Legal Restrictions on Buyout Fees: Theory and Evidence from German Soccer

We perform a theoretical and empirical analysis of the impact of transfer fee regulations on professional soccer in Europe. Based on a model of the interaction of moral hazard and heterogeneity, we show (i) how the regulations effect contract durations and wages, (ii) that contracting parties have an incentive to agree upon inefficiently long contracts, (iii) how these incentives vary with the legal system, and (iv) how the relationship between contract duration and performance also depends on the legal system. With one exception, all theoretical results are empirically confirmed using a comprehensive data set from the top German Soccer League (Bundesliga).


Introduction
Motivation In recent years, there has been an ongoing controversy in the economic and legal profession whether the freedom of contract should be restricted when two parties want to agree on binding long-term agreements. Examples include exclusive dealing clauses, long-term (labor) contracts precluding unilateral termination, and excessively high damage clauses for breach of contract.
Following the general lines of the early Chicago School, Stigler (1975, Ch. 7) argued that restricting the set of feasible contracts can never increase social welfare, because parties will not sign inferior contracts. However, modern contract theory has identified a variety of reasons why binding long-term agreements may be privately optimal but socially unwarranted. One argument is that the contracting parties may deliberately accept inefficiencies as to reduce the payoff of third parties. In these cases, the inefficiencies may be mitigated by appropriate restrictions on the freedom of contract (see the literature discussion below).
Although the theoretical literature provides many interesting insights, there is a lack of empirical evidence. This is owing to the fact that an empirical analysis requires the following conditions to be simultaneously fulfilled, which is rarely the case: i) the terms of the contracts must be observable or at least reconstructible, ii) there has been a change in the legal regime which generates some variation of the relevant contract terms, and iii) the sample must be representative and sufficiently large to allow for the results to be generalized.
In the present paper, we perform a theoretical and empirical analysis of the impact of transfer fee regulations for professional soccer players in Europe. This is an appropriate field of application since the legal regimes governing the transfers of players in Europe have been changed dramatically in recent years, and because we were able to collect contract and performance data for 1308 player years in the German Bundesliga from time periods where different legal regimes were in force.
Our paper aims at contributing to three lines of research. With respect to sports 1 economics, we are (to the best of our knowledge) the first to apply a coherent modeling approach to analyze the impact of changes in the legal environment in European soccer and to use a rich data set to test the predictions empirically. As for contract theory, we consider as interesting the theoretical analysis and empirical confirmation of the interplay between heterogeneity and moral hazard. Finally, our analysis sheds light on the impact of legal restrictions on economic variables such as the contract length, salaries, transfer fees actually paid and performance.
Legal situation Before turning to a description of our analysis, we need to provide some brief background knowledge on transfer fee regulations in European soccer. Up to 1995, the most important regulation was that a club could demand a transfer fee which was administered by the national soccer associations even if a player's contract had already expired. These fees were supposed to stabilize the league's competitive balance, and were therefore increasing in the strength of the new club and decreasing in the strength of the old club. 1 We label this regime the "pre-Bosman regime" P . Under regime P , clubs and players were not able to agree credibly upon a contract where a player could leave for free when the contract had expired.
In the famous "Bosman Case" in December 1995, the European Court of Justice ruled that this transfer system was not in accordance with article 39 of the Treaty of Rome, because it was judged to hamper the mobility of professionals. 2 Since then, clubs are no longer entitled to receive transfer fees for out-of-contract players. The verdict did not restrict the transfer fees for players with valid contracts. 3 We will refer to this situation as to the "Bosman regime" B.

Recently, even regime B was challenged by EU Competition Commissioner Mario
Monti by pointing to ordinary labor market relationships where firms and employees are 1 It is somewhat unclear whether this aim has ever been achieved, see e.g. the survey article by Szymanski (2003) who also discusses the literature on the impact of the comparable "reserve clause"system used in US sports.
2 See Court of Justice of the European Communities, Case C-415/93. 3 Another aspect of the judgement was concerned with the admissible number of foreign players in a team, which is not at issue here.
usually not allowed to agree upon any contract length and any transfer fee they want to. In general, "unreasonably" high buy-out-fees are usually declared void in court. According to a compromise between the Commission and the governing bodies of European Soccer, FIFA and UEFA reached in March 2001, a player can leave his current club without the club's approval when paying a fee for breach of contract and, depending on his age, a fee for compensation of educational expenses. This is in sharp contrast to regimes P and B, where the old club could always impede the transfer if it did not want to accept the transfer fee offered by another club as long as the players contract had not yet expired.
Summing up, by appropriately varying the contract length, any transfer fee the player and his club want to agree upon can be implemented under regime B ("freedom of contract"). To the contrary, regime M imposes an upper bound on the implementable transfer fee which is equal to the sum of the fee for breach of contract and the compensation payment for the education of the player. In a similar vein, regime P imposes a lower bound on the implementable transfer fee, which is equal to what the old club is entitled to after the player's contract has expired.

