The Effects of Minimum Salaries on Career Length: Evidence from the National Football League Johnny Ducking Assistant Professor of Economics Department of Economics and Finance North Carolina A&T State University jcduckin@ncat.edu and Christopher Bollinger Gatton Professor of Economics Department of Economics University of Kentucky crboll@uky.edu September 2012 Abstract We use National Football League (NFL) data to analyze the impact of minimum salaries on an employee’s career length. The NFL has a salary structure in which the minimum salary a player can receive increases with the player’s years of experience. Salary schedules similar to the NFL’s exist in public education, federal government agencies, the Episcopalian church, and unionized industries. NFL data allows us to control for a player’s productivity. We find statistically significant evidence that minimum salaries shorten career length when they require teams to increase a player’s base salary or total compensation from year t to year t+1. Introduction A significant body of research has examined the impact of minimum wages on employment (Brown, Gilroy, and Kohen, 1982; Card, 1992a&b; Card and Krueger, 1994; Dickens, Machin, and Manning, 1999) and on the earnings distribution (Behrman, Sickles, and Taubman, 1983; Dickens et al., 1999; Johnson and Browning, 1983; Katz and Krueger, 1992; Neumark, Schweitzer, and Wascher, 2004). The findings in this research have generally been that the minimum wage reduces employment among low skill workers, and teens in particular, while the overall effects on the income distribution are small but tend to redistribute income downward. However, the literature is far from complete agreement on any of these findings. A compensation structure similar to the minimum wage is a minimum salary, such as that found in the National Football League (NFL) which we study here. The key difference between a minimum wage and a minimum salary is that minimum wages place a lower limit on the amount of compensation a worker can receive for an hour of work while minimum salaries place a lower limit on the amount of compensation a worker can receive for a year of work. This is an important distinction because firms that encounter minimum wages have the ability to employ a worker for an entire year and reduce the total yearly income paid to the worker by reducing the worker’s hours or by hiring fewer workers. Firms that encounter minimum salaries do not have the ability to employ the worker for an entire year and reduce the total yearly income below the mandated minimum salary. Hence, we may expect more dramatic impacts on employment in a minimum salary setting. The minimum wage is also difficult to study since it is, in general, uniform across all workers, and does not change significantly very often. The minimum salary schedule in the NFL, by contrast, depends upon years of service (see table 1) and hence varies exogenously over the player's career. However, like the minimum wage, a significant portion of players (workers) in the NFL earn salaries well above the minimum wage. This allows measurement of employment effects of the minimum salary that have broader implications. Perhaps more importantly, the quality of individual productivity data in professional sports aids in identifying the value of the marginal product of workers (players), a key component for a complete analysis of any labor market. Finally, the NFL provides an interesting labor market structure because the 1 cap on the "active roster" and because of the clear entry of new workers each year. These components make the labor market structure a unique laboratory to study how firms react to the minimum wage structure (Kahn, 2000). Fort and Quirk (1995) demonstrate that professional sports firms appear to behave as profit maximizing firms. While the results here apply in a specific case, the implications aid in a broader understanding of the impact of price floors in labor markets, and other markets in general. Professional football is not the only place where minimum salaries are seen. Minimum salary schedules are often employed to protect older workers. One obvious place is within the federal government: the "GS" scale covers employees from low skill up through professionals such as Ph.D. economists. A number of union contracts also specify effectively a minimum salary schedule which is tied to experience and restricts hours worked. Other schedules of this type can be found in state governments and religious organizations. A major difference between most of these settings and the NFL, is that in most of the other settings involving minimum salary schedules, workers cannot be easily dismissed. The fact that rosters are constantly shifting, allows us to examine how these rising schedules affect career length, the margin on which the NFL can most obviously respond to these salaries. Understanding this response sheds light on the impact of minimums in many settings. We estimate hazard models for career length using players who appeared on the 53 man roster as a rookie player in one of six positions during any season from 2000 through 2008. We focus on players in three defensive positions (defensive backs, defensive lineman and linebackers) and three offensive positions (running backs, tight ends and wide receivers). Separate models are estimated for the defensive and offensive players, but the results on the measure of the impact of the minimum salary schedule are surprisingly similar. We find that the minimum salary schedule has statistically significant impacts on career length, shortening an effected player's career by as much as .43 of a season for every $10,000 increase in the minimum salary. Since typical increases are in the range of $50,000 to $100,000, careers are shortened by as much as 3 or 4 seasons. National Football League Labor Market Structure Each NFL firm has a roster constraint of 53 players during the regular season. Observationally, most teams maintain a 53 man roster throughout the season, indicating that this 2 is a binding constraint. The impact of the minimum salary schedule is necessarily on which specific players the team maintains on its roster. Table 1 presents the minimum salary schedule during the study period measured in real terms. In general, players with more experience have a higher minimum, and that minimum increases from year to year. However the increases are not uniform due to