What Can Merit-Aid Buy? The Effects of Financial Aid Packages...
Transcript of What Can Merit-Aid Buy? The Effects of Financial Aid Packages...
What Can Merit-Aid Buy? The Effects of Financial Aid Packages on the Enrollment Decisions of Applicants to a
Large Public University
Bradley R. Curs
Educational Leadership and Policy Analysis University of Missouri
202 Hill Hall Columbia, MO 65211-2190
Phone: 573.882.2759
E-mail: [email protected]
This Draft: March 2015
____________________________________________________________________
Abstract: The increasing prominence of merit-based grant programs at institutions of higher education as well as at the state level, make understanding the true effects of financial aid on needy students an important and timely inquiry. This paper builds on previous research through its focus on a large public university and the explicit modeling of the enrollment choice across different institutional types. The findings indicate that institutional merit-based aid is an effective tool in attracting students from out-of-state to attend a large state university. However, low-income students are found to be less responsive when compared to non-needy students, an indication that merit-aid may benefit the relatively well-off. ____________________________________________________________________
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What Can Merit-Aid Buy? The Effects of Financial Aid Packages on the Enrollment Decisions
of Applicants to a Large Public University
State budget crises have forced many states to lower their support of higher education.
These budget crises have been particularly troubling for public institutions which depend on state
funding and generally are the low-cost option in a student’s choice set. As a result, from 1991
through 2003, the average cost of attendance at a public four-year institution rose by 93 percent,
from $6,050 to $11,683, far outpacing the 35 percent growth in the Current Price Index. To
combat rising prices both states and institutions have implemented non-need based financial aid
packages to compete for the best students. While the marginal effects of merit aid on college
access are expected to be positive, it is unclear whether their effects are asymmetric across
income. In particular, it is important to understand whether merit aid relatively benefits the
financially well-to-do, simply because awards are determined based on merit and not need.
Following this trend the University of Oregon implemented the Dean’s Scholarship in the
late 1990s which awarded grants up to $2000 for in-state students and up to $5000 for out-of-
state students. This merit-based grant is awarded to applicants with high school GPAs in excess
of 3.6, with increasing support as an applicant’s GPA increases. This major financial aid policy
shift towards a merit-based approach was adopted to combat increasing competition for the best
and brightest students. Previous to the 1999-2000 academic year merit aid awards at the
University of Oregon were negligible but by the 2002-2003 year over $5 million was awarded.
This adoption of a merit aid program at the University of Oregon, combined with a unique
dataset with detailed information on applicants, provides a natural experiment to study how
merit-based grants affect the college choice of low-income students. The increasing prominence
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of merit-based grants programs at institutions of higher education, as well as at the state level,
make understanding the true effects on needy students an important and timely inquiry.
While there is an extensive literature on the effects of financial aid in general, previous
institutional level financial aid studies typically ignored the outside alternatives of students due
to a lack of suitable data. The few studies that have modeled the student’s choice set (Manski &
Wise, 1983; Ehrenberg & Sherman, 1984) focused on private institutions where applicants’
financial considerations are less likely to constrain their college choice as compared to public
institutions. This study will build on the previous financial aid literature for two reasons. First, its
focus on a large public university, whose applicants are more likely to choose an institution
based on financial considerations, as compared to an elite private university helps to identify the
effects of merit-based aid programs on needy students. Second, within the dataset the college
choice of each University of Oregon applicant is observed, thus enabling a detailed investigation
into the asymmetric effects across need of merit-aid on the choice of students by higher
education institutional type.
Theoretical and Empirical College Choice Research
Theoretical models of institutional choice within the higher education literature
hypothesize that individuals choose the particular institution that best matches their desired
characteristics (comprehensive reviews of the college choice literature can be found in: Cabrera
& La Nasa, 2000; Hossler, Braxton, & Coopersmith, 1989; Paulsen, 1990; Perna, 2006).
Institutional attributes expected to influence college choice include both economic and
sociological constructs. Economic factors theoretically expected to influence college choice
include net price (tuition minus aid), return on investment, and the consumption value of college.
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Sociological factors expected to influence institution choice include family background, socio-
economic status, high-school peers, and a preference for interacting with similar persons.
More complex models of college choice have developed which theorize that college
choice is a multi-stage decision making process (Hossler, Braxton, & Coopersmith, 1989;
Hossler & Gallagher, 1987). In the first stage, potential students develop aspirations for higher
education based primarily upon sociological factors. In the second stage, potential students
identify a set of institutions of which to apply, based upon both economic and sociological
factors. Finally, in the third stage students choose their ultimate institution of which to attend.
As a major policy lever for both institutions and governments to influence college access
and choice, the literature trying to estimate the link between financial aid and college is very rich
and detailed. The early financial aid studies typically estimated the probability of enrollment
based upon the existence or level of financial aid, price measures, and a set of individual
characteristics and generally find a positive effect of financial aid and college enrollment
(Jackson, 1978; Manski & Wise, 1983; Ehrenberg & Sherman, 1984). Numerous studies across a
number of disciplines provide consistent evidence that student responsiveness to tuition and aid
differ with need and ability (e.g, Ehrenberg & Sherman, 1984; Jackson, 1990; McPherson &
Schapiro, 1991; Linsenmeier, Rosen, & Rouse, 2002; Singell & Stone, 2002; Dynarksi, 2003).
