Income and Financial Aid Effects on Persistence and Degree Attainment in Public Colleges
Alicia C. Dowd
University of Massachusetts Boston
Citation: Dowd A.,
(2004, May 12). Income and financial aid effects on persistence and degree attainment in public colleges.
Education Policy
Analysis Archives, 12(21). Retrieved [Date] from
http://epaa.asu.edu/epaa/v12n21/.
Abstract
This study examined the distribution of financial aid among
financially dependent four-year college students and the
effectiveness of different types of financial aid in promoting
student persistence and timely bachelor’s degree attainment.
The findings of descriptive statistical and logistic regression
analyses using the NCES Beginning Postsecondary Students (1990-94)
data show that subsidized loans taken in the first year of college
have a positive effect on persistence. The first-year distribution
of aid does not close the income gap in bachelor’s degree
attainment. Living on campus and first-year grade point average
are the most important predictors of timely degree completion.
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In the latter half of the twentieth century, the states and
federal government of the United States developed a complex higher
education financing system. This system serves many purposes,
among them the stimulation of private investments in higher
education, economic development, and the redress of inequitable
access to college for groups that were traditionally excluded. The
financing system has many components, including direct subsidies
for public colleges and universities and financial aid for
students. Direct operating subsidies are the foundation on which
states offer higher education to all citizens at a much lower
price than that offered by the private sector. Further discounts
on the subsidized price are available to eligible students through
grants, scholarships, and loans. In addition, a student’s
ability to choose a private or public college is supported, as
financial aid is also made available to enroll in the more
expensive private sector (Policy of Choice, 2002). (Note 1) Alongside
affirmative action, the creation of public colleges and the
financial aid system has been a central mechanism for addressing
economic and social inequality in the U.S. However, despite the
development of this complex system over half a century, college
participation in the United States continues to show marked
differences by family income (Access Denied, 2001; Ellwood
& Kane, 1998; Kane, 1999 Chap.4).
The higher education financing system serves students from all
socioeconomic backgrounds. Not surprisingly, the distribution of
benefits among these groups is continually being reshaped amid
competing claims for resources. The work-study program, grants,
and subsidized loans emerged as part of the War on Poverty. The
federal subsidized loan program to aid low-income students was
institutionalized in 1965 by the Higher Education Act, and
today’s Pell grants were established in 1972 as the Basic
Education Opportunity Grant. Shortly thereafter, in 1978 when the
Middle Income Student Assistance Act made subsidized federal loans
available without income restrictions, the middle class was also
firmly established as an important and powerful financial aid
constituency (Hansen & Stampen, 1981). Today, new forms of
aid, such as merit-based scholarships and tax credits, appear to
favor the middle and upper classes (Heller & Schwartz, 2002;
Kane, 1999; Selingo, 2002). The purchasing power of Pell grants
has declined and students must finance a larger share of their
education through loans. This shift in the financing burden to
individuals and families has had a disproportionate impact on
low-income students (Empty Promises, 2002; Heller, 2001).
These changes may well represent a severe loss of opportunity for
low-income students and failure of the financial aid system to
achieve the goal of promoting equity in higher education
enrollments.
At the same time, public colleges are under pressure from state
legislatures and the federal government to educate students and
produce graduates at lower cost. In an era of increasing demand
for college and declining fiscal resources, colleges are expected
to operate more efficiently (Zumeta, 2001). State accountability
programs commonly identify college graduation rates as a measure
of institutional performance (Burke, Rosen, Minassians, &
Lessard, 2000; Burke & Serban, 1998). More recently, the
federal government has also proposed tying grant funds to
graduation rates (Burd, 2003). As part of this accountability
movement and to increase the capacity of overwhelmed public
campuses, many states are urging colleges to graduate students in
a timely way and to reverse the trend of lengthening times to
degree (Knight, 2002; Selingo, 2001).
A recent study by the National Center for Education Statistics
shows that public four-year colleges graduate students within the
traditional period at approximately half the rate of private
colleges. On average, 26% of students starting out at four-year
public colleges earned a bachelor’s degree within four
years. The graduation rate increases to 57% within six years
(Berkner, He, & Cataldi, 2002, p 23, Table 10). To explain low
rates of persistence and degree completion in public colleges,
administrators point to the diverse array of purposes and
conditions under which students pursue collegiate studies today.
Working parents who study part-time do not proceed at the pace of
full-time students fresh out of high school. In addition,
bachelor’s degree completion differs by income status,
whether measured in four years (26% of the lowest income students
compared to 50% of high-income students) or in six years (54%
versus 77%) (Berkner et al, 2002, pp. 26-32, Table 10). Timely
degree completion is desirable both for students, who face
opportunity and direct costs as long as they are enrolled in
college, and for taxpayers who subsidize each student’s
place in public higher education (Choy, 2002). If efficient
educational outcomes are desired, it is important to evaluate the
factors that contribute to those outcomes.
This study contributes to such an effort by evaluating the
relationship between parental income and student outcomes in
college, as it is mediated by different forms of financial aid. It
takes the strategy of observing the progress of public-college
students who are in the strongest position for timely degree
completion and examining the factors that affect their persistence
and degree attainment. Students who are financially dependent on
their parents and enrolled full-time in the public four-year
sector constitute the sample selected for analysis. The
experiences of this group of students in a study of timely degree
completion and financial aid are of interest for several reasons.
Students who are dependent on their parents in their first year of
college are following a traditional path to higher education. They
are not yet independent adults, with family and employment
commitments that impede degree attainment in complex ways that are
not easily mitigated by public policy interventions (Adelman,
1999).
In addition, as full-time students in four-year institutions,
their objective is very likely to obtain a degree, a goal that is
less clear among community college students who may be seeking
short-term vocational training or among part-time students who may
be “testing the waters” of college. Part-time students
are unable to graduate in a traditional four-year period, while
full-time students are. Their failure to do so can more accurately
be interpreted as due to academic or financial barriers than to a
partial involvement in higher education. The sample selected for
analysis reduces variation to the group that has the most time to
invest in their studies and, therefore, the most realistic
possibility of completing a bachelor’s degree. Having
selected this relatively homogeneous sample, the study then
focuses on observing whether parental income is a significant
predictor of academic outcomes and whether different forms of
financial aid reduce outcome gaps associated with income.
Finally, given that students in the public sector are first and
foremost beneficiaries of direct operating subsidies from states
to colleges and universities (Note 2), taxpayers have a particular interest in
their successful academic attainment. Financial aid expenditures
are in a sense marginal costs (albeit very large ones) to reduce
financial barriers to participation in a system already
established at great cost with a primary purpose of ensuring
equitable access to higher education. While the extent to which
taxpayer funds should finance enrollment in expensive private
institutions is debatable (Policy of Choice, 2002), it is
clear that as states are abandoning low and no-tuition policies
(Hauptman, 2001) the provision of financial aid takes on even
greater importance in creating low-cost opportunities for higher
education.
Literature Review
Educational researchers have extensively analyzed the
educational pipeline to identify the mechanisms by which
low-income students and students of color fall behind in their
college aspirations (Carter, 1999; McDonough, 1994), enrollment
(Heller, 1997; Jackson, 1990; Perna, 2000; St. John & Noell,
1989) and persistence in college among those who do enroll
(Braxton, 2000; Tinto, 1975, 1987). (Note 3) The effect of tuition pricing
and financial aid on persistence has received increasing attention
with the development of theories that assign an important role to
finances in determining students’ college participation
decisions (Bean & Metzner, 1985; Cabrera, Nora, &
Castaneda, 1992; Paulsen & St. John, 2002; St. John, Cabrera,
Nora, & Asker, 2000; St. John & Starkey, 1995). Empirical
studies utilizing these theories have examined the effects of
tuition and aid on within-year persistence (Paulsen & St.
John, 2002; St. John, Andrieu, Oescher, & Starkey, 1994; St.
John, Paulsen, & Starkey, 1996)and multi-year persistence (St.
John 1989, 1990; Stampen & Cabrera, 1988; Cabrera, Nora,
Castaneda, 1993, Titus, 2000).
The effect of financial aid on degree attainment has received
considerably less attention. However, with increasing availability
of data from the longitudinal Beginning Postsecondary Students
(BPS) surveys, which follow students for up to six years, recent
reports by the National Center for Education Statistics (NCES) and
higher education policy institutes have analyzed a wide range of
factors, including student finances, and their association with
both persistence and degree attainment (Berkner, Cuccaro-Alamin,
& McCormick, 1996; Lutz Berkner et al., 2002; Bradburn, 2002;
Choy, 2002; Horn & Kojaku, 2001; King, 2002; Wei & Horn,
2002). (Note 4) This
study builds on these reports and educational research by St. John
and colleagues (Paulsen & St. John, 2002; St. John, 1990; St.
John, 1989; St. John, Andrieu, Oescher, & Starkey, 1994)
focusing on the effect of different forms of financial aid on
persistence in four-year colleges using NCES data, particularly
the National Postsecondary Student Aid Study (NPSAS). It extends
the work of these researchers by studying persistence to the
second year of college and to degree attainment.
