs used in the analysis as well
as the data characteristics are listed in Tables 1.
<Table 3 here>
5. Results
Table 3 shows the bootstrapped technical efficiency results of Brazilian football
clubs between 2006 and 2007. Note that we followed the advice of Simar and Wilson
(1999) and we used 2000 bootstrap replications (B=2000) in obtaining the results.
According to the authors this should provide an adequate coverage of the confidence
intervals.
<Table 4 here>
The first column of Table 3 provides the original DEA efficiency scores, the
second column provides the DEA bootstrapped efficiency scores, the third column
provides the BIAS (computed as the difference between original DEA and
bootstrapped DEA) of the original DEA, the fourth column provide the standard error
of the bootstrap values, and the fifth and sixth columns it presents the lower and upper
bound of the DEA-bootstrap confidence intervals.
It is evident from the first column in Table 3 that there are four efficient
football club on the frontier of best practices with a technical efficiency score equal to
1(Grémio, São Paulo, São Caetano and Vitória). However, when considering the
bootstrapping results (column 2 of table 3) none of the football clubs appear to be
close to the frontier. Since the bias is large relative to the variance in every case, the
bootstrap estimates are preferred to the original estimates (Simar and Wilson, 1998).
The original efficiency estimates lie also outside the estimated confidence intervals in
the last two columns of Table 3 in every instance. This is due to the bias in the
12
original estimates, and the fact that the confidence interval estimates correct for the
bias. These results therefore reinforce the fact that the DEA double bootstrap model is
more superior to the traditional DEA model in estimating the efficiency scores of
Brazilian football clubs.
Relative to the second stage regression, we used the bootstrapping procedure
suggested by Simar and Wilson (2007) to overcome the serial correlation problem of
the DEA-efficiency estimates (for more details refer to Section 4.3). The model at this
stage can be expressed as follows:
λˆit = β + β1vicit + β 2 Defeatsit + β 3GoalsProit + β 4GoalsAgainstit + ε it
o
(3)
where λˆit is the bootstrapped technical efficiency score; vic is the number of victories
in the league; Defeats is the number of defeats in the league; GoalsPro is the
number of goals scored; GoalsAgainst against is the number of goals suffered, and
ε it is random error representing statistical noise. These sport variables aim to identify the
role of pit results on efficiency scores. The estimated coefficients and standard errors
for the model in (3) are presented in Table 4. Table 5 presents the results of equation
3.
<Table 5 here>
It is clear from that table 5 that all results are intuitive, with efficiency increasing with
the number of victories and goals pro and decreasing with defeats and goals against.
One possible justification to the results is that pit results and financial performance
are usually interlinked, and thus clubs success on the pitch is expected to be positively
correlated with technical efficiency. More discussions into the efficiency results as
well as the second stage regression are presented in the next section.
13
6. Discussions
This paper has proposed a simple framework to measure the technical efficiency
of Brazilian football clubs and the rationalisation of their management activities, with
a two stage procedure. The analysis is based on the bootstrapped DEA technical
efficiency and bootstrapped truncated regression. Technical efficiency scores were
presented for each football club.
It was clear from the standard efficiency scores in Table 3 that the most efficient
club is São Paulo Football, located in São Paulo, one of the largest Brazilian cities.
The second efficient football club is São Caetano a tiny football club from São
Caetano do Sul city in São Paulo state, located in the greater São Paulo Metropolitan
area. City location does not however seem to be playing a direct impact on efficiency.
Other regional clubs such as Grémio de Football Porto Alegrense, based in Porto
Alegre city, Rio Grande do Sul state and clube Esporte Vitória from Salvador da Baía
city, also appear to be highly efficient. Their efficiency is even higher than some city
clubs from big cities, such as Sociedade Esportiva Palmeiras a football club from São
Paulo city; Fluminense Football club and Clube de Regatas Vasco da Gama from
from the Rio de Janeiro city. Therefore, less efficient clubs are also from big cities,
since Rio de Janeiro is the second main Brazilian city
Another important finding from Table 3 is the large difference between the
standard and bootstrapped efficiency results. If we consider the bootstrapped results,
none of the football club appears to be close to full efficiency and even the rankings
are not preserved. This confirms previous results from Simar and Wilson (1998) who
argued that traditional DEA models tend sometimes to present firms as efficient,
when they are actually not. Based on the bootstrap results, the most efficient football
clubs ordered by their rank are: Coritiba football club from Paraná state, Santos
football club from Santos city in São Paulo State, Figueirense football club from
Florianopolis city and Gremio.
