Tuition and enrollment yield at selective liberal arts colleges

Ecorrontics ofEdtrcrr~io,~ Review. Vol. 12. No. 1. pp. 31 I-324. Prmted in Grrat Britain.

0272-7757/W $6.(N) + 0.00 @I993 PergamonPressLtd

1993.

Tuition and Enrollment Yield at Selective Liberal Arts Colleges JEFFREYPARKER*+ "Departmentof Economics. Reed College. Economics

and Business,

Linfield

and JEFFREYSUMMER@ Portland, OR 97202-8199, U.S.A.; and $Department College. McMinnville, OR 97128-6894, U.S.A.

of

Abstract -This paper investigates the effect of changes in tuition and fees on the matriculation rate of applicants admitted to a group of selective liberal arts colleges. Our sample is drawn from a detailed data base for 82 liberal arts colleges over the 1988 to 1990 period, compiled by the Higher Education Data Sharing (HEDS) Consortium. We find that an increase in the level of tuition and fees charged by a college causes a significant reduction in the share of admitted applicants who choose to enroll. The elasticity of this relationship is in the neighborhood of one-third, and is somewhat larger for financial aid recipients than for students who did not apply for or did not qualify for aid.

I. INTRODUCTION PAPER investigates the effect of changes in tuition and fees on the matriculation rate of applicants admitted to a group of selective liberal arts colleges. Our sample is drawn from a detailed data base for 82 liberal arts colleges over the 1988 to 1990 period. compiled by the Higher Education Data Sharing (HEDS) Consortium. We find that an increase in the level of tuition and fees charged by a college causes a significant reduction in the share of admitted applicants who choose to enroll. The elasticity of this relationship is in the neighborhood of one-third, and is somewhat larger for financial aid recipients than for students who did not apply for or did not qualify for aid. The numerous demand studies published over the last two and a half decades have examined the effects of tuition changes on enrollment at a variety of colleges, both public and private. A recent survey of this literature is provided by Leslie and Brinkman (1987). Many of these studies, such as the seminal work of Campbell and Siegel (1967), are aggregate time-series analyses measuring the overall effect of nationwide tuition increases in discouraging college attendance. These studies attempt to estimate what

THIS

+To whom [Manuscript

correspondence should be addressed. received 7 November 199 I; revision

accepted

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might be called an “industry demand curve”, relating aggregate quantity demanded to the average price for the industry. McPherson and Schapiro (1991) use longitudinal data on individual students and potential students to estimate the elasticity of the industry demand curve with private and public institutions treated separately. Other studies, such as those of Knudsen and Servelle (1978) and Hopkins (1974), use cross-section data and focus on measuring the effect of tuition differences on enrollment for a sample of institutions in a single state or across states. A few micro-institutional time-series studies, such as Funk (1972), measure the effect of tuition changes on enrollment over time at a particular institution. These studies, like the present one, investigate the demand curve for the product of the individual institution rather than industry demand. A recent study by Moore, Studenmund and Slobko (1991) examines the effect of cost, financial aid and other variables on the enrollment yield at Occidental College, one of the institutions in our WEDS sample. In terms of the dependent variable chosen to measure demand and the nature of the institution, this study is most directly comparable to the present work. The present study provides several innovations to

for publication

26 February

1993.1

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Economics

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this literature. We use pooled time-series crosssection data for a specific class of institutions those classified by the Carnegie Commission as ‘Liberal-Arts Colleges I’.’ Although there is considerable heterogeneity among the schools in our sample, they are likely to compete to a large extent for the same pool of prospective students, defining a recognizable market. By using observations both across schools and across several years, we allow both differences among colleges and changes in the behavior of individual institutions over time to identify the parameters of the demand equation. Our dependent variable is the (log of the) share of admitted applicants choosing to enroll at an institution in a particular year. In previous student demand studies, many diverse specifications of the dependent variable are employed. A common choice is the percentage of I8 to 24-year-olds (or of recent high-school graduates) who enroll in higher education. This specification is problematic because it assumes that all individuals in the chosen demographic group are interested in attending college. Changes in the propensity of young people to attend college or in their ability to gain admission can bias the estimates if their causes are not appropriately included as explanatory viarables. By restricting our attention to admitted applicants, we are able to focus exclusively on a pool of individuals who have the expressed interest and ability to attend the school in question. Many students purchasing higher education receive financial assistance, mostly in the form of government loans and grants and/or collegesupported financial aid. Colleges price-discriminate on the basis of calculated ability to pay, making it impossible to measure from institution-level data the price quoted by the college to any particular prospective student. Some studies attempt to account for this by measuring cost as ‘net tuition’, defined as the full tuition charge less the average amount of financial aid received by enrolled students, or by including both gross tuition and the average financial aid award as explanatory variables. There are several reasons why using the average aid award is unsatisfactory. Because student loans must be repaid (though they have subsidized interest rates), they should not be viewed by students as equivalent to grants which require no repayment. Some studies such as McPherson and Schapiro [1991] attempt to measure the present value of student-loan repayments and infer from this

