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: cursb@missouri.edu

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. ____________________________________________________________________

1

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

2

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.

3

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

4

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

5

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

6

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

7

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-

8

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.

9

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.

10

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

11

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

12

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

13

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

000

400

05

000

3 3.2 3.4 3.6 3.8 4High School GPA

Average Institutional Aid Dean's Scholarship

14

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,

15

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

16

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

05

.01

.01

5.0

2

250 300 350 400 450

17

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

05

.01

.01

5.0

2

250 300 350 400 450

18

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) .

19

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:

20

[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

References

Angrist, J. D. & Pischke, J. S. (2009). Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton, NJ: Princeton University Press.

Becker, W. E., (2004).Omitted variables and sample selection in studies of college-going decisions. In C. Teddlie & E. A. Kemper (Series Eds.) & E. P. St. John, (Vol. Ed.), Readings on Equal Education: Vol. 19, Public Policy and College Access: Investigating the Federal and State Roles in Equalizing Postsecondary Opportunity (pp. 65-86). New York: AMS Press.

Bettinger, E. (2004). How financial aid affects persistence. NBER Working Paper #10242. Cambridge, MA: National Bureau of Economic Research.

Cornwell, C., Mustard, D. B., & Sridhar, D. J. (2006). The enrollment effects of merit-based financial aid: Evidence from Georgia’s HOPE program. Journal of Labor Economics, 24(4), 761-786.

Curs, B. R. & Singell, L. D., Jr. (2002). An analysis of the application process and enrollment demand for instate and out-of-state students at a large public university. Economics of Education Review, 21, 111-24.

Dynarski, S. M. (2000). Hope for whom? Financial aid for the middle class and its impact on college attendance. National Tax Journal, 53(3), 629-661.

Dynarski, S. M., (2002). Does aid matter? Measuring the effect of student aid on college attendance and completion. American Economic Review, 93(1), 279-288.

Dynarski, S. M. (2004). The new merit aid. In C. M. Hoxby (Ed.), College choices: The economics of which college, when college, and how to pay for it. Cambridge, MA: The University of Chicago Press.

Ehrenberg, R. G. & Sherman, D. R. (1984). Optimal financial aid policies for a selective university. Journal of Human Resources, 19(2), 203-30.

Hansen, L. (1983). Impact of student financial aid on access. In J. Froomkin(ed.), The Crisis in Higher Education (pp.84-96). New York: Academy of Political Science.

Heller, D. E., (1997). Student price response in higher education: An update to Leslie and Brinkman. Journal of Higher Education, 68, 624-59.

Heller, D. E., (2004). NCES research on college participation: A critical analysis. In C. Teddlie & E. A. Kemper (Series Eds.) & E. P. St. John, (Vol. Ed.), Readings on Equal Education: Vol. 19, Public Policy and College Access: Investigating the Federal and State Roles in Equalizing Postsecondary Opportunity (pp. 65-86). New York: AMS Press.

Jackson, G. A. (1978). Financial aid and student enrollment. The Journal of Higher Education, 49(6), 548-574.

25

Kane, T. J. (1994). College entry by Blacks since 1970: The role of college costs, family background, and the returns to education. Journal of Political Economy, 102, 878-911.

Kane, T. J. (1995). Rising public college tuition and college entry: How well do public subsidies promote access to college? NBER Working Paper #5164. Cambridge, MA: NBER.

Kane, T. J. (2003). A quasi-experimental estimate of the impact of financial aid on college-going. NBER Working Paper #9703. Cambridge, MA: NBER.

Lesik, S. A. (2006). Applying the regression-discontinuity design to infer causality with non-random assignment. Review of Higher Education, 30(1), 1-19.

Leslie, L. L., & Brinkman, P. T. (1987). Student price response in higher education: The student demand studies. Journal of Higher Education, 58, 181-204.

Linsenmeier, D., Rosen, H., & Rouse, C. (2002). Financial aid policies and college enrollment decisions: An econometric case study. NBER Working Paper #9228. Cambridge, MA: National Bureau of Economic Research.

Manski, C. F. & Wise, D. (1983). College Choice in America. Cambridge, MA: Harvard University Press.

Nguyen, A. N. & Taylor, J. (2003). Post-high school choices: New evidence from a multinomial logit model. Journal of Population Economics, 16, 287-306.

Pantel, M. A., Podgursky, M., & Mueser, P. (2006). Retaking the ACT: The effect of a state merit scholarship on test-taking, enrollment, retention, and employment. University of Missouri Working Paper. Columbia, MO: University of Missouri.

Riegg Cellini, S. (2008). Causal inference and omitted variable bias in financial aid research: Assessing solutions. The Review of Higher Education, 31, 329-354.

Schneider, B., Carnoy, M., Kilpatrick, J., Schmidt, W. H., & Shalveson, R. J. (2007). Estimating causal effects: Using experimental and observational designs. Washington, DC: American Educational Research Association.

Seftor, N. & Turner, S. (2002). Back to school: Federal student aid policy and adult college enrollment. Journal of Human Resources, 37, 336-352.

Singell, L. D., Jr. (2004). Come and stay a while: Does financial aid effect enrollment and retention at a large public university? Economics of Education Review, 23, 459-472.

Singell, L. D., Jr , Waddell G. R., & Curs, B. R. (2006). Hope for the Pell: The impact of merit based scholarships on needy students. Southern Economic Journal, 73(1), 79-99.

Singell, L. D., Jr. & Stone, J. A. (2002). The good, the poor, and the wealthy: Who responds most to college financial aid? Bulletin of Economic Research, 54, 393-407.

26

St. John, E. P. (1990a). Price response in enrollment decisions: An analysis of the high school and beyond sophomore cohort. Research in Higher Education, 31(2), 161-176.

St. John, E. P. & Noell, J. (1989). The effects of student financial aid on access to higher education: An analysis of progress with special consideration of minority enrollment. Research in Higher Education, 30(6) 563-581.

Thistlewaite, D., & Campbell, D. (1960). Regression-discontinuity analysis: An alternative to the ex-post facto experiment. Journal of Educational Psychology, 51, 309–317.

Van der Klaauw, W. (2002). Estimating the effects of financial aid offers on college enrollment: A regression discontinuity approach. International Economic Review, 43, 1249-1287.

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