What Affects the Four Year Graduation Rate? : An Econometric Analysis of Public

Colleges and Universities in the United States

Clayton Eanes

Senior Thesis

Longwood University

Spring 2016

ABSTRACT:

This study empirically examines what factors affect the four year graduation rate at colleges and

universities throughout the United States. Econometric modeling is used in order to determine what

characteristics impact the four year graduation rate. Results suggest that retention rate of freshmen,

average amount of federal financial aid awarded, class sizes with 20 students or less, in-state tuition,

and average grade point average of incoming freshmen have a positive effect on the four year

graduation rate. Percentage of males, whether the institution is located in a city or not, and

percentage of Hispanics have a negative effect on the four year graduation rate. Surprisingly, the

percentage of Greek females and Greek males does not have an impact.

What Affects the Four Year Graduation Rate? : An Econometric Analysis of Public

Colleges and Universities in the United States

Clayton Eanes

Senior Thesis

Longwood University

Spring 2016

ABSTRACT:

This study empirically examines what factors affect the four year graduation rate at colleges and

universities throughout the United States. Econometric modeling is used in order to determine what

characteristics impact the four year graduation rate. Results suggest that retention rate of freshmen,

average amount of federal financial aid awarded, class sizes with 20 students or less, in-state tuition,

and average grade point average of incoming freshmen have a positive effect on the four year

graduation rate. Percentage of males, whether the institution is located in a city or not, and

percentage of Hispanics have a negative effect on the four year graduation rate. Surprisingly, the

percentage of Greek females and Greek males does not have an impact.

Table of Contents

I. Introduction………………………………………..pg.1

II. Background Information…………………………...pg.3

III. Literature Review……………………………….....pg.8

IV. Methodology……………………………….............pg.13

V. Econometric Results (Model 1)……………….........pg.19

VI. Econometric Results (Model 2)……………………pg.26

VII. Conclusion………………………………………..pg.33

VIII. Bibliography………………………………….......pg.35

XI. Appendix A: Data Set……………………………...pg.37

X. Appendix B: STATA outputs……………………….pg.46

List of Figures

Figure 1: Four Year Graduation Rates……………………pg.4

Figure 2: Time Use for Full Time Students……………….pg.5

Figure 3: Acceptance Rates……………………………….pg.6

Figure 4: U.S. Undergraduate Ethnicities…………………pg.7

List of Tables

Table 1: Variable Descriptions……………………………pg.14

Table 2a: Descriptive Statistics……………………………pg.19

Table 2b: Descriptive Statistics……………………………pg.20

Table 3: Regression Results (Model 1)…………………….pg.23

Table 4: Test for Multicollinearity (Model 1)…………........pg.25

Table 5: New Variable Descriptions………………………pg.26

Table 6: Descriptive Statistics……………………………..pg.27

Table 7: Regression Results (Model 2)…………………….pg.30

Table 8: Test for Multicollinearity (Model 2)……………....pg.32

1

I. Introduction

When a student enrolls in their college of choice they have almost the same odds as flipping

a coin as to whether or not they will graduate on time within four years. Currently in the United

States, the national average for the four year graduation rate at public institutions is 52%. The four

year graduation rate at public colleges and universities throughout the country differs greatly from

one to another. This rate ranges from as high as 87% to as low as 3%.

With tuition costs skyrocketing each year, extra time spent at college could have adverse

effects on completing a degree. College institutions argue that tuition is going up so fast because

public funding for state colleges has been cut dramatically. According to Paul Campos from New

York Times, “if over the past three decades car prices went up as much as college tuition then the

average new car would cost roughly 80,000 dollars” (Campos, 2015). To the American people this

should be very alarming and government policies should be implemented to limit tuition increases.

Students and parents who help pay for college tuition should care that the graduation rates are not

better than what they are. If a person is investing that much time and money into something it

should be assumed that they expect there to be very high odds of success. With the four year

graduation rate being where it is and the high costs of tuition, students and parents are left with a big

decision on whether or not to enroll in a college or university.

Current and prospective students, parents, as well as policy makers and government officials

should all be concerned with where graduation rates are currently at because they have a direct

impact on society. Studies show that workers with at least a bachelor’s degree have median annual

earnings of $45,500 versus workers with only a high school diploma who earn $28,000 (DeSilver,

2014). Recent college graduates help the middle class, and as many economists suggest, the middle

class is the largest contributor to economic growth. In addition, research shows that people with

college degrees are less likely to be affected by economic downturns and help lower unemployment.

This is because more college graduates participate in the labor force. The U.S. Department of

Education data suggests that “77% of people with at least a bachelor’s degree participated in the

labor force, and only 52% of people participated had only a high school diploma” (U.S. Department

of Education).

2

There are many factors contributing to why students do not graduate from school in four

years or at all. The goal of this paper is to look at public university statistics for on time four year

graduation rates and explore which different characteristics give students a higher probability of

graduating within four years. Using cross sectional data from the year 2014, this study uses 199

randomly selected public colleges and universities from a population of over 600. Regression

analysis and econometric modeling will be used in order to determine which factors impact the four

year graduation rate. Regressions will be run for two models. One model will show a linear

relationship and the second will show a nonlinear relationship. Diagnostic tests will be used to

satisfy the seven classical assumptions and ensure Ordinary Least Squares is the best linear unbiased

estimator.

The remainder of the paper is organized as follows. The next section provides background

information about college and university characteristics along with a section that summarizes

relevant literature to the topic. The literature review is followed by an overview of the methodology

employed and the data set with expected signs of variables and their descriptions. Then results of

the regression analysis are presented for the data set as a whole, followed by an analysis where

schools are segmented into three different categories; city, suburban, and rural. The final section

offers potential research ideas to improve upon and concludes.

3

II. Background information

For the past decade colleges and universities four year graduation rate has been on a steady

decline. However, tuition costs for these institutions continue to rise from year to year. Students are

taking on enormous amounts of debt only to not graduate on time or at all. This is very concerning

because students are expecting to graduate and land a better job because of their decision to pursue

a degree in higher education. When students do not end up graduating they become far worse off

than they would have been entering the workforce out of high school. This makes it much more

difficult for students to deal with financial pressures that are present in the real world.

The variation of graduation rates amongst universities in part is due to financial expenditures

and amount of financial aid provided. Universities who have more money and receive more

donations are more likely to get better students and have higher graduation rates. Students who are

offered less financial aid could be more likely to drop out due to financial pressures. Universities that

offer considerable Pell grants to students help to alleviate some of these financial problems students

and parents face. The average amount of financial aid that is currently offered to a student is $12,740

(Institute of Education Sciences) However, some universities offer far less. Furthermore, many

students choose to stay close to home mostly due to financial pressures. In fact, according to an

article in NBC news recent high school graduates were interviewed and 41% of them said that they

are seriously considered staying close to home due to the economic condition of the country

(Gloecker).

