INCREASING TIME TO - Specialized Research AI at MIT

INCREASING TIME TO

BACCALAUREATE DEGREE

IN THE UNITED STATES

Abstract
Time to completion of the baccalaureate degree has in-
creased markedly in the United States over the past three
decades. Using data from the National Longitudinal Sur-
vey of the High School Class of 1972 and the National Ed-
ucational Longitudinal Study of 1988, we show that the
increase in time to degree is localized among those who
begin their postsecondary education at public colleges
outside the most selective universities. We consider sev-
eral potential explanations for these trends. First, we
show that changes in the college preparedness and the
demographic composition of degree recipients cannot
account for the observed increases. Instead, our results
identify declines in collegiate resources in the less selec-
tive public sector and increases in student employment
as potential explanations for the observed increases in
time to degree.

John Bound

Department of Economics

University of Michigan

and National Bureau

of Economic Research
Ann Arbor, MI 48109-1220

jbound@umich.edu

Michael F. Lovenheim

(corresponding author)

Department of Policy Analysis

and Management

Cornell University

and National Bureau

of Economic Research

Ithaca, NY 14853

mﬂ55@cornell.edu

Sarah Turner

Department of Economics

University of Virginia

and National Bureau

of Economic Research

Charlottesville, VA 22904

sturner@virginia.edu

c(cid:2) 2012 Association for Education Finance and Policy

375

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

INCREASING TIME TO BACCALAUREATE DEGREE

INTRODUCTION

1.
Over the past three decades, the share of baccalaureate (BA) degree recipients
that graduate within four years has decreased and, more generally, the length
of time it takes college graduates to attain degrees has increased. This shift,
which involves substantial costs for graduates in terms of forgone earnings and
additional tuition expenditures, has drawn increased public policy attention.1
Although researchers have done some work to understand the determinants
of time to degree in the cross section, there has been little documentation or
examination of the determinants of the observed extension in time to degree.
In this article we examine how time to completion of the BA has changed
in the past three decades by comparing outcomes for two cohorts from the
high school classes of 1972 and 1992 using data from the National Longitudi-
nal Study of 1972 (NLS72) and the National Educational Longitudinal Study
of 1988 (NELS:88). We ﬁnd evidence of large shifts in the time to degree
distribution: in the 1972 cohort, 53 percent of eventual BA degree recipients
graduated within four years of ﬁnishing high school, but for the 1992 high
school cohort only 39 percent did so. This extension of time to degree, and the
associated reduction in “on-time” degree completion, did not occur evenly over
the different sectors of higher education. Increased time to degree is largest
among graduates beginning college at less selective public universities as well
as at community colleges.

The extension of time to degree cannot be explained by the lengthening of
the time between high school and college or by longer times to high school
graduation. We also document little change in “stopping out” among even-
tual graduates across cohorts, where students take time off from enrollment
and later return. Our data point to a reduction in the pace at which relatively
continuously enrolled students complete college credits. There also is no evi-
dence that increased time to degree reﬂects more human capital accumulation
among students; rather, students are accumulating the same number of col-
lege credits more slowly.

We seek to assess the underlying reasons behind the increases in time to
degree that we document over the past thirty years. Previous work has demon-
strated that time to degree is negatively related to student academic ability as
well as to student background characteristics, such as income and parental ed-
ucation (e.g., Flores-Lagunes and Light 2010; DesJardins, Ahlberg, and McCall
2002; Ishitani 2006; Adelman 2006; Bowen, Chingos, and McPherson 2009;
Garibaldi et al. 2012). As the returns to a college degree have increased over

To underscore this point, twelve states recently conducted studies of elongating time to degree in
the public postsecondary system, and California and Colorado passed legislation to attempt to curb
time to degree increases.

376

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

the past four decades (Autor, Katz, and Kearney 2008), more students with
relatively low levels of precollegiate preparedness are attending college. These
students are likely to require a longer period of enrollment to ﬁnish a degree.
Another important trend in higher education over the time period of our
analysis is an overall reduction in resources combined with increased strat-
iﬁcation of resources: the wealthier schools have become richer while the
less resource-intensive schools have become poorer (Hoxby 2009; Bound,
Lovenheim, and Turner 2010a; Ehrenberg and Webber 2010). To the extent
that institutional resources affect students’ ability to make it through degree
programs in a timely manner, the pace of degree progression may decline
among students at those institutions where available resources per student
have declined.