Likewise, research has found evidence that students respond asymmetrically to different kinds of
financial aid, with individuals more responsive to merit-based versus needs-based aid, grants
versus loans, and grants versus tuition (St. John, 1993; St. John & Starkey, 1995; Singell &
Stone, 2002; St. John, 2003). A handful of multiple stage empirical models show that price
responsiveness measures may be understated when an analysis exclusively focuses on the
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enrollment stage because price can also affect aspirations and application decisions (Abraham &
Clark, 2006; Curs, 2008; Curs & Singell, 2002; DesJardins, Ahlburg, & McCall, 2006).
The estimated effects of financial aid can be biased when an empirical analysis fails to
control for unobserved attributes related to a student’s likelihood of enrollment. In a critique of
techniques of the National Center for Educational Statistics, Heller (2004) documents how a
failure to model unobserved attributes may understate the importance of a student’s socio-
economic status in their college-going decisions. In the same volume, Becker (2004) further
critiques the education literature and outlines the various biases that arise through the omission
of relevant variables and sample selection, which could confound the identification of the true
effects of financial aid. To obtain unbiased causal estimates of the effect of financial aid, a
source of exogenous variation in financial aid that is uncorrelated with the unobserved student
attributes which affect educational outcomes must be found (Schneider, Carnoy, Kilpatrick,
Schmidt, & Shalverson, 2007).
The exploitation of natural (i.e quasi) experiments, discrete policy changes that affect one
group and not another, allow researchers to estimate the causal effects of financial aid on
college-going behavior (Dynarski, 2002; Riegg Cellini, 2008). Natural experiments allow the
researcher to estimate the effects of financial aid while controlling for the omission of important
unobservable individual characteristics that may be correlated with a financial aid offer.
Differences-in-differences is a quasi-experimental technique that allows a researcher to
exploit exogenous (i.e. unrelated to attributes of a particular student) changes in financial aid
programs to identify the causal effect of a policy change by looking at the difference in behaviors
after the implementation of a policy between groups that were and were not affected (Dynarski,
2002). This technique has been utilized to study the effects of large-scale merit-based grants
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programs, such as the Georgia Hope Scholarship, with findings indicating large impacts of merit-
based aid on the enrollment decision of potential students (Dynarski, 2000, 2004; Cornwell,
Mustard and Sridhar, 2004), including those from low-income backgrounds (Singell, Waddell, &
Curs, 2006). However, when applying the same technique, little evidence has been found to
support the efficacy of the Federal Pell Grant (Hansen, 1983; Kane, 1994, 1995) except in the
case of non-traditional students (Seftor & Turner, 2002).
A second quasi-experimental technique that is rapidly growing in use is regression-
discontinuity design. Regression-discontinuity design allows researchers to separate subjects into
control and treatment groups when random assignment is unavailable, through the use of a
decision rule (Riegg Cellini, 2008). This decision rule separates otherwise similar subjects into
groups that face distinctly different policy treatments. Van der Klauuw’s (2002) article, which
estimated the effect of an institutional financial aid program, brought the regression-discontinuity
technique back into the econometric toolbox of higher education researchers despite its use in
early research by Thistlewaite and Campbell (1960). Recently, a number of other researchers
have applied regression discontinuity to study the effects of financial aid due to discontinuities in
financial aid policies that determine awards based on distinct cut-off scores (Kane, 2003;
Bettinger, 2004). Other applications of regression discontinuity within the field of higher
education include the effects of remediation (Lesik, 2006) and ACT test-taking behaviors
(Pantel, Podgursky, & Mueser, 2006).
Empirical Framework and Identification Strategy
The detailed dataset utilized in this study provides an opportunity to exploit the powerful
econometric tools used in previous research to control for the potential endogeneity (i.e.
correlation of financial aid with unobserved attributes of a potential student) of financial aid
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awards. Specifically, discontinuities in the financial aid formula, detailed financial data of
applicants, and data which contains the ultimate college enrollment decision of all applicants
permits an investigation into the college choice applicants to a large public university that was
previously unavailable. The primary benefit of the natural experiment methodology is the ability
to identify the effect of financial aid based on exogenous changes in financial aid programs.
However, individual choice is not typically modeled in great detail as the individual controls to
investigate the effects of financial aid on subsets of the population, such as low-income students,
are lacking. Where the approach has attempted to estimate the effects of financial aid on needy
students identification typically has indirectly relied on differences in social categories such as
race. The evidence suggests that the impact of merit aid programs may be larger among
relatively higher income groups and among institutions that attract them (Dynarski, 2004;
Cornwell, Mustard and Sridhar, 2006). The detailed dataset in this analysis provides an insight
into the asymmetries in the effects of financial aid across demographic groups as was previously
unobserved in the literature.