Brazilian clubs are encouraged to consider the
bootstrap results to determine their performance, given that the bootstrap accounts for
14
the limitations of the traditional DEA method. What is important however is that the
bootstrap results appear also confirm the hypothesis that city location or club size
does not impact directly on technical efficiency.
What can be said from the above results is that technical efficiency appears to
be specific to the internal characteristics of each club. In other words, clubs with
similar asset configurations might pursue different operational strategies which might
impact on their performance (Porter, 1998). Note that inefficiency might sometimes
be due to some management mistakes inside each club. From the results of the second
stage regression it was also confirmed that efficiency increases victories and goals pro
and decreases with defeats and goals against, signifying that the pit results and
efficiency are interlinked. Therefore, the general conclusion is that efficient football
clubs are those that have strong performance on both football and financial results.
What should Brazilian football clubs do to improve the efficiency? Firstly,
they should adopt a benchmark management procedure in order to evaluate their
relative position in the league combining football and financial results. The game
gives a sport rank, but financial ranks are not available in the market, rather they
should be combined to obtain efficient scores that blend sport and financial results.
This procedure will induce the adoption of managerial procedures for catching up
with the frontier of "best practices". As the frontier is shifting over time, an effort is
needed to catch up with it. A team's financial strength is its profitability, and the
team's main cost is player salaries. Therefore the management has to increase players’
quality with the aim to increase the winning on the pitch, and consequently earn more
money from ticket sales, concession income, and sales of broadcast rights. All of
these factors vary directly with market size. This is why teams in large cities tend to
get better players than teams in small cities.
What should be the public policy in this context? Efficiency improvement is a
way to increase earnings when the prices do not increase. Therefore, the government
should induce the football clubs to adopt sustainable procedures combining sport and
financial results. This regulatory procedure will result in sound football clubs that are
sustainable in the long term. Moreover, the government should decrease the number
15
of clubs in the league, since the constant debts and constant club earnings reveal that
the market is shallow and cannot support all the clubs presently in the first league
with financial equilibrium. The maintenance of the present context will induce the
continuation of the present financial unbalance of the Brazilian football clubs.
8. Conclusions
In this paper, the technical efficiency in a representative sample of Brazilian
football clubs was estimated over the period 2006-2007. The analysis is based on a
two stage approach, in which in the first stage a bootstrapped DEA index is adopted
and in the second stage the Simar and Wilson (2007) procedure is used to bootstrap
the DEA scores with a truncated regression.
In the first stage it is the concluded that the technical efficiency is higher in the
standard DEA scores than in bootstrapped DEA scores, signifying that there is
significant efficiency differences when these two methods area adopted. In the second
stage it is concluded that positive sport results are positively correlated with technical
efficiency while negative sport results are negatively correlated with technical
efficiency.
Benchmarks are provided for improving the operations of inefficient performing
football clubs. Several interesting and useful managerial insights and implications
from the study are discussed. The general conclusion is that a public policy aiming to
increase efficiency should rely on benchmark regulation with the aim to define an
adequate contextual setting for football clubs.
16
9. References
Ascari, G., & Gagnepain, P. (2007). Evaluating rent dissipation in the Spanish
football industry. Journal of Sports Economics, 8, 5, 468-490.
Barros, C.P.; Garcia-del-Barrio, P. & Leach, S. (2009). Analysing the technical
efficiency of the Spanish Football League first division with a random frontier model.
Applied Economics (forthcoming).
Barros, C.P., del Corral, J., & Garcia-del-Barrio, P. (2008). Identification of segments
of soccer clubs in the Spanish League First Division with a latent class model.,
Journal of Sports Economics, 9, 5, 451-469.
Barros, C.P., & Garcia-del-Barrio, P. (2008). Efficiency measurement of the English
Football Premier League with a random frontier model. Economic Modelling, 25,
5, 994-1002.
Barros, C.P., Garcia-del-Barrio, P., & Leach, S. (2008). Analyzing the technical
efficiency of the Spanish Football League first division with a random frontier
model. Applied Economics (forthcoming).
Barros, C.P., & Leach, S. (2006A). Analyzing the performance of the English F.A.
Premier League with an econometric frontier model, Journal of Sports Economics,
7, 4, 391-407.
Barros, C.P., & Leach, S. (2006B). Performance evaluation of the English Premier
League with Data Envelopment Analysis. Applied Economics, 38, 12, 1449-1458.
Barros, C.P., & Leach, S. (2007). Technical efficiency in the English Football
Association Premier League with a stochastic cost frontier. Applied Economics
Letters, 14, 731-741.
