An Analysis of Student Loan Defaults

Michael Gehm

St. Norbert College

Abstract

Student loan defaults have been coming down in recent years, but there is still an issue when it comes those who do default on loans. There are three main types of institution in which a college graduate may attend a higher level of education: public universities, private not-for-profit colleges, and finally proprietary or for-profit. All of these institutions have experiences

drops in student loan default over the past five years credited to President Obama’s income based repayment plans. Using a sample of data obtained

from the Institution for Education, I test which types of schools have a higher chance of defaulting. My results indicate that if the school has a

graduate program they are less likely to have high student default rates, that private schools tend to default much less than public universities, and finally that for-profit schools have a higher chance of defaulting on student

loans than both public and private institutions.

Note: In the paper when I refer to private colleges, I am referring to private not-for-profit as opposed to private proprietary schools. Often, I refer to

proprietary schools as for-profit institutions.

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I. Introduction

One of the biggest choices a student makes in their life is what college

they go to. This choice will ultimately affect what they do in their life, who

they meet, and what they choose to major in. However, college institutions

keep rising in price as time goes on and if the student makes the wrong

choices, they may find themselves defaulting on their student loans. There

are several things that could happen when a default occurs: the IRS may

start withholding any tax refund to pay off the loan, the U.S. Government

may start garnishing the borrower’s paycheck, federal benefits may be

withheld, or they could just sue you. Going further, in most cases, the

borrower still has to pay off student loans after filing for bankruptcy unless

they can prove undue hardship that the loan would cost. This seems harsh

as most of the time, student loans are one of the biggest loans taken out in

the borrower’s name.

It is important to distinguish the different types of colleges when

addressing the issue of student loan defaults. When most people say they

are going to college, they are referring to one of three types: public

university, private university, or a proprietary college. A public university is

a college that is subsidized through taxes or other government funding.

These include popular institutions such as UW-Madison, UW-La Crosse, etc.

These colleges tend to have the lowest rates and so appeal to the mass

public. The next type of college is a private university. Private Universities

do not receive government money and are funding through donations and

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tuition collected from students. These colleges have different types that

include Liberal Arts Colleges, Fine Arts Colleges, and may be affiliated with

specific religious denominations. For example, St. Norbert College is a

Liberal Arts College that has an identity of a Norbertine College, which

stems from Catholicism. The final college that was mentioned was the

proprietary college or for-profit. These colleges are owned by private, profit

seeking businesses and try to profit off of post-secondary education.

Proprietary colleges tend to have the highest student default rate and

usually are more expensive than a comparable public school that would

offer the same degree.

These different institutions are distinctly different in some way that

leads us to question: how do these schools compare when looking at the

student loan default rate? Many parents encourage their children to obtain

the higher average earning the power that one can have with a college

degree of some sort. However, the degree is only helpful if the student is

able to manage the debt that they take on from the college they choose to

attend. Using statistical analysis on a random sample of schools, I try to

clarify which type of schools have the lowest default rate using a variety of

macroeconomic variables that pertain to the student loan default rates. In

addition to that, I also address the question: do colleges with graduate

programs tend to default more or less than colleges that only offer

undergraduate courses?

II. Literature Review

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There is literature that suggests that type of college institution

(public, private not-for-profit, and proprietary) does not matter and looks

more at the background of the students who default on student loans.

Research by Volkwein, Szelest, Cabrera, and Napierski-Prancl (1998) find

evidence to support that background information affects the amount of

student default rates. This study looked at a number of factors impacting

student loan rates, but finds that for-profit colleges tend to have a default

rate that is not much higher than accredited two year institutions. Using

micro level data, the research suggests that the gain in earnings from

attending institutions actually tends to “offset” the additional debt taken on.

More important, the authors find that other factors, such as married or

single, dependent children or not, and completion of degree are important

to whether the student will default on their loans or not. There is also

support that college GPA is a good indicator of student default rates, but

completion of degree is more important than the grades earned. These two

variables are tied together in the fact that a student who has a lower GPA is

less likely to complete his/her degree and is therefore less likely get

increased earnings for debt taken on. Overall, the authors find less support

for institution type and more support for background factors.

However, recent findings also indicate that employers may not prefer

for-profit graduates more than high school graduates or other associate

degree holders. Darolia, Koedel, Martorell, Wilson, and Perez-Arce (2014)

sent out 9000 fake resumes to employers looking to hire workers. The

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authors sent resumes in three categories: high school graduates, college

coursework but no formal credential, a non-academic vocation degree, or an

associate degree either from a community college or a for -profit college.

These resumes were posted in seven major U.S. cities. Results from this

experiment indicate that employers show no preference to for-profit

colleges against community colleges despite the higher tuition at for-profit

colleges. This could be one explanation to account for the fact that default

rates at for-profit colleges are much higher than community colleges. When

the students have to pay a much higher tuition than a community college

and are not able to find a job that uses their new degree to produce higher

income, the default rate will intuitively be higher.

In a more recent study, new empirical evidence offers similar findings.

Findings by Yannelis and Looney (2015) show that there may be a shift in

the borrowers who default on loans. Yannelis and Looney suggest that there

is a “non-traditional borrower” that comes from lower income families,

attended less successful schools, and may not be employed once they are

done with school. Specifically, these borrowers tend to attend for-profit

universities that also tend to be much more expensive than traditional

public universities. A student that does not have better job opportunities out

of school will have a more difficult time paying off large loans that college

may require leading to more defaults. Using a decomposition model,

Yannelis and Looney (2015) show that indeed a higher number of borrowers

are attending for-profit schools thus increasing the number loan defaults.

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Similar to the study done by Volkwein et. al. (2015), the shift in increased

student default loans show that it is the “non-traditional borrowers” who

default while the “traditional borrowers” seem to be defaulting at around

the same amount as before the recession. Combining the result of this

empirical study with the study conducted by Darolia, Koedel, Martorell,

Wilson, and Perez-Arce offers support for the same conclusion that for-profit

colleges do not necessarily lead to better job opportunities despite higher

tuition regarding for-profit colleges.

This paper does a very good job of identifying that most of the loan

defaults are coming from for-profit schools; however they leave out an

important variable – the private schools. I believe that since private schools

have a higher tuition rate on average than a public school that they also

need to be looked at for a higher possible default rate. To be exact, private

not-for-profit colleges had an average tuition of $39,173 while public

universities had an average tuition of $15,022 for the 2012-2013 school

year (via nces.ed.gov/fastfacts). These private institutions do tend to offer

more scholarships and discounts to students, which is why looking at tuition

may be not be the most accurate measure that there is to determine student

default rates. For this, I suggest looking at average debt for different types

of institutions to account for scholarships and monetary gifts given by

foundations or private schools. This is a large difference and actually

surpasses the amount that for-profit schools cost ($23,158). The two

previous literatures that suggest that the rate is more closely related to

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demographics use micro level data to identify issues and one suggests that

in fact for-profit colleges may not be hired any more than someone with an

associate’s degree who attended a community college. The question I want

to look at is macro level trends at all indicators of student loan default. For

example, Yannelis and Looney (2015) were able to look and individual

borrowers and identify family income, age, dropout, etc. This is good for

identifying risk in individual borrowers, but looking that the whole

institution of student defaults requires more macro level data such as

average income per capita and how that changes in that may be impacting

the overall change in student default loans.

