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Tuition Discounting for Revenue Management
Nicholas W. Hillman
Received: 25 March 2011 / Published online: 16 July 2011 � Springer Science+Business Media, LLC 2011
Abstract Over the past decade, institutionally-funded financial aid (or ‘‘tuition dis- counts’’) have been the fastest-growing item within most public four-year college and
university operating budgets. One explanation for this trend is due to the changing structure
of public colleges’ revenue streams, as tuition and fees have replaced state appropriations
as a viable and predictable source of funding. This analysis explores the extent to which
expenditures on institutionally-funded financial aid generates additional revenue for public
four-year colleges and universities. Using institutional data (n = 174) from 2002 to 2008, the analysis implements a generalized method of moments (GMM) technique and con-
cludes that aid indeed can be leveraged for revenue generation. However, this relationship
is only sustainable to a certain point. When unfunded tuition discount rates exceed
approximately 13%, institutions may experience diminishing revenue returns to this
financial aid investment.
Keywords Institutional aid � Enrollment management � Revenue generation � GMM
Public colleges and universities have traditionally relied upon state appropriations as a
primary revenue source for financing institutional operating budgets. Over the past two
decades, however, this source of support has been strained due to a variety of changes in
the nation’s economic, political, and demographic landscape (Archibald and Feldman
2008; Heller 2006). As these changes persist, public colleges and universities are seeking
out alternative sources of revenue to replace funds that were once publicly available.
Tuition and fees 1
have emerged as one of the most viable ‘‘alternative’’ revenue sources for
many public four-year institutions, as this source accounts for 30% of their total operating
revenues (Desrochers et al. 2010). To the extent that students are now viewed as a source
N. W. Hillman (&) Educational Leadership & Policy, University of Utah, 1705 Campus Center Dr. Milton Bennion Hall, Room 313, Salt Lake City, UT 84112, USA e-mail: [email protected]
1 Hereafter, ‘‘tuition and fees’’ is referred to as ‘‘tuition.’’
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Res High Educ (2012) 53:263–281 DOI 10.1007/s11162-011-9233-4
of revenue, colleges and universities are experimenting with enrollment and revenue
management strategies, such as ‘‘tuition discounting,’’ to capitalize on these resources
(Hossler 2004, 2006).
Tuition discounting is the practice of awarding institutionally-funded financial aid in the
form of non-repayable grants and scholarships to students. Similar to state and federal
grant programs, colleges provide aid to reduce the ‘‘sticker price’’ students pay for college.
In 2008, students attending public four-year institutions received over $14 billion in grant
and scholarship aid from federal, state, and institutional providers; campus-based aid
programs accounted for approximately 33% of this total amount (U.S. Department of
Education 2009). If federal and state government offer financial aid, then why do colleges
also aid students? This question has been asked by several scholars (Martin 2005;
McPherson and Schapiro 1998; Weisbrod et al. 2010) and a common conclusion is that aid
is used as an enrollment management tool to fulfill such objectives as enticing students to
choose their college over a competitor, recruiting academically or athletically talented
students, reducing price barriers for lower-income students, or to simply increase enroll-
ment capacity (Curs and Singell 2010; DesJardins and McCall 2010; Reed and Shireman
2008). By offering tuition discounts, colleges can ‘‘craft a class’’ of desirable students that
helps colleges reach various objectives (Duffy and Goldberg 1998).
However, colleges also offer tuition discounts for revenue management purposes
(Breneman et al. 2001; Cheslock 2006). This is particularly true given the tight financial
environment in which public institutions operate. Many institutions are becoming stra-
tegic in their use of tuition discounts so that aided students not only enhance institutional
prestige but they can also enhance institutional revenue goals. Institutions may desire to
achieve a variety of enrollment management objectives through the strategic use of
tuition discounts, but these efforts are ultimately conditioned by the financial benefits and
costs associated with aiding students. It is from this perspective that the following study
is framed because, from the budgetary standpoint, the most important reason colleges
engage in discounting is to generate or enhance net tuition revenue (Lasher and Sullivan
2005).
According to economic theory, the process of aiding students can yield financial ben-
efits for colleges. By enticing students and their associated tuition dollars to enroll, col- leges can strategically leverage aid to maximize (or at least enhance) the amount of net
tuition revenue generated per aided student. However, overly-aggressive or inefficient
discounting strategies can sometimes reduce, rather than enhance, revenue streams (Davis
2003; Massa and Parker 2007; Redd 2000). In today’s tight fiscal environment it is not in
an institution’s best financial interest to offer tuition discounts that erode tuition revenue
generation. If public institutions choose to engage in discounting to achieve revenue
generation objectives, then it behooves administrators and college leaders to understand the
impact this strategy has on the financial wellbeing of the institution. To that end, this paper
addresses the following research questions. To what extent does the provision of financial aid yield financial benefits to public colleges and universities? Secondarily, is there a point at which the provision of institutional aid no longer yields financial benefits to the institution?
This study uses a dynamic panel dataset of public four-year colleges (n = 174) between 2002 and 2008 to empirically examine the relationship between tuition discounting and
tuition revenue generation. The panel dataset is robust with 1,218 total observations.
Framed within microeconomic theory of firm behavior, this study finds that tuition dis-
counting can indeed be a tool for enhancing net tuition revenue, but only to a limited
extent. After controlling for various economic and institutional indicators, it appears that
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colleges offering unfunded tuition discount rates 2
beyond 13% begin to yield smaller
amounts of net tuition revenue. This finding implies that many public institutions are
diminishing their net tuition revenues by aiding students; institutions operating beyond this
threshold may find it in their financial best interests to design a more economically efficient
method of distributing financial aid. All institutions will design aid strategies that align
with their organizational culture, resource capacity, and academic mission, but findings
from this analysis urge them to take fiscal caution when engaging in discounting practices.
