ESTIMATING A DEMAND FUNCTION FOR UNIVERSITY ENROLLMENT: A CASE STUDY

Prepared for the Mountain Plains Management Conference Grand Junction, CO October 2004

Estimating a Demand Function for University Enrollment: A Case Study By R. Kim Craft, Joe G. Baker, and Brent E. Myers Southern Utah University Cedar City, Utah 84720 INTRODUCTION As public colleges and universities face rising budget shortfalls due to decreased state appropriations, their dependency on tuition as a source of revenue continues to increase. Noorbakhsh and Culp (2002) recently examined this greater reliance on tuition as a source of revenue for the period of 1981 to 1994 and found the percentage of revenues coming from tuition had risen from 16% to 23% while simultaneously the percentage of revenues from state appropriations declined by 14%. This increased tuition dependency has motivated many administrators of public institutions to develop a formal tuition strategy for their respective institutions. Developing a rational tuition strategy requires knowledge of the enrollment demand function and the respective price elasticity of demand. This paper presents a summary of how Southern Utah University estimated its enrollment demand function, analyzed its price elasticity of demand, and then subsequently used the results in its tuition policy decisions. Southern Utah University (SUU) is located in the rural, southwestern corner of Utah. With approximately 6,000 total enrollments, it is a relatively small four-year state university. Started in 1897 as a small public teacher training school, it has steadily evolved into its current role as a comprehensive, regional university. It serves the entire southern region of Utah and the contiguous counties of two states with undergraduate and graduate programs and also applied technology training. Because of its prominence and

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central location, the people of the region look to the University for outreach services, culture, economic and business development, public education, regional history, public affairs, and major academic specialties. SUU consistently enrolls students from all 29 counties in Utah, 45 states across the U.S., and 28 foreign countries. Approximately 56% of total enrollment is female while 44% is male. LITERATURE REVIEW Numerous studies have examined the relationship between tuition and enrollment at institutions of higher education. According to Wetzel et al. (1998) such studies can be appropriately classified by the specific type of data used. Studies concerned with national, higher education, tuition policy use nation-wide aggregate data. Studies attempting to reveal the tuition and enrollment relationship for a single, specific university, require the use of disaggregate data. A review of current literature on this issue shows the aggregate type of study to be the most prevalent, while studies using disaggregate data remain fairly sparse. Interestingly, this scarcity exists despite the aggregate studies frequently reporting considerable variances in tuition/price elasticity among demographically different institutions and calling for the commission of further specific university studies (Leslie and Brinkman, 1987; Wetzel et al., 1998; Heller, 1997). National aggregate enrollment demand studies generally find the expected downward-sloping demand curve for higher education. However, the tuition elasticity or degree of student responsiveness with respect to tuition rate changes appears to be quite inelastic over the tuition ranges considered (Campbell and Siegel, 1967; Heller, 1999; Leslie and Brinkman, 1987). In fact, Wetzel et al. argue that reviews of current empirical

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work by Hearn and Longanecker (1985), Leslie and Brinkman (1987), Becker (1990), and McPherson and Shapiro (1991) all “agree that the demand for university or college attendance is relatively price insensitive” (1998, p.49). As is well known, the broader the definition of the market the more inelastic the demand. That is, there are few substitutes for higher education in general; however there are many substitutes for higher education at a specific institution. One would therefore expect much more elastic demand at a specific university. There are other reasons why one would expect inelastic demand for higher education. The increasing human capital prerequisites for today's current technology and global economy may, in part, help explain this inelastic enrollment demand. Heller (1999) offers the fairly recent, yet substantial, increase in college earnings premium (the disparity between college wages versus non-college wages) as another explanation for the tuition rate insensitivity. Furthermore, Leslie and Brinkman (1987) postulate several reasons for the inelastic demand of a college education. First, tuition increases have not been significant in real terms until only recently. Second, students have been able to avoid tuition increases either directly by moving to lower-cost institutions or indirectly by passing the costs on to others through the increased growth and availability of need-based financial aid. Third, there has been an increased interest and participation of women in higher education. Fourth, there has been a recent introduction of aggressive marketing by institutions. And fifth, colleges and universities have continued to lower their admission standards.

