The Demand for Younger and Older Workers

Abstract

This study examines how worker productivity and risk factors affect the demand for younger and older workers modeled using concepts from labor economics. The two primary National Football League player labor markets—the draft process and veteran free agent market—provide rich empirical environments for testing hypotheses from the model. Clubs demonstrate greater demand for rookies by drafting them earlier and for veterans by signing them faster. Greater physical productivity enhances labor demand for all players, but risk factors exert a more severe labor market penalty for veterans, patterns consistent with theory and with previous research on the demand for risky workers and older workers.

Keywords

labor demand labor markets NFL

Introduction

Job seekers always carry an element of risk to potential employers in relation to their physical productivity: it may turn out less than expected due to shortfalls of pure ability. But workers carry other forms of risk unrelated to their skills—risk of injury or illness, turnover or shirking, and even illegal activity (on or off the job) that threatens their general availability and therefore their productivity. These risk factors make employers vulnerable to health care and turnover costs and losses of business due to inefficiency or a damaged reputation. Employers generally desire to use younger and older workers together, but each type presents benefits and risks that complicate the process of finding the optimal mix. Veterans bring experience, proven productivity, and the ability to mentor younger workers, but they are relatively more susceptible to health problems and are closer to retirement. Younger workers offer better health, longer expected work lives, and can eventually replace older workers, but they bring unproven productivity and may require training. How does the labor market respond to worker risk when employers seek younger and older workers?

To address this question conceptually, I apply job match and labor demand theory to demonstrate how the demand for younger and older workers can change, given variation in the productivity and risk factors associated with any given worker type and with the alternate worker type. I investigate hypotheses emanating from this model empirically using data relevant to labor markets within the National Football League (NFL): annual off-season markets for veteran free agent players and rookie players, the latter surrounding the NFL draft. NFL clubs continuously must weigh players' personal productivity and risk factors when determining which players to add to their rosters. They make these employment decisions within heterogeneous local markets (NFL cities), where labor demand decisions and their outcomes become very public and the reactions of consumers (fans) and other onlookers can become highly influential.¹ Empirically, I also take advantage of an exogenous institutional change: the NFL’s transition from 2006 to 2007 to a new commissioner, Roger Goodell, widely perceived to be committed to stronger sanctions for player misconduct. Interaction variables allow us to examine how the demand for a particular type of risky worker—players more likely to get into some sort of legal trouble—has changed, given that the cost of employing them apparently has exogenously increased.²

This article builds on previous economic research on the demand for risky, younger, and older workers as well as general labor market outcomes in professional sports. Bollinger and Hotchkiss (2003) defined risky workers as those with “variable, or uncertain, productivity” (p. 924), based on foundational models by Lazear (1998) and Li and Rosen (1998). This conceptualization motivates the incorporation of worker risk factors in the conceptual analysis developed in the following sections. Researchers studying the use of risky younger and older workers (Hutchens, 1986, 1988; Schøne, 2009; Scott, Berger, & Garen, 1995) have emphasized the demand side of the labor market, motivated by a desire to understand differential outcomes for older and younger workers as a consequence of employer actions. The key labor market outcome for younger workers in this context becomes how employers regard a pool of workers before the start of the employment relationship, thus making the NFL draft outcome the central empirical indicator of labor demand here. In the same literature, the key labor market outcome for older workers becomes the efficiency with which they transition between jobs, thus making the duration of a veteran player’s waiting time on the free agent market their central labor demand outcome.

The empirical results reinforce earlier findings from sports economics regarding the effect of player and team characteristics on labor market outcomes.³ More importantly, the results indicate that while more pronounced risk factors exert significant labor demand penalties in these markets, older players sustain more comprehensive such penalties, including in association with the commissioner change, as predicted theoretically. This article contributes to economic research on the demand for younger and older workers by examining outcomes for both types of worker in labor markets that operate independently within the same industry and occupation, thus eliminating elements of unobserved heterogeneity that can shape the experiences of each worker type. Previous studies have not done this. This article also probes labor market effects of a major institutional change that plausibly influenced the central labor demand decision of interest, an approach seldom pursued.⁴ Within the confines of its larger research question, this study also represents one of the first to examine economic consequences of misconduct by professional athletes, the subject of increasing public scrutiny and concern in recent years.

The Demand for Younger and Older Workers

Own Productivity and Risk Effects

Elements of job match and labor demand theory help illustrate the use of younger and older workers and motivate the empirical analysis. Suppose a potential employer uses inputs of younger workers (rookies), x_R , and older workers (veterans), x_V , to produce short-run output in accordance with the generalized production function q = q(x_R , x_V ) assumed to have traditional properties whereby rookies and veterans have positive but diminishing marginal products. Rookies are available at marginal wage W_R , veterans at W_V , and both bring to the market risk factors that threaten their productivity; I focus here on the risk of injury or illness, turnover, and illegal behavior.⁵ Let shift parameters φ _R and φ _V index exogenous risk factors associated with rookies and veterans, respectively, such that ∂² q/∂x_R∂φ_R < 0 and ∂² q/∂x_V ∂φ _V < 0: more pronounced own-risk factors reduce the marginal productivity of each. Let γ _R and γ _V index exogenous productivity factors that enhance younger and older worker productivity such that ∂² q/∂x_R ∂γ _R > 0 and ∂² q/∂x_V ∂γ _V > 0. The employer seeks levels of employment of each type of worker to maximize profit, π = P(q)q(x_R , x_V ; φ _R , φ _V , γ _R , γ _V ) − (W_Rx_R + W_Vx_V ), subject to the budget constraint W_Rx_R + W_Vx_V = I and the adding-up constraint x_R + x_V = X, the latter ensuring that all workers X are either rookies or veterans.⁶ The separate productivity and risk factors for each worker type allow direct comparison of the marginal impact of variation in these factors across younger and older workers.⁷ Higher wages attract and generate utility for workers, but stronger personal risk factors threaten a worker’s productivity, earnings ability, and ultimately his utility.

In Figure 1, U ₁ and U ₂ represent indifference curves for two hypothetical workers in (wage (W), risk (φ)) space, their convexity reflecting risk aversion and the availability of more utility in the northwest (wage) direction. The relatively steeper slope of U ₁ signifies that Worker 1 exhibits stronger risk aversion compared to Worker 2. At the margin, Worker 1 in principle would require a larger increase in wage to accept an arbitrarily higher level of personal risk and remain on the same indifference curve. Put another way, given a common wage offer, Worker 2 would willingly accept more risk than Worker 1. Hypothetical workers possess a degree of uncertainty about their own upside physical ability; as Li and Rosen (1998) write, this uncertainty “produces anxiety over how [they] will make out and to whom they will be matched” (p. 384). The worker’s respective tastes for risk, however, reflect their perceptions of their ability; in this formulation, Worker 2 possesses more confidence in that ability. If the workers accurately project their upside ability levels, then Workers 1 and 2 might reasonably represent older and younger workers, respectively. The isoprofit function π reflects the employer’s trade-off between wage offers and risk. To reduce worker risk and remain on the same isoprofit curve, the employer must offer a lower wage so as to defray the cost of that risk reduction, such as incurred through a more arduous search process. For analytical simplicity, I assume the existence of a homogeneous set of employers that exhibit this isoprofit function.

Figure 1.

Equilibrium player–club matches.

Equilibrium worker–employer (player–club) matches occur where an indifference curve reaches a tangency with the isoprofit curve, as shown in Figure 1. More risk-averse Worker 1 finds an equilibrium match with an employer at point A and receives wage W ₁ associated with risk level φ₁. Less risk-averse Worker 2 receives equilibrium wage W ₂ > W ₁ associated with risk level φ₂, the higher risk level reflective of the worker’s willingness to accept more personal risk in the labor market, associated with his greater upside ability. Because wages W are inversely related to labor market search time, a pattern documented empirically below, W ₂ > W ₁, implies that Worker 2 exhibits relatively stronger labor demand and therefore a shorter market wait time compared to Worker 1. The better worker receives the more favorable labor market outcome, linked to his own productivity characteristics, much in keeping with the conclusions of Li and Rosen (1998). I investigate this relationship empirically by incorporating measures of rookie and veteran productivity in econometric models of labor demand for each worker type.