changes in inflation as well as negotiations. Increasing the price of a player as his level of experience increases provide NFL teams with the incentive to substitute less experienced, and less expensive players for more experienced expensive players. This incentive exists as long as the younger, inexperienced players are more profitable than the older, experienced players. Therefore, the NFL’s minimum salary schedule can reduce career length through this incentive. We formally model this here. A number of previous studies of professional sports leagues have made the assumption that teams maximize profits (Hamlen Jr., 2007; Fort and Quirk, 1995; Scully, 1974; Vrooman, 1995). We also assume that NFL teams maximize profits. The revenue generated by player i is equal to the value of the marginal product from employing player i, VMPi. VMPi is also the maximum amount a team is willing to pay player i. In a perfectly competitive industry an employee’s salary is equal to the value of his marginal product. In the NFL, employers may have monopsony power because players chosen in the NFL draft can sign contracts only with the team that drafts them. Draft picks in the NFL are initially assigned in a manner that the teams with the lowest winning percentages have the earlier picks in each of the seven rounds. The maximum length for a rookie contract is 6 years for players chosen in the first half of the first round of the NFL draft, 5 years for players chosen in the second half of the first round of the NFL draft, and 4 years for players chosen in the second through seventh rounds of the NFL draft. Each round of the NFL draft typically has 32 selections, one selection for each team. Any undrafted free agents with 3 years of experience or less can only negotiate with their initial team when their contracts expire if the initial team offers them a 1 year contract. It should be noted that most of these contracts are not guaranteed, and some players with less experience can be cut from the team at little or no cost to the firm. Even though teams have some monopsony power, evidence reveals that player salaries are close to the value of their marginal products (MacDonald and Reynolds, 1994; Rosen and Sanderson, 2000). The salary paid to player i, Si, is an amount that is negotiated between the 3 player and the team (Conlin and Emerson, 2003). In the absence of a minimum salary, the negotiated salary will fall between the players outside wage, Oi, and his value of marginal product to the firm: Oi ≤ Si ≤ VMPi. When a player faces a mandated minimum salary, MMSi, at each level of experience, the player’s negotiated salary is less than or equal to the value of marginal product and greater than or equal to his mandated minimum salary, MMS i ≤ Si ≤ VMPi. Profits per player are the difference between the player’s VMP and the total amount of compensation paid to the player. The total compensation paid to the player includes the salary plus any bonuses. For simplicity, we define profits per player as the difference between the value of a player’s marginal product and the salary paid to the player, VMPi – Si. Even though profits per player are VMP minus the player’s total compensation, VMP – S captures the impact of minimum salaries. Teams employ the 53 players for which the sum of profits per player is the largest. Therefore, each team’s total profits are a function of profits per player, (1) profits = f(VMP1 – S1,VMP2 – S2, …,VMP53 – S53) Even though the value of a player’s marginal product may depend on the productivities of the other players employed by the team, team management has an idea of a player’s value of marginal product given various combinations of players. Management ultimately chooses the combination of players in a manner that maximizes profits. This implies that the profits for the marginal, 54th player, are less than the profits for any other player. The minimum salary schedule may shorten the career length of players through two mechanisms. The first mechanism operates when the minimum salary schedule causes the mandated minimum salary to exceed the player’s value of marginal product. In the absence of the minimum salary, the player’s salary would not exceed the VMP and the player would have been retained. However, the firm (and all firms) will dismiss a player when VMPi - MMSi < 0. This has the impact of dismissing players who otherwise would play additional seasons. The NFL’s salary structure artificially increases the minimum cost of an input for teams whether there is a corresponding increase in the value of the player or not. The second mechanism operates when the minimum salary schedule causes the profits per player from hiring player i to fall below the profits per player from hiring player 54, the marginal player. Player 54 is the individual with the largest profits per player not previously 4 employed by the team.1 If this occurs, the team is going to dismiss player i and hire player j. Player i’s career length is shortened if no other team employs player i. Therefore, when VMPi – MMSi < VMP54 – S54, player i’s career length may be shortened. Again, in the absence of the minimum schedule, the salary paid by the firm could be negotiated lower, and the player could be retained. This mechanism also shows that the NFL’s salary structure artificially increases the minimum cost of an input for teams whether there is a corresponding increase in the value of the player or not. When the career length of a player is shortened total employment at the firm and in the industry remains the same but the experience distribution of those employed is likely to change, as the marginal player is likely to be younger and hence facing a lower minimum salary. This salary structure is mainly expected to impact a marginal or average player because the value of marginal product for a star player is significantly larger than his mandated minimum salary. If a player’s salary is equal to or close to the mandated minimum salary, an additional year of experience could cause the player to lose his job due to the mechanisms described above. The minimum salary schedule is also expected to reduce efficiency by eliminating a set of outcomes that could be mutually beneficial for both teams and players. Empirical Model In order to analyze the impact of the NFL’s salary structure on a player’s career length, we estimate hazard models of career length using data from the NFL. The hazard model