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CONCEPTUAL MODEL Neoclassical demand theory is the basis for any rational enrollment demand function. This theory states that the demand of any good or service affected not only by the price of the good or service, but also by the incomes of the consumers, the prices of related goods and services (the cross-prices), the tastes or preference patterns of consumers, and the number of consumers in the respective market, and expectations. Previous empirical studies of enrollment demand generally confirm the expected relationships of this conceptual model. SUU tuition and fees, expressed in real terms, was evaluated as one measure of the price. Because of a high degree of collinearity of tuition rates among Utah institutions, several different measures of tuition were considered. Ratios and differences between SUU tuition and state averages or other school's tuition were explored. A ratio of SUU tuition and state averages was eventually settled upon as having acceptable variance. This price ratio variable was expected to be inversely related to enrollment, ceteris paribus. The other measure of the price of a SUU education was the corresponding opportunity cost of attending the university; foregone earnings from a full-time job forfeited to attend the university. Following the lead of previous researchers (i.e. Heller, 1999; Chressanthis, 1996), the unemployment rate was used to capture this opportunity cost. Being another measure of price, unemployment rate was expected to have a positive relationship, ceteris paribus. Per capita personal income was looked at as an indicator of the income effect on enrollment. The expected sign of this coefficient was ambiguous. If SUU is a normal

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good, then increases in per capita personal income would allow a student to purchase more college education. On the other hand, higher income may allow consumers to purchase education from a private university or one of Utah’s “flagship” universities; implying a negative income-demand relationship. Thus, the a priori sign of this coefficient was unknown, ceteris paribus. The cross-price effects were considered using tuition and fees data from each of the public universities throughout the state of Utah. Every public institution throughout Utah was considered as a possible substitute good since SUU consistently enrolls students from all 29 counties in Utah. The expected cross-price effects were also ambiguous. They were expected to be positively related to SUU enrollment, ceteris paribus, if they are a competitor (substitute) of SUU and unrelated if they are not a competitor. The cross-price of a two-year institution in a contiguous county was also included in the model. Historically, many of this two-year institution’s graduates transferred to SUU to complete their baccalaureate degree. It is possible that this institution is a complementary good; if so, one would expect a negative cross-price coefficient. A measure of lagged enrollment was also explored as an indicator of the effects of tastes or preference patterns of students on enrollment. Demand theory argues that, in general, a change in consumer's tastes or preference patterns for a product compared to other products will change the amount of the product they purchase at any given price. Thus, last year's enrollment was expected to have a positive relationship, ceteris paribus, due to an expected "snowball" effect on enrollment.

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Two variables were tested to capture the effect of the potential number of buyers of a SUU education: Utah counties' total populations and each county's total high school graduates. The expectation was to find a direct relationship with both of these variables, ceteris paribus. EMPIRICAL MODEL Empirical analysis began by obtaining pooled time series cross-sectional data for all 29 counties throughout Utah. The initial period for the model estimation was 19752002. However, due to missing values for some of these years, the actual period was limited to 1980-2002. The SUU enrollment, unemployment rate, per capita personal income, total population, and the high school graduates data were simultaneously collected for every county in each given year. The tuition and fees (tuition) for every college and university throughout Utah was also gathered for each given year (Table 1). All SUU enrollment data by county was obtained from SUU's provost office. Annual unemployment rates by county were collected from the Utah State Governor's Office of Planning and Budget. County per capita personal income figures came from the Bureau of Economic Analysis. The United States Census Bureau was used to gather county population totals for each year. Annual high school graduates data was tabulated using information from the United States Office of Education. Undergraduate tuition and fees for each of the higher education institutions in Utah was collected from the Utah State Board of Regents. Consumer Price Index (CPI) data came from the Bureau of Labor Statistics. This CPI data was used to convert all price-related data into real dollars.

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Table 1. Variable Definitions Variable ENROLL

Type Quantitative

TUITION TUITION1

Quantitative Quantitative

TUITION2

Quantitative

TUITION3

Quantitative

TUITION4

Quantitative

TUITION5

Quantitative

L1ENROLL

Quantitative

TREND1

Quantitative

GRADS

Quantitative

UNEMP PCINC BEAVER KANE SEVIER UTAH WASHINGTON SALTLAKE

Quantitative Quantitative Qualitative Qualitative Qualitative Qualitative Qualitative Qualitative