Carmichael, F., Thomas, D., & Ward, R. (2001). Production and efficiency in
Association Football. Journal of Sports Economics, 2, 3, 228-243.
Casual Report: Panorama Financeiro do futebol Brasileiro. December 2008. Causal
Auditores Independentes, SA; São Paulo, Brazil.
Coelli, T., Prasada Rao, D. S., & Battese, G. E (1998). An Introduction to Efficiency and
Productivity Analysis, Boston, Kluwer, Academic Publishers.
Coelli, T.J.; Estache, A.; Perelman, S. & Trujillo, L. 2003. A Primer on Efficiency
Measurement for Utilities and Transport Regulators. World Bank Institute, World
Bank, Washington D.C., USA.
17
Dawson, P., Dobson, S., & Gerrard, B. (2000A). Stochastic frontier and the temporal
structure of managerial efficiency in English Soccer, Journal of Sports
Economics, 1, 341-362.
Dawson, P., Dobson, S., & Gerrard, B. (2000B). Estimating coaching efficiency in
professional club sports: evidence from English Association Football. Scottish
Journal of Political Economy, 47, 4, 399-421.
El- Hodiri, M. & Quirk, J. (1971) An economic model of professional sport league.
Journal of Political Economy, 79, 1302-19.
Espitia-Escuer, M., & García-Cebrian, L.I. (2004). Measuring the efficiency of
Spanish First-Division Soccer Clubs. Journal of Sports Economics, 5, 4, 329-346.
Fred, H., Lovell, C.A.,& Shmidt, S. (2008). The Measurement of of Productive
Efficiency and Productvity Growth. Oxford University Press. UK
Haas, D.J. (2003A). Productive efficiency of English Football clubs – A Data
Envelopment Approach. Managerial and Decision Economics, 24, 403-410.
Haas, D.J. (2003B). Technical efficiency in the Major League Soccer. Journal of
Sports Economics, 4, 3, 203- 215.
Hadley, L., Poitras, M., Ruggiero, J., & Knowles, S. (2000). Performance evaluation
of National Football League clubs. Managerial and Decision Economics, 21, 6370.
Hofler, R.A. & Payne, J.E. (1996). How close to their offensive potential do national
football club clubs play. Applied Economics Letters, 3, 743-747.
Kahane, L.H. (2005). Production efficiency and discriminatory hiring practices in the
National Hockey League: a stochastic frontier approach. Review of Industrial
Organisation, 27, 1, 47-71.
Kern, M. & Süssmuth, B. (2005). Managerial efficiency in German Top League
Soccer: an econometric analysis of club performances on and off pitch, German
Economic Review, 6, 4, 485-506.
Neale, W. C. (1964) The peculiar economics of professional sports: a contribution to
the theory of the firm in sporting competition and in market competition.
Quarterly Journal of Economics, 78, 1, 1-14.
Porter, P., & Scully, G.W. (1982). Measuring managerial efficiency: the case of
baseball. Southern Economic Journal, 48, 642-650.
Quirk, J. & Fort, R. (1992) Pay Dirt: The Business of Professional Team Sport.
Princeton, N.J. Princeton University Press.
Sloane, P. (1971) The economics of professional football: The football club as a
utility maximizer. Scottish Journal of Economy, 17, 121-45.
18
Simar, L.., & Wilson, P. W. (1998). Sensitivity Analysis of Efficiency Scores: How to
Bootstrap in Nonparametric Frontier Models. Management Science, 44, 49-61.
Simar, L.,, & Wilson, P.W. (1999). Estimating and bootstrapping Malmquist indices.
European Journal of Operational Research, 115, 459-471.
Simar, L., & Wilson, P. W. (2007). Estimation and inference in two-stage, semi-parametric
models of production processes. Journal of Econometrics, l.136,.31-64.
Vrooman, J. (2000) The economics of American sport leagues, Scottish Journal of Political
Economy, 47, 364-98.
Yoshida, Y. (2004). Endogenous-Weight TFP Measurement: Methodology and its
Application to Japanese-Airport Benchmarking. Transportation Research Part E
40,151-182.