Following prior work, the decision to enroll at the University of Oregon is modeled to be
dependent on many factors (Ehrenberg & Sherman, 1984; Curs & Singell, 2002). Included in
this model are the student’s financial capability, their academic ability, opportunity costs of
attending college as well as an overall taste for attending an institution of higher education. To
estimate the effects of financial aid on an applicant’s enrollment choice, a random utility
approach is specified. In particular, applicant i’s decision to enroll at the University of Oregon is
observed if and only if the utility of their enrollment decision exceeds the utility of their next
best opportunity. Although the net utility for applicant i to enroll (Ei) is not directly observed, the
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student’s ultimate decision is observed. Specifically, the decision to enroll at the University of
Oregon is modeled as the linear index function:
[1]
enrolledif
enrollednotifEXAIDE iiiii 1
0,
where AIDi is applicant i’s financial aid package and Xi is a vector of variables thought to
influence the enrollment decision. In this specification, the coefficient represents the effect of
financial aid on the enrollment decision. The estimated parameters of equation [1] measure the
responsiveness of University of Oregon applicants to financial aid packages while controlling for
their attributes. The nature of the college choice model lends itself to a natural application of a
discrete choice empirical model. Typically, institutional college choice studies have focused on
the decision to enroll or not enroll at the given institution. In the initial analysis, a logistic
estimation procedure will be utilized to analyze the discrete choice of whether or not to enroll at
the UO.
While this approach provides valuable information to understand the enrollment choices
of potential students, it may hide important asymmetric behaviors in this decision. To take
advantage of this information regarding the choice across institutional type, a multinomial logit
model will be utilized to estimate how various factors affect an applicant’s choice between the
UO and competing categories of universities (i.e., 2-year colleges, in-state 4-year public
universities, out-of-state 4-year public universities, and private universities).
One inherent empirical problem with using the multinomial logit framework is how to
aggregate institutions into similar categories to facilitate interpretation. Nguyen and Taylor
(2003), using data on high school graduates, find that models with greater aggregation are
rejected in favor of models with a greater set of choices. They suggest the multinomial logit
model of college choice include the categories private two-year, public two-year, private four-
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year, public four-year, employed and unemployed. However, as the number of categories
increase by one, the number of coefficients estimated increases by the number of explanatory
variables, thus making interpretation more difficult. While multiple models were estimated, for
brevity of presentation a model with the following model is presented in this narrative: non-
attendance at an institution of higher education, attendance at the UO, attendance at a two-year
institution, attendance at an instate four-year institution, attendance at an out-of-state public four-
year institution and attendance at a private four-year institution.
Although this study follows the bulk of the literature that focuses on the enrollment
choice stage, the results from the multi-stage empirical research suggest that our single-stage
simulations may well offer lower bound estimates of the effect of financial aid on enrollment due
to price effects on stage prior to choice. However, as institutional financial aid is only awarded to
students who have applied for admissions the parameter of interest is most likely to be the effect
of institutional aid on the conditional probability of enrollment given their application.
Identifying the Causal Effects of Financial Aid: Regression Discontinuity Design
As institutional financial aid award decisions are made by financial aid administrators
there is a strong likelihood that the financial aid package are correlated with characteristics of the
applicant unobserved to the researcher (Riegg Cellini, 2008). This potential correlation of
financial aid and the error term (i.e. financial aid is said to be endogenous) causes concern that
the estimated coefficients on financial aid are biased when estimated through standard estimation
techniques (Becker, 2004). When the unobserved characteristics are correlated with the financial
aid offer, inferences about the true (or causal) effect of financial aid on college-going behaviors
can no longer be determined.
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One technique to control for the potential of unobserved heterogeneity being correlated
with financial aid awards is regression-discontinuity design (Riegg Cellini, 2008; Angrist &
Pischke, 2009). Intuitively regression discontinuity design separates subjects with otherwise
similar attributes into treatment and control groups based upon a decision rule that is exogenous
to the subjects (i.e. the subjects do not have a choice to participate in the treatment, or they can
not alter their behavior to adjust to treatment criteria). This rule that determines whether a subject
receives treatment is based upon an assignment variable that is exogenous to the subject as
opposed to the random placement of subjects as in experimental design.
The Dean’s Scholarship at the University of Oregon provides a unique natural experiment
to apply regression discontinuity design to investigate the causal impacts of financial aid on
college choices. From the 1999-2000 to the 2003-2004 academic years the determination of the
Dean’s scholarship for out-of-state students was based upon the applicant’s high school grade
point average (GPA). Specifically, students with GPAs in the ranges 3.6-3.69, 3.7-3.79, 3.8-3.99
and 4.0+ received $2,000, $3,000, $4,000, and $5,000 in merit aid, respectively. A similar
program exists for instate students, although financial aid administrators had more leeway in the
decision of aid amounts. As aid awards were not fully determined by the exogenous GPA
assignment rule the benefits of regression discontinuity design cannot be realized.
Figure 1 plots actual Dean’s scholarship awards and the Lowess smoothed average
Dean’s scholarship for out-of-state students by GPA. In general, institutional financial aid
awards increase with GPA with large increases at GPAs of 3.6, 3.7, 3.81. These discontinuities
award amounts at the GPA cutoff values can be exploited in this analysis to estimate the causal
effect of financial aid.
1 Due to the lack of ability to model high school GPA beyond 4.0, the sample has been restricted to students with high school GPAs below 4.0.