GARFIELD

Qualitative

MILLARD

Qualitative

NORTHWEST

Qualitative

DAVIS

Qualitative

NORTHEAST

Qualitative

CENTRAL

Qualitative

Definition Dependent variable: natural log of total freshmen enrollment, by county [(SUU tuition & fees)/state average)]*100 an interactive term isolating the TUITION effects for Region1 an interactive term isolating the TUITION effects for Region2 an interactive term isolating the TUITION effects for Region3 an interactive term isolating the TUITION effects for Region4 an interactive term isolating the TUITION effects for Region5 the natural log of freshman enrollment, by county, lagged one year an interactive linear trend variable for northern Utah (Region1) the natural log of the number of current year high school graduates, by county county unemployment rate, expressed as a percentage the natural log of real per capita county income a dummy variable indicating Beaver county a dummy variable indicating Kane county a dummy variable indicating Sevier county a dummy variable indicating Utah county a dummy variable indicating Washington county a dummy variable indicating Salt Lake and Summit counties a dummy variable indicating Garfield, Wayne and Piute counties a dummy variable indicating Millard, Juab, Tooele, and Sanpete counties a dummy variable indicating Box Elder, Cache, and Rich counties a dummy variable indicating Davis, Weber, and Morgan counties a dummy variable indicating Duchesne, Uintah, Wasatch, and Daggett counties a dummy variable indicating Emery, San Juan, Carbon and Grand counties

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Based upon data considerations, small individual counties were geographically aggregated. These aggregated counties were thus renamed. Table 2 contains the multicounty aggregate definitions referred to throughout the remainder of this paper. Also, to allow for the isolating and testing of differences in tuition elasticity across geographical regions of Utah, specific regions were strategically organized and defined. Table 2 contains these particular region definitions used throughout our analysis; Table 3 contains descriptive statistics based upon these regional definitions. Table 2. County and Region Definitions BEAVER KANE SEVIER UTAH WASHINGTON SALTLAKE GARFIELD MILLARD NORTHWEST DAVIS NORTHEAST CENTRAL Region1 Region2 Region3 Region4 Region5

Beaver county Kane county Sevier county Utah county Washington county Salt Lake and Summit counties Garfield, Wayne and Piute counties Millard, Juab, Tooele, and Sanpete counties Box Elder, Cache, and Rich counties Davis, Weber, and Morgan counties Duchesne, Uintah, Wasatch, and Daggett counties Emery, San Juan, Carbon and Grand counties Utah + Salt Lake + Northwest + Davis + Northeast Sevier + Millard + Central Beaver + Kane + Garfield Iron Washington

Table 3. Descriptive Statistics for Variables Variable Name Mean St. dev. Min. Max. Freshmen Enrollment ENROLL 41.34 36.51 5.00 240.00 SUU Tuition and Fees TUITION 1,405.13 525.27 606.00 2,350.00 Population POP 151,635.74 223,740.14 4024.00 951,165.00 High School Graduates GRADS 2,056.55 2826.86 49.00 12,428.00 Unemployment Rate UNEMP .06 .03 .03 0.33 Per Capita Personal Income PCINC 13,975.09 4,571.63 6,606.00 28,645.52 Number of Observations = 299 Note: these statistics are by county.

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A few similar enrollment demand functions were initially hypothesized and tested. Each model tested considered the natural log of enrollment as its appropriate dependent variable. The different functions tested did, however, vary in their consideration of explicit competitive effects. In other words, some functions included the cross-price effects and others did not. This consideration was motivated by the previously mentioned high degree of collinearity of tuition rates among Utah colleges and universities. And in fact, this collinearity led to the eventual exclusion of explicit competitive effects from our final estimation. Data, empirical, statistical, and strategic considerations led us to decide upon a model which considered the natural log of freshman enrollment as a function of tuition specific to each pre-defined region (see Table 2), one year lagged freshman enrollment, a trend variable for the northern Utah region, number of high school graduates, unemployment rate, per capita personal income, and dummy variables for each aggregate county (see Table 1). Interactive tuition variables were formed and used in the analysis to allow for the explicit isolating of differences in regional sensitivity to SUU's tuition or price. Thus, TUITION1 captures SUU's tuition elasticity for northern Utah (Region1) and so on. Likewise, interactive trend variables were developed to capture the trending effects for each various region of the state (e.g. TREND1). Aggregate county dummy variables were included in the estimation as control variables. Iron County, where SUU is located, was chosen to be the excluded or benchmark county against which comparisons may be made. These control variables

