An Analysis of the Undergraduate Tuition Increases at the University of Minnesota Duluth

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1 Proceedings of the National Conference On Undergraduate Research (NCUR) 2012 Weber State University March 29-31, 2012 An Analysis of the Undergraduate Tuition Increases at the University of Minnesota Duluth Matt Ploenzke Department of Mathematics & Statistics The University of Minnesota Duluth Duluth, MN Faculty Advisor: Richard Green Abstract Tuition inflation in higher education has greatly outpaced other industries, leading to extremely high annual undergraduate tuition. Regression analysis was performed on 25 s worth of data treating annual undergraduate tuition at the University of Minnesota Duluth as the dependent variable. The four explanatory variables included were state appropriations per student, academic support, instruction funds per student, and luxury services per student. All variables were then deflated to 1985 dollars to eliminate inflation. The findings from the analysis indicate that decreased real state support per student has been the main driver of the tuition increases, while the increased real instruction costs per student also plays a more diminished role. Keywords: High Tuition, Regression Analysis, Reduced State Support 1.Introduction: There is no doubt students are asked to pay more for tuition today than they were in For example, tuition at the University of Minnesota Duluth for in-state undergraduates was 561% higher in 2009 than it was 25 s prior, without accounting for inflation. Of course tuition is expected to increase as the dollar inflates and as economic times call for but it is this high rate of increase that has everyone worried. Some supporters of the current higher education system claim there is no problem and that the explosive tuition increases are just an illusion; that students are paying much less than the advertised sticker price (Vedder, 5). Advocates on the other side of the argument complain that tuition increases have outpaced inflation and something needs to be done, however disagreements on the root cause of the increases always surface. Blame usually gravitates toward the following reasons: decreased state support, increased faculty salaries coupled with decreased workloads, increased student services and luxuries, and/or increased size of administration. Although increased financial support for students has also been viewed as a cause, the data collected for the analysis of this university showed otherwise. Because of this, increased financial support for students will not be considered a possible factor. This analysis looks to uncover the cause (or causes) of tuition increases at the University of Minnesota Duluth by using regression analysis with the price of undergraduate in-state tuition regressed over various explanatory variables, each of which are intended to be a measure of one of the reasons listed above. 1.1 Data Source: The University of Minnesota Duluth is a comprehensive regional university with a total enrollment of 11,806 students, of which 9,782 are undergraduates. Set in the heart of Duluth overlooking Lake Superior, this public institution offers students the choice of 13 bachelor degrees in 74 majors. The analysis focused on the 25 s ( ) of data available through the National Center for Education Statistics Integrated Postsecondary Education Data System (NCES IPEDS). Other select variables, as well as missing values, were found in the UMD

2 Campus Data Books, an annual publication of official university records produced by the UMD Office of Institutional Research. HEPI and CPI values were located on their respective websites. The values for Tuition are the Twin Cities Office of Institutional Research reported values for Duluth Undergraduate Resident Annual Tuition. Stata 11 statistical software was used to aid in the regression calculations. 1.2 Independent Variable Definitions: The following variables were treated as time series data with delta = 1. It is important to note the scales on the following variable plots are not consistently scaled Instruction per Student: Instruction is defined by IPEDS as the sum of all operating expenses associated with the instructional divisions of the institution. This includes compensation for teaching faculty as well as funds for departmental research and public service that are not separately budgeted (for example, departmental research would be included). This sum is then deflated to real dollars using the Higher Education Price Index (HEPI) and divided by the total number of students at the university, yielding real Instruction Cost per Student. The variable represents the argument that the price of tuition has risen so steeply because of increased instructional inefficiency; professors are getting paid too highly while productivity has either held constant or decreased. This is referred to as the Baumol Effect, which states that teaching requires the same person-hours with students as in the past, but professor salaries have kept pace with industries where high increases in productivity provide justification for such salary raises (Smith, 2010). instr_per_student Instruction Cost per Student Figure 1: Real Instruction Costs per Student Luxury Services: Luxury Services is defined as the IPEDS variable Student Services, deflated to real terms using the Consumer Price Index, and then divided by the total number of students. The term luxury is used, but this variable can also be thought of as student services per student enrolled; the variable name itself is not as important as what it represents. Student Services is defined by IPEDS as the sum of all expenses contributing to the overall students well being, including intellectual, cultural, and social development not directly related to instructional expenses. Luxury Services encompass everything from dining centers and dorms, to recreation centers and student commons. By looking at the amount spent on services for students, an idea of how student amenities have changed over time can be gained. The graph below shows a large, unexplained increase in the amount spent on these services from