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the true economic value of each dollar of loans. Another difficulty with net tuition is that the available data usually apply only to students who actually enroll at the institution. No information is available on the offers made to students who decided not to come.’ Our data suggest that qualified students who are denied financial aid by an institution seldom attend that institution. By extension, if a college offers more and less attractive financial-aid packages to a pool of students, those receiving more attractive aid are more likely to matriculate. Thus, the amount of aid received by the average matriculant probably overstates the average amount offered to all admittees who received aid offers. Finally, the average value of net tuition is just that - an average - and does not necessarily represent the actual amount paid by any individual student or, more importantly, the amount that would be paid by an average student out of the pool of college applicants. Using the HEDS data, we are able to separate admittees and matriculants into three categories: (1) those who apply for, qualify for and receive financial aid (called Group A). (2) those who apply for and are qualified for financial aid, but to whom aid is denied (Group D), and (3) those who either do not apply for aid or who apply but do not qualify for aid (Group 0). Separate demand equations can be estimated for each group. Only for Group A is the magnitude of financial aid award relevant; the other groups pay the full price. In particular, the regressions for Group 0 should be relatively uncontaminated by the problems associated with measuring the value of financial aid. Disaggregating the pool of applicants in this way also allows us to compare the elasticities of aid recipients with those of non-aid students. This may be important since McPherson and Schapiro find that wealthy families have different sensitivity to college cost than less wealthy families. In the next section, details of the empirical specification are presented along with a description of our data set. Section III presents and interprets our econometric results. The final section discusses the study’s implications and proposes several extensions. II. SPECIFICATION Demand equations feature three prominent

AND DATA

in economics ordinarily sets of explanatory vari-

Tuition and Enrollment

Yield at Selective Liberal Arts Colleges

ables: the price of the product, the number of potential buyers and their incomes, and the prices of substrtutes and complements. Indeed, these kinds of effects figure prominently in most studies of the demand for higher education. In this section, we discuss in detail the specification of our demand equation, including our measure of quantity demanded, our treatment of each of these sets of explanatory variables and a third important class of explanatory variables: qualitative differences among colleges. Higher education is a heterogeneous product. Even among liberal arts colleges, the educational experiences offered by institutions vary in important ways, including the intensity and rigor of the academic program, the prestige of the institution’s brand name, the size of the college’s student body and the physical and social attractiveness of the campus and the community in which it is located. Students choosing a college take their perceptions of all of these factors into account in attempting to determine which school provides the best educational experience relative to its cost. Because schools differ markedly in these qualitative characteristics, demand equations estimated from crosssection data are likely to be meaningful only if such qualitative differences among schools can be adequately measured. Our demand equations include a collection of institutional quality variables that attempt to capture measurable differences in institutional characteristics. Measuring Quantity Demanded The process of purchasing college education can be viewed as a three-stage procedure, involving decisions by both the prospective students and the institutions. Initially. a prospective student chooses a set of schools to which to apply. The schools then admit a subset of those applying. Finally, among the set of schools admitting him or her, the student chooses which to attend. All three of these decisions play a role in determining the ultimate number of matriculants - the most obvious measure of quantity demanded. At the institutional level, the outcome of the first stage is the number of applicants. Although this is a potentially interesting measure of demand, its behavior is likely to be rather erratic. Application fees are generally quite low. so applications are often received from students who are relatively unlikely to be admitted or who would be unwilling to pay a college’s tuition cost unless he or

313

she received an unusually generous financial aid offer. The number of applicants is probably quite sensitive to the amount and effectiveness of the efforts exerted by a school’s admissions office in advertising the school and identifying and courting potential applicants. This aspect of demand is unexplored in the present study. The admission decision is made by the institution rather than by the potential buyers. Most liberal arts colleges have in mind a target size for their entering class, and admit the number of students that they believe will yield the appropriate number of matriculants.3 Thus, the ultimate size of the entering class is influenced and perhaps dominated by supply considerations governing the number of students admitted. This makes the number of entering students an inappropriate measure of quantity demanded, unless the number admitted is controlled for as an explanatory variable. We avoid this problem by focusing exclusively on the third stage: out of the pool of admitted applicants, what share choose to enroll?’ As discussed in the introduction, we estimate separate demand equations for three groups of freshman matriculants. For each group, we measure quantity demanded as the enrollment rate: the ratio of matriculants to (or yield) admittees. The data are obtained from the HEDS data base. Although enrollment yield reflects decisions that are made by the demanders of higher education services, admissions policies of institutions can affect yield in important ways. For example, those who apply under early-decision programs promise to enroll if admitted, so their yield is near 100%. Institutions that strongly encourage early-decision applications will have higher enrollment yields. Similarly, some colleges may choose to raise their yields by rejecting candidates that they believe are unlikely to enroll and accepting ones (such as children of alumni) who have a higher probability of enrollment.’ Unfortunately, admissions policies are not easily measured. Enrollment rates also depend crucially on the alternatives available to admitted applicants. Those admitted to only one institution are likely to enroll there, while those having several alternatives can enroll in no more than one. To the extent that enrollment yields vary across institutions or over time due to such differences in admissions policies and alternative enrollment options of the admissions pool, the dependent variable of our model is not a pure measure of demand. However,

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Economics

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we believe that by focusing on a broadly comparable set of institutions, the impact of these factors on enrollment yield is likely to be relatively small, and that the dominant effect on yield is likely to come from the decisions of admitted candidates about the merits of each institution relative to its cost. Measuring Cost The appropriate measure of the cost of a college education includes not only explicit charges such as tuition and fees, but also the opportunity cost of attending - perhaps measured by foregone wage earnings. When considering the aggregate rate of college attendance of the nation’s youth, considerations of opportunity cost and of the value of the human capital investment represented by a college education are paramount. However, candidates who are at the margin of deciding whether to attend college at all are most likely to find low-cost alternatives such as state universities and community colleges more attractive than relatively expensive private schools. Most applicants to selective liberal arts colleges have already decided to so the matriculation decision attend college, modeled by our equations usually represents a choice among colleges rather than between education and non-education alternatives. Thus, it may be unnecessary to consider non-college opportunity costs. The cost variables that are included in our empirical specification include tuition and fees, room and board charges and the average financial aid award for matriculating aid recipients. The aid award variable is sometimes disaggregated into grants and loans plus work study. All cost variables enter the regression in log form. Data for most schools are obtained from HEDS, supplemented where necessary from annual issues of the Life Insurance Marketing and Research Association publication College Costs. For students receiving financial aid, total tuition and fee charges overstate the actual cost of attending, so it is important to include some measure of financial aid support in the demand equation. An ideal measure would be data on the financial aid package offered to a set of individual applicants or applicant cohorts in Group A, say, the amount of loans and grants offered by each college to a student in the eightieth percentile of his or her high-school class, with an 1100 SAT composite score, with two siblings and a family income of $40,000. This would

