Journal of Sports Economics Market Competition and ...

Article

Market Competition andThreshold Efficiency inthe Sports Industry

Young Hoon Lee1, Hayley Jang1,and Sun Ho Hwang1

AbstractPrevious studies of competitive balance (CB) have analyzed the variations in gameoutcomes that is the second moment of winning percentage. This article differs in twoaspects. First, it analyzes market competition with respect to efficiency. Second, itanalyzes efficiency distribution (in particular, the third moment of the efficiency dis-tribution and the efficiency bound). It also suggests the efficiency bound as a newmeasure of market competition. By applying stochastic frontier models to a panel dataset of the European football leagues (English Premier League, Spanish La Liga, ItalianSerie A, and German Bundesliga), it derives important implications. First, the minimumefficiency estimates seem to reveal information relevant to market competition andadditional information from the conventional CB measure. Second, differences in theshapes of the efficiency distribution curves across the four leagues imply that the fourleagues faced different environments in terms of market competition.

Keywordsmarket competition, minimum efficiency, competitive balance, stochastic frontiermodels, football

Introduction

A joint product is a peculiar characteristic that is unique to the sports industry and

cannot be observed in other industries. The two sports teams (firms) are able to

1 Department of Economics, Sogang University, Seoul, Korea

Corresponding Author:

Young Hoon Lee, Department of Economics, Sogang University, Baekbeom-ro, Mapo-gu, Seoul 121-742,

Korea.

Email: [email protected]

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produce an indivisible product when they play each other in the same field. The

importance of competitive balance (CB) of playing talents among teams is driven

by this factor because two teams with equal strength generally produce a tight

match, which fans prefer. Neale (1964) called this the ‘‘league standing effect,’’

and said, ‘‘The closer the standings, and within any range of standings the more

frequently the standings change, the larger will be the gate receipts’’ (p. 3). There-

fore, studies on CB occupy a significantly large portion of the literature of sports

economics (e.g., Fort & Quirk, 1995; Noll, 1988; Szymanski, 2003). Fort and

Maxcy (2003) categorized the study of CB into the analysis of CB itself and the

relationship between CB and fan demand. The former study covers measurements

of CB, the impact of regulation changes on CB, and time-series analysis of CB,

while the latter study tests for uncertainty of outcome hypothesis.

This article focuses on the former study and approaches the study of CB in a

different way from previous studies. All of the previous studies examined the ulti-

mate outcome of matches, winning percentage, and the dispersion of wins across

member teams when they measure CB. That is, they analyzed CB by using the sec-

ond moment of winning percentage. For example, the relative standard deviation

of actual win percentage to the idealized standard deviation (RSD) is the second

moment of win percentage. However, the higher moments may include valuable

information relevant to CB. A positive skewness (the third moment) of win per-

centage implies that there are a few extremely good teams and the number of teams

with below 0.5 is greater than half of the total members, while a negative skewness

implies that there are a few teams with an extremely low win percentage and the

number of teams with above 0.5 is greater than half of the total members. The rem-

edy will be different depending on the sign of the skewness. In the case of positive

skewness, CB is worsened because of the teams with extremely high levels of

talent, meaning that a remedy would be most effective when it focuses on those

top teams. The luxury tax adopted in major league baseball may be an example

of this. On the other hand, imposing a high salary floor may be a legitimate remedy

for enhancing CB in cases of negative skewness.

This article differs from the previous studies in two aspects. First, it analyzes

market competition by examining technical efficiency. Second, it examines not only

the second moment of efficiency but also other characteristics of the distribution, in

particular, the threshold efficiency (efficiency bound). There have been empirical

studies on the relationship between market competition and productivity (De

Loecker, 2011; Dunne, Klimek, & Schmitz, 2008; Holmes & Schmitz, 2010; Matsa,

2011; Syverson, 2004). They presented empirical evidence that increased competi-

tion led to productivity improvement. In particular, Syverson (2004) pointed out the

importance of the efficiency bound in the way the market competition influences the

distribution in the market since low-productivity firms cannot survive when market

competition is tight. He presented two distributions of productivity: one for plants in

markets above median competition and another for plants in markets below median

competition.1 As expected, the mean (SD) of productivity in the high-competition

2 Journal of Sports Economics



market is higher (smaller) than the mean (SD) in the low-competition market. In

addition, the distribution of the high-competition market is skewed toward the left

(a negative skewness). That is, the minimum productivity is higher in the high-

competition market than in the low-competition market.

The minimum efficiency may also be informative in the sports industry. It can

be interpreted as the threshold efficiency for survival. League structure, the

strength of revenue sharing, and governance structure may influence market com-

petition. In an open league with relegation and promotion, the low-tier teams must

make their best efforts to build up efficiency. They are generally ‘‘low-budget

teams’’ and have to figure out an efficient way to win and to stay in the first divi-

sion. On the other hand, the low-tier teams in a closed league do not face the risk of

being thrown out of their league every season. The minimum efficiency is expected

to be different, based on league structure. Sports teams in East Asia are generally

supported by major corporations, while sports teams in North America and Europe

operate as independent businesses. It is expected that there is less competition in

East Asian sports leagues, since financial losses are subsidized by parent compa-

nies. The governance structure may influence the competition level and the min-

imum efficiency.