3 luxury_services Luxury Services Figure 2: Real Luxury Service Costs per Student Academic Support: The academic support variable is the sum of all operating expenses related to assisting the university in achieving the primary mission of instruction, research, and public service, and then deflated using the HEPI. This looks to measure how academic support to students, the primary goal of administration, has changed over the s. For instance, the number of employees whose work is not directly related to instruction increased from 243 in 1985 to 511 in More employees means more funds go to the administration costs, an increase that may impact the price of tuition. Academic Support e+07 Academic Support State Support per Student Enrolled: Figure 3: Real Academic Support Costs This variable accounts for the decreased real state support that might explain the tuition increases. It is defined as the funds received through acts of a state legislative body for meeting operating expenses, deflated with the HEPI, and then divided by total student enrollment. The graph below shows that real state appropriations per student have steadily declined over time. Nominal state appropriations per student do increase from around $3250 in 1985 to $4175 in 2009, but this increase does not keep pace with inflation, thus leading to the decreasing trend seen below in State Support per Student. It is also important to remember that all the predictive variables used in the regression will be in what will now be considered real dollars. 71

4 State Support per Student state_student_support Figure 4: Real State Support Dollars per Student Variable Summary: Table 1: Variable Summary Statistics Variable Observations Mean Std. Dev Academic Support Luxury Services State Support per Student Instruction Cost per Student Higher Education Price Index vs. Consumer Price Index: The Higher Education Price Index is based on the notion that education is a labor-intensive service that utilizes a market basket of goods and services orientated towards technology while the CPI focuses on a standard market basket. In order for a university to survive and be competitive, they must purchase the most recent technological advances, whose prices inflate at a rate faster than a standard market basket of goods and services. Many studies focusing on tuition increases at American universities (both public and private) use the CPI as the deflation factor for tuition, but because the HEPI is designed specifically with the main cost drivers of higher education in mind, the HEPI will be used to deflate the variables, with 1985 as the base. Because the variable Luxury Services does not deal with the instruction aspect of higher education, but rather student services and luxuries, it has been deflated by the Consumer Price Index, with base as 1985 to account for the general inflation. Student luxuries are based on a more standard market basket of goods so the CPI is a better deflator than the HEPI in this case. 2. Regression Analysis: 2.1 Pair-wise Correlation: The pair-wise correlation table below highlights the significant correlations the independent variables share with Tuition. At the p=0.05 significance level, Instruction per Student does not appear to share a significant relationship with Tuition. The table also shows that decreased State Support per Student has 72

5 the highest correlation with the increased Tuition. These relationships will further be examined in the following regression analysis. Table 2: Pair-wise Variable Correlation Tuition Tuition Academic Support Luxury Services State Support per Student Academic Support * Luxury Services * * State Support per Student * Instruction per Student * *Significant at the p=0.05 level 2.2 Preliminary Analysis: Regression analysis was performed on the dependent variable Tuition and the four independent variables mentioned above. Output is included. The included coefficient of determination (R 2 ) below shows the proportion of variability in the dependent variable that is accounted for by the model. Table 3: Preliminary Regression Results Tuition Coefficient Std. Err. t P>t Beta Luxury Services State Support per Student Academic Support Instruction per Student Constant R 2 = outliers: An added-variable plot (avplot) helps identify influential points by examining the expected value for tuition per each independent variable. The avplots indicated that 1991 appears to be an outlier, especially in the plots for Luxury Services and Academic Support. For this reason, 1991 will be excluded in the regression analysis. 2.3 Secondary Analysis: Regression was performed once again, this time excluding Regression results are as follows: 73