estimates the impact of minimum salaries and other relevant explanatory variables on the length of time a player spends in the NFL. Specifically we estimate a Weibull proportional hazard model for defensive positions and offensive positions. The baseline hazard is denoted by h0(t), time is denoted by t, the set of covariates is denoted by xj, and the Weibull proportional hazard model is denoted by h(t|xj). The parameter p describes the direct effect of time, net of other explanatory variables, in Weibull distributions. If p>1, the hazard increases over time, while if p<1, the hazard decreases over time. In sports, the hazard increases over time (p>1) because the 1 The position of player j may depend on the position of player i. If the team is looking for a replacement player to perform player i’s duties, the position of player j would be one of the positions capable of replacing player i’s duties on the field. Depending on player i’s role on the team, there may be one of many positions capable of replacing player i’s duties. If the team does not need a player to perform player i’s specific duties, the team will simply employ the player with the highest profits per player who was not previously employed by the team. 5 hazard of ending a career is large and growing year by year, based on aging. Formally, we estimate (2) h(t|xj) = ptp – 1exp(β0 + xjβx), where t is the number of seasons played, and the xj vector measures individual and team characteristics. The Weibull distribution allows for flexibility in the baseline hazard and is an appropriate choice as long as the baseline hazard is monotonically increasing or decreasing. The proportional hazard model allows both time-varying and time invariant covariates to have a proportional impact on the baseline hazard. There are many other possible functional forms, but the estimates from hazard models are not sensitive to these alternatives as long as there are no policy spikes, times at which many failures occur, such as 52 weeks of unemployment or the date of reauthorization of welfare benefits. See Manton, Singer, and Woodbury (1992). There are no such fixed policy times in sports careers. Data We use NFL data on defensive backs, defensive linemen, linebackers, running backs, tight ends, and wide receivers from 2000 to 2008. We create two samples using these six positions, a sample for defensive positions and a sample for offensive positions. We chose these six positional groups for two reasons: performance statistics that can be used to measure their productivity are readily available and there are typically at least 3 players that play these positions for each team during the course of a football game. The first reason is important because the availability of performance statistics allow us to control for a player’s productivity. The second reason is important because choosing positions where there is typically less than 3 players playing in a game will result in an extremely small sample size. We exclude quarterbacks, punters, and kickers because typically only one player plays these positions during the course of a football season. We exclude offensive linemen because they do not have any performance measures to control for productivity. Productivity, team, salary, and demographic information are used as control variables in this analysis. We obtain data on player performance and demographic information from the NFL official website (http://www.nfl.com/players). We use the minimum salary schedule (NFL collective bargaining agreement) to determine a player’s mandated minimum salary. We obtain 6 salary data on a player’s base salary, signing bonus, and other bonuses from the USA Today’s NFL salary database (http://content.usatoday.com/sportsdata/football/nfl/salaries/team). We used the CPI with 2009 as the base year in order to adjust for inflation. Players are not included in the sample for the following reasons: 1) their career started before the year 2000; 2) they play for more than one team in a season; 3) they have a missing or skipped season from the NFL’s official website or the USA Today’s NFL salary database, and 4) the base salary is less than the minimum salary in the USA Today’s NFL salary database indicating that the player only played a partial season. In both the offensive and defensive models, we include games played and games started. These, and all other player performance variables are time varying, and measured at season. Games played measures how often, overall, the player is used on the field by the team. This captures an intensity margin of productivity. Those players who are considered starters, and hence start the game, are typically considered the highest performing players. While these are crude proxies, they accurately measure the team's perception of the value of the player. Defensive player productivity is measured by tackles, sacks, passes defended, interceptions, and forced fumbles. Tackles are defined as the total number of times a player tackles an opponent during a season. Sacks are defined as the total number of times a player tackles the opposing quarterback behind the line of scrimmage during a season. Passes defended and interceptions measure the total number of times a player breaks up a pass or catches a pass thrown by the opposing quarterback. Forced fumbles are defined as the total number of times a defensive player causes an offensive player to lose the football. Tackles, sacks, passes defended, interceptions, and forced fumbles are expected to have a positive impact on career length because they measure the impact of the player’s ability to help his team stop their opponent from scoring. Offensive player productivity is measured by touches, yards, touchdowns, fumbles, and fumbles lost. Touches are defined as the sum of a player’s rushing attempts and receptions, that is when the player carries the ball and as such accounts for the number of opportunities a player has to gain yards. Touches are expected to have a negative impact on career length because holding yards (and other measures) constant, an additional touch is simply another opportunity for a player to get injured. Yards are defined as the sum of a player’s rushing and receiving yards. Yards are expected to have a positive impact on career length because they measure the 7 impact of the player’s ability to help the team get closer to a scoring opportunity. Touchdowns are defined as the sum of a player’s