Contracts as rent-seeking devices: evidence from German soccer.
Feess, Eberhard ; Gerfin, Michael ; Muehlheusser, Gerd 等
I. INTRODUCTION
Recent theoretical research has identified a variety of ways how
contracts can be used as rent-seeking devices vis-a-vis third parties.
Examples include breach penalties, exclusivity clauses, retroactive
rebates or, in the context of labor markets, long-term contracts, and
noncompete clauses. As a result of such rent-seeking incentives, various
forms of inefficiencies may arise, for example, with respect to entry
decisions (Aghion and Bolton 1987; Chung 1992), investment incentives
(Feess and Muehlheusser 2003; Segal and Whinston 2000; Spier and
Whinston 1995), or the allocation of workers (Posner, Triantis, and
Triantis 2004). While these mechanisms are reasonably well understood
from a theoretical perspective, there is a lack of empirical research.
In this paper, we aim at empirically testing some of the crucial
qualitative properties of strategic contracting models. In doing so, we
develop a theoretical and empirical framework in the context of European
professional soccer. We argue that the issue of strategic contracting
arises naturally in this industry and that teams and players have a
joint incentive to use long-term contracts as rent-seeking devices.
In European professional soccer, the contracts between teams and
players are in principle binding throughout the agreed duration, but
they are frequently renegotiated before they expire when other teams
want to hire the player. This triggers a (re)negotiation process between
the player, the current team (incumbent), and the new team (entrant) in
which they bargain over whether or not to transfer the player to the new
team. (1) According to long-standing regulations in European
professional sports, holding a valid contract with the player gives the
incumbent team the right to veto the transfer, which allows to extract a
payment from the new team (the transfer fee) for letting the player go.
By contrast, after an important regime change induced by the so-called
Bosnian judgment in 1995, after a player's contract has expired, he
is free to move to any other team without requiring his old team's
consent. (2) As this weakens the incumbent team's bargaining
position, the joint renegotiation payoff of the initial contracting
parties (player and incumbent team) is higher when the player's
contract has not yet expired. (3) Moreover, this joint renegotiation
payoff may be increasing in the remaining duration of the player's
contract, as the incumbent team can threaten to "lock up" the
player for a longer period of time.
Under the rent-seeking motivation alone, the contracting parties
would prefer their contract to last as long as possible. In reality,
however, there are countervailing effects, and we focus on the
detrimental effect of long-term contracts on the likelihood of
transfers: By diminishing future teams' stake in eventual
renegotiations, long-term contracts reduce their incentive to actually
trigger renegotiations even in cases where transfers are mutually
beneficial. In deciding on the contract duration, the incumbent team and
the player will hence compare the benefit from a higher joint
renegotiation payoff in case of a transfer to the forfeited gains due to
a lower transfer probability. In our data, we indeed find that the
transfer probability strongly depends on whether a player's
contract is still valid or has already expired.
In our model, a potential new team first needs to decide on
acquiring information about the player's true value for it, and
then about whether or not to trigger a renegotiation process in order to
realize a transfer. (4) Acquiring such information, however, will only
be worthwhile for the new team when its expected renegotiation payoff in
case of a transfer is sufficiently large, which in turn depends on the
remaining duration of the player's contract with the incumbent
team. We consider the simplest feasible framework where, at the time of
a potential transfer, the player's contract is either expired or
lasts for one more period. Our model first predicts that in case of a
transfer, the joint renegotiation payoff of the incumbent team and the
player is higher for nonexpired contracts. This establishes the role of
contract durations as rent-seeking devices. Second, a player's
probability of being transferred is higher for expired contracts which
leads to the tradeoff just described. This is in the spirit of Aghion
and Bolton (1987) where trade with the entrant is deterred more often
when the fee for breach of contract is high.
In the empirical analysis, we use data from Germany's top
professional soccer league (the "Bundesliga"), and we have
information on 422 contracts, as well as player- and team-specific
information such as age, performance, position, experience, or final
league position and budgets, respectively. The empirical results
strongly support our theoretical predictions: while the joint
renegotiation payoff of the player and the incumbent team is far larger
when a player's contract has not yet expired, the probability for a
transfer to occur is significantly lower. Moreover, but less crucial for
our main research question, we find that, given that a contract has not
yet expired, the remaining contract duration has no significant impact
on the transfer probability. For the joint renegotiation surplus,
however, our results are less clear-cut, and we do find some evidence
that the contracting parties benefit from a longer remaining contract
duration. In any case, our findings suggest that long-term contracts are
indeed useful rent-seeking devices.
A. Relation to the Literature
The role of contracts as rent-seeking devices has been stressed in
the economic literature since Diamond and Maskin (1979) who analyzed a
search model where parties contract with each other but continue to
search for better matches. They show that there is an incentive to
stipulate high damages in the initial contract as this will increase the
payoff in the new partnership. As they note (see p. 294), "the
rationale for these contracts is solely to 'milk' future
partners for damage payments."
Aghion and Bolton (1987) emphasize the close relationship between
breach penalties, contract durations and an entrant's
"waiting" costs, as the penalty determines the effective
duration of a contract. They show how excessive breach penalties tend to
deter efficient market entry. (5) However, as pointed out by Spier and
Whinston (1995), these inefficient entry decisions are driven by the
absence of renegotiation, and they show that ex post efficiency can be
restored once renegotiation is possible. Similarly, Posner, Triantis,
and Triantis (2004) analyze the role of noncompete clauses in labor
contracts. Again, the inefficiencies generated by such contract clauses
depend on whether or not renegotiation is permitted. (6)
Our framework is in-between the two polar cases of excluding
renegotiation altogether and having a renegotiation process in which any
allocative inefficiency is eliminated, respectively: we do allow for
renegotiation, and transfers are also efficient when they occur.
However, the likelihood of renegotiation is endogenous and depends on
the terms of the contract. Another difference to Spier and Whinston
(1995) is that they consider renegotiation between the initial
contracting parties only, while also the entrant participates in the
renegotiation process in our framework.
Another inefficiency identified in the literature refers to
relation-specific investment incentives as considered in Spier and
Whinston (1995), who show that inefficiencies of strategic contracting
may arise even when ex post efficiency is ensured by renegotiations
because the contract terms lead to inefficient levels of
relation-specific investment. Segal and Whinston (2000) analyze how the
efficiency properties of exclusive dealing clauses depend on the type of
investments. Also focusing on investment incentives, Feess and
Muehlheusser (2003) compare the impact of different legal regimes in
European professional soccer on teams' incentives to invest in the
training of young players. While long-term contracts are also jointly
beneficial for the contracting parties in renegotiations, allocative
inefficiencies are not taken into account.
In our paper, we focus on a reduction of transfer probabilities as
the disadvantage of long-term contracts, countervailing the benefit from
rent-seeking. Alternatively, one could consider a potentially
detrimental effect in the form of lower effort incentives
("shirking") after a long-term contract is secured. (7) This
issue has sparked a large amount of empirical research in the context of
sports, but the evidence is mixed, and the results are very sensitive to
the empirical frameworks used, see, e.g., Marburger (2003), Bern and
Krautmann (2006), Krautmann and Donley (2009), Krautmann (1990).