The study also draws on the findings of recent work analyzing
institutional and state-level data (Note 5), in which researchers have introduced new
statistical techniques for studying persistence, including event
history modeling (DesJardins, Ahlburg, & McCall, 2002;
DesJardins, McCall, Ahlburg, & Moye, 2002), two-stage
regression with sample selection (Note 6) (Singell, 2002a), and discontinuity analysis
(Bettinger, 2002). These techniques specifically model the
sequential, interrelated nature of students’ enrollment and
multi-year persistence decisions. The results of these studies
indicate that the analysis of cross-sectional data using
single-stage regression models produces biased estimates of the
effects of financial aid on persistence. This is due to the fact
that the personal and academic characteristics that lead students
to decide to enroll and persist in certain types of colleges also
play a role in determining the level and type of their financial
aid awards. Although multivariate analyses include control
variables for these characteristics, Dynarski (2002a) argues that
variables measuring observable student characteristics are
unlikely to provide an adequate control for unobserved
characteristics that are correlated with a student’s college
enrollment decisions. This study analyzes the effects of financial
aid received in the first year of college on outcomes in
subsequent years. Though the outcomes are longitudinal, the
analysis is cross-sectional, based on measures obtained for one
cohort at one point in time. This approach is consistent with
prior educational research analyzing persistence using national
data. This study draws on the new findings and methods introduced
largely in the field of economics to understand the direction of
potential bias in the estimates and to place the findings in the
context of prior research on persistence in both academic fields.
Thus the literature review informs the current study regarding the
effects of different types of aid on persistence and degree
attainment; the effectiveness of financial aid in improving
college persistence by low-income students, and the interpretation
of results obtained by single-stage logistic regression
models.
Prior research provides mixed evidence regarding the effects of
different forms of aid on persistence and degree attainment. In
studies of national data, grants, loans, and work-study awards
have been found to have positive effects on year-to-year
persistence (St. John, 1990), but negative effects on within-year
persistence (St. John, Andrieu, Oescher, & Starkey, 1994;
Paulsen & St. John, 2002). The results of institutional data
also provide inconsistent evidence. DesJardins, Ahlburg, and
McCall (2002) find that loans have a negative effect on
persistence, although this effect diminishes over the years in
college. Singell (2002) finds a positive effect of subsidized
loans and an insignificant effect of unsubsidized loans. Both
studies find positive effects of merit- and need-based grants. In
addition, Singell finds a negative effect of work-study awards.
Bettinger (2002), who focuses only on federal Pell grants, obtains
inconclusive results. Clearly, further research is needed to
develop a strong consensus on the effects of different types of
aid on persistence.
The conclusions of prior researchers suggest the financial aid
system is failing to provide equitable access to college for
low-income students. Studies of national data find family income
to be consistently associated with higher levels of persistence,
even with multivariate controls for demographic and academic
factors (St. John, 1990). Aid is found to have negative effects on
persistence among poor and working-class students, but not among
higher-income students (Paulsen & St. John, 2002). In a study
of students enrolled in the University System of Maryland, Titus
(2000) also found that aid effects on second-year persistence
differ by income group. He concluded that aid amounts are not
sufficient to promote the retention of low-income students. Merit
aid, which is often disproportionately awarded to higher income
students (Heller & Schwartz, 2002), is found to have positive
effects by DesJardins et al (2002) and by Singell (2002), with
Singell also observing a differential effect in favor of higher
income students. DesJardins et al find that graduation
probabilities do not differ by income level, but this may be due
to a more limited range of socio-economic status in the
institutional data they study from the University of Minnesota.
The work by Paulsen and St. John (2002) and Singell (2002)
demonstrates the importance of evaluating differences in the
effects of aid on students from different income groups. (Note 7) In this study,
these differential effects are evaluated by testing the
significance of interaction terms.
When Singell (2002)
Note 8 and Bettinger (2002) compare the results of statistical
models that do and do not control for sample selection
bias—the bias inherent in not observing the effects of
factors of interest on those with characteristics that
systematically remove them from the sample—they find
statistically and substantively different results. For example,
Singell’s research indicates that institutional merit-based
aid has the largest effect on second-year enrollment, with an
increase of $1,000 predicted to increase the probability of
reenrollment by 26.4%. This effect is half of what is estimated in
a model that does not control for self-selection bias. This
follows from the positive correlation of academic ability and
persistence. The students who received merit aid were more likely
to persist even in the absence of a scholarship. The difference in
results is less dramatic for other types of aid, but the
single-stage model appears to underestimate the effects of
need-based grants and overestimate the effect of subsidized loans
and work-study awards. Bettinger (2002) also finds that an
estimation strategy that omits from the sample students who may
have been eligible but did not apply for federal Pell grants
underestimates the positive effects of Pell grants on persistence.
This follows from the fact that Pell grant recipients have
characteristics associated with withdrawal. Between the two
models, the sign of the estimate changes, which indicates
misestimation of both the magnitude and the direction of the
effect. Such a misestimation would mask the positive effects of
means-tested grant aid and lead to an incorrect conclusion that
grant aid is not effective in promoting the college participation
of low-income students.
Finally, Singell (2002) finds that the effects of aid on
persistence (or “reenrollment”) smaller than but
similar in direction to effects on the initial enrollment
decision. These findings indicate that researchers studying
persistence can turn to the results of enrollment studies to
predict the direction of aid effects on what can be conceptualized
as students’ “re-enrollment” decisions, though
with the expectation that the magnitude of the effect is likely to
be smaller. However, the findings of national cross-sectional
studies of the effects of aid on enrollment are difficult to
generalize, because the findings differ by type of aid and by type
of student (Heller, 1997; Nora & Horvath, 1989). Generally the
results indicate that aid does promote enrollment, but, in
important departures from those findings, Perna (2000) found loans
have a highly negative effect on African American students, and
Jackson (Jackson, 1990) found positive effects of grants for
African American and white students, but not for those of Hispanic
descent. Summarizing findings of quasi-experimental studies,
Dynarski (2002a) shows that this body of research generally
demonstrates positive enrollment effects of both grants and loans.
Once again, these effects appear to differ by income and racial
group.
This literature review underscores the methodological
complexity of estimating the effects of different types of aid on
student decision-making. Student responses to different forms of
aid appear to vary based on their income class and other personal
characteristics. Whereas some studies find negative effects of aid
on persistence, others find that certain types of aid have a
positive effect for some groups of students. These methodological
challenges and contrasting results indicate that further work is
needed in this area. This study contributes to this literature by
analyzing the effects of parental income and financial aid on
second-year persistence and timely degree attainment among
full-time dependent students in the four-year college sector. It
analyzes national data, the Beginning Postsecondary Students
90/94, which has not previously been examined using the methods
and sample presented here. Institutional data tend to have rich
detail on individual student characteristics, academic
performance, and aid packages, but typically lack information
about student outcomes in the higher education system as a whole
for those students who transfer. Therefore, they overestimate
student attrition (Adelman, 1999, Berkner et al 2002). In this
respect, national data sets are preferable, as they allow the
observation of system-wide persistence and degree attainment.
Conceptual Framework
This study adopts a theoretical perspective described by
Beekhoven, De Jong, and Van Hout (2002) that combines
“integration-based student departure models” (p.577)
with rational choice theory to explain student enrollment
decisions across the multiple years of baccalaureate study.
Tinto’s (1975, 1987) student integration model focuses on
the degree of fit between student and institution and the extent
to which a student’s goal commitment is reinforced by
academic and social integration on campus. Cabrera and colleagues
(Cabrera, Castaneda, Nora, & Hengstler, 1992; Cabrera, Nora,
& Castaneda, 1993) subsequently developed an integrated model
of college persistence that combined Tinto’s theory with the
“student attrition” model of Bean and colleagues (Bean
and Metzner, 1985). Bean’s model differs most prominently
from Tinto’s by its inclusion of factors outside the college
environment, such as work and finances, as explanatory variables.
Through empirical testing, Cabrera et al found that the integrated
model provided a better understanding of the persistence process
than could be achieved with either model individually.
Similarly, Beekhoven, De Jong, and Van Hout (2002) believed
that the student integration model would benefit from greater
attention to the concept of individual agency in decision-making.
Therefore, they tested a combined model of student integration
theory and rational choice theory. Through an empirical test using
college student data from the Netherlands, they found that their
“extended model” performed better than either theory
independently. Their model emphasizes that student withdrawal
decisions are based on their expectations, modified from one year
to the next, of successful program completion. These expectations
are influenced by the extent to which students fit into the
college environment and are satisfied with their experiences,
where “fit” and “satisfaction” are
constructs measured by integration theory. As these authors
express it, “Students trying to integrate into the student
community are likely to be rational actors who make cost-benefit
analyses” (p. 581). Their empirical results are based on a
longitudinal data base and provide support for the assertion that
student integration in one period influences perceptions of the
likelihood of graduating. Conversely, positive perceptions of the
likelihood of graduation will positively affect integration (p.
597). Other researchers (DesJardins, Ahlburg et al., 2002; Manski
& Wise, 1983; Paulsen & St. John, 2002; Singell, 2002a;
Titus, 2000)have elsewhere emphasized the sequential nature of
college students’ enrollment decisions over time.