Framework and main results
To compare the three regimes, we develop a model where a club and a player sign a contract containing a wage and a contract length. We assume that the player's average productivity is the higher, i) the higher his potential and ii) the shorter his (remaining) contract length. While the first assumption is straightforward, as for the second one, note that less than 10% of the average player's annual salary is performance related (see Ziebs (2002, pp. 156-167)) and therefore, this is the simplest way of expressing that a player has lower effort incentives when he has a long-term contract anyway. 4 For our purpose, all that matters is that to a large extent, wages are not tied too closely to actual performance and that this reduces effort incentives. Since there is a (stochastic) relationship between the unobservable effort decision of a player and his observed actual performance, a player's actual performance tends to fall short of this potential maximum performance. Under slight abuse of terminology, we will refer to this as a moral hazard problem which clearly tends to become the more severe, the longer a player's contract lasts.
After having signed his contract, the player plays for his initial club unless an exogenous shock leads to higher productivity in another club. For instance, this other club may have hired a coach who prefers a tactical system in which the player fits extraordinary well. All we need is that there is a positive probability that a change of clubs is efficient within the total career horizon, which is clearly the case in reality. Since the potential of players is known in our model, the renegotiation process between the clubs and the player is efficient and results in a transfer whenever the productivity shock occurs. It follows that the contract length and the regime affect the division of surplus, but they will not directly influence the allocation of players. Note that legally administered or contractually fixed transfer fees are veto sums the initial club is entitled to, and thus establish upper bounds on the transfer fees actually paid. In the renegotiation stage, we assume (and confirm empirically) that the initial club benefits from a high veto sum and a high contract length, whereas the renegotiation payoffs of the player and the new club are both weakly decreasing in these arguments.
Our main results, however, refer to the impact of transfer fee regulations on the initial contract. We show that clubs and players indeed have an incentive to accept inefficiencies caused by long-term labor contracts to reduce the payoff of third parties. These incentives strongly depend on the different legal restrictions of transfer fees. In particular, when signing the initial contract, the player and the club face the following trade-off: on the one hand, a shorter contract reduces the moral hazard problem, thereby leading to a higher performance. But on the other hand, shorter contracts increase the new club's renegotiation payoff, which ceteris paribus reduces the expected joint payoff of the player and his initial club. In the initial contract, the club and the player are trying to balance these countervailing effects at the margin. The crucial point is that the distribution of 4 renegotiation payoffs does not only depend on the (remaining) contract length, but also on the transfer system. This feature drives our results, and leads to a higher contract length under regime B compared to regimes P and M. Furthermore, we show that the impact of the contract length on the initial wage and the transfer fee actually paid is maximum under regime B.
Our last and presumably most interesting finding from the point of view of empirical contract theory refers to the relation between the contract length and the actual performance. Again, we have two countervailing effects: on the one hand, the longer the contract, the lower the performance (moral hazard effect). But on the other hand, we show that the equilibrium contract length is increasing in a player's potential (selection effect). Comparing the three systems, we find that the relationship between performance and contract length should be minimum under system B since there, the moral hazard effect is most pronounced compared to the selection effect.
For the empirical analysis, we have compiled a comprehensive data set from the German Bundesliga covering 1308 player years. The data contains all available information on contract lengths, salaries, transfer fees and performance measures from 1994 to 2001. As the Monti system has been put into force only very recently, the data allows for a comparison between systems P and B only. All our theoretical results are empirically confirmed, one exception being the impact of a player's remaining contract length on his salary in the new club after a transfer which, according to our model, should be most pronounced under system B. However, we provide a plausible explanation based on unobservable sign-up fees which tend to generate systematic countervailing effects.
Relation to the literature As indicated above, our paper is related to three lines of research. With respect to the literature on sports economics, the impact of the Bosman judgement has been analyzed by Simmons (1997) and Antonioni and Cubbin (2000) who also argue that the average contract length should increase after the judgement. That more flexible labor markets lead to a higher contract length is also empirically shown by Kahn (1993) for Major League Baseball in the US. Szymanski (1999) argues that players benefit from the judgement, but takes the initial contract as being given.
To the best of our knowledge, all preceding empirical analyses on transfer fees including Speight and Thomas (1997), and Carmichael, Forrest, and Simmons (1999) (for the English Premier League), and Frick and Lehmann (2001) (for the German Bundesliga) do neither have data on the contract length nor performance measures. Therefore, all these papers were restricted to analyzing the impact of players' characteristics such as their position, age and experience on the transfer fees paid.
Our theoretical model partly builds on Feess and Muehlheusser (2003a) and Feess and Muehlheusser (2003b) who also compare the different regimes using a contract theoretic approach. In the second paper, the moral hazard issue is analyzed in more detail as a player's effort choice also affects his expected benefit from a transfer. Moreover, in both papers, the renegotiation process is modeled explicitly, and one main focus is on the comparison of the incentives to invest in the education of young talents under the different legal regimes. In this paper, we have to neglect such investment issues because the relevant data is unavailable.
To the best of our knowledge, our paper is the first one which analyzes the legal regimes both theoretically and empirically. Thereby, a novel feature is that it explicitly deals with the interplay of countervailing effects due to heterogeneity and moral hazard. It is wellknown among empirical contract theorists that the failure of adequately dealing with this issue may lead to severely biased empirical results (see e.g. Abbring, Chiappori, Heckman, and Pinquet (2003) and the survey by Chiappori and Salanie (2003)). Consequently, several papers are dealing with the issue of separating these effects to yield unbiased results (see e.g. Lazear (2000), Ackerberg and Botticini (2002) and Banerjee, Gertler, and Ghatak (2002)). While our data does not allow for a full separation of these effects, our empirical analysis nevertheless verifies that the relative importance of these effects under the different legal regimes behaves as predicted by the model. Our paper is also related to the literature about restrictions on the freedom of contract. Diamond and Maskin (1979) analyze situations where two parties to a contract have a joint incentive to use the contract as a commitment device to reduce the expected payoff 6 of future trading partners. Aghion and Bolton (1987) show that a buyer and a seller may stipulate a damage clause to prevent efficient trade with an outside party for some states of the world. Whereas their result holds only if renegotiation is excluded, Spier and Whinston (1995) extend the model to renegotiation and relation-specific investments, and they show that the result can qualitatively be preserved in such a framework. In all these situations, an appropriate restriction on the set of feasible contracts would be socially desirable. On the other hand, Segal and Whinston (2000) stress the potential beneficial effect of exclusive dealing clauses on investment incentives. We are not aware of any empirical results on these issues. As explained above, the different transfer regimes which we analyze also entail restrictions on the freedom of contract. Although we do not perform a welfare comparison of these three regimes, our analyses shows both theoretically and empirically how important economic variables such as the contract terms or performance are affected by these restrictions.
We proceed as follows: After developing our theory in section 2, we present the data and our empirical findings in section 3. Section 4 critically discusses our assumptions and suggests some lines for further research.