Recently, several studies in the literature of stochastic frontier models (SFMs)

have shown interest in the minimum level of efficiency (Almanidis, Qian, &

Sickles, 2014; Feng & Horrace, 2012; Hwang & Lee, 2014; Lee & Lee, 2013).

Almanidis, Qian, and Sickles (2014) and Lee and Lee (2014) focused on threshold

inefficiency. They implicitly perceived the argument of Syverson (2004) and spec-

ified their models, reflecting the fact that inefficient firms cannot survive in the

real world and, thus, there should be a bound of inefficiency. For example, Alma-

nidis et al. assumed the one-sided distribution of inefficiency as the tail-truncated

normal or the doubly truncated normal distribution. Incorporating threshold inef-

ficiency into SFMs not only improves the explanatory power of regression but

also allows the parameterization of the threshold inefficiency.

This article introduces the minimum efficiency as an alternative measure of

market competition. It is understood that this measure is not directly related to the

level of game outcome uncertainty but is closely related to market competition

that ultimately influences the balance of playing talents across member teams.

It applies the SFMs with the minimum efficiency to the panel data set of the

European football leagues (English Premier League, Spanish Primera Liga, Italian

Serie A, and German Bundesliga). We adopt both the semi-parametric and para-

metric approaches to compare efficiency distributions of the four leagues. The

study of Schmidt and Sickles (1984) is regarded as demonstrating the semi-

parametric approach since it does not impose any parameterization on the ineffi-

ciency distribution and the threshold efficiency is not considered in the model.

By applying this model, we estimate the efficiency of all individual teams

and compare the efficiency distributions of the four leagues. Hwang and Lee

(2014) constitute the extension to Lee and Lee (2014). This model imposes the

Lee et al. 3



group-specific minimum efficiency on their model specification and then is used

in our study to compare minimum efficiency among the four leagues. This is the

parametric approach, as it assumes a distribution of inefficiency and there are para-

meters defining the distribution.

The main purpose of this article was not to compare the market competition

levels of the four European football leagues in depth. Instead, it proposes an alter-

native measure of market competition and evaluates its validity by the applied

study. This article found that there are reasonably large variations in the minimum

efficiency across leagues and that the shape of the efficiency distribution is not the

same as the shape of the win percentage distribution. Moreover, the rank of the min-

imum efficiency among the four leagues is also not the same as the rank of RSD, the

conventional CB measure. We believe that our introduction of the alternative measure

of market competition and the empirical findings contribute to the literature of CB

since they nest information that is not found in previous studies on CB.

This article is organized as follows. In the second section, we introduce both the

semi-parametric and parametric SFMs. Data sources and the descriptive statistics are

discussed in the third section. Empirical results and their discussion are presented in

the fourth section. Finally, the fifth section contains our concluding remarks.

Econometric Models

In order to examine the distribution of efficiency, we utilize two different SFMs. The

first SFM is developed by Schmidt and Sickles (1984), which has been used widely.

This model assumes the time invariance of efficiency and is a semi-parametric

approach since it does not impose any distributional restriction on efficiency.

Another SFM is by Hwang and Lee (2014); this model focuses on the estimation

of efficiency bound and comparison of efficiency bounds across markets or groups.

It assumes a uniform distribution of technical inefficiency. A production function

and a parameter of inefficiency bound can be estimated simultaneously by the

method of moments or the maximum likelihood estimation (MLE), while the effi-

ciency of an individual firm is calculated by the conditional expectation that was

originally proposed by Jondrow, Lovell, Materov, and Schmidt (1982).

The SFMs were proposed by Aigner, Lovell, and Schmidt (1977, ALS) and

Meeusen and van den Broeck (1977). The SFM is of the form

yi ¼ aþ x0ibþ vi � ui; i ¼ 1; . . . ;N ; ð1Þ

where yi is a log of output. xi is a K-dimensional vector of exogenous variables and

b is the K-dimensional vector of parameters to be estimated. The vi represents an

uncontrollable disturbance term. The ui is a technical inefficiency (more spe-

cifically, logged output loss due to technical inefficiency) term and ui � 0. The

disturbances ui and vi are distributed independently of each other and of the




regressors. It is often assumed that vi is distributed normally with zero mean and

variance of s2v . ALS assumed ui is distributed either with a half normal density

or with an exponential density. Various SFMs arose by assuming different one-

sided distributions of ui. For example, Stevenson (1980) and Greene (1990)

assumed a truncated normal distribution and a gamma distribution, respectively.

In panel data setting, Schmidt and Sickles (1984) imposed the following produc-

tion function.

yit ¼ aþ x0itbþ vit � ui ¼ x0itbþ ai þ vit; i ¼ 1; . . . ;N ; t ¼ 1; . . . ; T ; ð2Þ

where ai ¼ a� ui. Equation 2 is exactly the same as the conventional panel data

model with individual effects. Thus, it can be estimated by the fixed effects (the

within estimation) and random effects (the generalized least squared (GLS) estima-

tion) treatments. They proposed the following max operator2 for the estimation of

technical inefficiency, ui and we will examine the distribution of the estimates.

ui ¼ a� ai; a ¼ maxi ai: ð3Þ

Recently, Almanidis et al. (2014) and Lee and Lee (2014) developed SFMs by

focusing on efficiency bound. Lee and Lee assume ui to be distributed uniformly

with a parameter y, that is, ui � Uð0; yÞ. Therefore, the probability density function

of ui is given by

f uið Þ ¼1

yIð0;yÞ uið Þ; ð4Þ

where Ið0;yÞðuiÞ is an indicator function and y > 0. This means that the support is

defined by the parameter y. The parameter y is the upper bound of the distribution

of ui, and we may call it the inefficiency threshold.3 Because the inefficiency

threshold represents the maximum level of inefficiency or minimum level of effi-

ciency, the parameter y identifies not only the dispersion of inefficiency but also

the degrees of competition. Hwang and Lee (2014) extended this model in order

to allow researchers to be able to compare efficiency bounds across markets or

across groups.

Hwang and Lee (2014) assumed the time invariance of inefficiency in the same

way as Schmidt and Sickles (1984), and thus Equation 2 is their regression equa-

tion. They also assumed ui to be distributed uniformly but allow for a different

parameter of y in different markets. That is, the probability density function of

ui is given by

fjðuiÞ ¼1

yj

Ið0;yjÞðuiÞ; i 2 Gj; j ¼ 1; . . . ;G; ð5Þ

where an individual firm i belongs to market j. This model allows for market-

specific inefficiency bounds. Hwang and Lee (2014) derived the probability density

function of ei ¼ vi � 1T ui, where 1T is a T dimensional vector of ones as

Lee et al. 5



fjðeiÞ ¼1

yj

1

ð2pÞðT�1Þ=2sT�1V

ffiffiffiffiTp exp � 1

2

ðei � 1T�eiÞ0ðei � 1T�eiÞs2

V

� �

Fyj þ �ei

sV=ffiffiffiffiTp

� �� F

�ei

sV=ffiffiffiffiTp

� �� ;

ð6Þ

where �ei ¼ ð1=TÞP

eit and F is a cumulative standard normal distribution.

This model can be estimated by the MLE and the method of moments. It is well

known that the maximum likelihood estimators are asymptotically efficient, but

both methods provide us with consistent estimators and our panel data sample is

not large.4 Therefore, this article utilizes the method of moments as explained

below. After estimating the production function (2) by either the within or GLS

estimator, we can estimate the variance of vi and yj by the following equations that

are derived by moments.

s2v ¼

T

T � 1m2 ð7Þ

y2j ¼ 12 m�2;j �

T

T � 1m2

� �for i 2 Gj; ð8Þ

where m2 is the sample second moment of the error term in the within trans-

formed production function, m2 � E½e2it� and ei � MT yi � Xibð Þ5 and m�2;j is the

demeaned sample second moment of the error term in the production function,

m�2;j � E½e�it � Eðe�itÞ�2

and e�it � yit � a� x0itb for i 2 Gj. Finally, the inefficien-

cies of individual firms are estimated by the conditional expectation method

of Equation 9:

EjðuijeiÞ ¼�sVffiffiffiffi

Tp F

yj þ �ei

sV=ffiffiffiffiTp

� �� F

�ei

sV=ffiffiffiffiTp

� �� 1

fyj þ �ei

sV=ffiffiffiffiTp

� �� f

�ei

sV=ffiffiffiffiTp

� �� ei:

ð9Þ

Data and Descriptive Statistics

We constructed a panel data set of four major European football leagues (English

Premier League, Spanish Primera Liga, Italian Serie A, and German Bundesliga)

over three seasons (2006-2007, 2008-2009, and 2010-2011). The source of our

data is www.transfermarkt.com, which has been used in many sports economics

studies (Battre, Deutscher, & Frick, 2009; Bryson, Frick, & Simmons, 2013; Frick,

2007). Production functions need to be estimated in order to obtain technical effi-

ciency estimates. The output of a soccer team is wins or points, and playing talents




are inputs. The website evaluates the market value of players based on their

collection of experts’ and supporters’ opinions. Torgler and Schmidt (2007) inves-

tigated the correlation between players’ effective reported salaries and estimated

market values as provided by Transfermakt.de6 and found a relatively strong pos-

itive correlation (.735). Finally, we constructed a panel data set with 234 observa-

tions for 105 teams. The promotion and relegation system makes it unbalanced.

Table 1 shows descriptive statistics for our sample data set. We calculated total

points in a season as 3 points for a win and 1 point for a draw. Bundesliga has a

smaller number of matches in a season than the other three leagues, and this dif-

ference results in lower average points. Thus, we use average points per match

in our regression. It is inferred that Bundesliga and Primera Liga are more

balanced than the Premier League and Serie A since the SDs of win percentage and

points in the former are smaller than those in the latter. On the other hand, Primera

Liga had the most variations in playing talents across member teams, while

Bundesliga had the least variations.

Figure 1 reveals the kernel density function of the winning percentage of each

league over the three seasons.7 It is clear that all four distributions are skewed to

the right. There are a few extremely outperforming teams in each league. Therefore,

the number of teams with a winning percentage below 0.5 is larger than that with

above 0.5. These positively skewed distributions are evidence that analysis on the

higher moments can provide additional information. For example, it is likely that a

few outstanding teams are the main source of competitive imbalance. Then, reme-

dies focusing on the few teams may be effective if a league decides to enhance CB.

Table 1. Descriptive Statistics.

Variable Observations Mean SD Maximum Minimum

Premier League Win% 60 0.50 0.18 0.93 0.20Total points 51.90 15.51 90.00 28.00Players valuea 1.59 1.16 4.30 0.33

Primera Liga Win% 60 0.50 0.16 0.94 0.23Total points 52.67 14.73 96.00 28.00Players valuea 1.25 1.22 6.02 0.29

Serie A Win% 60 0.50 0.18 0.97 0.17Total points 51.9 15.70 97.00 24.00Players valuea 1.11 0.85 3.46 0.23

Bundesliga Win% 54 0.50 0.16 0.82 0.22Total points 47.00 12.91 75.00 26.00Players valuea 0.89 0.56 3.09 0.26

Total Win% 234 0.50 0.17 0.97 0.17Total points 50.97 14.87 97.00 24.00Players valuea 1.22 1.02 6.02 0.23

Note. aMillion Euro.

Lee et al. 7



Empirical Results

Equation 2 is our production function for the four European football leagues. The

dependent variable, yit, is the winning percentage (Win%) or points per game. The

inputs in sports industry are playing talents and Value is our proxy variable for

playing talents. Since a quadratic form is adopted, xit ¼ fValue;Value2g.8 In the

manufacturing industry, various specifications of production have been studied

and typical functions, such as Cobb–Douglas and Translog production functions,

have been discovered. However, the specification of sports production function

has not been studied seriously yet. Our strategy was to estimate both linear and

logged production functions and then compare the estimates in order to check

robustness upon functional specification. Because of the joint product characteris-

tic of the sports industry, the outputs of a sports team (wins) are determined not

only by a given team but also by rival teams. An increase in the amount of playing

talent of a sports team does not necessarily guarantee increases in wins. The num-

ber of wins in a season may decrease if other teams hire more playing talents. It is

inferred that relative playing strength would be a more legitimate input variable.

Therefore, we make the playing talent variable, Value, to be a relative variable

by dividing it by league average playing talent.

Table 2 reveals the estimation results of Schmidt and Sickles (1984). The four

different specifications of production function are estimated. The winning percent-

age is a dependent variable in the first and second columns and Value (a relative

measure of playing talent) is included as a linear form in the first column and as a

Figure 1. Kernel Density Function of Winning Percentages.




logged form in the second. The dependent variable is points per game (Points) in

the third and fourth columns while the linear specification of production function

is adopted in the third column and the logarithmic specification in the fourth col-

umn. The four different specifications of production function generate similar esti-

mation results and the explanatory powers are more or less equal to each other. For

example, comparing the two Win% equations, the coefficient estimate of Value2 is

negative, but the coefficient estimate of (ln Value)2 is positive. However, both esti-

mates in the first and second columns produce diminishing marginal products of

Value. The last row presents the Hausman test results and the null hypothesis that

the random effects specification is correct cannot be rejected. Therefore, both

within and GLS estimates are consistent, but GLS estimates are more efficient.

We will discuss the GLS estimates of the Win% regression equation with the

logged Value hereafter.

Figure 2 displays the kernel density functions of technical efficiency estimates

for the four different football leagues that are calculated by the max operator of

Equation 3. That is, this distribution is obtained by the semi-parametric approach

of Schmidt and Sickles (1984). It is somewhat surprising that the distributions in

Figure 2 are distinctly different from those in Figure 1, which contains winning

percentage. The winning percentage distributions shown in Figure 1 were skewed

to the right, and all four distributions of different leagues are reasonably similar to

each other. However, the distributions of efficiency are noticeably different across

leagues and positive skewness can be found only in the English Premier League

according to Figure 2. There are a few extremely efficient teams in the Premier

League and the median efficiency is lower than the mean efficiency. On the other

Table 2. Production Function Estimates.

Variables Win% Win% Points lnPoints

Panel 1: Within estimationValue 0.206* (2.85) 0.472* (2.79)Value2 �0.013 (�0.80) �0.025 (�0.62)lnValue 0.191* (4.59) 0.299* (4.29)(lnValue)2 0.072* (2.02) 0.093 (1.56)

R2 .828 .828 .829 .826Panel 2: GLS estimation

Value 0.304* (11.78) 0.667* (11.36)Value2 �0.039* (�5.15) �0.075* (�4.38)ln Value 0.214* (23.11) 0.344* (19.63)(ln Value)2 0.040* (3.12) 0.028 (1.21)

Constant 0.253* (15.66) 0.527* (60.84) 0.827* (22.45) 0.345* (21.18)R2 .825 .825 .827 .822Hausman test 2.776 [.250] 2.041 [.360] 1.984 [.371] 2.913 [.233]

Note: The numbers given in parenthesis are t values and those given in square brackets are p values.*5% significance level.

Lee et al. 9



hand, the German Bundesliga has a symmetric distribution of efficiency estimates,

while the distributions in Primera Liga and Serie A are likely to be skewed to the

left. In particular, there are several extremely inefficient teams in Serie A. Table 3

also reveals descriptive statistics of the efficiency estimates obtained by the semi-

parametric approach. The mean efficiency is the highest in Primera Liga, whereas

it is the lowest in Serie A. The SD is the smallest in Primera Liga, in which the

distribution is skewed to the left the most. The estimation results of Primera Liga

(high mean, small variance, and negative skewness of efficiency) are consistent

with Syverson’s (2004) argument relevant to market competition. That is, our esti-

mation results with the semi-parametric approach imply that Primera Liga faces

the tightest competition among the four leagues. The Premier League seems to

be located on the opposite side. Its mean efficiency is located in the middle, but

the variance of efficiency is the largest and the skewness is positive, implying that

Figure 2. Kernel Density Function of Efficiency Estimates: the Semi-parametric Approach.

Table 3. Descriptive Statistics: Efficiency Estimates of Individual Teams by the Semi-Parametric Approach.

League Mean SD Maximum Minimum Skewness

Premier League 0.814 0.064 1.000 0.718 0.773Primera Liga 0.820 0.045 0.891 0.734 �0.359Serie A 0.809 0.056 0.943 0.674 �0.249Bundesliga 0.813 0.052 0.898 0.715 �0.004




a reasonably large number of inefficient teams can survive in the first division.

Therefore, it is inferred that the Premier League has the least tight competition

among the four different leagues.

Turning our attention to the efficiency estimates of the parametric approach, the

minimum efficiency of each league can be estimated by this approach. The mini-

mum efficiencies are estimated by the method of moments of Equation 8 and the

estimates are presented in the first column of Table 4. The means of efficiency esti-

mates with the semi-parametric approach and the conventional measure of CB and

RSD are presented in the second and third columns, respectively. Let’s compare

the minimum efficiency estimates with the mean efficiency estimates first and then

compare those with the RSDs. From this comparison, we may be able to see how

the implications of minimum efficiency estimates are different from those of the

mean efficiency and the conventional CB measure, which have been examined

in previous studies. Comparing the mean efficiency estimates driven by the

semi-parametric approach, Primera Liga has the highest minimum efficiency

(0.721) and mean efficiency (0.820) and both measures suggest that Primera Liga

has the tightest market competition. However, there are a few minor disparities

between the parametric and semi-parametric approaches. For example, the compe-

tition level of Bundesliga is the lowest with respect to minimum efficiency but is in

the middle with respect to the mean efficiency across the four leagues.

Bundesliga and Primera Liga have smaller RSDs than the Premier League and

Serie A. Thus, it is inferred that Bundesliga and Primera Liga are more balanced

than the other two leagues with respect to RSD. In other words, Bundesliga has the

tightest competition in the football field. According to the minimum efficiency

estimates, the tightest competition exists in Primera Liga, whereas the least com-

petition is in Bundesliga and this empirical finding contradicts the results of RSD.

The Premier League and Serie A have the same level of minimum efficiency and

their RSDs are rather similar to each other. In summary, the market competition

implied by the minimum efficiency is generally similar to that by the RSD, but

there are also some contradictory implications. The findings, that the minimum

efficiency estimation draws some different implications with regard to market

competition from the mean efficiency or the conventional CB measure, are not

revelatory since CB is concerned with game outcome, while efficiency distribution

Table 4. The Minimum Efficiency Estimates: The Parametric Approach.

MinimumEfficiency

Mean of Efficiency(the Semi-Parametric Approach) RSD

Premier League 0.697 0.814 2.244Primera Liga 0.721 0.820 1.960Serie A 0.697 0.809 2.256Bundesliga 0.679 0.813 1.889

Lee et al. 11



concerns not only game outcome but also input usages. The different implications

may be empirical evidence that minimum efficiency can reveal additional informa-

tion relevant to market competition.

Figure 3 displays the kernel density functions of technical efficiency estimates

for the four different football leagues that are calculated by the conditional expec-

tation of Equation 9. Note that the conditional probability density function fjðuijeiÞis not the same as the uniform density function even though ui is assumed to be

uniform. The kernel density functions in Figure 3 are somewhat different from

those in Figure 2. For example, the distributions in Figure 3 are located in a nar-

rower range. However, the main findings in Figure 2 can be observed in Figure 3

too. The Premier League has the efficiency distribution skewed to the right,

whereas the distribution of Primera Liga is skewed to the left. Based on the values

of skewness, it is inferred that Primera Liga faces the tightest competition, while

the Premier League has the least tight competition.

Turning attention to the efficiency of individual teams, Table 5 reports the most

efficient teams and the least efficient teams of each league based on the efficiency

estimates of the parametric approach. Reading FC and Manchester United are the

top two teams in efficiency ranking of the Premier League, while Charlton Athletic

and Newcastle United are the least efficient teams. Considering the fact that

Reading FC appeared in the Premier League only once during our sample periods,

the league standing is not directly equal to the efficiency ranking. Real Sporting

de Gijon in Primera Liga is another example that is generally a low-tier team in

league standing but is placed high in the efficiency ranking. Reading FC and Real

Figure 3. Kernel density function of efficiency estimates: the parametric approach.




Sporting de Gijon would have limited budgets and low payrolls in their leagues;

thus, they are unable to rise to the top in league standings even though they operate

their teams in technically efficient ways.

Table 6 (Table 7) selects the top (bottom) five teams from each league based on

average league standing during the sample period. It also reveals their efficiency

rankings and efficiency estimates. Generally speaking, highly ranked teams were

relatively efficient but not necessarily. For example, all top teams in Bundesliga

except for Bayern Munchen are very efficient. On the other hand, FC Barcelona

and Real Madrid, which are perennial winners in Primera Liga, have relatively low

Table 5. The Most Efficient and the Least Efficient Teams.

LeagueBestEfficiency

Second-BestEfficiency

BestInefficiency

Second-BestInefficiency

Premier League Reading FC(.961)

Manchester United(.927)

Charlton Athletic(.735)

NewcastleUnited (.739)

Primera Liga Malaga CF(.890)

Real Sporting deGijon (.881)

Real Betis (.756) UD Almerıa(.759)

Serie A FC Empoli(.932)

FC Genus (.879) AS Bari (.718) ACR Messina(.730)

Bundesliga Dortmund(.896)

Kaiserslautern (.894) Monchengladbach(.725)

Bremen (.733)

Note. The numbers given in parenthesis are efficiency estimates.

Table 6. Top 5 Teams in Average League Standings and Efficiency Estimates.

TeamRank

EfficiencyRank Team

TeamRank

EfficiencyRank Team

Premier League Primera Liga

1 2 Manchester United (.961) 1.3 17 FC Barcelona (.807)2.3 10 FC Chelsea (.838) 1.7 23 Real Madrid (.770)3.7 8 FC Liverpool (.845) 4.3 8 Sevilla FC (.852)4 5 Arsenal FC (.853) 4.3 15 Valencia CF (.814)6 18 FC Everton (.786) 4.7 4 Villarreal CF (.866)

Serie A Bundesliga

1.3 3 Inter Mailand (.877) 3 20 Bayern Munchen (.766)2.7 13 F.C. Milano (.820) 5.3 4 VfB Stuttgart (.872)4.5 20 Juventus (.797) 5.3 8 Leverkusen (.844)4.7 19 AS Roma (.799) 5.3 1 Dortmund (.896)6 4 Lazio Rom (.866) 6 3 Nurnberg (.880)

Note. The numbers given in parenthesis are efficiency estimates.

Lee et al. 13



efficiency. This implies that these two teams won many championships with large

payrolls and, thus, there is a lot of room to save on payrolls while still being able

to win championships if they can enhance their efficiency. Compared with Table 7,

it is clear that the average efficiency rankings of the top teams are higher than those

of the bottom in league standings. The bottom five teams in league standings are

also found to be inefficient technically. This implies that teams are placed in the

bottom of league standings not only because of small budgets but also because

of inefficient management of playing talent.

Table 8 also examines the technical efficiencies of the bottom teams in league

standings as a way to compare surviving teams in the first division with relegated

teams during the sample period. Five teams from each group are selected based

on average league standing. That is, the five surviving teams have the lowest league

standings on average among teams that remained in the first division during the sam-

ple period and the five relegated teams are also located on the lowest average league

standing among teams that were relegated at least once during the sample period.

Generally, efficiency rankings of surviving teams are better than those of relegated

teams even though there are several exceptions. For example, West Ham United and

Newcastle United in the Premier League are the exceptions since they had remained

in the first division in all three seasons, but their efficiency rankings are 24 and 26,

respectively. The average ranking of the five teams from each group suggests that

the surviving teams are more efficient than the relegated teams, since the survivors’

average rankings are higher than the relegated teams’ average rankings in the Pre-

mier League, Primera Liga, and Serie A. Bundesliga is the exception in that the

Table 7. Bottom 5 Teams in Average League Standings and Efficiency Estimates.

TeamRank

EfficiencyRank Team

TeamRank

EfficiencyRank Team

Premier League Primera Liga

20 25 FC Watford (.741) 20 24 Gimnastic de Tarragona (.763)19 9 FC Blackpool (.842) 19 22 Hercules CF (.777)19 27 Charlton Athletic (.735) 19 18 CD Numancia (.803)18 20 Birmingham City (.776) 18 21 Celta de Vigo (.782)18 12 Sheffield United (.827) 17 26 Real Betis (.756)

Serie A Bundesliga

20 27 ACR Messina (.730) 18 17 FC St. Pauli (.779)20 28 AS Bari (.718) 17 21 Karlsruher SC (.762)19 23 Brescia (.770) 17 14 Aachen (.801)19 26 Ascoli (.740) 16.3 24 Monchengladbach (.825)18.5 21 U.S. Lecce (.786) 15 15 Bielefeld (.788)

Note. The numbers given in parenthesis are estimated efficiency.




Tab

le8.

Effic

iency

Com

par

ison

ofth

eR

emai

ned

Tea

ms

inth

eFi

rst

Div

isio

nan

dth

eR

eleg

ated

Tea

ms

toLo

wer

Div

isio

n.

Rem

ained

Tea

mEffic

iency

Ran

kR

eleg

ated

Tea

mEffic

iency

Ran

kR

emai

ned

Tea

mEffic

iency

Ran

kR

eleg

ated

Tea

mEffic

iency

Ran

k

Pre

mie

rLe

ague

Pri

mer

aLi

ga

Wig

anA

thle

tic

15

FCW

atfo

rd25

Get

afe

CF

9G

imnas

tic

de

Tar

rago

na

24

Wes

tH

amU

nited

24

FCBla

ckpool

9O

sasu

na

14

CD

Num

anci

a18

New

cast

leU

nited

26

Char

lton

Ath

letic

27

Dep

ort

ivo

11

Her

cule

sC

F22

Bla

ckburn

Rove

rs13

Bir

min

gham

City

20

Mal

lorc

a6

Cel

tade

Vig

o21

Bolton

Wan

der

ers

7Sh

effie

ldU

nited

12

Ath

letic

Clu

b16

Rea

lBet

is26

Ave

rage

rank

17.0

18.6

Ave

rage

rank

11.2

22.2

Seri

eA

Bundes

liga

Chie

vo18

AS

Bar

i28

Monch

engl

adbac

h24

FCSt

.Pau

li17

Cag

liari

9A

CR

Mes

sina

27

Fran

kfurt

22

Kar

lsru

her

SC21

Sam

pdori

a24

Bre

scia

23

Wolfs

burg

19

Aac

hen

14

Cat

ania

8A

scoli

26

Bre

men

22

Bie

lefe

ld15

Udin

ese

15

U.S

.Le

cce

21

Han

nove

r5

Cott

bus

10

Ave

rage

rank

14.8

25.0

Ave

rage

rank

18.4

15.4

Not

e.Fi

vete

ams

with

the

low

est

aver

age

leag

ue

stan

din

gar

ese

lect

edfr

om

each

group.

15 at PENNSYLVANIA STATE UNIV on May 17, 2016jse.sagepub.comDownloaded from


survivors’ average efficiency ranking is 18.4, but the relegated teams have a higher

average ranking of 15.4. In particular, the gaps between the average efficiency

rankings between the surviving teams and the relegated teams are large in Primera

Liga (11.2 vs. 22.2) and Serie A (14.8 vs. 25.0). These results are consistent with

Syverson’s (2011) assertion which is called Darwinian selection or reallocation

effect. Darwinian selection is the process in which inefficient firms fall behind and

then the market moves toward more efficient firms and the efficiency threshold

rises. The empirical results of Primera Liga are consistent with the reallocation

effect, as the least efficient teams exited the market (the first division), as seen

in Table 8, and the minimum efficiency is the highest among the four leagues in

Table 4, and its efficiency distribution is skewed to left the most in Table 3. In

Serie A, the survivors’ average efficiency is also significantly higher than the rele-

gated teams’ average efficiency, so this implies that inefficient ‘‘firms’’ fell out of

the market. Table 3 shows that the efficiency distribution of Serie A is skewed to

the left, implying that the exits raised the efficiency bound. The empirical results

of the Premier League and Bundesliga are also consistent with the reallocation

effect. As shown in Table 3, the efficiency distribution of Bundesliga is more or

less symmetric and that of the Premier League is skewed to the right, implying that

the efficiency bounds are low. The minimum efficiency estimates in Table 4 con-

firm this implication. Bundesliga has the lowest minimum efficiency and the Pre-

mier has the second lowest. The potential reason can be found in Table 8. In these

two leagues, ‘‘firms’’ pushed out of the market are not more significantly ineffi-

cient than surviving ‘‘firms.’’

Conclusions

This article aimed to contribute to sports economics literature by developing an

alternative measure of market competition. Unlike previous studies, which have

focused on game outcome, winning percentage, and its second moment for analyses

of CB, we examined (1) the efficiency distribution (in particular, efficiency thresh-

old) and (2) the third moments (skewness) of the distribution. We adopted SFMs for

this purpose. The first SFM of Schmidt and Sickles (1984) has been used in various

empirical studies, and we analyzed the distribution of efficiency estimates obtained

by this model. The second SFM of Hwang and Lee (2014) was only developed

recently and has not been applied yet. The model allows for estimation of the effi-

ciency bound in a market and comparison of the efficiency bounds across different

markets in a sample. This is an alternative measure of market competition.

The empirical results that we obtained by applying the two SFMs to the unba-

lanced panel data set of the four major European football leagues permit us to

derive several remarkable implications. First, the minimum efficiency estimates

seem to reveal information relevant to market competition, additional to the infor-

mation provided by the mean efficiency or the CB measure. For example, the




distributions of efficiency estimates in the four leagues are strikingly different

from those of winning percentage. Second, the skewness and shapes of the effi-

ciency distribution curves are significantly different across the four leagues. This

implies that the four leagues faced somewhat different environments in terms of

market competition. This is a bit surprising because the player movement rulings

are uniform across European football leagues. There may be league-specific or

country-specific characteristics influencing market competition. Third, we found

that the reallocation effect, which has been observed in previous productivity stud-

ies of manufacturing industry (Foster, Haltiwanger, & Syverson, 2008; Syverson,

2011), is also confirmed in our empirical exercise of European football leagues. A

market is more efficient and has a higher efficiency threshold as inefficient teams

are drawn out of the market through the relegation system. In our empirical results,

this reallocation effect could be clearly observed. Primera League, in which inef-

ficient teams were driven out of the first division, could achieve a higher efficiency

threshold as well as a higher average efficiency. On the other hand, Bundesliga,

which failed to throw inefficient teams out of the first division, could not achieve

a high-efficiency bound. Fourth, the large variations in technical efficiency across

leagues and across different member teams imply that there is a lot of room to save

in the cost of playing talents. Lago, Simmons, and Szymanski (2006) argued that

overinvestment in players is one of main sources of financial crisis in European

football leagues. In other words, the overinvestment can be remedied if a team was

able to enhance its managerial efficiency.

With respect to future studies with our market competition measure, we would

like to address the following suggestions. First, more exact specifications of pro-

duction function would improve accuracy of efficiency estimates. As workforces

can be divided into skilled or unskilled workers, playing talents in a sport team can

be categorized based on skills. For example, Lee and Berri (2008) divided total

playing talents by positional playing talents (guards, small forwards, and big men)

in their analysis of basketball production. Second, studies on determinants of mar-

ket competition in sports industries would help in deriving practical policy impli-

cations. The league structure, regulations regarding revenue sharing, governance

structure, and regulations regarding foreign players, among other factors, may

influence market competition and, thus, efficiency threshold.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, author-

ship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship,

and/or publication of this article: This work was supported by the National Research Founda-

tion of Korea Grant funded by Korean Government (NRF-2013S1A3A2053312).

Lee et al. 17



Notes

1. Specifically, Syverson (2004) divided markets by density. Consumers’ substitutability

increases in a market with high density, and thus it can be inferred that firms in markets

above median density face tight competition.

2. For the properties of this max operator, refer to Kim, Kim, and Schmidt (2007).

3. The efficiency threshold can be calculated by e�y.

4. Olson, Schmidt, and Waldman (1980) compared the small sample properties of the max-

imum likelihood estimator (MLE) and the method of moments (corrected ordinary least

squared) estimator in the model of Aigner, Lovell, and Schmidt through the Monte Carlo

simulation. They found their mean biases and root mean squared errors (RMSEs) are sim-

ilar to each other, but RMSEs of the method of moments estimator are smaller than those of

MLE when the sample size is smaller than 200.

5. MT is the within transformation matrix defined as MT ¼ IT � ð1=TÞ1T 10T .

6. Transfermakt.de is the German version of transfermarkt.com.

7. The kernel density functions of points are analogous to Figure 1. They are available upon

request.

8. The cubic and quartic specifications of production function are often found in the labor

economics literature. However, adding them in our regression did not increase explanatory

power noticeably.

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Author Biographies

Young Hoon Lee, PhD, is a professor in the Department of Economics at Sogang University.

His research fields include econometrics (panel data models and productivity analysis) and

sports economics.

Hayley Jang, is a graduate student in the Department of Economics at Sogang University. Her

research fields include applied microeconomics and sports economics.

Sun Ho Hwang is a graduate student in the Department of Economics at Sogang University.

His research field includes econometric theory.




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