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Our team of actuaries and students presented this topic at Pinnacle University (Pinnacle U) in March 2022.
Most current (or recently graduated) college students are familiar
with several of the methods that can be used to finance a college education.
The most preferred options are college savings programs (529
plans), grants and scholarships, because they do not have to be paid back. Secondly
most-preferred are government loans, which have lower interest rates compared
to other loans. Once those avenues are exhausted, however, it is up to the
students and their families to find other alternatives.
Traditionally, this would mean that students (or their families) might
resort to taking out private loans with higher rates than those offered by the
government. But what if there was another funding method to consider – one that
relied more directly on the quantifiable expected return of the education being
An income share agreement (ISA) is a method of funding
where tuition is covered by an ISA provider in exchange for a fixed percentage
of future salary.
Unlike student loans, the ISA’s rate (meaning a percentage of
future earnings) is based not solely on past credit history and academic
performance, but also on projected career and salary. Majors that lead to
careers with higher expected salaries (e.g., engineering, actuarial science) will
result in lower interest rates, whereas majors with less lucrative salaries (e.g.,
philosophy, classics) will be charged higher rates for the same amount of
tuition. ISAs benefit students by giving them a less risky alternative to
student loans if they are uncertain about their salary post-graduation.
For this year’s Pinnacle University, our group decided to conduct research
to see if we could create a pricing model for an ISA that could compete with traditional
To accomplish this, we solved for the percentage of future income
that would be required to fulfill the agreement. We let the amount of tuition
being funded equal the present value of the expected future salary, and then
solved for the rate. Using statistical methods to predict the probability of
graduation and the expected salary after graduation, we used a formula for a
geometrically increasing annuity that accounted for inflation and salary growth
when valuing future payments. We made assumptions about the discount rate,
inflation, salary growth and length of agreement. We also chose to limit the
scope of our models to only include majors currently offered at Milwaukee
School of Engineering (MSOE).
Ideally, we were hoping to find student-level data related to
academic performance and financial information to calculate the expected
graduation rate. We found, however, that this information was impossible to
come by, so we resorted to using aggregate data at the university level
provided by a tool called Tuition Tracker (TT).
Likewise, finding salary data relevant to the academic majors for
which we were modeling ISAs was also difficult. Ultimately, we combined salary
data from the Bureau of Labor Statistics (BLS) with survey data from O*Net to
use information about different knowledge, skills and abilities associated with
various jobs as explanatory variables for our model.
The tools that we used to prepare our data and run our models were
primarily R, Excel and SQL.
One of the most difficult parts of our project was preparing and
cleaning the data.
To predict graduation rate, we began by trying a linear model, but
eventually opted against it when it failed the normality test and did not have
evenly distributed residuals.
We then used a quasibinomial model, because the values that we
were predicting were not Boolean, but rather, aggregate, percentages. While
this gave us a model that had usable coefficients and statistically significant
predictors, a quasibinomial model does not have an Akaike Information Criteria (AIC)
value for model comparison. The explanatory variables we used were retention
rate, in-state tuition fees, Pell grant aid and other grant aid.
The salary dataset contained 240 variables but only 59
observations. First, our group attempted a Principal Component Analysis (PCA)
to solve the problem, but this did not reveal any obvious insights.
Then, we decided to use a different method that would be more
interpretable in the long run. To reduce the dimensionality of our dataset, we
used Sure Independence Screening (SIS). SIS uses correlation learning to reduce
the number of columns in a dataset to be less than or equal to the number of
rows. It does this by filtering out the features that have a weak correlation
with the response.
After applying SIS, we were left with a dataset that had only 14
variables, and then proceeded to use normal elimination methods and run a
linear model. The variables that remained after using backwards elimination
with AIC were management of personal resources, judgement and decision making,
written comprehension, written expression, and fluency of ideas. We used these
variables to predict starting salary.
Using our models, we generated random values for the variables
within the ranges found in our datasets to see if the results were
intelligible. They seemed promising and comparable to what we would expect, but
they were still dependent on our assumptions and the quality of our data.
Though our research leaned more theoretical, the ideas and models
illustrated may lay the foundation for a practical use in the ever-innovative
insurance industry, such as developing some sort of tuition reimbursement
coverage. Potentially built into tuition costs, this coverage could be a
safeguard for students who must drop out of school or are unable to land a job
in their chosen field, or another field with similar income potential, upon
This coverage would strongly appeal to universities looking to
raise enrollment and help their reputation. Another potential market might be
trade schools looking to fill jobs now in high demand. Whether offered by a
traditional insurer or a captive insurance company, the likelihood of this
coverage becoming available is somewhat contingent on the data that is
In the future, we believe that our idea of creating competitive
ISA plans could be expanded and built upon by using larger quantities of student-level
data to predict graduation rate, and expanding the scope to include more majors
and different methods for predicting salary.
Steve Jagodzinski is a senior actuarial analyst with Pinnacle Actuarial Resources in the Chicago office. He holds a Bachelor of Science degree in actuarial science from Illinois State University and has experience in assignments involving loss cost projections, loss reserving and group captives. He is actively pursuing membership in the Casualty Actuarial Society (CAS) through the examination process.
Edwina Sofia Paredes is a
graduate of Milwaukee School of Engineering’s class of 2022 with a
Bachelor of Science in actuarial science and a double minor in finance and
business administration. She will be pursuing a Master of Analytics at the
University of California-Berkeley in the fall of 2022.
Janna Meyer-Steinhorst is a
business analyst with Capital Credit Union in the Green Bay office. She holds a
Bachelor of Science degree in actuarial science from Milwaukee School of
Noah Wagenknecht is currently
finishing his Bachelor of Science in actuarial science at the Milwaukee School
of Engineering and will graduate in November 2022.
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