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allow a direct comparison of the cost to a specific applicant cohort of attending alternative schools. Although the HEDS data base contains information about the income distribution of the families of each school’s financial aid recipients, there is no information on the amount of aid offered to families in each category and no data whatever about offers by a college to students who did not matriculate at that school. In short. we have no fully satisfactory measure of net tuition and the effective price paid by aid recipients. Our regressions for financial aid students include gross tuition and fees, room and board costs, and the average grant and loan-pluswork-study awards to matriculants receiving aid, all in natural logs. If aid is measured accurately and if net cost is the relevant price to potential students, then the grant variable should have a positive coefficient equal in absolute value to the tuition coefficient. The coefficient on loans and work study should be somewhat smaller, reflecting the smaller present value to the student of each dollar of these forms of aid. Measuring Other Prices and Income The nature of our pooled sample makes it difficult to control properly for changes in income and in the prices of substitutes (and complements). As discussed above, the most appropriate substitutes for the education services provided by a single liberal arts college are those of other liberal arts colleges and of universities. Each college in the sample has a set of other colleges and universities that are its closest available substitutes. This set will generally differ among schools, depending on such factors as institutional quality and location. If data were available, a substitute price for each school could be developed by averaging the costs of attending those particular colleges and universities with the greatest “cross-admissions” with the school.’ Lacking data on cross-admissions, we do not believe it is possible to identify the individual collection of close competitors for each school. Without identifying close substitutes for schools individually, the best substitutes for each liberal arts college seem to be other liberal arts colleges and major public universities, in general. Thus, for each observation, possible measures of the prices of substitutes would be the average cost of attending the liberal arts colleges in the sample in that particular year and the national average cost of attending public universities in that year.

Tuition and Enrollment

Yield at Selective Liberal Arts Colleges

Ideally, we would also like to measure changes in the number of eligible high school seniors and in the average income of their families individually for each college by identifying the demographic groups from which that particular college draws its students. However, the colleges in our sample draw from a large national student pool, so it is unlikely that income and demographic effects exhibit substantial cross-sectional variation. The discussion above suggests including the following variables in the demand equation: national real disposable income, the number of graduating high school seniors, the average cost of liberal arts colleges, and the average cost of public universities. However, each of the variables would be constant across the cross-sectional dimension of our sample, changing only over time. The HEDS data set that is available to us begins in 1988, affording us (at present) only three time-series observations. Clearly, at most two variables that change only over time can be included in the regression, and the effects of these would only be “just identified”. Since entering any single measure that varies only across time is likely to confound its effects with those of the omitted variables, we have resorted to the alternative of proxying for the collective effects of income, demographics and public university costs with a time trend. We believe that the nearest substitute for the services of a liberal arts school is other sample colleges. We embody this substitute price in our regressions by expressing the “own-price” -the tuition and roomand-board cost of each individual college - as a relative price, dividing it by the average current cost of all colleges in the sample. This is equivalent to including the substitute price in the regression and restricting its elasticity to be of the same absolute value and opposite sign as the own-price elasticity. Measuring Quality Prospective students’ (and their parents’) perceptions of the quality of a college are probably as important as cost in choosing among schools to which an applicant has been admitted. Accurate measurement of perceived quality is crucial to obtaining a good estimate of the responsiveness of demand to cost. Many variables have been proposed as measures of institutional quality, some more easily measured than others. A primary difficulty in measuring quality is incorporating intangibles such

315

as reputation and tradition (not to mention where a particular student’s boyfriend or girlfriend happens to attend), which may be important factors in choosing a college. An index of quality that is based on observable variables such as student/faculty ratios, graduation rates, share of the faculty having doctoral degrees, and expenditures per student, but which also includes the results of a reputational survey, underlies the rankings published each October by U.S. News and World Report (USNWR). In recent years, a list of the national top 25 liberal arts colleges has been published that includes many of the schools in our sample. Not only does this ranking incorporate many objective and subjective measures of quality, but because it is widely read by prospective students and their parents, it may have independent predictive value in explaining enrollment choices. In particular, the difference in enrollment effect between being number 25 (and included on the list) and being number 26 (and unmentioned) may be much larger than the actual underlying quality differences between the schools. There are five schools that appear in the USNWR top 25 in at least 1 year that are not among the 82 colleges in the HEDS data set. This makes a total pool of 87 colleges that we know to be eligible for consideration. Since nothing is known of the rank of colleges in our sample that are not in the top 25 in a particular year, they are all assigned a rank of 56.5, which is the mean of the ranks between 26 and 87.’ This discontinuous ranking may capture the importance of being on the list as well as the differences among the ranked schools.x If actual quality differences among unranked schools are important to student choices, the use of a constant, average value for unranked schools, which allows for no sample variation among unranked schools, may bias the coefficient on this variable toward zero relative to the coefficient that would be obtained by using the actual (unknown) rankings for all schools. However, if the publicity associated with being on the U.S. News list is what is important, then the coefficient on the variable with unranked schools averaged should measure the effect appropriately. Because the rankings are published after the beginning of the school year, we lag this variable by 1 year; the 1987 rankings are used to explain matriculations in 1988, etc. Since a small numerical value indicates a high ranking, the coefficient on this variable should have a negative sign.