Last, but not least, while our paper focuses on the rent-seeking
effect of long-term contracts and transfer fees, Tervio (2006)
emphasizes the positive role of transfer fees on the allocation of
players among teams. He assumes that player talent is initially
uncertain, but will be revealed in a first period, and that better
players have a higher marginal productivity in strong teams. Transfer
fees alleviate the efficient allocation of players as they enable small
teams to pay talent in the first period, which will then be transferred
to top teams if and only if capabilities turn out to be high. From a
theoretical point of view, we see our paper as complementary as both
aspects are likely to play an important role in reality: Transfer fees
facilitate the efficient allocation of players across teams due to the
mechanisms analyzed by Tervio (2006), but they may also prevent
efficient transfers due to rent-seeking motives.
The remainder of the paper is organized as follows: Section II
introduces a simple theoretical framework for analyzing the issue of
strategic contracting in the context of sports. The main model
predictions are then empirically tested in Section III. Section IV
discusses our findings and concludes.
II. THEORY
A. The Model
We consider a variant of the canonical buyer-seller framework with
the possibility of future entry as considered in the literature on
strategic contracting discussed in the introduction. We adopt it to our
context of European professional sports as follows:
At date t = 0, a player bargains with team i (the incumbent) over a
contract stipulating a wage W per period and a contract duration. To
make our points, it suffices to consider only two possible contract
durations, a short-term contract which lasts for one period (until date
t = 1), and a long-term contract which lasts for two periods (until date
t = 2). The player's career horizon is assumed to also last until t
= 2, such that it is fully covered by a long-term contract. After the
initial contract is signed at date t = 0, the player starts playing in
team i, where his productivity is Y > 0 per period throughout his
career. (8)
At date t = 1, a new team e (the entrant) may be interested in
hiring the player. The player's productivity in team e per period,
[Y.sub.e], is a random variable with two realizations, Ye = Y + [gamma]
where [gamma] > 0 or [Y.sub.e] = [Y.sub.L] < Y, both of which are
equally likely. Thus, it depends on the realization of [Y.sub.e] whether
or not the player is more productive in team e, and a transfer is only
mutually beneficial for [Y.sub.e] = Y + [gamma].
To find out the true value of the player's productivity, team
e must make a costly investment. For instance, it may need to collect
information about the player himself or it must figure out how well he
fits in its tactical system. The investment cost z is team e's
private information, and from the viewpoint of team i and the player at
the contracting stage, it is hence a random variable. For simplicity, we
assume that z can take on only two values, z [member of] {z, [bar.z]},
where Pr (z = [z.bar]) a [alpha] [member of] (0, 1) and Pr (z = [bar.z])
= 1 - [alpha]. As in Aghion and Bolton (1987), assuming private
information with respect to a cost parameter of the entrant is a
convenient way of modeling the basic idea that rent-seeking motives
might prevent entry even in cases where it might be mutually beneficial
to all parties. (9) After the investment decision is made, team e
decides whether or not to enter negotiations with team i and the player.
(10)
We follow the literature on incomplete contracts by assuming that
the eventual process of renegotiation occurs under complete information,
i.e., that the realization of [Y.sub.e] becomes common knowledge after
it has been revealed to team e. Also in line with the literature, we
assume throughout that at each stage, multiparty decisions are taken
cooperatively by all parties involved at that stage. (11) This implies
that single-party investment decisions are individually optimal.
Therefore, the choice of contract at date 0 maximizes the expected joint
surplus of the player and team i, while at date 1, team e will invest
whenever the cost (z) is lower than its own expected renegotiation
payoff. Finally, when it turns out that the player's productivity
is higher in team e (i.e., for [Y.sub.e] = T + [gamma]), he will be
transferred regardless of his contractual status with team i. For
[y.sub.e] - [Y.sub.L] < Y, the player keeps playing for team i until
his career ends at date t = 2. Figure 1 summarizes the sequence of
events and the respective parties involved. The analysis proceeds
backward.
B. Renegotiation
Assume that team e has invested and has learned that [Y.sub.e] = Y
+ [gamma]. Then, the player will be transferred at date 1, and for the
remaining time until the player's career ends at date 2, the
division of the total renegotiation surplus Y + [gamma] depends on the
player's contractual status: For nonexpired contracts, the
incumbent team has a veto right, which allows it to extract a transfer
fee from the new team. By contrast, after the contract has expired, the
player is free to move to the new team without requiring his old
team's consent.
[FIGURE 1 OMITTED]
For the surplus division in the resulting bargaining game, we use
the nucleolus solution as pioneered by Schmeidler (1969), and in
particular the approach by Leng and Parlar (2010) which provides a
closed-form solution for the resulting payoffs for the three-player
case. (12)
Out of all feasible coalitions and payoff divisions, the nucleolus
is the one that minimizes the difference between the value of the
coalition and the share of the player with the lowest payoff (the
"excess" or the "unhappiness of the most unhappy
player"). (13) It will become clear that all we need for our
results is that team e's share of the surplus is higher for expired
contracts compared to nonexpired ones. (14)
Recall that the player's contract ends at date t = 1 under a
short-term and at date t = 2 under a long-term contract. Denoting by R
[member of] (0,1) the remaining duration of the player's contract
at the renegotiation date 1, and by [V.sub.q] the payoff which coalition
q [member of] (p, i, e, ie, pi, pe, pie] can realize on its own, we have
[V.sub.p] = RW, [V.sub.e] = 0, [V.sub.i] = [V.sub.ie] = R (Y - W),
[V.sub.pi] = Y,
[V.sub.pe] = RW + (1-R)(Y + [gamma]), [V.sub.pie] = Y + [gamma].
For example, the player alone can generate a payoff equal to his
wage in team i for the remaining duration of his contract with team i
([V.sub.p] = RW), while for the same time period, team i alone would
receive the value of the player's service net of the wage payment
([V.sub.i] = R(Y - W)). Due to team i's veto power in case of a
non-expired contract, the coalition of the player and team e can achieve
a payoff only for the time period (1 - R), where the player's
contract with team i has already expired. (15) The different time
periods relevant for the renegotiation process are illustrated in Figure
2.
The parties' renegotiation payoffs [[PI].sub.j] R) for j = i,
e, p are given by the resulting nucleolus values which are derived in
the Appendix. (16) Moreover, we denote by [[PI].sub.ip](R) :=
[[PI].sub.p](R) + [[PI].sub.i] (R) the joint renegotiation payoff of
player and team i, where [[PI].sub.ip] (R) = T + [gamma] - [[PI].sub.e]
(R). This leads to the following result:
RESULT 1. Using the nucleolus solution to determine the division of
surplus at the renegotiation stage at date t = 1,
(i) the renegotiation payoff of team e is strictly higher when the
player's contract has expired, that is,
(1) [[PI].sub.e](0) = (1/2) [gamma] > (1/3) [gamma] =
[[PI].sub.e] (1)
(ii) the joint renegotiation payoff of the player and team i is
strictly lower when the player's contract has expired, that is,
(2) [[PI].sub.ip] (0) = Y + (1/2) [gamma] < Y + (2/3) [gamma] =
[[PI].sub.ip] (1)
[FIGURE 2 OMITTED]
Intuitively, as for part (i) when the player's contract with
team i is still valid (R = 1), all three parties are needed to realize
the additional surplus [gamma], which is then shared equally, so that
team e reaps (1/3)y. In contrast, for R = 0 team i has no more veto
power, so that only team e and the player are needed to realize y, which
leads to (1/2)y for team e. It follows that team e is better off under a
short-term contract (R = 0).
