Playing for keeps: pay and performance in the NBA.

Stiroh, Kevin J.

I. INTRODUCTION

A basic insight of agency theory is that properly designed incentive contracts can align the interests of agents with those of the principal, and recent empirical work shows that workers do indeed respond to financial incentives. (1) Contractual incentives, however, are not the only force motivating workers. Workers also have incentives to vary effort at different points of their contract cycle--to increase effort just before a new contract is signed to lock in a more lucrative deal and then reduce it after a multi-year contract is secured. These types of contract-related incentives create clear moral hazard problems but have received little empirical attention.

The motivating hypothesis in this paper is that imperfect information and multi-year contracts create an implicit incentive for workers to strategically alter effort over the contract cycle. In the year prior to signing the contract (their "contract year"), workers may exert above-average effort to convince employers that they are high quality and thus raise long-term compensation. Once the contract is signed, however, workers may exert less effort because wages are effectively independent of contemporaneous performance. An empirical difficulty is that this moral hazard may be obscured by two factors--a selection effect may lead only high-quality workers to receive contracts and career concerns may provide additional incentives and dampen the post-contract decline. (2)

This paper employs a unique dataset for professional basketball players in the National Basketball Association (NBA) from 1988 to 2002 to examine the contract-related incentive effects. The data include contract information (year signed, length of contract, and value of contract) for every active player in 2000 and performance measures (points scored, rebounds, assists, etc.) throughout each player's career. Contract-related incentive effects are estimated from changes in individual performance over the contract cycle: if performance systematically improves just before signing a new contract and falls afterward, some of the fluctuation is likely due to contract-related incentives. I also examine the traditional link between pay and past performance, which is necessary for these types of incentives to be relevant.

The critical advantage of this data is the detailed information on individual performance, individual contract status, and individual pay. (3) In contrast, previous work on individual incentives, for example, Lazear (2000), Paarsch and Shearer (2000), and Shearer (2004), studied changes infirmwide compensation plans, while the empirical literature on executive pay and performance, for example, Murphy (1985, 1986), Jensen and Murphy (1990), Gibbons and Murphy (1992), Kaplan (1994), and Hall and Liebman (1998), typically examined the link between individual pay and firm performance. The individual-level data constructed here have the critical variation across individuals, which is needed to identify the impact of these contract-related incentive effects.

The empirical work begins with a test of the link between pay and performance, which is necessary for contract-related incentives to be operational. Not surprisingly, better performers in the NBA are rewarded with higher salaries and longer contracts. More relevant to the incentive issue, players are strongly rewarded for improvements in performance in their contract year. A one-point increase in a player's scoring average, for example, is associated with an annual salary increase of over $300,000. This link provides the crucial motivation for the hypothesis that players will exert additional effort in their contract year to lock in the better contracts that they expect to follow.

The data then provide strong evidence of contract-related incentive effects as overall performance does in fact improve relative to a player's long-run average in the contract year and then declines after a long-run contract is signed. Given the visibility and competitiveness of professional sports, it is unlikely that players actually shirk during games, so these contract-related changes could reflect unobserved factors that determine performance like off-season conditioning or in-season practice habits. Performance declines tend to be smallest for those who signed the very longest contracts, suggesting that the moral hazard of a multi-year contract may be offset by the selection effect of who receives contracts.

A final set of results looks at the impact of these individual incentives on team performance. If players perform better in their contract year and if this effort is valuable to the team, team outcomes (measured as wins) should improve. In contrast, if players fade when multi-year contracts are in place, team performance should suffer. The data suggest that individual contract-related incentives do matter: team wins increase with the share of high-effort players in their contract year but fall with the number of low-effort players that just signed multi-year contracts. A shift of one player from the high incentives of a contract year to the low incentives after just signing a multi-year contract, for example, is associated with a decrease in the number of wins by about 4.5 games per season. Given that the average team wins 41 games, these incentive effects seem quite large.

These results show the importance of contract-related incentive effects and the corresponding moral hazard. Even in the world of professional sports, where performance is readily observable and detailed incentive contracts are possible, workers appear to strategically alter effort over the contract cycle in order to maximize personal gains. In other situations with similar contract cycles, for example, the professor working for tenure or the politician seeking election, these effects could be much larger due to larger informational asymmetries and reduced monitoring ability. In fact, these effects are likely to be present wherever there are multi-year contracts and some contracting friction. This highlights the double-edged nature of multi-year contracts--a valuable incentive and signal mechanism when workers are fighting for contracts, but an opportunity to shirk when workers have them.

II. CONTRACTS AND INCENTIVES

A large theoretical literature on optimal contract theory addresses agency costs and moral hazard in the basic framework where a worker (agent) must be compensated to provide costly effort, while the success of the employer (principal) depends on that effort. Holmstrom (1979) is a classic reference, while Hart and Holmstrom (1987) provide a broad overview; Sappington (1991) reviews additional issues in the standard principal-agent setting, and Prendergast (1999) presents a more recent perspective.

This paper examines the contract-related incentive effects of multi-year, fixed wage contracts when employers cannot perfectly distinguish between effort and ability. That is, the employer cannot perfectly observe either a worker's true ability or his effort but rather observes some indicator of worker performance that reflects both factors; long-term compensation depends on these perceptions. An obvious problem is that multi-year contracts sever the link between pay and contemporaneous effort once the contract is signed. As a result, an employee may have an incentive to strategically alter effort to impact these perceptions and garner a more attractive contract.

The main hypothesis is that incentive effects, and therefore effort, vary across a player's contract cycle and career. Rational workers observe the existing long-run contract environment, which is exogenous from the player's point of view, and choose effort optimally in all years. (4) In particular, effort may vary in the year prior to signing a long-run contract, the "contract year," and the year immediately after a contract is signed as players trade off the costs and benefits of exerting effort. In the contract year, optimal effort will equate the marginal gains from higher wages in the upcoming contract, better firm performance, and possibly long-run gains if higher wages are incorporated into subsequent contracts with the disutility of increased effort. In contrast, after the contract is signed, current compensation is essentially fixed so workers have less incentive to exert costly effort as marginal gains reflect only better firm performance and the possible impact on subsequent contracts.

The key implication is that effort should vary systematically around the contract cycle. The first testable hypothesis is that effort (and performance) is relatively strong in the contract year. The second hypothesis is that effort should fall immediately after the contract year because there is less financial reward for effort. The driving force behind this strategic variation in effort is the severing of the link between effort and immediate compensation once a long-run contract is signed.

The ability of workers to strategically alter effort to maximize payouts has been documented in various settings. Asch (1990) shows that Navy recruiters systematically varied effort, measured by the number of new recruits, in response to the introduction of a specific incentive-based compensation plan. Oyer (1998) highlights the nonlinearity of many incentive-based compensation schemes and exploits variation of fiscal years to show how manufacturing firms' sales and prices vary in response to these incentives. In particular, sales are higher and prices lower at the end of a fiscal year as agents try to close deals to maximize compensation. In terms of professional sports, Maxcy, Fort, and Krautmann (2002) reject the notion of strategic performance around the contract cycle for professional baseball players, while Woolway (1997) and Fernie and Metcalfe (1999) find strong evidence of contract-related incentive effects.