19
Table 1. Sample Characteristics (2007)
Year
unit
clubs
attendance (number)
total receipt
(R$1000)
points in the league
Operational cost
(R$1000)
Total assets
(R$1000)
Team payroll
(R$1000)
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Internacional
Grêmio
Juventude
São Paulo
AtléticoPR
Paraná club
São Caetano
Figueirense
Cruzeiro
Botafogo
Náutico
Vasco da Gama
Vitória
Coritiba
Corinthians
Palmeiras
AtléticoMG
Santos
Flamengo
Average
St.Dev
248371
416795
193858
515204
237645
213271
18280
274206
446568
319925
245331
287723
310741
184143
379591
334138
440789
685672
745207
360686
188871.11
155881
109031
62147
190081
54091
24910
23252
18981
77650
41160
19561
51079
11215
14916
134627
86290
58326
53102
89499
64840
50183.38
54
58
41
77
54
41
53
53
60
55
49
51
59
69
44
58
55
62
61
55
8.63
127239
132347
71911
336365
160800
59911
6001
27914
170130
55022
122498
227806
20727
60147
220550
262287
241581
200964
271589
138832
99910.08
164660
176688
83789
370964
167030
61464
6350
30091
176082
60857
120867
217190
16805
56098
211712
263557
240198
191500
250010
143459
101323.72
89818
88006
60033
301766
154570
58358
5652
25737
164178
49187
124129
238422
24649
64196
229388
261017
242964
210428
293168
134362
100988.66
20
Table 3: Characteristics of the variables
Variable
No. of Attendance
Total receipt
Points in the league
Operational cost
Mean
325519
55156
55.62
139758
Median
287401
50418
54.50
128155
St.Dev
178064
42613
9.05
107202
Min
18280
6544
36.00
853
Max
783625
190081
78.00
418177
Total assets
Team payroll
140203
139388
154058
109214
102080
116112
1372
532
370964
525762
Table 2: Football Tickets prices, marketing and TV receipts by football clubs (2002)
Country
Ticket médium price (US$)
German
18,1
France
15,1
UK
45,1
Italy
29,0
Spain
22,0
Brazil
5,0
Source: Melo (2002)
Tickets
(US$ million)
Marketing
(US$million)
TV
(US$ million)
TOTAL
180
106
372
258
159
18
228
92
386
119
116
20
460
410
730
400
283
130
863
608
1488
777
558
168
21
Table 4. Average Bootstrapped Efficiency Results (2006-2007)
Club
Internacional
Grêmio
Juventude
São Paulo
AtléticoPR
Paraná club
São Caetano
Figueirense
Cruzeiro
Botafogo
Náutico
Vasco da Gama
Vitória
Coritiba
Corinthians
Palmeiras
AtléticoMG
Santos
Flamengo
Fluminense
Average
Efficiency Score
0.9799
1.0000
0.7261
1.0000
0.8571
0.8243
1.0000
0.9656
0.8013
0.9058
0.8246
0.7196
1.0000
0.9317
0.8390
0.6559
0.8800
0.9912
0.8362
0.6795
0.8708
Bias Corrected
0.8303
0.8614
0.6670
0.8320
0.7406
0.7439
0.7808
0.8636
0.7499
0.8428
0.7759
0.6844
0.8108
0.8643
0.7622
0.6160
0.8266
0.8643
0.7537
0.6559
0.8303
22
Bias
0.1495
0.1386
0.0591
0.1680
0.1164
0.0803
0.2192
0.1020
0.0513
0.0629
0.0486
0.0351
0.1892
0.0674
0.0768
0.0399
0.0533
0.1268
0.0825
0.0235
0.1495
Standard
Error
0.0175
0.0075
0.0017
0.0154
0.0097
0.0026
0.0360
0.0048
0.0007
0.0011
0.0008
0.0004
0.0238
0.0014
0.0019
0.0006
0.0010
0.0083
0.0037
0.0003
0.0175
LB
0.7640
0.8188
0.6209
0.7883
0.7007
0.6994
0.7099
0.7918
0.7188
0.8015
0.7427
0.6563
0.7362
0.8181
0.7178
0.5815
0.7808
0.7908
0.7054
0.6256
0.7640
UB
0.9735
0.9929
0.7218
0.9925
0.8511
0.8179
0.9929
0.9594
0.7966
0.9006
0.8194
0.7161
0.9937
0.9258
0.8330
0.6524
0.8736
0.9839
0.8310
0.6775
0.9735
Table 5. Truncated second Stage Regression
Variable
Constant
Vict
Defeats
Goals Pro
Goals Against
Coefficient
t-statistic
0.6998**
4.1488
0.0074*
1.9850
-0.0028**
5.6000
0.0020**
2.8510
-0.0021
1.6210
* Significant at the 5% confidence level, ** Significant at the 10% confidence level
Number if iterations=2000
23