Rational choice theory (Becker, 1976, 1993; Elster,
1986)explains student enrollment decisions as a process of
cost-benefit analysis and utility maximization. From this
perspective, as the monetary and personal costs of college rise,
the benefits must rise commensurately, or a potential student will
perceive labor market opportunities as more attractive than higher
education. Monetary costs are determined by direct expenses (such
as tuition, fees, and books) and the loss of foregone wages.
Personal costs are largely determined by a person’s ability
to complete and enjoy academic work. Those who are less
academically prepared or able take longer to learn and endure
greater aggravation in the process. The use of Beekhoven, De Jong,
and Van Hout’s (2002) theoretical model combining rational
choice and student integration theories is particularly
appropriate for the data analyzed in this study. While the student
integration theories include propositions modeling the effects of
students’ motivations, satisfaction, and institutional
commitment, the BPS data are not rich in these variables. In
combination with rational choice theory, which assumes students
will rationally maximize their utility rather than attempting to
measure psychological factors, these variables may be omitted,
albeit with a loss of explanation of the mechanisms on campus that
influence students’ institutional experiences and loyalties.
Beekhoven et al omitted measures of commitment and motivation in
their combined model without loss of explanatory power; in fact,
their model explains a greater proportion of variance than either
of the theories applied independently. Further, the use of
rational choice theory facilitates the integration of results from
persistence studies in the field of economics, where it is a
dominant theory.
Study Design
Data and Sample
The U.S. Department of Education National Center for Education
Statistics (NCES) conducts the Beginning Postsecondary Students
(BPS) survey as a longitudinal component of the National
Postsecondary Student Aid Study (NPSAS). The BPS, which is a
nationally representative survey, includes only those students who
enrolled in postsecondary education for the first time in the
NPSAS base year; it excludes returning students who had previously
stopped out of college. This study analyzes BPS90/94, which has a
NPSAS base year of 1989-1990 and a follow-up of student outcomes
in the spring of 1994. This time frame allows for the observation
of “second-year persistence” (re-enrollment in the
second year) and “timely” bachelor’s degree
completion (within five years). Use of these data to analyze
student outcomes complements relatively short-term analyses of
within-year persistence. The exclusion of returning students
ensures that the data represent a student’s full persistence
and stop-out history. The results of a more recent BPS survey
covering the period 1996-2001 was not available for this analysis,
but those data make possible replication of the study in a more
recent time period, which is desirable given changes in financial
aid policies and trends in the 1990s.
BPS is a stratified and clustered probability sample, where the
strata represent the different sectors of higher education and the
clusters represent geographic regions (BPS9094 Technical
report, 1996).The public four-year doctoral granting and
comprehensive sectors (two strata) were included in this sample.
Due to the sampling design, this sub-sample is nationally
representative of the population of students in these two sectors.
Students were retained in the sample if they were financially
dependent on their parents and began their studies on a full-time
basis at a public four-year institution. The resulting sample size
for this study is 1,087 cases, which is 67% of the original 1,612
BPS cases who started out in public four-year institutions. These
sampling decisions restrict the analysis to
“traditional” students, as evidenced by the
sample’s mean age of 18 years.
Persistence is defined in this study as full-time enrollment in
the second year of the BPS survey (academic year 1990-91) at a
public or private four-year institution. This definition sustains
the focus of this study on students who are on a traditional path
towards the bachelor’s degree, as well as the focus on
public institutions because only a small proportion of the sample
transferred to private colleges. This definition omitted those who
left college or moved to part-time status (15%) and those who
transferred to public two-year colleges (4%) or private
postsecondary (not baccalaureate) institutions. These students
were considered to have left the persistence track for timely
bachelor’s degree completion. Those who transferred to
private four-year colleges in the second year (.006%) were treated
as on track, given the higher rates of degree attainment in the
private sector. This definition of persistence, which captures
reenrollment behaviors in the second year of college that keep
students on track for timely bachelor’s degree completion,
differs from other measures that focused on institutional
retention or within-year persistence. Based on this definition,
78% of the BPS90/94 sample persisted from the first to the second
year of college. Seventy-one percent were enrolled in the third
year of the survey (with or without stop-out in year 2) and 63%
were enrolled in the fourth year. Approximately 2% transferred
each year to the private sector. Fifty-five percent of students
obtained their bachelor’s degree within five years.
Thirty-nine percent of the sample was enrolled in the fifth year
of the survey, which, depending on stop-out behaviors, may or may
not have been the fifth year of study for the student.
Methods
The analysis focuses on the following research questions: (a)
What is the distribution of different types of financial aid among
dependent students in the public four-year sector by parental
income quartile? (b) What is the influence of parental income and
financial aid on reenrollment in the second year of study at a
four-year college? (d) What is the influence of parental income
and financial aid on timely (within five years) bachelor’s
degree completion?
Analyses of complex survey data, such as BPS, may be
“model”- or “design”-based (Hosmer &
Lemeshow, 2000; Thomas & Heck, 2001). Design-based analyses
adjust estimates to reflect the sampling structure by using sample
probability weights, the intra-class cluster coefficient, and
robust measures of standard errors, while model-based analyses
proceed as if the data were collected as a simple random sample.
This study presents a design-based analysis. (Note 9) This approach is of
particular importance when estimating differences in means and
proportions, where the sampling “design effect” has a
particularly large impact, greater than on the estimation of
regression coefficients (Hosmer & Lemeshow, 2000, p. 220). (Note 10) The
estimation of means for variables in this study is subject to
design effects in the range of .9 to 2.0. (Note 11) The sampling weight for
cross-sectional and retrospective analyses of data from the 1994
follow-up (BPS94AWT) is applied (National Center for Education
Statistics, 1996). The analysis is conducted using Stata
statistical software, version 7.
Descriptive statistics are analyzed by income quartile to
characterize the relationship between income, financial aid, and
other variables included in the regression analyses. (Note 12) Logistic
regression analyses were conducted to observe the effects of
factors bearing on student persistence and timely bachelor’s
degree attainment. Income was entered first as the sole predictor.
Groups of additional variables were then entered sequentially to
observe their mediating effect on income. A final model includes
interaction terms of the different forms of aid by parental income
to test for differences in the effects of aid by income, following
recent results that the effects of aid differ by income group
(Singell, 2002; Paulsen & St. John, 2002).
The magnitude of the effect of the predictor variables is
reported as odds ratios, with standard errors indicated as robust
z statistics (Stata, 2001, User's Manual, section 23.11),
and as “delta p” (change in the probability)
statistics (Peterson, 1985).
The changes in the probability of the positive dependent
outcome are reported for variables that were significant in the
final step of the sequential regression. The “delta p”
values are reported for a change from the minimum to maximum value
for all variables (Note
13) and for a one-unit change at the mean for continuous
variables. For dichotomous variables, the change from the minimum
to maximum value represents a comparison between membership in one
of two groups (e.g. on or off campus residence). These changes are
estimated with dichotomous covariates held at their modal values
(as proposed by Long, 1997)and continuous covariates held at their
means. (Note 14)
Statistically significant differences are reported at p<.05
based on two-sided tests, with the significance of design
variables (race and income quartile) adjusted for multiple
categories. The direction of insignificant effects that are
expected by theory and prior research to be significant are noted
if p<.10. (Note
15)
Several goodness-of-fit measures are presented. Some
statisticians argue that likelihood ratio (LR) statistics should
not be used for models that include weighting and clustering,
because under these conditions a “pseudo-likelihood”
is estimated rather than a true likelihood (Hosmer & Lemeshow,
2000; Scribney, 1997a, 1997b). Long (1997), on the other hand,
notes the heuristic nature of logistic goodness of fit statistics
and argues that the measures may appropriately be calculated using
the pseudo-likelihoods. Consistent with Long, the following LR
statistics are reported: the LR chi squared, McFadden’s
Rsquared, and the adjusted McFadden’s Rsquared (which
adjusts for increases due simply to the addition of predictors).
Stata provides a Wald chi squared statistic, which is not based on
the likelihood ratio, to test the significance of weighted,
clustered models. This value is also reported. (Note 16)
Predictor Variables
All predictor variables in the logistic regression models were
measured in the NPSAS base year, the students’ first year of
college. Therefore, the predictors are conceptualized as
components of the first-year experience. These components take on
four dimensions in this study: financial, cultural, social, and
academic (as defined below).
Some of the variables, such as gender, mother’s
education, and race or ethnicity will not change in subsequent
years. Other variables, particularly those measuring financial
aid, may well change. Thus, it is important to emphasize that the
observed financial effects are based on a student’s
situation in the first year.
Tuition is included to control for the amount of financial aid
required to meet higher education expenses. Tuition was defined as
the annual in-jurisdiction charge for students enrolled in their
home state and as the annual out-of-jurisdiction rate for students
enrolled in other states (12% of the sample). The tuition price
students faced in years subsequent to the first year is available
in the BPS90/94 data. A correlation analysis of tuition across the
five years of the survey shows that it is highly correlated at
.97-.99, which is consistent with the limitation of the sample to
four-year institutions and the small proportion of students
exiting to the private sector. Therefore, first-year tuition is a
good representation of the tuition charges students faced in
subsequent years.