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Economics of Education Review

Several additional measures of qualitative differences among schools were included in our regressions. Colleges in the sample differed greatly in the degree to which endowment and other nontuition income contributed to total revenue (ranging from 18 to 54%). To the extent that non-tuition revenue is plentiful at a college, students are likely to receive more services per dollar of tuition. The share of non-tuition revenue in total college revenue is included in our regressions as a measure of this and is expected to have a positive effect, coefficient.” Quality is often measured by the average scores of entering freshman on standardized tests such as the Scholastic Aptitude Test (SAT) administered by the College Entrance Examination Board. We include the sum of the SAT mathematics and verbal scores of the average entering freshman in the regressions as a quality measure. If prospective students are attracted to schools at which their peers have high measured academic potential, then this variable should have a positive effect on matriculation.“’ If applicants to liberal arts colleges have, on average, a preference for larger or smaller institutions, then the size of the college might have an effect on matriculation rates. Our enrollment data are taken from the HEDS survey, supplemented by data from College Costs. A positive or negative coefficient is plausible for this variable. Data on non-academic aspects of colleges are more difficult to find than on academic activities, yet these factors are probably quite important in the decisions of prospective matriculants. We include in our regressions the log of non-instructional expenditures per student relative the sample average for the year to provide some rough measure of the amount of resources that the college devotes to noninstructional activity. This variable is very broad, including general adminstrative costs, academic support services such as libraries, building and grounds maintenance, and other components that relate to student life in different ways. If prospective students view these non-instructional expenditures favorably, then the coefficient on this variable should be positive; if they see them as a waste of money that could have been used on academic programs, it should be negative. Finally, students (and their parents) may use the percentage of a college’s recent entering classes who have completed their degrees within a period of 4, 5 or 6 years as an indicator of how satisfied students

are with the college. This variable is believed by the government to be of such importance that the U.S. Department of Education has recently mandated that schools publish data on graduation rates. The regressions reported below include the percentage of students graduating in 5 years or less, averaged over all available observations from the entering classes of 1982 through 1984. Table 1 summarizes the variables included in our regressions together with the signs that we expect for their coefficients. We now proceed to a discussion of our results. ”

III. ECONOMETRIC

RESULTS

A list of the colleges in our sample can be found in the Appendix. As noted above, our study design calls for separate regressions for three categories of admittees: those receiving financial aid (Group A), those qualified for aid but denied (Group D), and those either not applying for aid or not qualified for it (Group 0). Most schools in the sample did not deny financial aid to any admittee who was qualified, leaving only 22 usable observations for Group D. A regression using this highly restricted sample yielded results of no apparent economic or statistical Thus, we report results only for significance.‘* Groups A and 0. Students falling into Group 0 are those for whom financial aid is not a factor; they pay the full price for tuition and fees. Most Group 0 students are probably from relatively wealthy families who are able to afford the tuition charged by private colleges without financial assistance. We expect these admittees to exhibit some elasticity with respect to tuition cost in their choice of colleges, but differences of a few thousand dollars in tuition levels may be relatively insignificant for the very wealthy. Group A comprises students who are receiving financial aid from the college to which they are admitted. The fact of their demonstrated financial need suggests that cost is probably an important factor for them in choosing a college and that their elasticity may be quite high. However, they are paying an amount (based on need) that is less than the full tuition price. Increases in gross tuition may be largely irrelevant to these admittees if they receive offsetting increases in aid, so the elasticity with respect to gross tuition may not be large. Table 2 presents the results of the regressions for Group 0, those who did not apply for aid or did not

Yield at Selective

Tuition and Enrollment

Table 1. Variables

appearing

Liberal

317

Arts Colleges

in regressions

Dependen/ variables 0 Log of matriculation rate of non-aid students: log of the ratio of enrolling to admitted freshman applicants who did not apply for aid or did not qualify 0 Log of matriculation rate of financial-aid recipients: log of the ratio of enrolling to admitted freshman applicants who received financial aid Cost variables 0 Log of relative tuition and fees: log of the ratio of gross tuition and fees to the average for the year of all schools in the sample (-) 0 Log of relative room and board charge: log of ratio of school’s room and board to the average for the year of schools in the sample (-) 0 Log of relative level of aid: log of the ratio of average total aid package received by matriculants receiving aid divided by the average for the year of schools in the sample (+) l Log of relative level of grants: log of the ratio of average grant received by matriculants receiving aid divided by the average for the year of schools in the sample (+) l Log of relative level of loans and work study: log of the ratio of average amount of loans and work study support received by matriculants receiving aid divided by the average for the year of schools in the sample (+) Quality variables l U.S. News and World Report Rank (-) 0 Share of non-tuition revenues: share of total college revenue coming from non-tuition sources (average of years available) (+) 0 Average freshman SAT score (mathematics plus verbal, average of years available) (+) 0 Log of relative non-instructional expenditures per student: log of ratio of school’s expenditures per student to the average for the year of schools in the sample (?) 0 5Year graduation rate: share of students graduating in 5 years or less (average of available years) (+) 0 Size of enrollment (?)

Table 2. Equations

predicting

matriculation

rates of non-aid

students

(Group

0)

(1) Constant Cost measures Log of relative

tuition

Log of relative

room

and fees and board

Quality measures U.S. News and World Report Rank Share Average

of non-tuition

revenue

SAT score

Size of enrollment

(thousands)

5-Year

rate

graduation

Log of relative

level of non-instructional

expenditures

per student

Time Adjusted R’ Standard error of estimate Number of observations Estimated t-statistics are in parenthesis below estimated coefficients. estimated coefficient is different from zero at the 10% (5%) significance

(2)

-2.24** (-4.19)

-2.37** (-5.36)

-0.30 (-1.44) -0.0059 (-0.04)

-0.36** (-2.36) -0.013 (-0.10)

-0.0024 (-1.14) 0.832** (1.98) 0.000701* (1.68) 0.104* (1.94) 0.000104 (0.52) -0.100 (-0.70) -0.051* (-1.74) 0.248 0.255 117

-0.0026 (-1.48) 0.759** (2.30) 0.000744** (2.16) 0.134** (3.50)

One asterisk level.