Rising college costs also may play a role in explaining the time to degree
trends we document. In particular, as students face increased challenges to
ﬁnancing full-time enrollment, they may increase labor supply while in college.
To the extent that employment crowds out credit attainment, increases in
student work hours may contribute to lengthening time to degree.

We take several empirical approaches to identifying the role of each of
these types of factors in explaining the elongation of time to degree. First,
using the detailed demographic data that we have linked to institutional-level
information for each student, we follow a semi-parametric reweighting strategy
based on DiNardo, Fortin, and Lemieux (1996) to determine the extent to
which changes in time to degree can be attributed to changes in observed
student background characteristics, changes in student academic preparation
for college, changes in institutional resources, and an unexplained residual
component.

Strikingly, despite the strong cross-sectional relationship between high
school academic ability and time to degree (Flores-Lagunes and Light 2010;
DesJardins, Ahlberg, and McCall 2002; Adelman 2006; Bowen, Chingos,
and McPherson 2009), we ﬁnd no evidence that changes in the academic
preparation of eventual college graduates or in the demographic characteris-
tics of these graduates can explain any of the time to degree increases. This
is because the less academically prepared students who were drawn into the
postsecondary sector over this interval graduate at very low rates (Bound,
Lovenheim, and Turner 2010a). Indeed, the observable characteristics of
college graduates, including high school test scores and high school grade
point average (GPA), have become more favorable across cohorts.

In contrast, we ﬁnd evidence that decreases in institutional resources at
public colleges and universities are important for explaining changes in time to
degree. With a signiﬁcant link between institutional resources (e.g., student-
faculty ratios) and time to degree, the declines in resources per student at

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

377

INCREASING TIME TO BACCALAUREATE DEGREE

public sector colleges and universities predict some of the observed extension
of time to degree.

Throughout this analysis, we proxy for institutional resources using
student-faculty ratios. However, no one measure of resources is a perfect proxy
(Black and Smith 2006). Thus we supplement the decomposition analysis with
a state-level analysis that uses changes in the population of eighteen-year-olds
in the state as a proxy for institutional resources (Bound and Turner 2007).
The results from this analysis support the ﬁnding from our decompositions
that changes to institutional resources are an important part of why time to
degree has increased.

Finally, we present suggestive evidence that students’ growing difﬁculties
in ﬁnancing a college education contribute to increased time to degree. We
show that the size of the increase in student labor supply is large enough to
explain a large portion of the increases in time to degree we document under
plausible assumptions about how work time crowds out school time. We also
show that time to degree among students from lower-income families has in-
creased the most, which suggests a relationship between increased difﬁculties
students have in ﬁnancing college and lengthening time to degree.

This article’s contribution is to combine a careful description of the change
in time to BA degree completion with consideration of the factors contributing
to this change. In other work (Bound, Lovenheim, and Turner 2010a) we have
considered the role of student background characteristics and supply-side
determinants in higher education in explaining the change over time in whether
students complete college; in this article we analyze the changes in the length
of time taken by degree recipients in their studies. The length of time it takes
students to complete degrees reﬂects the magnitude of individual investments
in college education, given the greater opportunity cost of extended enrollment,
and serves as an important indicator of how students move from enrollment
to degree attainment.

The rest of this article is organized as follows: section 2 describes the
increase in time to degree found in the data. Section 3 outlines the potential
explanations for these trends that inform our empirical analysis. Section 4
describes our data, and section 5 presents our empirical approach and the
results from our empirical analyses. Section 6 concludes.

INCREASED TIME TO DEGREE

2.
Evidence of increased time to college degree conditional on graduating can
be found in a range of data sources. The Current Population Survey (CPS)
provides a broad overview of trends in the rate of collegiate attainment by
age (or birth cohort). While the share of the population with some collegiate

378

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

Figure 1. College Completion Rates by Age, 1940–80 Birth Cohorts. Source: Data are from authors’
tabulations using the October CPS, 1968–2005. Individual weights are used. See Turner 2004 for
additional details.

participation increased substantially between the 1950 and the 1975 birth co-
horts, the share obtaining the equivalent of a college degree by age twenty-three
increased only slightly over this interval, as shown in ﬁgure 1. Extending the
period of observation through age twenty-eight, however, shows a more sub-
stantial rise in the proportion of college graduates among recent birth cohorts.2
Taken together, the inference is that time to degree has increased.