The financial variables represent different forms of financial
aid, including federal and state grants, institutional need- and
non-need-based grants, federal subsidized loans, and federal
work-study awards. The state grant variable does not distinguish
between need- and merit-based awards, but it should be noted that
these data were collected in 1989 prior to the tremendous growth
in state merit scholarships. The financial aid measures are
entered in dollar amounts, rather than as binary variables
indicating receipt of aid. Although researchers have previously
tested the latter approach to model the effects of aid (Nora,
Cabrera, Hagedorn, & Pascarella, 1996; St. John & Starkey,
1995), recent research demonstrates a preference for the use of
actual aid amounts (DesJardins, Ahlburg, & McCall, 2002;
Paulsen & St. John, 2002).
The cultural group of variables includes indicators of race or
ethnicity in four categories: African American (8% of the sample),
Hispanic (4%), Asian (5%), and White (the reference group, 87% of
the sample). While these broad categories are likely to mask
differences in educational experiences among students whose
cultural heritage differs quite significantly, finer distinctions
are not possible with these data. Gender is included in this group
of variables; females are in the majority, accounting for 53% of
the sample.
Based on the theoretical notion of “social capital”
(Coleman, 1988), which posits that parental education level
facilitates human capital production through knowledge of college
processes, norms, and networks, a binary variable indicating
whether the student’s mother is a college graduate is
included in the analysis. The other variables in this group also
represent measures of a student’s capacity to participate in
college social networks. They are delayed enrollment (a time gap
between high school and college, or disassociation from
one’s age cohort), living on or off campus, and the number
of hours spent working each week. An index measuring social
integration is also included, based on a four-item scale intended
to measure Tinto’s (1975, 1987) theoretical construct. These
items, which respondents rated on a frequency scale, included
making contact with faculty outside class; going places with
friends from school; spending time in student centers or
participating in student programs; and participating in school
clubs. (Note 17)
Three academic variables measure academic experiences and
performance. The first is a binary measure indicating whether the
student’s college is a doctoral-granting or a comprehensive
institution. The doctoral-granting group (57% of the sample) is
likely to enroll stronger students and to include flagship
campuses. Like the social integration index, the academic
integration index is based on a multi-item scale representing
Tinto’s (1975, 1987) construct. The items measure: attending
career-related lectures; participating in study groups with other
students; talking with faculty regarding academic matters; and
talking with an advisor about academic plans. The third variable
is the first-year grade point average (GPA). A standardized
measure of academic achievement would be desirable in controlling
for academic ability. While the Standardized Achievement Test
(SAT) scores are available in the BPS90/94 data, in the sample
analyzed for this study 62% of the cases were missing. Therefore
the variable was not included. High school grades are also not
available, but the absence of this measure is mitigated by
inclusion of actual academic performance in college, as indicated
by the GPA.
One fifth of the sample was lacking data on one or more
variables in the analysis. A missing cases analysis revealed that
the data lacked a GPA for 26% of African American students, in
comparison to 12% of students in other racial categories.
Therefore, the values of the missing GPA cases were imputed by a
linear regression using race and gender as predictors. A smaller
proportion of cases (less than 5%) were missing data on the
parental income and tuition variables. The missing values were
similarly imputed.
(Note 18)
Limitations
This study has several limitations. First, the analysis seeks
to understand whether parental income is a determinant of a
college student’s persistence and degree attainment, even in
the presence of state, federal, and institutional financial aid
programs designed to remove financial barriers to college. The
BPS90/94 data provides detailed financial information on
students’ financial aid packages only for the first year of
study. Data from subsequent years indicate whether or not students
received certain forms of aid, but do not reveal aid amounts.
Therefore, the study is limited to understanding the mitigating
effects of the first-year financial aid package on parental income
effects. This is valuable for analyzing second-year persistence.
However, aid packages and other variables, such as campus
residence and work hours, do change over a student’s
four-year career, and these changes are not observed here.
Second, the intention of this study (and others that precede it
using similar methods and data bases) is to draw conclusions about
the effectiveness of financial aid policies in reducing college
participation gaps based on family income. Dynarski (2002a)
cautions that cross-sectional studies of the type presented here
are not likely to estimate the relevant parameters accurately. She
argues that variables measuring observable student characteristics
are unlikely to provide an adequate control for unobserved
characteristics that are correlated with “schooling
decisions and schooling costs” (p.2). She notes, “This
is particularly problematic because point estimates in this
literature are often quite fragile, even changing sign with small
changes in specification” (p.2). These concerns raise new
challenges for higher education researchers studying financial aid
policy, who should be careful to test the robustness of their
findings across specifications and to interpret their findings in
light of the potential bias of omitted variables and student
self-selection into different types of colleges, programs, and
financial aid packages. In addition, it highlights the need for
strong theoretical frameworks in order to impose consistency on
the interpretation of findings based on studies using different
methods and data. The ongoing comparison of findings from the
higher education and the economics literature is also likely to
improve understanding of the effectiveness of financial aid
policy. With awareness of these limitations, the analysis of
national data bases is worthwhile to establish benchmarking
standards for institutional researchers and state-level policy
analysts, who can compare results for similar populations of
students enrolled on their own campuses.
Results
Distribution of Outcomes and Aid by Parental Income
The distribution of variables included in the regression
analysis is reported by parental income quartile in column (4) of
Table 1. The descriptive results indicate that rates of
persistence from the first to second years of college do not
differ by parental income quartile. However, timely
bachelor’s degree attainment does, rising from 47% in the
first quartile to 65% in the fourth quartile. Separate analyses by
income quartile of persistence to the third through fourth years
of study indicate no statistically significant differences in
these outcomes. These findings suggest that the difference in
degree attainment depends on eligibility for graduation at the end
of the fourth year, not on differences in year-to-year
persistence.
Table 1
Variable Definitions and Descriptive
Statistics
| (1) |
(2)
Estimated Means |
(3)
Std. Error |
(4)
Quartile Means and
Proportionsa |
| Variable (measurement units, range) |
(mean of 0/1 is percent) |
|
1st |
2nd |
3rd |
4th |
F-testb |
t-test 1st v.4th Quartile |
| Persistence to year2, 0/1, yes=1 |
.7759 |
.0133 |
74.9 |
79.3 |
77.3 |
78.8 |
.689 |
|
| Bachelor’s degree, 0/1, yes=1 |
.5470
|
.0180 |
46.9 |
51.1 |
56.3 |
64.8 |
6.27** |
|
| Parental income ($170-250000) |
46955 |
1207 |
17161 |
36542 |
51215 |
83599 |
|
25.03** |
| Tuition ($96-14095) |
2838 |
77.44 |
2555 |
2742 |
2832 |
3232 |
|
4.0** |
| Grant federal ($136-5950) |
1712 |
52.21 |
1698 |
1744 |
1702 |
1700 |
|
.02 |
| Grant federal 0/1 Received, yes=1 |
.3047 |
.0134 |
31.8 |
33.7 |
26.9 |
29.6 |
1.24 |
|
| Grant state ($100-4900) |
1035 |
58.12 |
1101 |
797.8 |
929.4 |
1585 |
|
1.07 |
| Grant state 0/1 Received, yes=1 |
.1633 |
.0137 |
39.1 |
33.7 |
26.9 |
29.6 |
51.44** |
|
| Grant institutional Need ($150-15166) |
3311 |
246.8 |
2991 |
2928 |
3189 |
4031 |
|
1.40 |
| Grant institutional need 0/1, Recd, yes=1 |
.1356 |
.0099 |
15.6 |
13.8 |
8.8 |
16.1 |
2.65* |
|
| Grant institutional (non-need) ($100-9000) |
2190 |
246.1 |
2100 |
2352 |
1763 |
2359 |
|
.37 |
| Grant institutnl (non-need) 0/1, Recd, yes=1 |
.0644 |
.0084 |
8.9 |
8.1 |
3.3 |
5.5 |
2.55 |
|
| Loan federal ($184-4625) |
1770 |
58.69 |
1790 |
1759 |
1608 |
2002 |
|
.60 |
| Loan federal 0/1 Received, yes=1 |
.1929 |
.0158 |
38.2 |
27.3 |
7.9 |
3.6 |
48.32** |
|
| Work study ($139-2998) |
977.1 |
54.72 |
991.8 |
1140 |
597.3 |
573.3 |
|
1.59 |
| Work study 0/1 Received, yes=1 |
.0762 |
.0088 |
20.2 |
6.6 |
2.9 |
0.7 |
32.82** |
|
| White,0/1, yes=1 |
.8653 |
.0147 |
78.7 |
85.7 |
88.9 |
92.9 |
7.34** |
|
| African American, yes=1 |
.0778 |
.0119 |
14.0 |
8.7 |
5.4 |
3.7 |
8.31** |
|
| Hispanic, 0/1, yes=1 |
.0367 |
.0067 |
4.9 |
4.5 |
1.8 |
3.5 |
1.45 |
|
| Asian, 0/1, yes=1 |
.0499 |
.0089 |
6.0 |
5.3 |
5.0 |
3.7 |
.483 |
|
| Male, 0/1, yes=1 |
.4696 |
.0166 |
43.2 |
45.0 |
51.6 |
48.0 |
1.48 |
|
| Mom college grad, 0/1, yes=1 |
.2785 |
.0164 |
17.5 |
18.8 |
29.2 |
46.2 |
24.43** |
|
|
Delay enrollment, 0/1, yes=1
|
.0458 |
.0075 |
4.3 |
6.8 |
4.3 |
2.9 |
1.40 |
|
| Live on campus, 0/1, yes=1 |
.4706 |
.0211 |
44.7 |
43.0 |
47.9 |
52.7 |
1.80 |
|
| Social index (1-4) |
2.475 |
.0213 |
2.45 |
2.40 |
2.51 |
2.53 |
|
1.32 |
| Work hours (0-70) |
20.40 |
.5326 |
19.21 |
19.16 |
20.90 |
22.37 |
|
2.16* |
|
Doctoral institution 0/1, yes=1
|
.5734 |
.0350 |
51.2 |
53.0 |
58.2 |
67.0 |
4.49** |
|
| Academic index, (1-4) |
2.702 |
.0233 |
2.71 |
2.60 |
2.72 |
2.69 |
|
1.43 |
| GPA (grade point average), 0-400 |
252.92 |
2.914 |
251 |
253 |
250 |
255 |
|
.60 |
Notes:
Observations = 1087, Population size = 433065.81
Data: BPS:90/94 NCES. Weight: BPS94AWT.