(two asterisks)

-0.044* (-1.73) 0.281 0.244 139 indicates

that the

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Economics of Education Review

qualify.” The column labeled (I) in Table 2 reports a regression of the log of the matriculation rate on all quality variables, as well as tuition and fees, room and board, and the time trend. The coefficients in this regression are generally not highly significant, suggesting the possibility that quality (and possibly cost) measures may be sufficiently collinear to confound the attempt to distinguish the effects of individual variables. Column (2) of this table reports the results of a regression that omits the two least significant quality variables, the S-year graduation rate and the share of non-instructional expenditures, whose effects were both individually and collectively insignificant. When these two variables are omitted, the sample size increases from 117 to 139 (as noted at the bottom of Tabie 2). This occurs because there are 22 observations for which one of these two variables cannot be observed, but for which all other variables in the model are available. The increase in the reported t statistics from column (1) to column (2) combined with the relatively small change in the values of the coefficients is consistent with the hypothesis of high collinearity among the quality measures. In column (2), both elements of cost exert negative effects on matriculation, though only tuition is statistically significant at conventional levels. The increase in the magnitude and significance of the tuition and fees variable in column (2) relative to column (1) seems to be due to the deletion of the non-instructional expenditures variable. Colleges with high levels of tuition probably also have high levels of non-instructional spending, so inclusion of the latter (statistically insignificant} variable may have robbed some of the effect of tuition changes. The reported coefficients can be interpreted directly as elasticities: a 1% increase in tuition and fees relative to the sample average causes a reduction of approximately 0.36% in the share of admitted Group 0 students matriculating.‘~ As expected, the sign of the U.S. News and World Report rank is negative, though not significantly so. This suggests that colleges achieving a higher rank (lower number) have somewhat more success in recruiting non-aid students, but the relationship is not consistently strong. The share of non-tujtion revenues has a significant positive effect on enrollment decisions; prospective students are attracted to colleges with larger non-tuition revenue sources such as endowments or private fund-raising ability.

As expected, higher average freshman SAT scores increase the share of non-aid admittees who matriculate. The significant positive coefficient for enrollment indicates that the non-aid students seem to show a strong preference for liberal arts colleges with higher enrollments. The negative coefficient on the time trend suggests that, other factors held constant, matriculation rates at selective liberal arts colleges have been decreasing at a rate of about 4% per year. This may reflect a substitution effect from 1988 to 1990 increases in the overall level of liberal arts tuition may have exceeded those of public colleges - or it may be caused by changes in other factors such as the perceived return to a liberal arts education. The adjusted multiple coefficient of determination of 0.281 suggests that although this collection of explanatory variables contributes substantially to changes in matriculation rates, much variation remains to be explained. To summarize, the results reported in Table 2 suggest that students not applying or qualified for financial aid exhibit considerable sensitivity to tuition cost in choosing whether or not to matriculate at a college to which they have been accepted, though the elasticity is considerably less than unity. They are more likely to enroll at colleges having large non-tuition revenue sources, at those having higher freshman SAT scores, at larger schools, and may be more likely to enroll at colleges ranked highly by U.S. News and World Report. Table 3 shows similar regressions for admitted applicants who receive financial aid offers. In the column headed (1) are the results when all quality variables are included in the regression and when total average financial aid (grants and loans/work study) relative to the yearly average are included. Several interesting conclusions emerge. First, both tuition and room and board costs have significant negative effects on enrollment among aid recipients -slightly stronger effects than for non-aid students. This suggests that the higher elasticity that we expect to arise from the lower income status of aid recipients dominates the cost-equalizing effects of the financial aid. The average aid award has a small and statistically insignificant effect on enrollments. Even when broken into components for loans/work study and grants in the column headed (2) in Table 3, aid seems to have no significant effect. As we suggested in an earlier section, we believe that the average award to matriculants is a poor measure of a school’s

Tuition

and

Table 3. Regressions

Enrollment

predicting

the matriculation

rate of financial

aid recipients

(1) 0.421 (1.11)

Constant Cost variables Log of relative tuition and fees

Log of relative Aid

319

Yield at Selective Liberal Arts Colleges

-0.347** (-2.14) -0.345** (-3.22)

room and board

(Group

A)

(4

(3)

0.673* (1.67)

0.175 (0.59)

-0.289* (-1.70) -0.339** (-3.19)

-0.482** (-4.76) -0.341** (-3.91)

variables

-0.0683 (-0.50)

Log of relative

level of aid

Log of relative

level of loans and work study

Log of relative

level of grants

Quality vrrriahles U.S. News and World

Share

of non-tuition

Average

Rank

revenues

SAT score

Log of relative S-Year

Report

-0.0228 (-0.49) -0.0319 (-0.31)

non-instructional

graduation

Size of enrollment

expenditures

per student

rate (thousands)

Time Adjusted R’ Standard error of estimate Number of observations

-0.00504** (-3.69) 0.650** (2.35) -0.00105*” (-3.82) -0.102 (-1.08) 0.000069 (0.32) -0.030 (-0.84) -0.0132 (-0.68) 0.384 0.168 118

Estimated t-statistics are in parenthesis below estimated coefficients. estimated coefficient is different from zero at the 10% (5%) significance

aid posture. Differences in offers between matriculants and non-matriculating admittees may be significant. Further, differences in income levels of applicants at different schools may bias this measure. For these reasons, and perhaps for others, we see no effect of the average size of matriculant financial aid awards on enrollment decisions in Table 3. Given the negligible effect of the measured aid variables, the strong effect of gross tuition is somewhat counterintuitive. To a considerable degree, changes in financial aid are likely to equalize (for any individual student) differences in costs over time or across colleges. If large changes in gross tuition cause smaller changes in costs for aid students, then the elasticity reported in Table 3 will underestimate the true elasticity with respect to financial

One asterisk level.