As the joint renegotiation payoff of the player and team i is just
the difference between the overall surplus Y + [gamma] and team e's
payoff, part (ii) of the result follows immediately. Hence, the
contracting parties benefit from nonexpired contracts that allow them to
extract a larger share of the total renegotiation surplus. This gives
rise to the rent-seeking motive which is at the core of this paper. Note
that in our model specification, [[PI].sub.e] (R)-and hence also
[[PI].sub.ip] (R)-is independent of the player's initial wage W in
team i, so that the choice of W is a purely distributive matter, and
therefore not used as a rent-seeking device.
C. Investment and Transfer Probability
Recall that renegotiation takes place only if [Y.sub.e] = Y +
[gamma] is realized, and that this occurs with probability (1/2). Thus,
team e's expected renegotiation payoff at the stage of the
investment decision is (1/2) [[PI].sub.e](R), and it will invest if this
exceeds the cost of investment, z [member of] {[z.bar], [bar.z]}. In
what follows, we confine attention to the case of interest where the
investment decision depends on the remaining duration of the
player's contract, which is ensured by the following assumption:
ASSUMPTION 1. [z.bar] < (1/2) [[PI].sub.e] (1) < [bar.z] <
(1/2) [[PI].sub.e] (0).
Hence, under a long-term contract (R = 1), team e will only invest
for z = [z.bar], while under a short-term contract (R = 0), it will
invest for both realizations of z. From the viewpoint of the contracting
parties (player and team i) who do not observe z, the probability for
team e to invest is hence simply equal to 1 under a short-term contract
and equal to [alpha] < 1 under a long-term contract. Denoting by p(R)
the probability that the player is transferred, and taking into account
that this happens only when team e invests and the high value [Y.sub.e]
= Y + [gamma] is realized, we straightforwardly get the following
result:
RESULT 2. The probability that the player is transferred is higher
for short-term contracts, i.e., p(0) = (1/2)> ([alpha]/2) - p(1).
D. Initial Contract
It remains to close the model by determining the optimal contract
type for the contracting parties at date t = 0, taking into account the
possibility of renegotiation and transfer at date t = 1, where the
remaining contract duration will then be R = 0 (R = 1) under a short
(long)-term contract. Their objective can therefore be expressed in
terms of choosing the value of R which maximizes their expected joint
payoff:
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Independently of the underlying contract, the player plays with
productivity Y for team i until date 1. The transfer occurs with
probability p(R) in which case the contracting parties get their joint
renegotiation payoff [[PI].sub.ip] (R). Recall from Results 1 and 2 that
[[PI].sub.ip] (1) > [[PI].sub.ip](0), but p(1) < p(0), so that a
long-term contract leads to a higher joint renegotiation payoff if a
transfer takes place, but decreases the probability of a transfer in the
first place. When no transfer occurs, the player continues to play for
team i for the final period of his career with productivity Y. This
leads to the following result (the proof is in the Appendix):
RESULT 3. There exists a critical threshold [bar.[alpha]] (3/4)
such that a long-term contract is strictly optimal for [alpha] >
[bar.[alpha]], and a short-term contract is strictly optimal for [alpha]
< [bar.[alpha]].
Intuitively, a higher value of a makes a long-term contract more
profitable for the contracting parties, as the expected cost in the form
of a lower transfer probability when z = [bar.z] is realized (resulting
in no investment by team e) becomes smaller.
III. EMPIRICAL ANALYSIS
In the following, we aim at testing our two predictions from the
theory part: the impact of the remaining duration of a player's
contract on the likelihood of a transfer and on the resulting joint
renegotiation payoff of the player and the old team in case of a
transfer (rent-seeking motive).
A. Data
We have compiled a data set which covers four consecutive seasons
from 1996/1997 to 1999/2000 of the "Bundesliga,"
Germany's major professional soccer league. (17) Using the leading
German soccer magazine "Kicker," apart from a number of
player- and team-specific variables, we have collected detailed
information on durations of contracts signed between players and teams,
player remuneration, and transfer fees paid by the player's new
team to his old team in case of a transfer. In total, we have
information on 421 contracts out of which 293 are first contracts (that
is, the first contract signed by the respective player during the
observation period) and 128 second contracts. Out of these 128 second
contracts 66 are renewals, where the player signs another contract with
his current team, and 62 are transfers. In our analysis, we focus on
these second contracts. In particular, we use the data on transfers to
test our theoretical predictions regarding the likelihood of a transfer
and the outcome of the resulting renegotiation process. By definition of
second contracts, these observations include the necessary information
from the players' first contracts such as the remaining contract
duration at the time of a transfer. In addition, the information about
the wage in the first contract and the performance prior to signing a
second contract yields important information on the players'
quality.
Table 1 presents the descriptive statistics for the variables used
throughout. The first row shows that for both transfers and renewals,
the yearly wages in the second contracts are on average higher than
those in the first contracts. Moreover, players who were transferred or
whose contracts were renewed earned above-average wages already in their
respective first contract. For example, for transferred players, the
mean wage in their previous (first) contract is 1.12 million DM compared
to a mean wage of only 0.84 million in the full sample of first
contracts. (18)
For the players who were transferred from one team to another
during the observation period, the average transfer fee paid by the
player's new team to his old one was 2.66 million DM. For about 27%
of these cases, the transfer fee was zero, because the respective
player's contract with his old team had expired, and the player was
free to leave. In line with our theoretical analysis, as a measure for
the joint renegotiation payoff of the player and his old team in case of
a transfer, we use the sum of the transfer fee which the old team
receives and the total value of the player's contract in this new
team, where the latter is defined as the annual wage times the duration
of his contract with the new team.
Finally, Table 1 also shows the descriptive statistics of all other
control variables used in the empirical analysis: player-specific
variables such as age, tenure with the current team, his wage in the
first contract, the number of league games, the number of international
games, and an indicator for above average performance in the season
prior to the transfer, where the latter variables serve as proxies for
player ability. In addition, we include team-specific variables such as
the annual budgets (19) and a team's final league position at the
end of the season. (20)
Overall, there is no difference in these variables for players with
transfers and players with renewals.
Further information on the distribution for contract durations
associated with transfers is provided in Table 2. The first contract had
expired in about 25% of all cases where a second contract had been
signed. In over 80%, the remaining duration was 2 years or less. About
73% of all second contracts signed after a transfer lasted for 3 years
or less.
B. Econometric Results
The econometric analysis focuses on our two main model predictions
(Results 1 and 2) concerning the impact of the remaining contract
duration (R):
HYPOTHESIS 1: A player' transfer probability is higher when
his contract has expired.
HYPOTHESIS 2: When a player is transferred to a new team, the joint
renegotiation payoff of the player and his old team is higher when their
contract has not yet expired.
The first prediction is addressed by using a Probit model, for the
second, we use OLS (with and without selectivity correction) as well as
a generalized linear model (GLM). Before turning to the econometric
analysis, we present some descriptive evidence for the two hypotheses.
Descriptive Evidence. Figure 3 shows the relationship between the
remaining contract duration R and our two main outcome variables. In
order to compute these results, all remaining durations weakly above 3
have been consolidated as there are only few observations with values
larger than 3 (see Table 2), so that R [member of] {0,1,2,3}.