Results from this analysis have implications on the financial risks and rewards of current
discounting trends, and they also draw attention to the tradeoffs that exist when aiding
students from unfunded sources.
The Economic Pressure to Discount
The expansion of institutional aid has steadily grown in recent years. This expansion can
be viewed in relation to state higher education spending and trends in rising tuition rates.
Nationally, states are scaling back appropriations for higher education which has resulted
in students carrying a greater cost-sharing burden for their education (Johnstone and
Marcucci 2010; Johnstone 2004). Due to this shift in cost-sharing, tuition and fees have
risen inversely with state appropriations and institutions are now relying on students as a
primary revenue source. This can be seen in the table below, where institutions received
nearly $5,000 in net tuition revenue per student in 2002 but by 2008 this value had
increased to $6,649. Alternatively, state appropriations per student declined by nearly
$1,000 during the same period. The financial structure of public institutions has slowly
shifted towards tuition reliance over the past several decades, but in recent years this trend
has been accentuated (McPherson and Schapiro 2006).
There is a wide degree of variation across the country with regard to state subsidization
of public institutions. Some institutions receive relatively low levels of state financial
support, resulting in greater pressure to generate revenue from students through tuition and
fees. These institutions may face greater pressure to discount tuition by providing aid from
their own operation budgets. Alternatively, institutions may generate high levels of state
subsidization which allow them to keep tuition levels low for all students. When tuition is
low, institutions may face little pressure to engage in discounting. The extent to which an
institution relies on students as a revenue stream is a function of state subsidies, and
discounting strategies will invariably be designed to account for these trends (Table 1).
Since public institutions charge resident and non-resident students two separate prices,
there may be an economic incentive to recruit non-resident students in order to generate
tuition revenue. Some public institutions seek to maximize non-resident enrollment levels
in order to capitalize on the substantially higher price these students pay compared to their
in-state peers (Zhang 2007). Colleges that seek to enroll non-resident students may have
financial gains, but they may also face greater economic pressure to provide non-residents
with financial aid. So, the extent to which an institution enrolls students from out-of-state
may not only impact net tuition revenue but it may also shape tuition discounting strate-
gies. In the private sector of higher education, these economic issues are not relevant since
institutions charge a unitary price to all students and endowments, rather than state
appropriations, serve as a primary source of subsidization.
2 Tuition discount rates are calculated by dividing total institutional aid expenditures by gross tuition
revenue, as advocated by Baum and Lapovsky (2006).
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Recent Discounting Trends
In 2008, public four-year institutions awarded more than $5.4 billion of institutional aid to
approximately 22% of their undergraduate students (U.S. Department of Education 2009).
To put this value into context of the national student financial aid landscape, institutions
provide approximately 33% of total grant aid to undergraduate students. That same year,
federal and state grant programs awarded $4.7 and $4.3 billion, respectively, to under-
graduate students enrolled in public four-year institutions. Despite being a primary source
of financial aid for a significant proportion of undergraduate students, little empirical
research has been conducted on expenditure patterns of institutional aid. Researchers tend
to examine financial aid expenditures patterns at the federal and state levels, but less often
at the campus level. Recently, this trend has begun to shift as more scholars are examining
public sector tuition discounting patterns (Curs 2008; Curs and Dar 2010; Doyle et al.
2009; Doyle 2010).
When studies have looked at tuition discounting at the campus level, researchers tend
to focus on private rather than public institutions. This is understandable, as private
institutions have a long history of aiding students and many of these colleges are tuition-
dependent which means they rely on aid to generate tuition revenue (Thelin 2004;
Wilkinson 2005). However, the trend towards tuition discounting is not isolated to the
private sector, and researchers have called for further inquiry into the role aid plays within
public college and university budgets (Baum and Lapovsky 2006; Hossler 2006). Not until
the late 1970s and early 1980s did public institutions began to experiment with leveraging
aid in similar ways as their private sector counterparts (Potter and Sidar 1978; Wilkinson
2005). Due to a low tuition model, combined with a relatively high degree of governmental
subsidization, many public institutions did not have much necessity to offer aid out of their
own operating budgets. But in today’s financial climate, new challenges exist for financial
planners who are charged with projecting net tuition revenues and for the strategic use of
financial aid (Brinkman and Morgan 2010). The provision of institutional aid is now a
standard business practice in the public sector of higher education. To be sure, expendi-
tures on institutional aid have been the fastest-growing item in most public four-year
college budgets during the past decade (Desrochers et al. 2010).
When public colleges offer grants and scholarships, the funds are generally available
from one of two sources. The most common source is institutional operating budgets, while
Table 1 Changes in public four- year college and universities’ (n = 174) revenues from net tuition and state appropriations
Inflation-adjusted to 2008 dollars
Academic year Per-FTE revenue from net tuition
Per-FTE revenue from state appropriations
2002 $4,956 $8,381
2003 $5,356 $7,774
2004 $5,789 $7,220
2005 $6,119 $7,049
2006 $6,337 $7,056
2007 $6,458 $7,304
2008 $6,649 $7,563
Dollar change, 2002–2008 $1,693 -$818
Percent change, 2002–2008 (34%) (-10%)
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the less common source is restricted endowment revenues. The former source of aid is
often classified as ‘‘unfunded’’ because the funds can be used for any variety of alternative
institutional objectives such as teaching, research, or service. The latter sources of aid are
considered ‘‘funded’’ when endowed funds are dedicated to supporting a specific financial
aid program; these funds cannot be used for other institutional objectives. Unlike funded
aid, unfunded aid is subject to the competing opportunity costs associated with various
institutional priorities and are thus subject to the law of diminishing returns (Martin 2004,
2005). The difference between funded and unfunded aid has significant policy implications
for campus officials, particularly among private colleges that operate large endowments
(Allan and Lapovsky 2005). Most public colleges do not have large endowment payouts, so
the way in which unfunded aid is leveraged bears significant financial implications for many of these institutions (Lapovsky 2007).