-0.00536** (-3.94) 0.784** (2.67) -0.00130** (-4.33) -0.151* (-1.55) 0.000060 (0.27) -0.028 (-0.79) -0.0098 (-0.49) 0.407 0.166 Ill (two asterisks)

-0.00424** (-3.69) 0.567** (2.86) -0.00085** (-3.76)

0.387 0.165 144 indicates

that the

changes in net cost. Hence, an elasticity considerably larger (in absolute value) than 0.5 is plausible. In both columns (1) and (2), the quality variables seem to affect the decisions of admittees with aid in a way mostly similar to their effects on non-aid students. Colleges with higher U.S. News and World Report rankings attract more of the Group A applicants they admit, and this effect is twice as large as for non-aid students and is statistically significant. Schools with greater non-tuition revenues are attractive to aid students. Other than SAT scores, the other quality variables (enrollment, non-instructional expenditures and graduation rates) are jointly and individually insignificant, as is the time trend. The coefficient on average freshman SAT scores for Group A is significantly negative, indicating that

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aid students are more likely to enroll at schools with lower scores. This is the opposite of the effect observed for non-aid students and contradicts our prior expectation. We propose two possible explanations for this result. It may be related to our inability to measure comparative individual financial aid offers. Any particular student is likely to receive a more generous offer (higher overall award or larger share of grants in the award) from a school with a lower average SAT score than from one with a high average. This is because his or her particular record will rank more favorably among the applicants to the low SAT college. This may occur even though the average aid offer of the high SAT school (to its stronger applicant pool) is as high or higher than the average offer of the less selective school. Thus, the difficulty in accurately measuring the relevant aid variable may also contribute to the anomaly that high freshman SAT scores reduce enrollment rates among aid students but increase rates for non-aid students. Another possible explanation is that aid students usually must complete their education in 4 years in order to be fully supported. This may make aid students more risk-averse in choosing schools - if an aid student chooses a school that is too competitive and is forced to transfer (which often entails an extra term to make up for inconsistencies in requirements), he or she may be unable to complete a degree on aid. The right-hand column of Table 3 headed (3) presents the regression for Group A with the aid variables, the time trend and the three insignificant quality variables omitted. As in the regression for Group 0, the omission of the non-instructional expenditures variable increases the magnitude of the negative effect of tuition. In the case of the aid students, there is no statistically significant difference between the elasticities with respect to tuition and fees and room and board.

Review

a result of a $100 change in tuition cost.‘s Because our study looks at the effect of changing the cost of a single institution on its enrollment (rather than the effect of a change in costs at the average institution on the total number of individuals attending college). no comparable coefficient can be reported. Among studies in the existing literature, the one that is most comparable to ours is the examination of individual applicants to Occidental College undertaken by Moore, Studenmund and Slobko (1991). Their study not only focused on the relationship between tuition and demand at the level of the individual school, but also used enrollment yield as a measure of demand.‘(’ Although their methodology and data set are very different from those employed here, the underlying measure of demand sensitivity to cost is similar to ours. The Moore, Studenmund and Slobko study indicated a mean elasticity of the probability of attending Occidental with respect to net tuition cost of -0.35 for non-aid students and -0.72 for those receiving aid. Although they were able to examine only one institution, their data on financial aid offers to individual applicants allowed them to measure net tuition much more accurately than is possible in our more aggregated setting. Our estimate of -0.36 for non-aid students is virtually identical to their -0.35 for the group for whom aid is not relevant (and thus for whom any inaccuracies in our measurement of aid are irrelevant). Their estimate of -0.72 for the aid group is higher than our -0.48, providing evidence that the inability to measure accurately financial aid awards gives us a low estimate for the effect of tuition on enrollment of aid students. In their results, higher freshman SAT scores increased enrollment among both groups of students. This lends support to our interpretation of the SAT scores as capturing the effect of the omission of the appropriately measured aid variables. V. COMPARATIVE

IV. COMPARISON

WITH OTHER

STATICS

STUDIES

As noted in the introduction, most studies of the demand for higher education attempt to measure the effect of changes in cost on aggregate enrollment of students at an entire class of colleges or universities. The results of these studies can be compared using a “student price response coefficient”. which measures the change in the proportion of the college-age population choosing to attend college as

To facilitate the interpretation of these statistical results. we now perform some hypothetical experiments to examine the magnitude of the effects implied by the coefficients in Tables 2 and 3. For purposes of illustration. we consider the case of a college that initially admits 1000 students, 500 of whom do not apply for aid and 500 of whom receive aid. Of these applicants. I.50 each of aid and non-aid students enroll (an initial enrollment rate of 30%.