Graduation rates for the top 10 public colleges and universities as well as the bottom 10

colleges and universities can be seen in figure 1. When looking at the graph you will notice that the

University of Virginia has the highest graduation rate of all schools. Student graduation rates are one

of many measures used in determining the overall rank of a school. All the colleges in the top 10 are

highly recognizable and have respectable reputations. On the other hand, when looking at the

bottom tier schools most of them if not all are unheard of to the average person.

4

Figure 1. Graph was generated using data from The Fiscal Times and The Kiplinger Washington Editors.

The amount of time students spend doing school work varies for different schools. Some

schools encourage students to get heavily involved with organizations, clubs, and fraternities or

sororities. All this involvement means lots of friends and always something to do but at the same

time it leaves less time for students to study and complete assignments. This paper will attempt to

prove whether or not there is a relationship between the involvement of Greek life and on time

graduation rates. It is predicted that schools who have a higher percentage of students in Greek life

are more likely to have a lower graduation rate. This is because when students get into these

fraternities and sororities they must dedicate almost all their time for the first couple months before

they are inducted. This leaves them less time to focus on their studies. The pie chart shows how the

average student allocates their time for a typical weekday. As you can see from the chart in figure 2.

Students spend a lot of time with leisure and sports.

5

Figure 2. Taken from Bureau of Labor Statistics, American Time Use Survey.

Retention rates, which can be defined as the rate in which a student returns to the university

after their first year shows an interesting relationship to graduation rates. Retention rates appear to

be closely related to graduation rates but there is not a guarantee that a student will go on to meet

all the requirements necessary to graduate after returning for their sophomore year. The more

students that return to the institution yields a higher probability that more students will not graduate.

This study will look at whether or not schools with higher retention rates also have a higher or lower

graduation rate.

6

There appears to be an inverse relationship between acceptance rates of colleges and

universities and the percentage of graduates from each school. This can be seen in Figure 3. In the

bar graph it can be seen that open admissions have the lowest graduation rates while less than 25%

accepted has the highest graduation rates. This indicates that universities who accept a large

percentage of students are more likely to have more of them fail out and universities who only

accept a small percentage are more likely to graduate. Intuitively it can be argued that a university

with a very small acceptance rate gets to be very picky about who they accept and as a result they get

better quality students.

Students who apply to the universities with the smallest acceptance rate are well prepared

and have a general understanding of what they need to have to get in. Whereas schools who accept a

lot of students do not really know the types of students they are going to get. In a sense the

university is taking a chance by accepting a student because they are allowed to accept so many per

academic year and they do not have enough information that suggests the student will perform well.

Figure 3. From the Institute of Education Sciences, data originally from U.S. Department of Education, National

Center for Education Statistics

7

This paper will look at whether or not there is a relationship between ethnicity and four year

graduation rates. This study will attempt to show whether or not a university with more minorities

has a lower or higher graduation rate. The latest data that is available comes from the academic year

of 2009 to 2010 and is represented in Figure 4. The chart illustrates that White non-Hispanic

accounts for the largest demographic while American Indian accounts for the smallest group. The

figure also shows that the largest two minority groups are black and Hispanic. It is predicted that

depending on the location of the University there will be more minorities. This will be the case

especially with Universities located in inner cities. It is predicted that inner city schools with high

minority rates will have the lowest four year graduation rate.

Figure 4. Found in 2010 Annual Academic Report University of Phoenix then recreated with original data

submitted by UOPX to NCES through IPEDS Fall Enrollment Survey 2009-2010

8

III. Literature Review

Historically Black Colleges

Xueyu, Sontachai and Wu (2015) researched Historically Black Colleges and the reasons for

why African American students are not graduating1. They claim that both quality of the college and

costs are essential factors in determining whether not a student graduates. Using data from 81

Historically Black Colleges, they compare college quality and graduation rates. College quality is a

measure of retention rate, student expenditures per full time student, rejection rate, and the median

ACT score from applicants2. The dependent variable is the graduation rate of the institution within

six years. In order to test their hypothesis they use a theoretical model and estimation strategy by

generating a production function. The production function shows that graduation is a linear

function of quality, costs, student characteristics, institutional characteristics, and the labor market

condition. The results show that college quality has a positive significant effect on graduation rates.

The results also reveal that college costs have a negative effect, while financial aid has a positive

effect on graduation rates3.

Xueyu, Sontachai and Wu (2015) neglects to consider student social involvement in Greek

life, clubs, and other organizations as reasons for not graduating. For this study these variables will

be accounted for. To improve upon this research, the researchers should have also accounted for

SAT scores as well because some students apply for colleges without taking the ACT test. Both ACT

and SAT scores are proxy variables for the measure of ability, so having both tests would better

represent ability. The data set for this paper is a small segment of the population of college

universities. This empirical work will attempt to prove whether or not the same results hold for a

larger data set of public universities that are not Historically Black Colleges.

1 Xueyu, Cheng, Sontachai Suwanakul, and Wu Ruohan. "Determinants of Graduation Rates of

Historically Black Colleges and Universities." Journal of Economics & Economic Education

Research 16, no. 2 (May 2015): 51-60.

2 Ibid P.51 3 Ibid P.58

9

Model Uncertainty

Goenner and Snaith (2004) argued that selecting variables that effect graduation rates should

not be based entirely on economic theory. In order to account for which variables to include they

used Bayesian Model Averaging (BMA). BMA is a statistical technique to account for uncertainty

when specifying a model4. Bayesian analysis generates the entire probability of the distribution of

the coefficients instead of just using a single estimate of the coefficient5. The dependent variable for

this research is the six year graduation rate at Doctoral universities. The main independent variables

they predict to have an effect on graduation rate are personal qualities of the student body and the

environment the student encompasses. Economic theory and previous research suggest that the

institutions with well-prepared students would yield higher graduation rates6. These personal

qualities of the students measure how well the student is prepared. Using data from 184 colleges,

Goenner and Snaith generate 24 candidate variables that affect graduation rates. The results indicate

that there is model uncertainty in predicting graduation rates. After the estimates from BMA are

generated, it can be seen that six variables have high probabilities to the test. A high probability also

shows that there is an effect. Goenner and Snaith controlled for many different ethnicities including

African American, Native American, Asian, White, and Hispanic, but found in their research that

only Native American had a negative effect on graduation rate. In addition, the age of the student,

and urban vs. non-urban both had a sizable negative effect. Male had a small negative effect while

top 10% of high school class and low SAT score, have a positive effect on graduation rate.