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Figure 1 Dean’s Scholarship Awards by High School GPA
Given this exogenous financial aid assignment rule equation [1] can be altered to employ a sharp
regression discontinuity design which will estimate the causal effect of financial aid on
enrollment decisions (Van der Klaauw, 2002; Angrist & Pischke, 2009). Sharp regression
discontinuity design estimates the effect of financial aid policy by regressing the enrollment
decision on the assignment variable and an indicator based upon the discontinuity. The
coefficient on the indicator variable then is interpreted as the causal estimate of the effect of
financial aid. To obtain unbiased estimates of the effect of financial aid sharp regression
discontinuity design requires perfect compliance with the assignment rule.
Figure 2, presents a local linear approximation of the relationship between attending the
UO and high school GPA estimated separate for each treatment region. The figure indicates that
02
000
400
06
000
800
0D
ean'
s S
cho
lars
hip
3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4High School GPA
Observed Lowess Smoothed Average
bandwidth = .07
L ow es s sm o ot he r
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a discontinuity in the likelihood exists at the 3.6 high school GPA cutoff, a $2,000 treatment
jump, but that treatment effects at other cutoffs are negligible.
Figure 2 Local Linear Regression of Enrollment at UO on High School GPA
While the Dean’s scholarship is the primary form of institutional aid at UO the
assignment rule does not explain Dean’s scholarship awards perfectly. Figure 3 portrays the
likelihood of receiving each Dean’s scholarship treatment by high school GPA. While the
decision rule explains differences in treatment well, it does not perfectly. In particular, the
likelihood a student receives a particular treatment remains less than 1 after each treatment cut-
off. Furthermore, as illustrated in Figure 1, different treatment levels appear both below and
above each cutoff value. The fuzziness in the assignment of treatment may help explain why
estimated probabilities of enrollment increase beyond the 3.6 and 3.8 cutoff values as illustrated
in Figure 2.
0.0
5.1
.15
.2.2
5P
roba
bilit
y of
En
rollm
ent
at U
O
3 3.2 3.4 3.6 3.8 4High School GPA
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Figure 3 Probability of Differential Dean’s Scholarship Treatment
The UO also offers a number of financial aid programs, including diversity scholarships
and need-based grants. However, during our sample the Dean’s scholarship was the primary
financial aid program and accounts for 78% of financial aid awarded at the UO. As Table 1
shows, the number of applicants whose financial aid packages coincide with the Dean’s
scholarship exactly is quite high, with 94% of the applicant’s packages fully determined by the
exogenous decision rule. Figure 4 illustrates the average total institutional aid offer in relation to
the Dean’s scholarship policy.
0.2
.4.6
.81
Pro
babi
lity
of T
rea
tme
nt
3.4 3.5 3.6 3.7 3.8 3.9 4High School GPA
$2000 Treatment (Lowess) $2000 Treatment Probability$3000 Treatment (Lowess) $3000 Treatment Probability$4000 Treatment (Lowess) $4000 Treatment Probability
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Figure 4 Average Total Institutional Aid Offer and High School GPA
A fuzzy regression discontinuity design can be employed when an exogenous assignment
rule is highly correlated with the actual treatment status, but does not fully explain the treatment
(Van der Klaauw, 2002; Angrist & Pischke, 2009). Fuzzy regression discontinuity design
employs a two-stage procedure to estimate the causal impact of a policy. In the first stage, the
predicted treatment level is estimated through a regression of the actual treatment status on the
assignment rule variable and indicator variables based upon the exogenous decision rule to
account for the discontinuity. The causal impact of the treatment is identified in the second stage
as the coefficient on the predicted treatment status variable from the first stage when regressed
upon the outcome variable controlling for the continuous assignment rule.
01
000
200
03
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400
05
000
3 3.2 3.4 3.6 3.8 4High School GPA
Average Institutional Aid Dean's Scholarship
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Specific to this analysis, the first stage analysis estimates the level of financial aid ( iAID )
an applicant is offered as a function of the discontinuities in the Dean’s Scholarship formula and
a flexible function of a student’s high school GPA:
[2] iii GPAfGPAGPAGPAAID )(383837373636
where GPAi is the student’s high school GPA, and GPA36, GPA37, and GPA38, are indicator
variables which equal one if the student’s GPA is larger than 3.6, 3.7, and 3.8, respectively.
The second stage then estimates the enrollment decision (Ei) on the predicted financial
aid level ( iDIAˆ ) and the student’s high school GPA:
[3] iiii GPAfDIAE )(ˆ
where , the coefficient on the predicted financial aid award, can be interpreted as the causal
effect of the financial aid program. While equation [3] can estimate the unbiased effect of the
financial aid program in question, adding covariates can increase the efficiency of the regression
discontinuity estimation procedure. Therefore, including covariates to equation [3] yields the
following estimation equation:
[4] iiiii XGPAfDIAE )(ˆ
where Xi is a vector of observed individual and university attributes assumed to affect the
enrollment decision including personal characteristics (sex, race, interest), academic ability (SAT
scores), state or region dummy variables (California, Washington, West, Midwest, South, and
Northeast), and year dummy variables.
Sample Data
The empirical analysis uses data from the UO admissions office for Fall-term freshman
out-of-state applicants for the academic years 1999-2000 through 2003-2004. Specifically,
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detailed individual level characteristics are contained in the dataset including an applicant’s
financial aid package, academic performance measures and detailed background information. For
students who choose not to enroll at the UO, their records were matched with the schools they
ultimately choose to attend through the National Clearinghouse database. As the effect of
financial aid is only valid for those students whom are able to attend, the sample is restricted to
only qualified applicants (93% of applicants are academically qualified. Further, students on
athletic scholarship have been removed as these students may respond very differently to
financial incentives compared to the typical student. The overall matched dataset contains
complete information on 13,782 out-of-state applicants. Table 2 presents the descriptive
statistics of the final sample utilized in this analysis.