Subpopulation: public 4-year (OFCON1 = 3 or 4)
Estimates adjusted for stratification and clustering.
Number of strata = 2, Number of PSUs = 260
aMeans of aid awards are conditional on aid type>0.
*p<.05 **p<.01
b The Pearson chi-squared statistic has been corrected for the
survey design and converted into an F statistic.
The mean tuition charge of tuition and fees was nearly $3,000,
a skewed value in comparison to the median of $2,200. This is due
to the presence in the sample of flagship public universities,
which typically charge higher tuitions than other public four-year
institutions. (Note
19) Students from the highest income families enrolled in
higher priced institutions, on average, than other students and
were disproportionately enrolled in doctoral-granting
institutions.
In the first year, 30% of the sample received a federal grant
averaging just over $1,700, an amount which is approximately
three-quarters the median tuition price. (The mean financial aid
values in Table 1 are reported conditional on the receipt of each
aid type.) State grants were received by a smaller proportion of
students (16%) and in smaller amounts (approximately $1,000 on
average). Fourteen percent of the sample received institutional
need-based grants with a relatively large mean value just over
$3,300, while 6% received institutional non-need-based grants
averaging nearly $2,200. These sizeable institutional awards were
clearly an important source of funds for a small percentage of the
sample. Eight percent received a federal work-study award
averaging nearly $1,000.
Nineteen percent of the sample took subsidized federal loans,
averaging $1,770. Over 98% of the sample borrowed an amount less
than or equal to the Stafford loan maximum for first-year
students, which was $2,625 in 1989. The maximum loan value in this
sample is $4,625, which reflects additional loan dollars available
to students with high financial need through the Perkins
program. Note
20
The greater tuition expenses of higher income students are
associated with the pattern of first-year aid awards exhibited in
Table 1. Students in the fourth income quartile receive awards in
proportions and amounts equal to those of the lowest income
students. In fact, award amounts in the fourth quartile are often
greater, though these differences are not statistically
significant. This pattern is observed for federal and state grants
and both need-based and non-need institutional awards, with the
exception that higher proportions of low-income students receive
state grants. Students in the third-income quartile receive these
types of aid in amounts similar to that awarded low-income
students, but smaller proportions receive state grants and
institutional need-based aid.
In contrast, federal loans are taken by much larger proportions
of low-income students (38% and 27% in the first and second
quartiles, respectively) than high income students (8% and 4% in
the third and fourth quartiles). Also, while 20% of students in
the lowest income quartile receive work-study awards, that
proportion falls steeply to 7% in the second income quartile and
to less than 3% among high income students. Although students in
the upper income quartiles do not typically receive work-study,
they do work, with students in the fourth quartile reporting 22
hours per week in comparison to 19 hours per week for those in the
1st quartile.
The proportion of white students increases as parental income
increases, while the proportion of African Americans falls. While
higher proportions of Hispanic and Asian students are observed in
lower income brackets, these differences are not statistically
significant. The educational level of students’ mothers is
significantly higher in the fourth income quartile, with 46% of
mothers in the fourth quartile having a college degree, in
comparison with just 18% of mothers in the first income quartile.
These differences by income group are not associated with
differences in academic experiences. No statistically significant
differences are observed by income quartile in delayed enrollment,
grade point average, or the indices of academic and social
integration.
A matrix of Pearson’s correlations (not shown) between
the variables in Table 1 showed that the federal and state grant,
federal loan, and work-study variables had low to moderate
positive correlations, with values in the range of r=.15 to .37.
The social and academic integration indexes were positively
correlated at r=.33. Other values were lower than r=.15. Overall,
these results do not indicate a collinearity problem for the
logistic regressions.
Factors Affecting Persistence
The results of the second-year persistence and bachelor’s
degree attainment regressions are reported as odds ratios in
Tables 2 and 3, respectively, for the sequential steps through the
addition of the academic variables. As demonstrated by joint tests
of significance and the change in the adjusted Rsquared statistic,
the addition of the terms representing the interaction of
financial aid with income status was not significant in either
model, and the results of this step are not shown. Table 4
presents the “delta p” statistics for variables
significant in the final model, shown in column 5 of Tables 2 and
3. As indicated by the Wald chi-squared tests in Table 2, the
persistence model is not significant in column 1, where income is
the sole predictor, but becomes significant in column 2 and
increasingly so as additional blocks of predictors are added. The
McFadden’s Rsquared statistics reported in Table 2 indicate
that the goodness-of-fit of the persistence model improves with
each additional block of predictors, reaching .1432.
Table 2
Persistence to Second
Year
| Variables |
(1)
income |
(2)
financial |
(3)
cultural |
(4)
social |
(5)
academic |
| Income quartile2 |
1.284 |
1.565 |
1.606 |
1.670 |
1.737 |
| |
(1.29) |
(2.19) |
(2.33) |
(2.41) |
(2.59) |
| Income quartile3 |
1.141 |
1.580 |
1.634 |
1.421 |
1.471 |
| |
(0.74) |
(2.34) |
(2.48) |
(1.65) |
(1.70) |
| Income quartile4 |
1.244 |
1.717 |
1.792 |
1.363 |
1.352 |
| |
(1.09) |
(2.46) |
(2.67)* |
(1.31) |
(1.19) |
| tuition |
|
1.015 |
1.016 |
1.030 |
1.017 |
| |
|
(0.70) |
(0.73) |
(1.34) |
(0.77) |
| federal grant |
|
1.036 |
1.035 |
1.055 |
1.065 |
| |
|
(0.88) |
(0.85) |
(1.25) |
(1.50) |
| state grant |
|
1.192 |
1.198 |
1.180 |
1.134 |
| |
|
(2.13)* |
(2.18)* |
(2.15)* |
(1.66) |
| inst'l need grant |
|
1.016 |
1.016 |
1.019 |
1.021 |
| |
|
(0.60) |
(0.64) |
(0.72) |
(0.80) |
| inst'l grant |
|
1.005 |
1.009 |
1.018 |
1.033 |
| |
|
(0.10) |
(0.18) |
(0.33) |
(0.54) |
| federal loan |
|
1.126 |
1.120 |
1.093 |
1.126 |
| |
|
(2.29)* |
(2.20)* |
(1.69) |
(2.12)* |
| work study |
|
1.327 |
1.317 |
1.196 |
1.202 |
| |
|
(1.91) |
(1.84) |
(1.24) |
(1.37) |
| African American |
|
|
1.336 |
1.131 |
1.108 |
| |
|
|
(1.05) |
(0.41) |
(0.34) |
| Hispanic |
|
|
0.855 |
0.964 |
0.806 |
| |
|
|
(0.44) |
(0.10) |
(0.57) |
| Asian |
|
|
1.965 |
2.228 |
2.243 |
| |
|
|
(1.71) |
(2.01) |
(1.88) |
| male |
|
|
0.849 |
0.971 |
1.234 |
| |
|
|
(1.10) |
(0.19) |
(1.29) |
| Mom college grad |
|
|
|
1.427 |
1.300 |
| |
|
|
|
(1.79) |
(1.27) |
| delay enrollment |
|
|
|
0.244 |
0.238 |
| |
|
|
|
(4.36)** |
(4.15)** |
| on campus |
|
|
|
2.304 |
2.211 |
| |
|
|
|
(4.37)** |
(3.97)** |
| social index |
|
|
|
1.271 |
1.175 |
| |
|
|
|
(1.98)* |
(1.20) |
| work hours |
|
|
|
0.986 |
0.986 |
| |
|
|
|
(2.74)** |
(2.80)** |
| Doctoral inst. |
|
|
|
|
1.339 |
| |
|
|
|
|
(1.86) |
| academic index |
|
|
|
|
1.253 |
| |
|
|
|
|
(1.74) |
| gpa |
|
|
|
|
1.008 |
| |
|
|
|
|
(7.17)** |
| Model Statistics |
|
|
|
|
|
| Wald chi2 (df) |
1.90(3) |
22.34(10) |
27.87(14) |
95.64(14) |
132.33(22) |
| Prob>chi2 |
.5937 |
.0135 |
.0148 |
.000 |
.000 |
| McFadden’s Rsquared |
.0016 |
.0165 |
.0211 |
.0831 |
.1432 |
| Adjusted McFadden’s Rsq |
-.005 |
-.003 |
-.005 |
.050 |
.103 |
| LR chi2(df) |
1.801(3) |
19.069(10) |
24.455(14) |
96.107(19) |
165.69(22) |
| Prob>LR |
.615 |
.039 |
.040 |
.000 |
.000 |
| Baseline prob |
.7759 |
|
|
|
|
Notes:
Observations:1087
Robust z statistics in parentheses
* significant at 5%; ** significant at 1% (multiple
comparisons tested jointly and significant joint tests
reported at alpha/k for k categories, alpha = .05)
NCES Data: BPS:90/94 Weight: BPS94AWT.