6 Table 4: Secondary Regression Results Tuition Coefficient Std. Err. t P>t Luxury Services State Support per Student Academic Support Instruction per Student Constant R 2 = linearity: Before proceeding with interpretation of the regression results, model assumptions need to be checked. A residual versus fitted plot (RVF plot) is used to check the assumption of linearity by looking at how the residuals vary. The RVF plot did not indicate any violations to this assumption, and also indicated homoskedasticity heteroskedasticity: The Cook-Weisberg test for Heteroskedasticity yielded a p-value of From this, the null hypothesis of constant variance (homoskedasticity) could not be rejected, further confirming the assumption of constant variance residual normality: Another assumption that needs to be verified before the regression output can be utilized is the assumption of normality of the residuals. A kernel density estimate can be thought of as a smoothed histogram checking the normality of the residuals by comparing the kernel density estimate with the normal density function (the bell curve). The kernel density plot showed that the residuals appear to be normally distributed multicollinearity: A variance inflation factor test (VIF) was performed as well to test the severity of multicollinearity within the factors. The results did not indicate any potential issues (a VIF value > 10 warrants further investigation) since the VIFs were all under regression model: The analysis produced the following predictive equation for Tuition: Tuition = *Luxury Services *State Support per Student *Academic Support *Instruction per Student (1) 74

7 Real Tuition Fitted values Nominal Tuition The plot above shows the fitted regression equation along with both the real (HEPI deflated) and nominal tuition values. There is a large jump in the 1991 for the predicted values, showing why 1991 was considered an outlier. This jump makes sense because in 1991 there was a drop in the State Support per Student by almost 31%. 3. Analysis Implications The table below lists the beta coefficients for the regression equation, as well as the standard deviation for each variable: Table 5: Beta Coefficients and respective standard deviations Tuition Beta Std. Dev. Luxury Services State Support per Student Academic Support Instruction per Student Beta Coefficients compare the relative strength of the predictors by standardizing the coefficients from the regression equation. In other words, for a single standard deviation change in a predictor variable, the response variable (Tuition) can be expected to change by that many standard deviations. Looking at the table above, State Support per Student is the strongest predictor of Tuition; for each standard deviation decrease ( state supported real dollars per student) Tuition can be expected to increase by standard deviations (the standard deviation for Tuition is ). To express this further, every real dollar decrease in state support per student is followed by an expected real dollar increase in tuition. A similar logic can be applied to Instruction per Student, the next strongest predictor. Every standard deviation increase in the real dollar cost of instruction per student ( ) is accompanied with an increase in Tuition of In other words, a real dollar per student increase in instruction is coupled with a real dollar increase in tuition of This way of looking at it can be misleading, however, because a real dollar increase for Instruction per Student is less likely than a real dollar decrease in State Support per Student (i.e. The standard deviation for State Support per Student is larger). The variables Luxury Services and Academic Support are relatively weak predictors in comparison to the other two, both of which lack statistical significance as regressors at a p-value=

8 Therefore, the decreased real state appropriations (State Support per Student) are the main driver of high tuition, while the Baumol Effect, represented by the Instruction per Student variable, also plays a role, albeit a much smaller role. 4. References: 1. Campus Data Book. Duluth: University of Minnesota - Duluth, Print. 2."Consumer Price Index (CPI)." U.S. Bureau of Labor Statistics. United State Department of Labor. Web. 17 Feb < 3. IPEDS Data Center. Integrated Postsecondary Education Data System. National Center for Education Statistics. Web. 31 Aug < 4. Kantrowitz, Mark. "Causes of Faster-than-inflation Increases in College Tuition." FinAid. FinAid, 10 Oct Web. 31 Aug < 5. "Home." Commonfund. Commonfund. Web. 17 Feb < 6."Regression with Stata Web Book: Chapter 2 - Regression Diagnostics." UCLA Academic Technology Services. University of California. Web. 31 Aug < 7. Smith, Charles H. "America's Economic Malady: A Bad Case of 'Baumol's Disease' - DailyFinance." Business News, Stock Quotes, Investment Advice - DailyFinance. AOL, 11 Dec Web. 31 Aug < 8. "University of Minnesota Annual Tuition Rates: to : Duluth Campus." Office of Institutional Research. University of Minnesota. Web. 31 Aug < 9. Vedder, Richard. "Over Invested and Over Priced." Center for College Affordability and Productivity. Center for College Affordability and Productivit, Nov Web. 31 Aug < 76