The average discount rate for public four-year institutions in this study is approximately
16%, which means that these institutions retain $0.84 for every tuition dollar they charge.
Funded and unfunded discount rates are approximately 4 and 12%, respectively. Other
analyses have found similar discount rates ranging between 14 and 20% in recent years
(Baum and Lapovsky 2006; Baum and Ma 2010; Desrochers et al. 2010) (Table 2).
Review of the Literature
Public colleges have invested a significant amount of resources into financial aid to meet a
variety of enrollment management and revenue management objectives. Literature on
tuition discounting tends to focus on the former objective, while there is a significant
amount of work to be done in understanding the latter. The purpose of this study is to
examine the revenue management objectives of aiding students, yet the enrollment man-
agement purposes can not be ignored. Colleges design aid programs to achieve a range of
such enrollment outcomes as encouraging academically talented students to enroll in
college (Curs 2008; Ehrenberg et al. 2006), reducing price barriers for students demon-
strating financial need (Perna et al. 2010), encouraging students to persist (Chen and
DesJardins 2010; Hossler et al. 2009; Perna 2010), and even simply meeting the institu-
tion’s enrollment capacity (Curs and Singell 2010; DesJardins and McCall 2010). Several
researchers have examined how aid influences these enrollment outcomes, revealing a
Table 2 Public four-year colleges and universities’ (n = 174) average institutional aid expenditures and discount rates by source of funds
Academic year
Average aid expenditures Average discount rates
Funded aid per FTE
Unfunded aid per FTE
Total aid expenditures per FTE
Funded discount rate (%)
Unfunded discount rate (%)
Total discount rate (%)
2002 $326 $691 $1,017 5.3 11.5 16.8
2003 $310 $708 $1,018 4.7 10.9 15.6
2004 $302 $798 $1,100 4.2 11.2 15.4
2005 $311 $835 $1,146 4.0 11.1 15.1
2006 $326 $897 $1,223 4.0 11.6 15.6
2007 $310 $994 $1,304 3.8 12.4 16.2
2008 $338 $1,016 $1,354 4.0 12.3 16.3
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nontrivial relationship between aid and student participation or persistence behaviors.
When one turns attention towards the revenue management purposes of tuition discount-
ing, however, the literature becomes less comprehensive.
McPherson and Schapiro (1998) provide a starting point from which one can frame the
revenue management objectives of tuition discounting. Reflecting upon their experiences
with campus leadership teams and their observations of national trends, the authors explain
that financial aid is a necessary revenue management tool that has developed from the
‘‘intense competition among colleges and universities for dollars and students.’’ To them,
student financial aid is a ‘‘strategic variable’’ for ensuring the financial wellbeing of an
institution. In order to achieve desired financial outcomes, McPherson and Schapiro (1998)
explain that colleges can intentionally exploit students’ willingness to pay in order to
extract their consumer surplus. Engaging in this revenue management tactic will, in theory,
maximize tuition revenue for the institution. In practice, however, institutions offer aid
without a thorough interpretation of each student’s willingness to pay. As a result, some
students end up paying a significantly lower price than what they would actually be willing
to pay and the provision of aid can be viewed as an economically inefficient allocation of
resources if an institution is awarding ‘‘too much’’ aid to students.
Martin (2005) offers an economic model to further describe the relationship between aid
and revenue generation. To ensure that an institution is maximizing its tuition revenue, he
explains that the revenue associated with enrolling an additional student should always
exceed the average cost of institutional aid. If an institution spends more money on a
student compared to the amount it generates from that student’s tuition payment, then the
college will operate an inefficient aid program that diminishes overall net tuition revenue.
A degree of inefficiency is expected within the higher education production function;
however, aid expenditures are one of only a few variable cost items within operating
budgets. More uniquely, aid expenditures are one of very few budgetary items that can also
generate short-term revenue gains.
An example of strategic alignment of discounts for revenue generation can be seen in
Massa and Parker’s (2007) analysis of a private liberal arts college. In the late 1990s,
Dickinson College had been discounting their tuition by more than 50% to incoming
freshmen. The institution was only generating $0.48 cents for every dollar charged in
tuition. At this pace, the institution would approach long-run fiscal insolvency or at least
fiscal strain. To avoid this ‘‘net tuition revenue dilemma,’’ the institution reduced its
discount rate to approximately 30% by 2007 and actually generated greater amounts of
tuition revenue in the process. Their solution included a strategic effort to target aid to a
smaller portion of the student body while simultaneously analyzing students’ willingness to
pay. Between the late 1990s and mid 2000s, students continued to express high demand for
a Dickinson College degree, so they continued to enroll even if they did not benefit from as
deep of discounts earlier cohorts received. The authors concluded that ‘‘discounting gone
wild can handcuff a college…where it doesn’t have sufficient revenue to cover expendi- tures or it reduces expenditures and threatens the quality of educational experience’’
(Massa and Parker 2007). Many public institutions do not have as inelastic demand curves
as Dickinson College or other elite private institutions, yet the fundamental economic
lessons from the private sector experience remain relevant to public institutions.
An additional empirical example of aid’s relationship to net tuition revenue is found in
Summers (2004). Here, the author utilizes institution-level data from 1997 to 2000 to
uncover a statistical relationship between institutional aid awards and net tuition revenue
among private colleges and universities. After implementing an econometric model, net
tuition revenue was found to increase when expenditures on institutional aid increase. This
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linear and positive relationship led the author to conclude that aid is being ‘‘distributed in a
manner that boosts enrollment and earns a net revenue return from these expenditures.’’