Empirical Results
Key Assumptions of Regression Discontinuity Design
The validity of regression discontinuity design to make causal inferences rests on four
key assumptions. First, there must be no manipulation of the running variable. If subjects are
able to manipulate the decision variable the assignment of treatment above and below the cutoffs
is no longer exogenous. In our case, this would mean students were able to manipulate their high
school GPA to increase their likelihood of receiving a Dean’s scholarship. While students are in
control of their GPA over the course of their high school careers, it is unlikely they have the
ability to alter their GPA upon learning of the Dean’s scholarship. However, possible
endogeneity may exist in the decision to apply to the UO, and thus appear in our sample. Thus,
to test whether manipulation has occurred we employed the discontinuity test outlined by
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McCrary (2008)2. Figure 4 plots a histogram of high school GPA above and below the 3.6 cutoff
and shows that a discontinuity may exists, but is not statistically significant.
Figure 4 Density of High School GPA – Total Sample
Manipulation would be most likely to occur when information is most prevalent about the
decision rule. In the case of this study, that would be in the final year of the sample, 2003. If
students were learning about the scholarship award and manipulating the running variable,
through either increasing their reported high school GPA or being more likely to apply if they
qualify for scholarship awards, the most recent year would be the most likely candidate to
contain a discontinuity in high school GPA at the treatment cutoff. Figure 5 presents the
distribution of high school GPA for the most recent year in the sample, 2003. However, the
2 Specifically, the stata ado file DCdensity which can be found at http://emlab.berkeley.edu/~jmccrary/DCdensity/ was applied.
0.0
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pattern is similar to the full sample with an observed discontinuity which is well within the
confidence intervals.
Figure 5 Density of High School GPA – 2003
The second critical assumption to the validity of regression discontinuity design is that
the association of a jump in the outcome variable should only be associated with the
discontinuity of the running variable, and not due to discontinuities in other variables. Appendix
A contains replications of the local linear regression model presented in Figure 2, but with
alternative control variables as the dependent variable. Visually, it appears discontinuities may
exist in the likelihood a student is nonwhite and the age at which they applied when regressed
upon high school GPA3. However, not discontinuities appear to exist for the likelihood a
students is female or SAT scores across the discontinuities in the financial aid award formula.
The Decision to Enroll at the University of Oregon or Not: A Logistic Analysis
3 This is a bit puzzling to me. I am not sure if this calls into question my validity or not.
0.0
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.01
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2
250 300 350 400 450
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Table 3 presents the logistic regression results of an applicant’s decision of whether or
not to enroll at the UO. To make the interpretation of the effects of financial aid consistent with
subsequent analyses, this analysis differs from normal convention and defines the dependent
variable to be equal to 0 if the applicant enrolls at the UO and 1 if the applicant does not enroll.
As the results are presented in odds ratio form the coefficients represent the change in the odds
(i.e. the probability of not attending the UO divided by the probability of attending the UO) of
not attending the UO given a change in the independent variable. Thus, a coefficient value less
than one (greater than one) indicates that the independent variable has a positive (negative) effect
on the likelihood that an applicant enrolls at the UO.
The first two columns of Table 3 present the fuzzy regression-discontinuity results based
upon the full sample of out-of-state applicants to the UO without (eq. [3]) and with (eq. [4])
control variables. The results of the estimation of equation [3] indicates that increasing the
financial aid offer to out-of-state applicants by $1000 would decrease the odds that a student
would not attend the UO by 0.907. Alternatively, the odds that an applicant enrolled at UO
would increase by 10.3% given a $1000 increase in their institutional financial aid offer4. When
controls are added to the model, the effect of the same increase in financial aid on the odds of not
enrolling at the UO is .884, or roughly an increase in the odds of enrolling of 13.1%.
To differentiate across need the sample was split into those that did not file a FAFSA
(Table 3, columns 3 and 4), those that did file a FAFSA and were not determined to be needy by
Federal needs calculations (columns 5 and 6), and those that did file the FAFA and were
determined to be needy (columns 7 and 8). With respect to non-filers, the results were
statistically similar to the total sample. Non-needy FAFSA were estimated to be very responsive
4 To change the estimated results into the odds an applicant enrolls at the UO given a one-unit increase in an independent variable, you must calculate the inverse of the coefficient (i.e. 1/0.907=1.1025) .
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to changes in institutional financial aid offers with a $1000 increase in aid estimated to change
the odds of not attending UO by between 0.846 and 0.812 (or alternatively increase the odds of
attending UO by 18% to 23%). However, needy FAFSA filers were estimated to be the least
responsive group, with $1000 in aid changing the odds of not attending UO by between 0.926
and 0.903 (or alternatively increase the odds of attending UO by 8% to 11%).
The results indicate that institutional merit aid is an effective tool in the enrollment of
out-of-state students, particularly for non-needy students. It is, however, unclear from these
results what types of applicants the merit aid is effective in attracting. The following section
explicitly models what type of institution an applicant chooses, and provides a better
understanding of how financial aid affects the choice across institution type.
