Monitoring cartel behavior and stability: evidence from NCAA football.

Humphreys, Brad R. ; Ruseski, Jane E.

1. Introduction and Motivation

Many economists view the intercollegiate athletic programs that make up the National Collegiate Athletic Association (NCAA) as a cartel. If the cartel model of industry behavior applies to NCAA members, then this setting represents a unique opportunity to test economic theories of cartel behavior because the NCAA has operated for over 100 years, and a considerable amount of data about member organizations exist for much of this period. Very few other examples of cartel behavior can be found in such a visible setting. (1)

In this paper, we develop a model of the behavior of members of the NCAA football cartel under incomplete information and reaction lags. This paper extends the research of Fleisher et al. (1988) and Fleisher, Goff, and Tollison (1992) on the enforcement of the NCAA football cartel to explicitly include the dynamic aspect of monitoring behavior among cartel members both in the model and in the empirical work. The model permits analysis of the enforcement mechanism when signals about rivals' behavior contain a random component and are observed with a lag. This dynamic stochastic approach has not been applied to the NCAA football cartel in previous research. Empirical estimation of this model reveals that past on-field performance is significantly linked to enforcement of the cartel agreement.

The incentive for individual members to cheat on a cartel agreement represents the basic problem faced by any cartel. In the case of the NCAA, reducing competition for inputs, in this case student-athletes, by controlling input prices, constitutes a key component of the cartel agreement. According to NCAA regulations, each prospective student-athlete can be offered an identical compensation package from each institution, the "full-ride" grant-in-aid package consisting of tuition and fees, room and board, books, and a small stipend, often called "laundry money." In addition, the number of football scholarships that institutions can provide is currently limited to 85; from 1977 to 1992 the limit was 95 scholarships. Requiring each institution to offer recruits the same compensation package and limiting the number of scholarships clearly restricts competition in the input market. Absent this restriction, institutions could offer highly regarded recruits other inducements to attend an institution; in a competitive market, each student-athlete would be offered up to the expected value of his value of marginal product by institutions.

Cartel implications in the output market in college football have also been empirically investigated. Most of this research has focused on the distribution of wins in college football, in the context of competitive balance. Eckard (1998) found that NCAA enforcement of the cartel agreement improved competitive balance in five out of seven Division I football conferences. Depken and Wilson (2004) found that institutional changes in the NCAA related to enforcement of the cartel agreement offset a secular decrease in competitive balance in Division I football. Depken and Wilson (2006), in a closely related paper, investigated the effects of enforcement of the NCAA cartel agreement on competitive balance in college football. Depken and Wilson (2006) find that the greater the level of enforcement in a conference, the better the competitive balance, but the more severe the punishment, the worse the competitive balance. This research suggests that cartel enforcement has an effect on output and underscores the importance of understanding the monitoring process in the NCAA football cartel.

As in any cartel, the payoff to an individual school for cheating on the agreement can be considerable. By attracting star-quality athletes, institutions can improve their performance on the playing field and draw more fans, make more appearances on television, increase opportunities for merchandise licensing and corporate sponsorship, and make lucrative postseason appearances, all of which increase revenues directly and indirectly by increasing the prestige of the institution. Brown (1993) estimates the marginal revenue product of a premium college football player to be over $500,000 annually. NCAA regulations restrict the effective player wage to an amount considerably below this marginal revenue product estimate.

In the NCAA, the incentive to cheat on the cartel agreement also extends to coaches. Relatively successful coaches earn more than unsuccessful coaches in all NCAA-sponsored sports, even in non-revenue-generating sports such as women's basketball (Humphreys 2000); this is in part because of the ability of coaches to extract rents from teams. Higher winning percentages also signal higher quality coaching ability and raise coaches' opportunity wage in the labor market.

Monitoring all institutions' actions in the input market would be prohibitively expensive. Thousands of high school seniors are recruited by NCAA member institutions each year. Each NCAA institution has thousands of alumni, many of whom are interested in promoting the athletic success of the institution and are organized into well-financed athletic booster clubs. To avoid these high monitoring costs, cartels typically turn to indirect and probabilistic methods to detect cheating on the cartel agreement (Stigler 1964). Fleisher et al. (1988) and Fleisher, Goff, and Tollison (1992) posit that NCAA member institutions and the NCAA Committee on Infractions, the body charged with enforcing the NCAA recruiting regulations, monitor outputs (on-field performance) rather than inputs to determine if an institution has cheated on the cartel agreement. Further, because the staff of the NCAA Committee on Infractions is relatively small (in 1988 it consisted of 28 employees), much of the monitoring must be done by individual institutions.

Monitoring of the cartel agreement creates a rich environment for strategic interaction among the members of the NCAA cartel and provides an interesting setting for the analysis of cartel behavior. Consider two possible scenarios: A perennial .500 team begins to consistently attract high-quality recruits and enjoys several years of winning records, conference championships, etc. This team's rivals infer that the school has been violating the cartel agreement by offering cash payments to recruits in exchange for enrolling. The rivals request an investigation by the NCAA Committee on Infractions into the school's recruiting practices. As a second example, consider two institutions that are both violating the cartel agreement by bidding for the services of an athlete. The loser knows it was outbid by the other school and can turn in its rival to the NCAA.

The NCAA Committee on Infractions can impose severe penalties on institutions found to be cheating on the cartel agreement. These penalties include bans on television and postseason appearances, reductions in the number of scholarships that could be offered, and even the "death penalty," a complete shutdown of an athletic program. The "death penalty" is not imposed frequently but it was imposed on Southern Methodist University in the mid-1980s. All of these penalties carry potentially large economic consequences, given the average size of the payment for an appearance on television or in a bowl game. (2)

Evidence exists suggesting that sanctions imposed for violations of recruiting rules are used to enforce the NCAA cartel agreement. Fleisher et al. (1988) and Fleisher, Goff, and Tollison (1992) studied 85 big-time football programs over the period 1953-1983 and found that the probability of a school receiving sanctions to be positively correlated with the variability of an institution's on-field performance in football. However, these studies did not examine the dynamic interaction among NCAA member institutions.