However, such a conclusion is counter-intuitive to the economic theory and to that which
was found in Massa and Parker’s (2007) analysis. Aid is expected to increase tuition
revenue, but after a certain point there is a high likelihood that aid actually diminishes this
source of revenue. In other words, the cost of aiding students is expected to eventually
outweigh the (financial) benefits of enrolling students. Summers’ model does not account
for this possibility.
Considering the limited empirical findings that have tested this economic model, in
addition to the conflicting results that have surfaced, questions remain regarding aid’s
relationship to net tuition revenue. Do similar patterns found in Massa and Parker (2007)
hold when multiple institutions are analyzed? Also, to address Summers’ work (2004), is it
possible that the relationship between aid and revenue is hill-shaped rather than linear,
where aid can generate additional revenues only to a certain threshold at which time
revenues begin to decline when ‘‘too much’’ aid is awarded?
Conceptual Framework
Microeconomic theory of nonprofit firm behavior serves as the conceptual framework
informing the empirical model. Under this framework, colleges and universities are
expected to maximize their utility by allocating resources according to each institution’s
unique social and academic missions. Despite the heterogeneity of institutional missions,
one measure of ‘‘utility’’ that all institutions desire to maximize is reputation and prestige
(Bowen 1980; Brewer et al. 2002). In their pursuit of these ends, many institutions engage
in strategic enrollment management (SEM) practices that are designed to ‘‘craft a class’’ of
the ‘‘best and brighetest’’ students (Duffy and Goldberg 1998; Ehrenberg et al. 2006).
Financial aid has emerged as a common SEM practice for recruiting and retaining students
since scholarships and grant aid can entice students to make enrollment decisions (Hossler
2000).
By strategically allocating financial aid, colleges are able to enhance their academic
reputations by recruiting students who have high SAT scores. Similarly, institutions that
are able to recruit nationally may be perceived as being more prestigious than those that
recruit regionally (Brewer et al. 2002). A utility-maximizing college using SEM practices
may decide to offer deep discounts to students based on SAT scores or ‘‘out-of-state’’
residency status if institutional decision-makers believe these students will enhance the
institution’s academic reputation. Similarly, institutional leaders may target discounts to
minority and low-income students in order to ‘‘build or maintain prestige at a national and
general level…[by] becom[ing] more and more inclusive’’ (Brewer et al. 2002, p. 62). To the extent these discounting practice enhance reputation and prestige, colleges will pursue
them even if it diminishes net tuition revenue.
However, as public colleges become increasingly tuition-dependent, they are becoming
increasingly concerned about the revenue implications of discounting practices (Hossler
2006). When shifting attention to the fiscal impact of SEM strategies, tuition discounts can
be viewed as a revenue management tool that helps institutions enhance their financial conditions. The following discussion will briefly demonstrate how institutional decision-
makers and SEM professionals might approach tuition discounting as a revenue man-
agement tool; for further discussion please see Breneman et al. (2001)and Cheslock (2006).
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In Fig. 1, an institution charging tuition at point P1 will enroll students up to the point Q1, where the downward-sloping line (D) represents the students’ aggregate elasticity of demand. If the institution discounts its price to P2, then enrollment will increase to the point of demand, or Q2. The area within points P1, A1, Q1, represents the institution’s gross tuition revenue from non-aided students, and the area under A1, A3, Q2, Q1, represents the gross tuition revenue of aided students. The area within A1, A2, A3 represents the amount of institutional aid necessary to entice students to enroll to the point Q2, so this amount is subtracted from gross tuition revenue to calculate net tuition revenue. Net tuition revenue
is expressed in this figure as the non-shaded region below P1, A1, A3, Q2, and the origin. Due to the two-tiered pricing structure of public institutions, resident and non-resident
students face two distinctly different tuition levels and consequently, two different demand
elasticities.
The nature of this relationship is subject to the economic phenomenon of diminishing
returns. For instance, if an institution offered a 100% discount rate to all students, then it
would reduce the price they pay to zero and enrollment could be maximized to the point of
capacity. As a result of fully discounting tuition for all students, however, this institution
would no longer yield any net tuition revenue. The shaded area of A1, A2, and A3 would be greater than the gross tuition revenue associated with enrolling students; the financial
returns of aiding students would diminish to zero. Because of this tradeoff, it would be
inefficient and unsustainable for tuition-dependent institutions to offer full discounts to all
students. Microeconomic theory suggests that institutions can only provide discounts up to
a certain point and any additional movement beyond this point will begin to diminish net
revenues. It may be tempting for colleges to spend additional money on aid simply to
maximize their net tuition revenue because of the potential financial benefits; however, the
risk of diminishing tuition revenues is profound.
To the extent that colleges seek to maximize reputation and prestige, they will likely
design tuition discounting strategies that allocate aid in relation to students’ SAT scores,
residency status, racial/ethnic diversity, or socioeconomic status. Using aid to craft a class
Fig. 1 The economic relationship between enrollment, tuition, and aid
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of desirable students is an SEM practice that can help institutions improve their perceived
reputation and academic profile. However, tuition discounts can also be utilized for rev-
enue management purposes as demonstrated in Fig. 1. While the ultimate goal of tuition
discounting may be to enhance the reputational profile of the institution, we cannot
overlook the financial implications associated with these SEM trends.
Empirical Techniques
Data Sources
Public four-year colleges and universities in the U.S. are the primary unit of analysis for
this study. Because of the unique financial environment and microeconomic frameworks in
which state-funded institutions operate, this analysis excludes all private institutions. The
Delta Cost Project provided institution-level data from the U.S. Department of Education
IPEDS database. Delta Cost Project data disaggregates financial aid data between ‘‘fun-
ded’’ and ‘‘unfunded’’ sources, which is unavailable through IPEDS.