Overall, the empirical relationships with regard to the non-aid-related controls generally
confirm prior expectations. For example, out-of-state applicants with higher SAT scores are
more likely to attend other institutions. Applicants that attended private high schools are less
likely to attend the UO. Non-white applicants are less likely to attend the UO. These results are
similar to other research on enrollment patterns at the UO which indicate that the UO attracts
good but not great students (Curs & Singell, 2002; Singell & Stone, 2002; Singell, 2004). For
brevity, discussion of the effects of control variables from this point on is minimized.
As Figure 2 illustrated, the response to discontinuities in the financial aid award formula
may not be equal at different treatment cutoff points. To investigate whether the response is
different at different levels of treatment, the fuzzy regression estimation strategy is altered as
described in Van der Klauuw (2002). Specifically, to test the effect of the discontinuity at the
3.6 treatment cutoff, dummy variables for students with high school GPAs above 3.7 and 3.8 are
included, as represented by equation 5:
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[5] iiiii XGPAGPAGPAfDIAE 38383737)(ˆ
Table 4 presents the results when the estimated regression discontinuity effect of
financial aid on enrollment at the UO is allowed to differ for the different treatment levels.
Similar to the visual representation of the relationship provided in Figure 2, only the 3.6 high
school GPA cutoff which provides a $2,000 increase in the Deans scholarship is found to be
related to enrollment at the UO. For the overall sample, the estimated increase in the likelihood
of a student enrolling at the UO is found to be between 23% and 27%. The effect appears to be
slightly stronger for non-needy students but is nonetheless effective for needy students as well.
In contrast, the discontinuities associated with high school GPAs of 3.7 and 3.8 (a $1,000
increase at each step) are not found to increase the likelihood of enrollment at UO. It may be the
case as a student’s high school GPA increases they become more attractive for financial aid from
other higher education institutions.
The Decision Where to Enroll: A Multinomial Logistic Analysis
While understanding an applicant’s decision to enroll or not at the UO is important from
the institution’s perspective, there is the potential for some asymmetries to exist across the
alternative choices a student may make. Accordingly, to relax the restriction in the logit model
that the effects of financial aid and other control variables are equal across institution type,
equation [4] is estimated using a multinomial logit. As enrolling at the UO is the base category,
all coefficients are interpreted as the change in the odds ratio between enrolling at the alternative
(non-attendance, two-year, instate four-year, out-of-state public four-year, and private four-year)
as compared to the UO when the independent variable changes by one unit.
For the total sample of out-of-state applicants, each column of Table 5 presents the
estimated effect of increasing the independent variable by one unit on the odds that the applicant
21
enrolls at the alternative institutional type (as indicated by the column title) as compared to
enrolling at the UO. Specifically, coefficients less than (greater than) one indicate that a one unit
increase increases (decreases) the odds that an applicant enrolls at the UO as compared to the
alternative institution type. A $1000 increase in institutional financial aid is estimated to decrease
the likelihood of enrolling at all of the options when compared to enrolling at the UO, as
evidenced by coefficients all less than 1. The largest effect of institutional financial aid is
estimated to decrease the odds that an applicant enrolls at an instate four-year as compared to the
UO by 0.815, or increase the odds that an applicant enrolls at UO by 22.7%. The effect is
smaller, although still statistically significant, for public out-of-state and private four-year
institutions with estimated increases in the odds of attending the UO of 10.1% and 12.7%,
respectively.
The results would indicate that UO’s financial aid program is most successful at
attracting those students who otherwise would have enrolled at four-year institutions, with the
largest affects on those likely to attend instate. One possible interpretation of these results is that
the financial aid program at the UO is most effective at pulling the cost-conscious student away
from other lower cost institutions now that the relative cost of the UO has declined.
Differences in the Response to Financial Aid by Income Class
To assess the response across need to financial aid offers, the sample has been split into
three subsamples. Within the data set an applicant’s financial need is only observed if they filed
a FAFSA, thus all non-FAFSA filers have been placed into one subsample. For FAFSA filers,
an applicant is defined to be needy if they have positive eligibility for financial aid as determined
by through the FAFSA process. Financial eligibility is determined through the calculation of the
applicant’s expected family contribution and their cost of attendance at the UO. Positive
22
financial eligibility implies that the applicant qualifies for Federal assistance through the Pell
Grant, Stafford Subsidized Loan, and/or Work Study. Table 6 present the results of estimating
equation [4] through the multinomial logit estimation procedure on the three subsamples.
The results are striking when comparing the effect of financial aid on needy-students to
those that are non-needy and those that did not file a FAFSA. In general, financial aid is less
effective in changing the odds that a student will choose UO over alternative institutions types
for needy students than when compared to non-needy and non-filers. The one exception is for
public out-of-state four-year institutions where the financial aid effects are not significantly
different across subsamples. The one set of institutions that institutional financial aid appears to
be effective in attracting needy students away, is from public institutions in their own state.
Thus, merit-aid is not found to be particularly effective in attracting needy out-of-state students
to the UO as compared to financially well-off students. However, because the sample is out-of-
state applicants, caution should be given to the interpretation of the efficacy of merit-based
programs on the access margin of the needy based upon these results, as the majority of needy
students attend institutions within their own state.