III. Model

For my model, I feel that there are a few characteristics that would

help explain student loan defaults with these cohort rates. So I believe that:

StudentLoanDefaults = f (Student Debt, Income, Unemployment, For-profit,

Graduate, Private)

Clearly an increase in tuition should have a positive impact on student

loan defaults. The higher the tuition is in each institution, in theory the

higher the expected student loan default rate will be. Each year, college

tuition increases should induce a higher number of student loans into the

population, including some that will not be repaid. However, college tuition

is not necessarily the best indicator as to what students have to repay. So I

have chosen to use student debt coming out of college and this is reflected

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by institution lagged one year as the students would not enter repayment

until the following fiscal year. For instance, a graduate may graduate in

May and they will enter repayment in November. However, under the

Institute of Education’s fiscal year, this falls in the next year as their fiscal

year ends in September.

Income should be negatively associated with student loan defaults. As

average income after college rises, the amount of defaults should go down.

If the students cannot find higher paying jobs after college, it can be

assumed that this would cause an increase in the amount of defaults.

Unemployment should be positively associated with student loan defaults as

well. If there is a higher unemployment rate at any given time, students will

not be able to find the necessary jobs to pay off loans and thus will have a

higher rate of defaulting on their loans. With a lower unemployment rate,

we would expect to see fewer defaults on loans.

My next variables in the model are dummy variables and have to do

with institution type. Previous research looked at for-profit, graduate, and

two year schools as dummy variables (Yannelis & Looney, 2015). I plan to

use all of these as well and am looking to see if there is a statistical

difference between the for-profit schools and not-for-profit schools (both

public and private), looking to see if there is a difference between schools

that offer a graduate program as opposed to schools that do not offer any

graduate program, and finally looking for a difference in student default

rates between public and private institutions (both not-for-profit). These

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new variables will help rank which types of institutions default the most and

which default the least based on the sample used. The for-profit dummy

variable should be positively correlated with student default rates. These

are often some of the highest tuition rates and based on previous work by

Yannelis and Looney (2015), I would expect the “non-traditional” borrowers

to default more than the “traditional” borrowers. Public universities are

typically the least expensive and have traditional borrowers, so a’priori I

expect that private schools will end up having a slightly higher default rate

than public schools. This means that private schools will be positively

correlated with student loan default rates. Graduate schools are the most

expensive; however the increase in earnings by going to these schools

should offset the increased debt taken on by the student. So I expect this to

have a negative relationship with student default rates. In addition to

running this regression on fiscal year data, I will also be running it on year

to year changes to see if there is a change over the years that may indicate

a shift in student defaults. I found the yearly change percentage for each of

my quantitative data sets (student default rates, income, unemployment,

and student debt) and ran more regressions to see if there was a change in

time for the significance of the variables. I expect that over time, the income

variable will become more significant due to the surge of borrowers using

President Obama’s income based repayment plan that would result in less

defaults. I split up the data into three panels: FY2010 - FY2011 changes,

FY2011 - FY2012 changes, as well as a cumulative change from FY2010 –

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FY2012. I will be using OLS to model this relationship. These will be

reflected in a regression that uses the same model but in a separate table.

The finished models look like:

Student Loan Defaultsi = Ci + ẞ1 (StdentDebti) -ẞ2 (Incomei) +ẞ3

(Unemploymenti) +ẞ4 (For-Profiti)

- ẞ5 (Graduatei) + ẞ6 (Privatei) + ei

and

Student Loan Defaults % Changei = Ci + Α1(StudentDebt%Changei) – Α2

(Income%Changei)

+ Α3 (Unemployment%Change) + ei

IV. Data

Previous studies have looked at micro level default rates with access

to the National Student Loan Data System where there is individual

information on each borrower. This would have been the ideal data set to be

able to look at institution level data for what types of colleges are getting

more loans and exactly how much each investor is borrowing in each case.

However, due to limitations in the data that I can successfully obtain, I am

doing a different type of study than Yannelis and Looney (2015). Unlike

previous studies, this will be more of a macro study using cohort default

rate by institution and not borrower data. It will not be able to capture the

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individual borrower demographics or information but it will be able to look

at data made available by the Department of Education on three-year cohort

default rates. Ideally, I would have been able to expand the data to

encompass the complete data database as well as borrower data on how

much was borrowed from the government to help borrowers pay for

colleges.

Another hurdle that may work against my data includes the restrictive

nature of getting institution data on for-profit colleges. I had difficulty

finding any other data than the national average debt of for-profit colleges

other than the average in 2008 and 2012. The only way that I was able to

use this was to find the average change over time, and then figure out what

the average college debt would have been for for-profit colleges if the

growth rate was constant. This takes away any standard deviation and any

variability based on the individual colleges. However, I still will include for-

profit schools into my regressions to show statistical evidence that students

who attend for-profit colleges default more frequently than other borrowers.

This also helped me focus in on the dummy variables of the public and

private institutions and looking at the difference between schools with no

undergraduate program and schools that do offer a graduate program.

My sample that I am using is another issue in that it may be too short

to make any big claims. It only covers three fiscal years and overall about

five years of data. The results obtained by this will be representative of that

time, but may have trouble trying to explain any past behaviors in the

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student loan default data. Another obstacle that may impact my results is

that the table used is only a reflection of two kinds of federal loans: The

FEEL (Federal Family Education Loan) and the Direct Loans (William D.

Ford Federal Direct Loan). On the Department of Education website, they

also have a disclaimer that smaller schools may be less borrowers and

therefore may be less representative of the total default although they are

weighted the same. With those limitations in mind, this was still the best

sample that I could achieve based on the random sample that was taken and

difficulty finding complete information. The data I used for my regression

was pulled from the Institute of Education Sciences for default rates, the US

Census Bureau for per capita income, and the US Labor Bureau for

unemployment, Graduate Guide, and College-Insight for student debt.

For loan defaults, I will be looking at the three-year cohort default

rate. These are measured in the number of defaults within three years of

entering repayment for the years of 2010, 2011, and 2012. This is stored in

a data base in the Federal Student Aid website. There are over 6000

institutions in the database each provided with the number of federal loans

given out and the number defaults on these loans producing a default rate

over time for institutions. I will be taking a sample of randomly selected 50

institutions for each type (50 public schools, 50 private not-for-profit, and

50 propriety). The reason why I am using a sample is due to time

constraints. For each of the institutions that were selected, I had to find an

average student debt coming out of that institution, the unemployment rate

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in the state, the income per capita per state, as well as figure out if the

institution offered a graduate program. This took some time to compile and

would take even longer had I chosen a bigger sample. The random sample

was achieved by dividing the spread sheet into three sections, public,

private not-for-profit, and proprietary schools. Then using the total number

of each institution, I generated a random list and used only schools that had

complete data for the three years with no repeats. In addition, using

Graduate Guide, I was able find data on what schools have graduate

programs and I am able to account for these using dummy variables in my

model.