2. Model

We adapt the model developed by Spence (1978) to examine the effects of imperfect information on tacit coordination in the NCAA football cartel. The principal proposition of this model is that randomness and imperfect monitoring interact to make collusion difficult. We believe this setting offers an appropriate framework within which to develop our model because it focuses on the detection of cheating on the cartel agreement. We analyze monitoring of the enforcement mechanism in a cartel, not the collusive and competitive strategies played by member schools. Models in which noisy signals serve as triggers for cartel members to play both monopolistic and Cournot strategies at certain points in time--for example, Green and Porter (1984)--focus on the equilibrium strategies. The model developed by Spence (1978) focuses on monitoring the cartel agreement, detection of cheating, and sustainability.

The NCAA cartel members play a game in which each school must choose the level of commitment to athletic and nonathletic activity in each period. School i's commitment to athletics is denoted by [[theta].sub.i] and commitment to nonathletic activities is denoted by [x.sub.i]. Although [[theta].sub.i] can be interpreted in several ways, we find it natural to think of commitment to athletics as representing the quality of athletic programs or the prestige generated by high-quality athletic programs. Schools can increase [[theta].sub.i] with investment in time, money, and cheating. Returns from successful football programs could be revenue from ticket sales, television contracts, postseason bowl game appearances, licensed merchandize sales, increased donations from alumni, and for public institutions, increased state appropriations. (3)

Cartels are difficult to sustain because there are incentives to cheat on the cartel agreement. If members could directly observe their competitors' behavior, then detecting cheating and enforcing the cartel agreement would be relatively easy. However, schools have imperfect information to the extent that they cannot directly or immediately monitor each other's strategies. In addition, schools cannot perfectly control all factors that affect the utility they derive from their respective commitments to athletic and nonathletic activity. When the imperfect monitoring capability is coupled with exogenous randomness, the set of sustainable collusive outcomes is reduced.

To formalize the notion of imperfect information, schools choose their levels of commitment to athletic activity based on signals, denoted [s.sub.i], they receive from the environment. The signals depend upon the cartel members' levels of athletic commitment and the random variable, which is denoted [alpha]. An important aspect of the signals is that the same signal can suggest good luck, good management, or cheating on the cartel agreement. The inability to differentiate the meaning of signals further weakens cartel stability and allows for the possibility of a school being falsely accused of cheating.

Signals are determined by [S.sub.i] = [M.sub.i]([[theta].sub.i],[[theta].sub.j], [alpha]). The specification of [M.sub.i] determines the informational structure of the market. An example of a signal for the NCAA football cartel is on-field performance, which can be measured by winning percentage. Schools can directly observe its competitors' winning percentages over time and make inferences about adherence to the cartel agreement. A perennial loser may suddenly have a higher winning percentage either because it cheated on the cartel agreement by inappropriately compensating players or because the team overachieved or was on the right side of the scoreboard in some closely contested games. Rival school responses to the observed winning percentage will depend on how the signal is interpreted. It is possible that a signal may be misinterpreted as cheating on the cartel agreement, resulting in an unwarranted investigation.

The set of possible equilibrium outcomes are defined by reaction function equilibria. In general, a reaction function specifies an action for a firm given its rivals' actions. In context of the NCAA football cartel, the reaction function for school i specifies the level of commitment to athletic activities given other member schools' levels of commitment to athletic activities. In a game of imperfect information, school i cannot observe its competitors' behavior directly but must instead rely on signals it receives such as winning percentage or success in recruiting athletes. The reaction functions in this situation depend on the signals rather than competitors' actions. The reaction function for school i is denoted by [R.sub.i]([S.sub.i]).

Suppose that a set of reaction functions for the NCAA cartel given by [R.sub.j]([S.sub.j]), j = 1, ..., n, and a vector of actions, [[theta].sup.*.sub.j], constitute the status quo strategy adopted by the cartel such that [R.sub.i]([S.bu.i]) = [[theta].sup.*.sub.i]. The status quo strategy is to compensate each student-athlete with an identical package and to adhere to particular rules regarding recruiting visits and signing periods. Cartel members are better off by following the status quo strategy than a noncooperative strategy because the cost to the football program is reduced and revenues are increased, holding all else equal. The extent to which the status quo strategy is sustainable depends upon the expected payoff to following the cartel agreement, the expected payoff to cheating, the penalties associated with cheating, and the probability of detecting cheating.

The expected payoff to following the cartel agreement is given by [[??].sub.i] ([[theta].sup.*]). The members of the cartel must have an incentive to maintain the outcome [[theta].sup.*]. The set of reaction function equilibria includes a maximum penalty that each school can impose on the others should a deviation from [[theta].sup.*] occur. If an incentive to maintain [[theta].sup.*] cannot be created with the maximum penalty, then it cannot be created with any set of reaction functions. The maximum penalty is the minimum payoff school j can impose on school i and is defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where [[THETA].sub.i] and [[THETA].sub.j] are the feasible sets of actions for schools i and j, respectively.

In the NCAA cartel, the maximum penalty is the "death penalty," which is a complete shutdown of an institution's football program for a period of years. As indicated earlier this penalty was imposed on Southern Methodist University in the mid-1980s. Note that the maximum penalty is more severe than the penalty required to sustain the cartel agreement. The NCAA football cartel has been sustained for a number of years without frequent imposition of the maximum penalty; thus, we interpret the imposition of less severe penalties such as probation or public reprimand as sufficient penalties to maintain the cartel agreement.