In 2002, a broad range of accounting standards changed the way some institutions report
financial aid records. Accordingly, this analysis includes those institutions charging tuition
and offering financial aid for each year between 2002 and 2008 (the most recent year
available) creating a panel dataset of 174 institutions over 7 years (n = 1218). Institutions voluntarily reported interstate migration data for odd-numbered years, thus reducing the
sample size to include only those reporting data in all years between 2002 and 2008. All
financial data are inflation-adjusted using the 2008 Consumer Price Index.
Outcome Variable
Variables are selected based on the conceptual theory outlined above. The outcome of
interest is net tuition revenue per full-time equivalent student (NTR) which is calculated by the gross tuition revenue less tuition discounts excluding tuition waivers. Under this def-
inition, net tuition revenue is the final amount of funds brought into institutional budgets
from student tuition payments.
Predictor Variables
Net tuition revenue is expected to be a function of the following economic factors
described in the conceptual framework: resident and non-resident sticker price, resident
and non-resident enrollment, and the tuition discount rate. Sticker price is the published
amount charged to students during the fall semester and does not include other charges
such as room, board, books, supplies, or transportation. Enrollment levels by student
residency status are reported for first-time, full-time incoming freshmen students. The
percent of in-state and out-of-state freshmen is multiplied by the institution’s undergrad-
uate FTE to estimate total institutional enrollment levels based on residency status. While
not an exact measure, this procedure serves as a proxy for institutional enrollment mix.
Funded and unfunded tuition discount rates are the key predictor variables of interest and
are introduced into the model both linearly and quadratically to account for the potential
diminishing returns described in the conceptual framework.
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The purely economic model does not control for unique institutional characteristics that
are expected to influence net tuition revenues. To that end, additional variables described in
the literature review and conceptual framework are introduced in a second model. This
model includes the economic predictors in addition to such predictors as: percent of
undergraduate students who are ethnic/racial (i.e. non-white) minorities, the median SAT
score for the incoming freshman cohort, institutional selectivity, and the degree of state
subsidization. For SAT, only the 25th and 75th percentile verbal and math scores are
available in the dataset, so the average of these two data points are added together as an
estimated median SAT score. In the event that ACT is the dominant standardized test for
an institution, then these scores are converted to SAT scores based on the College Board
concordance tables (College Board 2010). Institutional selectivity is calculated by dividing
the number of admitted freshmen by the number of applicants, and state subsidization is
the total amount of current-year state appropriations by FTE. Each of these variables is
continuous in scale and is described in Table 3.
Several of these predictor variables are introduced into the model endogenously: esti-
mated in-state and out-of-state enrollment, SAT, selectivity, percent minority, and percent
low-income. While this analysis is framed around the assumption that the outcome insti-
tutions seek to maximize (or at least enhance) is net tuition revenue, there are several
alternatively compelling outcomes related to tuition discounting practices. The pursuit for
high-achieving students as measured by SAT score and selectivity, the priority of ensuring
greater student diversity along the lines of race and ethnicity, and assisting low-income
students are but three motivations driving colleges to engage in discounting. It is unclear
whether gains in net tuition revenue are leveraged to ‘‘craft a class’’ of desirable students,
or whether the opposite may occur; these variables both influence and are influenced by net tuition revenue. Additionally, the key variable of interest (the unfunded tuition discount
rate) is endogenous to the model because aid is utilized to generate revenue but institutions
generating greater revenue are able to provide additional aid to students. As a result, this
model runs the risk of yielding biased or inefficient parameter estimates. Accordingly, a
generalized method of moments (GMM) model is designed which utilizes instrumental
Table 3 Descriptive statistics of explanatory and outcome variables used in regression equation, public four-year colleges and universities only (n = 174)
Variable Mean SD
Institution’s net tuition revenue per undergraduate FTE $5,952 $2,429
Percent of undergraduates who are ethnic minorities 26.7% 18.7%
Estimated median SAT score of incoming freshman class 1,062 108
Percent of undergraduate applicants admitted (selectivity) 73.3% 15.7%
Percent of undergraduates whose family income is less than $30,000 10.0% 5.0%
Institutional revenue from state appropriations per undergrad. FTE $7,478 $3,599
In-state estimated undergraduate FTE enrollment 9,847 7,736
Out-of-state estimated undergraduate FTE enrollment 2,329 3,247
Published in-state tuition and fees $5,352 $1,810
Published out-of-state tuition and fees $13,999 $4,780
Average funded discount rate 4.3% 4.9%
Average unfunded discount rate 11.6% 9.8%
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variable techniques to improve model consistency and efficiency. Unit root tests concluded
that no endogenous predictors were stationary, thus warranting the use of this technique.
Analytical Techniques
This analysis implements an Arellano-Bond GMM technique designed for dynamic panel
data estimation (Blundell et al. 2000; Bond 2002; Roodman 2006). Within higher edu-
cation literature, GMM techniques have been used to study the impact of state higher
education finance on degree productivity (Titus 2009) and how changes in student loan
interest rates affect student loan volume (Austin 2010). One of the reasons why researchers
have found utility in GMM is because the technique allows for the inclusion of lagged
values of the outcome variable on the right-hand side of the regression equation. It is quite
likely that past outcomes (e.g. past degree productivity or loan volume) are strong pre-
dictors of current and future outcomes, but standard OLS and fixed-effects regression will
produce biased parameter estimates if lagged dependent variables are included as pre-
dictors (Kiviet 1995; Nickell 1981). In this study, we expect that past levels of net tuition
revenue are relevant predictors of future net tuition revenue values. Researchers recom-
mend using GMM to estimate dynamic models that include lagged dependent variables as
predictors (Arellano and Bond 1991; Blundell and Bond 1998).