In regards to student debt, I will be using the base number from the

previous year as the last year they were in college, i.e. for FY2010, I will use

the 2009 data for tuition rates. This is because students do not start to

repay until six months after college. Assuming that the students graduated

college in May of 2009, they would not start repayment until December

2009, which will fall into the next fiscal year which is FY2010 as the fiscal

year starts on October 1st of each year. With income, I will be using the

state level data for the three years that are incorporated into the model. For

example, for FY2010, I will be using the average income per state per capita

averaged for the 2010-2012 years. This captures the entirety of the three-

year cohort default rates that I am looking at. For interest rates, I will use

the average rate for federal loans over the perceived time period that it is

over. Finally, unemployment will come from the US Labor Bureau and it will

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be by state and in each given year set (i.e. FY2010 will be an average of

2010-2012 similar to how income was done). I

manipulated the data to come up with yearly changes in the data. Table 1

shows the averages and standard deviation for student loan defaults college

debt, unemployment, and income. As seen in the

FY10 FY11 FY12 FY10 FY11 FY1215.81% 15.23% 12.89% $27,247.75 $29,961.25 $29,778.40(9.00) (8.73) (8.05) (6893.37) (18749.98) (7247.39)

13.78% 14.15% 12.79% $20,248.96 $21,302.88 $22,775.56(8.17) (8.15) (7.88) (3216.37) (3438.62) (3572.30)8.56% 9.65% 7.03% $26,149.28 $27,280.86 $28,144.64(6.21) (7.05) (7.03) (4004.07) (4020.73) (4251.94)

24.17% 20.96% 16.35% $33,837.50 $35,875.00 $37,912.50 (9.27) (8.25) (7.71) (0) (0) (0)

FY10 FY11 FY12 FY10 FY11 FY128.00% 7.10% 6.17% $38,565.10 $39,469.03 $40,199.31(1.54) (1.33) (1.10) (4369.8) (4460.91) (4474.24)7.77% 6.89% 6.05% $38,111.12 $38,985.01 $39,696.29(1.45) (1.28) (1.08) (4449.86) (4502.63) (4514.15)7.90% 7.03% 6.12% $39,074.47 $39,919.87 $40,600.50(1.38) (1.18) (0.98) (4378.60) (4445.29) (4464.82)8.36% 7.39% 6.39% $38,509.70 $39,502.19 $40,301.14(1.73) (1.49) (1.22) (4314.32) (4475.42) (4486.47)

(Std Dev)Private Colleges

(Std Dev)For Profit Colleges

(Std Dev)

Public Colleges

(Std Dev)For Profit Colleges

(Std Dev)

Average Student Loan Default Data (in Percent) Average College Debt

Total Sample(Std Dev)

Public Colleges(Std Dev)

Private Colleges

Total Sample

Table 1. Summary Statistics

Unemployment (in Percent) Income Per Capita

(Std Dev)

table, there is a sharp decrease in the amount of student loan defaults in

FY2012. Department of Education officials who first reported this credit

President Obama’s efforts to protect borrowers. These include the

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administration pushing for more income based repayment plans than a

monthly payment plan that was typically seen on student loans. We see that

unemployment and income do not vary much among institutions because

this was taken at state level data instead of institution level data. We see

that private colleges tend to have the lowest number of student loan default

rates, followed by a slight increase in public and then what seems to be

much larger at for-profit colleges. Again, the issue I run into is the lack of

standard deviation in the for-profit college debt due to the lack of available

information about these institutions. Although I will be running a regression

and interpreting the results of the dummy variable dealing with for-profit

colleges, that is not my main focus as the data is not as encompassing as I

would like. This lack of variation in the data may lead to bias in my

regression and results should be analyzed knowing that. In the sample there

are 34% public schools that have a graduate program, 56% of private not-

for-profit schools have a graduate program, and finally 4% of the for-profit

schools have graduate programs. For this reason, when I am comparing

graduate to undergraduate, I only used public and private not-for-profit to

not skew the regressions results as most for-profit programs do not have

any graduate program. I also included private schools as dummy variable

with graduate programs to see if there is a statistical difference between

public colleges and private not-for-profit institutions. By doing this, I chose

to run three separate regressions: one with the dummy variable as for-profit

schools, another with the dummy variable as graduate schools, and final

Gehm 15

regression that looks at the change rates over time for the quantitative

variables.

V. Empirical Evidence

For the first regression that I ran, I looked at the dummy variable of

for-profit colleges. These results are seen on Table 2. We can see that over

time, the for-profit dummy variable gets less and less significant (that being

said, it is still significant at the 1% level in every regression). The Adjusted

R-squared value also goes down over between FY2010 to FY2012 with

values of 0.16 in FY2010, 0.10 in FY2011, and finally 0.075 in FY2012. We

can also see that average student debt is statistically significant throughout

the model. For FY2010 and FY2011, we can see that it is significant at the

1% level and is at the 5% level of significance when looking at the FY2012

data when the dummy variable of for-profit is included. Also found to be

significant was income, in both FY2011 and FY2012 regressions that omit

the for-profit dummy variable and again in FY2012 when using the dummy

variable. Each of the models was tested for heteroskedasticity and was

found to not have heteroskedasticity (results from these tests are seen in

Appendix I). As this was not time series data but yearly data regressed

separately, we do not suspect any serial correlation (more in depth statistics

and regression diagnostic tests can be found in Appendix II, Tables i & ii).

In all three tests, we find that the models are jointly significant when using

the for-profit dummy variable, otherwise the model was not jointly

significant as seen by the high P-values in regressions (A), (C), and (E). The

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results of this test help to show that the biggest factor that I tested in

looking at

student

default rates

is clearly

whether or

not the

college is a

for-profit

college or

not-for-profit

college. In

each of the tests, we also see that student debt is clearly a major issue that

impacts student defaults rates. On average, if student debt were to increase

by $1,000.00, results indicate that the student loan default rate would

decrease by 0.669%. This may be capturing the next question that shows

public schools against private schools. This also plays into the factor that

the biggest factor in a school is whether or not the school is for-profit. For-

profit schools had the highest average of student debt when leaving school

(see Table 1), and this helps show that the more debt that an individual

takes on, the more likely the borrower is to default on that specific loan. My

regression results prove that the decision to attend a for-profit college could

in fact lead to more loans when combined with the statistical significance of

(A) (B) ( C ) (D) (E) (F) Coefficent Coefficent Coefficent Coefficent Coefficent Coefficent(P-Value) (P-Value) (P-Value) (P-Value) (P-Value) (P-Value)

17.65324** 34.15071*** 26.04734*** 38.81113*** 26.38042*** 36.13068***(0.0361) (0.0001) (0.0013) (0.0000) (0.0006) (0.0000)

-0.000231 -0.000157 -0.000304* -0.000225 -0.000341* -0.000278*(0.1772) (0.3195) (0.0617) (0.1474) (0.023) (0.0571)