An important result in the literature on the employment of younger and older workers indicates that under reasonable conditions an employer may have a greater incentive to hire risky younger workers than risky older workers. This conceptual possibility emerges in the application to NFL labor markets when we consider, first, how exogenous variation in the own-risk factor for a given worker type—rookie or veteran—influences the set of equilibrium job matches he can obtain and, second, how this variation likely exerts a differential impact on employer profit.

As Li and Rosen (1998) discuss, variation in a worker’s own risk alters the payoffs of the worker and the employer and therefore affects the equilibrium job match. Because a worker gains utility from compensation but disutility from the potential loss of productivity associated with his personal risk factors, a higher level of risk φ implies lower utility, ceteris paribus. If veterans do exhibit graphically steeper and rookies graphically flatter indifference curves, reflective of their respective degrees of risk aversion, then an arbitrarily higher level of risk forces the hypothetical veteran onto an indifference curve such as U_V ′ as shown in Figure 2 and the hypothetical rookie onto an indifference curve such as U_R ′. These lower indifference curves embody less desirable combinations of wage and risk, irrespective of physical ability. Any new equilibrium job match must then occur at a tangency with a graphically lower isoprofit function (signifying increased actual employer profit), associated with paying a lower wage and thus lower total costs. In this eventuality, the employer uses a riskier worker and yet has the opportunity to prosper, consistent with the option value proposition expressed by Lazear (1998).

Figure 2.

Impact of own risk across worker types.

But younger and older workers do not necessarily face the same labor market penalty traceable to own-risk factors. Figure 2 depicts an asymmetric downward shift of the isoprofit function, such that a given change in the risk factor φ exerts a larger marginal effect on profit in association with veterans than with rookies. This results in a demonstrably larger reduction in the equilibrium wage and by implication a larger increase in the market wait time for veterans (the equilibrium moves from A to A′) than for rookies (B to B′). If the isoprofit function shifted symmetrically across worker types, one would anticipate little or no difference in these effects.

The key to this outcome lies in how variation in the worker risk factor impacts profit across the worker types. Formally, a larger marginal effect on profit in association with veterans would mean that ∂π/∂φ _R < ∂π/∂φ _V or, following simplification, that P(1 + 1/∊)(∂q/∂φ _R −∂q/∂φ _V ) < (∂W_R /∂φ _R )x_R − (∂W_V /∂φ _V )x_V , where ∊ is the price elasticity of demand for q. Deconstructing this inequality, P(1 + 1/∊) < 0 owing to ∊ < 0. The terms ∂q/∂φ _R < 0 and ∂q/∂φ _V < 0 represent the negative marginal effect on output of variation in rookie and veteran own-risk factors, respectively. If own-risk factors exert a stronger reductive effect on the efficiency of veterans than on the efficiency of rookies, plausible if veterans play more important roles in the production process than rookies, then |∂q/∂φ _V | > |∂q/∂φ _R |, rendering ∂q/∂φ _R − ∂q/∂φ _V > 0 and the left side of the inequality negative. The inequality thus holds most definitively if the right side is positive, that is, if |(∂W_V /∂φ _V )x_V | > |(∂W_R /∂φ _R )x_R |. Consider how these patterns might hold in the context of labor markets for NFL players and how the patterns inform this inequality condition.

The worker risk factors most central to the present analysis pertain to the risk of injury or illness, turnover, and illegality. Compared with older workers, younger workers may have less susceptibility to health problems than older workers, owing to their younger bodies, and they may exhibit less turnover risk than older workers. Economic research demonstrates the logically greater likelihood of job displacement, including most notably retirement, present among older workers. Also, because younger workers have less complete careers, their productivity may be relatively more sensitive to, or influenced by, job training (the coaching process in a pro sports context). At the margin, they have more potential to benefit from training, including in the form of higher compensation later in their careers, and so may have a greater incentive to accept such training as an antecedent to furthering their careers, thus reducing the likelihood of turnover.

Younger workers may also exhibit a lesser propensity for, or risk of, illegality in this context. NFL clubs draw from a larger pool of younger work candidates than older candidates in that they scrutinize many more available players during the draft process than during the veteran free agent process. The draft process involves evaluation of nonunionized amateurs scouted from hundreds of college football programs, while the free agency process involves evaluation of unionized veterans scouted from among 32 NFL clubs that typically lose only a handful of free agents in a given market year. This facilitates a greater degree of competition on the supply side of the market for rookies. Because younger players have minimal history of employment and production within the industry in which they seek employment, they cannot rely heavily on their performance potential to outweigh the risk associated with illegality (or other factors). This creates a natural incentive for them to keep that risk low. Older players by contrast have known, industry-specific productivity and so may have more of an opportunity to engage in illegality and reasonably expect to gain continued employment in this market. Given the narrower distribution of illegality risk exhibited by a typical pool of veteran free agents, employers likely recognize that a veteran carries a greater probability of running afoul of the law or league rules, thus making that type of player more vulnerable to productivity losses due to legal trouble. Because NFL clubs generally prefer to use veterans rather than rookies in starting positions, clubs would have a greater potential for on-field productivity losses attributed to illegality risk.⁸

Returning to the inequality condition, NFL clubs' greater use of veterans than rookies implies that x_V > x_R on the right side, ensuring that the right side is positive even if the marginal effect on wage of risk factors is common across the worker types (i.e., ∂W_V /∂φ _V = ∂W_R /∂φ _R ). But if employers carry less tolerance for risk among veterans than among rookies in this respect, a reasonable possibility in light of earlier research on the demand for risky and older workers and the option value proposition expressed in various works, then |∂W_V /∂φ _V | > |∂W_R /∂φ _R |, further reinforcing the positive sign of the right side.

These observations motivate the hypothesis that own-risk factors will exert a more demonstrable labor market penalty for older players (veterans) than for younger players (rookies). I investigate this hypothesis empirically by examining the extent to which measures of risk factors relevant to veteran free agents exhibit more comprehensive statistical significance than comparable measures relevant to drafted rookies. Analytically, the exogenous introduction of the Goodell commissionership ramps up φ because his administration arguably increases the probability that a player who engages in illicit behavior will receive punishment by the league, resulting in lost productivity. Given the analysis above, one therefore anticipates that the Goodell commissionership will exert a more severe labor market effect for veteran players. I examine this hypothesis empirically by probing the extent to which measures of own risk exert differential effects during the Goodell era, ascertained through interaction variables.

Cross Productivity and Risk Effects

Because employers use younger and older workers together, productivity and risk factors associated with one worker type can plausibly influence the use of the other. The adding-up constraint assures a trade-off between the two types. Therefore, lesser productivity or more enhanced risk factors among rookies logically increases the demand for veterans, and the opposite holds for veteran productivity and risk factors and the demand for rookies. From a labor demand perspective, the cross-productivity effects reflect ∂x_R */∂γ _V < 0 and ∂x_V */∂γ _R < 0; the cross-risk effects reflect ∂x_R */∂φ _V > 0 and ∂x_V */∂φ _R > 0. From a job-match perspective, factors that make the employer’s isoprofit function graphically steeper, reflective of lesser tolerance for questionable worker productivity and risk, allow tangencies to occur more readily with relatively steeper indifference curves. The market becomes more favorable to older workers who then may exhibit demonstrably shorter market waiting times. Factors that make the isoprofit function graphically flatter, reflective of greater such tolerance, more readily facilitate equilibrium job matches favorable to younger workers who have flatter indifference curves.

The cross-productivity effects motivate the inclusion of measures of veteran productivity in empirical models of rookie demand and measures of rookie productivity in models of veteran demand. As in the empirical investigation of own-risk effects, I investigate cross-risk relationships (1) by incorporating measures of rookie risk factors in models of veteran demand and veteran risk factors in models of rookie demand and (2) by probing, through interaction variables, the extent to which risk factors associated with one labor type impact the demand for the alternate type differently in the era of the Goodell commissionership.

