The Impact of Salary Caps in Professional Team Sports

In this paper we analyse the impact of a salary cap on a professional team sports league. We concentrate on the competitive balance, on the level and the distribution of player salaries, on owner profits and total league revenue. A simple model shows that a salary cap can improve the competitive balance among clubs as well as the salary distribution among players. We also investigate how the recent individual salary cap in NBA might affect the competitive balance.     

THEORY OF THE BEAUTIFUL GAME: THE UNIFICATION OF EUROPEAN FOOTBALL

European football is in a spiral of intra‐league and inter‐league polarization of talent and wealth. The invariance proposition is revisited with adaptations for win‐maximizing sportsman owners facing an uncertain Champions League prize. Sportsman and champion effects have driven European football clubs to the edge of insolvency and polarized competition throughout Europe. Revenue revolutions and financial crises of the Big Five leagues are examined and estimates of competitive balance are compared. The European Super League completes the open‐market solution after Bosman. A 30‐team Super League is proposed based on the National Football League.     

OVERINVESTMENT IN TEAM SPORTS LEAGUES: A CONTEST THEORY MODEL

This paper applies contest theory to provide an integrated framework of a team sports league and analyzes the competitive interaction between clubs. We show that dissipation of the league revenue arises from 'overinvestment' in playing talent as a direct consequence of the ruinous competitive interaction between clubs. This overinvestment problem increases if the discriminatory power of the contest function increases, revenue-sharing decreases, and the size of an additional exogenous prize increases. We further show that clubs invest more when they play in an open league compared with a closed league. Moreover, the overinvestment problem within open leagues increases with the revenue differential between leagues.     

The invariance principle in baseball: new evidence

This article considers the change in revenue sharing in Major League Baseball that occurred prior to the 2007 season and its effects on parity via its effects on marginal revenues. Based on the results from an empirical specification for team revenue, we find evidence that the reduction in revenue sharing increased marginal revenue by more for large market clubs than for small market clubs, despite holding constant other differences in how small and large market club revenues are determined. The upshot of this result is that the modest reduction in revenue sharing could have worsened league parity by 11 to 17 points in winning percentage between small and large market clubs, although other factors affect parity as well. The well-known invariance principle in the economics of sport literature does not appear to hold; however, the current consensus of theoretical models is not confirmed.     

Fan welfare maximization as a club objective in a professional sports league

Motivated by aspects of European soccer club governance (members' clubs supporters' trusts), a first formal analysis of fan welfare maximization as a club objective in a sports league is provided, with comparisons to objectives studied previously (profit and win maximization). Positive comparisons focus on team qualities, ticket prices, attendances and the impact of capacity crowds; empirically observed ticket black markets and inelastic pricing are consistent only with fan welfare maximization. Normatively, social welfare (aggregate league surplus) is well-served by a league of fan welfare maximizers, or sometimes win maximizers, but not profit maximizers; leagues should not normally make profits.     

Competitive balance in football leagues when teams have different goals

In the standard two-team model of professional league sports it is shown that if teams have different objectives (the maximization of, respectively, wins and profits) the competitive balance conditions get worse with respect to the case when teams share the same goal. A similar, though less clear-cut, result obtains in the three-team setup. These outcomes call for policy measures to restore the balance. Three such measures are examined here: market-size-based revenue sharing, general salary cap and team-specific salary cap. It is shown that, contrary to the same-goal-for-all case, each of them may bring more intra-league competition. A ranking of the three measures is also suggested.     

Performance and revenue in professional league football: evidence from Granger causality tests

Using a dataset comprising annual performance (measured by final league position) and gate revenue for 77 Football League clubs which maintained unbroken league membership between 1946 and 1994, the relationship between performance and revenue is investigated using cointegration and causality tests. A cointegrating relationship between performance and revenue is established in only 10 cases out of 77, although it is argued that some caution is required in interpreting these results, due to the low power of the relevant tests in relatively small samples. In Granger causality tests, more evidence is found of causality running from lagged revenue to current performance than of causality in the opposite direction, while the dependence of performance on revenue seems to be greater for the smaller clubs than for the larger. These results lend empirical support to the popular view that, unless checked by mechanisms for revenue redistribution within the league, the natural tendency is for success to become concentrated increasingly among a small group of elite, wealthy clubs.     