The model
We consider a model where at date −1, a player and his initial club ("club i") bargain over a contract containing a contract length T and a wage W per unit of time. At date 0, the player starts playing in the league, and his career horizon is normalized to 1. We suppose that the player's performance e per unit of time in club i depends both on his potential e 0 and his contract length T , and we make the following assumption: Assumption 1 The player's performance per unit of time in club i is the higher, the higher his potential e 0 and the lower the length of the initial contract T , i.e. e = e(e 0 , T ) satisfying ∂ ∂e 0 e(·) > 0, ∂ ∂T e(·) < 0 and ∂ 2 ∂T 2 e(·) < 0.
That e increases in the player's potential is straightforward, and the moral hazard problem behind the negative relationship between e and T has been explained in the introduction (see, however, our remarks at the end of subsection 2.1). For simplicity, we will continue with the explicit functional specification e(e 0 , T ) = e 0 − 1 2 T 2 , where e 0 > 1 2 . Thus, the player's actual performance e is lower than his potential e 0 for all T > 0. 5 Finally, we assume that the monetary surplus generated by the player is simply equal to e, so that the terms "productivity" and "performance" are used synonymously throughout.
With probability g ∈ (0, 1), a shock occurs at some certain date t ∈ (0, 1) leading to a performance e max = γe 0 where γ > 1 per unit of time in another club, called the "new club" (club n). Thus, whenever the shock occurs, the player is more productive in club n, independent of the terms of the initial contract. We assume common knowledge of e(·) and e max at date −1, the only uncertainty being whether or not the shock occurs.
Since there is no asymmetric information in the model, we make the standard assumption that negotiations are efficient such that they maximize the joint surplus of the parties involved in the negotiations. This implies that i) at date −1, the initial contract will maximize the joint surplus of the player and club i, and ii) in the renegotiation process at date t, the player joins club n at date t regardless of the terms of the initial contract, and regardless of the transfer system. The player then plays for club n with productivity e max per unit of time until the end of his career at date 1. When the shock does not occur, we simply assume that the player keeps playing for club i with productivity e(T ) until his career ends. The sequence of events is summarized in Figure 1: 5 Note carefully that the assumption refers to the partial derivative, i.e. for a given potential e 0 ; we will show below in subsection 2.4 that, in equilibrium, high potential players will sign longer contracts so that the oberserved relationship between contract length and absolute performance may well be positive. To avoid confusion, there is one point concerning Assumption 1 which we would like to discuss right away (and not only in the discussion in section 4). Our model will be driven by the trade-off between the advantage of long contracts through higher payoffs in the renegotiation game at date t and the disadvantage of long contracts captured by the moral hazard problem ∂ ∂T e(·) < 0. The economic logic behind the moral hazard problem is that a player knows that he will be paid in the future as long he has a valid contract, even if he performs poorly. Hence, the moral hazard problem at each point in time depends on the remaining contract length, and not on T itself. Accounting for this would require a continuous model where e varies over time. And in our model where the productivity shock leading to a change of clubs can only occur once at a certain date t, it would then be optimal for club i and the player to agree upon an infinite number of short-term contracts up to t − ε (where ε → 0), and to a long-term contract covering the whole remaining time horizon at t − ε. To avoid these unrealistic features, it would then be necessary to assume that the shock can occur at any point in time during the player's career. In fact, we considered a model where e is decreasing in the remaining contract length, and where g = g(s) > 0 ∀s ∈ (0, 1). This continuous setting has two advantages -it is more realistic and it is more convenient when turning from theory to the empirical part. However, since the analysis then becomes extremely tedious without changing any of our results, we finally decided to use this simpler discrete version. The reason why all results remain unchanged is that the only aspect that matters is that the average performance decreases in the original contract length, and this is true in both variants.