Data and Empirical Methodology

The data used for this study relate to the two primary labor markets within which NFL clubs acquire player talent: the annual NFL draft, which brings collegiate players into the league as rookies, and the veteran free agent market, which allows eligible veteran NFL players to change teams when their previous contracts have expired.

Kahn (1992) observed that the outcome of the NFL draft, the actual draft positions of the players selected, reflects “the league’s estimate of [each player’s] desirability at the start of his career” (p. 300). Hendricks, DeBrock, and Koenker (2003) further observed that the draft offers labor economists a rare opportunity to observe a market-based ranking of workers—directly reflecting employer’s expectations of their productive potential—prior to the workers receiving additional training or starting any probationary employment period. The NFL draft thus becomes a useful empirical setting for studying labor demand outcomes pertinent to younger workers.⁹

As with employers in all industries, NFL employers add older workers (veteran players) to their payrolls as those workers transition from one employer to another, acquiring them through free agency. In the larger economy, the reality of such transitions lies at the heart of extensive economic research on the employment of older workers in general, the relatively less frequent new hiring of older workers, and their more severe frictional unemployment relative to younger workers.¹⁰ A key artifact of this last labor market outcome becomes the length of time required for a transitioning veteran worker to find a new job match. Because we can observe samples of NFL veteran free agent players, how long they last on the free agent market, and quantifiable indicators of their productivity and risk factors, the NFL free agent market provides a valuable empirical setting for studying labor demand outcomes relevant to older workers.

This study concentrates on players participating in these labor markets over the four market years (NFL off-seasons) ranging from 2005-2008. This selection of sample years reflects a desire to exploit the change in NFL commissioner that took place at the end of the 2006 season: the retirement of Paul Tagliabue and his replacement by Roger Goodell. Because of the seemingly greater emphasis placed on the punishment of players for on- and off-field transgressions within Goodell’s tenure, this event creates a natural experiment in institutional change whereby the cost of acquiring illegality risky players may have exogenously increased. The sample period thus allows a focus on labor demand activity for a common number of years in each commissionership: the last two market years within the Tagliabue era (2005-2006) and the first two years of the Goodell era (2007-2008).¹¹

For each subsample of players, data were hand collected from a variety of print and online sources, most critically from NFL statistical compendiums published annually by The Sporting News and the websites espn.com, NFLDraftScout.com, pro-football-reference.com, and NFL.com. Lexis/Nexis searches allowed collection of historical data on player injuries, fines, and suspensions, where necessary. Each subsample contains a measure of labor demand relevant to that specific labor market (draft position or free agent waiting time), as well as measures of the player’s productivity and risk factors, employer traits, and institutional and individual controls.

Rookie Subsample

Table 1 displays descriptive statistics for the variables relevant to the subsample of rookie draft selections, numbering 1,017. The primary labor demand outcome variable, Draft Position, ranges from 1 to 255 for the analysis period, lower figures corresponding to earlier selections. The NFL draft consists of seven rounds; 255 players were selected in each draft from 2005-2007, 252 players in 2008. One can readily establish the essential inverse relationship between player salaries and waiting time (draft position), a key theoretical assumption. Data on rookie-year salaries exist within the commonly used USA Today online sports salary database for 878 of the 1,017 draftees (86%). First-round picks received a mean salary of $2.75 million, second-round picks $1.58 million, third-round picks $900,160, fourth-round picks $668,093, and fifth- and later-round picks $341,816. As Böheim and Lackner (2011) note, the NFL Collective Bargaining Agreement (CBA) stipulates that earlier draft selections must obtain higher salaries, but this pattern of variation provides quantitative evidence of the inverse relationship between compensation and labor market waiting time in the market for rookies.

Table 1.

Descriptive Statistics for Rookie Subsample (N = 1,017).

	Mean	Standard Deviation	Minimum	Maximum
Outcome Variable
Draft Position	127.6	73.44	1	255
Measures of Own productivity
Division 1A	0.907	0.291	0	1
Underclassman	0.138	0.345	0	1
College Awards	0.074	0.399	0	5
College Winning Percentage	63.28	20.89	0	100
Conference Winning Percentage	54.505	5.354	31.507	64.356
Measures of Own Risk
Off-Field Incidents	0.125	0.434	0	4
Games Suspended	0.107	0.738	0	14
Injury Games Lost	0.277	1.234	0	13
Surgeries	0.341	0.679	0	6
Junior College Transfer	0.073	0.260	0	1
College Captain	0.274	0.446	0	1
College Program Infractions	0.296	0.478	0	2
Measures of Cross Productivity
Pro Bowlers at Position	0.250	0.485	0	3
Measures of Cross Risk
Injured Reserve at Position	0.703	0.875	0	5
Fines at Position	0.069	0.340	0	4
Suspensions at Position	0.030	0.172	0	1
Net Veteran Losses at Position	0.222	0.912	−3	4
Institutional Controls
Market Year 2006	0.251	0.434	0	1
Goodell (Commissioner)	0.499	0.500	0	1
Individual Controls
Height (inches)	74.158	2.633	66	81
Weight (pounds)	245.38	45.66	169	355
Height × Weight	18,281.86	3,883.63	11,799	27,176
White	0.279	0.449	0	1
Offensive Player	0.514	0.500	0	1

Five variables capture own productivity, thereby also controlling for uncertainty of player’s ability levels: Division 1A (equal to 1 if a player played college football at a bowl-eligible program, 0 otherwise), Underclassman (equal to 1 if a player left college with scholarship eligiblity remaining, 0 otherwise), the number of postseason college awards won by a player, and the whole-number winning percentage of the player’s last college team and of the conference in which his college team played. Conlin and Emerson (2006) used a similar control for “small school” programs in their study of hiring and promotion discrimination by NFL employers. As discussed by Dumond, Lynch, and Platania (2008), the most skilled high school players disproportionately attend D-1A universities rather than programs at lower levels. Players who declare for the draft prior to their senior seasons—willingly foregoing at least 1 year of subsidized higher education and collegiate competition—carry an element of risk associated with their lesser experience, as Groothuis, Hill, and Perri (2007) observe in the context of professional basketball. But such players also generally possess comparatively better physical skills than those who use their entire collegiate eligibility.¹² This may also hold among players who receive postseason awards. Because football players play on teams rather than individually, NFL employers may place a higher market value on rookie players who recently contributed to more successful college teams competing in more successful conferences.¹³

Seven variables capture own risk for the rookie subsample. The variables Off-Field Incidents and Games Suspended capture illegality risk. The variable Off-Field Incidents represents an actual count of specific off-field incidents in which a player was involved during his amateur career, as documented within standardized player scouting reports published at NFLDraftScout.com. Games Suspended represents the actual number of college games (not including spring games or other exhibition games having no competitive consequences) for which a player was suspended for disciplinary reasons. The variables Injury Games Lost and Surgeries, capturing a rookie player’s injury risk, represent specific counts of the number of college games during his last season that a player missed due to injury or illness and the number of surgical procedures a player underwent prior to his draft year, documented in player scouting reports. Two variables capture turnover risk. The dummy variable Junior College Transfer equals 1 if a player transferred from a junior college to his 4-year institution during his collegiate career and 0 otherwise. In this setting, junior college transfers resemble veteran players who have played for multiple NFL clubs prior to a given free agent market, such as due to previous trades or releases. (Such history becomes important for the veteran subsample, as discussed in the following section.) As Bollinger and Hotchkiss (2003) discuss in the context of major league baseball, such players may possess less reliable productivity than those with more stable employment histories.¹⁴ The variable College Captain equals 1 if a player ever served as a team captain (including captaincies of position groups) during his collegiate career and 0 otherwise. If captains are team leaders, NFL clubs might expect such players to exhibit a lesser likelihood of individual turnover or shirking. The variable College Program Infractions, representing the number of official sanctions imposed on a player’s football program from January 2000 through March 2009, serves as a control for the culture of rules’ violations within which the player interacted.¹⁵

The variable Pro Bowlers at Position, representing the actual number of players selected to the previous Pro Bowl at a draftee’s position present on his drafting team, captures cross productivity for the rookie subsample. A greater presence of existing Pro Bowlers indicates significant veteran productivity at a given position, potentially translating to lesser demand (a later draft position) for any rookie selected at that position by a given club. A greater presence of Pro Bowlers at a position might not discourage a club from drafting any players at that position, but it might encourage clubs to place a lower value on rookies at that position. Measures of cross-risk account for the number of players placed on the season-ending injured reserve (IR) list during the previous season, the number of players at the rookie’s position levied fines or suspensions (from either the league or club) during the previous season, and the net losses of veteran players at a rookie’s position during the off-season in question. Teams that have experienced losses of productivity traceable to serious injuries or player wrongdoing may exhibit greater demand for rookies.¹⁶ Although monetary fines do not translate to losses of physical productivity, they do suggest a greater potential productivity loss to the extent that offenses resulting in fines can escalate into offenses resulting in suspensions. Net Veteran Losses represents the number of veteran players subtracted from a team (due to trades, free agency, or retirements) minus the number of veteran players added to a team (through whatever mechanism) at a given position. A larger value suggests a greater number of vacancies at a position, potentially translating to a greater demand for rookie players at that position. Cymrot (1983) used a similar variable to measure “net body count” in his study of individual migration patterns exhibited by the earliest cohorts of veteran free agents in major league baseball.

The two dichotomous institutional control variables incorporated for this study account for market year 2006 and for the period 2007-2008, the first 2 years of the Goodell commissionership. Incorporation of the latter variable allows a glimpse of whether the seemingly more punitive era affected rookie draft positions, independent of other influences. However, as discussed further in the section on Empirical Results, the more meaningful use of this variable will involve its interaction with measures of worker risk to probe whether the market exerted a more demonstrable penalty (or any penalty) for risk factors in the Goodell era. In 2006, a delay in reaching a new CBA delayed the opening of the free agent market to March 11, about 10 days later than usual. This shortened the amount of time clubs had available to sign free agents before the start of training camp for the 2006 season, possibly hastening their actions in acquring veteran player talent. (A more extreme shortening of the market period occurred after the lifting of the NFL lockout prior to the 2011 season) Whether this market delay affected rookie labor demand becomes solely an empirical curiosity, as the CBA delay did not affect the date of the 2006 draft. Individual player control variables incorporated for this subsample capture a player’s height (in inches), weight (in pounds), a height–weight interaction, whether the player was White, and whether the player competed on offense.

Veteran Free Agent Subsample

Table 2 displays descriptive statistics for the variables relevant to the veteran free agent subsample, numbering 978. For veterans, the primary labor demand outcome variable is Days on Market. The market for veteran free agents opens each off-season at the end of the official “league year,” typically at the end of February. Days on Market represents the actual number of calendar days a free agent waited on the market before signing with a new club. A player who signed with a new club on the day the market opened is coded as having one day on the market before signing; players signed on subsequent days accordingly have higher values for this variable. Players who remained unsigned as of the end of the observation period in a given market year, corresponding to the customary opening of training camps in late July, have Days on Market equal to the number of days between the opening of the market and that end date. They consequently have right-censored durations.¹⁷ One can interpret this duration as an older player’s individual-level waiting time associated with a transitional job search process. Due to the right censoring of this duration, the most meaningful labor demand interpretation becomes the probability that a player signed a contract with a new team, conditional on him having lasted on the market up to that point: the hazard of signing. As discussed further in the following section, I estimate parametric hazard models to investigate variation in and the determinants of this hazard as well as the hazard of draft selection among rookies.

Table 2.

Descriptive Statistics for Veteran Free-Agent Subsample (N = 978).

	Mean	Standard Deviation	Minimum	Maximum
Outcome Variable
Days on Market	68.807	79.315	1	198
Unsigned	0.291	0.455	0	1
Measures of Own Productivity
Career Games Played	80.163	47.522	0	382
Career Games Started	40.682	41.072	0	208
Career Playoff Games	0.907	2.041	0	17
Career Pro Bowls	0.290	0.961	0	10
Drafted	0.746	0.435	0	1
Wins by Previous Team	7.795	3.028	1	16
Measures of Own Risk
Previous Suspensions	0.022	0.185	0	3
Previous Fines	0.064	0.279	0	3
Times on IR	0.525	0.725	0	4
Previous Teams	2.189	1.320	1	11
Measures of Cross Productivity
NFL Rookie Starts at Position	36.024	14.223	3.5	77
Measures of Cross Risk
Mean Experience of IR Players at Position	5.009	1.202	3.18	12
Mean Experience of Players Subtracted	6.131	0.892	4	10.6
Mean Experience of Fined Players	6.171	2.580	1	14
Mean Experience of Suspended Players	5.718	2.960	1	14
Institutional Controls
Market Year 2006	0.272	0.445	0	1
Goodell (Commissioner)	0.496	0.500	0	1
Average Gate Revenue ($ millions)	44.830	4.314	36.2	68
Individual Controls
Height (inches)	73.736	2.451	67	80
Weight (pounds)	241.98	44.755	165	375
Height × Weight	17,928.78	3,772.43	11,220	29,250
White	0.291	0.455	0	1
Offensive Player	0.462	0.499	0	1

Note. IR. injured reserve.

Scrutiny of veteran salaries reveals further evidence of the assumed inverse relationship between compensation and labor market waiting time. Of the 703 free agents in the sample who signed contracts, 541 (77%) had complete salary data within the USA Today database, and of course none of the 275 unsigned free agents had such data. Overall, veteran free agents received a mean first-year salary of $3.35 million. Those signed in either February or March, within the first 30 days of the opening of the free agent market, received mean first-year salaries of $3.84 million, while those signed in later months received $1.28 million on average.

Six variables capture veteran player’s productivity. The variables Career Games Played, Career Games Started, Career Playoff Games, and Career Pro Bowls represent a player’s respective experience in each dimension prior to a given market year.¹⁸ The dummy variable Drafted equals 1 if the veteran player entered the league as a draft selection and 0 if as an undrafted rookie free agent; if drafted players possess more talent than undrafted players, they may exhibit shorter waiting times than undrafted veterans. The productivity measures also include the number of wins posted by the player’s previous team in the regular season preceding a given market year. These measures, like counterparts in the rookie subsample, allow us to examine the influence of both individual- and team-level indicators of player productivity.

Four variables capture own risk for this subsample. Previous Suspensions and Previous Fines capture illegality risk, representing counts of the number of league-level or (less frequently) club-level suspensions and monetary fines levied on a player during his pro career prior to a given market year. Over the observation period, these sanctions stemmed from a variety of on- and off-field transgressions, ranging from excessively rough play to substance-use violations to arrests. Times on IR captures injury risk. A more extensive history of being placed on IR might make a veteran player more likely to lose productivity due to injury in future, thus reducing his current market value. Previous Teams represents the total number of NFL clubs for which a veteran had played prior to his market year, comparable to Junior College Transfer in the rookie subsample. Because a greater number of previous employers may signal a more transient career, or possibly unobserved traits that reflect badly on potential productivity (Simmons and Berri 2009), this serves as a measure of turnover risk for this subsample.

