Table : Institutions Included in the Data Set

This research is significantly different from other research because the institutions in the analysis are broken down into divisions of athletics and tiers of academia allowing to explore their effects on graduation rates. Divisions and tiers enter regressions as dummy variables. Hence, an example of these variables is given as follows: Division I-AA = 1; No Division I-AA = 0 and Tier 3 = 1; No Tier 3 = 0. By breaking the institutions into these categories, this analysis attempts to control for large discrepancies among the graduation rates of these institutions. The dependent variable (AGRADRATE) is the percentage of student-athletes that graduate at a given institution, in a given year. The (GRADRATE2) variable is an independent variable that is shown as the percentage of total undergraduates that graduate at an institution. The other control variables are ethnicity (ASIAN2, WHITE, BLACK2, HISPANIC2), supported by Gaston-Gayles (2004), size of school (SIZE2) supported by Adams, Bean, and Mangold (2003), and athletic success (ATHSUC) supported by Tucker (1992). Each ethnicity is a percentage of the student-athletes at a given institution that are of Asian, white, black or Hispanic ethnicity, in the given year. The size of a school is the total enrollment of students at an institution in the given year. Athletic success is calculated as the average winning percentage, corresponding to the institutions two major sports, which are football and basketball. Each of these sports is given equal weight. For example, if in 2007 Dayton University’s football team was 4-6 (40%) and their basketball record was 16-14 (53%) then their athletic success rate would be 46.5% for the given year. This is calculated differently than past studies. Other variables regressed in the study is whether an institution is considered public or private (PUBPRI) and Title IX compliance (TITLEIX). Past studies have used Title IX compliance as a dependent variable. In this analysis, the compliance rate represents an independent variable. Table 2 lists the variables that I will use in my study and the sources from which I obtained the data.

I used an OLS regression as a benchmark, but opted to use an EGLS model because the results show a more accurate measure of the data. As asserted by Tucker (1992), an EGLS model is a more efficient panel data model. The data issues in the next section corrected for the EGLS model. The empirical models estimated via OLS and EGLS in this study are shown as follows:

I expect to find a positive relationship between both the division and tier of an institution, with regard to the graduation rate, because athletic graduation rates among institutions fluctuate in large proportions. I expect the White and Asian races, ceteris paribus, to have a positive relationship, whereas I expect the Black and Hispanic races to have a negative impact on the graduation rates. Also, I expect the size of the school to be consistent with the findings of (Hamagami and McArdle 2004 and Tucker 1992), ceteris paribus, each showing a positive relationship. Overall, I expect to find Title IX compliance to be a significant variable. As the discrepancy in gender related athletic participation compared to the overall proportion of male and female student’s decreases, ceteris paribus, the larger the positive relationship on graduation rates. Women athletes graduate at much higher rates than male athletes, a smaller discrepancy means more female athletes receiving aid are present at the institution; therefore, the graduation rate will be higher.

In order to obtain accurate results I must first control for a variety of data issues that plague panel data. The first issue is non-stationarity. Non-stationarity is a stochastic process whose total probability does not change when the regression is shifted in time or space. In order to correct for this issue, I completed a unit root test for each variable in the study. I concluded that the variables ASIAN2, HISPANIC2, BLACK2, GRADRATE2, and SIZE2 showed significant signs of non-stationarity at the level regressor. Therefore, I chose the first difference level for these variables and chose a level regressor for the variables that showed no initial signs of non-stationarity. The variables that showed signs of non-stationarity are represented with a 2 after the variable in order to show that they are being regressed in the first different.

The next data issues prevalent in the study were heteroskedasticity and serial correlation. Heteroskedasticity is present when the error term no longer has a constant variance. I employed both cross-sectional weights and a Period SUR to solve for heteroskedasticity. By doing this, I was able to solve for the different variances in the error terms across cross-sections and throughout each period. In order to solve for serial correlation I employed an AR(1) term, which solved for first order correlation. Many variables showed signs of correlation in the first order auto-regressor and no significant signs in the subsequent orders.