Renegotiation at Date t
Before we solve the model backwards starting with the renegotiation stage at date t, we must first describe the three regimes more formally.
Definition 1 A transfer system r l = (r lV , r lN ), l = P, B, M is characterized by two legally administered transfer fees (veto sums) per unit of time which club i must accept if the player wants to join club n at date t under contract situation c ∈ {V, N}.
The upper index V indicates that the player still has a valid contract, whereas N means that the contract has expired. These fees are veto sums for the initial club, and thus constitute upper bounds for the transfer fees actually paid. To distinguish between the administered fees and the transfer fees actually paid, we refer to the first ones as veto sums. Expressing all magnitudes per unit of time is helpful to separate the impact of the transfer fee system from the impact of the remaining contract length. Note that r BN = r MN = 0, since there are no veto sums (and hence no transfer fees actually paid) for expired contracts after the Bosman judgement. Furthermore, r P V = r BV = ∞, since there is no fee under systems P and B which the initial club must accept if the player has a valid contract. Finally, 0 < r P N , r MV < ∞, since club i can not prevent the transfer upon receiving some finite amount when the player's contract has expired under regime P , and when the player has a valid contract under regime M. We summarize the legal situation in the following table: To determine the renegotiation payoff, assume that the player has signed a contract with club i stipulating some contract length T , and that he wants to join club n at date t. Define α j (e 0 , r lc ) as party j's renegotiation payoff per unit of time as a function of e 0 where l = P, B, M captures the transfer fee system, c = V, N the contractual situation, and where the index j = i, p, n stands for club i, the player and club n, respectively.
Instead of modeling this three-party renegotiation process explicitly, we take a reducedform approach and introduce the following assumptions on the renegotiation payoffs per unit of time: Assumption 2 For all r c ∈ [0, ∞], renegotiation payoffs per unit of time have the following properties: Part i) of Assumption 2 expresses that club i's renegotiation payoff per unit of time (i.e. the actual transfer fee per unit of time) is weakly increasing in its veto sum r c , whereas the player's payoff (i.e. his new wage) and club n's payoff (i.e. the remaining surplus) are weakly decreasing in r c . The assumption can be justified for two reasons: first, it is quite natural that club i benefits from more veto power. Second, we have shown elsewhere that these properties can be endogenously derived from a bargaining game in which the player negotiates simultaneously with both clubs in Nash-bargaining fashion. 6 Note that we assume the partial derivatives with respect to r c to be only weak, since in reality it does not seem to make any difference for the threat points in the renegotiations whether the veto sum for a mediocre player is 200 or 300 million Euro.
Part ii) of the assumption expresses that club n benefits from an increase in e 0 which determines the size of the renegotiation surplus, but this increase becomes smaller when the veto sum of club i, r c , rises (i.e. when the transfer system becomes stricter). To see that this also seems natural, note that a sufficient condition for this assumption to hold is that club n gets a fixed percentage of the renegotiation surplus for a given r c whereas this percentage is decreasing in r c due to part i) of the assumption. For example, suppose club n gets 1 4 of the surplus for r = r V and 1 2 for r = r N < r V . When the renegotiation surplus increases from 100 to 200, say, his payoff increases by 25 (from 25 to 50) if r = r V and by 50 (from 50 to 100) if r = r N < r V .
Finally, each regime l = P, B, M is completely specified by two numbers r lV and r lN .
Thus, when no confusion is possible, instead of writing α j (e 0 , r lc ) we save on notation and from now on simply write α lc j (e 0 ). Recalling that all α lc j (e 0 ) are expressed per unit of time, the overall payoffs from renegotiation are obtained by summing over time. In doing so, we can restrict attention to T ∈ [t, 1], since it does not make any difference whether the contract length is T = t or some T < t. In both cases, the player is out-of-contract when the shock occurs, so that only r lN would matter for the renegotiation game. The idea behind the renegotiation process is again illustrated in figure 2:  Moreover, for our empirical purposes it will be useful to express total renegotiation payoffs not as a function of the contract length T but, equivalently, as a function of the remaining contract length R := T − t. Denoting by π j (e 0 , R, r l ) party j's total renegotiation payoff as a function of the player's potential e 0 , the player's remaining contract length R and the veto sums under system l, we get: In each line, the first term gives the payoff for the period for which the player has a valid contract, while the second term is the payoff for the period for which the contract has expired. Thus, π i (·) is the total transfer fee actually paid, π p (·) is the total wage of the player in club n, and π n (·) is club n's share of the total surplus (1 −t)γe 0 to be shared in the renegotiation process. This leads to the following results: Proposition 1 i) Under each regime, the total renegotiation payoff is increasing in R for club i and decreasing for the player and club n, i.e. d dR π i (·) > 0, d dR π p (·) < 0, and d dR π n (·) < 0, ∀l = P, B, M.
ii) Under regime P , club i (weakly) benefits from an increase in r P N while the player and club n are (weakly) worse off, i.e. dπ i (e 0 ,R,r P N ) iii) Under regime M, club i (weakly) benefits from an increase in r MV while the player and club n are (weakly) worse off, i.e. dπ i (e 0 ,R,r MV ) iv) The marginal effect of an increase in R is largest under regime B, i.e.¯d dR π j (·, r B )¯> d dR π j (·, r P )¯,¯d dR π j (·, r M )¯∀j = p, i, n.
Proof. Follows immediately from Assumption 2 and Table 1. ¥ The proposition is just a simple transformation of Assumption 2 and the entries in Table 1; but it is very useful for our purposes of testing the proposition in the empirical part of the paper. The reason for part i) is that due to r lV − r lN > 0 ∀l, club i gets the higher payoff for a longer period of time, while the reverse is true for the player and for club n. Parts ii) and iii) follow directly from Assumption 2 part i). Finally, as for part 13 iv), the impact of the contract length is highest under regime B, because the difference of veto sums is highest, too.
For our empirical purposes, let us emphasize another aspect of Proposition 1: Although our statements refer to a player's total wage π p in club n, they also hold for π p 1−t , i.e. for a player's average wage in the new club per unit of time as (1 − t) is a constant.
In the empirical tests, we will use the annual wage of a player in the new club.