Goenner and Snaiths’ research refutes Xueyu, Sontachai and Wu, because they argue that the

ability and performance of the student not the quality of the education, affect graduation rates. The

variables that were significant in this paper should be included in the model for this study to avoid

omitted variable bias. These variables will be important and are expected to be significant in this

study. Also, caution should be used when generating a model because this empirical research

suggests that a single estimated variable selection method can produce misleading results that do not

represent the true relationship of graduation rates.

4 Goenner, Cullen F., and Sean M. Snaith. 2004. “Accounting for Model Uncertainty in the

Prediction of University Graduation Rates”. Research in Higher Education 45 (1). Springer: 25–

41.

5 Ibid p.29 6 Ibid p.30

10

Class Size

Diette and Raghav (2014) discussed how class size at four year liberal arts colleges effect

student performances in different courses. They conjecture that colleges push for higher graduation

rates and lower retention rates but struggle to do so because they have to account for costs7. This

becomes problematic when colleges have to cut down, they often raise class size in order to lower

their costs per student. Using data from private selective liberal arts colleges from 1986 to 2008,

Diette and Raghav compare student’s grades for many courses including demographic information.

They calculate class size by the number of students who receive a grade for each course for that

semester and year. The dependent variable in their model “grades” is measured by the subscript isdft

which stands for individual grade, section, department, faculty member, and term. There is one

outlier of 110 in the data for class sizes but the bulk of the data is class sizes under 30. This indicates

that most liberal arts colleges have small class sizes. Deitte and Raghav use both OLS and Tobit

regressions for their empirical research. For tobit, they use a lower limit of 0 and an upper limit of

4.33 because this value represents an A+. The results show that there is a negative effect on class

size. The results also indicate that males get lower grades than females in the study. Students who do

well on the SAT received higher grades, and specifically students who scored well on the math part.

The data Deitte and Raghav collected only represents private small liberal arts colleges and

this study will determine if the same results hold for large public universities. Also, Deitte and

Raghav used observations of students for their research while this study intends to use universities

as observations. This work will attempt to predict why the graduation rate varies between

universities who have similar qualities. This paper helps to explain the effect of class size on the

performance of students. This empirical research will look at class size averages at universities to see

whether or not more or less students graduate.

7 Diette, Timothy M., and Manu Raghav. "Class Size Matters: Heterogeneous Effects of Larger

Classes on College Student Learning." Eastern Economic Journal Eastern Econ J 41, no. 2

(2014): 273-83.

11

Greek Life

Walker, Martin, and Hussey (2015) investigated the effects of being involved in a fraternity

or a sorority on different collegiate outcomes such as graduation rate. In order to collect data that

wasn’t already available, the researchers used a survey method to get student responses. They used a

panel study with only one observation (Duke University), and they compared students who are

involved in Greek life and those who are not. Previous studies have used cross sectional data but

haven’t been able to separate the effects after becoming Greek with the factors of why they chose to

do so beforehand8. The advantage this group had over other researchers was the ability to administer

a survey before the Greek rush, (approval of new members) and after members were initiated into

the organization. This allows them to control for non-Greeks and eliminates some selection bias9.

To further combatant the selection problem they use propensity score of the students. A

propensity score can be defined as the conditional probability of joining a Greek organization10. The

control group is matched with other students who have decided to go Greek with similar estimated

propensity scores. The researchers first collected data for the pretreatment period before going on to

collect data after the student’s second and fourth year at the University. In order to estimate the

propensity score weights they use Probit regressions. The results show that Greek members are

more concerned with socializing with others than non-Greek members. Walker, Martin, and Hussey

found that Greek members feel the need to have a strong presence on campus and become more

involved with campus life. The results also show that Greek members are more likely to branch out,

and 60 percent of Greeks study abroad as opposed to 38 percent of non-Greeks who do11. They

8 Walker, Jay K., Nathan D. Martin, and Andrew Hussey. 2015. "Greek Organization

Membership and Collegiate Outcomes at an Elite, Private University." Research In Higher

Education 56, no. 3: 203-227 9 Ibid 10 Ibid 11 Ibid

12

conclude from their research that Greek members have a stronger likelihood of graduating. Greeks

are also significantly more likely to remain full time completing their degrees in five years or less.

There is a small magnitude of positive significance that Greeks in their third and fourth years in

college have a higher GPA then non Greeks. For further reading about Greek academic

performance see Grubb (2006).

For this empirical research, data will be collected on percent of males who are in a fraternity

as well as the percent of females who are in a sorority at many different universities, and test

whether or not there is a positive or negative effect on graduation rates. Walker, Martin, and Hussey

(2015) looked at graduation rates for five years. This paper will measure the effect of Greek

involvement and if students graduate on time in four years. This paper only captures Greek

involvement at one institution and the purpose of this work is to investigate the effect of Greek

involvement on a much larger university wide scale.

13

IV. Methodology

This empirical research consists of cross sectional data with many explanatory variables that

are predicted to affect the four year graduation rate at public universities across the country. The

data is from the year 2014 and represents 200 randomly selected public colleges and universities

from a population of 617 public schools. Regression analysis will be used in order to determine

significance for each variable in the equation. For this study Ordinary Least Squares will be used to

run the regression. The model this study will use can be seen below.

Model:

4yearGradRti = ßo + ß1RetentionRti + ß2AverageAidi + ß3AcceptanceRti + ß4malei + ß5GreekFemalei +

ß6GreekMalei + + ß7Studentsi + ß8ClassSizeover50i + ß9ClassSizeunder20i + ß10tuitioni + ß11Blacki +

ß12AvgGpai + ß13 DryCampusi + ß14Hispanici+ ß15Urbani + ei

Dependent Variable

The dependent variable in this study is the four year graduation rate for public universities in

the United States. This variable is measured as a percent of the total amount of students who have

graduated on time within four years at each public university i. For this paper the five year and the

six year graduation rate will not be considered. Many studies before have used the five and six year

rate. In almost all cases, the four year graduation rate is considerably lower than the five and the six

year rate. This study attempts to differentiate itself from past works by exploring the effects of

graduating on time. Table 1. Illustrates variables and their expected signs that are predicted to have

an impact on the four year graduation rate.