[FIGURE 3 OMITTED]
The left panel shows that the probability of a transfer increases
sharply from roughly 10% to over 50% when the remaining duration
decreases from one to zero. For nonexpired contracts (R > 0), the
differences in the transfer probabilities appear to be small.
The right panel displays the expected joint renegotiation payoff of
the contracting parties (i.e., transfer fee plus the player's total
earnings under his new contract), which is minimum for R = 0, and then
increasing in R (note that the confidence intervals are large due to the
relatively low number of 62 transfer observations). In summary, Figure 3
is supportive of both hypotheses, which we now investigate in more
detail using regression models.
Transfer Probabilities. To assess the impact of the contractual
status on the transfer probability (Hypothesis 1), we estimate a binary
probit model, where a player has only two options at the end of each
season: either to move to another team or to stay with his current team.
In this simple model, when R = 0, staying with the current team implies
that the player has renewed his contract. Thus, there is no distinction
between no changes in a player's contractual status and renewals;
all that matters is whether a player is transferred or not (we will get
back to this below).
The effect of the categorical variable R e {0,1, 2,3} is captured
by three dummy variables with R = 1 as the base category. As additional
control variables we use two age dummies (< 25 and > 30), the
current wage, a dummy indicating above average performance in the past
season, a dummy for more than 10 international games, the tenure with
the current team, the team's budget, and the final league position.
(21)
Table 3 reports the average marginal effects which are obtained by
taking the mean of all individual marginal effects in the sample.
Inference is based on standard errors obtained using the delta method.
While expired contracts (R- 0) are significant, remaining contract
durations of two and three years are not. The estimated marginal effect
indicates an increase in the transfer probability by 45 percentage
points when the contract expires. In line with the descriptive evidence
presented in Figure 3, this shows that contract expiration is a crucial
determinant for transfers.
Note that for the trade-off between the higher joint renegotiation
payoff in case of a transfer and the resulting lower transfer
probability underlying our theory, it does not matter whether the
transfer probability is continuously decreasing in the remaining
contract duration or only higher for expired contracts. Moreover, our
simple framework does not allow to capture this distinction since, at
the date of the transfer decision, contracts either cover the
player's whole remaining career horizon or are expired. This issue
will therefore be discussed in more detail in Section IV.
Apart from the remaining contract duration, the transfer
probability is also driven by above average performance which increases
the probability of a transfer by 8 percentage points. Moreover, both
young players and old players have lower transfer probabilities.
In the specification reported in Table 3, renewals are ignored in
the sense that they are treated as ongoing contracts with the first
club. This may potentially bias the estimated probit coefficients and
marginal effects. In order to analyze this possibility we also estimated
a multinomial probit which explicitly accounts for transfers and
renewals being different actions. The results, reported in Appendix C,
indicate that accounting for renewals has no influence on the results
regarding transfer probabilities reported in Table 3.
Joint Renegotiation Payoff. Turning to Hypothesis 2, recall our
theoretical prediction that long-term contracts are useful rent-seeking
devices, as they increase the initial contracting parties' joint
payoff in renegotiations with the new team (Result 1). Therefore, the
dependent variable of interest in all regressions reported in Table 4
below is the joint renegotiation payoff for the player and his old team
(i.e., the transfer fee plus the total wage value of the player's
contract with his new team) when a transfer occurs.
There are several ways to specify the regression model. Given a set
of explanatory variables x, we must specify the functional relationship
between the dependent variable y and x. As the dependent variable has a
very skewed distribution it is well known that OLS may be problematic.
This is confirmed by a RESET test which strongly rejects this
specification. The traditional approach to deal with skewed dependent
variables is to take the log of y, ln(y). The OLS regression of lnfy) on
x is not rejected by the RESET test. This is the first model we
consider, and the results are reported in column 1 of Table 4.
Furthermore, because transferred players differ from other players,
estimating using the subsample of transferred players may cause
selection bias. In order to address this issue, in column 2 of Table 4
we report the results of a classic Heckman selection model, where the
control term for possible selectivity is based on the binary probit
model discussed under "Transfer Probabilities" in Section
III.B. Comparing the results in columns 1 and 2 indicates that there is
no evidence for selection bias as the t-statistic of the correction term
[lambda] is almost zero (assuming that the statistical assumptions
underlying the Heckman model are satisfied). Furthermore, note that the
point estimates for the OLS and the selection model are almost
identical. For these reasons, we will not pursue the selection model any
further.
Even though the log-linear model displayed in column 1 is not
rejected by the RESET test, it needs to be treated with caution. Santos
Silva and Tenreyro (2006) have shown that OLS of the log-linear model is
consistent only under strong assumptions. Assume that the true model can
be written as y = exp(x[beta])v, where v is an error term with E[v|x] =
1. The log-linear model is ln(y) = x[beta] + ln(v). Due to Jensen's
inequality, E[ln(v)|x] [not equal to] 0. This will affect the estimate
of the intercept. More importantly, Santos Silva and Tenreyro (2006)
show that if v is heteroskedastic, then E[ln(v)|x] will be a function of
x. This in turn leads to inconsistent estimates of [beta] in the
log-linear model. For this reason, Santos Silva and Tenreyro (2006)
suggest to directly estimate the GLM y = exp(x(3)v by Maximum
Likelihood. This so-called Pseudo-ML (PML) estimator is consistent if
the mean function E[y|x] = exp(x[beta]) is correctly specified, even
when the remainder of the distribution of y is misspecified (see
Gourieroux, Monfort, and Trognon 1984). This feature is important
because the GLM estimator with log link is numerically equal to the
well-known Poisson ML estimator for count data. Given the described
feature of PML, however, the data do not have to follow a Poisson
distribution and y does not even have to be an integer for the estimator
based on the Poisson likelihood function to be consistent. (22) The GLM
results are reported in column 3 of Table 4, and they are similar to
those obtained from the OLS model in column 1. (23) In the GLM the
quality indicators previous annual wage and more than 10 international
games become significant, as do the two age dummies. One possible
explanation for this change is heteroskedasticity with respect to these
variables. (24)
As for the impact of the remaining contract duration R, the three
respective dummies R = 0,2,3 measure the effect relative to R = 1.
Moreover, some additional tests are required which are provided at the
bottom of Table 4. In the OLS specification (column 1), only the dummy
for R = 0 is significant, and the tests at the bottom of the Table show
that both the difference between R = 0 and R = 2, and between R = 0 and
R = 3 are significant, while the difference between R = 2 and R = 3 is
not. Thus, similar to our empirical analysis of transfer probabilities,
this model indicates that the effect of the remaining contract duration
on the joint renegotiation payoff is mainly driven by out-of-contract
players.
In the GLM specification with log link (column 3), however, the
dummies for both R = 0 and R = 3 are significantly different from the
base level R = 1. Furthermore, the tests reported at the bottom of the
table indicate that R = 2 and R = 3 are statistically different from R =
0, and that R = 2 is different from R = 3. All in all, these finding
suggest that, while contract expiration (R = 0) is still a major
determinant of the joint renegotiation payoff, the latter is also
affected by the actual remaining contract duration in case of
non-expired contracts (R > 0). Figure 4 illustrates the estimated
effect of R on the log of the joint renegotiation payoff for the OLS and
GLM models. In both cases, there is an increase in the joint
renegotiation payoff with increasing R, but given the small sample size,
not all differences are significant. Whether the joint renegotiation
payoff increases in R even for nonexpired contracts or only compared to
expired ones is an interesting issue which we will discuss in more
detail in Section IV below.
