Modeling the Effects of Financial Aid on Student Enrollment Decisions: A Quantitative Case Study of a Private Catholic University

Abstract

Over the last two decades, many institutions of higher education have experienced admissions-related problems due to fluctuations in student enrollment and the increasing need for institutional financial aid. Because of this, administrators need tools that can help them modify policy as the market changes. The purpose of this research was to develop a tool for a private, more selective institution that would answer the following questions: (1) what is the probability of enrollment for each admitted student, and (2) how would changes in the financial aid package affect this probability? The model in this research was based on both economic theory and the results of other empirical work, and was refined through statistical analysis. Its goal was to develop the best predictive model using the data collected by the institution and available to it at the time admission and financial aid decisions are made. The methodology was carried out in three steps. First, an enrollment probability model was estimated using three years (1998-2000) of admissions data from the institution, using both logistic and probit regression. The model included a unique set of explanatory variables, including religious affiliation and distance from home, showing the ease at which institutions can look at the variables that are important for their goals, policies, and practices. The second step was a tem poral validation against additional data. The model was tested for predictive accuracy against the admissions data for 2001. After rerunning the model for all four years, the final step in the methodology was to simulate the effects on enrollment of various changes in the tuition and financial aid policy, and to calculate price sensitivity. The results of this study, for the most part, confirm ed economic theory and general empirical findings. The signs and significance of most coefficients were as expected. A unique finding was that a linear, constantly decreasing functional form for net price was not the best fit for the data. Rather, a cubic relationship between net price and enrollment probability provided a better fit. Classification accuracy within each model and predictive accuracy for 2001 were all near 70%. Sensitivity to price was calculated differently in this research than in other existing research. Due to mathematical shortcom ings discussed in the study, delta-Ps and student price response coefficients (SPRC) were not used. Rather, sensitivity to a $1,000 decrease in net price was calculated for each student. The mean sensitivity to a