The last problem I was concerned with is multicollinearity. Multicollinearity exists when two or more independent variables in a multiple regression model are highly correlated. To solve for this issue I used the Variance Inflation Factor (VIF). The VIF is a measure of the degree to which an independent variable is correlated with other independent variables in the model. The formula below shows the computation of the VIF.

(2)

Occasionally, variables can be considered strongly correlated if they reach a total value that is close to 10. Normally, a variable is not dropped from the model unless the VIF reaches a magnitude of 10. None of the variables in my study had to be removed due to multicollinearity. The VIF of each variable represented in the study is shown in the appendix.

The results of the OLS Regression are shown below in Table 4:

Coefficient	Estimate	Standard Error
	58.2445***	6.6973
Division1AA	0.9167	2.5848
Division2	-5.2469*	3.7142
Tier3	-8.8518***	3.2357
Tier4	-11.6261***	3.6547
Title IX	10.4654**	5.2201
Asian2	0.4036	0.4696
White	0.2074***	0.0750
Black2	0.1181	0.1069
Hispanic2	0.1604	0.2191
Gradrate2	0.1450*	0.0825
Pubpri	6.3283**	3.0420
Size2	0.0004	0.0003
Athsuc	-2.9475	4.4339
AR(1)	0.5085***	0.0529
Weighted Statistics
R - squared	0.6125	Adj. R - Squared	0.5907
S.E. of Regression	9.0375	Durbin-Watson stat	2.2689

After correcting for data issues the results of the OLS regression model shown above were used as a benchmark and showed several variables that were insignificant. Thus, I chose to use an EGLS regression because it is optimal in a panel data analysis. Moreover, the results in the subsequent sections of this paper are constructed using the EGLS regression. The results of the EGLS regression are shown below in Table 5:

Coefficient	Estimate	Standard Error
	58.0938***	4.8277
Division1AA	2.7688*	1.9950
Division2	-4.6602**	2.4872
Tier3	-8.1018***	2.4552
Tier4	-10.1603***	2.7681
Title IX	12.1705**	4.7377
Asian2	0.7921**	0.3479
White	0.2024***	0.0627
Black2	0.1216*	0.0904
Hispanic2	-0.0222	0.1710
Gradrate2	0.2025**	0.0800
Pubpri	9.0160***	2.1436
Size2	0.0006*	0.0003
Athsuc	-4.5052*	2.3813
AR(1)	0.5416***	0.0426
Weighted Statistics
R - squared	0.7468	Adj. R - Squared	0.7326
S.E. of Regression	8.8738	Durbin-Watson stat	2.2259
Un-weighted Statistics
R - squared	0.7328
Sum Squared Resid	20696.38	Durbin-Watson stat	2.3150

The first collection of independent variables in the regression can be grouped together as divisions of athletics and tiers of academia. The Division-IA and Tier1 variables are represented together as the constant, which equals (58.0938). In order to calculate the other divisions and tiers you must add either the selected division of athletics or tier of academia to the constant. For example, a DIVISION-IAA/TIER1 institution would graduate at the rate of the constant (58.0938) plus the DIVISION-IAA estimate (2.7688), which equals (60.8618). The coefficient estimates suggest that Division-IAA institutions graduate at higher rates than Division-IA and Division-II institutions. Consequently, as you decrease the tier of academia, in each division of athletics, the graduation rates decrease. For example, the DIVISION-IA/TIER1 graduation rate is (58.0938), the DIVISION-IA/TIER3 graduation rate is (49.9921) and the DIVISION-IA/TIER4 graduation rate is (47.9336). This is consistent for each division of athletics. Overall, the results are strikingly similar to what I expected. The table below shows the estimates for each of the divisions of athletics and tiers of academia that are significant in the study.