0.0000929 -0.000669*** 0.0000616 -0.000536*** 0.0000303 -0.000422**(0.4295) (0.0003) (0.5675) (0.0031) (0.7472) (0.0129)

0.468374 0.062937 -0.280041 -0.631626 -0.279695 -0.531576(0.3341) (0.8891) (0.6053) (0.2272) (0.6412) (0.3657)

12.80293*** 10.36133*** 8.02604***(0.0000) (0.0001) 0.0016

Adj. R2= 0.01 Adj. R2= 0.16 Adj. R2= 0.01 Adj. R2= 0.10 Adj. R2= 0.02 Adj. R2= 0.075P(F) = 0.2935 P(F) = 0.0000 P(F) = 0.2901 P(F) = 0.0006 P(F) = 0.1545 P(F) = 0.0041

Table 2. Student Loan Default - For Profit Dummy VariableFY2010 FY2011 FY2012

*Denotes Signficant at the 10% Level**Denotes Signifcant at the 5% Level

***Denotes Significant at the 1% Level

For-Profit

Unemployment

Student Debt

Income

C

Variable

Gehm 17

the student debt. According to my regression results, the choice to attend a

for-profit college seems to increase student loan defaults by as much as

12.82% and 8.03% on the lower side. To my surprise, the unemployment

rate in the state of the college is found to be not statistically significant at

all. I would have assumed that this would have been a major factor.

However, the explanation for this could be an issue with data. I chose to use

the annual average for the state that the institution was in. This may not

reflect the amount of unemployed that are just coming out of college in each

state, but rather a reflection of overall employment conditions. The final

result that was a little shocking was that income was only statistically

significant in one case, FY2012. However, FY2012 also had the lowest

amount of student default loans. My hypothesis is that the lower the student

default rate, the more important income becomes. With President Obama

pushing for income related payment plans, this puts more emphasis on the

average income. This is a shift away from tradition federal loans that were

based on a fixed payment plan based on the amount of the loan.

Gehm 18

The second regression that I show uses the graduate program dummy

variable as opposed to the for-profit school dummy variable. The important

change in this regression is the omission of for-profit schools as data which

drops my sample size down to 100 observations. I also added in a private

school dummy variable to see if there was a statistically significant

difference between public schools and private not-for-profit schools. The

regression results are shown in Table 3. The Adjusted R-squared value is

higher with this regression than with the previous regression and is a jointly

significant model when using either or both of the dummy variables in the

regression. Again with this model, we can see that there is no sign of serial

correlation as reported by the Durbin-Watson statistic (see Appendix II,

Tables iii – v for more detailed results on this regression). Testing this

model for heteroskedasticity, we find that in regression (I) was the lone

model that exhibited signs of this after running the White test and was

corrected for (results from this test are shown in Appendix I). There are

(G) (H) ( I ) (J) (K) (L) (M) (N) (O) (P) (Q) (R)Coefficent Coefficent Coefficent Coefficent Coefficent Coefficent Coefficent Coefficent Coefficent Coefficent Coefficent Coefficent(P-Value) (P-Value) (P-Value) P-Value P-Value (P-Value) (P-Value) P-Value P-Value (P-Value) (P-Value) P-Value

32.51324*** 35.10419*** 21.48563*** 25.49395*** 32.30915*** 34.81162*** 21.17181** 24.99742*** 29.74199*** 30.84141*** 22.31197** 24.25899***(0.0005) (0.0007) (0.0193) (0.0035) (0.0013) (0.0003) (0.0301) (0.0077) (0.0022) (0.0009) (0.0180) (0.0075)

-0.000228 -0.000326 -0.00021 -0.000299* -0.000228 -0.000332* -0.000247 -0.000333* -0.00019 -0.000285 -0.000207 -0.000289(0.1984) (0.1595) (0.00016) (0.0592) (0.2392) (0.0707) (0.1731) (0.0563) (0.2990) (0.1054) (0.2339) (0.08790)

-0.000639*** -0.000524 -0.00015 -0.000126 -0.000505*** -0.000399** 0.0000208 0.0000323 -0.000429*** -0.000307* -0.0000488 0.00000816(0.0002) (0.5853) (0.4176) (0.5091) (0.0067) (0.0228) (0.9249) (0.8774) (0.0147) (0.0690) (0.8073) (0.9661)

0.534464 -0.000524 0.854889 0.944157* 0.211276 0.473457 0.637641 0.797364 -0.034469 0.305773 0.217597 0.483645(0.3340) (0.3000) (0.1145) (0.0572) (0.7615) (0.4694) (0.3363) (0.2067) (0.9647) (0.6813) (0.7703) (0.5004)

-6.071696*** -5.907372*** -6.22609*** -5.325089*** -5.448448*** -4.792697***(0.0001) (0.0013) (0.0002) (0.0009) (0.0007) (0.0020)

-7.015532*** -5.311184*** -7.708206*** -6.541812*** -6.151477*** -5.340181***(0.0002) (0.0002) (0.0003) (0.0012) (0.0012) (0.0033)

Adj. R2= 0.15 Adj. R2= 0.28 Adj. R2= 0.25 Adj. R2= 0.35 Adj. R2= 0.11 Adj. R2= 0.20 Adj. R2= 0.19 Adj. R2= 0.27 Adj. R2= 0.09 Adj. R2= 0.16 Adj. R2= 0.15 Adj. R2= 0.22P(F) = 0.2935 P(F) = 0.0000 P(F) = 0.0000 P(F) = 0.0000 P(F) = 0.2935 P(F) = 0.0000 P(F) = 0.0001 P(F) = 0.0000 P(F) = 0.0002 P(F) = 0.0005 P(F) = 0.0006 P(F) = 0.0000

Variable

C

Table 3. Student Loan Default - Graduate Program and Private Dummy VariablesFY2010 FY2011 FY2012

***Denotes Significant at the 1% Level

Private

Income

Student Debt

Unemployment

Graduate Program

*Denotes Signficant at the 10% Level**Denotes Signifcant at the 5% Level

Gehm 19

several variables that significant throughout these tests. We can see that

both of the dummy variables, private colleges and graduate programs, are

significant at the 1% level throughout the years that were being tested. The

implication is that private schools will tend to have about a 5 – 6% lower

rate of student defaults than schools that offer no graduate program as well

as private schools having about 5 – 7% lower student default rate than

public institutions. In addition, we see that income is significant in (J), (L),

and (N) at the 10% level of significance. This means that an increase of

$1,000 of disposable income per capita in the state where the institution is

located yields a lower default rate about 0.3%. We find that student debt

was significant when there was no dummy variable used, but only twice

when the graduate dummy variable was used (regression L at 5% and

regression P at the 10% level of significance). This suggests that possibly

the amount of college debt does not play a major role in the amount student

loan defaults when looking at public and private institutions (see Appendix

III for interaction effects). This is further emphasized by the data as seen in

Table 1. The table states that private colleges had a much higher average

student debt when they were finished but also had a far lower rate of

defaulting on rates in the cohort rate. This seems to be counter-intuitive to

what intuition would tell us if we use the results from Table 2. Results

based on the results of Table 2 tell us that if there is a higher student

average student debt, the rates of defaulting should also be higher. Now,

Table 3 runs contrary to this with the addition of dummy variables. As each

Gehm 20

dummy variable is added, we see reduced significance of the student debt.