GMM is also able to produce consistent and efficient estimates that are robust to model
endogeneity. Two-stage least squares (2SLS) methods are more commonly utilized to
improve model consistency and efficiency when endogenous variables are present, but it is
often difficult in social science research to find ‘‘good’’ instruments that are both strong and
valid (Baum et al. 2003; Halaby 2004). To generate consistent and efficient estimates,
2SLS techniques require the researcher to identify and introduce exogenous instrumental
variables that correlate with the endogenous predictor(s) while also being orthogonal to the
error term. Researchers warn, however, that the ‘‘cure’’ of introducing an exogenous
variable via 2SLS can be worse than the ‘‘disease’’ of endogeneity if the instruments are
weak or invalid (Wooldridge 2002). Alternatively, through first-differencing the equation,
GMM utilizes the lags of the differences to serve as instruments. By creating a set of
instruments from within the existing dataset, GMM generates a larger number of instru-
ments than what would be available in 2SLS (Bond 2002).
In this study, the GMM estimates are implemented in two stages, beginning with the
following equation:
yi;t ¼ ayi;t�1 þ cWi;t þ cXi;t þ gi þ ui;t � �
ð1Þ
where y is the outcome variable (net tuition revenue per FTE) for institution i in period t, yi,t-1 is the lagged value of the outcome, c is the parameter estimate, W is the vector of endogenous variables, X is the vector of exogenous variables, g is the unobserved time- invariant institution-specific effect and u is the error term. If we were to apply OLS regression to this model, the estimates would be inconsistent because the lagged variable
(yi,t-1) is correlated with the error term (gi ? ui,t) through the subscript i (Bond 2002). The first stage takes the first-difference of Eq. 1 to eliminate the unobserved institu-
tional-specific effects (gi):
yi;t � yi;t�1 ¼ a yi;t�1 � yi;t�2 � �
þ c Wi;t � Wi;t�1 � �
þ cXi;t � cXi;t�1 � �
þ ui;t � ui;t � �
ð2Þ
In the second stage (3), the lagged values of endogenous predictors are instrumented in
subsequent first-differences. These new instruments are correlated with the predictor
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variable, while remaining orthogonal to the error term. The ‘‘system’’ GMM technique
implemented in this study takes advantage of both levels and differences of the data, for
more details see Blundell and Bond (1998) and Roodman (2006). The final model is
expressed through the following equation:
yi;t ¼ a þ b1yi;t�1 þ c2 Wi;t � Wi;t�1 � �
þ c3 Xi;t � Xi;t�1 � �
þ ui;t � ui;t�1 � �
ð3Þ
where y is the inflation-adjusted net tuition revenue per FTE, a is the intercept, W is the vector of endogenous variables and X is the vector of exogenous variables for each institution (i) in each period of time (t). The error term, u, is robust to small sample sizes (Windmeijer 2005).
The successful implementation of GMM requires that the instruments meet two con-
ditions. First, instruments must provide a source of variation for the model and secondly
the lags must provide an exogenous source of variation for the model (Roodman 2006). To
meet the first condition, instruments must be strong and this strength can be identified
through the first-stage 2SLS F-value. If the F-value is greater than 10, then the instruments are generally considered to be strong although this is only a rule of thumb that econo-
metricians have yet to agree upon (Angrist 2006; Bound et al. 1995; Stock and Yogo
2002). To meet the second condition, instruments must be valid; the Hansen-J test with a chi-square distribution is implemented to address instrument validity. If the Hansen-J test is significant, then the instruments are systematically correlated with the error term, ren-
dering them invalid. Table 4 provides information on the strength and validity of the
instruments, concluding that all instruments are valid and three are unambiguously strong.
After implementing the GMM model, autocorrelation has successfully been addressed
and eliminated from the model as evidenced by the rejection of the null AR(2) Arellano-
Bond hypothesis (Arellano and Bond 1991). One additional caveat when implementing
GMM techniques rests with the total number of instruments utilized in the model. It is
possible for researchers to include too many instruments, which yields an artificial
improvement to the consistency of parameter estimates (Roodman 2009). One rule of
thumb is that the number of instruments does not exceed the number of groups. When this
occurs, the model is over-identified and estimates are biased. This analysis utilizes 73 and
99 instruments for Models 1 and 2, respectively, and a total of 174 groups.
Models with Quadratic Predictors
The funded and unfunded discount rates are introduced into the model as linear predictors
of net tuition revenue. Their quadratic values are also introduced to account for the
Table 4 F-statistics for first- stage 2SLS fixed effect estimate of instrument strength (n = 174)
* p \ 0.01, ** p \ 0.005, *** p \ 0.001
F-statistic
Percent minority enrollment 406.45***
Selectivity (% admitted) 9.52***
Median SAT of incoming cohort 99.28***
In-state FTE enrollment 97.07***
Out-of-state FTE enrollment 27.98***
Percent low-income enrollment 12.67***
Funded discount rate 16.59***
Unfunded discount rate 19.20***
274 Res High Educ (2012) 53:263–281
123
potential diminishing returns that are expected to exist with the outcome variable. Under
the diminishing return principle, the linear relationship should yield positive coefficient
estimates representing an upward-sloping relationship between discount rates and net
tuition revenue. The quadratic value is expected to be negatively-sloping which would
indicate that at some point the linear value begins to diminish downwards toward zero. By
calculating the vertex of these coefficients, one is able to estimate the point at which
discount rates begin to diminish net tuition revenues.
Limitations
This study is limited in various ways. First, the data source does not enable us to examine
all public four-year institutions for all years between 2002 and 2008. Only those submitting
state residency data and those providing institutional aid were included in this study, which
limited the total number of observations to account for approximately one-third of the total
public four-year population. While there is no way to address this data limitation, caution
should be taken when interpreting and generalizing these results. Second, the GMM
technique cannot be implemented for separate Carnegie Groups because the number of
instruments would invariably be larger than the number of within-group observations. It is
possible that variations among Carnegie groups exist, but the GMM technique used in this
paper would be inappropriate for such an analysis. Finally, the GMM model is designed to
offer a parsimonious solution to the challenges associated with instrumental variables.