For non-needy and non-filer applicants it is interesting to note that financial aid awards
have a large impact in changing the odds that an applicant chooses the UO over attending instate
two-year and four-year institutions. Financial aid appears to be an effective tool in attracting
students to attend college out-of-state by lowering the costs they face. This is similar to results
in Curs and Singell (2002) which found that instate public institutions may be inferior goods to
instate applicants, and used as a college choice backup plan should the student not be accepted or
able to attend due to poor financial aid offers from their primary choices.
Discussion
23
One particular question of interest this analysis may help to answer is whether merit aid
simply redistributes needy students across similar institutions, or does it help low-income
students enroll in more selective yet higher cost institutions. The patterns suggest that merit aid is
an effective tool for influencing out-of-state students to enroll at the University of Oregon, likely
because it is targeted at specific students and is institution specific. However, the small effect of
the financial aid program on the enrollment decisions of low-income applicants indicates that
merit-based aid programs may benefit the relatively well-off. This finding is particularly
troubling given the increasing reliance on merit in the award decisions of financial aid programs.
This analysis provides a significant empirical extension in an area where policy
implications are important. State budget crises have forced many states to lower their support of
higher education. It therefore becomes imperative that colleges use limited financial aid dollars
as effectively as possible. The budget crises have been particularly troubling for public
institutions, which generally are the low-cost option in a student’s choice set. Given the move
towards merit-based financial aid programs at public universities, understanding their effects
across different classes of students is of pressing concern.
24
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27
Table 1: The University of Oregon Dean’s Scholarship
Grade Point Average Less than
3.6 3.6- 3.69
3.7- 3.79
3.8- 3.99 4.0+
Dollar value of the Dean’s Scholarship $0 $2000 $3000 $4000 $5000 Percentage of applicants whose scholarship package 93.9% 80.6% 80.2% 78.4% 78.6% is entirely composed of the Dean’s scholarship Average total scholarship package across applicants $102 $2131 $3206 $4449 $5499
28
Table 2: Sample Characteristics – Out-of-State Applicants to the University of Oregon
Characteristics are reported for the sample of 13,782 out-of-state applicants.
Mean
Standard Deviation
Minimum Maximum
Enrolled at the University of Oregon 0.16 0.37 0 1
Institutional-based aid $1559.5 2344.5 0 $15,350
Dean’s Scholarship $1314.0 1830.8 0 $7000
Institutional need-based grant $45.3 188.2 0 $1000
Diversity Scholarship $18.3 247.5 0 $4900
Other Scholarships $177.9 1213.1 0 $12,700
Non-institutional-based aid $184.5 723.6 0 $5451
Federal Pell Grant $179.7 700.4 0 $4050
State-based grants $4.8 76.8 0 $1401
Loans $5273.0 8396.5 0 $29,628
Filed a FAFSA 0.48 0.50 0 1
Female 0.57 0.50 0 1
Nonwhite 0.26 0.44 0 1
Age at application 17.8 0.42 15.0 23.1
High school GPA 3.45 0.36 2.14 4
Math SAT 5.85 0.78 2.20 8
Verbal SAT 5.80 0.78 2.50 8
Attended private high school 0.26 0.44 0 1
29
Table 3: The Choice of Out-of-State Applicants to Enroll or Not to the University of Oregon Logistic regression estimates of the change in the odds ratio an applicant
does not enroll at the University of Oregon: Independent variable Total sample Applicant did not file a
FAFSA Applicant filed a FAFSA but determined to be not needy
Applicant filed a FAFSA and was determined to be needy
Institutional financial aid 0.907*** 0.884*** 0.903*** 0.883*** 0.846*** 0.812*** 0.926* 0.903** (0.0230) (0.0234) (0.0344) (0.0352) (0.0484) (0.0491) (0.0416) (0.0426) High school GPA 3.896*** 4.319*** 3.805*** 4.508*** 6.271*** 7.177*** 4.969*** 4.647*** (0.439) (0.515) (0.580) (0.733) (1.819) (2.218) (1.083) (1.058) Federal and state financial aid 0.965 0.977 (0.0310) (0.0355) Female 1.031 1.020 0.923 1.154 (0.0543) (0.0771) (0.113) (0.109) Nonwhite 1.272*** 1.228** 1.127 1.624*** (0.0759) (0.113) (0.149) (0.165) Age at application 0.952 0.917 1.013 0.960 (0.0547) (0.0777) (0.135) (0.0954) Math SAT 1.325*** 1.313*** 1.394*** 1.279*** (0.0504) (0.0728) (0.122) (0.0860) Verbal SAT 1.110*** 1.069 1.208** 1.177** (0.0413) (0.0585) (0.104) (0.0767) Attended private high school 1.481*** 1.651*** 1.525*** 1.138 (0.0895) (0.140) (0.211) (0.130) Year dummy variables No Yes No Yes No Yes No Yes State/region dummy variables No Yes No Yes No Yes No Yes Observations 12,651 12,651 6,715 6,715 2,094 2,094 3,842 3,842 Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