Five variables capture cross productivity and risk for this subsample related to the performance and actions of rookies and younger players in general within the preceding NFL season. These variables resemble but are not identical in structure to those used for the rookie subsample. Players in the veteran subsample who did not sign with a new club within the observation period do not have destination clubs that allow construction of variables capturing evidence of physical productivity and risk factors at specific positions on those clubs. As a substitute, the comparable measure of cross productivity used here represents the mean number of games started by rookies in the league as a whole during the previous season at a free agent’s position. A greater number of starts by rookies at certain positions suggests significant rookie productivity among NFL employers, possibly reducing their demand for new veteran players at those positions. Similar variables capture cross risk by measuring the mean NFL experience (in seasons played) of players placed on IR, players subtracted from NFL team rosters, and players fined and suspended during the previous season at a free agent’s position. The question becomes whether lower values of these mean experience variables (corresponding to enhanced risk factors among relatively younger players) translate to swifter signing of veteran free agents at those positions, as hypothesized. In any event, the performance of these variables in hazard models will provide empirical evidence on how specific cross-risk factors influence the use of older workers. Given the absence of destination clubs for unsigned veterans, the incorporation of these variables allows each veteran player in the sample to have a common measure of the market-wide (league-wide) prevalence of the various cross productivity and risk factors.

I incorporate the institutional and individual player control variables seen in the rookie subsample as well as the average gate revenue of clubs that lost at least one player at a free agent’s position in the previous off-season. This variable, also commonly definable for signed and unsigned players, controls for NFL club’s financial capacity for acquiring free agents. One might suspect that greater revenue aids affordability, allowing wealthier clubs to sign free agents relatively more quickly.¹⁹ Because the veteran free-agent market opens before the NFL draft (the 2011 off-season represents an exception due to the league lockout), Net Veteran Losses becomes irrelevant to the veteran subsample and so will not appear in hazard models.

Empirical Methodology

For both subsamples, I estimate parametric hazard models of Draft Position and Days on Market, respectively, as a function of the productivity, risk, and control variables detailed above. A given player j exhibits a survival time t_j , interpretable for rookies as the number of selections that occur from the opening of the NFL draft until his own selection and for veterans as the amount of time between the day the free agent market opens and either (1) the day the player signs with a new team or (2) the last day of observation, if the player has not signed.²⁰ We might characterize this survival time in log-linear regression form as lnt_j = X_j β + u_j , with covariates X_j , parameters β, and an error term u_j having probability density function f. In this study, I specify f using the parametrically flexible Weibull distribution, which has the survival function S(t) = df(t)/dt = exp(−λ _jt_j ^α) and hazard function λ _j (t) = exp(−α X_j β), where β and the ancillary parameter α are estimated through the method of maximum likelihood. The magnitude of α relative to 1 indicates the nature of duration dependence, that is, how the hazard of draft selection or signing varies as each market unfolds over time. The outcome α > 1 implies positive duration dependence, indicating that the hazard increases over time; α < 1 implies negative duration dependence, a decreasing hazard; and α = 1 implies constant duration dependence, a constant hazard statistically equivalent to the survival time exhibiting the exponential distribution. Tables of hazard results will include estimates of α; parameter estimates of β will indicate how marginal variation in the covariates affects the hazard. For additional details on parametric hazard model estimation, see Kalbfleisch and Prentice (1980) and Greene (2008).

Empirical Results

Determinants of the Hazard of Draft Selection

Table 3 displays results from an initial Weibull parametric hazard model focusing on the duration outcome Draft Position. Estimated marginal hazard ratios greater than 1 indicate explanatory factors that contribute to a shorter waiting time before selection, a greater hazard of selection, and hence stronger labor demand. Hazard ratios less than 1 signify the opposite.

Table 3.

Hazard Results for Rookie Subsample (Outcome: Draft Position).

	Hazard Ratio	Standard Error	p Value
Measures of Own Productivity
Division 1A	1.240	.139	.05
Underclassman	2.587	.256	.00
College Winning Percentage	1.005	.002	.00
College Awards	2.007	.162	.00
Conference Winning Percentage	1.001	.006	.89
Measures of Own Risk
Off-Field Incidents	0.866	.078	.11
Games Suspended	1.025	.052	.62
Injury Games Lost	1.037	.030	.21
Surgeries	1.036	.049	.46
Junior College Transfer	0.767	.095	.03
College Captain	1.180	.086	.02
College Program Infractions	1.074	.073	.30
Measures of Cross Productivity
Pro Bowlers at Position	0.894	.059	.09
Measures of Cross Risk
Injured Reserve at Position	1.097	.040	.01
Fines at Position	1.073	.103	.46
Suspensions at Position	0.723	.137	.09
Net Veteran Losses at Position	1.077	.038	.04
Institutional Controls
Market Year 2006	0.920	.084	.36
Goodell Commissioner	0.984	.078	.84
Individual Controls
Height (inches)	0.885	.063	.09
Weight (pounds)	0.952	.021	.03
Height × Weight	1.001	.000	.03
White	0.854	.069	.05
Offensive Player	0.903	.062	.13
ln(α)	0.550	.026	.00
α	1.733	.045
1/α	0.577	.015
Likelihood Ratio χ²	179.49		.00
Sample Size	1,017

All but one of the five measures of own productivity emerge as statistically significant and with marginal hazard ratios consistent with predictions. Based on the hazard ratio estimates, NFL clubs over the period of analysis selected underclassmen and players who had received a larger number of collegiate awards significantly earlier than other players. Results also show that clubs selected players from Division 1A collegiate programs significantly earlier than players from lower tier programs, echoing Berri and Simmons' (2011) recent finding pursuant to quarterbacks. The significant hazard ratio for College Winning Percentage indicates that players who recently contributed to a more successful college team received a benefit in the market, but the estimate of 1.005 indicates a relatively small marginal impact on the hazard of selection. Draft position appears statistically unrelated to the quality of the player’s collegiate conference.

A smaller proportion of the own-risk factors emerge as statistically significant in the context of the rookie subsample. Hazard results indicate a mildly significant labor market penalty, in the form of a later draft position, associated with players having been involved with a greater number of off-field incidents (p = .11). But the results reveal no significant penalty associated with a greater number of game suspensions while in college or injury (a greater number of recent college games lost to injury or more surgeries prior to market entry). The absence of significant effects in this context is somewhat surprising, but, as discussed further in the next subsection, the pattern makes more sense—and helps support a key theoretical prediction—when viewed in the context of comparable results for the veteran subsample. Meanwhile, results indicate that NFL clubs draft junior college transfers significantly later than nontransfers, consistent with the expectation that employers place less market value on players with relatively more itinerant college careers.²¹ College Captain takes on an estimated hazard ratio greater than 1, indicating that NFL clubs select team leaders, by this measure, significantly earlier than noncaptains. To the extent that team captains exemplify players least likely to exhibit turnover behavior in future, this result further supports the hypothesis that a smaller turnover risk enhances labor demand.

Results pursuant to measures of cross productivity and risk shed additional light on the determinants of the labor market value placed on rookies. As expected, clubs with a greater number of Pro Bowl players already on their roster at a rookie’s position select rookie players at that position significantly later in the draft (p = .09). By contrast, clubs that had more players placed on IR and that had a greater number of net veteran players lost at a rookie’s position selected rookies at those positions significantly earlier. A greater prevalence of veteran players fined at specific positions exerted no significant influence on rookie draft positions, but clubs do appear to have drafted rookies significantly later when faced with more league suspensions of veterans at those positions (p = .09), raising the possibility that clubs responded to greater levels of veteran illegality risk by targeting new veteran players, not rookies. Overall, however, employers in this environment appear to have altered their demand for younger workers demonstrably in response to perturbations in worker productivity, injury risk, and routine turnover among their existing workers. Later results will reveal whether the demand for older workers follows a comparable pattern in relation to rookie productivity and risk factors.

Elsewhere, the rookie hazard model indicates significant market penalties for greater height and weight, although the estimated hazard ratio of 1.001 for the interaction of these variables shows that players who exhibit above-average combinations of height and weight get selected marginally earlier, sensible given the premium on physical size and play in the NFL. White players receive significantly later draft positions than non-Whites, a pattern that tracks with Conlin and Emerson’s (2006) finding that non-White players more likely remain on their drafting clubs when observed as many as 3 years later. Neither of the institutional control variables significantly influences rookie draft positions; the role of the Goodell commissionership will have more meaning in extended analysis that incorporates interactions of this indicator variable with measures of productivity and risk.