While all instruments are jointly valid in this study, some are only moderately strong (SAT and percent poor) demonstrating that GMM models are not necessarily immune to the
challenges associated with instrumental variable techniques. Difference GMM techniques
significantly suffer from weak instrument bias, so system GMM is employed in this paper
to address this limitation.
Key Findings
The average discount rate for institutions in this sample is 15.9%; disaggregated by aid
source, the unfunded discount rate is 11.6% and the funded rate is 4.3% (Table 3). These
rates have remained relatively stable between the years 2002 and 2008. However, total
expenditures on institutional aid have increased 54% during the years studied, increasing
from $2.4 in 2002 to $3.7 billion in 2008 as have net tuition revenues. This paper has
explored the nature of this relationship, asking to what extent tuition discounting may be a
mediating factor in tuition revenue generation. Is there a systematic relationship between
aid and net tuition revenue after controlling for other factors such as tuition, enrollment,
and other institutional characteristics?
Results from this study identify a non-trivial and systematic pattern between average
institutional tuition discount rates and net tuition revenue. More specifically, unfunded
discounts generate gains in net tuition revenue, ceteris paribus, but these gains will eventually begin to diminish after a certain threshold. The economic model (Model 1)
offers a conservative estimate of this threshold, as this model does not control for such
important contextual factors as enrollment profile, external subsidies, and selectivity; the
full model (Model 2) accounts for these factors and offers a less conservative estimate for
this threshold. When interpreting the results, it is important to bear in mind that the
discount rate represents the average institution-level discount rate which is expected to
vary for each individual aid recipient.
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Results from Model 1 conform well to the economic theory described above. Holding
all else equal, tuition rates for in-state students express a positive relationship with net
tuition revenue. Institutions charging higher tuition prices yield greater net tuition revenue,
which would be expected according to the economic model. Similarly, institutions
enrolling a greater quantity of students (from both in- and out-of-state) also generate
greater quantities of net tuition revenue, holding all else equal. Tuition and enrollment are
expected to have positive relationships with net tuition revenue, as expressed in Model 1.
The Model 1 coefficient estimates for funded and unfunded tuition discounts also
behave in ways that conform to economic theory. One-unit increases in both funded and
unfunded average discount rates yield positive gains to net tuition revenue, ceteris paribus. However, the squared value of these discount rates is negative, indicating a hill-shaped
relationship between discounts and net tuition revenue. Financial gains from discounting
are experienced, but only to a certain point. The point at which gains begin to level off and
diminish towards zero differs for both funded and unfunded aid. A one-unit increase in the
funded discount rate is associated with an $83.42 per FTE increase in net tuition revenue.
When the funded discount rate reaches approximately 19%, however, these marginal
benefits begin to diminish. Similarly, unfunded discounts yield $13.21 per FTE gains in net
tuition revenue but this financial benefit begins to diminish when unfunded discounts reach
9%.
Using the purely economic model, one can empirically support the theoretical rela-
tionships described in Cheslock (2006), Martin (2005) and Breneman et al. (2001).
However, the relationship between aid and net tuition revenue is expected to vary
depending on institutional characteristics. Such factors as state appropriations, minority
and low-income student enrollment, selectivity, and SAT scores are expected to be
mediating factors that shape the extent to which aid can be leveraged for net tuition
revenue gains. Model 2 builds upon the purely economic model by controlling for these
additional variables, which results in a less conservative tipping-point estimate between
discounts and net tuition revenue gains. After adding these controls, Model 2 finds similar
patterns with all the economic variables except for funded discount rates which are no
longer found to be statistically significant.
In Model 2, the economic variables continue to conform to the expectations of eco-
nomic theory where tuition and enrollment remain positively associated with net tuition
revenue. Unfunded tuition discounts express a positive relationship with net tuition rev-
enue where a one-unit increase in the discount rate yields a $14.40 increase in net tuition
revenue per FTE. The point at which the marginal financial benefit of unfunded discounts
begins to level off and diminish towards zero is estimated at 12.7%. So, an institution that
offers unfunded tuition discounts will be expected to generate net tuition gains up to
approximately 13%, but beyond this point the net tuition revenue per FTE is estimated to
decline.
Findings from Models 1 and 2 empirically support what has been theoretically described
in the tuition discounting literature. That is, tuition discounts from unfunded sources can
yield financial benefits to public colleges and universities. Public sector institutional
leaders may be inclined to follow their private sector counterparts by leveraging aid to
generate tuition revenues; however, results from this study indicate that discounting
practices run the risk of fiscal insolvency. Institutions may desire to aid all students for
various reasons, but the financial reality is that there are significant financial risks asso-
ciated with aiding students from unfunded revenue streams. Findings suggest that unfunded
tuition discounts can be used for revenue management but they begin to erode revenues
when the rate exceeds 13%. Funded discount rates do not have a systematic pattern across
276 Res High Educ (2012) 53:263–281
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the two models, so the following section will synthesize the implications associated with
unfunded tuition discounts and will offer suggestions for further research. Results from the
two models are provided in Table 5.
Conclusions and Further Research
The primary purpose of this study was to identify whether or to what extent tuition
discounting yields net financial benefits to public four-year college and university budgets.