Rational employers, of course, anticipate this strategic variation in effort but have difficulty isolating changes in effort from intrinsic ability. That is, performance outcomes may vary due to changes in effort, due to exogenous changes in ability like age or due to random shocks like injuries or bad luck. Employers want to identify the high-ability workers and not those who temporarily increase effort, so a selection effect confounds the hypothesis that performance will decline after a contract is signed. That is, if employers can effectively screen workers and at least partially distinguish ability from effort, measured performance may steadily improve for those players actually signed to contracts. This selection effect works against the hypothesized contract-related incentives, so it is ultimately an empirical question about which dominates post-contract performance.

Post-contract declines may also be mitigated by career concerns, that is, the recognition that current effort will impact not only the current contract, but also subsequent contracts as given in Fama (1980), Holmstrom (1982), and Gibbons and Murphy (1992). If workers have large concerns about their future (e.g., a high probability of a second contract, short contract length, or small discount rate), there is additional incentive to exert effort in order to maintain a reputation as a high-quality worker. This also works against the contract-related incentive to reduce effort once a multi-year contract is signed. As discussed by Gibbons and Murphy (1992), however, career concerns are weakest for workers close to retirement, so the post-contract decline in effort should be largest for older workers.

This suggests two additional testable hypotheses. One, the decline in effort should be linked to the length of the contract. If workers sign very long contracts, there is less need to be concerned about the future and the employer's perception of ability and therefore less incentive to exert costly effort after the contract is signed. Two, the decline in effort should be linked with age. Older workers near retirement have fewer career concerns and have less incentive to convince employers that they are high quality. The selection effect, however, again works against these predictions.

Given some of the agency problems linked with multi-year, fixed wage contracts, it is worth discussing why employers do not simply offer pure incentive contracts or a series of short-term contracts. Beginning with the extreme alternative of pure incentive contracts, Prendergast (1999) emphasizes the additional risk they impose on workers, who must be compensated through higher average wages. In high-risk activities like professional sports, pure incentive contracts may be not be practical. In fact, the majority of pay for professional basketball players is through guaranteed contracts, although explicit incentive contract provisions do exist. Second, the multidimensional nature of performance makes explicit incentive contracts difficult to design optimally. Holmstrom and Milgrom (1991), for example, argue that incentive pay may have perverse reallocation effects as workers shift their effort towards those duties that are measured and rewarded. (5) As a result, subjective performance evaluations are often used to overcome this multi-tasking problem [Prendergast (1999)]. Third, the collective bargaining agreement in the NBA, discussed below, limits the value of pure incentive pay, likely in response to some of these difficulties.

The second alternative, a series of short-run contacts, also creates difficulties. Williamson (1979) and Joskow (1987), for example, point to the importance of relationship-specific investments that might make repeated bargaining impractical due to ex post hold-up problems after the investments have been made. In the case of professional athletes, these relationship-specific factors could relate to the complementarity of different players on a team or the creation of fan loyalty via brand and player association. A long-run contract could mitigate the ability of one side from exploiting these sunk investments. More generally, Joskow (1987) points to information lags, income effects, risk aversion, and improved monitoring as reasons for the existence of long-run contracts, where risk aversion seems the most relevant for professional athletes.

III. NBA CONTRACT BACKGROUND AND DATA

To examine these contract-related incentive effects empirically, I constructed a unique database on performance and contract status for professional basketball players in the NBA. This section first discusses the salary structure as governed by the current collective bargaining agreement (CBA) between the NBA and the player's union, the National Basketball Players' Association (NBPA), and then describes the data in detail.

A. NBA Contract Background

Labor issues in the NBA are governed by a CBA that has been in effect since January 1999 and runs through 2004. The CBA determines virtually every labor practice such as league minimum and maximum salaries, trade rules, draft issues, benefits, and team salary caps (maximum team payroll), and prevents the NBA from violating antitrust laws. (6)

The key factors for this study relate to the contracting framework. The CBA imposes minimum and maximum salary restrictions based primarily on player experience and the team's salary cap. (7) Minimum salaries currently range from $301,875 for a first-year player to $1,000,000 for a player with more than nine years' NBA experience [CBA, Article II(6)(a)]. Salary maximums depend more directly on the team salary cap and also vary with player experience. For example, a player with less than seven years' experience may earn the greater of 25% of the team salary cap, 105% of the player's last annual salary, or $9 million, while a player with more than ten years' experience may earn the greater of 35% of the salary cap, 105% of the player's last annual salary, or $14 million [CBA, Article II(7)(ac)]. These restrictions apply to the first year of a player's contract and are then adjusted upward for the life of the contract.

The maximum salary applies to the player's salary and individual incentive clauses [Article II(7)(a-c)]. The CBA distinguishes between "likely bonuses" and "unlikely bonuses," where likely bonuses are included in a player's salary and unlikely bonuses are not [CBA, Article VII(3)(d)(2)]. These incentives can be based on pre-agreed benchmarks for individual or team performance, or on pre-agreed benchmarks for physical condition or academic achievement [CBA, Article II(3)(c)]. The distinction between likely and unlikely is based on historical comparisons via negotiation or, if necessary, an independent arbitrator. It is interesting that the CBA explicitly mandates that these incentive clauses "must be structured so as to provide an incentive for positive achievement by the player and/or team [CBA, Article II(3)(c)(iv)]." Finally, unlikely bonuses cannot exceed 25% of a player's regular salary [Article VII(5)(d)] and thus limit the prevalence of these incentive clauses.

Contract lengths are also restricted under the current CBA. The standard limitation is six years in length for most players, but up to seven years for certain veteran players. All players drafted in the 1998-2004 college draft, however, are restricted to three-year contracts, with a fourth option year for the team [CBA, Article IX(1)]. Under the previous CBA, signed in 1995, contract length was not as restricted for veterans, but certain rookies faced a three-year limit. Finally, there are significant restrictions on contract extension and negotiations. For example, extensions cannot occur before the fourth year of a six- or seven-year contract, a contract may be renegotiated no sooner than the third year, renegotiations are limited by the team salary cap, and contracts can only be renegotiated or extended upward [CBA, Article VII(7)].

Finally, NBA contracts are typically guaranteed. The specific type of guarantee (against disability due to basketball injury, against disability unrelated to a basketball injury, or loss of skill), however, is negotiated between the player and the team. Within this highly restricted framework, players and teams negotiate contracts.

B. Data

The data used in this paper include all historical performance statistics collected by the NBA for all players from 1988 to 2002. (8) Data are from allsports.com, a proprietary provider of sporting statistics. (9) Data on the performance of each team, for example, wins and losses, in each year are also available. The individual data include 6195 player/year observations, an average of 413 observations per year, for an unbalanced panel of 1343 different players. Fourteen players were active in all 15 years, 320 were active for only one year, and the median number of years per player was three. Information on each player's team and position, for example, center, forward, or guard, are also available.

There are many performance statistics in basketball, for example, points scored, field goal percentage, rebounds, assists, and blocked shots, but most vary in relevance across position. The empirical work examines many statistics but concentrates on a "composite rating" that summarizes a wide range of performance statistics and provides a comprehensive measure of overall performance. (10)

Contract information was collected by the USA Today. (11) These data include all NBA players with active contracts for the 2000 season and contain information about when the contract was signed (signing date), contract length, last year of the contract (end year), and the total value of the contract. An annual salary is calculated as the value of the contract divided by the length. All values were put into 1996 dollars using the CPI deflator, This contract information was compiled by a third party from a variety of sources, because the NBA does not publish comprehensive contract details. The data were checked against other private compilations where possible and 419 observations, approximated 95% of the 441 active players in 2000, contained reasonable and non-missing data that were suitable for analysis.

As discussed above, NBA contracts may have explicit incentive clauses that stipulate increased pay if certain performance criteria are met, but these details were not available on a comprehensive basis. The unlikely bonuses, which are most likely to provide incentives, are capped at 25% of a player's regular salary. Moreover, contract incentives would tend to improve performance after a contract is signed, thus making it more difficult to find a decline in performance. A second data issue is that players may have signed earlier contracts in earlier years, but this should not introduce bias and simply adds variation to the early data as effort and performance may vary around those earlier dates.

C. Summary Statistics

The remainder of the paper examines 349 players that were signed to long-term contracts during the 2000 season. Players with one-year contracts are excluded because there would be competing incentive effects and because these players are typically marginal players signed to short-term deals (as short as ten-day contracts). In addition, players that were signed to contracts but did not play in 2000 due to injury or retirement were excluded. This left a sample of 2646 player/year observations for 349 players from 1988 to 2002.

The first panel of Table 1 reports summary statistics for primary performance variables--points, rebounds, assists, blocks, and the composite rating--and the bottom panel shows summary contract information for the 349 players with complete long-term contract data in 2000. The average length of contract was 4.4 years, which included contracts ranging from two to 12 years in length, and was signed in 1998. The average value of the contract was $21 million, with a range of $0.7 million to $193 million, but the median was $10 million due to relatively few "superstar" contracts.

At this point, it is useful to be very clear about the structure of the data. For each player signed to a multi-year contract in 2000, performance statistics are observed in every year from 1988 to 2002 that the player is active, while contract data are observed only once in 2000. The contract itself, however, may have been signed in any earlier year. Figure 1 shows this schematically. Player A was active from 1988 to 1993 but was not active in 2000 and so has no contract information. Player B was active from 1991 to 2002 and a new contract began in 1996; 1995 is his contract year. Player C was active from 1995 to 2001 and a new contract began in 2000; 1999 is his contract year. Player D entered in 2001 and has no contract information. The differences in signing date and the corresponding changes in relative performance provide the critical variation to identify the incentive effects of contract status. Table 1 shows that some contracts were signed as early as 1993 and the typical contract was signed in 1998.

IV. EMPIRICAL RESULTS

This section begins with an analysis of the factors that determine the features of a player's contract like salary and length. Because contract-related incentive effects are the underlying motivation for the main hypotheses, one must first establish a link between pay and performance to identify those performance measures that are most rewarded. If improved performance, in fact, was not rewarded with better contracts, then contract-related incentive effects would be irrelevant. The second subsection tests several hypotheses related to contract status and performance--effort increases in the contract year, effort falls after a multi-year contract is signed, and the decline increases with contract length and with age. The final subsection examines the ultimate impact of contract-related incentives on the performance of the team. If players really do expend different amounts of effort depending on their contract status, then this could affect the team's overall performance.

[FIGURE 1 OMITTED]

A key feature of this study is the detailed data on individual compensation and individual performance. In contrast, the empirical literature on executive pay and performance, in Murphy (1985, 1986), Jensen and Murphy (1990), Gibbons and Murphy (1992), Kaplan (1994), and Hall and Liebman (1998), typically examined the link between individual pay and firm performance. Obviously corporate executives have considerable impact on firm outcomes, but individual data allow a cleaner and more straightforward test for contract-related incentive effects.

A. Individual Performance and Wages

The maintained hypothesis is that salary depends on the employer's perception of worker ability. Ability and effort are not easily distinguished, but actual performance is observed; so there should be a link between individual wages and observable performance statistics. In particular, I am interested in whether changes in performance in the contract year are associated with more lucrative subsequent contracts, which would provide the incentive to increase effort in the contract year.

I have few priors on the process that employers use to form perceptions of worker ability or how they value specific types of performance; so I use the following regression:

(1) [Z.sub.i,t] = [[beta].sujb.1][[bar.P].sub.i,t-N,t-2] + [[beta].sub.2][DELTA][P.sub.i,t-1] + [[beta].sub.3][NAGE].sub.i,t] + [[alpha].sub.p] + [[alpha].sub.j] + [[alpha].sub.t] + [[epsilon].sub.i,t]

where [Z.sub.i,t] are contract features like total pay, length of the contract, and average annual pay that are determined in year t, [[bar.P].sub.i,t-N,t-2] is "historical performance" before the contract year (averaged for years t - N to t - 2), [DELTA][P.sub.i,t-1] is the "contract year change" in performance ([DELTA][P.sub.i,t-1] = [P.sub.i,t] 1 - [[bar.P].sub.i,t-N,t-2]), and [NAGEi.sub.i,t] is the player's age (normalized by subtracting out the average age) to control for predictable age-related variation in contracts due to seniority or tenure effects. (12) Dummy variables for position ([[alpha].sub.p]), team ([alpha].sub.j])), and year ([alpha].sub.t])) control for other factors that affect contract features such as different salaries across positions, the ability of certain teams to maintain higher payrolls than others, or the general trend toward higher valued contracts.

Equation (1) is estimated for each contract attribute using a cross-section of 264 players with contract information and a historical performance record. (13) Estimation is via weighted least squares (WLS), with weights equal to the average number of games played before the contract is signed. (14) All standard errors are corrected for heteroskedasticity. Three different dependent variables and two sets of independent variables are used. The dependent variables, [Z.sub.i,t] are contract features--the total value of the contract signed in year t (measured in the log of millions of 1996 dollars), the length of the contract (measured in years), and the annual value of the contract (measured in the log of millions of 1996 dollars). The independent variables are the lagged performance measures, which is either the composite rating (a linear combination of many statistics) or a vector of the most important specific statistics (points scored, rebounds, assists, and blocked shots).

Table 2 shows a strong correlation between historical performance and contract features as players with better performance receive more lucrative and longer contracts. Moreover, the effect is economically large. A one-point increase in a player's historical composite rating is associated with a 13% increase in average annual pay; with a mean salary at about $4 million per year, this amounts to over $500,000 in annual salary. (15)

With the vector of individual statistics as independent variables, all are positive and are jointly significant. In the last column with annual salary as the dependent variables, for example, three are individually significant at the 99% level and are jointly significant at the 99% level. Recall that this controls for the effects of team differences, signing year, and position due to the dummy variables, so the explanatory power is notable. Again, the magnitudes seem large: a one-point increase in historical scoring is associated with an increase in annual salary of the next contract of almost 5%, which is $184,000 at the mean contract.

Age is clearly an important factor: the negative and highly significant coefficient in all regressions shows that older players receive worse contracts, conditional on performance. This goes against the literature on deferred compensation, in Lazear and Moore (1984) and Kotlikoff and Gokhale (1992), where employers use back-loaded contracts as a selection and incentive mechanisms, and likely reflects the relatively ease of mobility of players between teams and the predictable deterioration of skills as players age. (16) Also, older players signed their contracts earlier in less favorable markets.

The important conclusion is that contract year changes in performance, conditional on historical performances, are associated with more lucrative and longer-term contracts. This implies improvements in performance lead to better contracts. The change in composite rating is significant at the 99% level in all three regressions. For the individual statistics, they are jointly significant at the 99% level in all three regressions, almost all are positive, and changes in points are clearly the most important factor. Here, a one-point increase in average points scored in the contract year raises the annual salary of the next contract by about 7%, or about $280,000.

These results show a strong and economically important link between player performance and subsequent pay. This is not particularly surprising, of course, but the fact that both historical performance and recent changes predict contract features suggests a complex process determining employer's perceptions of worker ability where all past information is incorporated and potential moral hazard issues are recognized. A naive employer, on the other hand, might not understand the players' incentives to increase effort in the contract year and might just look at the most recent performance. This does not seem to be the case, although these results do not say whether these estimated prices are right in the sense that future compensation corresponds to expected returns for the employer. (17) In either case, the strong link between contract features and contract year performance provides an operational channel for contract-related incentive effects.

B. Individual Performance and Contract Status

The previous results show that players with improved performance in their contract year are rewarded with more lucrative and longer-term contracts, which provides a clear financial incentive for players to increase effort in their contract year and motivates the contract-related incentive hypothesis. A selection and signaling story, however, offers an alternative interpretation. If recent improvement provides a strong signal to employers about a player's long-term prospects, then this type of correlation might exist without any contract-related incentive effects as players with large upside potential are rewarded with better contracts.

One can distinguish the contract-related incentive effects by examining the changes in performance across the full contract cycle. Under the contract-related incentive interpretation, performance should rise before the contract is signed and then decline once the multi-year contract is signed. Under the selection interpretation, performance should continue to improve after the contract is signed. This section presents empirical evidence on the performance profile around the contract year in order to distinguish these explanations and test additional predictions.

The basic idea is that performance, [P.sub.i.t], depends on indicators of contract status, for example, a dummy variable for the contract year and another one for the year immediately following the contract year, so I estimate the following regression:

(2) [P.sub.i,t] = [[beta].sub.PRE] [PRE.sub.i,t] + [[beta].sub.POST] [POST.sub.i,t] + [[beta].sub.AGE] [NAGE.sub.i,t] + [[alpha].sub.i] + [[alpha].sub.p] + [[alpha].sub.t] + [[alpha].sub.j] + [[epsilon].sub.i,t]

where [PRE.sub.i,t] is a dummy variable set equal to 1 in the contract year and 0 otherwise, [POST.sub.i,t] is a dummy variable set equal to 1 in the year after the contract year and 0 otherwise, and [[alpha].sub.i] is an individual fixed effect to control for unobserved individual ability. All other variables are defined above and are included to account for predictable variation in performance over a player's career.

[[beta].sub.PRE] and [[beta].sub.POST] are the coefficients of interest and measure the conditional impact of contract status on a player's performance. The main predictions of the contract-incentive hypotheses are [[beta].sub.PRE] > 0 and [[beta].sub.POST] < 0 as effort rises in the contract year and falls once the contract is signed. As discussed above, however, a selection effect works in the opposite direction for [[beta].sub.POST]; if only improving players receive contracts, performance might improve as changes in ability swamp changes in effort.

Table 3 presents results using eight measures of performance as dependent variables--composite rating, points scored, total rebounds, assists, blocked shots, shots attempted, free throws attempted, and minutes played. The composite rating is the preferred measure because it encompasses a wide range of performance attributes into a single, meaningful index. Points, rebounds, assists, and blocks are important individual measures of performance and the evidence in Table 2 points to financial gains, and therefore incentive effects, from improvement in these areas. Shots and free throws attempted are included because they may be a better proxy for player effort, that is, a player has more control over how many shots he takes than how many he makes. Finally, minutes played are included because they are determined by the coach who will presumably reward overall performance with more playing time, so this variable includes the impact of intangible contributions that might be missed by standard statistics.

Each regression is estimated via WLS with games played as the weights. The regressions include up to 2646 observations from 1988 to 2002 for the 349 players with multi-year contracts in 2000. Note that [PRE.sub.i,t] and [POST.sub.i,t] can equal one in any year prior to 2001 depending on when the contract was signed, but each equals one in only a single year for each player. All regressions include player, year, team, and position dummy variables and standard errors are corrected for heteroskedasticity.

The first column in Table 3 uses the summary composite rating as the dependent variable and shows a significant increase in performance in the contract year ([[beta].sub.PRE] > 0) and a significant decline in the following year ([[beta].sub.POST] < 0). Recall that these regressions control for separate team, year, player age, and position effects, and remove individual effects, so the fact that [[beta].sub.PRE] and [[beta].sub.POST] are jointly and individually significant is strong evidence of contract-related incentive effects as effort varies over the player's contract cycle. This variation is similar to the results in Oyer (1998), who showed improved performance (measured by sales) in the fourth quarter of the fiscal year as agents try to meet their incentive goals and declines in the following quarter.

The next four columns use the individual performance measures as the dependent variable. Here, the evidence strongly shows improvement in the contract year, but there is no evidence of a post-contract decline. Because these regressions include individual fixed effects and age, this implies that post-contract year performance is the same as the player's conditional mean. Both shots and free throws attempted increase, showing similar patterns. Finally, minutes played increases in the contract year, suggesting that overall performance does indeed rise as players are rewarded with additional playing time.

Age is negatively related to performance (significant in more than half of the regressions) as performance declines steadily with age due to eroding skills and deteriorating ability. This is similar to Kotlikoff and Gokhale (1992), who report that productivity declines with age for a single Fortune 1000 firm.

These results are consistent with contract-related incentive effects. All measures show an improvement in performance in the con tract year, but the results are mixed regarding the post-contract decline. With the preferred measure of overall performance, there is a significant decline after the long-term contract is signed, while the individual performance measures are essentially flat. This pattern is more consistent with the hypotheses about contract-related incentive effects than with the alternative selection story. If it were only the case that improving players were receiving contracts, one would expect performance to steadily improve after the contract is signed. In fact, performance after the contract is signed returns to a player's long-run conditional average, which suggests a change in effort over the contract cycle.

Table 4 provides robustness tests of these results using the preferred composite rating as the measure of individual performance. Column 1 repeats the base regression from Table 3. The next column drops the age variable and all dummy variables, while column 3 just drops the dummy variables. Here, the negative post-contract effect becomes larger and more significant, while the precontract effect disappears. This is not surprising: overall performance measures like the composite rating and points scored have been trending steadily downward over this sample period, and so it is difficult for the data to show an increase until the leaguewide trend is removed via the year dummy variables. When the dummy variables are include but estimation is via ordinary least squares (column 40), [[beta].sub.POST] remains large and significant, while [[beta].sub.PRE] becomes much larger, but not quite statistically significant (p-value is equal to 0.14). When age is included as a quadratic (column 5) or an indicator of whether the player is on a new team is included (column 6), the results are similar.

In all regression in Table 4, the data clearly show that information about an individual's contract status is useful in predicting overall performance. The estimates coefficient on the contract status variables are almost always the correct sign and typically statistically significant. Moreover, [[beta].sub.PRE] and [[beta].sub.POST] are jointly significant in all cases and the data always reject the null hypothesis that they are equal. This provides substantial and robust evidence of predictable changes in performance over the contract cycle.

One caveat about this interpretation is the possibility of endogenous renegotiation. If a random shock improves performance and a player is rewarded with a new, more lucrative contract, for example, this would confound the specific contract cycle interpretation. Two observations, however, suggest that this is not the whole story. First, the empirical finding that composite performance tends to fall significantly after the contract is signed supports the interpretation that players have meaningful discretion about effort around the contract cycle. If endogenous renegotiation were the dominant force, performance might fall to expected levels after the contract is signed, but it would not necessarily fall significantly below expected levels in the year after the contract is signed, as is found. Second, this type of endogenous contract renegotiation appears to be relatively infrequent in the NBA, although there is not comprehensive evidence on this.

The third hypothesis is that the decline in performance after a contract is signed depends on the length of the contract. Ceteris paribus, longer contracts mean that any career concerns occur farther in the future and are thus discounted more strongly, which reduces the incentive to exert effort after the contract is signed. The final hypothesis is that the post-contract year decline increases with a player's age because older players have relatively small future career concerns. A selection effect, however, again works against these predictions, as better players are likely to be signed to longer-term contracts or at later ages.

To examine these issues, equation (2) is extended with an interaction between the post-contract year dummy variable and the length of the contract or with interactions between the post-contract year dummy variable and player age. I allow the interactions to enter as both a linear and squared interaction as

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [L.sub.i] is the relative length of the contract (contract length less average contract length). (18,19)

Table 5 reports estimates of the regressions in equations (3) and (4) for the composite rating. [[beta].sub.PRE] remains positive and significant in all cases, while [[beta].sub.POST] is negative in all cases and significant in two cases. The data strongly reject the hypothesis that performance in the contract year and the following year are the same, which supports the earlier results.

Column 1 includes only the linear interaction with contract length and shows longer contracts are associated with a smaller post-contract decline. This goes against the moral hazard prediction and likely reflects a selection bias with better, improving players receiving longer contracts. When the quadratic term is included in column 2, however, the post-contract decline increases, which shows the problems from very long-term contracts. There is no evidence that the post-contract decline varies with age. In both the regression with the linear interaction (column 3) and quadratic interaction (column 4), the effect is positive.

These results provide support for the main hypotheses about contract-related incentive effects: performance improves in a player's contract year and falls afterward. This specific up-and-down pattern around the year the contract is signed is consistent with powerful contract-related incentives, and inconsistent with the alternative selection hypothesis. The secondary hypotheses that the incentive effects should fluctuate with contract length and player age are only weakly supported. This could reflect either an offsetting selection effect or the lack of power in the data to identify these secondary effects.

C. Individual Performance and Team Performance

The final set of results examines whether these contract-related changes in individual performance affect team outcomes. If these performance measures are valuable to the team, one would expect team outcomes to follow the player's performance, rising when many players are in their contract year and falling when many sign long-run contracts. Leonard (1990) and Abowd (1990), for example, found that firms where executives' pay was linked to long-run performance showed above-average firm performance.

Several factors complicate this issue, however, and may drive a wedge between individual and firm performance. Holmstrom and Milgrom (1991) argue that if only some valuable tasks are measurable, incentive effects can lead workers to misallocate resources toward the measurable tasks and away from other, equally valuable ones. Alternatively, quality could suffer under some contract structures, for example, if workers are paid a piece rate as given in Lazear (1986), Holmstrom and Milgrom (1991), and Baker (1992). Finally, Holmstrom (1982) discusses the free-rider problem associated with joint output production by a team when agents who cheat cannot be identified. All of these are potential concerns as players might misallocate their effort toward activities with high individual returns and away from those that might be more beneficial to the team. Whether these perverse incentives are strong enough to actually affect team performance is the empirical question addressed next.

To examine whether changes in contract status and the induced change in individual performance actually affects the team performance, I estimated variants of the following cross-sectional regression:

(5) [WIN.sub.j] = [alpha] + [[beta].sub.C][SHC.sub.j] + [[beta].sub.M][SHM.sub.j] + [[epsilon].sub.j].

where [WIN.sub.j] is the number of wins in 2000, [SHC.sub.j] is the share of players in their contract year in 2000 and [SHM.sub.j] is the share of players that signed multi-year contracts in 2000, all for team j in year 2000. (20)

If individual performance improves in the contract year and if this positively affects team performance, [[beta].sub.C] > 0. Conversely, if individual performance falls immediately after a long-run contract is signed and this negatively affects team performance, [[beta].sub.M] < 0. Because [SHC.sub.j] and [SHM.sub.j] are shares, the coefficients can be interpreted as follows: [alpha] is predicted number of wins for a team with no players in their contract year and no players that just signed multi-year contracts, [alpha] + [[beta].sub.C] is the predicted number of wins if all players are in their contract year, and [alpha] + [[beta].sub.M] is the predicted number of wins if all players just signed multiyear contracts.

The important limitation is that contract data are only available for 2000 and I can only estimate equation (5) for a single cross-section of 29 teams, so omitted variables clearly cloud the interpretation. Certain teams, for example, may have better management skills that determine the player roster, the number of wins, and their contracting strategies. (21) To try to control for this problem, I include other characteristics of the players and of the team. Player characteristics include average length of the remaining contracts of the team and the average age of the team (linear and quadratic) because earlier results show they help predict individual performance, while team characteristics include total team payroll in 2000 and average wins in the previous five years. This will help, but one would prefer to have information about exogenous changes in these shares and changes in team performance. In addition, this is a test of the joint hypothesis that player performance depends on contract status and that these performance variables help predict team wins.

Table 6 presents results of several versions of equation (5). The first column shows the simplest regression with only the two contract-related shares as independent variables. As predicted, the data show a positive (though not statistically significant, p-value is equal to 0.14) link between team wins and the percentage of players in their contract year and a significant, negative link with the share of players that just signed multi-year contracts. The two variables are jointly significant (p-value is equal to 0.013) and suggest that the contract-related incentive effects documented above have an impact on firm performance. Just these two variables explain about one-quarter of the variation in team wins.

When the player characteristics are included in column 2, the estimated impact of the share of players in their contract year increases substantially, while the share of players that just signed multi-year contracts declines only slightly. Both are individually significant and jointly significant. Neither average remaining contract length nor average age is significant. Column 3 includes the total team payroll, while column 4 also adds lagged wins; in both cases, the magnitude and significance of the share in contract year variable falls, although the two contract variables remain jointly significant. As a reference column 5 only includes the team characteristics. (22)

To provide some perspective on the magnitude of these coefficients, consider the following hypothetical experiment. The average team had 15 players on its roster during the 2000 season, 28% of them were in the contract year, 3l% just signed multi-year contracts, and the remaining 41% were in other stages of their contract cycle. The estimates in column 1 suggest that moving one player to contract year status from having just signed a multi-year contract would lead to 4.5 additional wins [4.5=0.067 * 26.7 - 0.67 * ( - 42.0)]. Given that the average team wins 41 games per season, this is a substantial improvement.

These results open the possibility that employers are naive in some sense because post-contract moral hazard appears to be hurting the team. That conclusion, however, rests on the assumption that owners are maximizing the number of wins. In reality, owners are surely concerned with team profitability as well and the rational owner may anticipate these changes in effort and price them accordingly. Without data on team revenue and costs, it is hard to draw conclusions about employer strategies, but one can get some idea by using wins per dollar of total payroll as the dependent variable. The final two columns report estimates. Here, team outcomes also decline with the share of players that just signed multi-year contracts, but there is no impact from the share of players in their contract year.

These results on team performance are tentative due to their cross-sectional nature and lack of information on team profits, but they do suggest that contract-related incentive effects are large enough to affect the outcome of the entire firm. This suggests an important impact on the firm's bottom line. Moreover, there are implications on how a team's performance may vary over time. A team with coordination of contracts, for example, all contracts expiring at the same time, would likely be more variable than a team with staggered contracts where changes in incentives may offset each other. Evaluation of these factors, however, would require a time series of contract data.

V. CONCLUSIONS

This paper uses a unique database with individual-level measures of performance, contract status, and compensation to examine the importance of contract-related incentive effects. The results show that performance improves in the year before a new contract is signed as workers increase effort to convince employers of their high ability and earn more lucrative long-run contracts. Once the contract is signed, however, overall performance declines, which provides evidence that these changes are indeed contract-related incentive effects. Finally, these individual incentive effects affect the performance of the team as the number of wins is positively correlated with the share of players in their contract year, but negatively correlated with the share that just signed multi-year contracts.

Contract-related incentive effects and the ultimate impact on firm success are issues that have received considerable theoretical attention, but data limitations have made empirical tests difficult. The finding of considerable contract-related incentive effects in an industry where performance is easy to measure and contract for attests to the practical importance of this issue. These types of moral hazard problems are likely to be even worse where individual performance is harder to measure, where employers have less ability to monitor employee effort and where individual contracts are more difficult to write. This suggests considerable scope for employees to optimally vary effort to maximize personal gains, even at the expense of firm gains, and the evidence presented here suggest that this is exactly what employees do.

doi: 10.1111/j.1465-7295.2006.00004.x

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Fernie, S., and D. Metcalfe. "It's Not What You Pay, It's the Way that You Pay It and That's What Gets Results: Jockey's Pay and Performance." Labour, 13(2), 1999, 385-411.

Gibbons, R., and K. J. Murphy. "Optimal Incentive Contracts in the Presence of Career Concerns." Journal of Political Economy, 100, 1992, 468-505.

Hall, B. J., and J. B. Liebman. "Are CEOs Really Paid Like Bureaucrats?" Quarterly Journal of Economics, 113, 1998, 654-91.

Hart, O., and B. Holmstrom. "The Theory of Contracts," in Advances in Economic Theory, 1985, Econometric Society Monograph No. 12, 1987, edited by T. Bewley. Cambridge, MA: Cambridge University Press, 1987. 71-92.

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--. "Moral Hazard in Teams." The Bell Journal of Economics, 13, 1982, 324-40.

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Kaplan, S. "Top Executive Rewards and Firm Performance: A Comparison of Japan and the United States." Journal of Political Economy, 102, 1994, 510-46.

Kotlikoff, L. J., and J. Gokhale. "Estimating a Firm's Age-Productivity Profile Using the Present Value of Workers' Earning." Quarterly Journal of Economics, 107, 1992, 1215-42.

Lazear, E. P. "Salaries and Piece Rates." Journal of Business, 59, 1986, 405-31.

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Lazear, E. P., and R. L. Moore. "Incentives, Productivity, and Labor Contracts." Quarterly Journal of Economics, 99, 1984, 275-96.

Leonard, J. S. "Executive Pay and Firm Performance." Industrial and Labor Relations Review, 43, 1990, 13S-29S.

Maxcy, J. G., R. D. Fort, and A. C. Krautmann. "The Effectiveness of Incentive Mechanisms in Major League Baseball." Journal of Sports Economics, 3, 2002, 246-55.

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(1.) Prendergast (1999) surveys this literature, but emphasizes that evidence of incentive effects is not a test of agency theory, but rather one necessary input for agency theory.

(2.) See Fama (1980), Holmstrom (1982), and Gibbons and Murphy (1992) for formal discussions of career concerns.

(3.) Ehrenberg and Bognanno (1990) cite advantages of professional sports data as a motivation for their study of tournament incentives, while Asch (1990) uses individual data for Navy recruiters. Maxcy. Fort. and Krautmann (2002) utilize similar data for professional baseball players.

(4.) The contracting environment, and how it is determined through a collective bargaining agreement, is discussed in the following section.

(5.) Prendergast (1999) summarizes strong empirical evidence for this type of "dysfunctional behavior."

(6.) This information is based on the CBA available from the NBPA at http://www.nbpa.com and "NBA Salary Cap/Collective Bargaining Agreement FAQ," http:// members.cox.net/lmcoon/salarycap.htm. Note: a new CBA was signed in June 2005, but is not relevant for this analysis.

(7.) The salary cap limits a team's maximum expenditure on player salaries and depends, with some exceptions, on a team's basketball-related income (gate receipts, broadcast rights, team sponsorships, seat licenses, parking, concessions, etc.).

(12.) To be clear about the timing, the contract is determined in year t. Year C = t - 1 is the contract year. and years t - N to t - 2 are all years prior to the contract year.

(13.) This is less than the 349 players with contract information in 2000 because some of these players are new to the league and do not have previous performance records.

(14.) Weights are used because some players with limited opportunities can have very noisy statistics. Results are qualitatively similar without weights.

(15.) It is likely that this understates the true effect on income because outside compensation like endorsement contracts and appearance fees are likely to depend on performance.

(16.) In other regressions (not shown), including age as a quadratic function did not change the results substantially, and there were no significant interaction effects between performance and age as a determinant of contract parameters.

(17.) A similar difficulty is discussed by Prendergast (1999) in the context of the pay and performance literature.

(18.) Defining contract length relative to the average helps with the interpretation of the results, that is. [[beta].sub.POST] is the effect at mean contract length.

(19.) Note that equation (4) includes [NAGE.sub.i,t] directly. while equation (3) does not include contract length directly. This is because contract length is only observed for those players with a new contract and thus cannot be identified independently of the interaction.

(20.) These two shares do not sum to I because some players signed multi-year contracts in earlier years that extend beyond 2000.

(21.) As a concrete example, Brooks, May, and Mishra (2001) find that firm performance improves after incentive contracts are adopted, which they attribute this primarily to a signal of private information rather than the gains from better aligned incentives for managers.

(22.) If one includes only average salary and average wins as explanatory variables, the data show a modest positive relationship between team performance and total payroll. This link, however, is not very robust and vanishes when average age of the players is included. Note also that including lagged wins rather than average wins eliminates the significance of the contracting variables. If one wants to control for omitted management characteristics, average performance is probably a better measure than lagged performance.

KEVIN J. STIROH *

* The author thanks Adam Ashcraft, Dave Gulley. Don Morgan, Jeremy Stein. Lauren Stiroh, Phil Strahan, Joe Tracy, anonymous referees, and seminar participants at the Federal Reserve Bank of New York and the 2003 National Bureau of Economic Research Summer Institute for helpful comments and suggestions. The views expressed in this paper are those of the author only and do not necessarily reflect those of the Federal Reserve Bank of New York or the Federal Reserve System.

Stiroh: Vice President, Federal Reserve Bank of New York, New York, NY 10045. Phone (212) 720-6633, Fax (212) 720-8363, E-mail [email protected]

TABLE 1
Summary Statistics

 No. Standard
 Observations Mean Deviation

Performance Variables
 Points 2646 10.3 6.2
 Rebounds 2646 4.5 2.8
 Assists 2646 2.4 2.1
 Blocks 2646 0.6 0.7
 Composite Rating 2646 18.8 5.1
 Season 2646 1997.4 3.6
Contract Information
 Signing Date 349 1998.6 1.5
 Length 349 4.4 1.8
 End Year 349 2003.0 1.6
 Contract Value 349 21.2 25.4
 Annual Salary 349 4.0 3.7

 Minimum Maximum

Performance Variables
 Points 0.0 32.1
 Rebounds 0.0 16.3
 Assists 0.0 14.5
 Blocks 0.0 4.6
 Composite Rating -2.3 43.5
 Season 1988.0 2002.0
Contract Information
 Signing Date 1993.0 2001.0
 Length 2.0 12.0
 End Year 2001.0 2007.0
 Contract Value 0.7 193.4
 Annual Salary 0.2 20.3

Notes: Summary statistics for performance variables include all
player/year observations for 15 seasons from 1988 to 2002 for 349
players that have signed multi-year contracts. Points, Rebounds,
Assists, and Blocks are average per game values for a season.
Composite Rating is for the season. Season is the observation year.
Summary statistics for contract information include one observation
per individual and is reported for all individuals that signed a
multi-year contract. Data include the year the contract was signed
(Signing Date), the length of the contract (Length), the last year
under contract (End Year), total value of contract (Contract Value),
and value per year (Annual Salary). Contract Value and Annual Salary
are in millions of 1996 dollars.

TABLE 2
Contract Features and Individual Performance

 Contract Value

Historical Performance
Composite Rating 0.169 ***
 (0.018)
 Points 0.047 **
 (0.020)
 Rebounds 0.158 ***
 (0.055)
 Assists 0.210 ***
 (0.057)
 Blocks 0.186
 (0.169)
Contract Year Change
 Composite Rating 0.120 ***
 (0.024)
 Points 0.107 ***
 (0.027)
 Rebounds 0.035
 (0.066)
 Assists 0.084
 (0.070)
 Blocks 0.359
 (0.226)
 Age -0.095 *** -0.104 ***
 (0.018) (0.017)
 Jt. Sig. Historical Performance 0.000
 Jt. Sig. Contract Year Jump 0.000
 Adjusted [R.sup.2] 0.52 0.62
 No. Observations 264 264

 Contract Length

Historical Performance 0.117 ***
Composite Rating (0.026)
 0.006
 Points (0.032)
 0.158 *
 Rebounds (0.089)
 0.139
 Assists (0.093)
 0.270
 Blocks (0.276)

Contract Year Change 0.106 ***
 Composite Rating (0.035)
 0.123 ***
 Points (0.044)
 (0.054)
 Rebounds (0.107)
 0.065
 Assists (0.115)
 0.312
 Blocks -0.368
 -0.214*** -0.213 ***
 Age (0.027) (0.028)
 0.000
 Jt. Sig. Historical Performance 0.001
 Jt. Sig. Contract Year Jump 0.56 0.58
 Adjusted [R.sup.2] 264 264
 No. Observations

 Annual Salary

Historical Performance 0.132 ***
Composite Rating (0.012)
 0.046 ***
 Points (0.012)
 0.107 ***
 Rebounds (0.033)
 0.167 ***
 Assists (0.034)
 0.118
 Blocks (0.101)

Contract Year Change 0.081 ***
 Composite Rating (0.016)
 0.073 ***
 Points (0.016)
 0.024
 Rebounds (0.039)
 0.065
 Assists (0.042)
 0.249 *
 Blocks (0.135)
 -0.040 *** -0.049 ***
 Age (0.012) (0.010)
 0.000
 Jt. Sig. Historical Performance 0.000
 Jt. Sig. Contract Year Jump 0.48 0.65
 Adjusted [R.sup.2] 264 264
 No. Observations

Notes: Dependent variables are Contract Value (in logs), Contract
Length (in years), and Annual Salary (in logs). Results are from
weighted least squares regressions with year, team, and position
dummy variables. Weights are equal to the average number of games
played prior to contract year. Robust standard errors in parentheses.
Contract Value and Annual Salary are in logs. Historical Performance
variables are averages for all years prior to the contract year.
Contract Year Change variables are differences between contract year
performance and historical performance. Jt. Sig. Historical Performance
reports the p-value associated with an F-test of the joint significance
of the Historical Performance variables. Jt. Sig. Contract Year Change
reports the p-value associated with an F-test of the joint significance
of the Contract Year Change variables. ***, **, * indicate statistical
significance at the 1%, 5%, and 10% level, respectively.

TABLE 3
Relative Performance and Contract Status
Major Indicators of Performance

 Composite Points Total
 Ranking Scored Rebounds

Pre 0.381 ** 0.847 *** 0.295 ***
 (0.172) (0.244) (0.095)

Post -0.325 ** 0.164 0.165 *
 (0.146) (0.215) (0.091)

Age -0.374 *** -0.168 *** -0.019
 (0.038) (0.064) (0.024)

Jt. Sig. of Pre 0.001 0.002 0.005
and Post

Test of 0.013 0.013 0.248
Pre = Post

Adjusted [R.sup.2] 0.776 0.699 0.761

No. Observations 2646 2646 2646

 Assists Blocked Shots
 Shots Attempted

Pre 0.161 ** 0.054 *** 0.587 ***
 (0.075) (0.020) (0.184)

Post 0.042 0.026 0.170
 (0.059) (0.018) (0.169)

Age -0.017 -0.014 *** -0.093 *
 (0.023) (0.005) (0.048)

Jt. Sig. of Pre 0.097 0.019 0.006
and Post

Test of 0.150 0.195 0.050
Pre = Post

Adjusted [R.sup.2] 0.818 0.851 0.698

No. Observations 2646 2646 2646

 Free Throws Minutes
 Attempted Played

Pre 0.273 *** 102.924 **
 (0.078) (41.468)

Post 0.083 59.341
 (0.067) (36.636)

Age -0.081 *** -6.612
 (0.019) (9.552)

Jt. Sig. of Pre 0.002 0.029
and Post

Test of 0.029 0.352
Pre = Post

Adjusted [R.sup.2] 0.731 0.537

No. Observations 2646 2646

Notes. All results are from weighted fixed effects (player) regressions
with year, team, and position dummy variables. Weights are equal to the
number of games played by each player in the year. Robust standard
errors are in parentheses. Pre is a dummy variable set equal to 1 in
the contract year; equal to 0 otherwise. Post is a dummy variable set
equal to 1 in the year the contract is signed; equal to 0 otherwise.
Jt. Sig. of Pre and Post reports thep-value associated with an F-test
of the null hypothesis that [[beta].sub.PRE] = [[beta].sub.POST] = 0.
Test of Pre = Post reports the p-value associated with a test of the
null hypothesis that [[beta].sub.PRE] = [[beta].sub.POST]. ***, **, *
indicate statistical significance at the 1%, 5%, and 10% level,
respectively.