Determinants of the Hazard of Veteran Free Agent Signing

Table 4 displays results from an initial Weibull hazard model focusing on the veteran duration outcome Days on Market. In the context of the veteran free agents, estimated marginal hazard ratios greater than 1 indicate explanatory factors that contribute to a shorter wait on the labor market, a greater hazard of signing, and hence stronger labor demand. Marginal hazard ratios less than 1 signify the opposite.

Table 4.

Hazard Results for Veteran Free Agent Subsample (Outcome: Days on Market).

	Hazard Ratio	Standard Error	p Value
Measures of Own Productivity
Career Games Played	0.989	.002	.00
Career Games Started	1.014	.002	.00
Career Playoff Games	1.247	.022	.00
Career Pro Bowls	0.929	.044	.12
Drafted	1.198	.113	.05
Wins by Previous Team	0.979	.012	.09
Measures of Own Risk
Previous Suspensions	0.537	.178	.06
Previous Fines	0.406	.084	.00
Times on Injured Reserve	0.751	.045	.00
Previous Teams	0.588	.027	.00
Measures of Cross Productivity
NFL Rookie Starts at Position	1.001	.003	.69
Measures of Cross Risk
Mean Experience of IR Players at Position	0.900	.037	.01
Mean Experience of Players Subtracted	1.002	.061	.97
Mean Experience of Fined Players	1.051	.019	.01
Mean Experience of Suspended Players	1.067	.019	.00
Institutional Controls
Market Year 2006	1.286	.168	.05
Goodell Commissioner	1.384	.183	.01
Average Gate Revenue	0.996	.012	.75
Individual Controls
Height (inches)	1.103	.105	.31
Weight (pounds)	1.048	.033	.13
Height × Weight	0.999	.000	.16
White	1.234	.122	.03
Offensive Player	0.741	.073	.00
ln(α)	-0.424	.031	.00
α	.654	.020
1/α	1.529	.047
Likelihood Ratio χ²	561.87		.00
Sample Size	978

Several of the measures of own productivity emerge as statistically significant, indicating stronger demand for veterans who had started more games in their careers, appeared in more playoff games, and entered the league as draft selections. By contrast, players who had merely played in more games in their careers show a significantly smaller hazard of signing. The market for veterans thus rewards not merely a greater quantity of NFL experience but greater quality of that experience as a starter, indicative of a greater marginal contribution to team success. Experience as a Pro Bowler and greater success of a player’s previous team reduce the hazard of signing more mildly (p = .12 and p = .09, respectively). NFL clubs typically retain prime-aged star players with long-term contracts rather than allow them to leave as free agents, and so older age likely counteracts the market advantage of Pro Bowl experience for most veteran free agents.

As expected, stronger results pertaining to worker’s own-risk factors emerge for the veteran subsample compared to those seen for rookies, as all four measures emerge as significant. With respect to illegality risk, players who entered the free agent market having received more suspensions and fines in their NFL careers exhibit significantly smaller hazards of signing: veteran troublemakers (by these measures) wait longer on the market, ceteris paribus. Regarding injury and turnover risk, players who had been placed on IR more often prior to their market year also show a significantly lesser hazard of signing, as do players who exhibit less stable employment histories, as indicated by having played for a larger number of previous teams. In general, these results further support the hypothesis that more pronounced worker risk factors reduce labor demand, other things equal.

As the analysis moves from the rookie to the veteran subsample, the pattern of empirical results pertaining to the effects of worker’s own productivity and risk factors demonstrates that greater own productivity significantly improves labor demand outcomes for both player types. But own-risk factors do exert a more comprehensive influence within the sample of veteran players, especially in relation to illegality risk and injury risk. This pattern of results conforms to a key prediction emanating from the conceptual model and is qualitatively consistent with the results from previous economic research on labor market outcomes associated with older workers—most importantly, lengthier waiting times in the transition from one employer to another in relation to fundamental, personal risk factors. Patterns predicted and documented for the broader economy appear to have parallels in at least one set of pro sports labor markets.

Turning to the cross productivity and risk effects, first recall from the rookie hazard model that NFL clubs appeared to increase their demand for rookies when they had a lesser existing (veteran) presence of Pro Bowl talent at specific positions and when they encountered more problems with severe injuries and turnover among their existing players. The earlier model showed evidence of lesser demand for rookies as a consequence of enhanced illegality risk (in the form of league suspensions) among veterans. Within the hazard model for veterans, neither rookie productivity (as indicated by the average prominence of rookie starts by position) nor the experience profile of player turnover appears to have influenced the hazard of signing veteran free agents. However, the hazard ratio for mean experience of IR players emerges as significant and less than 1, while those for mean experience of fined and suspended players are significant and greater than 1. The first of these significant results implies that an older average age of players at a given position placed on IR motivates NFL clubs to sign new veterans at those positions at a slower rate, other things equal: clubs evidently seek to supplement the most severely injured veterans with rookies, quite consistent with the hazard result for rookie draft position. Expressed another way, the result indicates that a younger average age of IR players motivates clubs to sign new veterans at those positions at a swifter rate, consistent with a prediction from the labor demand model in relation to the cross-risk effect. The other significant results indicate that an older average age of players at specific positions who had recently received fines or suspensions motivates clubs to sign veterans at those positions at a faster rate: clubs evidently seek to supplement the lost or potentially lost productivity associated with veteran wrongdoing not with rookie draft selections (recall the insignificance of fines at position and the mild significance of suspensions at position in the rookie model) but with new veterans.

As a practical matter, NFL players who receive fines or suspensions for various transgressions play regularly.²² Logically, a player has to participate in games to have the opportunity to engage in on-field activities that expose him to official sanctions, and NFL clubs undoubtedly recognize the high-risk/high-reward element of illegality risky players, which explains why some remain on NFL rosters. But NFL clubs evidently think about supplementing the potential lost productivity associated with those players (at least to the extent that finable offenses can presage suspendable offenses) with other players exhibiting proven productivity: veterans. Compared to rookies, veteran newcomers to teams also more likely bring credible leadership qualities to teams that have experienced problems with player wrongdoing. Players also must participate in games to sustain serious injuries. But NFL clubs appear to try to supplement that lost productivity and human capital with the promise of future productivity embodied by younger players. Overall, NFL employers exhibit striking heterogeneity in their patterns of labor demand in reaction to worker risk factors across different worker age categories.

The institutional control variable Market Year 2006 emerges with a marginal hazard ratio significantly greater than 1, indicating, as expected, that NFL clubs signed veteran players more aggressively in that more time-compressed market year than in the other market years. The variable Goodell Commissioner also emerges with a marginal hazard ratio significantly greater than 1, evidence that NFL clubs signed veteran free agents more aggressively in the initial years of the Goodell era than in the last years of the Tagliabue era. In contrast to the rookie subsample, neither player height, player weight, nor the height–weight interaction exerts a significant impact on labor demand among veterans. Simple measurables like height and weight may matter more for rookies because they have no industry-specific performance statistics on which clubs can base their evaluations of future productivity. Defensive players signed with new clubs more quickly than offensive players, an insignificant factor in the context of the rookie subsample. NFL clubs in this period appear to have placed a greater marginal value on veteran defensive players than on veteran offensive players within the context of the free agent market. While the rookie hazard model revealed that clubs drafted White players significantly later than non-Whites, the veteran hazard model reveals that clubs sign White veterans significantly earlier than non-Whites.