The difference in the estimates between the athletic divisions make intuitive sense because D-IAA athletes, on many occasions, have less athletic ability and do not dedicate as much time to their sport as D-IA athletes. Moreover, it would be understood that D-IA athletes show a higher priority for athletics than do D-IAA athletes, because of team obligation factors. The practice time spent during the season among all divisions of athletics is approximately equal, but DI-A athletes have more obligations to weight lift, watch films, attend events on campus, and off-season workouts than D-IAA and D-II athletes. Thus, because D-IA athletes are given more there is more demanded out of the student-athlete. Also, many D-IA schools do not care if the athlete stacks up academically with the overall student body. For example, it is well documented that D-IA institutions contribute financially to their athletics with television deals and other endorsements in order to attract the best athletes and have the best on-field success. Many times this success is empowered by athletes who do not have a corresponding academic record to validate the acceptance to the institution. Hence, this causes highly athletic institutions (D-IA) to attract high quality athletes and low quality students-athletes. The reason that D-II graduate at the lowest rates is because they attract low quality athletes and lower quality students-athletes. Moreover, D-IA athletes have a better chance of going professional in their given sport. This gives the student-athlete more incentive to concentrate on athletics rather than academics because the possibility of making a large amount of income.

From an academic standpoint this also makes intuitive sense. The higher the tier or ranking of the school, the better the school is academically. This translates into more academically competitive students or students that are harder working. As you decrease the overall tier or ranking of the institution the academic capability or devotion of the students should also decrease simultaneously. I can make this assumption because Tier1 institutions have harder acceptance standards than Tier3 or Tier4 institutions. Hence, students that go to Tier3 or Tier4 schools, in most cases, are not as academically competitive as Tier1 students or they did not work hard enough in high school to reach the appropriate acceptance standards. Thus, it is understood that students should graduate at lower rates if they go to a Tier 3 or Tier 4 institution. This is shown above in Table 5.

Second, ASIAN2 indicates that a 1% increase in the Asian athletic population, ceteris paribus, is consistent with a 0.7921% increase in the athletic graduation rate at that institution. Next, I find that, a 1% increase in the white athletic population, ceteris paribus, is consistent with a 0.2024% increase in the athletic graduation rate at that institution. Last, the BLACK2 estimate suggests that, a 1% increase, ceteris paribus, in the black athletic population is consistent with a 0.1216% increase in the athletic graduation rate at that institution. These findings parallel the results of Gaston-Gayles (2004), corresponding to the overall student body. As asserted by Gaston-Gayles (2004), ethnicities such as Asians and whites often come to college more academically prepared than other minorities. Consequently, they consistently graduate at higher rates than other minorities both as students and student-athletes. The Journal of Blacks in Higher Education asserts that blacks have the lowest graduation rate among all races, which is also consistent with my study. The relative insignificance of the HISPANIC2 variable could reflect their under representation at the chosen schools. This means the graduation rate of Hispanic athletes was not large enough to have a major effect on the overall graduation rate.

The estimate for GRADRATE2, the first difference of the overall student body graduation rate makes intuitive sense. The estimate indicates that, ceteris paribus, a 1% increase in the overall graduation rate at an institution corresponds to a 0.2025% increase in the athletic graduation rate. This makes sense theoretically, as I believe that people are attracted to the norm. Hence, if the overall student body is striving to graduate, then student-athletes would also feel obligated to graduate. For example, if a student-athlete has friends that do not play a sport and their ultimate goal is to graduate, the student-athlete himself is more inclined to graduate because he is going to follow the norm set by his friends.

The PUBPRI estimate suggests that athletes at a private institution graduate at a 9.0160% higher rate than athletes at public institutions. This makes intuitive sense because private institutions often have a smaller discrepancy of female to male athletic participation. As Hamagami and McArdle (1994) asserted, females graduate at higher rates than males both as students and student athletes. Moreover, because private schools show a smaller bias between athletic gender proportions, athletes graduate at higher rates at private institutions.