This tells us that the omission of for-profit colleges and adding of dummy

variables for graduate schools and private schools, the average amount of

student debt does not matter as much anymore. One way to look at this is to

see that for-profit colleges are no longer in the mix, so the remaining

institutions are much closer in average student debt (public universities

have about $6,000 lower average student debt than private colleges).

However, another explanation could be the size of the institution and the

quality of the career services. Most public schools have larger classes and

therefore it is harder to network within a certain class. In contrast, some

private schools such as St. Norbert College in De Pere, WI pride themselves

in their job placement rate after graduating. St. Norbert reports that about

93% of their graduates are either employed full time or enrolled in

additional education nine months after graduating. Table 4 shows the rates

at which St. Norbert graduates are either employed or attend graduate

school since 2007. We see a large fall in the total amount of students either

attending graduate school or finding employment. It appears that 2014 was

an anomaly looking at past results. Typically, when the employed rate is

lower, the graduate school rate is higher. However, ignoring the 2014 data,

we see that St. Norbert maintained a high placement rate after and during

2007 2008 2009 2010 2011 2012 2013 2014Response rate 0.523 0.372 0.372 0.354 0.443 0.67 0.569 0.5435

Employed 0.87 0.675 0.675 0.713 0.785 0.7823 0.811 0.706Full Time Work 0.746 0.537 0.537 0.515 0.593 0.7823 N/A N/APart Time work 0.124 0.138 0.138 0.198 0.192 N/A N/A N/A

Enrolled in additional education N/A 0.2 0.2 0.23 0.137 0.1255 0.121 0.131Total 0.87 0.875 0.875 0.943 0.922 0.9078 0.932 0.837

Table 4. St. Norbert Job/Graduate School Placement Rate

Gehm 21

the Great Recession. It may be that these smaller schools have more

resources and more incentive to allocate larger resources to getting

students jobs when they graduate. An alternative explanation of this could

also be that students at private universities may not be using as many

federal loans to help finance further education. A large number of private

schools end up giving away many different kinds of scholarships and

monetary awards to people who may not otherwise be able to go that

private institution with the help. It also may be the fact that both of these

types of institutions have what was referred to as the “traditional borrower”

by Yannelis and Looney (2015). As the traditional borrower is more likely to

get a better job and is typically a better borrower, this could reduce the

amount of student loan defaults and may reduce emphasis on the overall

debt. The unemployment is never a statistically significant variable expect

in regression (J) which is FY2010 using both dummy variables. It is tough to

draw conclusions using unemployment as it is not significant in most of the

regressions. What can be said about unemployment though is that it is

steadily decreasing as we move from FY2010 to FY2012 (see Table 1).

Unemployment in the state seems to have an impact, small, but present.

This however, still does not lead to a statistical difference in the student

loan defaults in all cases but one.

Gehm 22

The third and final regression that I ran was to see if the change rates

over time with quantitative variables were significant to addressing the

issue of student loan defaults. These results looked at change rate in

percentages of the data over time, omitting the dummy variables that I used

in the previous regressions. The results of this statistical test are found in

Table 5. This regression did not yield anything, minus two variables, that

was statistically significant. The model was not jointly significant and had

adjusted R-squared

values that did not

exceed 0.02. The

Durbin Watson

statistic found that

there was no auto or

serial correlation (see

Appendix II, Table vi

for more specific details on the regression). In testing this regression for

heteroskedasticity, I found that this model was afflicted by this in the

FY2010 – FY2012 results (results from this test are in Appendix I). As low as

the Adjusted R-Squared was for this regression, the test did find that there

were two significant variables. In the change rate between FY2010-FY2011,

we find that income is significant at the 5% level. This confirms what I

originally suspected but only in one of my tests. As the percentage change

of income rises, we see a rapid decrease in the percent change of student

FY2010 - FY2011 FY2011 - FY2012 FY2010 - FY2012(S) (T) (U)

Coefficent Coefficent Coefficent(P-Value) (P-Value) (P-Value)

-31.06904 -8.226638 -3.649697(0.1447) (0.6026) (0.9234)

14.85041** 0.548292 3.617585(0.0337) (0.9330) (0.3380)

-0.435306 -0.738781 -0.979921*(0.5759) (0.2780) (0.0870)

0.472679 0.093643 0.796873(0.7618) (0.9339) (0.5011)

Adj. R2= 0.01 Adj. R2= -0.01 Adj. R2= 0.02P(F) = 0.2027 P(F) = 0.7546 P(F) = 0.3271

Variable

C

Income

***Denotes Signifcant at the 1% Level

Table 5. Student Loan Default - Over Time Changes

Unemployment

*Denotes Signficant at the 10% Level**Denotes Significant at the 5% Level

Student Debt

Gehm 23

loan defaults. Results suggest that between FY2010-FY2011, if income rose

by 1%, we would see a decrease of 14.85% in student loan defaults. Also,

the change in student debt over the length of the time (FY2010-FY2012), we

also find that change percentage in student debt was significant at the 10%

level. I do have an explanation as to why student debt may be significant. As

we can see from Table 1, the student default rate has been going down as

time goes on. So the average change in student loan defaults has also been

going down which means that the dependent variable must be negative in

this change rate. In regards to change in student debt, it is positively

correlated in the fact that when one falls, so does the other one. However,

when we look at the next year’s changes and the cumulative changes over

time, we see that this income variable does not remain statistically

significant. The regressions utilizing yearly data in levels better captures

the differences in the student default rate when regressed on my particular

variables. This tells me that my prediction may be right to an extent,

however in the short time periods I allowed for in my regression may not

show the income change I was hoping for. Possibly if this test could be

extended out to encompass more and more years, we would see the

relationship that I predicted.

VI. Conclusion

My end results indicate that the macro economic variables, i.e.

unemployment, income, do not have as big as an impact on student default

loans as the type of institution. Based on my regressions that I ran, the data

Gehm 24

suggests that for-profit colleges have a statistically significantly higher

student default rate than not-for-profit colleges (both public and private).

However, this result should be looked at with a minor hesitation as my data

was not as complete as I would have liked it to be for proprietary schools. In

addition to that, private schools have a statistically significantly lower rate

of student defaults than public schools when only looking at not-for-profit

schools. This was surprising as on average, private schools tend to cost

more and have higher student debts. Again, I tend to attribute this to the

smaller class sizes and a Career Services program that has more resources

allocated to it (although I don’t have data to back that up). Also, schools

with graduate programs were found to have statistically significantly less

student loan defaults than institutions that don’t (this test was only on not-

for-profit schools). This could be because graduates may tend to take out

more loans, but on average they will earn more than someone who did not

attend a graduate program. This result was a confirmation of my a’priori

expectations.