The Initial Contract
We can now turn to the analysis of the initial contract. Under each regime l, this contract will maximize the expected joint surplus of the player and club i given by Regardless of the shock, club i and the player get the surplus e(·) up to date t. If the shock occurs (which happens with probability g), they get the new total surplus e max minus club n's renegotiation payoff. This payoff is α lV n (e 0 ) for period (T − t) for which the player's contract is still valid, and α lN n (e 0 ) for period (1 − T ) when the contract has expired. With probability (1 − g), there is no shock, and club i and the player share surplus (1 − t)e(·). Substituting e(·) = e 0 − 1 2 T 2 , and rearranging yields The optimal contract length under regime l is denoted T l and solves arg max T JS(e 0 , T, r l ).
Since d 2 dT 2 JS(·) = − (1 − g (1 − t)) < 0, the problem is strictly concave in T , so that T l satisfies the first order condition and is thus given by: 14

This leads to
Proposition 2 i) The optimal contract length is highest under regime B, i.e. T B > T P , T M .
ii) Under each regime, the higher a player's potential e 0 , the higher the length of the initial contract, i.e. dT l de 0 > 0 ∀l = P, B, M.
Proof. See Appendix A.
The intuition for part (i) can be seen from Eqn. (6): When deciding on the optimal contract length, club i and the player trade-off two inefficiencies: the longer the contract, the lower the player's performance as d dT e(·) < 0. But the shorter the contract, the higher is club n's renegotiation payoff. The first effect is independent of the transfer system, whereas the second effect depends on the difference between club n's payoff per unit of time with and without a valid contract. The higher this difference, the higher club i's and the player's incentive to increase T . And this difference is maximum under system B, because r BV = ∞ and r BN = 0 (see Table 1 above). Ordering T P and T M is not possible without specifying respective values of r P N and r MN as r P V > r MV , but also r P N > r MN so that the difference is indeterminate. Note that, without any negative effect associated with long term contracts (modeled here as a moral hazard problem via Assumption 1), we would get a corner solution T l ≡ 1∀l as there would only remain the incentive to reduce the renegotiation payoff of club n. 7 Part (ii) follows from assuming that the impact of T on club n's renegotiation payoff increases in e 0 since the amount to be divided is e max = γe 0 . While it can easily be shown that T l is also increasing in g, so that players with a higher shock probability would also sign a longer contract, we focus here on the impact of a player's potential e 0 to explain why we observe different contract lengths in reality. 8 It remains to determine how the surplus is split between club i and the player via the wage W . As for this, we simply assume that the player gets some share β of the surplus, where 0 < β < 1. β may vary from player to player, depending for instance on the initial competition of clubs for players, on the position or on the relative bargaining skills of the parties. All we need is that β is neither zero nor one, and this seems to be quite plausible.
Denote by Π p (e 0 , T l , r l ) the player's overall payoff when the jointly optimal contract length T l is chosen, i.e.
Whenever the player is playing for club i (which happens with probability one until date t and with probability (1−g) for period (1−t)), he gets wage W per unit of time. If the shock occurs, he gets renegotiation payoff π p (e 0 , T l , r l ) = (T l −t)·α lV p (e 0 )+(1−T l )·α lN p (e 0 ). Since the player gets a fraction β of the joint surplus, we have Π p (e 0 , T l , r l ) = β · JS(e 0 , T l , r l ), and the initial wage W l = W (e 0 , T l , r l ) per unit of time is thus implicitly given by

This leads to
Proposition 3 i) Under each regime, a higher optimal contract length leads to a higher initial wage, i.e. d dT W l (·)¯T =T l > 0 ∀l = P, B, M. ii) At the margin, this effect is largest under regime Proof. See Appendix B.
As for part i), recall from Proposition 2 part ii) that the privately optimal contract length increases in e 0 . And for anyê 0 > e 0 (which implies T l (ê 0 ) > T l (e 0 ) for the optimal contract length T (·)) we must have JS(ê 0 , T l (ê 0 )) > JS(e 0 , T l (e 0 )) since the player and club i could otherwise simply choose the same contract length forê 0 as for e 0 which would still lead to JS(ê 0 , T l (e 0 )) > JS(e 0 , T l (e 0 )). And since the player's wage is increasing in JS, part i) follows. For an intuition of part ii), recall that the negative impact of T on club n's renegotiation payoff is highest under system B, so that the impact of T on JS (and hence on W ) must be highest, too. 9