The estimate for SIZE2, the first difference in the size of an institution, suggests a 1% increase, ceteris paribus, is correlated with a .0006% increase in the athletic graduation rate. This is consistent with Adams, Bean, and Mangold (2003) and Tucker (1992), as they asserted that the size of the school is directly correlated to the graduation rate of the entire student body. An increase in students at an institution causes the institution to recruit more student athletes. Thus, there are more female athletes at the school, which increases the overall athletic graduation rate.

Next, the ATHSUC estimate suggests a 1% increase in the athletic success at an institution, ceteris paribus, is correlated with a -4.5052% decrease in the athletic graduation rate. This estimate also makes theoretical sense because I believe the better the season is going for an athlete, the more time they devote to their sport. Also, other athletes are drawn to watch sports such as football and basketball when their institution is winning. For example, if an institution has a basketball or football team that is undefeated, the athletes will make their sport a higher priority and concentrate less on academics. This is seen in both sports. If the football team does well, they can extend their season for approximately a month and play in a bowl game. The same is true for college basketball. Basketball schools that have well in season records could play in the NCAA tournament or the NIT tournament at the end of the season. An example of this is the University of Pittsburgh football team. Their football season ends November 28^th this season. If they win their leagues championship they will play a bowl game close to January 1^st. Hence, they must continue to practice and prepare physically for the game, which makes their season a month longer.

The last estimate, TITLEIX compliance suggests a 1% increase in closing the proportionality gap, ceteris paribus, is correlated with a 12.1705% increase in the athletic graduation rate. The estimate shows a large estimate because female athletes graduate at a much higher rate than male athletes. Consequently, because a large majority of the schools have a bias towards male athletics, such a small change in the proportionality gap gives institutions large changes in their graduation rates. However, this is not simple to do, because this type of change would be accompanied, in most cases, with either adding or detracting scholarships. Unfortunately, from an economic standpoint, the sports that are going to be cut first from an institution are the programs that bring in the least amount of revenue. As asserted by the Daily Wildcat, a newspaper in Arizona, from 2003 – 2007 the football and basketball revenues at major D-IA conferences both exceeded their expenses nearly 2 to 1. This large profit margin for the football programs makes it difficult for institutions to comply with Title IX because football is strictly a male sport and can give up to 85 athletic scholarships at the D-IA level. Although there is no set number of scholarships for D-IAA and D-II football programs, the number is much lower than 85. Below I will choose a school from each division of athletics and tier of academia and show how an institution can be run more efficiently by applying this estimate to real life situations.

NCAA Reconfiguration Rules:

Division-IA and Division-IAA:

“ Division I member institutions have to sponsor at least seven sports for men and seven for women(or six for men and eight for women) with two team sports for each gender. Each playing season has to be represented by each gender as well. D-IA football schools have to meet minimum attendance requirements (17,000 people in attendance per home game, OR 20,000 average for all football games in the last four years, OR, be in a member conference in which at least six conference members sponsor football or more than half of football schools meet attendance criteria.) D-IAA schools do not have attendance requirements for football programs.”

Division-II:

“Division II institutions have to sponsor at least four sports for men and four for women, with two team sports for each gender, and each playing season represented by each gender. D-II teams do not have attendance requirements for football”

Table : Title IX Configuration

In 2008, approximately 30,000 student-athletes receiving athletic financial aid are eligible to graduate college. Hence, the same number of scholarships will be available for incoming freshmen in 2009. With that said, understanding at what rates divisions of athletics and tiers of academia graduate could help institutions obtain larger revenues. Within each division of athletics, the higher the ranking or tier, the more revenue the institutions convey from their athletic programs. Therefore, not only do the athletic graduation rates decrease in subsequent order throughout tiers of academia, but also the economic implications decrease in subsequent order. For example, the D-IA/Tier 1 institutions on average bring in more revenue than D-IA/Tier 3 and D-IA/Tier 4 institutions. The study shows that athletes are attracted to high quality athletic programs and high quality academic institutions. Consequently, the data shows that Tier 1 institutions on average have more athletic success because they are recruiting higher quality athletes. Thus, higher athletic success at an institution leads to an increase in ticket sales, higher game attendance, more merchandise sales, and televised games, all of which increase the revenue at an institution. Moreover, by understanding what affects the graduation rates, as shown in the study, an institution can increase their overall student-athlete graduation rate, which can increase their tier ranking.