NEGOTIATED SETTLEMENT UNDER MLB FINAL‐OFFER SALARY ARBITRATION SYSTEM

This paper provides a detailed analysis of negotiated salaries under Major League Baseball's final‐offer arbitration process using data from the 2007–2010 seasons. There is a wage premium of 25% for hitters and 14% for pitchers filing for arbitration. Interestingly, there is an additional premium for exchanging offers for hitters but not for pitchers. The additional premium in salary for hitters who exchange offers with their clubs amounts to 7%. (JEL J31, J52)     

MAINTAINING MARKET POSITION: TEAM PERFORMANCE,REVENUE AND WAGE EXPENDITURE IN THE ENGLISH PREMIER LEAGUE

This paper investigates the relationship between playing success and commercial success in team sports. Utilizing a data set relating to the English Premier League that combines both financial measures and indicators of playing skills and performances, our empirical analysis is based on three behavioural equations. Our analysis indicates that on‐field success can be directly related to players’ skills and abilities and that revenue is positively related to on‐field success. Wage expenditure is also shown to systematically reflect player skills and performances. One interpretation of this evidence is that investment in players’ skills and ability buys on‐field success, with richer teams becoming ever richer and able to maintain or even build upon success by spending more on players than less successful clubs. To the extent that richer clubs are successful in their objective there is a causal link between revenue earned and competitive imbalance via investments in players. The implications of this tendency within a league are discussed in our conclusion, which also considers the potentially wider implications of our study as they relate to the evolution of firm size and issues of market share.     

MULTIPLE OWNERSHIP,COLLUSION AND UNUSUAL RESULT PATTERNS IN SOCCER

Expanding on the literature on antitrust, multiple ownership, and collusion in sports, this paper finds a very unusual result pattern between two clubs competing in the Croatian soccer league—Lokomotiva and Dinamo Zagreb. Their close sporting and business relationship has raised many questions about the possible collusion between them, potentially affecting the integrity of the competition. We analyze all matchups in the competition's 25‐year history to single out those characterized by biggest under‐ and overperformances by competing clubs. Our findings provide some support to the allegations of a possible collusion between the clubs as Lokomotiva's underperformance against Dinamo is so far in the tail of normal distribution that it has a lower occurrence probability than a random person being hit by lightning. (JEL Z29, K21, L83).     

THE EFFECT OF GATE REVENUE SHARING ON SOCIAL WELFARE

This paper provides a theoretical model of a team sports league based on contest theory and studies the welfare effect of gate revenue sharing. It derives two counterintuitive results. First, it challenges the "invariance proposition" by showing that revenue sharing reduces competitive balance and thus produces a more unbalanced league. Second, the paper concludes that a lower degree of competitive balance compared with the noncooperative league equilibrium yields a higher level of social welfare and club profits. Combining both results, it concludes that gate revenue sharing increases social welfare and club profits in our model. ( JEL L83)     

Spillovers,subsidies, and second‐best socially optimal R&D

This paper provides a thorough second‐best welfare analysis of the standard two‐stage model of R&D/product market competition with R&D spillovers. The planner's solution is compared to the standard non‐cooperative scenario, the R&D cartel, and the cartelized research joint venture (or joint lab). We introduce the notion of a social joint lab, as a way for the planner to avoid wasteful R&D duplication. With no spillovers, the non‐cooperative scenario, the joint lab, and the second‐best planner's solutions coincide. However, with spillovers, all three scenarios yield R&D investments that fall short of the socially optimal level. To shed light on the role of the spillover level on these comparisons, we observe that the gaps between the market outcomes and the planners solutions widen as the spillover parameter increases. Finally, we establish that a social planner and a social joint lab solutions may be achieved starting from any of the three scenarios by offering firms respective suitably weighted quadratic R&D subsidization schedules.     

GATE REVENUE SHARING AND LUXURY TAXES IN PROFESSIONAL SPORTS

This paper examines the impact of gate revenue sharing and luxury taxes on professional sports leagues within the context of a less restrictive demand function than those used in prior models. In contrast to previous studies, the analysis finds that the increased sharing of revenues may enhance competitive balance. Consistent with other models, the analysis finds that player salaries will diminish as the percentage of shared gate receipts rises. The analysis also explores several variations of luxury taxes. All have the effect of lowering salaries. The impact on league balance depends on how the tax is implemented and on how its proceeds are distributed. As with salary caps, enforcement problems exist with the tax.     

Two universal,probabilistic measures of competitive imbalance

I propose two universal measures of competitive imbalance. The first is, like those in the existing literature, based on team season win–loss records. The second is based solely on the outcomes of the various series of individual matchups during a season. Both measures will on average equal (2p ? 1)², where p is the ‘typical’ probability that the stronger team will win any particular game. Both measures will average zero when a league is competitively balanced and will converge to 1 as the league approaches perfect imbalance. In addition, both measures are universal, in that they are on average independent of the number of teams in the league and the number of games played during the season.     