rushing and receiving touchdowns. Touchdowns are expected to have a positive impact on career length because they measure the impact of the player’s ability to help the team score points. Fumbles represents the number of times a player has possession of the football and loses possession while fumbles lost measures those fumbles where the opposing team recovers possession. Fumbles and fumbles lost are expected to have a negative impact on career length because they represent either an opportunity for the opposing team to gain possession, or an actual loss of possession. In addition to direct performance measures, we include demographic variables believed to be associated with performance. Height, weight and age are all measured during the first season the player enters professional football. Weight is expected to have a positive impact on player career length, while age is expected to have a negative impact. Height is ambiguous as it can be beneficial due to improved visibility on the field, but may increase injuries for a variety of reasons. We also include overall team performance to account for interactions with other players. Win percentage and playoff appearance measure overall success of the team. We also include the difference between the team salary cap and the total payroll of a player’s team (Millions under salary cap). Due to the exception in the salary cap that allow veterans to receive the minimum salary up to 810,000 and only count $425,000 against the salary cap, a team’s total payroll is allowed to be larger than the salary cap value without incurring a penalty. Millions under the salary cap is expected to have a positive impact on career length because the more a team is under the salary cap, the more money they are allowed to spend on players. The explanatory variables of interest in this analysis are measures of the salary minimum on the individual player. We calculate this in two different ways: mandatory raise and mandatory income increase. Mandatory raise is defined as the base salary increase a team must give to a player from year t to year t+1 in order for the player to earn the minimum salary for year t+1. For those players whose year t salary is above the year t+1 minimum, a value of zero is entered. Mandatory income increase is defined as the total increase in income a player must receive from year t to year t+1 in order for the player to earn the minimum salary for year t+1. The difference between these two measures is that a player requires a mandatory raise when his 8 base salary is less than the next year’s minimum salary but a player requires a mandatory income increase when his base salary plus bonuses is less than the next year’s minimum salary. We also create two indicator variables, mandatory raise indicator and mandatory income increase indicator, which are coded as one when a player has to receive a mandatory raise or mandatory income increase. We also include signing bonus, other bonuses and pension eligibility variables to control for a player’s non-salary compensation. These measures control for the cases where players receive small base salaries but a large amount of compensation in the form of bonuses. The signing bonus is a bonus a player receives when he signs a new contract with a team. Other bonuses typically are bonuses given to players when they achieve a specific goal outlined in their contract. Pension eligibility is a dummy variable indicating whether a player is eligible for the pension plan which occurs when they earn four credited seasons. Both signing and other bonuses are expected to have a positive impact on the player's career length as it indicates both expectations of high performance and realizations of that high performance. Both bonuses can be viewed as expectations of future high performance and hence control for future performance. The effect of Pension eligibility is ambiguous since it may induce players to leave the uncertainty of participation in favor of a guaranteed income, or it may indicate continued high performance and high performance expectations. The defensive sample contains 653 players and 2,347 player years. Defensive backs represent 42.7% of the defensive players while defensive linemen represent 29.6% of the defensive players. Linebackers represent the remaining 27.7% of the defensive players. Defensive backs have slightly shorter careers than other defensive positions and hence represent only 40.5% of the defensive player years, while linemen and linebackers represent 31.1% and 28.4% of the defensive player years respectively. The offensive sample contains 418 players and 1,368 player years in the offensive positions sample. Running backs and wide receivers represent 39.7% and 41.4% of the offensive players respectively. Tight ends account for only 18.9% of the offensive sample. Running backs have slightly shorter careers than other offensive players and represent only 38.5% of the offensive player years. Tight ends have slightly longer careers and represent 20.5% of the player years, while wide receivers represent 41.0% of player years. 9 Table 2 presents player year averages for both samples. Because these are player year averages, they tend to over-represent players who have longer careers. Of particular note are the variables measuring mandatory raises and mandatory income increases. A mandatory raise is required by 69.2% of the defensive sample and 70.0% of the offensive sample. A mandatory income increase is required by 34.6% of the defensive sample and 37.4% of the offensive sample. Defensive players, on average, have 13.0 games played, 7.3 games started, 41.2 tackles, 1.3 sacks, 3.0 passes defended, 0.7 interceptions, and 0.6 forced fumbles. Offensive players, on average, have 12.2 games played, 5.5 games started, 54.2 touches, 391.3 yards, 2.5 touchdowns, 0.8 fumbles, and 0.5 fumbles lost. Table 3 presents the distribution of how the minimum salary schedule effects mandatory raises and mandatory income increases through the distribution of seasons played. A large number of star players require a mandatory raise because they receive a large amount of their income in bonuses. Only a few star players require a mandatory income increase. Both mandatory raises and mandatory income increases are concentrated among players with less experience. There is one interesting notch occurring at seven years of experience. Referring back to table 1, we note that beginning at 7 years of experience, the minimum is the same through season 9, but represents a relatively large increase over season 6. This accounts for the higher percent of increases at season 7, and the nearly zero necessary increases after that. Survival Estimates Before turning to the parametric estimates of the survival function using the Weibull model, it is instructive to consider Kaplan Meier survival estimates. This provides a simple check to determine if survival functions are monotonic, and also provides useful baseline insights. Figures 1 through 4 present the Kaplan Meier survival estimates for our two samples. In each case the sample is split by whether a player ever required a mandatory raise or mandatory income increase. Two conclusions are drawn from these results. First, the monotonicity assumption necessary for the Weibull model does not appear to be violated. Second, players who require at least one mandatory increase have lower survival curves than those who do not. This indicates that the mandatory raise is correlated with shorter careers on average. However, these results do not control for ability or other factors. 10 We present four basic models for both samples. Two models (labeled (1) and (3) in the tables) use the indicator for mandatory raise and mandatory income increase respectively as the variable of interest, while models (2) and (4) use the monetary values of mandatory raise and mandatory income increase. Tables 4 and 5 display the Weibull regression results for the defensive and offensive positions. Mandatory raise indicator, mandatory raise in $10,000s, mandatory income increase indicator, and mandatory income increase in $10,000s are all negative and statistically significant for the defensive and offensive positions. This provides evidence that minimum salaries shorten career length for both the defensive and offensive positions. Indeed, since the coefficients in the Weibull Regression reported in tables 4 and 5 are the marginal effects on the average career length, the implication is that players who are impacted by the salary minimum have a career length between 2.5 and 3.5 seasons shorter than those with similar characteristics who are not impacted by the salary minimum. The largest impact is seen in models 3 and 4 where the actual increase in income is measured, accounting for any bonuses the team may have paid the player in previous seasons. Bonuses often shift the risk associated with uncertain future performance to the player. Players with high incentive bonuses who are typically earning those bonuses are less likely to be the marginal player and hence the salary increase, while potentially changing the risk profile, may not be indicative of a marginal player. The set of players requiring an income increase is smaller than the set requiring a salary increase. Typically, when an income increase is required, the income and salary are identical. For this reason, we argue that models 3 and 4 better capture the implications of the minimum salary structure. Overall, we prefer model 4 (or 2) using the measure of income (or salary) increase needed. It should be noted, however, that when the model is evaluated at average values of income (or salary) increase, the impact on number of seasons played is quite comparable with the simple indicator measure. Hence, the simple indictor still serves a purpose as a summary measure of average impact on players. In examining the impact on specific types of players, as we do below, the more detailed measures of model 4 are preferred. Specifications for each of the six positions were estimated separately, but the results were similar. While not the focus of this study, the coefficients on other variables are reasonably sensible. Those that are statistically significant match general expectations. For example, more tackles and more sacks as a defensive player increase career length, while being older decreases 11 career length. Many of the coefficients, while sensible in sign are not statistically significant. Joint tests of performance measures indicate statistical significance of at least some of these variables. It is likely that high correlation between the measures of productivity lead to imprecise estimates. The model appears to be functioning well to control for ability. Figures 5 through 8 present the Weibull regression survival estimates for the defensive and offensive positions. These figures show the survival rate simulated by the hazard model for players who require a mandatory raise and for players who require a mandatory income increase. Players who require a mandatory raise have a lower survival rate during their careers than players who do not require a mandatory raise for both the defensive and offensive positions. Players who require a mandatory income increase also have a lower survival rate during their careers than players who do not require a mandatory income increase for both the defensive and offensive positions. Both of these results are consistent with the results from the Kaplan-Meier survival estimates. Controlling for other covariates, these Weibull regression survival estimates provide evidence that players who are required by minimum salaries to receive a mandatory raise or a mandatory income increase have shorter careers. Estimated Earnings Implications While the focus of this research is the impact on the length of the career, the impact on lifetime earnings is clearly important. A comprehensive examination of this would require modeling both base salary and bonuses and is well beyond the scope of this paper. We focus on using the results of models 1 and 2, using the base salary amounts, combined with a simple Tobit model of base salary to estimate the impact on career base salary. Table A1 presents our base salary model. The log of the player’s base salary in 2009 dollars is the dependent variable. We use the same explanatory variables as in the duration models and include a linear number of seasons played term to capture increases in pay with experience. Specifications which were quadratic in seasons played were estimated, but not substantially improve the fit of the models. Table 6 presents in sample comparison of actual to predicted salaries. The predicted salary used here is the exponential of the predicted log salary plus 1/2 the estimated variance (see Madala, 1984) as is well known for the log-normal distribution. It is not surprising that the 12 predicted is substantially lower than the actual, as about 70% of the players years are affected by the salary minimum. In order to estimate total career earnings without the salary minimum, we construct a median player based upon the statistics in table 2. We use the estimated Tobit model of base salary to predict salary through a ten year career. Ten years was chosen, since the survival probabilities after ten years were below 2%. We multiply the predicted salary in each year by the probability that a player would still be employed in that year (the unconditional survival probability). Summing the total provides the expected career earnings of a median player. We construct this for each of the three offensive and defensive positions (no position was a majority of the players, so the "median player" would have defaulted to the base category). In order to estimate the total career earnings with the salary minimum, we again begin with the Tobit predictions. We compare these to the 2009 minimum salary schedule. The predicted salary is now the maximum of the Tobit prediction and the minimum salary. We also construct the indicator for whether the player would need a salary increase the next year and incorporate this into the prediction from the survival model. Perhaps surprisingly, the model predicted that players’ salaries rose above the minimum by the third or fourth season and remained above those salaries. The predicted survival rates are then multiplied by the predicted salary and the resulting ten year profile is summed to arrive at a predicted salary for the player. It is important to note that this is not the average player, but rather a player with median statistics. Given the non-linearity of both models, it is best to interpret the results as indicative, rather than comprehensive. Our results suggest that perhaps players are quite rational in their desire for a minimum salary. Table 7 presents the results of this simulation. What is striking is that under both models, the defensive players stand to gain the most from the minimum salary. The predicted earnings for both tight ends and wide receivers were higher than the minimum salary for all years, and hence there is no predicted gain or loss from these positions. For the running backs, the gains under the raise amount variable specification (model 2) were modest, only $73,119 on a base of $6.2 million and similarly the loss, under the raise indicator specification (model 1) were modest as well ($165,411). The results in table 7 should be taken cautiously. A more comprehensive model of salary, bonus and career length would be necessary to fully capture the complex endogeneity of total career earnings. However, the results are important in that while there is strong evidence 13 from our analysis that the minimum salary significantly shortens players’ careers, this is not evidence that players have agreed to a contract which is detrimental. Conclusions This paper uses NFL data to measure the impact of minimum salaries on career length. We present Kaplan Meier survival estimates that demonstrate that players who require a mandatory raise or a mandatory income increase have lower survivor rates than players who do not require a mandatory raise or a mandatory income increase. In a parametric model, based on the Weibull distribution, variables measuring the required salary and income increases are negative and statistically significant for both the defensive and offensive positions. We find strong evidence that minimum salaries have a negative impact on career length. In a simple extension to examine the impact on career earnings, we find that the minimum more than offsets the loss of career, suggesting that players may be behaving optimally in obtaining a minimum salary. These results have important implications for other industries because whenever minimum salaries force a worker’s pay to be higher than their value to the firm, the worker’s career length is expected to be shortened regardless of industrial structure, gender, or magnitude of minimum salaries. However, the magnitude of the minimum salaries in the NFL is far greater than the magnitude of the minimum salaries in most other industries. The market structure in the NFL differs from most other market structures that employ minimum salary schedules. The NFL only employs males but other industries with minimum salary schedules employ both males and females. In spite of all of these differences between the NFL and any other industry that utilizes a minimum salary schedule, we argue that career lengths will be shortened any time the employer has the ability to dismiss or fire workers and the salary structure forces the firm to pay the worker more than the value of the worker to the firm. Therefore, any industry that has a minimum salary schedule in place should be aware that this salary structure has the ability to shorten the career length of an employee when it forces the employer to pay the employee more than the employee’s value to the firm. 14 References Brown, Charles, Curtis Gilroy, and Andrew Kohen. 1982. The effect of the minimum wage on employment and unemployment. Journal of Economic Literature 20 (June): 487-528. Behrman, Jere R., Robin C. Sickles, and Paul Taubman. 1983. The impact of minimum wages on the distributions of earnings for major race-sex groups: a dynamic analysis. American Economic Review 73 (September): 766–78 Card, David. 1992a. Using regional variation in wages to measure the effects of the federal minimum wage. Industrial and Labor Relations Review 46 (October): 22-37. Card, David. 1992b. Do minimum wages reduce employment? A case study of California 1987-1989. Industrial and Labor Relations Review 46 (October): 38-54. Card, David and Alan B. Krueger. 1994. Minimum wages and employment: a case study of the fast-food industry in New Jersey and Pennsylvania. American Economic Review 84 (September): 772–93 Conlin, Mike and Patrick M. Emerson. 2003. Multidimensional separating equilibria and moral hazard: an empirical study of the national football league contract negotiations. Review of Economics and Statistics 85 (August): 760–65. Dickens, Richard, Stephen Machin, and Alan Manning. 1999. The effects of minimum wages on employment: theory and evidence from Britain. Journal of Labor Economics 17, no. 1: 1–21. Hamlen Jr., William A. 2007. Deviations from equity and parity in the national football league. Journal of Sports Economics 8 (December): 596-615. Fort, Rodney and James Quirk. 