Our measure of the joint renegotiation payoff might under-estimate
the actual payoff when transferred players receive signing bonuses from
their new teams. Anecdotal evidence suggests that signing bonuses are in
fact sometimes paid for top players with expired contracts. When these
payments are sufficiently large, then the estimated payoff difference
between expired and nonexpired contracts might vanish. Presumably, when
a player's contract has expired, the new team will pay part of the
saved transfer fee to the player in the form of a signing bonus.
Unfortunately, signing bonuses in European soccer are notoriously hard
to observe and our data set contains no respective information.
Therefore, we have performed a sensitivity analysis where we add a
fraction of the average transfer fee in our sample to a player's
salary in case he is transferred and his contract has expired. It turns
out that the results remain robust even when adding as much as 50% of
the average transfer fee (which includes the large amounts paid for
transfers with long remaining contract durations). Therefore, we
conclude that our results concerning the impact of the remaining
duration of a player's contract on joint renegotiation payoff of
the contracting parties are not driven by unobserved signing bonuses.
IV. DISCUSSION
We have developed a framework in the context of European soccer in
order to test some of the central hypotheses concerning the strategic
use of contract terms as rent-seeking devices, which have been derived
in the previous theoretical literature. We view our results as first
empirical evidence in this respect.
Our framework emphasizes the role of long-term contracts as
rent-seeking devices from which the contracting parties can benefit in
case of a transfer. We show that their joint renegotiation payoff is
considerably higher for nonexpired compared to expired contracts, and we
provide evidence that this payoff is also higher for nonexpired
contracts with a longer remaining duration. In our view, the positive
relationship between remaining contract duration and renegotiation
surplus would be hard to explain by relying on factors other than
bargaining power. Of course, one might argue that better players get
longer contracts, so that they have ceteris paribus also longer
remaining contracts when the probability for a transfer is equally
distributed over time. However, recall that we find that long-term
contracts remain beneficial to the contracting parties even when
controlling for player ability or taking into account that transferred
players might statistically differ from nontransferred ones. (25)
Obviously, the rent-seeking motive alone would create an incentive
to sign contracts of unlimited duration. In reality, this incentive is
countervailed by a number of factors such as liquidity constraints or
legal restrictions. (26) In our paper, and in line with the relevant
literature on strategic contracting discussed above, we focus on the
adverse effect of long-term contracts on the likelihood of transfers.
(27) Again, our empirical analysis strongly corroborates the view that
the remaining contract duration is an empirically important factor, and
it also reveals that the effect is driven by out-of-contract players.
[FIGURE 4 OMITTED]
In our model, we have conveniently assumed that long-term contracts
last until the end of the player's career horizon, so that there
are no different remaining durations of nonexpired contracts. We did so
not only for analytical tractability, but also because the question
whether the impact of a player's contractual status on the
entrant's (and hence also on the contracting parties) renegotiation
payoff is exclusively driven by expired contracts or also affected by
the remaining duration of (nonexpired) contracts is a subtle one. The
reason is that cooperative bargaining theory suggests that even the
theoretical answer to this question depends rather delicately on the
exact model structure applied.
For example, when considering a larger career horizon for the
player (denoted by k), then under the nucleolus concept as considered in
our paper, it can easily be shown that the entrant's payoff
decreases in the remaining contract duration R if the player's
career horizon k is low compared to R. By contrast, if k is sufficiently
large, then all that matters is whether the contract is expired or not.
(28) Recalling that for the rent-seeking motive, it is sufficient that
the entrant's payoff is highest when the player's contract has
expired, it is clear that these subtle case distinctions, which occur
even within the same cooperative bargaining concept, are not at the
heart of our paper. (29)
In our model, we stipulate a causal link from the remaining
contract duration to the transfer probability, driven by the new
team's share in renegotiations. One might challenge this
interpretation by suggesting that transfer probabilities are in fact
independent of the terms of a player's contract, and that the
negative relationship is driven by sorting of players into different
contracts. (30) Note first that this alternative theory would be
difficult to reconcile with our empirical finding that it matters
strongly whether or not a player's contract has expired, thereby
giving rise to a discontinuous jump of the respective outcome variable
when the remaining duration becomes zero. Even more importantly, unlike
such an explanation, our framework is also consistent with observed
changes in average contract durations occurring in response to an
institutional change (the Bosman judgment of 1995), which has occurred
just before our observation period starts. Before the Bosman judgment,
incumbent teams retained some veto power even after a player's
contract had expired, thereby receiving a (smaller) transfer fee also in
this case. In line with our model, the incentive to sign longer
contracts under the pre-Bosman regime is smaller, because of the less
pronounced difference between non-expired and expired contracts in terms
of the incumbent team's veto power. Therefore, our model would
predict a stronger incentive to sign longer contracts as a result of the
Bosman judgment. Table A1 shows the average contract durations in the
two seasons before the judgment (1994/1995 and 1995/1996) and the four
seasons afterwards. Consistent with our theoretical prediction, there
has indeed been an upward jump of the average duration by approximately
half a year in the aftermath of the judgment.
The literature on strategic contracting discussed in the
Introduction exhibits a further common feature, namely that not only
outsiders, but also some of the contracting parties themselves may be
harmed in the course of using contracts as rent-seeking devices, and
must hence be compensated ex ante in exchange for agreeing to such a
contract. (31)
In our context, this issue arises naturally as in renegotiations,
players tend to be better off when their contract is expired, while the
reverse is true for incumbent teams who are better off when the
remaining contract duration is large. (32) This suggests that when a
long-term contract is jointly optimal, a player would have to be
compensated ex ante for agreeing to such a contract in the form of a
higher wage. In contrast, when a short-term contract is optimal, then
the incumbent team would demand compensation from the player, leading to
a lower wage. In either case, this argument would predict a positive
correlation between wages and contract durations. Our data allow to
tentatively investigate this issue and, controlling for ability, we find
that on average, one more year of contract duration increases a
player's annual wage by 24%. However, because of potential
endogeneity issues with respect to the contract duration and the lack of
appropriate instruments, this result has to be treated with caution, and
a more detailed analysis is warranted in further research.
While fully consistent with our theory based on strategic
contracting and rent seeking, we believe that any empirically observed
positive correlation between wages and contract durations would be hard
to reconcile with alternative explanations: For example, under the
realistic assumption that players ceteris paribus prefer higher wages
and longer contracts, these two variables should be substitutes rather
than complements, leading to a negative correlation. In particular,
consider the case where risk-aversion of players (leading to a strong
preference of long-term over short-term contracts) is a major force in
determining contract durations. In this case, players should be willing
to sacrifice part of their wage in return for a longer contract. Again,
this would suggest that the two variables are negatively correlated.
Let us now get back to our results from a broader perspective.
Because the driving forces in our framework are not only relevant for
contracting in the sports sector, our results might also be of interest
for other contexts where long-term contracts are used. For instance,
there is a recent debate in the European Commission (EC) about how to
deal with long-term contracts in the electricity sector. (33) On the one
hand, the EC emphasizes that long-term contracts might be helpful in
promoting investment incentives as firms are facing uncertainty, e.g.,
concerning future legislation with respect to interstate grids.