The expected payoff to school i to deviating from the status quo strategy conditional on school j being unable to detect the deviation from status quo is [D.sub.i]([[theta].sup.*],[[theta].sup.**]). In other words, this is the expected payoff to school i from playing strategy [[theta].sup.*], conditional on the signal to school j being the same as it would have been if school i played strategy [[theta].sup.**]. The conditional payoff to deviating, from the status quo strategy, [[theta].sup.*], to [theta] can now be defined as [Q.sub.j] ([[theta].sub.i],[[theta].sup.*.sub.j], [[D.sub.j]([[theta].sub.i], [[theta].sup.*.sub.j], [[theta].sup.*])] + (1 - [Q.sub.j]([[theta].sub.i], [[theta].sup.*.sub.j], [[theta].sup.*])) [m.sub.i]. The first term is the expected payoff to undetected cheating on the cartel agreement, and the second term is the expected payoff to getting caught. School i has no incentive to cheat if and only if for all [[theta].sub.i], the conditional payoff to deviating from the status quo strategy is less than or equal to the expected payoff of playing the status quo strategy; that is,

[Q.sub.j]([[theta].sub.i], [[theta].sup.*.sub.j], [[theta].sup.*]) [less than or equal to] [[[??].sub.i] ([[theta].sup.*]) - [m.sub.i] / [D.sub.i]([[theta].sub.i], [[theta].sup.*.sub.j], [[theta].sup.*]) - [m.sub.i]]. (1)

If Equation 1 holds for all schools, then the status quo strategy [[theta].sup.*] can be a reaction function equilibrium. For the NCAA cartel, the status quo strategy includes compliance with agreed upon rules governing compensation for athletes and recruiting practices. The longevity of the NCAA football cartel suggests that members of the cartel are playing the status quo strategy [[theta].sup.*] rather than some noncooperative strategy.

Next consider the effect of reaction lags on the incentives not to cheat. Reaction lags can occur if there is time between when a school adopts a course of action and rival schools either observe or respond to it. This case clearly applies to the NCAA football cartel where monitoring takes place one or more years after the occurrence of a potential deviation from the status quo strategy, since many of the players contributing to a current winning season were recruited several years before.

Divide time into periods where the number of periods between the occurrence of cheating by school i and the response to cheating by rival schools is k. The probability of detection is [phi]. The expected payoff of deviating from the status quo strategy [[theta].sup.*] to [[theta].sub.i] given a maximum penalty [m.sub.i] is [P.sub.i]([[theta].sub.i], [[theta].sup.*.sub.j])(1-[[phi].sup.k])+[m.sub.i]([[phi].sup.k]). This expected payoff is a weighted average; the first term weights the payoff to deviation by the probability of not being detected, and the second term weights the penalty by the probability of detection. As k increases, and more time passes since the deviation, the weight on the penalty declines and the weight on the payoff to deviation increases because the probability of not being detected increases. The amount of time that passes between an incident of cheating and detection is unknown and can vary across institutions, so it is not possible to specify the lag length, k, a priori.

Recall that the expected payoff of playing the status quo strategy is [[bar.P].sub.i] ([[theta].sup.*]). Under this scenario, school i finds it preferable not to deviate from the status quo strategy, [[theta].sup.*.sub.i], if for all [[theta].sub.i]

1 - [[phi].sup.k] [less than or equal to] [[P.sub.i]([[theta].sup.*]) - [m.sub.i]/[P.sub.i]([[theta].sub.i]([[theta].sub.i], [[theta].sub.i], [[theta].sup.*.sub.j]) - [m.sub.i]]. (2)

This equation shows the determinants of the probability ([phi]) of an institution being detected deviating from the status quo strategy. The model shows that this probability depends on the ratio of the expected benefit to standing pat ([[bar.P].sub.i]([[theta].sup.*]))to the expected benefit from switching away from the status quo strategy ([P.sub.i] [[theta].sub.i], [[theta].sup.*.sub.j]. In addition, this relationship incorporates reaction lags because the probability of detection declines with k, the number of periods since deviation. Note that this equation also implicitly defines the probability of not being detected [Q.sub.j] = 1- [[phi].sup.k].

3. Empirical Analysis

Consider an empirical model based on the equilibrium conditions from the model developed in the previous section. Equation 2 forms the basis for our empirical model. This equation shows the probability of a deviation from the status quo strategy going undetected. It can be rearranged to

[[phi].sup.k] [greater than or equal to] 1 - [[bar].sub.i]([[theta].sup.*]) - [m.sub.i]/[P.sub.i]([[theta].sub.i]([[theta].sub.i], [[theta].sup.*.sub.j]) - [m.sub.i]], (3)

where [[phi].sup.k] is the probability of a deviation from the status quo strategy being detected. As was the case above, the right-hand side of Equation 3 depends on the ratio of the expected payoff to following the status quo strategy to the expected payoff to deviating from the status quo strategy.

From Equation 3, factors that raise the expected payoff to adhering to the NCAA cartel agreement relative to the expected payoff to deviating from the agreement reduce the probability of institutions being detected. Factors that raise the expected payoff to deviating from the cartel agreement relative to the expected payoff of standing pat will increase the probability of institutions being detected. The payoff for schools to adhering to the NCAA football cartel agreement stem from the monoposony power they gain in input markets.