The good news is it seems that the student default rate is on a

downward trend. It seems that President Obama’s and government policies

help to reduce the amount of students entering default on their loans. The

policy that seems to be doing a better job of cutting down is starting

repayment options that are based on income after graduation. This policy

helps reduce the financial burden of going to school by reducing the

percentage of a paycheck that goes to pay student loans every month.

Gehm 25

However, over the long run, these lower payment loans may end up being

more expensive to borrowers even if they are done at more of a comfortable

rate. This burden lies on the borrower to make sure they pay as much as

they can off the student loan while still maintaining their standard of living.

These policies push a 10% of discretionary income to go to repaying student

loans over 20 years (25 years if graduate degree). Future research may

want to look into the lifetime payments and interest accumulation on the

standard loans that enter repayment after six months of graduating schools

against the loans that offer the more flexible income based repayment loans.

More studies should look into private not-for-profit schools as well.

These were found to have statistically significantly less percent of student

loan defaults when compared to regular public universities. Whether it

could be the Career Services Department as previously suggested or the

possibility for more scholarships that do not come from the government,

even though the average debt coming out of private not-for-profit colleges is

higher, they still manage to have lower default rates than other public

universities. In either case, this study opens the door to other potential

research dealing with the low rates of student loan default at private

colleges and capitalizing on what makes private schools so successful at

maintaining these low student loan defaults when compared to public

universities.

Gehm 26

Works Cited

Bureau of Economic Analysis. New Jersey Department of Labor and

Workforce Development, Mar. 2016. Web. 21 Apr. 2016.

CollegeInSight. The Institute for College Access & Success, 2015. Web. 21

Apr. 2016.

Darolia, Rajeev, Cory Koedel, Paco Martorell, Katie Wilson, and Francisco

Perez-Arce. "Do Employers Prefer Workers Who Attend For-Profit

Colleges? Evidence from a Field Experiment." SSRN Electronic Journal

Gehm 27

SSRN Journal(2014): n. pag. National Center for Analysis of

Longitudinal Data in Education Research. Web. 21 Apr. 2016.

GraduateGuide. Myles Ridder, 1995. Web. 21 Apr. 2016.

Looney, Adam, and Constantine Yannelis. "A Crisis in Student Loans? How

Changes in the Characteristics of Borrowers and in the Institutions

They Attended Contributed to Rising Loan Defaults." The Brookings

Institution. The Brookings Institution, 10 Sept. 2015. Web. 21 Apr.

2016.

"Quick Facts about Student Debt." (Mar. 2014): n. pag. The Institute for

College Access & Success. Web.

21 Apr. 2016.

St. Norbert College Annual Graduate Survey, St. Norbert College, 2007,

Web. 26 Apr. 2016.

Three-year Official Cohort Default Rates for Schools. U.S. Department of

Education, 28 Sept. 2015. Web. 21 Apr. 2016.

Unemployment Rates for States. RI Department of Labor and Training,

2016. Web. 21 Apr. 2016.

Volkwein, J. Fredericks, Bruce P. Szelest, Alberto F. Cabrera, and Michelle

R. Napierski-Prancl. "Factors Associated with Student Loan Default

among Different Racial and Ethnic Groups." The Journal of Higher

Education 69.2 (1998): 206-37. JSTOR. Ohio State University Press.

Web. 21 Apr. 2016.

Gehm 28

Appendix I

In this table, I show the results of my heteroskedasticity tests in each of my

three regressions (nine total variations). These tests were conducted into

eVews under the White diagnostic of residual tests. In most of regression

results, I failed to find evidence of heteroskedasticity and therefore fail to

reject the null hypothesis that there is no heteroskedasticity. However, in

two cases I did find heteroskedasticity: FY2010 with the private dummy

variables and the FY2010-FY2012 changes over time. Yellow highlighting

indicates that the regression suffered from heteroscedasticity. These issues

were both addressed in the regression results shown in the paper. The

letters in parenthesis indicate which regression that goes with in the paper

as shown on Table 2, Table 3, and Table 4. There is also the dummy variable

used in each regression listed, both meaning graduate program dummy and

private school dummy. The one asterisk indicates violation at the 10% level

and the three asterisks in indicates a violation at the 1% level of

Gehm 29

significance.

0.6267 0.5603 0.1859

0.218 0.5581 0.2882

0.1815 0.3745 0.3467

0.63 0.0586* 0.1034

0.3582 0.7281 0.6762

0.4539 0.7259 0.918

0.1759 0.9347 0.0037***

Yearly Percent Changes in Student Default Rate FY2010 - FY2011 (S) FY2011 - FY 2012 (T) FY 2010 - FY 2012 (U)

Prob. Chi-Square(9) Prob. Chi-Square(9) Prob. Chi-Square(9)

FY2012 (P - Grad) FY2012 (Q - Private) FY 2012 (R - Both)Prob. Chi-Square(13) Prob. Chi-Square(13) Prob. Chi-Square(18)

FY2011 (L - Grad) FY2011 (M - Private) FY 2011 (N - Both)Prob. Chi-Square(13) Prob. Chi-Square(13) Prob. Chi-Square(18)

Prob. Chi-Square(9) Prob. Chi-Square(9) Prob. Chi-Square(9)

Student Default Rates: Graduate Program and Private School Dummy VariablesFY2010 (H - Grad) FY2010 (I - Private) FY2010 (J - Both)

Prob. Chi-Square(13) Prob. Chi-Square(13) Prob. Chi-Square(18)

Student Default Rates: For-Profit Dummy VariableFY2010 (B - For-Profit) FY2011 (D - For-Profit) FY2012 (F - For-Profit)

Prob. Chi-Square(12) Prob. Chi-Square (12) Prob. Chi-Square (12)

Student Default Rates (No Dummy - 100 Observations)FY2010 (G) FY2011 (K) FY2012 (O)

Student Default Rates (No Dummy - 150 Observations)FY2010 (A) FY2011 ( C ) FY2012 ( E )

Prob. Chi-Square(9) Prob. Chi-Square(9) Prob. Chi-Square(9)

Heteroskedasticity Test: The White Test

Appendix II

In this appendix, the more extensive results from each regression are

shown. For each regression, the tables below show the coefficient, standard

error, T-Statistics, P-values, as well as overall regression diagnostics

(Durbin-Watson Stat, Prob. Chi Squared as results of the White test). Each

regression has a letter next to it as an indication of the regression in the

paper that it is giving more details on. The tables are arranged in order that

roughly matches the order they are discussed in the regression sections.

One asterick indicates the varaible is significant at the 10% level, two

Gehm 30

astericks indicate that the variable is significant at the 5% level, and finally,

three astericks indicate the the varaible is significant at the 1% level.

Coefficent Coefficent Coefficent(Std Error) (Std Error) (Std Error)

17.65324** 26.04734*** 26.38042***(8.34678) (7.966553) (7.526958)-0.000231 -0.000304* -0.000341*(0.00017) (0.000161) (0.000148)0.0000929 0.0000616 0.0000303(0.000117) (0.000107) (0.0000939)0.468374 -0.280041 -0.279695

(0.483321) (0.54064) (0.598898)Obs. Obs. Obs.