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helped to isolate and review the various dependent variables' effects for specific counties. Thus, WASHINGTON isolates the specific enrollment, high school graduates, unemployment, per capita personal income, and tuition effects specifically for Washington County as compared to Iron County. EMPIRICAL RESULTS AND DISCUSSION The estimated OLS demand function and its accompanying overall model diagnostics are presented in Table 4. Functional form was evaluated using Ramsey's RESET general test for functional form misspecification. The log-level model described earlier was found to be acceptable. Further diagnostic tests revealed no problematic serial correlation. As illustrated in Table 4, overall model quality appears acceptable. First, the standard error of the regression was found to be 0.274; showing the estimate of the population error's standard deviation to be quite low. Second, the adjusted R-squared was 0.891, which means that roughly 89% of the variation in SUU freshman enrollment is explained by the variables captured in our current model. Third, the joint significance of our model was found to be relatively high, as evidenced by an overall F statistic of approximately 112. The key finding is that, historically, changes in SUU's tuition level (relative to the state average) have had no measurable negative effects on freshman enrollments. This is evidenced by the fact that the TUITION3, TUITION4, and TUITION5 variables are all statistically equal to zero and the variables TUITION1 and TUITION2, which are statistically significant even at the 5% level, are positive coefficients. In fact, in central (TUITION2) and northern (TUITION1) Utah, increases in SUU tuition rates are

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associated with increases in enrollment. This is possibly because tuition increases coincide with state-wide perceptions of increases in quality. Table 4. OLS Regression Results Dependent Variable: ENROLL Independent Estimated Standard Variable Coefficient Error Constant 5.334* 2.534 L1ENROLL 0.108** 0.056 TREND1 .035* 0.008 GRADS .508* 0.140 UNEMP 0.002 0.008 PCINC -0.351 0.286 TUITION1 .019* 0.008 TUITION2 .026* 0.007 TUITION3 -0.003 0.007 TUITION4 -0.004 0.011 TUITION5 0.012 0.013 BEAVER -1.264 1.182 KANE -1.444 1.181 SEVIER -4.692* 1.235 UTAH -5.197* 1.467 WASHINGTON -3.461* 1.489 SALTLAKE -4.769* 1.521 GARFIELD -1.325 1.190 MILLARD -4.791* 1.264 NORTHWEST -5.835* 1.444 DAVIS -5.607* 1.503 NORTHEAST -5.301* 1.398 CENTRAL -5.469* 1.270 Standard error of regression = 0.274 Adjusted R-squared = 0.891 Overall F statistic = 112.117*

tstatistic 2.105 1.926 4.223 3.624 0.289 -1.227 2.326 3.958 -0.419 -0.343 0.869 -1.069 -1.223 -3.800 -3.541 -2.324 -3.130 -1.113 -3.790 -4.042 -3.732 -3.791 -4.305

Pvalue [.036] [.055] [.000] [.000] [.773] [.221] [.021] [.000] [.676] [.732] [.385] [.286] [.222] [.000] [.000] [.021] [.002] [.266] [.000] [.000] [.000] [.000] [.000]

* means significant at the 5% significance level ** means significant at the 10% significance level

Another important finding is the clear “snowball” effect (L1ENROLL); a one percent increase in freshman enrollment one year is associated with a .11 percent increase in freshman enrollment the following year, ceteris paribus. This implies that any increase in enrollment will have a positive effect in following years. Conversely, this "snowball"

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effect also works in the opposite direction, where declines in freshman enrollment in a given year will translate into lower enrollment the following year, ceteris paribus. After accounting for all other factors in the model, enrollment from northern Utah shows an increasing trend of about 3.5 percent per year (TREND1). This suggests that the perception of SUU in northern Utah is improving and that, if the trend continues, much of SUU’s future growth may come from that geographical region. Obviously, the number of high school graduates (GRADS) should be a strong determinant of SUU freshman enrollment. The regression results indicate that for every one percent increase in high school graduates across the state, there is a .51 percent increase in SUU freshman enrollment (GRADS), and the effect is statistically significant at the 1% level. This finding indicates that while SUU is growing steadily with increases in market size, it is continually losing market share to other schools.1 The statistical insignificance of the respective dummy variables suggests that enrollment patterns of high school graduates from Beaver, Kane, Garfield, Wayne and Piute counties are essentially the same as Iron County. This is not surprising since these are all rural counties, similar in many respects to Iron County, and located relatively close to SUU. On the other hand, a notable finding is that enrollment from Washington County, a close neighbor expected to be part of SUU’s service area, is far below other Southern Utah counties (WASHINGTON). Washington County differs in important respects from other counties in the region; in particular, it is the most populous and highest income county in Southern Utah. Moreover, is has a popular two-year college 1

In an alternative regression model that allowed for interaction terms between the high-school-grads variable and regional dummy variables, it was discovered that effects of high school graduates is near zero in Iron County where SUU is located. In other words, after controlling for other factors, changes in Iron County high school graduates have little impact on the number of SUU enrollments from Iron County. Since the county has been growing steadily, it appears that SUU is doing poorly in its immediate area.