Moreover, with respect to the final allocation, it acknowledges that
long-term contracts are not necessarily fully predetermining as there is
the possibility of "secondary trade" (see p. 183), i.e., entry
by another firm (as a result of renegotiation with the incumbent firm)
which tends to improve efficiency. However, on the other hand it also
emphasizes that long-term contracts "... raise search cost
(transaction costs) for any player interested.... This raises barriers
to entry.... Hence, both the Court and the Commission has concluded that
long-term contracts should, with certain exceptions, be disqualified
..." (see p. 183). Obviously, this latter argument is analogous to
the one made and empirically confirmed in our context.
APPENDIX A: PROOF OF RESULT 1
To derive the surplus division under the nucleolus concept, we
adopt Theorem 2 in Leng and Parlar (2010, 671) which provides a closed
form solution for the (normalized) three-player case when the core is
nonempty as in our context. For this purpose, we first normalize the
payoffs so that all "coalitions" consisting of one party only
are zero. Starting from the original values for the different coalitions
[V.sub.p] = RW, [V.sub.e] = 0, [V.sub.i] = [V.sub.ie] = R(Y - W),
[V.sub.pi] = Y, [V.sub.pe] = RW + (1 - R)(Y + [gamma]), [V.sub.pie] = Y
+ [gamma], the normalized values are
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
It can easily be checked that, for expired contracts (R = 0), we
are in case 3 of Theorem 2 in Leng and Parlar (2010), (34) while we are
in case 1 for nonexpired ones (R = 1).
For the case R = 0, the normalized nucleolus payoffs are
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Adding the values we subtracted for the normalization and taking
into account that we consider expired contracts (R = 0) leads to
renegotiation payoffs
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
For the case R = 1, the normalized nucleolus payoffs are
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Adding the values we subtracted in the course of the normalization
leads to the following renegotiation payoffs
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Hence, for team e we get [[PI].sub.e] (1) = (1/3)[gamma] and
[[PI].sub.e] (0) = (2/2)[gamma] as stated in Result 1. As for the joint
payoff of the player and team i, adding up their payoffs gives
[[PI].sub.ip] (0) = Y + (1/2) [gamma] and [[PI].sub.ip](1) = Y +
(2/3)[gamma] as stated in Result 1.
APPENDIX B: PROOF OF RESULT 3
Substituting from Results 1 and 2, we have
E[J(0)] = 2Y + (1/4)[gamma] and E[J (1)] = 2T + ([alpha]/3)[gamma].
Defining [DELTA] := E[J(1)] - E[J(0)] as the expected joint surplus
difference between a long- and a short-term contract, it follows that
[DELTA] = (1/12)[gamma](-3 + 4[alpha]) which is strictly positive for
[alpha] > (3/4) (in which case the expected joint surplus is higher
under a long-term contract) and strictly negative for [alpha] < (3/4)
(in which case the expected joint surplus is higher under a short-term
contract).
APPENDIX C: TRANSFER AND RENEWAL PROBABILITIES
Besides transferring to another team, another option to change the
contractual status is a renewal of the contract with the incumbent team.
In order to take this possibility into account, we estimate a
multinomial probit model with three outcomes: at the end of each season,
a player either (i) is transferred, (ii) renews his contract, or (iii)
does not change his contractual status. Including the dummy for expired
contracts (R = 0) into such a model would cause an identification
problem as, for the third option, this dummy is always zero by
definition. When a player's contract has expired, he can only
continue his career when either being transferred or signing a new
contract with his current team, i.e., the option of not changing the
contract is not available. For this reason, we estimate the multinomial
probit only for the subsample with R > 0, and the marginal effects
for the two choices transfer and renewal (no contract change is the
reference category) are displayed in columns 3 and 4 of Table Al. In
order to compare these results with the binary model, we also report
estimates of the binary model for the subsample with R > 0 in column
2. Also for comparison reasons, column 1 repeats the results reported in
Table 3. Comparing columns 1 and 2 reveals no major differences in the
relevant point estimates of the marginal effects.
The results for the transfer probability based on the multinomial
model in column 3 are also almost identical to those of the binary model
reported in column 2. This indicates that, in order to identify the
impact of the remaining contract duration on the transfer probability,
it is not necessary to distinguish between renewals and no change in
contractual status. Therefore, we conclude that it is sufficient for our
purposes to restrict attention to the binary probit model.
TABLE Al
Average Marginal Effects of Probit Estimations
Binary Probit
Transfer Transfer (a)
R = 0 0.455 (4.99) --
R = 2 0.015 (.55) 0.019 (0.70)
R = 3 -0.016 (.58) -0.010 (0.37)
# International games > 10 0.039 (1.43) 0.051 (2.03)
Annual wage in first contract 0.016 (1.32) 0.011 (0.88)
Age < 25 -0.047 (1.91) -0.045 (1.93)
Age > 30 -0.078 (3.53) -0.059 (2.71)
Above average performance
previous season 0.083 (3.47) 0.080 (3.38)
Tenure in current team -0.001 (.39) -0.001 (0.29)
Yearly budget current team -0.001 (1.04) -0.002 (1.57)
Final league position of current
team in previous season 0.004 (1.35) 0.003 (1.15)
Log Likelihood -162.76 -140.77
Observations 613 581
Multinomial Probit
Transfer (a) Renewal (a)
R = 0 -- --
R = 2 0.018 (0.67) -0.044 (1.48)
R = 3 -0.010 (0.37) -0.049 (1.57)
# International games > 10 0.052 (2.06) 0.043 (1.58)
Annual wage in first contract 0.011 (0.85) 0.022 (1.68)
Age < 25 -0.044 (1.83) -0.036 (1.23)
Age > 30 -0.058 (2.63) 0.019 (.65)
Above average performance
previous season 0.081 (3.40) -0.005 (.21)
Tenure in current team -0.001 (0.28) 0.007 (2.41)
Yearly budget current team -0.002 (1.62) -0.003 (2.48)
Final league position of current
team in previous season 0.003 (1.16) -0.006 (2.05)
Log Likelihood -291.43
Observations 581
Note: Absolute t-statistics in parentheses.
(a) Only subsample with R > 0.
ABBREVIATIONS
DM: German Marks
EC: European Commission
GLM: Generalized Linear Model
PML: Pseudo-Maximum Likelihood
doi: 10.1111/ecin.12098
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(1.) In contrast to US sports, it is very common for European
soccer players to play for several teams throughout their career.
Moreover, in roughly 75% of all transfers in our data set, the
respective player's contract with his old team had not yet expired.
(2.) See Court of Justice of the European Communities, Case
C-415/93. The data used in the empirical part are all taken from this
period.
(3.) For the German Bundesliga, for example, there is plenty of
anecdotal evidence suggesting that in the course of contract
negotiations, both teams and players have very well in mind the
possibility of a future transfer of the player, including the
anticipated payoff consequences in the resulting renegotiation process.
For example, according to Meinolf Sprink, an executive at Bayer 04
Leverkusen, "... the motive of influencing (later) transfer fees is
always present." Furthermore, Claus Horstmann, former CEO of 1. FC
Koln (Cologne) says that "we use long-term contracts to protect our
investments." Source: Spiegel online, August 6, 2010,
http://www.spiegel,de/sport/fussball/0,1518,710282,00.html
(4.) We follow the literature on incomplete contracts by assuming
ex post efficiency of the renegotiation process, given that it occurs
(see, e.g., Hart and Moore 1990, Segal and Whinston 2000, Spier and
Whinston 1995). That is, after the entrant has invested in information
collection, a transfer will occur if and only if the player is more
valuable in the new team, independent of the remaining duration of the
player's contract with the incumbent team.