On the equilibrium and welfare consequences of getting ahead of the Smiths

This paper provides an analysis of the social consequences of people seeking to get ahead of the Smiths. All individuals attempt to reach a higher rank than the Smiths, including the Smiths themselves. This attitude gives rise to an equilibrium in which all individuals have equal utilities but unequal (gross) incomes. Due to a rat‐race effect, individuals devote too much energy to climbing the social scale. However, laissez‐faire equilibrium is an equal‐utility constrained social optimum. Conversely, a utilitarian social planner would not choose utility equality. Unexpectedly, this social ambition theory fairly well accounts for empirical intermediate wage inequality.     

PROGRESSIVE TAXATION AS A MEANS FOR IMPROVING COMPETITIVE BALANCE

The existing instruments for improving the competitive balance within a sports league, such as revenue sharing, restrictions on free agency and salary caps, all have their shortcomings. In this paper, we show that a progressive sports tax, the revenues of which are not redistributed to smaller teams in the league, could be a better instrument. From the broader perspective of the theory of optimum taxation, this instrument may have advantages as well.     

STADIUM CONSTRUCTION AND MINOR LEAGUE BASEBALL ATTENDANCE

The established literature shows that new stadium construction for major league baseball (MLB) teams can increase attendance, but there are limited studies at the minor league level. We use a data set encompassing all A, AA, and AAA minor league baseball teams from 1992 to 2006 to estimate the impact of stadium construction on minor league attendance. This data set includes almost 200 teams, over half of which constructed a new stadium during the 15‐year observation period. Over a 10‐year period our results show that new stadiums increase attendance by 1.2 million fans at the AAA level, 0.4 million at the AA and high A level, and 0.2 million at short season low A. A cost benefit analysis suggests that increased ticket sales do not offset the stadium costs, in line with previous works on MLB. (JEL H0, L83)     

On the Growth and Welfare Effects of Defense R&D

In the United States, defense R&D share of GDP has decreased significantly since 1960. To analyze the implications on growth and welfare, we develop an R&D‐based growth model that features the commonly discussed crowding‐out and spillover effects of defense R&D on civilian R&D. The model also captures the effects of defense technology on (a) national security resembling consumption‐type public goods and (b) aggregate productivity via the spin‐off effect resembling productive public goods. In this framework, economic growth is driven by market‐based civilian R&D as in standard R&D‐based growth models and government‐financed public goods (i.e., defense R&D) as in Barro (1990). We find that defense R&D has an inverted‐U effect on growth, and the growth‐maximizing level of defense R&D is increasing in the spillover and spin‐off effects. As for the welfare‐maximizing level of defense R&D, it is increasing in the security‐enhancing effect of defense technology, and there exists a critical degree of this security‐enhancing effect below (above) which the welfare‐maximizing level is below (above) the growth‐maximizing level.     

THE CHOICE OF APPORTIONMENT FACTORS UNDER FORMULA APPORTIONMENT*

This paper investigates the choice of apportionment factors under a corporate tax system of Formula Apportionment. In contrast to perceived wisdom, we show that the apportionment formula contains both mobile (capital) and immobile (labor) factors, regardless of whether the formula is determined decentrally by jurisdictions or centrally by a central planner. The central planner uses the formula as a corrective instrument to internalize fiscal externalities. We calibrate the model to the European Union and show that replacing the current system of Separate Accounting by Formula Apportionment would substantially increase tax revenue and welfare under both centralized and decentralized formula choices.     

SOCIAL NORMS,LOCAL INTERACTION,AND NEIGHBORHOOD PLANNING*

This article examines optimal social linkage when each individual's repeated interaction with each of his neighbors creates spillovers. Each individual's discount factor is randomly determined. A planner chooses a local interaction network or neighborhood design before the discount factors are realized. Each individual then plays a repeated Prisoner's Dilemma game with his neighbors. A local trigger strategy equilibrium (LTSE) describes an equilibrium in which each individual conditions his cooperation on the cooperation of at least one “acceptable” group of neighbors. Our main results demonstrate a basic trade‐off in the design problem between suboptimal punishment and social conflict. Potentially suboptimal punishment arises in designs with local interactions since in this case monitoring is imperfect. Owing to the heterogeneity of discount factors, however, greater social conflict may arise in more connected networks. When individuals' discount factors are known to the planner, the optimal design exhibits a cooperative “core” and an uncooperative “fringe.”“Uncooperative” (impatient) types are connected to cooperative ones who tolerate their free riding so that social conflict is kept to a minimum. By contrast, when the planner knows only the ex ante distribution over individual discount factors, then in some cases the optimal design partitions individuals into maximally connected cliques (e.g., cul‐de‐sacs), whereas in other cases incomplete graphs with small overlap (e.g., grids) are possible.