14

Table 1. Variables and Expected Signs

Variable Name Definition Expected Sign

Hypothesis Test

4yearGradRti

(dependent variable)

The four year graduation rate for each university i measured in %

------ ------

RetentionRti The freshman retention rate for each university i measured in %

? Ho: ß1 = 0 Ha: ß1 ≠ 0

AverageAidi The average amount of financial aid offered to a student at each university i measured in $

+ Ho: ß2 ≤ 0 Ha: ß2 > 0

AcceptanceRti The acceptance rate of each university i measured in %

_

Ho: ß3 ≥ 0 Ha: ß3 < 0

Malei The amount of males at each university i

measured in %

_

Ho: ß4 ≥ 0

Ha: ß4 < 0

GreekFemalei % of females in a sorority at university i ? Ho: ß5 = 0 Ha: ß5 ≠ 0

GreekMalei % of males in a fraternity at university i ? Ho: ß6 = 0 Ha: ß6 ≠ 0

Studentsi Amount of undergrad students enrolled full time at each university i

? Ho: ß7 = 0 Ha: ß7 ≠ 0

ClassSizeover50i % of classes that are larger than 50 students at university i

_ Ho: ß8 ≥ 0 Ha: ß8 < 0

ClassSizeunder20i % of classes that are smaller than 20 students at university i

+ Ho: ß9 ≤ 0 Ha: ß9 > 0

Tuitioni Tuition at university i measured in $ ? Ho: ß10 = 0 Ha: ß10 ≠ 0

Blacki % of black students at each university i _ Ho: ß11 ≥ 0 Ha: ß11 < 0

AvgGpai The average grade point average of students applying to each university i

+ Ho: ß12 ≤ 0 Ha: ß12 > 0

DryCampusi Dummy variable for 1 if Dry campus (no alcohol

allowed on campus) at university i

+ Ho: ß13 ≤ 0

Ha: ß13 > 0

Hispanici % of Hispanic students at each university i _ Ho: ß14 ≤ 0 Ha: ß14 > 0

Urbani Dummy=1if university is urban ? Ho: ß15 = 0 Ha: ß15 ≠ 0

15

Independent Variables

For every known expected sign this study will run a one tailed test, and for unknown signs a

two tailed test will be run. When holding all else constant, the freshman retention rate (RetentionRti)

is expected to be unknown. An institution with a high retention rate will yield more graduates.

Retention rate and graduation rate will have some correlation. However returning to school after the

first year does not ensure the student will graduate, but the probability becomes greater. Retention

rate is an important variable when comparing the four year graduation rate, because if a student fails

their first semester it will become more difficult to still graduate on time.

Holding all else constant, the average amount of financial aid offered (AverageAidi) is

expected to have a positive impact on the four year graduation rate. This is because a student is

more likely to stay in school with more financial aid awarded. With state funded schools, the more

credits a student takes in a semester the more financial aid he or she will be awarded. This gives

students an incentive to take more credits and graduate on time.

Controlling for all other variables, the acceptance rate (AcceptanceRti) is expected to be

negative. Acceptance rate and graduation rate have an inverse relationship (refer back to background

information). The higher percentage of students accepted at a university i, the lower the graduation

rate for university i will be. A college or university with a low and selective acceptance rate has the

ability to seek students with higher scores and higher class rankings.

The percentage of males (Malei) is expected to have a negative impact on graduation rates

when holding all other variables equal. On average females graduate at higher rates than males in

high school. It is expected that this will also hold true for upper level education. Since the study is

looking at public co-ed schools, every additional male the school has will cause the graduation rate

to drop.

16

Holding all other variables constant, the percentage of females who are in a sorority

(GreekFemalei) and the percentage of males who are in a fraternity (GreekMale i) have unknown

expected signs. Evidence suggests that Greeks are more likely to stay at the university and graduate

on time (Walker, Martin, and Hussey 2015). However some Greek members especially in the

beginning stage of pledging do not meet grade requirements. Some of these students do not return

to the school and do not graduate.

Holding all else equal, the amount of students (Studentsi) could have a positive or negative

sign. The variable could be positive if there are enough majors and there is no overcrowding where

every student has access to everything essential to graduating. The variable Studentsi could be

negative if students are denied this access and there are not enough instructors. A university that

provides the opportunity to establish relationships with faculty and mentors regardless of size will

have higher graduation rates. Students at universities who do not receive proper guidance and

counseling will be more likely to fail out or not graduate on time.

Ceteris Paribus, the percentage of classes with more than 50 students (ClassSizeover50i) is

expected to be negative because as research shows students in larger classes tend to not do as well.

This is because it is much harder to develop a student teacher relationship with large classes. In a

large class students are just a number and there is not much accountability. However, holding all else

constant, the percentage of classes with fewer than 20 students (ClassSizeunder20i) is expected to be

positive because there is a student teacher relationship and students are often held accountable for

attending class and participating when there.

The amount of in-state tuition for each university i (tuitioni) has an unknown sign when

holding all else constant. In-state tuition is being captured in this model because the study is looking

at financial factors as a cause for lower graduation rates. In addition, colleges and universities have

more students who attend in state than out of state. The variable Tuitioni could have an expected

positive sign if a student realizes how much money their education costs and this causes them to

take it more seriously. This would especially be the case if the student is using student loans to pay

for it. Tuitioni could have an expected negative sign if tuition at the university i is too much and

causes the student to not complete their degree because of financial instability.

17

The percentage of African American students (BlackRti) and the percentage of Hispanic

students (HispanicRti) at each university are expected to be negative when controlling for all other

variables in the study. Historically, black and Hispanic/ Latino students have had a lower graduation

rate. Intuitively the more minorities enrolled at the institution the lower the graduation rate will be

overall. The study predicts that these two variables will be highly significant.

The average GPA (AvgGpai) is expected to be positive when holding all else constant. It

must be noted that the variable AvgGpai could be strongly correlated with the acceptance rate. This

is because the GPA as well as other measures are used as determinates of acceptance. Therefore,

caution will be used when testing for significance in this study. AvgGpai is a measure of a student’s

ability and is a prediction of how well the student will perform throughout their college career. The

higher the GPA the student has, the more likely they are to graduate. Therefore, the higher the

institution sets the bar for minimum score requirement for grade point average, the greater the

graduation rate will be overall for the institution.

Ceteris Paribus, a dry university (DryCampusi) is expected to have a positive effect on the

four year graduation rate. Statistical evidence shows that drinking alcohol hinders the ability to

perform well in school (refer back to literature review). A dry campus holds strict sanctions on

students to not consume alcohol. It is predicted that students will be better suited to graduate if the

campus is dry.

Holding all else constant, a university that is located in a city (Urban i) is expected to have an

unknown sign. Urban could be negative if instead university i is in an inner city with a low level of

income and a high rate of crime. An urban setting for a college or university could cause too many

distractions for students which could lead to a lower four year graduation rate. The variable urban

could also be positive because many colleges and universities located in cities are more closely

together and this would make it easier and more likely that a student would attend class.