Comparison of actual player performance
In this subsection, we investigate the impact of the legal systems on the relationship between the equilibrium contract length T l and the actual performance e. As for this, denote for all l = P, B, M by e l = e(e 0 , T l ) the actual performance of a player with potential e 0 when the optimal contract length T l is chosen.
To determine the sign of de l dT l , we have to take into account the following countervailing effects: On the one hand do we know from part ii) of Proposition 2 that players with higher potential sign longer initial contracts. Since high potential players perform better than low potentials if the contract length is identical, this suggests a positive relationship between e l and T l . We call this the "selection effect". But on the other hand, it is clear from Assumption 1 that the moral hazard problem ceteris paribus increases with the contract length, and this suggests a negative relationship between e l and T l . As mentioned in the Introduction, this interplay between moral hazard and heterogeneity is a well-known problem in empirical contract theory, and it implies -in our modelthat the sign of the overall effect can be either positive or negative. 10 However, we get a precise prediction concerning the relative importance of these two effects under the different regimes: Proposition 4 For the relationship between the actual performance e l and the equilib- Proof. See Appendix C. 9 Note, however, that Proposition 3 holds only if the optimal contract length T l is chosen. For any other contract length, the moral hazard effect could outweigh the renegotiation effect, thereby reducing JS and thus W for any β given.
10 Note that we cannot exclude de l dT l < 0 by arguing that it can never be optimal for club i and the player to sign a contract such that the selection effect is dominated. If the impact on club n's renegotiation payoff is strong enough, this can be consistent with joint surplus maximization.
Intuitively, the reason for de B dT B < de P dT P is as follows: Recall from Proposition 2 part i) that the incentive to increase the initial contract length is highest under regime B.
Thus, the corresponding level of e 0 for each T is lower than under regime P . In other words, since a long contract is chosen even for mediocre players, the moral hazard effect is relatively more important under system B compared to system P . An analogous argument holds for the result de B dT B < de M dT M . As in Proposition 2 part i), the comparison between regimes P and M is ambiguous and depends on the difference between the renegotiation payoffs when the player's contract is valid or expired and thus on the sign of (r P N − r P V ) − (r MN − r MV ). Summing up, we find that the legal restrictions expressed in the systems P , B and M not only influence the terms of the contract and the payoffs, but also the relationship between the equilibrium contract length and the performance.

Description of the Data
In this section we aim at providing empirical support for the predictions of our model.
Since system M has been enacted just recently, we have to restrict attention to systems B and P . Our data cover six consecutive seasons in the German top professional soccer league ("Bundesliga") of which the first two (1994/95 and 1995/96) have been played under system P and the remaining four (1996/97-1999/2000) under system B. Using the two leading German soccer magazines "Kicker" and "Sport-Bild", we have compiled a data set with detailed information on player performance, contract duration, annual remuneration and transfer fees paid. Player performance per season is measured by a composite index, called "kick index", that takes into consideration both position-specific factors such as the number of assists per match for a striker, and team specific factors as the result of a match. 11 Our data set includes information on 1308 different contracts. In 695 cases, these 11 More information about the composition of this performance index is provided in Appendix D.
contracts were signed following a transfer, while in the remaining 613 cases, players resigned with their current club. Altogether, we know the annual salaries agreed upon in 937 cases, and the duration of the contract in 975 cases. When a player has been transferred from another club, we have information about the remaining contract length at the time of the transfer in this old club for 239 cases. Moreover, we have the actual transfer fees for 684 cases (in 142 of them, the transfer fee was zero). Overall, our sample includes 53% of all transfers in which a non-zero transfer fee was paid during the time period under consideration. These are all cases where the transfer fee has been reported in the media, and we see no reason for a sample selection bias. Nevertheless, we will account for this possibility by also using a Heckman Two Step Procedure in the empirical analysis.
Finally, since the composite index is only calculated for "regular" players who appeared in a match for at least 30 out of the 90 minutes a soccer match lasts, we have information on performance for 1318 player years. Table 2 gives more information on the dependent variables and shows how many cases refer to the Pre-Bosman-and the Bosman-period, respectively. As will become clear below, our estimations will involve the simultaneous use of these variables. This tends to reduce the available number of observations as we do not have all relevant information for all cases. For example, we have information on the contract length and the salary for 604 cases, and on the contract length and the performance in 739 cases.
insert table 2 here During the time period of our sample, the soccer industry in Europe has seen a huge increase in TV revenues (during the 6-year period under consideration the increase was 100% ), a fact which we have to take into account. In our estimations, we will therefore not use the nominal values of the variables which are measured in monetary units (i.e. transfer fees and wages), but instead use the standardized values ln( transfer fee average transfer fee ) and ln( annual salary average annual salary ). 12 As control variables we use measures that have been identified in a number of studies as (potential) determinants of player salaries and transfer fees in European soccer (see the literature review in the Introduction). As can be seen in The table shows that our theoretical results concerning the impact of the remaining contract length on the transfer fees actually paid are empirically confirmed. One more remaining year of contract in the old club increases the transfer fee by 3.2%, and this effect is significant at the 1%-level. Moreover, we also find that this effect has become stronger under the Bosman regime B, i.e. we get another increase by 0.9% and thus 28% more compared to regime P . Also, our control variables confirm the findings by, among others, Carmichael, Forrest, and Simmons (1999) and Frick and Lehmann (2001) First, recall that part (i) of Proposition 1 is expressed with respect to the player's total wage π p , whereas part (i) of Hypothesis 1 refers to the annual wage (which can be interpreted as the wage per unit of time, i.e. as πp 1−t in the theoretical model). As explained in subsection 2.2, this is clearly the adequate measure for testing the Proposition. The estimation confirms our theoretical result that a higher remaining contract length has a negative effect on the player's annual wage in his new club: one more remaining year of contract reduces his annual wage by 2%. Again, this effect is highly significant. Finally, a Heckman Two-Step estimation yields basically identical results.
However, it cannot be empirically confirmed that the impact on wages is higher under system B. By contrast, we find at a low significance level that the negative impact of the remaining contract length on the wage in the new club has become weaker under regime B. In our view, this might be attributed to hidden sign-up fees which clubs pay "under the table" to players whose contracts with their old clubs have expired. There is abound anecdotal evidence that this practice has become quite common only in the aftermath of the Bosman judgement. Of course, these payments should be interpreted as part of a player's salary. Unfortunately, they are notoriously hard to observe and consequently, we have no information in which cases such fees have been paid in our sample. 13 If such fees are paid in addition to the regular wage to out-of-contract players, and if this phenomenon is more pronounced under regime B, then our regression under-estimates the benefit from being out-of-contract under system B, and thus also the wage reduction from having a positive remaining contract length.