Time to Degree in NLS72 and NELS:88

To measure changes in time to degree in connection with microdata on individ-
ual and collegiate characteristics, this analysis uses the National Longitudinal
Study of the High School Class of 1972 (NLS72) and the National Educational
Longitudinal Study (NELS:88). These surveys draw from nationally represen-
tative cohorts of high school and middle school students, respectively, and

2. Data from cross sections of recent college graduates assembled by the Department of Education
from the Recent College Graduates and Baccalaureate and Beyond surveys corroborate this ﬁnding.
For example, from 1970 to 1993 the share of graduates taking more than six years rose from
less than 25 percent to about 30 percent, while the share ﬁnishing in four years or less fell from
about 45 percent of degree recipients in 1977 to only 31 percent in the 1990s (see Horn, Knepper,
and McCormick 1996 and Bradburn et al. 2003). Adelman (2004) uses data from the NLS72
and NELS:88 to trace time to degree and shows an increase from 4.34 years to 4.56 years. The
differences between Adelman’s estimates and ours are likely due to the fact that we examine only
students attending college within two years of high school and he focuses only on students who
have complete college transcripts.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

379

INCREASING TIME TO BACCALAUREATE DEGREE

track the progress of students through collegiate and employment experi-
ences. These microlevel surveys afford two principal advantages over the CPS.
First, the data include measures of precollegiate achievement that allow us to
analyze the relationship between time to degree attainment and precollegiate
academic characteristics. Second, these data identify the colleges attended,
permitting us to analyze outcomes by collegiate characteristics.

To align these longitudinal surveys, we focus on outcomes within eight
years of high school graduation among those who entered college within two
years of their cohort’s high school graduation. We measure time to degree in
each survey as the number of months between cohort high school graduation
and BA receipt.3 Cohort high school graduation is June 1972 for NLS72 re-
spondents and June 1992 for NELS:88 respondents. With the NELS:88 cohort
followed for only eight years after high school graduation, our approach affords
eight years of post–high school observation for both cohorts.

Our sample includes those who do not graduate high school on time. Be-
cause the NLS72 survey follows a twelfth-grade cohort and the NELS:88 survey
follows an eighth-grade cohort, there are more late high school completers
in the latter sample. However, when one conditions on college completion
within eight years, over 99 percent of respondents ﬁnish high school on time
in both samples. The focus of this analysis is on explaining the increase in
time to degree among “traditional” college students beginning college soon
after high school graduation; our data do not permit analysis of time to de-
gree among nontraditional students entering the collegiate pipeline in their
twenties.

In table 1, we show the cumulative share of BA recipients who attained their
degree in years 4–8 beyond their cohort’s high school graduation. The table
demonstrates that there has been a sizable outward shift in time to degree
among BA recipients across the two cohorts. Not only did the proportion
ﬁnishing within four years decline by a statistically signiﬁcant 13.7 percentage
points, or 25.8 percent relative to the NLS72 baseline, but the entire distribution
shifted outward. In addition, mean time to degree increased from 4.48 to 4.81
years (a 7.1 percent increase).

Because the last NELS:88 follow-up was conducted in 2000, we are forced to truncate the time
to degree distributions at eight years, reﬂecting the time between cohort high school graduation
and the last follow-up. Empirically, however, the proportion of eventual college degree recipients
receiving their degrees within eight years has not changed appreciably. The 2003 National Survey
of College Graduates allows us to examine year of degree by high school cohort. For the cohorts
from the high school classes of 1960 to 1979 for which there are more than twenty years to degree
receipt, we ﬁnd that the share of eventual degree recipients ﬁnishing within eight years holds nearly
constant at between 0.83 and 0.85. Focusing on more recent cohorts (and hence observations with
more truncation), we ﬁnd that in the 1972 high school graduating cohort, 92.3 percent of those
ﬁnishing within twelve years had ﬁnished in eight years, with a ﬁgure of 92.4 percent for the 1988
cohort.