Tuition und Enrollment

Yield ut Selective

which we suppose to be the same for both aid and non-aid students). We shall suppose that this college charges $12,000 per year in tuition and fees, is not ranked in the top 25 by U.S. News and World Report, and relies on tuition for 70% of its total revenue of $20 million (its non-tuition share is 0.30). Consider first the effect of an increase in tuition of 10% relative to other liberal arts colleges compared with the case of no tuition increase. This effect would result, for example, if the college increased its tuition to $13,200 while all other liberal arts colleges in the sample maintained their original levels. Alternatively, if the average of all schools in the sample raised tuition by 4%. then this experiment would show the effects on the example school if it increased tuition by an additional 10% (14% total) compared with the base case of matching the national 4% rise. Using the coefficients in the righthand columns of Tables 2 and 3. we see that if everything else is unchanged, the enrollment rate of non-aid students should decrease by 3.6% (of 30%) to 28.9%, meaning that if the college continues to accept 500 non-aid students, about five or six fewer students will enroll. Aid students are predicted to reduce enrollment by 4.8%, leading to an enrollment rate of 28.3% and about seven fewer matriculants out of 500 admitted. To maintain its assumed target levels of 300 freshmen of whom half receive aid, the college would have to increase its number of admittees by about 1Y non-aid and 25 aid applicants. Next, suppose that the college receives a gift of $lO,OOO.OOO to add to its endowment. At a 5% annual payout rate, this augmentation to the endowment will yield $500,000 per year in nontuition revenue. If tuition and other income sources are held constant, this increases total revenue to $20.5 million and raises the share of non-tuition revenue from 0.30 to 0.317. Multiplying this increase of 0.017 by the coefficient 0.759 shown in Table 2 gives 0.013. or about a 1.3% increase in the number of matriculants out of a given pool of accepted non-aid applicants. The effect on students to whom financial aid is offered is about 1%. Finally, suppose that the school reaches the bottom of the U.S. News and World Report top 25, raising its rank from 56.5 to 25. This reduction of 31.5 rating points, multiplied by the coefficient 0.00257 reported in Table 2. leads to an 8.1% increase in matriculation out of a given pool of nonaid admittees. The corresponding increase in aid students enrolling is a whopping 13.3%. If the

Liberal Arts Colleges

school did not change its admission standards reduce the number admitted, it would enroll additional 12 non-aid and 20 aid students.

321 to an

VI. CONCLUSION In this paper, we use detailed data for 3 years on a sample of selective liberal arts colleges to examine the sensitivity of enrollment decisions of admitted applicants to cost and to measures of institutional quality. We look separately at the decisions of financial aid recipients and at those who did not apply for or did not qualify for aid. We find that an increase in tuition and fees tends to discourage both aid and non-aid admittees from enrolling. In addition, colleges ranked highly by U.S. News and World Report and ones with large non-tuition revenue sources attract a larger share of their admitted pool. The inelasticity of demand at the level of the individual college, together with the significance of the quality variables, confirms that selective liberal arts colleges are not extremely close substitutes for one another. This may have important implications for economists studying the structure of the higher education industry. There are several promising directions in which the approach taken by this paper can be extended. Most fundamentally, we anxiously await the emergence of additional years of data in the HEDS sample. As the time-series component of the sample increases, sharper identification of the parameters should be possible, as well as the explicit introduction of an income variable and prices of substitutes and complements and the implementation of more sophisticated econometric techniques for handling pooled data. In particular, estimation of a fixed-effects model (or the use of changes rather than levels of the variables) would be possible with a more extensive time-series sample. We believe that the weakest aspect of this and other studies is the treatment of financial aid. Data on financial aid offers to non-matriculating admittees and, in particular, data on financial-aid offers to specific cohorts of students would be most helpful in identifying these effects. Unfortunately, we are unaware of any data set at present that would allow this information to be inferred for a broad cross-section of colleges. Finally, it should be possible to extend this study to encompass other aspects of the admission process by incorporating a model of how students choose the

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schools to which they apply and a model of the colleges’ admission decisions. With these three models integrated together, it should be possible to examine in some detail the effects of a college’s tuition

and

matriculant

admissions

policies

on its applicant

and

pools.

Acknowledgements

-

An earlier

version

of this paper was

Review

presented to the Western Economic Association conference in Seattle, Washington in July 1991. We wish to acknowledge our gratitude to Jon Rivenburg, Director of Institutional Research at Reed College. This study could not have been undertaken without his support, assistance and guidance. Heloful comments were orovided bv two anon&nous referee’s, Early exploration oi the HED!? data set was done in a 1991 Reed senior thesis by Christopher Brown. Any remaining errors or shortcomings are. of course. the sole responsibility of the authors.

NOTES I. This classification is defined in the July 8. 1987 issue of the Chronicle of Nigher Edlrcrrfion as highly selective institutions that are primarily undergraduate colleges and that award more than half of their baccalaureate degrees in arts and science fields. 2. A notable exception is the recent paper by Moore, Studenmund and Slobko [l9Yl], in which a sample of applicants was surveyed about their financial aid offers both at Occidental College and at their alternative school. 3. This process has become more refined in recent years through the use of early decision application processes and wait-list admissions. Under the early decision program, students are accepted or denied admission to one preferred school early in their senior years (in advance of the normal admissions process) with the understanding that they will attend the school if they are admitted. Wait-list admissions are students who are admitted only if sufficient regular admittees choose not to matriculate. 4. This may not entirely purge the equation of supply side effects. If a school accurately foresaw a random reduction in its enrollment rate (such as would be caused by the disturbances in our demand equation) and responded to this by changing its level of tuition. then tuition is an endogenous variable and should be modeled simultaneously. We believe this effect is unimportant both because schools typically set tuition levels before random shocks to enrollment rtes are apparent and because they are more likely to respond to such shocks by varying the number of students admitted. particularly through the use of wait lists. 5. We would like to thank an anonymous referee for bringing this potential measurement problem to our attention and for suggesting these examples. 6. Cross-admissions occur between two schools when an individual student is admitted to both schools, giving the student a choice between them. 7. For 1987, they are assigned the value 57. because two schools tied for 25th in the USNWR ranking. making it appropriate to treat the remaining schools as being tied for ranks 27 through 87. 8. Assigning the number 26 rather than 56.5 to unranked schools did not significantly affect the qualitative results of the study. It did. of course, change the magnitude of the coefficient on the li.S. News variable and the comparative statics of changing this variable that are reported later in the paper. 9. Many schools responded to some parts of the HEDS surveys in only one or two of the three sample years. Inclusion of this variable in year-specific form would have necessitated the deletion of many observations from the sample. Because most of the variation in the quality variables is across colleges rather than across time, this variable and some others were averaged for each school across all years in which a value was reported, with the school’s average used for each of the 3 years’ observations. 10. A few schools in the HEDS data base reported a frequency distribution of test scores but did not report an average. For these observations, the projections from a regression of average scores on the fractions scoring in each interval of the frequency table were used. (Separate regressions were run for verbal and mathematics scores.) The SAT variable was also averaged across all available sample years as discussed in the previous footnote. I I In addition to the variables discussed above, several sets of dummy variables were added to the specification. Dummies for the region in which the college is located and for whether or not the college has ever been listed in the U.S. News 11nn World Report top 25 proved collectively and individually insignificant. 12. Most students who are denied aid at one institution choose not to attend - matriculation rates for Group D are very low and are zero for many schools. Colleges vary in their aid policies for such students. For example, some deny aid for the freshman year but promise aid for subsequent years if on which we have no data, are probably the student performs satisfactorily. Such considerations,