18

Data Sources

The data for the dependent variable has been collected from College Board’s Four-Year

Graduation Rates for Four-Year Colleges which originally came from the U.S. Department of

Education data from 2008 to 2011. The explanatory variable freshman retention rate was collected

from the US News and World Report college rankings. The average amount of financial aid offered

was collected from the US News and World Report college rankings. The acceptance rate for each

university was collected from the US News and World Report college rankings. The percentage of

males collected from the US News and World Report college rankings. The percentage of females

who are in a sorority and the percentage of males who are in a fraternity was collected from the US

News and World Report college rankings. The amount of students was collected from the US News

and World Report college rankings. The percentage of classes with more than 50 students was

collected from the US News and World Report college rankings. The percentage of classes with less

than 20 students was collected from the US News and World Report college rankings. The amount

of instate tuition was collected from the US News and World Report college rankings. The percent

of black students and percent of Hispanic students was collected from collegedata.com. The average

GPA of incoming freshmen was found at collegedata.com. Whether or not a campus is dry or not

was determined from the US News and World Report college rankings. Whether or not a campus is

urban or not was determined from the US News and World Report college rankings. Note: All data

from the US News and World Report college rankings comes from 2014.

19

V. Econometric Results (Model 1)

This empirical study has taken data from 250 randomly selected public colleges and

universities using a random number generator. In addition, the observations that did not have

sufficient data were removed from the study leaving a total of 199. The data uses cross sectional data

of colleges and universities throughout the United States from the year 2014. The results of various

diagnostic tests for the first Ordinary Least Squares regression model can be seen below. The

descriptive statistics for the first model is broken up into two sections for clarity. Table 2a displays

the dependent variable (4 year Graduation Rate) as well as other independent variables that

characterize each institution. The descriptive statistics show that the mean percentage of the four

year graduation rate at all colleges and universities is 32.94. This is interesting because on average

less than half of students who enroll in college graduate in four years. The data implies that on

average 78% of freshmen returned (Retention Rate) to the institution they enrolled in after

completing their first year. Average financial aid awarded was $7,168 but it ranged from $2,595 to

$22,135. Percent of Greek Female and Greek Male both have very high maximums with 70% for

female and 45% for male. The number of students also varies drastically. The average number of

students is 15,935 and ranges from 1,234 students to 47,093.

Table 2a. Descriptive Statistics

Variable Observations Mean Std. Dev. Min Max

4 Year Graduation Rate

199 32.94 18.38 3 87

Freshmen Retention Rate

199 77.85 10.35 48 97

Average Federal Financial Aid

199 7168.84 2952.53 2595 22135

Acceptance Rate 199 68.43

17.97 16 100

Percent of Males

199 46.33 6.82 28 89

Percent of Greek Females

199 11.55 10.66 0 70

Percent of Greek Males

199 9.40 7.94 0 45

Number of Students

199

15935.82 9909.03 1234 47093

20

The descriptive statistics are continued below and can be seen in Table 2b. The results

indicate that the class size under 20 variable has a mean of 41.56% and varies from 16.7% to 77.5%.

36% of institutions are considered a dry campus meaning that alcohol is banned at that institution.

The average GPA for incoming freshmen is 3.41 and ranges from 2.48 to 4.59. In-state tuition has

an average of $9,351.33 and it varies from $4,892 to $18,192. The results also display that almost half

of the colleges and universities are considered to be in an urban area. On average 7.82% of students

are Hispanic/Latino.

Table 2b. Descriptive Statistics

Table 4 displays the regression results for the first econometric model (OLS Linear

Specification). The results indicate that there are six statistically significant variables at the 1% level.

The retention rate of freshmen has a positive impact on the four year graduation rate and is

significant at the 1% level (t = 7.56 > tc = 2.347). When controlling for all other variables, a 1%

increase in retention rate results in a .9765% increase in the four year graduation rate. Average

amount of federal financial aid awarded has a positive effect on the four year graduation rate and is

statistically significant at the 1% level (t = 2.39 > tc = 2.347). A 1% increase in average aid results in

a .0007% increase in the four year graduation rate. Class sizes under twenty students has a positive

impact on the four year graduation rate and is statistically significant at the 1% level (t = 2.47 > tc =

2.347). When holding true to the theory, a 1% increase in class size under twenty will result in a

.202% increase in the four year graduation rate.

Variable Observations Mean Std. Dev. Min Max

Class Size Over 50 199 10.92 8.29 .1 26.1

Class Size Under 20

199 41.56 10.87 16.7 77.5

In State Tuition

199 9351.33 2741.45 4892 18192

Average GPA for Incoming Freshmen

199 3.41 .32 2.48 4.59

Dry Campus

199 .37 .48 0 1

Urban

199 .50 .50 0 1

Percent of Black Students

199 14.36 21.84 .7 95.9

Percent of Hispanic Students

199 7.82 7.67 .4 55.7

21

In-state tuition has a positive impact on the four year graduation rate and is statistically

significant at the 1% level (t = 4.13 > tc = 2.347). When controlling for all other variables, a 1%

increase in tuition results in a .0013% increase in the four year graduation rate. Whether or not a

college or university is in a city or not has a negative impact on the four year graduation rate and is

statistically significant at the 1% level (t = -2.95 > tc = 2.603). Ceteris Paribus, when an institution is

located in a city the four year graduation rate decreases by 4.170%. The average grade point average

of incoming freshmen has a positive impact on the four year graduation rate and is statistically

significant at the 1% level (t = 3.02 > tc = 2.346) . When holding all else constant, a one point

increase in GPA increases the four year graduation rate by 11.125%.

The regression results also indicate that there are two variables that are statistically

significant at the 5% level. The percentage of males at each institution has a negative impact on the

four year graduation rate and is statistically significant at the 5% level (t= -1.98 > tc = 1.653). When

controlling for all other variables, a 1% increase in males results in a .250% decrease in the four year

graduation rate. The percentage of Hispanic/Latino students has a negative impact on the four year

graduation rate and is statistically significant at the 5% level (t = -1.90 > tc = 1.653).

Results from this study show that the remaining seven variables are not statistically

significant. The acceptance rate, number of students, and class sizes over 50 are not statistically

significant. Interestingly, the dummy variable for whether not a school is a dry campus or not is not

significant. The results indicate that schools who ban alcohol on their campuses do not suffer from a

lower four year graduation rate. One would believe that banning alcohol would give students less

access to it and they could focus more on their studies. Another surprising finding is that the

percentages of both Greek males and Greek females are not statistically significant. As mentioned

above in the literature review, this could likely be because students who engage themselves in Greek

organizations are more outgoing and make better use of their resources to perform well in school.

Lastly, with this specification of model 1, the percentage of black students is not statistically

significant but the percentage of Hispanic students is. More thought and consideration should be

used in future research because many studies before have concluded that black students are less

likely to graduate in four years.

22

The R squared for the first econometric model is .828. This means that the variables

included in the model account for 82% of the variation in the dependent variable. The remaining

18% of the variation is captured by the error term. Table 3 which can be seen below presents the

coefficients of each variable as well as the constant, the standard error of each variable, the t-score,

and the p-value of all the variables in the model. The p-value was adjusted for one tailed tests with

expected signs. After running the regression there were no false predictions of statistically significant

variables. And of the eight variables that were statistically significant, only urban was run as a two

tailed test.