(5.) In a similar vein, Chung (1992) shows that contracting parties
have an incentive to choose socially excessive damage clauses which also
lead to ex post inefficiencies.
(6.) A related issue is the controversy whether parties to a
contract are able to commit not to renegotiate, see, e.g., Hart and
Moore (1999), Maskin and Tirole (1999). Carbonell-Nicolau and Comin
(2009) design and implement an empirical test which, using data from the
Spanish soccer league, leads them to reject the commitment hypothesis.
(7.) Another issue in this context concerns the role of long-term
contracts as a pre-contractual incentive device. Here, a long-term
contract serves as a reward for good performance and therefore tends to
have a positive effect on effort incentives, see, e.g., Stiroh (2007).
(8.) As is standard in the literature on the economics of
professional sports, this productivity is meant to capture the marginal
revenue that can be attributed to a player such as, for example,
increases in TV money, merchandizing sales or premia from international
competitions.
(9.) All that is needed for our results is that, at the date of
contracting, the contracting parties are facing some uncertainty
concerning future entrants' willingness to hire the player.
(10.) We assume that [Y.sub.L] is sufficiently small such that team
e does neither negotiate when [Y.sub.e] = [Y.sub.L] is realized nor
without having invested in information acquisition. A similar assumption
is made in Aghion and Tirole (1997) in the context of taking uninformed
investment decisions with respect to projects of unknown profitability.
(11.) As for our context, see, e.g., Aghion and Bolton (1987),
Spier and Whinston (1995), and Segal and Whinston (2000). Moreover, also
in the broader context of incomplete contracting models, canonical
frameworks such as Grossman and Hart (1986) and Hart and Moore (1990)
exhibit this feature.
(12.) We are grateful to an anonymous referee for bringing this
paper to our attention.
(13.) The Shapley value as the most popular cooperative bargaining
concept for more than two players is not suitable here as it is not
necessarily in the core. The reason is that it assigns a positive payoff
to incumbent teams even after a player's contract has expired. This
is at odds with the institutional framework of our context, according to
which incumbent teams lose their veto power after contract expiration.
Hence, when a player's contract has expired, the incumbent team is
not needed since the player and his new team alone can realize the same
surplus as the grand coalition. In fact, in our data set the transfer
fee is zero for all transfers for which the respective player's
contract had expired.
(14.) See, e.g., Segal and Whinston (2000), Burguet, Caminal, and
Matutes (2002), Feess and Muehlheusser (2003), and Tervio (2006) for
alternative specifications of the renegotiation game.
(15.) One might argue that players can reduce the incumbent
team's veto power simply by threatening not to perform well on the
pitch. However, even if this effect mattered in our context, all we need
is the realistic assumption that holding a nonexpired contract with a
player gives a team some bargaining power in the course of
renegotiation.
(16.) Of course, [[PI].sub.j](*) depends on all model parameters,
but as to not convolute the notation, we will throughout use as function
arguments only those variables which are of particular interest at the
respective stage of the model.
(17.) This 4-year horizon of our sample is due to two regime
changes with respect to the transfer rules in European professional
sports: The first regime change is the Bosman judgment explained above
(effective since season 1996/1997), according to which teams lose any
veto power once a player's contract has expired. The second regime
change resulted from a decision of the European Commission (effective
since season 2000/2001) which makes it easier for players to resign from
their current contracts, thereby reducing teams' veto power also
when a player's contract is still valid. Our modeling of the
renegotiation process in the theoretical framework is therefore
consistent with the legal regime in place during the seasons
1996/1997-1999/2000.
(18.) All monetary variables are measured in the German pre-Euro
currency "Deutsche Mark" (DM), where 1 DM [approximately equal
to] 0.5 EUR [approximately equal to] 0.65 USS.
(19.) Yearly budgets also seem to capture well any variation in the
available total (nominal) funds to be spent by teams on their rosters
across seasons (e.g., due to inflation or higher league income from
selling TV rights which is then distributed among teams); in all
regressions, including season dummies in addition to team budgets has no
effect on the estimation results.
(20.) There are 18 teams competing in the Bundesliga, and rank one
is the best.
(21.) The number of league games was never significant in any
specification and is therefore omitted in all estimations.
(22.) For more details, see Santos Silva and Tenreyro (2006).
(23.) The [R.sub.2] are also almost identical. Note that these
[R.sub.2] measure the fit of the log dependent variable. It is also
possible to compute a [R.sup.2] for the fit of the untransformed
dependent variable by computing the square of the correlation
coefficient of y and [??]. For the log-linear model, it is sufficient to
use [??] = exp (x[??]) even though this is only correct up to a
proportional factor, see Wooldridge (2009, 213). The corresponding
[R.sup.2] are .61 for the OLS model and 0.65 for the GLM, respectively.
Hence, the GLM fits the untransformed total payoff slightly better.
(24.) Informally, this is confirmed by comparing the variances of
the total payoff differentiated by the dummy for more than 10
international games and by being below or above the median of the
previous wage. The variance is twice as large for international players
and for players with high previous wages. Even more pronounced is the
increase in the variance of the total payoff with increasing R. For R =
0 and R = 1 the variance is roughly 8, for R = 2 it is 66, and for R = 3
it is 100.
(25.) Long-term contracts could also be used as commitment devices
for investments in (general) human capital of players. While such
investments are crucial for transforming young talents into
professionals, this motive seems of minor importance in the present
study, as all players under consideration are already full-fledged
professionals. Moreover, to maintain incentives to invest in junior
athletes, long-term contracts might be useful precisely because of the
mechanism considered in our paper: they reduce the likelihood of
transfers of junior players, and if this nevertheless happens, the team
that has invested receives a compensation in the form of a transfer fee.
See Segal and Whinston (2000) for a related argument in the context of
exclusivity provisions.
(26.) For example, according to a rule enacted in 2002 (i.e., after
the end our observation period) by the governing body in soccer, FIFA,
the duration maximum for contracts signed between players and teams is 5
years. Another relevant factor in this context might be risk-sharing
considerations, and the effect on the optimal contract duration would be
ambiguous, depending on the degrees of risk-aversion of teams and
players. For instance, if players are more risk-averse then clubs are,
then a longer contract duration serves as an insurance device for
potential injuries, and longer contracts increase the joint utility of
the two parties due to improved risk-sharing.
(27.) In our approach, the joint surplus ex ante depends only on
the probability of a transfer, and on the resulting renegotiation payoff
in case of a transfer. When in addition considering other relevant
factors such as risk-sharing, then the contract duration would also
directly affect the joint surplus of the contracting parties even when
no transfer occurs.
(28.) Details are available from the authors upon request.
(29.) Under the Shapley value, it can be shown that the
entrant's payoff decreases in R, but recall that the Shapley value
is not necessarily in the core and hence not a convincing concept in our
context.