380

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

Table 1. Eight-Year Cumulative Time to Degree (TTD) Distributions for the Full Sample and by First
Institution

TTD Distribution

Mean HS
Lag
TTD

Attendance
Lag

Any

Number of
Stop-out Stop-outs

Full sample:

NLS72
NELS:88

53.1
39.4

Difference −13.7
(1.9)

81.8
72.7

−9.1
(1.3)

Non–top 50 public:

NLS72
NELS:88

49.7
29.1

82.3
68.8

Difference −20.6 −13.6
(2.1)

(2.7)

Top 50 public:

NLS72
NELS:88

52.7
39.7

Difference −13.0
(3.8)

81.5
82.0

0.5
(2.5)

Less selective private:

90.6
88.3

−2.3
(0.9)

91.1
87.8

−3.3
(1.4)

89.2
93.7

4.5
(1.8)

96.3
94.7

4.48 −0.01
4.81 −0.03

0.30
0.25

−1.7
(0.7)

0.32 −0.01
(0.04)

(0.004)

−0.04
(0.01)

96.3
95.1

4.49 −0.02
4.93 −0.03

0.29
0.23

−1.2
(1.0)

0.44 −0.01
(0.01)
(0.05)

−0.06
(0.01)

96.4
96.6

4.49 −0.01
4.66 −0.03

0.28
0.22

0.2
(1.3)

0.16 −0.02
(0.01)
(0.07)

−0.05
(0.02)

NLS72
NELS:88

Difference

66.7
58.0

−8.7
(3.1)

87.3
84.6

−2.7
(2.2)

94.0
93.4

−0.6
(1.7)

98.7
98.6

4.28 −0.01
4.60 −0.02

0.29
0.24

−0.01 0.15 −0.02
(0.01)
(0.06)
(0.6)

−0.04
(0.01)

Highly selective private:

NLS72
NELS:88

Difference

65.2
73.1

7.9
(6.1)

88.2
91.9

3.7
(3.3)

93.8
98.1

4.3
(1.8)

96.8
99.8

0.00
4.31
4.20 −0.01

0.29
0.26

2.9 −0.12 −0.01
(0.01)
(1.2)

(0.08)

−0.03
(0.01)

Community colleges:

36.5
15.5

83.0
NLS72
70.8
NELS:88
Difference −21.0 −23.6 −12.2
(3.5)
(4.4)

67.8
44.2

(4.2)

92.6
83.6
−9.0
(2.8)

4.90 −0.00
5.58 −0.02
0.68 −0.02
(0.01)
(0.11)

0.37
0.35
−0.02
(0.04)

0.06
0.04

−0.02
(0.01)

0.07
0.03

−0.04
(0.12)

0.05
0.05

0.01
(0.02)

0.04
0.04

0.00
(0.02)

0.05
0.01

−0.04)
(0.01)

0.06
0.05
−0.01
(0.02)

1.48
1.56

0.08
(0.23)

1.33
1.18

−0.15
(0.12)

1.56
2.00

0.44
(0.72)

1.50
1.21

−0.29
(0.20)

2.04
1.93

−0.11
(0.61)

1.68
1.80
0.12
(0.29)

Notes: NLS72 calculations were made using the ﬁfth follow-up weights included in the survey. Fourth
follow-up weights were used for the NELS:88 survey calculations. Only those participating in these
follow-ups are included in the tabulations. The variable “HS Lag” refers to the number of months
between high school graduation and cohort high school graduation. “Attendance Lag” is the number
of months between cohort high school graduation and ﬁrst college enrollment. “Any Stop-out” is an
indicator equal to 1 if a student has a semester of non-enrollment between ﬁrst enrollment and
graduation, and “Number of Stop-outs” is the number of stop-out spells, conditional on having any
spell. The NLS72 and NELS:88 samples are restricted to those who attend college within two years
of cohort high school graduation and who ﬁnish within eight years of cohort high school graduation.
Cohort high school graduation is deﬁned as June 1972 for the NLS72 sample and June 1992 for the
NELS:88 sample. The difference between NELS:88 and NLS72 is in each third row. The standard
error of this difference is in parentheses and is clustered at the high school level, which is the
primary sampling unit.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

381

INCREASING TIME TO BACCALAUREATE DEGREE

Higher education in the United States is characterized by substantial het-
erogeneity across institution types. Moreover, students beginning a commu-
nity college must transfer in order to obtain a BA, and, to the extent that
transfer-related factors and between-school non-enrollment spells slow down
the pace of collegiate attainment, it is important to distinguish students by the
type of ﬁrst institution. To capture differences among institutions, we cate-
gorized the ﬁrst colleges and universities attended by BA recipients into ﬁve
broad sectors:4 non–top ﬁfty ranked public universities, top ﬁfty ranked public
universities, less selective private schools, highly selective private schools, and
community colleges. Table 1 presents cumulative time to degree distributions
by these sectors and shows that the elongation of time to degree is far from uni-
form across types of undergraduate institutions. Extensions are pronounced
in the non–top ﬁfty public sector, in which the likelihood of a BA recipient
graduating within four years dropped from 49.7 percent to 29.1 percent, a
statistically signiﬁcant decline of 20.6 percentage points (or 41.4 percent); as
with the full sample, the proportion graduating within each subsequent time
frame also declined signiﬁcantly. Mean time to degree consequently increased
in the non–top ﬁfty public sector from 4.49 to 4.93 years.

The time to degree increases were even more dramatic for BA recipients
whose ﬁrst institution was a community college, where there was a 21 per-
centage point decline in the likelihood of completing within four years, a 23.6
percentage point decline in completion within ﬁve years, and a 0.7 year in-
crease in mean time to degree. In the NELS:88 cohort, less than 16 percent of
BA recipients who started at a community college earned their degree within
four years.

In the top-ﬁfty public sector, while the share of degree recipients ﬁnishing
within four years declined, the share ﬁnishing within ﬁve years did not. Mean
time to degree increased only by a small amount as well. We also ﬁnd little
evidence of time to degree increases in the private sector. While the likelihood
of graduating within four years dropped by 8.7 percentage points in the less
selective private sector, this is only a 13 percent decline. Mean time to degree
also increased by 0.15 years, or 3.5 percent. In the elite private sector, time
to degree declined, although the standard errors are relatively large due to
small sample sizes. Table 1 illustrates one of the central descriptive ﬁndings
of this analysis: time to degree increased most dramatically across surveys

4. We use the 2005 U.S. News and World Report undergraduate college rankings to classify institutions
into these ﬁve categories. The highly selective four-year private schools are the top sixty-ﬁve ranked
private universities and the top ﬁfty private liberal arts schools. Less selective four-year private
schools are all other private universities. Highly selective private schools and top ﬁfty public schools
are listed in appendix table A.2. While admittedly crude, this breakdown correlates well with several
measures of quality, such as average SAT scores and high school GPAs. Other metrics, such as
resources per student or selectivity in undergraduate admissions, give similar results.

382

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

among graduates beginning their studies at less selective public schools and
at community colleges.

Credit Attainment and Time Spent in College

Given observed increases in time to degree, it is natural to ask whether
these changes reﬂect increased difﬁculty in passing through the course se-
quences, increased course taking, or less time spent in college. In the remain-
ing columns of table 1, we examine whether elongating time to high school
graduation (Deming and Dynarski 2008), the lag between high school grad-
uation and college entry, and enrollment breaks in college (i.e., stopping out)
can contribute to the lengthening time between high school cohort graduation
and BA receipt. The HS Lag column shows time (in months) between actual
graduation and cohort high school graduation. These differences are all very
small and show no evidence of a change over time. The Attendance Lag col-
umn demonstrates that students are not taking longer between high school
and college either.

The ﬁnal two columns of the table show the incidence of non-enrollment
spells among eventual degree recipients. We deﬁne a stop-out spell as a
semester of non-enrollment between ﬁrst enrollment and graduation, which
we measure using the transcript data. Stopping out is not prevalent, which is
due mostly to the fact that the likelihood of graduating conditional on stop-
ping out is low (DesJardins, Ahlberg, and McCall 2002, 2006). Furthermore,
if anything, non-enrollment spells have declined over time among eventual
graduates. Conditional on stopping out, the number of stop-out spells also has
not increased, which is shown in the ﬁnal column of table 1.