R-squared R-squared R-squaredAdj. R-Squared Adj. R-Squared Adj. R-Squared

F-Statistic F-Statistic F-StatisticProb (F-Statistic) Prob (F-Statistic) Prob (F-Statistic)

Durbin-Watson stat Durbin-Watson stat Durbin-Watson statProb - Χ2 (9) Prob - Χ2 (9) Prob - Χ2 (9)

Table i. Student Default Rates (No Dummy - 150 Observations)FY2010 (A) FY2011 (C) FY2012 (E)

Variable T-Stat P-Value T-Stat P-Value T-Stat P-Value

C 2.114976 0.0361 3.269587 0.0013 3.504792 0.0006

Income -1.355934 0.1772 -1.882664 0.0617 -2.298048 0.023

Student Debt 0.792166 0.4295 0.572994 0.5675 0.322884 0.7472

Unemployment 0.969074 0.3341 -0.517981 0.6053 -0.467016 0.6412

150 150 1500.025061 0.025254 0.0351810.005028 0.005225 0.0153561.250998 1.260888 1.7745700.293546 0.290086 0.1545951.650444 1.803941 1.943126

0.18590.627 0.5603

Coefficent Coefficent Coefficent(Std Error) (Std Error) (Std Error)

34.15071*** 38.81113*** 36.13068***(8.273741) (8.18724) (7.901338)-0.000157 -0.000225 -0.000278*(0.000157) (0.000155) (0.000145)

-0.000669*** -0.000536*** -0.000422**(0.00018) (0.000178) (0.000167)0.062937 -0.631626 -0.531576

(0.450436) (0.520818) (0.585852)12.80293*** 10.36133*** 8.02604***

(2.415691) (2.533175) (2.494838)

Obs. Obs. Obs.

R-squared R-squared R-squaredAdj. R-Squared Adj. R-Squared Adj. R-Squared

F-Statistic F-Statistic F-StatisticProb (F-Statistic) Prob (F-Statistic) Prob (F-Statistic)

Durbin-Watson stat Durbin-Watson stat Durbin-Watson statP - Χ2 (12) P - Χ2 (12) P - Χ2 (12)

FY2010 (B)

0.1832750.160745

8.134582***0.000006

5.299906 0.0000

C

Income

Student Debt

Unemployment

For-Profit

T-Stat P-Value

0.00014.127602

-0.998888 0.3195

0.0003-3.725085

-1.917891 0.0571

-2.519019 0.0129

-0.907355 0.3657

Variable P-Value

4.740441

-1.456423

-3.00724

0.139724 0.8891 -1.212757

4.090254

0.0000

0.1474

0.0031

0.2272

0.0001

T-Stat

FY2011 (D)

0.1260870.101979

5.230097***

2.140635

Table ii. Student Default Rates - For Profit Dummy

150 150 150

3.217059 0.0016

0.099458

FY2012 (F)

T-Stat P-Value

4.572729 0.0000

0.2882

0.0746154.003524***

0.0041300.0005792.0769681.992899

0.218 0.5581

Coefficent Coefficent Coefficent Coefficent(Std Error) (Std Error) (Std Error) (Std Error)

32.51324*** 35.10419*** 21.48563*** 25.49395***(9.094035) (8.419053) (7.540552) (8.510244)-0.000228 -0.000326 -0.00021 -0.000299*(0.000176) (0.000164) (0.00016) (0.000156)

-0.000639*** -0.000524 -0.00015 -0.000126(0.000167) (0.000156) (0.000184) (0.000191)0.534464 -0.000524 0.854889 0.944157*

(0.550444) (0.509643) (0.536694) (0.490374)-6.071696*** -5.907372***

(1.446636) (1.77515)-7.015532*** -5.311184***

(1.82236) (1.394394)Obs. Obs. Obs. Obs.

R-squared R-squared R-squared R-squaredAdj. R-Squared Adj. R-Squared Adj. R-Squared Adj. R-Squared

F-Statistic F-Statistic F-Statistic F-StatisticProb (F-Statistic) Prob (F-Statistic) Prob (F-Statistic) Prob (F-Statistic)

Durbin-Watson stat Durbin-Watson stat Durbin-Watson stat Durbin-Watson statProb - Χ2 (9) Prob - Χ2 (13) Prob - Χ2 (13) Prob - Χ2 (18)

0.0002651.810709

0.1815

H - Graduate Dummy I - Private School Dummy J - Both Dummies

0.0035

Variable T-Stat P-Value T-Stat P-Value T-StatT-Stat P-Value

G - No Dummy VariableTable iii. Student Default Rates - Graduate and Private Dummy Variables FY2010

C 3.480661 0.0007 2.849344 0.0054 2.995678

Student Debt -0.546923 0.5853 -0.814079 0.4176 -0.662698 0.5091

Income -1.414139 0.1595 -1.316955 0.191 -1.909915

Graduate -4.10192 0.0001 -3.327816 0.0013

Unemployment 1.040217 0.3 1.592881 0.1145 1.92538

1.763517

10.55391*** 9.468349*** 11.55336***0.0000 0.0000 0.0000

100 100 1000.307659 0.285034 0.3806290.278508 0.254930 0.347683

Private -3.849696

1.711533 1.889248

0.0002 -3.808956 0.0002

0.0572

0.0592

P-Value

0.1034

1000.1792790.1536326.990109

0.63 0.0586*

3.575227 0.0005

-1.295149 0.1984

-3.827306 0.0002

0.970968 0.334

Gehm 31

Coefficent Coefficent Coefficent Coefficent(Std Error) (Std Error) (Std Error) (Std Error)

32.30915*** 34.81162*** 21.17181** 24.99742***(9.771841) (9.152067) (9.615245) (9.180341)-0.000228 -0.000332* -0.000247 -0.000333*(0.000192) (0.000182) (0.00018) (0.000173)

-0.000505*** -0.000399** 0.0000208 0.0000323(0.000182) (0.000172) (0.00022) (0.000209)0.211276 0.473457 0.637641 0.797364

(0.694) (0.651887) (0.659869) (0.62709)-6.22609*** -5.325089***(1.608054) (1.551891)

-7.708206*** -6.541812***(2.033683) (1.957072)

Obs. Obs. Obs. Obs.R-squared R-squared R-squared R-squared

Adj. R-Squared Adj. R-Squared Adj. R-Squared Adj. R-SquaredF-Statistic F-Statistic F-Statistic F-Statistic

Prob (F-Statistic) Prob (F-Statistic) Prob (F-Statistic) Prob (F-Statistic)Durbin-Watson stat Durbin-Watson stat Durbin-Watson stat Durbin-Watson stat

Prob - Χ2 (9) Prob - Χ2 (13) P - Χ2 (13) P - Χ2 (18)

