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 pursued? 

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 funding methods. 

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 graduation. 

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 available. 

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 Engineering.

Noah Wagenknecht is currently finishing his Bachelor of Science in actuarial science at the Milwaukee School of Engineering and will graduate in November 2022.