Tuition and Enrollment Yield at Selective Liberal Arts Colleges than the variables included in our much more important for these potential “come-anyways” regressions. 13. All regressions were performed by ordinary least squares using RATS 3.11 on a Macintosh personal computer. When pooling time series and cross section observations, it is often desirable to allow at least the constant term of the regression to vary systematically or randomly across time or crosssectional units. The random-effects (variance-components) niodel is not feasible for our unbalanced data set (cross-sectional units are not always observed for the same number of years). To implement the fixed-effects model, one includes dummy variables for each cross-sectional unit. This is equivalent to performing the regression in terms of first differences rather than levels. With no more than three time-series observations for any college, (and fewer than three for many) implementation of this model would reduce degrees of freedom by more than one-half and would eliminate useful crosscollege variation from the sample. As additional years of data become available, it may be feasible to reestimate the model using these methods. 14. The actual elasticity of demand may be larger than this if the pool of applicants shrinks when tuition rises. The coefficients in these tables reflect only the matriculation decisions of admitted applicants. 15. For example, Leslie and Brinkman [1987] report the SPRCs implied by the results of many studies of the aggregate damand for higher education. 16. Other studies that use the enrollment yield as a measure of demand include Tierney (198Oa, 198Ob).

REFERENCES CAMPBELL, R. and SIEGEL, B. (1967) The demand

for higher education in the United States. Am. Econ. Rev. 57, 482-494. FUNK, H.J. (1972) Price elasticity of demand for education at a private university. J. E&c. Res. 66, l30134. HOPKINS, T.D. (1974) Higher education enrollment demand. Econ. Inquiry 12, 53-65. KNUIXEN, 0. and SERVELLE, P. (1978) The demand for higher education at institutions of moderate selectivity. Am. Econ. 22, 30-34. LESLIE, L. and BRINKMAN, P. (1987) Student price response in higher education: the student demand studies. J. Higher Educ. 58, 181-204. MCPHERSON, M. and SCHAPIRO, N. (1991) Does student aid affect college enrollment? New evidence on a persistent controversy. Am. Econ. Rev. 81, 309-318. MOORE, R.L., STUDENMUND, A.H. and SLOBKO, T. (1991) The effect of the financial aid package on the choice of a selective college. Econ. Educ. Rev. 10, 31 I-321. TIERNEY, M. (1980a) Student matriculation decisions and financial aid. Rev. Higher Educ. 3, 14-35. TIERNEY, M. (1980b) The impact of financial aid on student demand for public/private higher education. J. Higher Educ. 51, 527-545.

APPENDIX Our data are drawn from the surveys of the Higher Education Data Sharing (HEDS) Consortium for 1988, 1989 and 1990. There are 82 institutions within the Liberal Arts Colleges I classification of the Carnegie Commission that have in at least 1 year shared data with the HE6S Consortium. Data are collected from annual surveys sent to each of these colleges and are subsequently made available for the institutional use of the members of the consortium. Of the 82 colleges, 76 granted us permission to utilize their data, three refused and three failed to respond to our initial and follow-up requests. Of the 76 usable institutions, many provided to HEDS no data on one or more of the variables of our model in one or more of the 3 years. Of the 228 potential observations (76 schools times 3 years), the actual feasible size of the sample varied between 109 and 143, depending on which variables were included in the particular regression. Each regression was run on the maximum number of usable observations. Table 4 lists the 82 Liberal Arts I schools in the HEDS sample and identifies those that could be used in this study.

323

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Table 4. Colleges Albright College Allegheny College Alma College Amherst College (no response) Augustana College, IL Austin College Bard College Barnard College Beloit College Bethany College, WV Bowdoin College Brvn Mawr College Bucknell University Carleton College Carroll College, WI Centre College of Kentucky Claremont McKenna College Colgate University Colorado College Connecticut College University of Dallas Davidson College Denison College DePauw University Dickinson College (permission refused) Drew University Eckerd CollegeFranklin and Marshall College Furman University Gettysburg College Goucher College Grinnell College Guilford College Gustavus Adolphus College Hamilton College Hamline University Hampden-Sydney College Haverford College Hobart and William Smith Colleges Hollins College (permission refused) College of the Holy Cross

in the HEDS

Review data base

Hope College Juniata College Kenyon College (permission refused) Lafayette College Lawrence University Lewis and Clark College Macalester College Manhattenville College Middlebury College Mills College Mt Holyoke College (no response) Muhlenberg College Oberlin College Occidental College Oglethorpe Uni&sitv Pitzer College _ Randolph-Macon Colleee Randolph-Macon Woman’s College Reed College Rhodes College Ripon College Scripps College Skidmore College Smith College St John’s College (no response) St Lawrence Uiiversity ’ Swarthmore College Sweet Briar College Trinity College, CT Union College University of the South Ursinus College Vassar College Washington College Washington and Lee University Wellesley College Wesleyan University Whitman College Sillamette University Williams College College of Wooster