0.191681

Private -3.79027 0.0003 -3.808956 0.0012

100 100 100

Unemployment 0.726287 0.4694 0.966315 0.3363 1.92538 0.2067

Graduate -3.871817 0.0002 -3.327816 0.0009

0.304432 0.7615

Student Debt -2.313816 0.0228 0.094568 0.9249 -0.662698 0.8774

-1.184473 0.2392

-2.774182 0.0067

C 3.803689 0.0003 2.2019 0.0301 2.995678 0.0077

Income -1.828109 0.0707 -1.372663 0.1731 -1.909915 0.0563

L - Graduate Dummy M - Private School Dummy N - Both Dummies

Variable T-Stat P-Value T-Stat P-Value T-Stat P-Value

3.306353 0.0013

0.358 0.728 0.676

0.2740167.044024*** 6.869094*** 8.473347***

0.0000 0.000067 0.0000012.004274 2.142566 2.0679910

0.228746 0.224340 0.3106820.196273

0.3745

Table iv. Student Default Rates - Graduate and Private Dummy Variables FY2011K- No Dummies

T-Stat P-Value

1000.1070430.0791383.8359890.0121402.045563

Coefficent Coefficent Coefficent Coefficent(Std Error) (Std Error) (Std Error) (Std Error)

29.74199*** 30.84141*** 22.31197** 24.25899***(9.467962) (8.962493) (9.269442) (8.876912)-0.00019 -0.000285 -0.000207 -0.000289

(0.000182) (0.000174) (0.000173) (0.000167)-0.000429*** -0.000307** -0.0000488 0.00000816

(0.000173) (0.000167) (0.000199) (0.000191)-0.034469 0.305773 0.217597 0.483645(0.777817) (0.742225) (0.743223) (0.714976)

-5.448448*** -4.792697***(1.555721) (1.50926)

-6.151477*** -5.340181***(1.835443) (1.772034)

Obs. Obs. Obs. Obs.R-squared R-squared R-squared R-squared

Adj. R-Squared Adj. R-Squared Adj. R-Squared Adj. R-SquaredF-Statistic F-Statistic F-Statistic F-Statistic

Prob (F-Statistic) Prob (F-Statistic) Prob (F-Statistic) Prob (F-Statistic)Durbin-Watson stat Durbin-Watson stat Durbin-Watson stat Durbin-Watson stat

Prob - Χ2 (9) Prob - Χ2 (13) Prob - Χ2 (13) Prob - Χ2 (18)

P - Graduate Dummy Q - Private School Dummy R - Both Dummies

Variable T-Stat P-Value T-Stat P-Value T-Stat P-Value

C 3.441164 0.0009 2.407046 0.018 2.732818 0.0075

Income -1.634795 0.1054 -1.198057 0.2339 -1.724539 0.0879

Student Debt -1.839544 0.069 -0.244644 0.8073 0.042625 0.9661

Unemployment 0.411968 0.6813 0.292775 0.7703 0.67645 0.5004

-2.484474 0.0147

-0.044315 0.9647

Graduate -3.5022 0.0007 -3.175527 0.002

Private -3.351494 0.0012 -3.013588 0.0033

0.2220295.569316*** 5.286991*** 6.650824***

0.000452 0.000689 0.0000241.961003 2.052890 2.017238

0.918

100 100 1000.189954 0.182078 0.2613210.155847 0.147639

0.454 0.726

3.141329 0.0022

-1.044163 0.299

T-Stat P-Value

G - No DummyTable v. Student Default Rates - Graduate and Private Dummy Variables FY2012

1000.0853690.0567872.9867920.0349421.965078

0.3467

Coefficent Coefficent Coefficent(Std Error) (Std Error) (Std Error)-31.06904 -8.226638 -3.649697(21.18693) (15.76596) (37.87449)14.85041** 0.548292 3.617585(7.07881) (6.513123) (3.76279)-0.435306 -0.738781 -0.979921*(0.776324) (0.678468) (0.568651)0.472679 0.093643 0.796873

(1.556333) (1.127818) (1.181445)Obs. Obs. Obs.

R-squared R-squared R-squared

Adj. R-Squared Adj. R-Squared Adj. R-SquaredF-Statistic F-Statistic F-Statistic

Prob (F-Statistic) Prob (F-Statistic) Prob (F-Statistic)Durbin-Watson stat Durbin-Watson stat Durbin-Watson stat

Prob - Χ2 (9) Prob - Χ2 (9) Prob - Χ2 (9)

Table vi. Change in Student Default Rates in PercentagesFY2010 - FY2011 (S) FY2011 - FY2012 (T) FY2010 - FY2012 (U)

C -1.466425 0.1447 -0.521797 0.6026 -0.096363 0.9234

Variable T-Stat P-Value T-Stat P-Value T-Stat

Change in Unemployment

0.303713 0.7618 0.08303 0.9339 0.67449

0.338

Change in Student Debt

-0.560727 0.5759 -1.088896 0.278 -1.723238 0.087

Change in Income

2.097868 0.0377 0.084183 0.933 0.96141

0.008339 0.023602

0.011217 -0.012612 0.0032611.555887 0.0398025 1.1602930.202731 0.754623 0.3271262.060771 1.806385 2.134691

0.5011

P-Value

150 150 150

0.031397

0.004***0.1815 0.3745

Gehm 32

Appendix III

Here I report data about the interaction effects that were reported. I tested

the interaction effects between graduate programs and student debt as well

as private schools and student debt as well. In each regression, I only use

one dummy variable to see if there is any statistically significant

relationship between student debt and the particular dummy variable used.

Gehm 33

We see that the interaction terms are not significant with the exception of

the graduate*student debt in FY2010. This also washed out the effects of

the private dummy variable making it insignificant in all tests. All the tests

were tested for heteroscedasticity and found not to have any. The number in

parentheses is the p-value. One asterisks signifies significant at the 10%

level, two signifies significant at the 5% level, and signifies significant at the

1% level.

C 17.73904 39.63394*** 25.83731** 38.74436*** 22.57062** 34.54426***(0.1400) (0.0000) (0.0340) (0.0001) (0.0496) (0.0005)

Income -0.000179 -0.000313* -0.000286 -0.00033* -0.000209 -0.00029*(0.3168) (0.0570) (0.1361) (0.0711) (0.2473) (0.0994)

Student Debt -2.48E-05 -0.000721*** -0.000139 -0.000545* -0.0000578 -0.000438**(0.9401) (0.0002) (0.6746) (0.0100) (0.8488) (0.0326)

Unemployment 0.858786 0.620613 0.674607 0.399735 0.220561 0.26244(0.1057) (0.2225) (0.3125) 0.5416 (0.7696) (0.7243)

Private Dummy -2.238792 -14.8069 -6.561546(0.8242) (0.1846) (0.5311)

Private*Student Debt -0.000212 0.000296 0.0000163(0.6296) (0.5161) (0.9682)

Gradaute Dummy -19.70738** -17.2786* -15.48166*(0.0119) (0.0555) (0.0843)

Graduate*Student Debt 0.000582* 0.00045 0.000389(0.0742) (0.2104) (0.2537)

Adjusted R2 0.29 0.3 0.19 0.20 0.14 0.16Prob (F-Statistic) 0.0000 0.0000 0.0002 0.0001 0.0018 0.0007

Interaction Terms Results

FY2010 FY2011 FY2012