Also note that from Equation 3, as k, the length of the reaction lags, increases [[phi].sup.k], the probability an institution is detected cheating on the cartel agreement falls. This result highlights the importance of dynamics in the model. Averaging explanatory variables over long periods of time, a common practice in this literature, may obscure the relationship between recruiting violations and the observable factors schools use to monitor compliance with the NCAA cartel agreement. Define

[ENF.sub.it] = [[beta].sub.1,i] + [[beta].sub.2] [WPCT.sub.i,t-k] + [[beta].sub.3] [CEXP.sub.it] + [[beta].sub.4] [TEGE.sub.it] + [[beta].sub.5] [STA.sub.it] + [gamma] [Z.sub.it] + [[eta].sub.it] (4)

as an estimable version of Equation 3. The variables in Equation 4 are defined in Table 1. The [beta]'s and [gamma]'s are unknown parameters to be estimated, and [[beta].sub.1,i] is an institution-specific intercept capturing factors common to institution i that affect the probability of detection but do not vary over time. These factors include relative age of the institutions, geographical location of the institution, institution-specific monitoring costs, and other factors. Here [[eta].sub.it] is an institution-specific random error term that reflects the randomness inherent in the monitoring process due to the inability of institutions to directly monitor the behavior of other institutions.

The dependent variable, ENF, is a dummy variable that takes the value 1 in years when an institution's football program was on probation and banned from appearing on television and/ or appearing in a bowl game for violating NCAA regulations governing recruiting of football players and zero in other years. Football programs were on probation in about 3% of the institution-years in our sample. Nineteen different football programs, out of 104 programs in the sample, were on probation at some point during the sample period.

WPCT, the winning percentage of institution i's football team, is predicted to have a positive sign. From Equation 3, the winning percentage of an institution's football team has no effect on the benefit to complying with the cartel agreement because the benefit flows from rents generated by paying players less than their value of marginal product. Higher winning percentages increase the benefit to not complying with the cartel agreement by increasing the prestige of the athletic program and the revenues generated by higher quality football programs. This increases the denominator of the fraction on the right-hand side of Equation 3 and the probability of detection.

CEXP is the years of head coaching experience of the head football coach at institution i in season t. We use this as a proxy for the discount rate of the decision maker, which affects [[phi].sup.k] directly. The sign on the parameter on this variable should be negative. The longer a head coach remains at an institution, the more closely the coach becomes associated with the institution and the more the coach cares about the future of the institution. This lowers the discount rate of the head coach and decreases the probability of detection breaking the cartel agreement. The less time a head coach has been at an institution, the less certain he or she is that he or she will remain at the institution for a long period of time, and the higher the coach's discount rate, other things equal.

TEGE is total educational and general expenditure per full time equivalent (FTE) student at institution i in year t. Total educational and general expenditure per student is a commonly used measure of the quality of education at an institution. This variable excludes expenditure on athletics, which are classified as part of expenditures on auxiliary enterprises in the Integrated Post-secondary Educational Data System (IPEDS), as well as its predecessor, the Higher Education General Information Survey (HEGIS), which are the source of this variable.

TEGE can be interpreted as a measure of an institution's commitment to nonathletic activity. Commitment to nonathletic activity also affects the payoff to cheating on the cartel agreement. The greater the institution's commitment to nonathletic activity, the smaller the payoff to cheating and the lower the probability of being detected cheating.

STA is the capacity of the football stadium at institution i in year t in thousands. As Fleisher et al. (1988) point out, one common problem in cartels is that individual members often face different demand-cost configurations. In the NCAA cartel, institutions that have higher and more inelastic demand for their football program have larger benefits to cheating and will have a higher probability of being detected breaking the cartel agreement. Stadium size is a reasonably good proxy for demand when the size of the stadium adjusts to meet changes in demand conditions. Many of the institutions in the sample have increased stadium capacity at one or more points in the sample.

Z is a vector of observable institution-specific factors that affect the probability of detection. This vector includes conference dummy variables, a dummy variable indicating institutions that have been placed on probation for recruiting violations in men's basketball, dummy variables for football teams ranked in the previous season's final top 20 or 25 poll, and a dummy variable indicating schools that changed their head football coach. A number of the explanatory variables in Equation 4 were mentioned by Fort and Quirk (2001) when speculating about factors that might be related to cheating on recruiting regulations in NCAA football.

Equation 4 is estimated using a panel data probit technique on a panel of data drawn from NCAA member institutions that play football in Division IA, the top classification of football playing schools. The panel probit estimator used is a "random effects" estimator that models the intercept term in Equation 4 as a random variable

[[beta].sub.1,i] = [[bar.[beta].sub.1] + [[mu].sub.i], (5)

where E[[mu].sub.i]] = 0 and var([[mu].sub.i]) = [[sigma].sup.2.sub.[mu]]. The intercept term for each institution should be modeled as a random variable because it captures the effect of the institution-specific signal function on cartel behavior. This function captures the notion that incomplete information and high monitoring costs make it difficult for cartel members to detect cheating on the cartel agreement as well as the fact that schools cannot perfectly control all factors that affect the utility they derive from their respective commitments to athletic and nonathletic activity. An important aspect of signals is that the same signal can suggest good luck or cheating on the cartel agreement.

4. Data

Our sample consists of all 104 institutions that played Division IA football in each year from 1978 to 1990. This sample was selected because of the relative stability of conference membership over the period. Most of the major college football conferences (Atlantic Coast Conference, Southeastern Conference, Southwest Conference, Big 8 Conference, Big 10 Conference, and Pacific 10 Conference) had relatively stable membership over this period. The Atlantic Coast Conference added one member (Georgia Tech), one school moved from the Southwest Conference to the Southeastern Conference (the University of Arkansas), and the membership of the other conferences was static during this period. The Big East football conference began play in the last year of the sample. The early 1990s brought widespread changes to football conferences that affected every major conference except the Pacific 10 Conference. The Southwest Conference disappeared entirely and its members were absorbed by the Big 8 and Big West Conferences. The Southeastern Conference added schools and began divisional play, as did the Big 12 (formerly the Big 8) Conference.