TABLE 4
Robustness Tests of Link between Composite Rating and Contract Status
Dependent Variable: Composite Rating

 Base
 Regression

Pre 0.381 ** -0.012 0.065
 (0.172) (0.178) (0.161)

Post -0.325 ** -0.800 *** -0.596 ***
 (0.146) (0.139) (0.131)

Age -0.374 *** 0.411 ***
 (0.038) (0.019)

[Age.sup.2]

Traded

Year Dummy Variables Y N N

Team Dummy Variables Y N N

Position Dummy Variables Y N N

Weights Y Y Y

Jr. Sig. of Pre and Post 0.001 0.000 0.000

Test of Pre = Post 0.000 0.000 0.001

Adjusted [R.sup.2] 0.776 0.698 0.768

No. Observations 2646 2646 2646

Pre 0.303 0.359 ** 0.406 **
 (0.204) (0.163) 0.171

Post -0.370 ** -0.179 -0.262 *
 (0.176) (0.135) 0.149

Age 0.385 *** -0.267 *** -0.360 ***
 (0.041) (0.036) 0.038

[Age.sup.2] -0.048 ***
 (0.003)

Traded -0.437 ***
 0.117

Year Dummy Variables Y Y Y

Team Dummy Variables Y Y Y

Position Dummy Variables Y Y Y

Weights N Y Y

Jr. Sig. of Pre and Post 0.016 0.014 0.001

Test of Pre = Post 0.005 0.003 0.000

Adjusted [R.sup.2] 0.702 0.805 0.777

No. Observations 2646 2646 2646

Notes: All results are from weighted fixed effects (player)
regressions. Weights are equal to the number of games played by each
player in the year. Robust standard errors are in parentheses. Pre is
a dummy variable set equal to 1 in the contract year: equal to 0
otherwise. Post is a dummy variable set equal to 1 in the year the
contract is signed, equal to 0 otherwise. Jt. Sig. of Contract
Variables reports p-value associated with an F-test of the joint
significance of Pre and Post. Test of Pre = Post reports the p-value
associated with a test of the null hypothesis that [[beta].sub.PRE] =
[[beta].sub.POST]. ***, **, *, indicate statistical significance at
the 1%, 5%, and 10% level, respectively.

TABLE 5
Tests for Interaction Effects between Contract Status, Contract Length,
and Age Dependent Variable: Composite Rating

 Contract Interaction
 Length Effects

Pre 0.370 ** 0.381 **
 (0.173) (0.173)
Post -0.356 ** -0.214
 (0.144) (0.165)
Age -0.373 *** -0.372 ***
 (0.038) (0.038)
[Age.sup.2]

Post*Length 0.142 * 0.195 ***
 (0.073) (0.074)
Post*[Length.sup.2] -0.04
 (0.022)
Post*Age

Post*[Age.sup.2]

Jt. Sig. of 0.000 0.000
Contract Variables
Test of Pre = Post 0.000 0.00
Adjusted [R.sup.2] 0.776 0.776
No. Observations 2646 2646

 Interaction
 Age Effects

Pre 0.381 ** 0.357 **
 (0.173) (0.163)
Post -0.312 ** -0.279
 (0.145) (0.173)
Age -0.381 *** -0.271 ***
 (0.038) (0.036)
[Age.sup.2] -0.049 ***
 (0.003)
Post*Length

Post*[Length.sup.2]

Post*Age 0.071 ** 0.043
 (0.029) (0.030)
Post*[Age.sup.2] 0.006
 (0.006)
Jt. Sig. of 0.000 0.009
Contract Variables
Test of Pre = Post 0.000 0.003
Adjusted [R.sup.2] 0.776 0.805
No. Observations 2646 2646

Notes: All results are from weighted fixed effects (player) regressions
with year, team, and position dummy variables. Weights are equal to the
number of games played by each player in the year. Robust standard
errors are in parentheses. Pre is a dummy variable set equal to 1 in
the contract year: equal to 0 otherwise. Post is a dummy variable set
equal to 1 in the year the contract is signed: equal to 0 otherwise.
Length is the number of years in the contract, measured in years and
normalized by the average contract length. Age is player's age,
measured in years and normalized by the average age. Jt. Sig. of
Contract Variables reports p-value associated with an F-test of the
joint significance of Pre. Post, and the Post interactions. Test of
Pre=Post reports the p-value associated with a test of the null
hypothesis that [[beta].sub.PRE] = [[beta].sub.POST].
***, **, * indicate statistical significance at the 1%, 5%, and 10%
level, respectively.

TABLE 6
Team Performance and Player Contract Status

 Dependent Variable

 Team Wins

Share in 26.701 60.254 ** 14.843
Contract Year
 (17.647) (29.137) (16.212)

Share with -42.037 *** -31.542 * -39.676 **
Multi-Year Contract (17.755) (17.452) (18.715)

Average Remaining -8.805
Contract Length (35.882)

Average Remaining 4.232
Contract (6.127)
[Length.sup.2]

Average Age -14.089
 (22.436)

Average [Age.sup.2] 0.308
 (0.406)

Log Total Payroll 15.558 **
 (6.545)
Average Wins,
1995-1999

Jt. Sig. of 0.013 0.046 0.049
Contract Shares

Adjusted [R.sup.2] 0.221 0.365 0.275

No. Observations 29 29 29

 Dependent Variable

 Wins per Dollar
 Team Wins of Payroll

Share in 9.784 -0.026 0.213
Contract Year
 (16.962) (0.388) (0.352)

Share with -42.752 ** -0.760 * -0.867 **
Multi-Year Contract (17.676) (0.443) (0.387)

Average Remaining
Contract Length

Average Remaining
Contract
[Length.sup.2]

Average Age

Average [Age.sup.2]

Log Total Payroll 12.026 * 17.863 * -0.461 ***
 (7.014) (10.470) (0.166)
Average Wins, 0.346 * 0.318 0.005
1995-1999 (0.202) (0.222) (0.005)

Jt. Sig. of 0.049 0.207 0.064
Contract Shares

Adjusted [R.sup.2] 0.327 0.168 0.076 0.200

No. Observations 29 29 29 29

Notes: Results from ordinary least squares regressions. Robust
standard errors in parentheses. Constant not shown.

Share in Contract Year is the percent of individuals on a team with
a contract that expires in 2000. Share with Multi-Year Contracts is
the percentage of players on a team with a multi-year contract that
began in 2000. Average Remaining Contract Length is the average
number of years on remaining on the contract of all players on the
team in 2000. Average Age is the average age of players on the team
in 2000. Log Total Payroll is the mean annual salary of individuals
on a team in 2000. Average Wins is the average number of team wins
from 1995 to 1999. Jt. Sig. of Contract Shares reports p-value
associated with an F-test of joint significance of Share in Contract
Year and Share with Multi-Year Contracts. indicate statistical
significance at the 1%, 5%, and 10% level, respectively.