23

Table 3. Regression Analysis Results

4 Year Graduation Rate

Coefficient Standard Error

t-score P> |t|

Freshman Retention Rates

.9765348 .1291678 7.56 0.000***

Average Federal Financial Aid

.0007577 .0003174 2.39 0.009***

Acceptance Rate

.0071728 .0539521 0.13 0.894

Percent of Males

-.2498279 .1259791 -1.98 0.012**

Percent of Greek Females

-.1270546 .1598857 -0.79 0.428

Percent of Greek Males

.3236023 .2172887 1.49 0.139

Number of Students -2.27e-06 .0001186 -0.02 0.985

Class Size Over 50

.0545146 .1828305 0.30 0.766

Class Size Under 20

.201813 .0815828 2.47 0.007***

In-State Tuition

.0013358 .0003232 4.13 0.000***

Dry Campus

-2.4678 1.648698 -1.50 0.137

Urban

-4.169987 1.412457 -2.95 0.004***

Percent of Black

Students

-.0058895 .0541295 -0.11 0.914

Percent of Hispanic Students

-.2049693 .1080781 -1.90 0.030**

Average GPA for Incoming Freshmen

11.12585 3.683805 3.02 0.001***

N=199; R2=.8275; Adj. R2=.8090;***=significant at 1%; **=significant at 5%; *=significant at 10%

24

In order to test whether or not there are omitted variables, the Ramsey RESET test was run

in STATA. The p-value from the test was .0006. The results indicate that the null hypothesis should

be rejected, which states that the model has no omitted variables, in favor of the alternative that the

model does have possible missing variables at the 1% level. It is likely that the model suffers from

endogeneity causing biased coefficient estimates. This is expected because it is likely that some of

the data that impacts the four year graduation rate is unobtainable. The second model will address

these specification issues and correct them. Possible omitted variables that were not found are

percent of students who transferred, SAT scores or ACT scores, and number of repeated classes.

These variables are considered private information in most cases and are not easily accessible by the

public.

Next, a diagnostic test was run in order to validate classical assumption VI which states that

no explanatory variable is a perfect linear function of any other explanatory variables. If this

assumption is violated the regression suffers from multicollinearity. In order to check for this the

variance inflation factors is generated from the data. This can be seen in Table 4. The results indicate

that Greek Female and Greek Male suffer from sever multicollinearity (VIF > 5). The VIFs for the

Greek variables are high but are likely collinear with each other. However, overall the average VIF is

2.92 which suggests that the model does not suffer from multicollinearity.

25

Table 4. Test for Multicollinearity

Variable VIF 1/VIF

Greekfemalei 7.15 0.139814

Greekmalei 7.13 0.140188

Retentionrti 4.16 0.240549

Avggpai 3.43 0.291459

classsiz~50i 3.33 0.300549

Studentsi 2.76 0.362237

Blackrti 2.71 0.369001

Acceptancei 2.17 0.461629

Averageaidi 2.11 0.474588

Tuitioni 1.76 0.566936

Classsiz~20i 1.72 0.581239

Malei 1.50 0.666393

Drycampusi 1.42 0.704696

Hispanicrti 1.29 0.776771

Urbani 1.17 0.856977

Mean VIF | 2.92

This study also ran a diagnostic test to validate classical assumption V which states that the

observations of the error term are drawn from a distribution that has a constant variance. The

violation of this classical assumption is heteroscedasticity. In order to test the model to see if it

suffers from heteroscedasticity the Breusch-Pagan / Cook-Weisberg test was run. The results for

this test show that there is a chi squared value of 1.00 and the p-value is 0.3176. A model suffers

from heteroscedasticity when the null hypothesis is rejected. (H0: constant variance). Since the p-

value is not statistically significant at the 5% level, it can be concluded that the model does not suffer

from heteroscedasticity and nothing should be done about fixing it

26

VI. Econometric Results (Model 2)

After running the first regression model, there are some specification issues that must be

addressed. In order to fix this problem a quadratic variable (retention rate squared) is added to the

regression. This addition can be seen and interpreted below in the new results. This new model also

has three new variables added to capture location more closely. Two dummy variables are included

that represent whether a college or university is located in a rural or suburban setting. To avoid

collinearity, suburban is omitted from the model. The amount of students who live on campus is

also captured in the new model. Below in table 5 the new variables are defined and the expected sign

is given as well as the hypothesis tests. These variables were collected from the U.S. News and

World Report College Rankings.

Model 2:

4yearGradRti = ßo + ß1RetentionRti + ß2AverageAidi + ß3AcceptanceRti + ß4malei + ß5GreekFemalei +

ß6GreekMalei + + ß7Studentsi + ß8ClassSizeover50i + ß19tuitioni + ß10Blacki + ß11AvgGpai + ß12

DryCampusi + ß13Hispanici+ ß14Urbani +ß15Rurali+ ß16OnCampusi + ß17RetentionRtSquared +ei

Table 5. New Variables defined and Expected Signs

Variable Name Definition Expected

Sign

Hypothesis Test

Rurali Dummy= 1 if university i is rural _ Ho: ß15 ≥ 0

Ha: ß15 < 0

OnCampusi % of students who live in campus owned

housing at each university i

+ Ho: ß176 ≤ 0

Ha: ß16 > 0

RetentionRtSquaredi The freshman retention rate for each

university I measured in %

+ Ho: ß17 ≤ 0

Ha: ß17 > 0

27

The descriptive statistics for the new variables can be seen below in table 6. The descriptive

summary shows that only 22% of the colleges and universities included in the study are in a rural

setting. The results also show that the average percentage of students who live on campus is 32.03

and ranges from 4% to 100%. The freshmen retention rate squared has a mean of 6,167.54 and

varies from 2,304 to 9,409. It is worth noting that the observations are different for the three

variables because some colleges and universities did not record this data.

Table 6. Descriptive Statistics

Table 7 displays the regression results for the second econometric model (OLS Non-linear

Specification). The results indicate that there are seven variables that are statistically significant at the

1% level. The retention rate of freshmen has a negative impact on the four year graduation rate and

is significant at the 1% level. (t=-4.01 > tc=2.603) When controlling for all other variables, a 1%

increase in retention rate results in a 3.66% decrease in the four year graduation rate. The retention

rate of freshmen squared has a positive impact on the four year graduation rate and is also

statistically significant at the 1% level. (t=-4.80 > tc=2.603) This means that retention rate has a

negative impact at an increasing rate. So a 1% increase in freshmen returning goes down by 3.66%

but the change in four year graduation rate increases the higher the retention rate goes up.