Subpopulation: public 4-year OFCON1=3or4
Table 3
Bachelor's Degree Attainment Over
Five Years
| Variables |
(1)
income |
(2)
financial |
(3)
cultural |
(4)
social |
(5)
academic |
| Income quartile2 |
1.185 |
1.262 |
1.250 |
1.265 |
1.252 |
| |
(0.97) |
(1.24) |
(1.20) |
(1.19) |
(1.13) |
| Income quartile3 |
1.457 |
1.585 |
1.623 |
1.484 |
1.557 |
| |
(2.50)* |
(2.69)* |
(2.75)* |
(2.14) |
(2.29) |
| Income quartile4 |
2.082 |
2.165 |
2.173 |
1.831 |
1.940 |
| |
(3.77)** |
(3.74)** |
(3.62)** |
(2.65)* |
(2.91)* |
| tuition |
|
1.049 |
1.048 |
1.061 |
1.060 |
| |
|
(2.61)** |
(2.56)* |
(2.99)** |
(2.68)** |
| federal grant |
|
0.995 |
0.999 |
1.011 |
1.018 |
| |
|
(0.14) |
(0.02) |
(0.32) |
(0.49) |
| state grant |
|
1.115 |
1.116 |
1.103 |
1.068 |
| |
|
(1.67) |
(1.58) |
(1.39) |
(0.91) |
| inst'l need grant |
|
1.027 |
1.023 |
1.026 |
1.029 |
| |
|
(1.34) |
(1.15) |
(1.26) |
(1.19) |
| inst'l grant |
|
0.980 |
0.996 |
1.000 |
1.013 |
| |
|
(0.50) |
(0.11) |
(0.01) |
(0.33) |
| federal loan |
|
1.018 |
1.019 |
0.995 |
1.021 |
| |
|
(0.36) |
(0.39) |
(0.10) |
(0.41) |
| work study |
|
1.004 |
0.978 |
0.934 |
0.927 |
| |
|
(0.04) |
(0.20) |
(0.59) |
(0.62) |
| African American |
|
|
0.687 |
0.610 |
0.630 |
| |
|
|
(1.59) |
(2.02) |
(1.77) |
| Hispanic |
|
|
0.937 |
1.065 |
0.965 |
| |
|
|
(0.18) |
(0.18) |
(0.10) |
| Asian |
|
|
1.210 |
1.329 |
1.233 |
| |
|
|
(0.53) |
(0.81) |
(0.56) |
| male |
|
|
0.551 |
0.585 |
0.657 |
| |
|
|
(4.23)** |
(3.66)** |
(2.68)** |
| Mom college grad |
|
|
|
1.253 |
1.167 |
| |
|
|
|
(1.47) |
(1.01) |
| delayed enroll |
|
|
|
0.316 |
0.334 |
| |
|
|
|
(3.13)** |
(2.96)** |
| on campus |
|
|
|
1.809 |
1.798 |
| |
|
|
|
(4.20)** |
(4.04)** |
| work hours |
|
|
|
0.994 |
0.995 |
| |
|
|
|
(1.53) |
(1.28) |
| social index |
|
|
|
1.186 |
1.126 |
| |
|
|
|
(1.72) |
(1.14) |
| Doctoral inst. |
|
|
|
|
1.037 |
| |
|
|
|
|
(0.23) |
| academic index |
|
|
|
|
1.105 |
| |
|
|
|
|
(0.96) |
| gpa |
|
|
|
|
1.008 |
| |
|
|
|
|
(7.45)** |
| Model Statistics |
|
|
|
|
|
| Wald chi2 (df) |
17.6(3) |
32.2(10) |
53.6(14) |
91.44(19) |
142.78(22) |
| Prob>chi2 |
.0005 |
.004 |
.000 |
.000 |
.000 |
| McFadden’s Rsquared |
.0130 |
.0219 |
.0384 |
.0696 |
.1248 |
| Adjusted McFadden’s Rsq |
.008 |
.007 |
.018 |
.043 |
.094 |
| LR chi2(df) |
19.477(3) |
32.803(10) |
57.470(14) |
104.20(19) |
186.906(22) |
| Prob>LR |
.000 |
.000 |
.000 |
.000 |
.000 |
| Baseline prob |
.5470 |
|
|
|
|
Notes:
Observations: 1087
Robust z statistics in parentheses
* significant at 5%; ** significant at 1% (multiple comparisons
tested jointly and significant joint tests reported at alpha/k for
k categories, alpha = .05)
NCES Data: BPS:90/94 Weight: BPS94AWT.
Subpopulation: public 4-year OFCON1=3or4
Income is not a significant predictor of persistence, with the
exception that income quartile 4 is positive and significant in
the third step of the model, when the race and gender variables
are added. Income quartile 4 is not significant when social and
academic factors are added. Among the financial aid variables,
state grants and federal loans have a positive effect, while the
effects of other forms of aid are insignificant. With the
exception of mother’s college education, the variables
measuring social context are significant predictors with
substantive effect sizes, where campus residence and social
integration both have positive effects, and delayed enrollment and
increasing work hours have negative effects. The social
integration index loses significance when the academic variables
are added and the model controls for GPA, which is a positive and
significant predictor. This suggests that social integration
promotes academic achievement. Attendance at a doctoral-granting
institution and academic integration are positive, but not
significant. Gender and the racial indicator variables are not
significant predictors once the tests on individual categories are
adjusted for multiple comparisons.
The conversion of the odds ratios of column 5 to changes in
probability of persistence are presented in the top portion of
Table 4. These indicate that, with covariates held at their mean
or modal values, the probability of persistence increases .14 by
living on campus, .05 with an increase of $1,000 in federal loans,
and .16 with an increase of 100 (of 400) GPA points. The
probability of persistence decreases
-.34 by delayed enrollment and -.03 for an increase of 10 hours
of work. For continuous variables, the change in probability in
persistence from the minimum to the maximum value of that variable
is indicated in Table 4 to show the full range of probabilities
associated with that factor.
Table 4
Odds Ratios from Final Models as
Changes in Probability
“Delta P” of Persistence,
Significant Variables, Final Model, Table 2, Step 5
| Variable(1/0)a |
Minimum to Maximum |
| |
from: |
to: |
deltaP |
| |
x=0 |
x=1 |
0->1 |
| Delay enroll |
0.6911 |
0.3475 |
-0.3435 |
| Live on campus |
0.6911 |
0.8318 |
0.1407 |
| Variable(delta)b |
Change(d) Centered at
Mean |
Minimum to Maximum |
| |
from: |
to: |
deltaP |
from: |
to: |
deltaP |
| |
x-d/2 |
x+d/2 |
-+d/2 |
x=min |
x=max |
min->max |
| Loan fed ($1000) |
0.6652 |
0.7158 |
0.0506 |
0.6715 |
0.8597 |
0.1881 |
| Work hours (10) |
0.7056 |
0.6761 |
-0.0295 |
0.7472 |
0.5292 |
-0.2180 |
| GPA (100) |
0.6037 |
0.7666 |
0.1629 |
0.2417 |
0.8733 |
0.6316 |
“Delta P” of Bachelor’s
Degree, Significant Variables, Final Model, Table 3, Step
5
| Variable (1/0)a |
Minimum to Maximum |
| |
from: |
to: |
deltaP |
| |
x=0 |
x=1 |
0->1 |
| income q3 |
0.4631 |
0.5731 |
0.1100 |
| income q4 |
0.4631 |
0.6259 |
0.1628 |
| Male |
0.4631 |
0.3617 |
-0.1013 |
| Delay enroll |
0.4631 |
0.2234 |
-0.2396 |
| Live on campus |
0.4631 |
0.6079 |
0.1448 |
| Variable(delta)b |
Change(d) Centered at
Mean |
Minimum to Maximum |
| |
from: |
to: |
deltaP |
from: |
to: |
deltaP |
| |
x-d/2 |
x+d/2 |
-+d/2 |
x=min |
x=max |
min->max |
| tuition ($1000) |
0.4487 |
0.4775 |
0.0288 |
0.3859 |
0.7607 |
0.3748 |
| GPA (100) |
0.3690 |
0.5599 |
0.1909 |
0.1072 |
0.7291 |
0.6219 |
Notes:
a(1/0) Indicates a dichotomous variable. For dichotomous
variables the minimum to maximum change is the difference between
membership in the variable group coded zero and the group coded 1
(indicated by the variable label).
b(delta) Indicates the unit change of a continuous variable.