Much of the literature on tuition discounting focuses on the enrollment management
Table 5 Regression models explaining net tuition revenue per FTE, 2002–2008
Small sample standard errors (Windmeijer 2005) presented in parenthesis
* p \ 0.01, ** p \ 0.005, *** p \ 0.001
Model 1 Model 2
Lagged net tuition revenue per FTE 0.503*** (0.022)
0.804*** (0.018)
In-state FTE enrollment 0.023*** (0.004)
0.012*** (0.003)
Out-of-state FTE enrollment 0.079*** (0.008)
0.062*** (0.006)
In-state sticker-price tuition 0.395*** (0.025)
0.149*** (0.014)
Out-of-state sticker-price tuition 0.025** (0.008)
0.008 (0.005)
Funded discount rate (%) -0.228* (0.121)
54.724*** (9.009)
Funded discount rate (% squared) -1.374*** (0.331)
-2.134*** (0.289)
Unfunded discount rate (%) 5.513 (9.600)
13.530** (6.393)
Unfunded discount rate (% squared) -1.439*** (0.234)
-0.513*** (0.131)
Selectivity (% admitted) – -354.017** (172.135)
Percent minority enrollment – -190.896 (147.037)
Median SAT of incoming cohort – 1.143*** (0.349)
Percent low-income enrollment – 1,834.410** (403.259)
State appropriations per FTE – -0.047*** (0.007)
Constant 536.047*** (90.016)
-686.346* (397.674)
Num. of groups 174 143
Num. of instruments 73 99
Post-hoc tests
Arellano-Bond test for AR(1) 0.000*** 0.000***
Arellano-Bond test for AR(2) 0.321 0.412
Hansen-J test statistic 0.071 0.444
Difference-in Hansen 0.421 0.778
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function of aiding students, leaving a gap in what is known concerning discounting’s role
in revenue management. Given the austere fiscal environment in the public sector, colleges
and universities are looking for ways to maximize revenue from all sources—particularly
student tuition revenue.
This study concluded that public institutions are able to leverage unfunded discounts to
generate net tuition revenue, but after the rate exceeds approximately 13% these benefits
begin to diminish. The average unfunded discount for the sample is 11.6% indicating that a
significant amount of institutions may be running discounts near or beyond a point of
economic efficiency. Of the 174 institutions included in this study, 89 offered unfunded
discounts in excess of 13% between the years 2002 and 2008. These institutions may be at
the greatest risk of diminishing their net tuition revenues due to their discounting practices.
Three key implications are associated with these findings. First, the practice of aiding
students from unfunded sources has significant opportunity costs that may potentially
interfere with other institutional objectives. Since unfunded discounts are made available
through operating budgets, resources that support aid programs may be competing with
other institutional priorities. While the scope of this analysis did not examine the tradeoffs
associated with spending money on financial aid, the nature of aiding students from
unfunded sources will inevitably impact other institutional objectives.
Institutional aid expenditures are the fastest-growing item in most public colleges’
budgets. This practice accounts for billions of dollars each year and in tight financial times
every dollar spent is viewed with scrutiny. This is especially true with regard to expen-
ditures that are not central to the teaching, research, and service missions of public
institutions. If a college is aiding students through unfunded sources, then internal stake-
holders such as faculty, trustees, and non-aided students may begin to scrutinize the
collective benefits (particularly those associated with net tuition revenue) that are gener-
ated by engaging in this practice. The ability to anticipate and identify these opportunity
costs may become increasingly relevant to those institutions seeking to increase their
unfunded tuition discount rate. Further research could examine whether and to what extent
changes in institutional aid expenditures are associated with systematic changes in ‘‘mis-
sion-critical’’ or other institutional expenditures items.
Second, an institution’s desire to achieve enrollment management objectives and their
capacity to generate tuition revenue are two competing but reconcilable goals. Tuition
discounting programs are often viewed as enrollment management tools for crafting a class
of desirable students, but they also serve revenue management functions. By strategically
targeting aid, it is possible for institutions to maximize (or at least enhance) net tuition
revenues. Therefore, it is not unreasonable to posit that institutions can jointly strive for
crafting a class of desirable students while simultaneously enhancing their revenue profiles.
Further research should continue to explore how institutional aid programs are impacting
the enrollment profile of students and revenue outcomes for institutions. Some colleges have initiated ‘‘no-loan’’ programs where funded discounts are targeted to students who
qualify for need and non-need-based criteria. Research could examine the extent to which
the initiation of these programs has simultaneously enhanced enrollment goals (e.g. student
diversity) and revenue goals. And third, aggressive price discounting from unfunded sources has non-trivial impacts
on the financial wellbeing of public institutions. University administrators may be inclined
to offer discounts to craft a class, but these efforts can only be sustained to a certain
threshold. Eventually, institutions that aid students from unfunded sources will approach
economic inefficiencies that are neither politically nor financially sustainable. In today’s
financial climate where institutions are challenged to ‘‘do more with less,’’ campus leaders
278 Res High Educ (2012) 53:263–281
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will face greater accountability demands from trustees, budget officials, and academic
leadership to operate discounting programs that enhance tuition revenues. Institutions that
operate ‘‘deep’’ discounts will likely need to revisit their strategies and find new ways to
achieve enrollment objectives without accentuating financial risks. To inform practice in
this area, further research could examine the characteristics associated with those insti-
tutions falling beyond the 13% threshold found to diminish net tuition revenues; perhaps
these institutions enroll many lower-income students that have unmet financial need, or
perhaps they are positioned low in college ranking guides and are using aid to recruit
students with high SAT scores. These questions are beyond the scope of this paper, but
further research could examine how these institutions allocate aid based on need and
non-need criteria.
In conclusion, colleges offering no tuition discounts are bound to set themselves at a
competitive disadvantage in today’s academic marketplace. Today’s environment makes
aiding students from campus operating budgets a common business practice in the public
sector of higher education. Institutions may desire to offer aid to all students, but they are
economically constrained from doing so; as a result, they offer aid to a select group of
students in ways that are not always economically efficient. Ultimately, every institution
must design its discounting strategy that fits its own unique circumstances, but this study
raises awareness of the financial risks associated with tuition discounting.
Acknowledgments The author would like to thank David Tandberg and two anonymous reviewers for comments on previous versions of this paper.
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