Because conference membership may have a strong effect on the signal function of institutions--conference members play each other annually and are located in the same regions of the country--we restrict our sample to a period of conference stability in order to control for any impact of changes in conference membership on the behavior of cartel members. For this reason, we ended our sample in 1990.

A second reason for restricting the sample to exclude data beyond the early 1990s is provided by Zimbalist (1999). In 1994 the NCAA eliminated mandatory penalties for recruiting violations. Since this time, institutions have been allowed to "investigate themselves" when accused of committing a recruiting violation. The effects of this change in operating procedure on the model presented here are unclear. On the surface, it would seem to lead to a reduction in the maximum penalty imposed on members, which affects both the numerator and denominator of Equation 3 and thus has an ambiguous impact on the probability of being detected. However, this change could signal some fundamental change in the operation of the cartel, which could reduce the set of possible equilibrium outcomes. In any case, the NCAA appears to have been operating by a different set of rules, in terms of the monitoring and enforcement of recruiting violations, since the early 1990s.

Data on winning percentage, stadium capacity, and coaching experience come from various issues of NCAA Football, an annual publication of the National Collegiate Athletic Association (1977-1991). Data on recruiting violations were provided to the authors by the NCAA, based on the Committee on Infractions Summary Cases.

5. Results and Discussion

Empirical estimates of Equation 4 using a random effects panel data probit estimator are shown in Table 2. Details on the estimator can be found in Butler and Moffitt (1982) or Greene (2000). This table shows both the parameter estimates and the P-values on a two-tailed test of the significance of these parameter estimates. The hypothesis tests that the reported P-values represented have null hypotheses of the form [H.sub.o]: [[beta].sub.i] = 0, for i = 2, 3, 4. The parameter estimates for the vector of institution-specific control variables, Z, are not reported.

Model 1, shown in the first two columns of Table 2, includes the winning percentage variable lagged one year. The results from this empirical specification support the predictions of the model. The winning percentage variable is positive and significant, suggesting that higher winning percentages in the previous year are associated with a higher probability of being detected cheating in the current year, other things held constant. The sign and significance of this variable support the idea that institutions use the observed winning percentage of football teams to monitor compliance with the cartel agreement.

The other parameters have the expected signs and are statistically significant at conventional levels. The parameter on the years of experience of the head football coach is negative and significant, suggesting that coaches with higher discount rates are less likely to be detected cheating. This is consistent with the predictions of the model. Real educational and general expenditure per FTE is negative and significant (at slightly over the 5% level), suggesting that institutions with greater commitment to nonathletic activities are less likely to be detected cheating. The stadium capacity variable is positive but not statistically significant. Here 9 is the proportion of total variance contributed by the panel-level (in this case institution-level) variance component. For Model 1, about 27% of the total variance is contributed by variation across schools in the sample. The pseudo-[R.sup.2], calculated from the log-likelihood of Model 1 and a model with only a constant term, suggests that about 17% of the observed variation of the dependent variable is explained by the regressors in Model 1.

Reaction lags are an important feature of the model. The longer the time between the adoption of a particular course of action, like cheating on the cartel agreement, and its observation by rival institutions, the smaller the probability of an institution being detected cheating. We perform a simple test of the effect of reaction lags on the probability of detection by adding additional lags of the winning percentage variable to Equation 4. A second lag of WPCT was statistically significant, but a third lag of this variable was not. Adding these additional lags of WPCT had little effect on the sign and significance of the other variables in the model. (4) The differences in the significance of WPCT across these three specifications suggests that although a team's winning percentage in the previous two seasons help to explain which schools were on probation in a given year, that team's winning percentage three seasons before being put on probation does not.

Fleisher et al. (1988) estimated a model similar to Equation 4. They found that the coefficient of variation of winning percentage, and not the winning percentage, had significant explanatory power. Model 2, shown in the last two columns in Table 2, replaces the lagged winning percentage with [CV.sub.i,t-3], the coefficient of variation in program i's winning percentage over the past three seasons. The coefficient of variation is clearly not statistically significant in this empirical specification, although the other explanatory variables have similar signs and significance. Furthermore, when both [WP.sub.i,t-1] and [CV.sub.i,t-3] are included in the model, the lagged winning percentage variable is positive and statistically significant (P-value 0.021), and the coefficient of variation is not statistically significant. (5)

A plausible explanation for the differences in the results is the lack of dynamics in the Fleisher et al. (1988) model. In their model, a similar set of variables for 85 institutions that played Division 1A football over the period 1953-1983 were used and the variables were averaged over the entire sample period. Averaging over the entire sample period removes any randomness from the signal function because it implicitly treats the entire time-path of each football team's win-loss record as a part of the information set for each institution. Removing randomness from the signal function effectively removes much of the imperfect information from the monitoring function of the cartel.

6. Assessing the Results

We use within-sample forecasts based on the results reported for Model 1 in Table 2 to investigate the performance of the model. In part, the lack of good measures of goodness of fit in limited dependent variable models motivates this assessment. However, we also recognize that our dependent variable reflects only cases where cartel members have violated recruiting rules, been caught, and been punished; whereas, our empirical model reflects a reduced form outcome from a set of underlying functions. In other words, we observe only rule breakers that are caught and punished but do not observe the underlying rule-breaking behavior. An unknown number of cartel members could have violated recruiting rules and not been detected during the sample period. We also analyze only punishment and do not directly observe other enforcement activity by the NCAA. By examining the predicted probabilities, we hope to shed some light on this unobserved behavior.