(30.) Note that such a theory would also need to explain why
players with high transfer probabilities systematically sign short-term
contracts. This would be puzzling since our empirical analysis clearly
shows that contracting parties benefit from long-term contracts when a
transfer occurs, which suggests that players with high transfer
probabilities should have higher incentives for signing longer
contracts, resulting in a positive relationship between contract
durations and transfer probabilities.
(31.) In the literature, the issue of ex ante compensation is
typically not explicitly analyzed when the focus is on investment
incentives which are not affected by the ex ante division of surplus,
see, e.g.. Hart and Moore (1988), Spier and Whinston (1995). The same is
true for other contexts such as asset ownership where incomplete
contracting frameworks are used, see, e.g., Hart and Moore (1990),
Roider (2004).
(32.) In our model, the incumbent team is always better off under a
long-term contract which is not yet expired at the date of
renegotiation. For the player, a sufficient condition being better off
in renegotiations under a short-term (and hence expired) contract is
that his wage (W) is not larger than his total value for team i (Y), see
Result 1 and the Appendix.
(33.) See European Commission, "DG Competition Report on
Energy Sector Inquiry," January 10. 2007, http://
ec.europa.eu/comm/competition/sectors/energy/inquiry/full_report_part2.pdf
(34.) In our context, the cases 3 and 4 of Theorem 2 in Leng and
Parlar (2010) turn out to be equivalent.
EBERHARD FEESS, MICHAEL GERFIN and GERD MUEHLHEUSSER *
* We are grateful to two anonymous referees and the editor Jeff
Borland for their very useful suggestions. Moreover, we thank Yeon-Koo
Che, Bernd Frick, Sebastian Kranz, and in particular Francine Lafontaine
for their comments on earlier drafts of the paper. We have also
benefited from comments by seminar participants at the universities of
Bielefeld, Innsbruck. Heidelberg, Marburg, Wurzburg and Tubingen, and
participants of the workshops on "Frontiers in the Economic
Analysis of Contract Law" (Bonn) and "Club Finances and Player
Remuneration" (Paderborn), respectively. Financial support from the
Swiss National Science Foundation (grant 100012-116178) is also
gratefully acknowledged.
Feess: Professor, Frankfurt School of Finance and Management,
Frankfurt 60314, Germany. Phone 49-69154008398, Fax 49-691540084398,
E-mail e.feess@frankfurt-school.de
Gerfin: Professor, Department of Economics, University of Bern,
Bern 3001, Switzerland, and IZA. Phone 41-616314092, Fax 41-316313992,
E-mail michael.gerfin@vwi.unibe.ch
Muehlheusser: Professor, Department of Economics, University of
Hamburg, Hamburg 20146, Germany, IZA and CESifo. Phone 49-40428385575,
Fax 49-40428389226, E-mail gerd.muehlheusser@wiso.uni-hamburg.de
TABLE 1
Descriptive Statistics
First Second Contract (a)
Contract (3)
Transfer Renewal
Variable Mean (SD) Mean (SD) Mean (SD)
Annual wage (b) 0.84 (0.75) 1.63 (1.31) 1.67(1.33)
Annual wage previous
contract 1.12(0.94) 1.19(1.12)
Transfer fee 2.66 (3.52)
Total joint
renegotiation
payoff (c) 7.33 (7.48)
Contract duration 3.20 (0.95) 2.97 (0.97) 3.21 (1.21)
Remaining contract
duration 1.53 (1.25) 1.44(1.15)
Number of league games 77.36(91.76) 132.03 (99.97) 153.97 (112.87)
Number of international
games 7.67(15.23) 18.61 (27.48) 22.29 (29.11)
Above average
performance in
previous season 0.62 0.48
Age 26.71 (3.81) 28.21 (3.23) 29.39 (3.44)
Tenure in current team
(years) 2.93 (3.91) 0 4.30(5.10)
Yearly budget current
team 37.91 (10.59) 43.05 (d) (15.77) 45.00(13.55)
Final league position
in previous
season 9.48 (5.05) 7.55 (4.85)
Number of observations 293 62 66
(a) These figures refer to the first season of the contract.
(b) All monetary variables are measured in million German Marks
(DM), where 1 DM [approximately equal to] 0.5 EUR ss 0.65 US$.
(c) Total joint renegotiation payoff is defined as (Annual wage X
Contract duration) + Transfer fee.
(d) In case of a transfer, the player's current team is the one to
which he is transferred.
TABLE 2
Distribution of Contract Durations in Case of a
Transfer
Years
0 1 2 3 4 5 6 Average
Duration second 3 17 25 13 4 0 2.97
contract
Remaining duration 17 12 21 8 3 1 0 1.53
first contract
TABLE 3
Average Marginal Effects on Transfer
Probability (Probit)
Transfer
Probability
R = 0 0.455 (4.99)
R = 2 0.015 (0.55)
R = 3 -0.016 (0.58)
# International games > 10 0.039 (1.43)
Annual wage in first contract 0.016 (1.32)
Age < 25 -0.047 (1.91)
Age > 30 -0.078 (3.53)
Above average performance previous
season 0.083 (3.47)
Tenure in current team -0.001 (0.39)
Yearly budget current team -0.001 (1.04)
Final league position of current team in
previous season 0.004 (1.35)
Log likelihood -162.76
Observations 613
Note: Absolute f-statistics in parentheses.
TABLE 4
Joint Renegotiation Payoff of Player and Old Team in Case
of Transfer
Selection
OLS (a) Model (a) GLM (b)
R = 0 -0.821 (3.36) -0.699(1 -0.517(1
R = 2 0.176 (0.71) 0.189 (0.81) 0.216 (0.90
R = 3 0.358 (1.33) 0.347 (1.38) 0.561 (1.91
# International
games> 10 0.267 (1.37) 0.287 (1.42) 0.317 (1.67
Previous annual wage 0.150 (1.46) 0.152 (1.42) 0.163 (3.59
Age < 25 -0.249 (0.95) -0.286 (0.85) -0.394 (1.98
Age > 30 -0.384 (1.53) -0.434 (1.33) -0.461 (2.25
Above average
performance
previous season 0.414 (2.38) 0.459 (1.75) 0.461 (3.07
Yearly budget new team 0.022 (3.82) 0.022 (4.10) 0.021 (4.37
[lambda] (c) 0.098 (0.22)
Constant 0.239 (0.78) 0.046 (0.05) 0.267 (.87)
Observations 62 62 62
[R.sup.2] .68 .68 .67 (d)
[H.sub.0] p value p value p value
[[beta].sub.R=0]
[[beta].sub.R=2] .00 .10 .00
[[beta].sub.R=0]
[[beta].sub.R=3] .00 .11 .00
[[beta].sub.R=0]
[[beta].sub.R=3] .46 .53 .08
Note: t-statistics based on robust standard errors in parentheses.
(a) Dependent variable: ln(joint renegotiation payoff).
(b) Dependent variable: joint renegotiation payoff.
(c) [lambda] = [phi]/(x[??])/[PHI](x[??]), where x[??] is the
estimated linear index of the probit model and [phi] and [PHI] are
the standard normal density and distribution function,
respectively.
(d) [R.sup.2] is computed as the square of the correlation
coefficient between ln(y) and [??, where [??]] is the prediction
based on the GLM.
TABLE 5
Average Contract Durations Before and After
Bosman Judgment
Season 94/95 95/96 96/97 97/98 98/99 99/00
Average Duration 2.917 2.831 3.224 3.295 3.278 3.266
