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.
Gehm 1
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
Gehm 2
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
Gehm 3
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
Gehm 4
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.
Gehm 5
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
Gehm 6
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
Gehm 7
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
Gehm 8
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 –
Gehm 9
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
Gehm 10
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
Gehm 11
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
Gehm 12
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
Gehm 13
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
Gehm 14
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
Gehm 16
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