In studies of the role of race in sports labor market outcomes, Kahn and Sherer (1988) and Kahn (1992) documented the presence of racial segregation by position, which conceivably could affect the labor demand outcomes studied here. For both subsamples, a significantly greater proportion of White players play on offense than on defense, and the veteran hazard model indicates that clubs acquire new offensive players less aggressively than defensive players. Furthermore, among the non-White draft selections, 31.7% played an offensive skill position (quarterback, running back, wide receiver, or tight end), compared to 28.9% who were White, a statistically insignificant difference. By contrast, among the non-White veteran free agents, 25.6% played an offensive skill position compared to 34.0% who were White, a significant difference at p = .01. In addition, for each subsample a significantly greater proportion of offensive linemen were White, and a significantly greater proportion of defensive backs were non-White. (For both subsamples no predominant race emerges for defensive linemen.) Nevertheless, the results for White documented in Tables 3 and 4 (and later in this article) remain robust in exploratory models that explicitly control for player position (specifically, indicators for those who played offensive skill positions and defensive back); the position variables themselves emerge as statistically insignificant determinants of the hazard outcomes of interest in these models.²³

The hazard model for veteran free agents yields an estimate of the structural parameter α of .654, its value less than 1 indicative of negative duration dependence: the hazard of veteran free agents signing with new clubs decreases over the observed time period after the market opens. This parametric result makes sense, given that each free agent market contains a finite rather than a continuously replenished pool of players available to sign and that clubs have an incentive to compete aggressively to acquire the best players as soon as they can. Such factors do not apply in the context of the NFL draft, where the hazard model for rookies yielded an estimate of α of 1.733, indicative of positive duration dependence.

The Change of Commissioner

Did the transition to the new NFL commissioner, which arguably increased player risk factors exogenously, affect employers' actions in relation to player productivity and risk factors? To probe this, I estimate extended hazard models that incorporate each of the explanatory variables used heretofore as well as interactions of the Goodell Commissioner variable with measures of own and cross productivity and risk (see Tables 5 and 6).

Table 5.

Extended Hazard Results for Rookie Subsample (Outcome: Draft Position).

	Hazard Ratio	Standard Error	p Value
Measures of Own Productivity
Division 1A	1.165	.197	.37
Underclassman	2.337	.310	.00
College Awards	2.310	.268	.00
College Winning Percentage	1.007	.002	.01
Conference Winning Percentage	1.018	.013	.14
Measures of Own Risk
Off-Field Incidents	0.986	.128	.91
Games Suspended	0.978	.069	.75
Injury Games Lost	1.058	.051	.24
Surgeries	0.979	.062	.74
Junior College Transfer	0.782	.144	.18
College Captain	1.154	.120	.17
College Program Infractions	1.287	.124	.01
Measures of Cross Productivity
Pro Bowlers at Position	0.933	.095	.49
Measures of Cross Risk
Injured Reserve at Position	1.096	.052	.05
Fines at Position	1.068	.148	.64
Suspensions at Position	0.968	.330	.92
Net veteran Losses at Position	1.120	.063	.05
Institutional Controls
Market Year 2006	0.889	.086	.22
Goodell Commissioner	4.523	3.441	.05
Individual Controls
Height (inches)	0.898	.065	.14
Weight (pounds)	0.957	.022	.05
Height × Weight	1.001	.000	.05
White	0.849	.070	.05
Offensive Player	0.926	.064	.27
Interaction Variables
Division 1A × Goodell Commissioner	1.069	.243	.77
Underclassman × Goodell Commissioner	1.425	.280	.07
College Awards × Goodell Commissioner	0.864	.138	.36
Conference Winning Percentage × Goodell Commissioner	0.977	.014	.11
College Winning Percentage × Goodell Commissioner	0.995	.003	.13
Off-Field Incidents × Goodell Commissioner	0.742	.135	.11
Games Suspended × Goodell Commissioner	1.189	.139	.14
Injury Games Lost × Goodell Commissioner	0.976	.059	.69
Surgeries × Goodell Commissioner	1.111	.110	.29
Junior College Transfer × Goodell Commissioner	1.063	.266	.81
College Captain × Goodell Commissioner	1.061	.157	.69
College Program Infractions × Goodell Commissioner	0.708	.099	.01
Pro Bowlers at Position × Goodell Commissioner	0.940	.129	.65
Injured Reserve at Position × Goodell Commissioner	1.016	.074	.83
Fines at Position × Goodell Commissioner	1.045	.200	.82
Suspensions at Position × Goodell Commissioner	0.608	.253	.23
Net Veteran Losses at Position × Goodell Commissioner	.940	.069	.40
ln(α)	0.562	.026	.00
α	1.754	.045
1/α	.570	.015
Likelihood Ratio χ²	202.11		.00
Number of Observations	1,017

Table 6.

Extended Hazard Results for Veteran Free-Agent Subsample (Outcome: Days on Market).

	Hazard Ratio	Standard Error	p Value
Measures of Own Productivity
Career Games Played	0.988	.002	.00
Career Games Started	1.016	.002	.00
Career Playoff Games	1.265	.032	.00
Career Pro Bowls	0.914	.061	.18
Drafted	1.071	.146	.61
Wins by Previous Team	.995	.018	.78
Measures of Own Risk
Previous Suspensions	.348	.166	.03
Previous Fines	0.403	.130	.01
Times on Injured Reserve	0.958	.086	.63
Previous Teams	0.573	.036	.00
Measures of Cross Productivity
NFL Rookie Starts at Position	1.001	.005	.82
Measures of Cross Risk
Mean Experience of IR Players at Position	0.955	.057	.44
Mean Experience of Players Subtracted	1.126	.099	.18
Mean Experience of Fined Players	0.964	.045	.43
Mean Experience of Suspended Players	1.058	.040	.13
Institutional Controls
Market Year 2006	1.609	.248	.00
Goodell Commissioner	3.319	4.996	.43
Average Gate Revenue	0.985	.019	.43
Individual Controls
Height (inches)	1.059	.104	.56
Weight (pounds)	1.038	.034	.25
Height × Weight	1.000	.000	.30
White	1.250	.124	.03
Offensive Player	0.722	.073	.00
Interaction variables
Career Games Played × Goodell Commissioner	1.000	.003	.99
Career Games Started × Goodell Commissioner	0.997	.003	.36
Career Playoff Games × Goodell Commissioner	0.976	.033	.48
Career Pro Bowls × Goodell Commissioner	1.029	.098	.76
Drafted × Goodell Commissioner	1.160	.224	.44
Wins By Previous Team × Goodell Commissioner	0.976	.025	.34
Previous Suspensions × Goodell Commissioner	2.629	1.765	.15
Previous Fines × Goodell Commissioner	0.954	.404	.91
Times on Injured Reserve × Goodell Commissioner	0.642	.077	.00
Previous Teams × Goodell Commissioner	1.028	.092	.76
NFL Rookie Starts at Position × Goodell Commissioner	0.999	.007	.88
Mean Experience of IR Players at Position × Goodell Commissioner	0.883	.079	.16
Mean Experience of Players Subtracted × Goodell Commissioner	0.741	.100	.03
Mean Experience of Fined Players × Goodell Commissioner	1.134	.059	.02
Mean Experience of Suspended Players × Goodell Commissioner	1.026	.042	.54
Average Gate Revenue × Goodell Commissioner	1.027	.026	.30
ln(α)	−0.406	.031	.00
α	0.666	.020
1/α	1.501	.046
Likelihood Ratio χ²	592.61		.00
Number of Observations	978

The extended model estimated for the rookie subsample (Table 5) reveals telling alterations of NFL clubs' demand for rookies linked to the Goodell era. The model suggests greater demand for rookies in the Goodell era overall, evidenced by the significant hazard ratio greater than 1 for the uninteracted Goodell Commissioner. Finer patterns of results emerge in relation to underclassmen, rookies' college team and conference winning percentage, their proclivity for off-field incidents, and the extent of infractions at their collegiate programs. The uninteracted Underclassman retains its significance with a marginal hazard ratio greater than 1, and the interaction yields a hazard ratio greater than 1 (p = .07), indicating that NFL clubs place a premium on riskier but very talented college underclassmen in general and in the more recent market years studied here. College Winning Percentage, uninteracted, retains its marginal hazard ratio above 1, but the interaction yields a hazard ratio less than 1 (albeit at p = .13), suggesting that recent college team success has become less valued in this labor market compared to the last years of the Tagliabue era (Conference Winning Percentage, in both forms, exhibits the same essential pattern at lower significance levels). Off-Field Incidents, previously significant uninteracted at p = .11, yields a hazard ratio of less than 1 at that level of significance, indicating that clubs placed a lower market value on more trouble-prone rookie draft selections particularly in the Goodell era. Consistent with this interpretation, College Program Infractions, uninteracted, yields a significant hazard ratio greater than 1 but significantly less than 1 in its interaction. Clubs also appear to have placed lower values on players coming out of more trouble-prone college football programs in the Goodell era.