The changes in probability are calculated with the dichotomous
covariates indicated in Table 5 held at their modal value and
continuous covariates held at their means.
Data: BPS:90/94 NCES. Weight: BPS94AWT.
Subpopulation:public 4-year (OFCON1=3or4)
Factors Affecting Timely Bachelor’s Degree
Attainment
The logistic regression model predicting bachelor’s
degree attainment becomes increasingly significant and the
goodness of fit improves with the sequential addition of
predictors, as indicated by the Wald chi-squared and
McFadden’s Rsquared statistics reported in Table 3. The
Rsquared value of .1248, compared to .1432 for the persistence
model, indicates the predictors do a poorer job of explaining
outcomes over the long term to bachelor’s degree
attainment.
The variables measuring parental income in the third and fourth
quartiles are positive and significant across the models. Among
the financial variables, only tuition is significant. Contrary to
theoretical expectations and prior empirical results, it has a
positive effect, a finding that is likely due to the higher costs
of selective flagship institutions. Being male has a significant
negative effect, while the racial indicators are not significant
when the tests on individual categories are adjusted for multiple
comparisons. As in the persistence model, campus residence and
first-year GPA are positive predictors of success, while delayed
enrollment has a significant negative effect.
The conversion of the odds ratios of column 5 to changes in
probability of persistence are presented in the lower portion of
Table 4. These indicate that, with covariates held at their mean
or modal values, the probability of bachelor’s degree
attainment increases .11 and .16 by being in the 3rd
and 4th income quartiles, respectively; .14 by living
on campus; .19 with an increase of 100 GPA points; and .03 with an
increase of $1000 in tuition and fees. The probability of degree
attainment decreases .-10 for men in comparison to women and
-.24 for those who delay enrollment instead of starting college
with their age cohort after high school.
Discussion
The results of this study demonstrate that among four-year
public college students who are financially dependent on their
parents, family income is not a determinant of second-year
persistence, but it is a determinant of bachelor’s degree
attainment. State grants and federal subsidized loans received in
the first year have positive effects on persistence, but no form
of financial aid is observed to have a significant effect on
degree attainment. Thus, financial aid packages as they are
distributed in the first year do not offset the advantages of
family income for timely degree completion. The most important
factors positively affecting both persistence and degree
attainment are living on campus and academic performance in the
first year. The observed benefit of living on campus is consistent
with student integration theory, as it is likely to promote a
greater sense of belonging and commitment to an institution. As
Beekhoven, DeJong, and VanHout (2002) argue in linking integration
theory to a student’s perception of costs, “if a
student cannot succeed in feeling at home or ‘fitting
in,’ the costs of proceeding will increase. At the same
time, the perceived likelihood of success will decrease” (p.
581). These perceptions are important in determining outcomes
because they affect a student’s willingness to integrate in
campus activities and invest in their studies.
Grants certainly do reduce the costs of college, and
theoretically they should be associated with positive effects.
Grants tend to have negligible or positive effects in this study,
but no form of grant aid is statistically significant in either
final model. The positive effects of grants are difficult to
observe and are likely biased downwards because the model cannot
fully control for the correlation between the receipt of
need-based grants and student characteristics that are negatively
associated with persistence (Bettinger, 2002; Dynarski, 2002a).
Students have no reason not to accept the full amount of
scholarship and grant aid offered them by financial aid officers.
In contrast, students may decide to reduce their course load and
increase work hours rather than incur debt by taking student
loans, a form of financial aid that is observed to have a positive
effect. Each student’s decision about loans is likely based
on personal risk aversion, information about loan availability and
terms, and expectations for academic success and
post-baccalaureate earnings. These decisions and variations in the
amount borrowed serve to distinguish the effects of loans even
among a group of already enrolled students.
The state grant variable has a substantive and statistically
significant positive effect on persistence until the final step
when the academic variables are entered. The sequential analysis
suggests, then, that state grants foster academic success, but
this positive effect could be due to the inclusion of merit awards
for academically prepared students in this aid category. Both
Singell (2002) and DesJardins et al (2002) observe strong positive
effects of merit aid on persistence. The same positive effect is
not observed for institutional non-need based grants, another
source of aid which would include merit awards. This insignificant
result may be due to the relatively small number of students
receiving institutional non-need based grants (5-8% in comparison
to 30-39% receiving state grants) or to the inclusion of non-merit
awards in the variable. Studies of other NPSAS financial data in
which researchers also could not clearly disaggregate need-based
from merit aid have found insignificant and negative effects of
grants on within-year persistence (Paulsen & St. John, 2002;
St. John et al., 1994). Paulsen and St. John (2002) find a
negative and significant delta p of -.04 for a $1,000 change in
grant aid for students in the lowest income quartile and
insignificant effects for other income groups. The authors
interpret this effect as an indication that grant aid was
inadequate to meet college costs for low-income students. This
conclusion is not supported by this study. The difference in the
findings may be due to the exclusion from this study of
financially independent students, who may not be able to draw on
additional family resources in the event they enroll and then find
grant aid to be insufficient to meet their financial needs.
Loans have a positive effect on persistence, but not on degree
attainment. Loan-taking patterns among students are likely to have
shifted after the first year, as students gained a better sense of
their prospects for degree completion and their capacity to
combine work and schooling. Students who opted out of borrowing in
their first year may have taken loans, the most readily available
form of new aid, in subsequent years to reduce their out-of-pocket
costs. This new borrowing may have had positive effects on degree
attainment that are not observed here. The distribution of aid in
the first year did not close the gap in timely degree attainment
between low and high income students. This implies that the
distribution of aid in subsequent years must have improved in
favor of low-income students for the aid system to achieve its
equity goals. In fact, federal policies changed during the
five-year span covered by the BPS data in a manner favorable to
middle- and upper-income students, as revisions to the federal
formula for calculating financial need allowed the exclusion of
home equity (Berkner, 2000; Dynarski, 2002b). The early nineties
also marked the beginning of the shift in state aid towards upper
income students through merit and institutional awards (Heller
& Schwartz, 2002). These changes, combined with evidence that
the effects of different forms of aid decline with each subsequent
year of study (DesJardins, Ahlburg et al., 2002), suggest that the
benefits of the aid system were not effectively redistributed in
subsequent years to reduce the degree attainment gap.
The effect estimated in this study of an increased probability
of persistence of .05 given an increase of $1,000 in loans is
consistent with the findings of Singell (2002) who found an
increase of .06 (.04 when correcting for self-selection bias).
These findings are contradictory to those of Paulsen and St. John
(2002), who found negative effects of loans on within-year
persistence in the range of -.01 to -.03 for low income and lower
middle income students and insignificant effects for upper middle
and upper income students. DesJardins et al (2002) also find a
negative effect of loans on persistence. A test of interaction
effects in this study indicated no significant differences in the
effect of loans by income quartile. This may be due to small
sample size in the upper quartiles when this comparison is made.
In the population examined in this study, loans were taken by
relatively large proportions of students in the 1st and
2nd quartiles and small proportions of students in the
upper quartiles.
The final estimated effect of loans on persistence of a delta p
of .05 may be overestimated due to the selection bias created when
more confident and capable students decide to incur debt. In
addition, the potentially differential effects of the
“intangible” components (St. John et al., 2000) of
loan-taking by ethnic group have not been examined in this study.
There is some evidence to suggest that students of color are more
risk averse than white students (Baker & Velez, 1996;
Linsenmeier, Rosen, & Rouse, 2001).
One possible interpretation of the positive effect of loans on
persistence is that it is due to a greater likelihood of
loan-taking among students attending more expensive (and often
more prestigious) institutions. However, the receipt of loans in
this study is not correlated with the level of tuition and fees
(r=.025). In addition, a supplementary cross-tabulation of the
proportion of students taking loans by income quartile and tuition
quartile shows the proportion of students taking loans to be
similar across tuition quartiles, with no statistically
significant differences for any income group. The positive effect
of loans is consistent with theoretical expectations, as they
lower the costs of college attendance. The present value of
subsidized loans is considerable, approximately equal to one-third
the value of grants, because the federal government pays the cost
of credit while a student is enrolled (Dynarksi, 2002).