Variable Observations Mean Std. Dev. Min Max

Rurali 199 .22 .42 0 1

OnCampusi 189 32.03 15.45 4 100

RetentionRtSquaredi 199 6167.54 1598.92 2304 9409

28

The percentage of males at each institution has a negative impact on the four year graduation

rate and is statistically significant at the 1% level. (t=-3.27 > tc=2.603) When holding all else

constant, a 1% increase in males results in a .39% decrease in the four year graduation rate. The

percentage of black students has a negative impact on the four year graduation rate and is statistically

significant at the 1% level. (t=-3.27 > tc=2.603). When holding true to the theory, a 1% increase in

black students results in a .13% decrease in the four year graduation rate. The percentage of students

who live in campus owned housing has a positive effect on the four year graduation rate and is

statistically significant at the 1% level. Ceteris Paribus, a 1% increase the amount of students who

live on campus will result in a .36% increase in the four year graduation rate.

In-state tuition has a positive impact on the four year graduation rate and is statistically

significant at the 1% level (t=2.94 > tc=2.603). When controlling for all other variables, a one dollar

increase in tuition yields a .0007% increase in the four year graduation rate. The magnitude of this

coefficient is very small when using a one dollar increase so instead it will be interpreted as a $1,000

increase will result in a .07% increase in the four year graduation rate. Lastly, the results show that

there is one statistically significant variable at the 5% level. Average financial aid awarded has a

positive impact on the four year graduation rate and is statistically significant at the 5% level (t=1.68

> tc=1.65). Holding all else constant, a one dollar increase in the amount of financial aid rewarded

results in a .0005% increase in the four year graduation rate. This magnitude is very small but when

looking at a $1,000 increase, the four year graduation rate goes up by .05%.

29

Model 1 and model 2 have some similarities and differences. After adding a quadratic

variable (RetentionRtSquaredi) the R2 went up from .827 to .887. The model also no longer suffered

from omitted variables and wrong specification which can be seen later in this section. After running

both regressions some variables became insignificant and others became significant. In the second

model the acceptance rate is insignificant but was actually came out to be significant but the wrong

sign was predicted. The percentage of males became more significant with the second regression and

went from being significant at the 5% level to the 1% level. Whether or not the school is urban,

percentage of Hispanic students and average GPA variables in the second model are no longer

significant. Interestingly, no location variables for universities are statistically significant with the

second model specification. Class size under 20 was no longer significant and it was removed from

model 2. The percentage of black students is now significant at the 1% level. The new addition of

the on campus variable is statistically significant and the new quadratic variable is significant as

expected.

The R Squared for the second econometric model is .887. This means that the variables

included in the model account for 88% of the variation in the dependent variable. The remaining

12% of the variation is captured by the error term. Table X which can be seen below presents the

coefficients of each variable as well as the standard error of each variable, the t-score, and the p-

value of the variables in the model. The p-value was adjusted for one tailed tests with expected signs.

After running the regression there were two false predictions of statistically significant variables. The

acceptance rate was expected to be negatively correlated with the four year graduation rate but after

running the regression the results show that there is a positive relationship. Since there was an

expected sign this variable is no longer significant. Of the seven variables that were statistically

significant, urban, in-state tuition and retention rate were run as two tailed tests.

30

Table 7. Regression Results (Model 2)

N=199; R2=0.8870; ***=Significant at 1%; **=Significant at 5%; *=Significant at 10%

4 Year Graduation Rate Coefficient. Standard

Error

t-score P > |t|

Freshmen Retention Rate -3.662409 .9137987 -4.01 0.000***

Average Federal Financial

Aid

.0005052 .0003 1.68 0.047**

Acceptance Rate .0864887 .0424997 2.04 0.044

Percent of Males -.3880614 .1187071 -3.27 0.000***

Percent of Greek Females -.0781902 .1172953 -0.67 0.506

Percent of Greek Males .2043781 .1607511 1.27 0.206

Number Students .0001848 .0001405 1.32 0.191

Class Size Over 50 -.1194083 .1520181 -0.79 0.434

IN-State Tuition .0007582 .0002577 2.94 0.002***

Dry Campus -1.352598 1.433539 -0.94 0.347

Percent of Black Students -.1325252 .0405477 -3.27 0.000***

Percent of Hispanic

Students

-.0755261 .0782207 -0.97 0.336

Urban .2836976 1.49198 0.19 0.849

Average GPA for

Incoming Freshmen

3.113846 3.409551 0.91 0.363

Rural -1.81776 1.525506 -1.19 0.236

Percent on Campus .3571294 .058665 6.09 0.000***

Freshmen Retention Rate

Squared

.0306 .0063707 4.80 0.000***

31

In order to test whether or not there are omitted variables and the specification is correct,

the Ramsey RESET test was again run in STATA. The p-value from the test was 0.2264. The results

indicate that the model now does not suffer from omitted variable bias.

Next, the variance inflation factors test was run in order to check for perfect collinearity

amongst independent variables. These results can be seen below in table 8. The results indicate that

Greek male and Greek female still are perfectly collinear with one another. The results also show

that Retention rate and Retention rate squared are perfectly linear. This is expected because both

variables are needed in order to see the level of impact the freshmen retention rate has on the four

year graduation rate.

32

Table 8. Test for Multicollinearity

Variable VIF 1/VIF

rentention~d 311.45 0.003211

retentionrti 272.45 0.003670

greekfemale 7.62 0.131273

greekmalei 7.57 0.132101

studentsi 3.87 0.258220

avggpa 3.69 0.270833

classsiz~50i 2.90 0.344423

blacki 2.74 0.364840

acceptance~i 2.60 0.384497

urbani 2.51 0.398918

oncampus 2.31 0.432524

suburban 2.28 0.437890

averageaidi 2.22 0.449643

tuitioni 1.96 0.509764

malei 1.60 0.624032

drycampusi 1.39 0.720451

hispanici 1.36 0.735669

Mean VIF | 37.09

Lastly, the Breusch-Pagan / Cook-Weisburg test was run to check for heteroscedasticity.

The results for the test show that there is a chi squared value of 5.49 and the p-value is 0.0192. A

model suffers from heteroscedasticity when the null hypothesis is rejected. (Ho: constant variance)

Since the p-value is statistically significant at the 10% level, it can be concluded that the model does

suffer from heteroscedasticity. In order to fix this, the STATA command Robust is entered. This

corrects for the heteroscedasticity.

33

VII. Conclusion

Students and their parents have to pay large sums of money in order to go to college and

they are left often times with an enormous amount of debt afterwards. For this reason, it is vital

that a student completes his or her degree in order to pursue a career path and pay off this debt.