Statistically stronger patterns relating to labor market effects of worker risk factors emerge in the context of the veteran free agent subsample (Table 6), again consistent with the theoretical prediction that older workers would experience more dramatic alterations of their labor demand in relation to risk factors. First, the interaction of Times on IR with Goodell Commissioner shows a significant marginal hazard ratio of less than 1, while the uninteracted IR variable loses significance from the initial model. So, to the extent that NFL clubs signed veteran players less aggressively when those players entered the free agent market with more pronounced injury histories, this pattern primarily occurred within the first 2 years under Goodell. Second, the interaction of mean experience of subtracted players emerges with a significant marginal hazard ratio of less than 1, while the uninteracted variable remains insignificant. This suggests that NFL clubs tended to respond to an older average age among lost players by signing new veteran free agents less fervently in the first 2 years of the Goodell era. To some extent, this may reflect the presence of long-term contracts signed by free agents in 2005 or 2006; teams that signed such players had less of a desire to pursue additional free agents at those positions only 1 or 2 years later, especially in the presence of a salary cap that limits perpetual big spending on free agents. Finally, the interaction of the mean experience of fined players yields a significant marginal hazard ratio greater than 1, while the uninteracted variable loses its initial significance. As in the initial model, this pattern suggests that NFL clubs tended to respond to the phenomenon of generally older players receiving fines for wrongdoing by turning aggressively to the veteran free agent market. But again this activity appears concentrated within the Goodell commissionership.

Conclusion

This article has investigated how labor markets respond to various forms of worker risk factors, controlling for worker productivity factors, in an environment where employers demand both younger and older workers. Analytical tools from labor demand and job match theory illustrate how a hypothetical employer might use these worker types and allows formulation of testable hypotheses, suggesting how the demand for one labor type might vary in its own productivity and risk factors and in those of the alternate labor type. It also reveals how older workers plausibly may incur a more severe labor market penalty for personal risk factors.

Empirical analysis conducted using data from two distinct labor markets in the same industry, the NFL, reveals the presence of labor market rewards for greater promises of physical productivity and labor market penalties for more pronounced worker risk factors. Probing deeper, the analysis shows, as predicted theoretically, that older workers (veteran free agents) encounter more comprehensive labor market penalties for risk factors compared to younger workers (rookies) and that NFL clubs altered their labor demand in this respect at the beginning of Roger Goodell’s seemingly more punitive term as NFL commissioner. Such patterns conform to earlier economic research documenting generally greater tolerance for risk factors among younger workers, and this study further demonstrates this link in association with an institutional change that ostensibly increased the cost of employing older workers.

Commenting on similar labor market patterns at issue in the National Basketball Association, Groothuis, Hill, and Perri (2007) noted that team owners “now find free agents and rookies are no longer close substitutes… [A] very talented new entrant costs much less than a veteran player and is more productive” (p. 227). The present research reveals specific avenues—productivity and risk factors—by which owners willingly substitute rookies for veterans, other avenues in which they do not, and finally how the potentially higher cost of veterans, which can take the form of a greater probability of illegality, can influence the use of both worker types in the context of labor markets present within another popular pro sport.

Footnotes

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

Notes

References

Berri

D. J.

Simmons

(2011). Catching a draft: On the process of selecting quarterbacks in the national football league amateur draft. Journal of Productivity Analysis, 35, 37–49.

Blass

A. A.

(1992). Does the baseball labor market contradict the human capital model of investment? Review of Economics and Statistics, 74, 261–268.

Böheim

Lackner

(2011). Returns to education in professional football. IZA Discussion Paper No. 5665, 1–27.

Bollinger

C. R.

Hotchkiss

J. L.

(2003). The upside potential of hiring risky workers: Evidence from the baseball industry. Journal of Labor Economics, 21, 923–944.

Boulier

B. L.

Stekler

H. O.

Coburn

Rankins

(2010). Evaluating national football league draft choices: The passing game. International Journal of Forecasting, 26, 569–605.

Bruggink

T. H.

Rose

D. R.

Jr (1990). Financial restraint in the free agent labor market for major league baseball: Players look at strike three. Southern Economic Journal, 56, 1029–1043.

Carpenter

C. S.

(2006). The effects of employment protection for obese people. Industrial Relations, 45, 393–415.

Conlin

Emerson

P. M.

(2006). Discrimination in hiring versus retention and promotion: An empirical analysis of within-firm treatment of players in the NFL. Journal of Law, Economics, and Organization, 22, 115–136.

Cymrot

D. J.

(1983). Migration trends and earnings of free agents in major league baseball, 1976-1979. Economic Inquiry, 21, 545–556.

10.

Dumond

J. M.

Lynch

A. K.

Platania

(2008). An economic model of the college football recruiting process. Journal of Sports Economics, 9, 67–87.

11.

Fort

R. D.

2011. Sports economics. Upper Saddle River, NJ: Prentice Hall.

12.

Greene

W. H.

2008. Econometric analysis (6th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.

13.

Groothuis

P. A.

Hill

J. R.

Perri

T. J.

(2007). Early entry in the NBA draft: The influence of unraveling, human capital, and option value. Journal of Sports Economics, 8, 223–243.

14.

Hendricks

DeBrock

Koenker

(2003). Uncertainty, hiring, and subsequent performance: The NFL draft. Journal of Labor Economics, 21, 857–886.

15.

Heywood

J. S.

Wei

(1999). The determinants of hiring older workers: Evidence from Hong Kong. Industrial and Labor Relations Review, 52, 444–459.

16.

Hotchkiss

J. L.

Melinda Pitts

(2007). The role of labor market intermittency in explaining gender wage differentials. American Economic Review, 97, 417–421.

17.

Hotchkiss

J. L.

Melinda Pitts

(2010). The demand side of the penalty for intermittent labour market behaviour. Applied Economics Letters, 17, 531–535.

18.

Hutchens

(1986). Delayed payment contracts and a firm’s propensity to hire older workers. Journal of Labor Economics, 4, 439–457.

19.

Hutchens

R. M.

(1988). Do job opportunities decline with age? Industrial and Labor Relations Review, 42, 89–99.

20.

Kahn

L. M.

(1992). The effects of race on professional football players’ compensation. Industrial and Labor Relations Review, 45, 295–310.

21.

Kahn

L. M.

Sherer

P. D.

(1988). Racial differences in professional basketball players’ compensation. Journal of Labor Economics, 6, 40–61.

22.

Kalbfleisch

J. D.

Prentice

R. L.

(1980). The statistical analysis of failure time data. New York, NY: Wiley.

23.

Lazear

E. P.

(1998). Hiring risky workers. In Ohashi

Tachibanaki

(Eds.), Internal labor markets, incentives and employment (pp. 143–158). New York, NY: St. Martin’s.

24.

Rosen

(1998). Unraveling in matching markets. American Economic Review, 88, 371–387.

25.

Maske

Carpenter

(2006, December 16). Player arrests put the NFL in a defensive mode; high number alarms league as it works to protect its image. Washington Post, p. A01.

26.

Rhoden

W. C.

(2007, June 2). Principal goodell is setting a new tone. The New York Times, Section D, Column 1, p. 6.

27.

Schøne

(2009). New technologies, New Work practices and the age structure of the workers. Journal of Population Economics, 22, 803–826.

28.

Scott

F. A.

Berger

M. C.

Garen

J. E.

(1995). Do health insurance and pension costs reduce the job opportunities of older workers? Industrial and Labor Relations Rreview, 48, 775–791.

29.

Simmons

Berri

D. J.

(2009). Gains from specialization and free agency: The story from the Gridiron. Review of Industrial Organization, 34, 81–98.