This approach uses the parameter estimates shown in Table 2 to generate a predicted probability that a given institution's football program was on probation for each year in the sample. These predicted probabilities are based on the assumption that the institution specific random effect was zero in each year. The mean predicted value of a team being put on probation in the sample is 0.018 (standard deviation 0.032). The unconditional mean probability of any team being on probation in any year in the sample period is 0.029. (6) The mean predicted value for teams that were actually on probation during the sample period is 0.059, while the mean predicted value for teams not on probation during the sample period is 0.016. The null that these two means are equal is rejected at better than the 1% level of significance, so the model does a reasonable job differentiating teams punished for violating the cartel agreement from those who were not punished for violating the cartel agreement.

Table 3 summarizes the institutions in the tails of the distribution of predicted probabilities. The left three columns of this table show most of the institutions that make up the smallest 10% of the predicted values in the sample. The column "Years" contains frequency counts for the left tail of the distribution of predicted probabilities. It shows the number of institution-years in the smallest 10% of the predicted probabilities accounted for by each institution. The data set contains 12 observations for each school. So, for example, all 12 of the predicted probabilities that the United States Air Force Academy would be on probation fall in the smallest 10% of all predicted values. None of these schools were on probation during the sample period, so we refer to these schools as "law-abiding citizens" based on our model's predictions. The empirical model identifies these institutions as the least likely to be caught and punished for violating the recruiting regulations. The predicted probability of being on probation in all of these institution-years is less than 0.001%.

This group of unlikely cheaters is primarily composed of three types of schools: service academies (the United States Air Force Academy, the United States Military Academy Army, and the United States Naval Academy), private universities with elite academic reputations (Northwestern University, Leland Stanford Junior University, Vanderbilt University, Duke University, Wake Forest University) that play in high-profile conferences, and perennially weak programs from low-profile conferences (Utah State University, Colorado State University, New Mexico State University, Eastern Michigan University, and Rutgers University, cumulative within-sample winning percentage 0.357). The service academies and the small, elite private universities are very selective and may have difficulty recruiting football players at all. The perennially weak teams may also have trouble attracting any players, although for different reasons. Fort and Quirk (2001) speculated that elite academic schools would be unlikely to cheat, and our model confirms this. These results may indicate that the TEGE variable included in the empirical model captures commitment to academics.

The right five columns of Table 3 contain a majority of the institutions that make up the 10% of the institution-years with the largest predicted probabilities in the sample. Our model identifies these institutions as the "usual suspects" in terms of enforcement actions. The column headed "Probation" contains a Y if that institution was detected cheating on the cartel agreement and punished with a ban on television appearances and/or postseason bowl appearances during the sample period. Multiple Ys in this column indicate multiple spells of probation in the sample period. Ys in the "Probation" column identify institutions that cheated and were detected and punished. For example, based on the estimates reported in Table 2, the empirical model predicts that there was a 23% probability that the University of Houston would be on probation in 1990 (among the highest predicted probabilities in the sample). That predicted probability, and the predicted probabilities for three other institution-years for Houston, fall in the largest 10% of the predicted values in the sample. Houston's football program was on probation in 1989, so there is a Y in the "Probation" column.

From the right panel of Table 3, the empirical model does a relatively good job of predicting the most likely candidates for probation. Of the 22 institutions that appear in the highest 10% of the predicted probabilities for more than one year, only two were not on probation or found to be in violation of NCAA recruiting rules and not put on probation: the University of Alabama and the University of Arkansas. The predicted probabilities for these two schools range from 5% to 13%. Seven institutions that were on probation during the sample period did not have a predicted probability in the highest 10%, so they do not appear in Table 3: Texas Christian University, the University of Arizona, the University of Cincinnati, the University of Illinois, the University of Kansas, Memphis State University, and the University of Miami.

The column headed "Violation" contains a Y if an institution was found to be in violation of NCAA football recruiting rules but was not placed on probation. The "Violation" column contains information about NCAA enforcement activity that did not result in sanctions. To identify these events, we examined the detailed records of each recruiting violation the NCAA investigated during the period 1978-1990 in the NCAA Infractions Database. The NCAA refers to these records as the "Committee on Infractions Summary Cases." These instances represent a unique diagnostic tool for the performance of the empirical model because we can compare the predictions from the model to a set of "near misses"--cases where an institution was detected violating the cartel agreement but was not punished for the infraction.

There were 38 instances where institutions were investigated for violations but were not banned from appearing on television and/or a postseason bowl game in the sample period. Fourteen of these involve the "usual suspects" in the right-hand panel of Table 3. In these cases, the NCAA's sanctions stopped short of actual probation but included actions like public reprimands. For example, the predicted probabilities that Louisiana State University (LSU) would be on probation for the period 1980-1990 all fall in the top 10% of predicted values in the sample, including a 26.4% probability in 1986, among the largest predicted values in the sample. LSU was never banned from television or postseason appearances during the sample period; although, the football program was found to be in violation of NCAA football recruiting rules in 1986. In this case, because the violations were not deemed "serious in nature," the "punishment" meted out by the NCAA included a public reprimand and the submission of a written report to the NCAA that identified measures taken to ensure that this would not happen again. The dependent variable [ENF.sub.i,t] is equal to zero in 1986, and in all other years in the sample period, for LSU. However, the predicted probability of LSU being on probation in 1986 is 15.1%. (7) In terms of the underlying, unobservable behavior, the 1986 NCAA investigation suggests that something was going on in Baton Rouge during this period. The relatively high predicted probability from the empirical model supports this, but the NCAA was able to document only a single instance of an assistant coach driving a recruit to dinner and buying him a meal in their investigation, and no punishment was levied.