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which began offering selected baccalaureate degrees in 2001. The regression results are probably reflecting both the effects of different demographics as well as the impact of this new competitor. Neither unemployment (UNEMP) nor per capita personal income (PCINC) has statistically significant effects on freshman enrollment. However, it is interesting to note that the estimated coefficient sign of per capita income is negative; implying that SUU might be considered an “inferior good” by some consumers. POLICY RESULTS In fall 2002 the Utah Board of Regents met with all higher education institutions in Utah to determine tuition rates for the upcoming year. Southern Utah University requested and was granted an increase of 23 percent, the highest increase of any institution in the state. The Board of Regents granted this increase for several reasons. First, SUU was the only institution to back up their tuition request with an empirical analysis of the expected tuition effects on enrollment. Secondly, the SUU administration had worked very closely with the SUU student government to outline the fiscal health of the institution and consequences of not increasing tuition (e.g., increased faculty turnover, larger class size, lagging campus technology). Through negotiations with the SUU student government, part of the tuition increase was used to hire academic advisors for each college (student satisfaction surveys had consistently shown this to be a high priority item). Also, a portion of the increased tuition revenue was used to fund a number of student work-study positions on campus. As a result, the SUU administration was

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able to present the Board of Regents with evidence of strong institutional support for the tuition increase by students, faculty, and administration. Subsequent enrollment data validated the model’s predictions regarding tuition increases. In fall of 2003 SUU enrollment was 6,048, and increase of 2.8 percent over fall 2002 enrollment of 5,881. During the same period freshman enrollment changed from 2,153 (fall 2002) to 2,322 (fall 2003). CONCLUSION In pursuit of providing guidance to the administration of Southern Utah University, who were seeking to formalize an appropriate tuition strategy in the wake of ever-decreasing state appropriations, this study defined an appropriate SUU enrollment demand function for freshman using neoclassical demand theory as its basis, isolated and analyzed SUU's tuition elasticity by geographical regions, and contributed to SUU's successful tuition policy decision. The enrollment demand model is now part of the SUU policy process and is maintained and updated annually. Further analysis of the results do indicate possible needs to explore a non-resident model, to examine the explicit effects of student financial aid and employment on SUU enrollment, and to attempt to increase the number of observations by obtaining data series to 1975; thereby improving the overall model estimation. REFERENCES Becker, W.E. (1990). The demand for higher education. In The Economics of American Universities: Management, Operations, and Fiscal Environment, eds S.A. Hoenack, and E.L. Collins, pp. 155-188. State University of New York Press, Albany. As referenced in Wetzel et al. (1998)

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Campbell, R. and Siegel, B.N. (1967). The demand for higher education in the United States 1919-1964. American Economic Review, 57, 482-494. Chressanthis, G.A. (1986). The impacts of tuition rate changes on college undergraduate head counts and credit hours over time - a case study. Economics of Education Review, 5, 205-217. Hearn, J.C. and Longanecker, D. (1985). Enrollment effects of alternative postsecondary pricing policies. Journal of Higher Education, 56, 485-508. As referenced in Wetzel et al. (1998) Heller, D.E. (1997). Student price response in higher education: an update to Leslie and Brinkman. Journal of Higher Education, 68, 624-659. Heller, D.E. (1999). The effects of tuition and state financial aid on public college enrollment. The Review of Higher Education, 23, 65-89. Leslie, L.L. and Brinkman, P.T. (1987). Student price response in higher education: the student demand studies. Journal of Higher Education, 58, 181-204. McPherson, M.S. and Shapiro, M.O. (1991). Does student aid affect college enrollment? New evidence on a persistent controversy. American Economic Review, 81, 309318.

As referenced in Wetzel et al. (1998)

Noorbakhsh, A. and Culp, D. (2002). The demand for higher education: Pennsylvania's nonresident tuition experience. Economics of Education Review, 21, 277-286. Wetzel, J., O'Toole, D. and Peterson, S. (1998). An analysis of student enrollment demand. Economics of Education Review. 17, 47-54.

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