Testing Proposition 2
Whereas Proposition 1 referred to the renegotiation game, Proposition 2 analyzes the impact of the transfer fee system and a player's potential e 0 on the contract length. Since we have no empirical proxy for e 0 (our index measures only the actual performance e), we have to restrict our attention to part (i) of Proposition 2: Hypothesis 2 The average contract length is higher under system B than under system P , i.e. T B > T P .
When testing the hypothesis, the LM-test statistic suggests that an OLS estimation is inferior to a Random Effects-model. The results of the RE-estimation are reported in The average contract length has indeed been increasing from 2.43 years to 2.91 years after the Bosman ruling, and controlling for a number of different dimensions of a player's 13 One example is the transfer of German "prodigal" Sebastain Deisler from Hertha BSC Berlin to Bayern Munich in 2002. The fact that Munich had paid a sign-up fee of 10 Mio. € became publicly known only after an obvious leakage in the administration of one of the clubs. This resulted in a copy of the cheque being printed on the title page of Germany's largest tabloid "Bild". performance, we find that this is statistically significant at a high level. This lends broad support to our hypothesis that this difference has to be attributed mainly to the changes in the underlying incentive structure. Furthermore, most of the statistical controls have the expected sign and are statistically different from zero. For example, older players sign shorter contracts while more "established" players (those with a high number of career games and those who have played for their respective national team) get longer contracts. 14

Testing Proposition 3
Let us first recall that, in Proposition 1, we were interested in the impact of a player's remaining contract length in his old club on the new contract terms (i.e. the transfer fee and the wage paid by the new club). In other words, we considered the impact of the old contract on the renegotiation game for a new contract. Now, we are testing the impact of the contract length in a club on the wage in this club itself. Since it is precisely the anticipated gain in the renegotiation game that sets incentives for long-term contracts, Proposition 1 was the basis for Proposition 3. Of course, the adequate measure for testing the Hypothesis is again not the total wage but the annual wage (see the remarks after Proposition 1). 15 We test the following hypothesis: Hypothesis 3 a) Under both systems P and B, the annual wage in the current club is increasing in the contract length in the current club.
b) This effect is larger under system B.
The fact that we are now concerned with the impact of the contract length on the wage in the current club implies that, compared to the test of Proposition 1, the sample size increases from N = 239 to N = 604. This is due to the fact that we can now also use those cases in which a player and his club renewed their contract without a transfer taking place (of course, this new contract will typically stipulate a different length and/or wage than the previous one). This also increases the degree of unobserved heterogeneity, because we now have up to four different contracts per individual player. Therefore, in addition to the OLS model used for testing Hypothesis 1, we also estimate a Random Effects model, the results of both being shown in table 7:   insert table 7 here Our RE estimates strongly confirms the hypothesis: When the contract length increases by one year, the annual wage goes up by 0.7%. This effect is significant at the 1%-level. Moreover, the interaction term (Contract Duration times Bosman Dummy) is positive and significant, implying an additional increase of about 0.5% per year under regime B. In turn, this implies an increase by more than 50% compared to regime P .
Again, the signs of the standard control variables are as expected, and as predicted in previous studies (see e.g. Lucifora and Simmons (2003)): For example, the number of career games has a positive but decreasing influence on wages, and being selected for the national team also increases a player's income.

Testing Proposition 4
We now move to testing the relationship between the contract duration and the actual performance. Let us first mention that, conversely to Proposition 4, Hypothesis 4 is stated with respect to the remaining contract length instead of the absolute (initial) contract length. As explained at the end of subsection 2.1, this difference comes from the fact that in our model, we have expressed the moral hazard problem with respect to the absolute contract length for simplicity. For empirical purposes, however, it seems adequate to choose the remaining contract length instead. As explained above, the underlying economic logic is the same since in both cases, the average performance is decreasing in the contract length.
As pointed out in section 2.4, this relationship between the remaining contract length and performance is indeterminate from a theoretical point of view: on the one hand do players with a higher potential sign longer contracts, while on the other hand, a longer 24 remaining contract length leads to lower performance incentives ("moral hazard effect"), thereby driving the overall result ambiguous.
However, our theory unambiguously predicts how the net impact of the two effects changes as one moves from regime P to regime B: While the moral hazard problem is basically the same under both regimes, the incentive for the initial club i and the player to sign a long-term contract is higher under system B, which reinforces the impact of the moral hazard problem in equilibrium. We thus test the following hypothesis: Hypothesis 4 A larger remaining contract length has a stronger negative impact on observed performance under system P than under system B.
To identify the determinants of a player's performance, we again estimate a RE-model, because we have up to six observations per player. The estimation results are shown in The table shows that the hypothesis is supported by the data: First, a remaining contract length of one more year increases average performance by 2.15 index points, thereby suggesting that the selection effect dominates in our sample. Second and more importantly, this effect becomes weaker under the Bosman regime (−1.21 index points).
We take this result as supportive of the basic idea of our model that the legal change affects the trade-off between the selection-and the moral hazard-effect, thereby not only leading to a different equilibrium contract length, but also to a different relationship between contract length and performance.