1995. Cross-subsidization, incentives, and outcomes in professional team sports leagues. Journal of Economic Literature 33 (September): 1265-1299. Johnson, William R. and Edgar K. Browning. 1983. The distributional and efficiency effects of increasing the minimum wage: a simulation. American Economic Review 73 (March): 204– 211. Kahn, Lawrence M. 2000. The sports business as a labor market laboratory. Journal of Economic Perspectives (Summer): 75–94. Katz, Lawrence F. and Alan B. Krueger. 1992. The effects of the minimum wage on the fastfood industry. Industrial and Labor Relations Review (October): 6-21. MacDonald, Don N. and Morgan O. Reynolds. 1994. Are baseball players paid their marginal products?. Managerial and Decision Economics 15 (September/October): 443-457. National Football League, 2010. http://www.nfl.com/players. 15 Neumark, David, Mark Schweitzer, and William Wascher. 2004. Minimum wage effects throughout the wage distribution. Journal of Human Resources 39 (Spring): 425-450. Manton, Kenneth G., Burton Singer and Max A. Woodbury. 1992. Some issues in the quantitative characterization of heterogeneous populations. In James Trussell, editor, Issues in Event History Analysis. Oxford University Press. NFL Players Association and NFL Management Council. 2006. NFL collective bargaining agreement 2006-2012 (March). Rosen, Sherwin and Allen Sanderson. 2000. Labor markets in professional sports. NBER Working Paper 7573 (February). Cambridge, MA. Scully, Gerald W. 1974. Pay and performance in major league baseball. American Economic Review 64 (December): 915-30. USA Today. National Football League Salaries, 2010. http://content.usatoday.com/sportsdata/football/nfl/salaries/team. Vrooman, John. 1995. A general theory of professional sports leagues. Southern Economic Journal 61 (April): 971-90. 16 Figures Figure 1: Kaplan-Meier Survival Estimates for Defensive Backs, Defensive Linemen, and Linebackers by Mandatory Raise 0.00 0.20 0.40 0.60 0.80 1.00 Kaplan-Meier Survival Estimates by Mandatory Raise 0 1 2 3 4 5 Season 6 MANDATORY_RAISE = 0 7 8 9 10 MANDATORY_RAISE = 1 Figure 2: Kaplan-Meier Survival Estimates for Defensive Backs, Defensive Linemen, and Linebackers by Mandatory Income Increase 0.00 0.20 0.40 0.60 0.80 1.00 Kaplan-Meier Survival Estimates by Income Increase 0 1 2 3 4 5 Season INCOME_INCREASE = 0 17 6 7 8 9 10 INCOME_INCREASE = 1 Figure 3: Kaplan-Meier Survival Estimates for Running Backs, Tight Ends, and Wide Receivers by Mandatory Raise 0.00 0.20 0.40 0.60 0.80 1.00 Kaplan-Meier Survival Estimates by Mandatory Raise 0 1 2 3 4 5 Season 6 MANDATORY_RAISE = 0 7 8 9 10 MANDATORY_RAISE = 1 Figure 4: Kaplan-Meier Survival Estimates for Running Backs, Tight Ends, and Wide Receivers by Mandatory Income Increase 0.00 0.20 0.40 0.60 0.80 1.00 Kaplan-Meier Survival Estimates by Income Increase 0 1 2 3 4 5 Season INCOME_INCREASE = 0 18 6 7 8 9 10 INCOME_INCREASE = 1 Figure 5: Weibull Regression Survival Estimates for Defensive Backs, Defensive Linemen, and Linebackers by Mandatory Raise 0 .2 .4 .6 .8 1 Weibull Regression Survival Estimates by Mandatory Raise 0 1 2 3 4 5 Season 6 Mandatory_Raise=0 7 8 9 10 Mandatory_Raise=1 Figure 6: Weibull Regression Survival Estimates for Defensive Backs, Defensive Linemen, and Linebackers by Mandatory Income Increase 0 .2 .4 .6 .8 1 Weibull Regression Survival Estimates by Income Increase 0 1 2 3 4 5 Season Income_Increase=0 19 6 7 8 9 Income_Increase=1 10 Figure 7: Weibull Regression Survival Estimates for Running Backs, Tight Ends, and Wide Receivers by Mandatory Raise 0 .2 .4 .6 .8 1 Weibull Regression Survival Estimates by Mandatory Raise 0 1 2 3 4 5 Season 6 Mandatory_Raise=0 7 8 9 10 Mandatory_Raise=1 Figure 8: Weibull Regression Survival Estimates for Running Backs, Tight Ends, and Wide Receivers by Mandatory Income Increase 0 .2 .4 .6 .8 1 Weibull Regression Survival Estimates by Income Increase 0 1 2 3 4 5 Season Income_Increase=0 20 6 7 8 9 Income_Increase=1 10 Tables Table 1: Minimum Salaries by Credited Seasons in 2009 Dollars Credited Seasons Year 0 1 2 3 4 5 or 6 2000 240,451 342,611 446,018 479,656 514,540 548,178 2001 253,180 360,994 471,230 506,361 542,702 577,833 2002 268,320 357,760 447,201 536,641 626,081 626,081 2003 262,341 349,789 437,236 524,683 617,960 617,960 2004 261,215 346,394 431,573 516,751 607,609 607,609 2005 252,655 335,042 417,430 499,817 593,190 593,190 2006 292,647 372,460 452,273 532,086 622,540 622,540 2007 294,890 372,492 450,095 527,698 615,647 615,647 2008 293,951 368,684 443,417 518,150 602,848 602,848 2009 310,000 385,000 460,000 535,000 620,000 620,000 21 7-9 548,178 577,833 775,148 763,705 749,573 730,502 755,562 744,985 727,403 745,000 10 plus 548,178 577,833 894,401 880,301 863,145 840,352 861,979 848,455 827,047 845,000 Table 2: Summary Statistics Variable Time Invariant Seasons Played Age at Rookie Year Weight at Rookie Year Height (inches) at Rookie Year Defensive Back Defensive Lineman Linebacker Tight End Wide Receiver Running Back Time Varying Mandatory Raise Indicator Mandatory Raise (in 10000s) Mandatory Income Increase Indicator Mandatory Income Increase (in 10000s) Games Played Games Started Pension Eligibility Win Percentage Playoff Appearance Signing Bonus (in 10000s) Other Bonuses (in 10000s) Millions Under Salary Cap Tackles Sacks Passes Defended Interceptions Forced Fumbles Total Touches Total Yards Touchdowns Fumbles Fumbles Lost Defensive Positions Mean Median n= 653 3.59 3 22.6 23 238.3 235 73.4 73 0.437 0 0.296 0 0.277 0 na na na na na na n = 2347 0.692 1 5.641 7.379 0.346 0 Offensive Positions Mean Median n =418 3.27 3 22.7 23 220.4 217 72.9 73 na na na na na na 0.189 0 0.414 0 0.397 0 n = 1368 0.7 1 5.834 7.383 0.374 0 2.477 0 2.847 0 13.049 7.305 0.216 0.509 0.385 99.604 29.45 3.265 41.196 1.293 2.985 0.728 0.637 na na na na na 15 6 0 0.5 0 1.552 0.497 4.069 35 0 2 0 0 na na na na na 12.186 5.471 0.221 0.496 0.363 89.835 28.79 2.727 na na na na na 54.21 391.273 2.461 0.841 0.474 14 3 0 0.5 0 1.034 0.456 3.352 na na na na na 25 243 1 0 0 22 Table 3: Percentage of Players Requiring a Mandatory Raise or Mandatory Income Increase Defensive Sample Offensive Sample Mandatory Mandatory Mandatory Income Mandatory Income Raise Increase Number Raise Increase Number of Required Required of Required Required Season Players (%) (%) Players (%) (%) 1 653 94.5 32.8 418 93.1 40.4 2 504 94.6 