The purpose of this study was to shed light on what factors cause such large variation in the four

year graduation rate at public universities and how this number can be improved. This paper

used Ordinary Least Squares with two models to show both a linear relationship and nonlinear

relationship. The purpose of the first model was to look at a linear relationship between student

characteristics and the four year graduation rate. The second model was generated to show a

nonlinear relationship with a quadratic variable. The second model also broke down location

variables to observe them more closely. The data used for research was collected from the U.S.

news college rankings website and a total of 200 public colleges and universities were randomly

selected from 2014. Important explanatory variables that were predicted to explain the variation

in the four year graduation rate were; percent male, average federal financial aid awarded,

retention rates of freshmen, and the percent of black and Hispanic students.

The results from model 1 of this study suggest that the retention rate of freshmen has a

positive impact on the four year graduation rate. The average amount of federal financial aid

awarded to students also has a positive effect and explains some of the variation in the

dependent variable. Both Class sizes under twenty students and in-state tuition have a positive

impact on the four year graduation rate. The average grade point average of incoming freshmen

has a positive impact on the four year graduation rate. Whether or not a university is located in a

city or urban setting has a negative effect on the four year graduation rate. The percentage of

males at each university negatively affects the dependent variable. The percentage of Hispanics

also negatively affect the dependent variable. The acceptance rate, number of total

undergraduate students, and class sizes over 50 students are not statically significant.

Interestingly, the dummy variable for whether or not a school is a dry campus or not is not

statistically significant. Another surprising finding is that the percentages of both Greek Males

and Greek females are not statistically significant. Lastly, the percentage of black students is not

statistically significant in model 1.

34

The results from model 2 suggest very different results from model 1. Model 2 used a

quadratic variable, which was the freshmen retention rate squared, in the regression. The new

results indicated that the freshmen retention rate had a negative impact on the four year

graduation rate at an increasing rate. The more students that return to the institution the larger

the level of impact occurs on the four year graduation rate. This is likely because more students

returning means there are still lower quality students at the institution and as they continue their

college career only the higher quality students will be able to complete upper level courses and

meet graduation requirements. This also might indicate that the freshmen year course load at

colleges and universities with higher retention rates might be easier.

Other significant variables that negatively affect the variation in the four year graduation rate

in model 2 are percent of males and the percent of black students. The percentage of students

who live on campus is statistically significant and has a positive effect on the dependent variable.

In-state tuition and the amount of financial aid awarded are both statically significant and

positively affect the dependent variable but at a very small magnitude. Other variables that are

significant in model 1 but not model 2 are; Whether or not the school is urban, percentage of

Hispanic students and average GPA variables in the second model are no longer significant.

These results are contradicting to one another and given more time for this study this would be

further addressed. Different estimation techniques should be considered when specifying the

model. It would be interesting to look at probit and logit regressions

Perhaps one of the biggest shortcomings of looking at graduation rates is that they are not

entirely accurate. According to Bryan Cook, Director for Center of Policy Analysis, American

Council of Education, graduation rates are calculated without accounting for mid-year enrollment,

part time college students and students who transfer one institution to another. Controlling for these

variables in this study would have likely yielded better results. Studies suggest that students who

transfer from one university to another often do not graduate on time. Policy implications have been

proposed by the Obama Administration to require state governments to create education databases

to track student behavior from kindergarten to college. These databases could collect information

and make it possible for state governments to follow students when moving out of state. Improving

the accuracy of graduation rates will provide a better understanding of them and how to improve

them. For future research, investigating individual students instead of institutions would likely yield

better results to the probability of graduating on time within four years.

35

VIII. Bibliography

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Campos, Paul F. "The Real Reason College Tuition Costs So Much." The New York Times. April

04, 2015. Accessed May 03, 2016. http://www.nytimes.com/2015/04/05/opinion/sunday/the-real-

reason-college-tuition-costs-so-much.html?_r=0.

"Charts by Topic: Students." U.S. Bureau of Labor Statistics. October 26, 2015. Accessed May

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Cook, Bryan, and Terry Hartle. "Why Graduation Rates Matter-and Why They Don't." Why

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Cole, Marine. "10 Public Universities with the Worst Graduation Rates." The Fiscal Times. May 6,

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"CollegeBoard." FOUR-YEAR GRADUATION RATES FOR FOUR-YEAR COLLEGES,

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four-year-colleges.pdf.

"COLLEGEdata: College Search, Financial Aid, College Application, College Scholarship,

Student Loan, FAFSA, Common Application." COLLEGEdata. 2016. Accessed May 02, 2016.

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DeSilver, Drew. "5 Facts about Today's College Graduates." Pew Research Center RSS. May 30,

2014. Accessed May 03, 2016. http://www.pewresearch.org/fact-tank/2014/05/30/5-facts-about-

todays-college-graduates/.

Diette, Timothy M., and Manu Raghav. "Class Size Matters: Heterogeneous Effects of Larger

Classes on College Student Learning." Eastern Economic Journal Eastern Econ J 41, no. 2

(2014): 273-83.

Gloecker, Geoff. "Fewer Out-of-state College Students." Msnbc.com. May 26, 2009. Accessed

May 02, 2016. http://www.nbcnews.com/id/30870925/ns/business-us_business/t/fewer-out-of-

state-college-students/#.VrvykfkrLIU.

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Goenner, Cullen F., and Sean M. Snaith. 2004. “Accounting for Model Uncertainty in the

Prediction of University Graduation Rates”. Research in Higher Education 45 (1). Springer: 25–

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Grubb, Farley. 2006. “Does Going Greek Impair Undergraduate Academic Performance? A Case

Study”. The American Journal of Economics and Sociology 65 (5).

"The Condition of Education - Postsecondary Education - Completions - Institutional Retention

and Graduation Rates for Undergraduate Students - Indicator May (2015)." The Condition of

Education - Postsecondary Education - Completions - Institutional Retention and Graduation

Rates for Undergraduate Students - Indicator May (2015). May 2015. Accessed May 02, 2016.

http://nces.ed.gov/programs/coe/indicator_cva.asp.

Xueyu, Cheng, Sontachai Suwanakul, and Wu Ruohan. "Determinants of Graduation Rates of

Historically Black Colleges and Universities." Journal of Economics & Economic Education

Research 16, no. 2 (May 2015): 51-60.

Walker, Jay K., Nathan D. Martin, and Andrew Hussey. 2015. "Greek Organization Membership

and Collegiate Outcomes at an Elite, Private University." Research In Higher Education 56, no.

3: 203-227.

37

XI. Appendix A: Data Set

38

39

40

41

42

43

44

45

46

Appendix B: STATA Outputs

Model 1 Results:

Ramsey RESET Test:

47

Heteroscedasticity:

Variance Inflation Factor:

48

Model 2 Results:

Model 2 after Robust:

49

Ramsey RESET Test:

Heteroscedasticity:

Variance Inflation Factors: