Productivity and efficiency at english football clubs: a random coefficient approach
| Published date | 01 November 2021 |
| Author | Guohua Feng,Todd Jewell |
| Date | 01 November 2021 |
| DOI | http://doi.org/10.1111/sjpe.12178 |
PRODUCTIVITY AND EFFICIENCY
AT ENGLISH FOOTBALL CLUBS:
A RANDOM COEFFICIENT APPROACH
Guohua Feng* and Todd Jewell**
ABSTRACT
This paper analyzes productivity and efficiency of English professional football
clubs from 1981–1982 to 2010–2011, using a random coefficient stochastic dis-
tance frontier (SDF) model. Our Bayes factor analysis indicates that this
model is strongly favored over the commonly used fixed coefficient SDF
model. Our empirical results show that clubs in our sample operate at differ-
ent levels of technical efficiency and technical change. Our further analysis
using ordered logistic regression suggests that technical efficiency is more
important than technical change in predicting whether clubs in our sample are
promoted or relegated.
II
NTRODUCTION
In the recent past, measurement of performance/efficiency in professional
sports has attracted a great deal of attention in the sports economics literature
(see, for example, Koop, 2002; Cooper et al., 2009). The purpose of this pre-
sent study is to contribute to this literature by applying, for the first time, a
random coefficient stochastic frontier model to assess the productivity and effi-
ciency of clubs in English (and Welsh) professional football
1
. Most studies in
the literature follow the classic works of Rottenberg (1956) and Scully (1974)
and view the operation of professional football clubs as a production process
that transforms sports inputs (such as labor and capital) into sports outputs
(such as attendance, revenue, or on-field success). Methodologically, this liter-
ature has been dominated by two approaches: the non-parametric data envel-
opment analysis (hereafter DEA) and the parametric stochastic frontier
analysis (hereafter SFA).
*University of North Texas
**Texas State University
1
Barros et al. (2009) estimated a true random effects stochastic frontier model, which is
essentially a special case of the random-coefficient stochastic frontier model used in this
paper. For a discussion on differences between the true random effects stochastic frontier
model and the random-coefficient stochastic frontier model, see Greene (2005).
Scottish Journal of Political Economy, DOI: 10.1111/sjpe.12178, Vol. 68, No. 5, November 2021
©2018 Scottish Economic Society.
571
First put forward by Charnes et al. (1978), the DEA approach is a linear
programming technique where the efficient frontier is formed as the piecewise
linear combination that connects the set of best practice observations in the
dataset under analysis, yielding a convex production possibility set. The esti-
mated efficient frontier can then be used to calculate various productivity and
efficiency measures, such as technical change and technical efficiency. The
SFA approach, based on the seminal works of Aigner et al. (1977) and Meeu-
sen and Broeck (1977), involves the estimation of a specific parameterized effi-
cient frontier with a composite error term consisting of non-negative
inefficiency and noise components. The parametric frontier can be specified as
a production, cost, profit, or distance frontier, depending on data availability
and the issue under investigation. As with the DEA approach, the estimated
frontier can then be used to compute productivity and efficiency measures of
interest.
As pointed out by Dietl et al. (2012), it is common practice in the sports lit-
erature to assume that owners of professional sports clubs maximize either
profits or wins; however, these authors further point out that (p. 285): “These
assumptions are restrictive and not supported by the evidence.” In the case of
European professional football, Garcia-del-Barrio and Szymanski (2009) pro-
duce estimates of predicted league ranking for clubs in the English and Span-
ish leagues under the assumption of profit maximization and under the
assumption of win maximization (Table 5, p. 58-59). The authors compare
these predictions to actual league rankings and conclude that clubs behave
more like win-maximizers than like profit-maximizers. However, their results
cannot be seen as definitive since the authors make several simplifying
assumptions for estimation purposes. Furthermore, while it appears that –as
stated by the authors –constrained win-maximizing behavior is a good
approximation of clubs’ behavior on average, a closer look at the Garcia-del-
Barrio and Szymanski (2009) results tells a more nuanced story for individual
clubs. Specifically, behavior for the top-10 clubs in English football is clearly
better approximated by win maximization, but the behavior of bottom clubs
is more-closely approximated by profit maximization. The top-10-ranked Eng-
lish clubs have an average absolute difference between actual and predicted
ranking of 3.2 places for win maximization and 24.1 places for profit maxi-
mization, but for the bottom-10-ranked clubs, the average difference is 13.5
for win maximization and 2.0 for profit maximization.
In the context of the present paper, the observations of Dietl et al. (2012)
and the results of Garcia-del-Barrio and Szymanski (2009) suggest that the
“true” objective function for English football clubs falls somewhere between
pure win maximization and pure profit maximization. Dietl et al. (2012) create
a theoretical model of utility maximizing behavior with an objective function
including both profits and wins, in which clubs assign different weights to the
two objectives. Such a model of utility maximization fits well into the litera-
ture on productive efficiency in association football, since existing literature
commonly uses several different measures of output. The multiple outputs can
be generally classified as on-field production, measures such as wins or league
572 GUOHUA FENG AND TODD JEWELL
Scottish Journal of Political Economy
©2018 Scottish Economic Society
points, and off-field production, generally measured as revenues due to lack of
appropriate data on profit. For example, Barros and Leach (2007) estimate
efficiency using a cost-function frontier for the English Premier League and
three outputs: total league points (on-field), total revenue (off-field), and total
attendance (off-field). Barros et al. (2009) use a similar methodology to esti-
mate productive efficiency in the Spanish Primera Liga.
The aforementioned papers also indicate the importance of dealing with
unobserved heterogeneity in production. If, as posited by Dietl et al. (2012),
clubs maximize some weighted average of wins and profit, then it is likely that
some unobserved factors lead to different weighting among clubs, which will
lead to productive heterogeneity. And if, as shown in the results of Garcia-
del-Barrio and Szymanski (2009), some English clubs behave consistent with
win maximization and some with profit maximization due to unobserved fac-
tors, then productive heterogeneity clearly exists and must be dealt with in an
estimation of the production technology. One potential source of unobserved
production heterogeneity is club management. Recent studies find that in the
United Kingdom, football clubs with different ownership structures have dif-
ferent financial management approaches, and thus different technologies
(Hamil and Chadwick, 2010; Wilson et al., 2013). For instance, foreign-owned
clubs, usually take an aggressive approach to financial management, investing
heavily in adopting the latest and most advanced training technologies and
facilities and hiring world-class players. In contrast, supporter-owned clubs,
with their commitment to community benefit, normally take a prudent
approach to financial management, and thus are less likely to invest heavily in
the latest training technologies and facilities and the best players. Besides
ownership structure, there are other factors that could cause unobserved tech-
nology heterogeneity among football clubs, which include, but are not limited
to, club history and market size. Given variation in financial management, as
well as wide disparities in market size, we expect that unobserved technology
heterogeneity is widespread among football clubs in the United Kingdom.
Thus, an appropriate analysis will model productivity and efficiency in the
presence of unobserved technology heterogeneity.
To account for unobserved technology heterogeneity among English foot-
ball clubs, we, for the first time in the sports economics literature, estimate a
random coefficient translog stochastic distance frontier (hereafter SDF) model
(see, for example, Greene, 2005 and 2008). This model has the advantage of
allowing its coefficients to vary across sports clubs according to a multivariate
normal distribution, thus allowing each sports club to have its own efficient
frontier (i.e., production technology). In other words, production technology
is modeled in a club-specific manner.
Compared with the commonly used fixed coefficient translog SDF model,
the random coefficient translog SDF model can provide a second-order
approximation to each club’s underlying “true” efficient frontier. This is
because the coefficient vector of the latter model consists of two components:
a deterministic mean vector that is common to all sport clubs and a random
vector that captures technology heterogeneity. The first component can
EFFICIENCY AT ENGLISH FOOTBALL CLUBS 573
Scottish Journal of Political Economy
©2018 Scottish Economic Society
Get this document and AI-powered insights with a free trial of vLex and Vincent AI
Get Started for FreeStart Your Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