In addition, loans may enable students to work fewer hours and
become more integrated into college activities, a conclusion
previously reached by King (2001) in a study of BPS data covering
the years 1996-98. Work hours are shown to have a relatively small
negative effect on persistence in this study. The effect may be
underestimated due to the inclusion of on-campus work hours, which
have been shown to be positive, with off-campus hours in one
combined variable (Nora et al., 1996) .
Recent developments in student integration theory emphasize the
indirect positive effects of aid on persistence (Cabrera, Nora,
& Castaneda, 1993; Nora et al., 1996). This interpretation is
supported by the sequential regression analysis. Loans are not
significant in step 4 when the social variables are entered, but
are significant in prior steps and regain significance once the
control for GPA is added in step 5. This suggests that loans
enable social integration, which has a positive effect by enabling
better academic performance. The social index variable is
significant in step 4, but not in step 5 once GPA and the academic
integration index are added. When variation due to academic
performance is controlled, the independent positive effect of
loans due to the reduction in costs is once again observed.
Male students, who can earn higher wages than female students
without a bachelor’s degree and therefore have more
lucrative opportunities when they stop out of college, have lower
predicted probabilities of timely degree attainment. Those who
delay enrollment are also less likely to attain their degree
within five academic years, an outcome consistent with their prior
progress at a slower rate than their high school graduation
cohort. However, only 5% of the first-time full-time financially
dependent students in this study delayed enrollment, so this
factor affects relatively few.
Implications
Prior empirical work estimating the effects of financial aid on
college student persistence have led to contradictory results.
This study contributes to this literature by estimating the
effects of different types of aid on the persistence of
financially dependent full-time students in the public four-year
sector using national data. The findings show that subsidized
loans have a positive effect on persistence. Grants have a
negligible non-significant effect. A review of developments in the
econometric modeling of the effects of aid on persistence
(Bettinger, 2002; DesJardins, Ahlburg et al., 2002; Dynarski,
2002a; Singell, 2002a) suggest that the single-stage regression
model employed here is likely to underestimate the effects of
grants and overestimate the effects of loans, because, as
discussed above, it does not fully control for self-selection
bias. The effect of loans is estimated here at an increased
probability of persistence of .05 with a $1000 increase in loan
value. This estimate falls between Singell’s (2002)
estimates of .06 in a single-stage model and .04 in a two-stage
model correcting for self-selection bias, which suggests the
magnitude of the overestimation is not substantial.
From a policy perspective, it is important to accurately
estimate the magnitude of the relative effects of subsidized loans
and grants. Loans have come to play an increasingly prominent role
in the financial aid system, and in many states public higher
education is not accessible to low-income students unless they
incur substantial debt (Kipp III, Price, & Wohlford, 2002). As
loans replace grants in aid packages, firmer estimates of their
relative effects are needed. The application of new modeling
techniques in this area is promising, particularly as they may be
able identify differential effects of various types of aid on
students of different economic classes, cultural backgrounds, and
academic abilities and over different points in time of their
academic careers.
This study examined the persistence and degree attainment of
students who were financially dependent on their parents. As
evidenced by the mean age of eighteen, this was a traditional
college-going population of young adults who were not raising
families of their own or juggling careers while they pursued their
degrees. Nevertheless, in the first year they worked an average of
20 hours per week, and only 55% earned their bachelor’s
degree within five years. Consistent with student integration
theory, living on campus in the first year was a substantive and
significant positive predictor of degree completion. This finding
indicates that policy makers who wish to promote timely
bachelor’s degree completion should favor policies that
enable public college students to live on campus. Campus living
fosters immersion in the academic environment, the development of
peer groups and social networks, and easier access to faculty and
administrative advisors. In turn, students with these advantages
develop a firmer goal commitment and confidence in their ability
to complete their degrees.
In this population, family income is a determinant of timely
bachelor’s degree completion. Financial aid packages as they
are distributed in the first year did not offset the advantages of
family income. Therefore, the distribution of aid had to improve
in subsequent years of the data collection in favor of low-income
students in order for the aid system to fully achieve its equity
goals of providing the benefits of higher education to all
qualified students regardless of their financial status. Two
financial aid trends indicate that the distribution of aid more
likely shifted in favor of high-income students from 1989 to 1994.
These are the increased popularity of state merit aid, which is
distributed disproportionately to wealthier students who benefit
from better schooling, and the revisions to the financial aid
formula that allowed for the exclusion of home equity and opened
the subsidized loan program to more affluent families.
If the amount of time public college students spend working to
pay tuition and fees can be reduced by more favorable aid
packages, it follows from both human capital and student
integration theory that their graduation rates will increase.
Similarly, if students who are tempted to live in the parental
home in order to economize are offered enough aid to cover
dormitory costs, they will more likely be able to immerse
themselves in student life and proceed steadily towards
completion. For those campuses without dormitories, the
construction of campus housing may in fact be a good investment to
improve student retention and outcomes. As significant public
dollars are spent on public colleges through operating subsidies,
it is important to align financial aid programs to support those
investments. While existing aid levels appear adequate to promote
year-to-year persistence, they do not promote timely degree
completion for low-income students. If timely degree completion is
truly a priority of state policymakers, they should look for ways
to enable students to spend more time in academic environments
pursuing their studies.
Acknowledgment
I would like to acknowledge Ronald Ehrenberg and Laura Perna
for helpful comments on a previous draft of this article.
Notes
See Kane (1999)
and McPherson & Shapiro (1998) for timely reviews of public
higher education finance goals, and the Carnegie Commission
(Who Pays?, 1973) for a historic treatment.
Hauptman (2001)
emphasizes “States spend roughly twice as much as the
federal government to support higher education” (p. 65) and
state student aid averages only about 5% of total state funding
for higher education (p. 73).
Economists have
also studied the effects of financial aid on student choices and
outcomes, such as enrollment, institutional choice, academic
performance, and major field of study. See Ehrenberg (forthcoming)
for a comprehensive review.
Adelman (1999)
analyzed several other national longitudinal data bases to
construct a detailed portrait of enrollment patterns and
bachelor’s degree attainment. His analysis, which utilized
rich high school curriculum data to emphasize the primary
relationship between academic experiences and college outcomes,
relied on more limited measures of student finances and is less
informative on this topic.
With the
development of accountability policies, institutional researchers
have also analyzed individual campus and state system data to
estimate the effect of financial and other factors on timely
degree completion. Knight (2002) provides a review of these.
See Heckman
(1979) and Willis (1979) regarding the concept of self-selection
bias.
Dynarski (2001)
reaches the same conclusion after reviewing studies showing that
different forms of financial aid have different effects on
enrollment depending on students’ income group.
See also
Singell (2002b) for additional methodological and empirical work
by this author on this topic.
There are two
exceptions. First, the logistic regressions do not adjust for
stratification because preliminary analyses showed the strata had
little effect on the estimates. This decision enabled use of a
wider range of software features. Second, model-based Pearson
correlation coefficients were obtained because the statistical
software used (Stata, version 7) does not offer a design-based
correlation function.
Some argue
that it is better not to use sampling weights in regression
analyses, particularly when the weights are a function of the
dependent variable. See Winship and Radbill (1994) for a thorough
discussion of this issue.
Skinner,
Holt, and Smith (1989, Table 2.1, p. 29) show that a design effect
of 1.5 or 2.0 will change a nominal confidence interval from 95%
to an actual interval of 89% or 83%, respectively. Failure to
adjust for design effects of this size will considerably inflate
findings of statistical significance.
A
design-based F statistic (calculated from the Pearson chi-squared
statistic) is reported as the test of association for categorical
variables (Stata, 2001, svytab, p. 86), while a design-adjusted
t-test is reported to compare means of the continuous variables
(Stata, 2001, svymean, p. 69-70).
See Peng, So,
Stage, and St. John (2002) for a rationale for presenting the
change in probability at other values besides the mean.
Both Long
(1997) and Peng, So, Stage, and St. John (2002) advise against
reporting marginal effects for binary response models, given the
inherent non-linearity between the predictors and the
probabilities. Peng et al. (p. 270) caution “the concept of
marginal probability is not useful for explaining logistic
regression models,” whether the marginal effects are
calculated at the mean or by computing the average over all the
observations. The marginal effect is a good summary measure only
when the “independent variable varies over a region of the
probability curve that is nearly linear” (Long, p. 75).
This approach
is consistent with the NCES Statistical Standards (Seastrom,
2002).
A comparison
of the results obtained for the McFadden’s adjusted R
squared to results of a model estimated without weighting and
clustering showed that the difference between these values does
not exceed .01 for these models.
These items
measuring social integration were included in the initial 1989
survey and precede more recent scholarship (see, for example,
Nora, 2001-2002; Rendon, Jalomo, & Nora, 2000) that has
enriched the conceptualization of social integration.
The variables
measuring mother’s education and race/ethnicity were
predictors to impute 35 cases (3.14%) of parental income. The
variables parental income, mother’s education, and living on
campus were predictors to impute 52 cases (4.66%) of tuition.
The higher
cost of flagship institutions is reflected in the mean
out-of-jurisdiction tuition charge, which was 2.5 times the mean
in-state tuition. Prestigious institutions are more likely to
attract academically talented students who conduct a national
college search and travel out of their home state.
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