7. Conclusions

In this paper, we develop and estimate a model of the enforcement of the NCAA football cartel. Our model is dynamic in that reaction lags are explicitly modeled. It also accounts for imperfect information in monitoring compliance with the cartel agreement stemming from the inability of schools to directly observe rivals' behavior. Instead, schools must infer this behavior from observable factors.

Our empirical results confirm the key predictions of the model. Lagged winning percentage, an observable indicator, is a significant predictor of cartel enforcement, but the significance of this variable declines over time. Decision makers' discount rates, as proxied by years of head coaching experience and variables related to the demand for football at institutions, also significantly affect cartel enforcement.

This paper increases our understanding of cartel behavior. Cartels are formed because the expected rewards to cooperative behavior are greater than the rewards obtainable under noncooperative regimes. However, cartels are difficult to sustain because the payoffs to undetected deviation from the cartel agreement are even higher. Despite these difficulties, the NCAA football cartel has successfully sustained itself for over 100 years.

In a paper on the dynamics of a stable cartel, Grossman (1996) suggests that two factors are key to creating stability: proficiency in deterring entry and the ability to prevent defection among members. With respect to entry, the NCAA requirements for participating in Division IA football, which include a minimum stadium size and fielding a minimum number of other athletic programs at the Division I level, are sufficiently onerous to deter entry. In addition, the possibility of a start-up professional minor league football league competing with college football seems remote.

With respect to preventing defection, our results show that, even under imperfect information, effective signals of deviation from the status quo strategy exist, enhancing the ability of members to monitor and maintain the cartel agreement. Furthermore, even in the presence of large payoffs to cheating and relatively modest payoffs to complying, effective deterrents can be employed to maintain cartel agreements.

The effect of enforcement of the cartel agreement on competitive balance of the major football conferences was investigated in a recent paper by Depken and Wilson (2006). Their empirical results suggest that on average the net effect of enforcement of the cartel agreement is an improvement in competitive balance. This result implies that the members of the NCAA cartel are relatively accurate when interpreting the signal emanating from on-field performance; cartel enforcement improves competitive balance because cheaters are usually detected and punished. Our empirical results reinforce those in Depken and Wilson (2006). Our empirical model contains only variables that are observable, and available to all cartel members, and does a reasonable job of predicting instances where cartel violators are detected and punished. According to our results, Stigler's (1964) model of monitoring in a cartel by making probabilistic assessments based on observable outcomes explains which members of the NCAA cartel are punished for violating the cartel agreement. Depken and Wilson's (2006) result also rests on this assumption.

Certain industry characteristics also contribute to cartel stability. For example, differences in cost structures among cartel members can lead to instability because members with larger cost structures have a greater incentive to cheat. This cartel has removed much of the variation in cost structures by standardizing compensation packages for student-athletes and the size of coaching staffs. The variation in cost structures attributable to differences in athletic staff salaries may not be sufficiently large to encourage cheating by higher cost programs.

A particularly striking characteristic of this cartel is the large number of participants, which suggests that market power would not be easily obtained or persistent. A key to the cartel's success in monitoring members' behavior may lie in the absoluteness of the observable output. Unlike other industries that do not have perfect information about production, on-field performance is accurately and publicly reported in this cartel. The strength contained in that signal appears to outweigh the inherent weakness in a cartel with many members.

We thank Brian Goff, Bill Shughart, Lawrence White, and Andy Zimbalist for their valuable comments on previous drafts of this paper.

Received July 2006; accepted January 2008.

References

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Depken, Craig A., II, and Dennis P. Wilson. 2004. Institutional change in the NCAA and competitive balance in intercollegiate football. In Economics of college sports, edited by John Fizel and Rodney Fort. Westport, CT: Prager, pp. 178-210.

Depken, Craig A., II, and Dennis Wilson. 2006. NCAA enforcement and competitive balance in college football. Southern Economic Journal 72:826-45.

Eckard, E. Woodrow. 1998. The NCAA cartel and competitive balance in college football. Review of Industrial Organization 13:347-69.

Fleisher, Arthur A., Brian L. Goff, William F. Shughart, and Robert D. Tollison. 1988. Crime or punishment? Enforcement of the NCAA football cartel. Journal of Economic Behavior and Organization 10:433-51.

Fleisher, Arthur A., Brian L. Goff, and Robert D. Tollison. 1992. The National Collegiate Athletic Association: A study in cartel behavior. Chicago: University of Chicago Press.

Forrest, David, Rob Simmons, and Stefan Szymanski. 2004. Broadcasting, attendance and the inefficiency of cartels. Review of Industrial Organization 24:243-65.

Fort, Rodney, and James Quirk. 2001. The college football industry. In Sports economics: Current research, edited by John Fizel, Elizabeth Gustafson, and Lawrence Hadley. Westport, CT: Prager, pp. 11-26.

Green, Edward J., and Robert H. Porter. 1984. Noncooperative collusion under imperfect information. Econometrica 52:87-100.

Greene, William H. 2000. Econometric analysis. 4th edition. Upper Saddle River, NJ: Prentice Hall.

Grossman, Peter Z. 1996. The dynamics of a stable cartel: The railroad express 1851-1913. Economic Inquiry 34:220-36.

Humphreys, Brad R. 2000. Equal pay on the hardwood: The earnings gap between male and female NCAA Division 1 basketball coaches. Journal of Sports Economics 1:299-307.

Humphreys, Brad R. 2006. The relationship between big-time college football and state appropriations to higher education. International Journal of Sport Finance 1:119-28.

Humphreys, Brad R., and Michael Mondello. 2007. Intercollegiate athletic success and donations at NCAA Division I institutions. Journal of Sport Management 21:265-80.