60.1 284 94.4 60.6 3 392 84.9 56.1 213 83.1 58.7 4 291 41.6 19.6 151 45.0 22.5 5 201 12.9 2.0 118 10.2 1.7 6 150 16.0 3.3 88 15.9 1.1 7 93 25.8 7.5 57 36.8 14.0 8 44 4.5 2.3 29 17.2 0.0 9 19 0.0 0.0 10 30.0 10.0 Total 2347 69.2 34.6 1368 70.0 37.4 23 Table 4: Weibull Regression Results for Defensive Positions (n=2347) Variables (1) (2) (3) (4) Mandatory Raise Indicator -2.773*** (0.001) Mandatory Raise (in 10000s) -0.305*** (0.000) Mandatory Income Increase -3.427*** Indicator (0.000) Mandatory Income Increase -0.451*** (in 10000s) (0.000) Games Played 0.299*** 0.286*** 0.307*** 0.296*** (0.000) (0.000) (0.000) (0.000) Games Started -0.173 -0.167 -0.203 -0.191 (0.145) (0.153) (0.113) (0.125) Tackles 0.144*** 0.144*** 0.158*** 0.153*** (0.001) (0.000) (0.001) (0.000) Sacks 2.113*** 2.172*** 2.243*** 2.361*** (0.001) (0.001) (0.001) (0.001) Passes Defended 0.779*** 0.759*** 0.770*** 0.753*** (0.000) (0.000) (0.001) (0.001) Interceptions 0.427 0.402 0.533 0.555 (0.482) (0.503) (0.409) (0.394) Forced Fumbles -0.208 -0.261 -0.162 -0.216 (0.740) (0.668) (0.811) (0.741) Pension Eligibility 0.825 0.691 0.674 0.601 (0.300) (0.389) (0.429) (0.474) Win Percentage 0.074*** 0.073*** 0.085*** 0.086*** (0.001) (0.001) (0.001) (0.000) Playoff Appearance -0.929 -0.976 -1.164 -1.21 (0.248) (0.224) (0.175) (0.156) Signing Bonus (in 10000s) 0.005* 0.005* 0.004 0.004 (0.070) (0.078) (0.137) (0.113) Other Bonuses (in 10000s) 0.014 0.014 0.014 0.014 (0.107) (0.109) (0.129) (0.115) Millions Under Salary Cap 0.032* 0.032 0.033 0.034 (0.091) (0.102) (0.114) (0.110) Age at Beginning of Career -0.975*** -0.986*** -0.981*** -0.965*** (0.000) (0.000) (0.000) (0.000) Height (in inches) -0.046 -0.027 -0.032 -0.021 (0.805) (0.886) (0.868) (0.914) Weight 0.092*** 0.091*** 0.093*** 0.097*** (0.000) (0.000) (0.000) (0.000) Defensive Back 3.293*** 3.294*** 3.282*** 3.491*** (0.003) (0.003) (0.004) (0.003) Defensive Linemen -3.711*** -3.720*** -3.720*** -4.067*** (0.004) (0.004) (0.005) (0.002) Note.-Marginal Effects are reported. P-values are in parentheses. Significance Level: ***1%, **5%, *10%. 24 Table 5: Weibull Regression Results for Offensive Positions (n=1368) Variables (1) (2) (3) (4) Mandatory Raise Indicator -2.587*** (0.004) Mandatory Raise (in 10000s) -0.290*** (0.000) Mandatory Income Increase -2.686*** Indicator (0.000) Mandatory Income Increase -0.291*** (in 10000s) (0.001) Games Played 0.342*** 0.343*** 0.362*** 0.358*** (0.000) (0.000) (0.000) (0.000) Games Started 0.212 0.201 0.217 0.221 (0.104) (0.116) (0.120) (0.111) Touches -0.069*** -0.067*** -0.071*** -0.071*** (0.007) (0.008) (0.009) (0.009) Yards 0.018*** 0.018*** 0.019*** 0.019*** (0.003) (0.003) (0.003) (0.003) Touchdowns 0.132 0.128 0.171 0.155 (0.649) (0.653) (0.583) (0.621) Fumbles 0.066 0.041 -0.015 0.049 (0.913) (0.945) (0.982) (0.940) Fumbles Lost 0.266 0.324 0.343 0.320 (0.767) (0.713) (0.716) (0.732) Pension Eligibility 2.683*** 2.407*** 2.397** 2.678*** (0.004) (0.008) (0.016) (0.006) Win Percentage 0.044** 0.043** 0.038* 0.038* (0.029) (0.034) (0.081) (0.080) Playoff Appearance -1.027 -0.963 -0.853 -0.807 (0.213) (0.243) (0.340) (0.367) Signing Bonus (in 10000s) 0.010** 0.010** 0.007* 0.008** (0.017) (0.017) (0.058) (0.047) Other Bonuses (in 10000s) -2.296 x 10-4 -3.849 x 10-4 -3.555 x 10-4 -0.001 (0.957) (0.947) (0.856) (0.947) Millions Under Salary Cap 0.001 0.001 -0.006 0.009 (0.947) (0.739) (0.942) (0.641) Age at Beginning of Career -1.150*** -1.155*** -1.070*** -1.117*** (0.000) (0.000) (0.000) (0.000) Height (in inches) -0.267 -0.251 -0.263 -0.238 (0.130) (0.143) (0.152) (0.190) Weight 0.063** 0.058** 0.062** 0.060** (0.011) (0.016) (0.016) (0.019) Tight End -0.058 0.001 -0.045 -0.197 (0.953) (0.999) (0.966) (0.850) Wide Receiver 1.175 1.092 1.148 0.966 (0.247) (0.276) (0.285) (0.364) Note.-Marginal Effects are reported. P-values are in parentheses. Significance Level: ***1%, **5%, *10%. 25 Table 6: Predicted and Actual Salaries Offensive Positions Defensive Positions Mean Base Salary 613093 675729 Median Base Salary 417429 431572 Mean of Predicted Salary 440789 408500 Median of Predicted Salary 298843 203637 Note.-Within Sample predictions from Tobit Model. Table 7: Career Base Salary for a player with median statistics Model 1: Career Base Salary with Raise Indicator Gain From Offensive Players Without Minimum With Minimum Minimum Running Backs 6097955 5932544 -165411 Tight Ends 13010509 13010509 0 Wide Receivers 10340233 10340233 0 Defensive Players Linebackers Defensive Backs Defensive Linemen Offensive Players Running Backs Tight Ends Wide Receivers 3663742 3783662 119920 3874801 4704789 829988 3402577 3434094 31517 Model 2: Career Base Salary with Raise Amount Variable Gain from Without Minimum With Minimum Minimum 6161518 6234637 73119 13253111 13253111 0 10355017 10355017 0 Defensive Players Linebackers 3622317 5106650 1484333 Defensive Backs 3854131 6017656 2163525 Defensive Linemen 3333067 3437267 104200 Note.-Prediction based on Tobit Model and Survival Model for player with median statistics. 26 Appendix Table A1: Tobit Model of Log Base Salary Games Played Games Started Pension Eligibility Win Percentage Playoff Appearance Signing Bonus (in 10000s) Other Bonuses (in 10000s) Millions Under Salary Cap Age at Rookie Year Weight at Rookie Year Height (inches) at Rookie Year Total Touches Total Yards Touchdowns Fumbles Fumbles Lost Tight End Wide Receiver Tackles Sacks Passes Defended Interceptions Forced Fumbles Defensive Back Defensive Lineman Seasons Played Intercept Sigma Offensive Model Coeff. Std. Err. -0.05382 0.023726 0.021348 0.023741 0.222885 0.256568 -0.33928 0.581423 0.159419 0.231385 0.000446 0.000254 0.000963 0.000586 -0.0026 0.00588 -0.15698 0.045671 -0.00559 0.00677 -0.09761 0.050521 -0.00153 0.00205 0.000474 0.000458 0.026329 0.036048 -0.07877 0.112086 0.286598 0.155799 0.76574 0.369837 0.389895 0.376888 n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a 0.240214 0.069532 24.54302 3.684981 0.817158 0.081869 27 Defensive Model Coeff. Std. Err. -0.0865 0.023447 0.041963 0.0189 0.920341 0.230026 -0.39141 0.469809 0.155208 0.184641 -0.00042 0.000211 -0.00211 0.000621 -0.00069 0.004708 -0.11211 0.035515 -0.00618 0.003522 0.045549 0.041588 n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a n.a 0.00678 0.003599 0.013367 0.027275 0.013359 0.019961 0.093362 0.052571 0.099218 0.058829 -0.28203 0.246097 0.619573 0.286532 0.293435 0.057399 12.78919 3.207292 0.904242 0.068879