30
Table 4: Differential Effects of Dean’s Scholarship at Different Treatment Cutoffs Logistic regression estimates of the change in the odds ratio an applicant
does not enroll at the University of Oregon: Independent variable Total sample Applicant did not file a
FAFSA Applicant filed a FAFSA but determined to be not needy
Applicant filed a FAFSA and was determined to be needy
Discontinuity at 3.6 0.809*** 0.787*** 0.805*** 0.790*** 0.770** 0.740** 0.806** 0.791** $2,000 Treatment (0.0419) (0.0419) (0.0623) (0.0630) (0.0901) (0.0898) (0.0715) (0.0724) Discontinuity at 3.7 1.047 1.017 1.270 1.203 0.716 0.653* 1.118 1.097 $1,000 Treatment (0.122) (0.121) (0.245) (0.238) (0.169) (0.160) (0.215) (0.217) Discontinuity at 3.8 0.989 0.973 0.794 0.800 1.234 1.254 0.993 0.953 $1,000 Treatment (0.0966) (0.0982) (0.133) (0.138) (0.232) (0.247) (0.159) (0.158) Year dummy variables No Yes No Yes No Yes No Yes State/region dummy variables No Yes No Yes No Yes No Yes Observations 12,651 12,651 6,715 6,715 2,094 2,094 3,842 3,842 Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
31
Table 5: The Choice of Out-of-State Applicants to Enroll at the University of Oregon as Opposed to Alternative
Institution Types Multinomial logistic regression estimates of the change in the odds ratio a student enrolls at:
(as compared to enrolling at the University of Oregon)
Independent variable Does not enroll Two-year Public instate
four-year Public out-of-state four-year Private four-year
Institutional financial aid 0.912*** 0.879** 0.815*** 0.908*** 0.887*** (0.0302) (0.0551) (0.0256) (0.0299) (0.0290) High school GPA 2.603*** 2.430*** 11.12*** 2.756*** 5.161*** (0.392) (0.702) (1.732) (0.416) (0.808) Federal and state financial aid 0.938 1.069 1.020 0.826*** 1.050 (0.0400) (0.0739) (0.0399) (0.0388) (0.0420) Female 0.988 1.073 0.963 1.002 1.196*** (0.0654) (0.132) (0.0607) (0.0661) (0.0795) Nonwhite 1.330*** 1.295* 1.244*** 0.963 1.587*** (0.0977) (0.174) (0.0880) (0.0730) (0.115) Age at application 0.928 1.119 0.941 0.909 1.005 (0.0677) (0.149) (0.0664) (0.0658) (0.0732) Math SAT 1.228*** 1.036 1.327*** 1.337*** 1.464*** (0.0588) (0.0918) (0.0610) (0.0638) (0.0702) Verbal SAT 1.016 0.879 1.230*** 0.940 1.364*** (0.0477) (0.0774) (0.0549) (0.0440) (0.0636) Attended private high school 1.359*** 0.826 1.142* 1.400*** 2.447*** (0.102) (0.125) (0.0833) (0.104) (0.177) Year dummy variables Yes State/region dummy variables Yes Observations 12,651 Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
32
Table 6: The Effect of Financial Aid on Enrollment Decisions by Income Multinomial logistic regression estimates of the change in the odds ratio a student enrolls at:
(as compared to enrolling at the University of Oregon)
Independent variable Does not enroll Two-year Public instate
four-year Public out-of-state four-year Private four-year
FAFSA Filers - Needy Institutional financial aid 0.947 1.065 0.874** 0.862** 0.876** (0.0569) (0.109) (0.0489) (0.0549) (0.0510) High school GPA 2.449*** 0.863 7.837*** 4.062*** 8.694*** (0.723) (0.430) (2.301) (1.320) (2.677) Controls Yes Observations 3,842 FAFSA Filers – Non-needy Institutional financial aid 0.856* 0.756 0.697*** 0.909 0.830** (0.0693) (0.131) (0.0520) (0.0733) (0.0633) High school GPA 3.841*** 10.32** 21.17*** 2.917** 8.808*** (1.620) (9.816) (8.730) (1.220) (3.663) Controls Yes Observations 2,094 Non-Filers Institutional financial aid 0.898** 0.761*** 0.820*** 0.925* 0.865*** (0.0433) (0.0734) (0.0380) (0.0432) (0.0425) High school GPA 3.012*** 3.976*** 12.29*** 3.081*** 4.426*** (0.600) (1.540) (2.583) (0.603) (0.927) Controls Yes Observations 6,715
Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
33
Appendix A Local Linear Regressions of Alternative Dependent Variables on High School GPA
A. Age at Application
B. Female
17.
71
7.75
17.
81
7.85
17.
9A
ge
at A
ppl
ica
tion
3 3.2 3.4 3.6 3.8 4High School GPA
.4.5
.6.7
.8F
ema
le
3 3.2 3.4 3.6 3.8 4High School GPA
34
C. Nonwhite
D. SAT Mathematics
.15
.2.2
5.3
.35
Non
-Wh
ite
3 3.2 3.4 3.6 3.8 4High School GPA
5.6
5.8
66
.26
.4S
AT
ma
th
3 3.2 3.4 3.6 3.8 4High School GPA
35
E. SAT Verbal
5.4
5.6
5.8
66
.26
.4S
AT
Ve
rba
l
3 3.2 3.4 3.6 3.8 4High School GPA