National Collegiate Athletic Association. 1977-1991. NCAA football. Mission, KS: National Collegiate Athletic Association.

Siegfried, John, and Molly Burba. 2004. The college football association television broadcast cartel. Antitrust Bulletin 49:799-819.

Spence, Michael. 1978. Tacit co-ordination and imperfect information. Canadian Journal of Economics 11:490-505.

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Zimbalist, Andrew. 1999. Unpaid professionals: Commercialism and conflict in big-time college sports. Princeton, NJ: Princeton University Press.

Brad R. Humphreys * and Jane E. Ruseski [[dagger]]

* Department of Economics, 8-14 HM Tory, Edmonton, Alberta T6G 2H4, Canada; E-mail brad.humphreys@ ualberta.ca; corresponding author.

[[dagger]] Department of Economics, 8-14 HM Tory, Edmonton, Alberta T6G 2H4, Canada; E-mail [email protected].

(1) Another example is the practice of sports leagues collectively selling broadcasting rights. See Forrest, Simmons, and Szymanski (2004) and Siegfried and Burba (2004) for recent examinations of this type of cartel behavior.

(2) In 2007, the average payout to teams playing in bowl games was $3.9 million, and the 10 teams that appeared in Bowl Championship Series games each received $17 million.

(3) See Humphreys (2006) for evidence regarding Division IA football and state appropriations and Humphreys and Mondello (2007) for evidence regarding football success and donations.

(4) The estimated parameter on the second lag of winning percentage is 1.36 with a P-value of 0.01.

(5) Including the squared coefficient of variation had no impact on the results; both terms were not statistically different from zero. Note that we calculate CV over three years; whereas, Fleisher et al. (1988) calculate their CV over 30 years.

(6) Note that the predicted probability may be lower than the actual probability in the sample because of omitted variables bias. The most likely candidate for this omitted variable is the interaction between short-run demand for tickets and long-run supply of seats in stadiums. We thank an anonymous referee for pointing this out.

(7) The predicted probabilities for 1985 and 1987 are 13.5% and 18.7%, respectively.

Table 1. Variables in Equation 4

Variable                          Definition

[ENF.sub.i,t]      Dummy variable, = 1 if institution i detected
                     cheating on the NCAA football cartel agreement
                     and punished in period t
[WPCT.sub.i,t-k]   Winning percentage of football team at institution
                     i in year t - k
[CEXP.sub.it]      Years of head coaching experience of head football
                     coach at institution i in year t

[TEGE.sub.it]      Total educational and general expenditures per FTE,
                     in real 1982 dollars, by institution i in year t
[STA.sub.it]       Capacity of football stadium in 1000s at
                     institution i in year t

Table 2. Estimation Results

                                                 Model 1

Variable                Mean     Std Dev.   Coeff.    P-Value

[WPCT.sub.i,t-1]         0.509      0.232     1.146     0.019
[CEXP.sub.i,t]            7.80       6.50    -0.065     0.002
[TEGE.sub.i,t]             117         80    -0.008     0.023
[STA.sub.i,t]            50.70      20.80     0.009     0.275
[CV.sub.i,t-3]           0.275      0.198      -         -
[[bar.[beta]].sub.i]                         -2.955     0.000
[rho]                                         0.273
N                                              1243
pseudo-[R.sup.2]                               0.17

                            Model 2

Variable               Coeff.    P-Value

[WPCT.sub.i,t-1]          -         -
[CEXP.sub.i,t]           -0.07      0.007
[TEGE.sub.i,t]          -0.009      0.042
[STA.sub.i,t]            0.005      0.519
[CV.sub.i,t-3]          -0.079      0.899
[[bar.[beta]].sub.i]    -2.351      0.000
[rho]                    0.469
N                          925
pseudo-[R.sup.2]          0.51

Table 3. Predicted Probability of Violation

"Law-Abiding Citizens"

Smallest 10% of Predicted Values

Institution            Years

Air Force              12
Navy                   11
Army                   10
Northwestern           9
Stanford               7
Iowa                   5
Utah State             5
Vanderbilt             4
Wake Forest            4
Colorado State         4
New Mexico State       4
Eastern Michigan       3
Michigan               3
Alabama                2
Boston College         2
Duke                   2
Michigan State         2
Notre Dame             2
Rutgers                2

                       "The Usual Suspects"

Largest 10% of                 Predicted Values

Institution            Years   Probation   Violation   [[??].sub.Max]

Texas                    12                    YY      19.30%
Louisiana State          10                    Y       18.70%
Arizona State            9         Y                   19.90%
Texas Tech               9                     Y       19.70%
Oklahoma State           7                     Y        9.40%
Alabama                  7                             13.70%
Arkansas                 6                             11.70%
Nebraska                 6                     YY       9.30%
Oklahoma                 6         Y                   16.50%
Southern California      6         YY                  12.70%
Auburn                   4         Y                   10.80%
Clemson                  4         Y                    8.80%
Southern Methodist       4         Y                   12.40%
Texas A&M                4                     Y       12.10%
Houston                  4         Y                   23.10%
Oregon                   4         Y                   13.80%
California               3                     YY       8.10%
Southern Mississippi     3         YY                   9.60%
Florida                  2         Y                    7.40%
UCLA                     2                     Y        6.00%
Georgia                  2                     YY       8.00%
Missouri                 2                     Y        7.30%

[[??].sub.Max] is the largest predicted probability generated for each
institution among those institution-years in the largest 10% of the
predicted values. "Y" indicates a single incidence of probation or
repeated violation during the sample period. "YY" indicates multiple
spells of probation or repeated violations during the sample period.