Discussion
We have developed a model for analyzing the impact of the three different transfer systems in European soccer. Our main theoretical and empirical results can be summarized as follows: (i) under all regimes, the initial club benefits at the renegotiation stage from high veto sums and from long contracts. (ii) since the impact of the contract length on the renegotiation payoffs is maximum under the Bosman regime B, the contract length is highest under this regime, too. (iii) when a player signs a longer contract, then he is compensated for his lower renegotiation payoff by receiving a higher initial wage per unit of time. This effect is again maximum under regime B. (iv) finally, the relationship between the contract length and the observed performance can theoretically be either positive (when the selection effect dominates) or negative (when the moral hazard effect dominates), but in any case, it is higher under regime P than under system B.
Although all but one of our theoretical propositions are confirmed empirically at a highly significant level, one may nevertheless challenge some of our underlying assumptions. First, recall that an interior solution for the contract length arises due to the trade-off between the new club's renegotiation payoff (which decreases in T , respectively R) and the moral hazard problem (which increases in T , respectively R). Thereby, we assume that the moral hazard problem is independent of the transfer fee system, whereas the renegotiation impact of the contract length depends on the system. Alternatively, one might assume that the moral hazard problem also depends on the transfer fee system, for instance because a player's incentive may be higher if he expects a high payoff in renegotiations. 16 However, we believe it to be reasonable that at least part of the problem arises simply due to the fact that the player is "insured" by the long-term contract.
Furthermore, different contract durations within one regime (B, say) in our model arise due to different potentials (e 0 ). Let us emphasize that we are far from denying that there are many other aspects influencing the optimal contract length: risk preferences may be different, 17 the shock probability g may vary from player to player, and in a dynamic model where the shock can arise at any point of time, the probability densities may differ across players. Moreover, the moral hazard exposure may also vary across players which could be captured in our model by assuming that e k = e 0 − b k T 2 , thereby expressing the player-specific moral hazard exposure via b k . However, it is well known in empirical sports economics that high-potential players sign longer contracts (see i.e. Kahn (1993)). In addition, explaining different contract durations via differences in e 0 leads to interesting insights on the impact of transfer regimes which are perfectly compatible with our empirical findings. Finally, with respect to the issue of identification, our result that the relationship between the remaining contract length and observed performance should be more pronounced under regime P seems rather specific and can hardly be explained with other approaches. We therefore tend to take the empirical confirmation of this result as being supportive of our theory.
Although the impact of legal restrictions on contract terms has so far hardly been tested empirically so that our approach seems to be important, there exists a clear drawback of our analysis: the theoretical literature aims at analyzing potential restrictions on the freedom of contract from a normative perspective, and this is clearly missing in our paper -we have no propositions like "system B is socially superior to system P ". From a theoretical point of view, our model allows for such a prediction: since actual performance is decreasing in the contract length, and since the contract length is maximum under regime B, the quality of the league should be lower after the Bosman judgement as the moral hazard problem becomes more severe. However, we have not tested such a hypothesis because we believe that our performance measure only allows for relative, but not for absolute performance comparisons -it seems to us that the grades assigned to players in the soccer magazines do not relate to the absolute quality of the league.
In other words, it is not possible that both, the defender and the striker loose the same tackle at the same time. Furthermore, social welfare also depends on competitive balance and on the incentives to invest in the training of young talents, which both are aspects that are not incorporated in our theoretical model.
Although these issues are clearly important and deserve further research, we are also interested in extending our framework in the following two directions: First, the fact that only about 10 percent of a player's salary is related to performance indicates that setting incentives is not costless. And since the moral hazard problem is most severe under regime B due to higher contract durations, our model would also predict that the performance-27 related payments should be higher after the Bosman judgement, too. Second, Proposition 4 sheds light on the interplay between the selection effect and the moral hazard-effect, but it does not allow to fully separate these two effects. This requires to gather more detailed data at the individual player level, and we are currently working on such a project. Preliminary results show that, controlling for age, position and other factors, the ratio between actual performance and maximum performance is indeed decreasing in the remaining contract length, thereby supporting the moral hazard assumption underlying our theory.    The following regressions test the empirical validity of Proposition 1. The dependent variable is log standardized transfer fee. The estimation technique in (1) is OLS with robust standard errors (White (1980)) and the Heckman Two-Step Procedure in (2) where the instrument used is "tenure in the current club".

D Composition of the Performance Index
(1)  The following regressions test the empirical validity of Proposition 1. The dependent variable is log standardized annual wage in the new club. The estimation technique in (1) is OLS with robust standard errors (White (1980)) and the Heckman Two-Step Procedure in (2) where the instrument used is "tenure in the current club". (1) (  Since some individual characteristics of the players, such as nationality and position, are usually time-invariant, they can not be included in a fixed effects estimation. Therefore, we report the results of a random effects GLS regression instead. The most important coefficient in the present context (the Bosman-Dummy) remains unchanged in a fixed effects approach. The following regressions test the empirical validity of proposition 3. The dependent variable is the log Standardized Annual Wage in the current club. The estimation technique used is OLS with robust standard errors (White (1980)) in (1) and a Random Effects Model in (2).
(1) .6*** ‡ Coefficient multiplied by 100 for presentational purposes ‡ ‡ Coefficient multiplied by 1,000 for presentational purposes # Dummy variable + Not significant * Significant at the 10% level ** Significant at the 5% level *** Significant at the 1% level Since some individual characteristics of the players, such as nationality and position, are usually time-invariant, they can not be included in a fixed effects estimation. Therefore, we report the results of a random effects GLS regression instead.