It is well known that the athletic revenues at an institution are attributed to the men’s football and basketball programs. By leaving these two sports untouched and re-configuring the compliance among other sports, the institution can keep the economic implications relatively constant. Moreover, at each institution represented in Table 6, the sports in which the scholarships were taken away had negative revenue. With that said, by re-configuring, institutions can keep their revenue stream consistent, but increase their athletic graduation rate substantially. Thus, the athletic revenue impact from Title IX is minimal, but its effect on athletic graduation rates is large.

Third, as seen in the calculation of collegiate rankings, 5% of the ranking system comes from the institutions graduation rate. The study suggests if student-athletes are graduating at higher rates, then the institutions overall ranking will also increase simultaneously. Although this increase is very minuscule, the institutions US News and World Report ranking would increase slightly. This increase in ranking is known to increase the overall revenue at an institution and the tier of academia.

In the future, this model could be updated to include variables designed to better understand the self-selection bias among student-athletes, regarding an athlete’s choice of major concentration. Many athletes among different divisions of athletics and tiers of academia may choose easier majors because they understand the amount of time devoted to their sport. For example, an athlete at a DI-A school may choose a sport as their number one priority for attending school. In order to increase their productivity in that sport, the student could choose an easier path academically to ensure that they are reaching their optimal training level or practice level. Coinciding with data availability this study could use the chosen majors of students as well as student-athletes as independent variables. By doing this the study could find how different majors affect graduation rates? How these results change among divisions of athletics? Are the discrepancies in other variables such as race determined by their choice of major?

Another idea for future research is to increase the sample size. Currently, the model only pertains to years 2001 – 2007. Future research could update the data and increase the number of years used in the study. The NCAA website started collecting data on graduation rates of student-athletes in 2001; therefore, each subsequent year after 2001 through the given year will be available. A longer period of time would conclude more accurate results or solidify the results obtained in this study. Also, the larger pool of data could help to reduce problems in the data such as autocorrelation, multi-collinearity and heteroskedasticity.

7. Conclusion

Overall, the purpose of this analysis was to determine the impact of multiple variables on the graduation rates of collegiate athletes. The results that I have obtained from this analysis agree concretely with the hypothesis that I generated based on literature review and economic logic. The division and tier dummy variable estimates show that D-IAA institutions graduate athletes at the highest rate among collegiate athletics. Also, among tiers of academia, Tier 1 institutions graduate at the highest rate. With that said, the model provides support for the assertions of Gaston-Gayles (2004) that Asians and Whites make graduation a higher priority than other races, regardless of the division of athletics or tier of academia. Moreover, the study provides evidence that determinants in the study prove the other races can graduate at higher rates. The Title IX compliance rate showed a significant positive estimate when introducing more women’s athletic scholarships to an institution. Moreover, I conclude, institutions should reconfigure their athletic department if they show a bias toward male participation. Although this sounds counterintuitive because male athletics bring in more revenue for the school, a decrease in the gender proportion discrepancy increases the athletic graduation rate substantially. After studying real life situations among athletic departments in the different divisions of athletics and tiers of academia in the study, I was able to conclude what changes should be made. More specifically, D-IA institutions show an easier transition to close the proportion gap because of larger revenue discrepancy and the higher number of sports.

"Academics and Athletics." National Collegiate Athletic Association. 5 Oct. 2008