Table 1 indicates that time to degree has lengthened due to longer periods
of time spent enrolled relatively continuously in college. However, it could be
that more time spent enrolled has led to more human capital accumulation.
At the extreme, if increased time to degree primarily captures increased at-
tainment in the form of course credits, policy concern over the effects of time
to degree might be misplaced. Using transcript data, we chart time paths of
credit accumulation, which are shown in ﬁgure 2. For students at non–top ﬁfty
four-year public institutions and community colleges, we ﬁnd a slower pace of
credit accumulation in the 1992 cohort relative to the 1972 cohort; although
students in both cohorts accumulated a similar number of credits after eight
years, students in the 1992 cohort took longer to do so. For example, students
starting at non–top ﬁfty public schools in the later cohort accumulated, on
average, about 9.7 fewer credits within four years of high school graduation
than did their counterparts in the 1972 cohort. After four years, the credit gaps
track the time to degree gaps from table 1 closely within each school type.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

383

INCREASING TIME TO BACCALAUREATE DEGREE

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

Figure 2. Credit Accumulation by Type of Initial Institution for Eight-Year BA Recipients

We also have explored cross-cohort differences in the ratio of attempted
credits to accumulated credits. We found only a small increase in this ratio
over the period of study. Furthermore, we considered double majoring, but its
prevalence is too low in the sectors that experienced increased time to degree
to explain a signiﬁcant portion of the phenomenon. Finally, we examined
whether graduates took more difﬁcult courses in areas such as mathematics
and science and reduced the number of courses they took per term to better
their chances of success in such classes. Using the course-level transcript ﬁles,
we ﬁnd no large changes in course-taking behavior or majors across ﬁelds that
could explain the time to degree increases we document.

With no supporting evidence of greater credit accumulation to suggest
a link between time to degree and human capital accumulation, we interpret

384

John Bound, Michael F. Lovenheim, and Sarah Turner

observed increases in time to degree as a reduction in the rate of human capital
accumulation rather than an increase in the amount of human capital, with this
change concentrated outside the top public schools and private institutions.5
We now turn to explanations of why time to degree has shifted in the manner
observed in the data.

3. POTENTIAL EXPLANATIONS FOR INCREASED TIME TO DEGREE
There are multiple theoretically plausible explanations for the observed
changes in time to degree, and we consider these explanations as a frame-
work for guiding our empirical approach and interpreting our results. Note
that, ceteris paribus, an increase in the returns to education, which raises the
opportunity cost of time spent in school, will reduce time to degree. One expla-
nation for the rise in time to degree is a change in the composition of college
graduates to include more students who are less academically prepared for col-
lege and who likely require a longer time to obtain a BA. Such a compositional
change would shift outward average time to degree. Second, decreases in col-
legiate resources per student may extend time to degree through, for example,
reductions in course offerings needed for degree progress. Third, increases
in the direct cost of education may lead students to increase employment and
reduce the rate of credit accumulation. We discuss the theoretical grounding
for each of these explanations in turn.6

Demand-side explanations for increased time to degree are driven by the
changing characteristics of the student body: increasing returns to education
since the 1980s have resulted in higher enrollment among less prepared stu-
dents (Bound, Lovenheim, and Turner 2010a). If this change in the composi-
tion of enrolled students has led to a change in the composition of students who
complete college, aggregate time to degree may increase because more stu-
dents are completing with weaker academic backgrounds. Several articles have
established a strong cross-sectional relationship between academic ability and
time to degree, which leads to the question of whether academic preparation

It is unclear from the data whether the reduced pace of credit accumulation is due to part-time
enrollment. If one deﬁnes part-time enrollment as taking less than a full course load, then our data
indicate a sizable rise in part-time enrollment among eventual BA recipients. Because the data do
not indicate students’ actual part-time/full-time status, we are unable to examine this issue in more
detail.

6. Another potential explanation for increasing time to degree is the rise in student transferring behav-
ior and the associated challenges of articulation, which may lead to inefﬁcient degree progression
(McCormick 2003; Adelman 2006; Goldrick-Rab 2006; Goldrick-Rab and Pfeffer 2009). While
we view the role of transferring as interesting and important, we lack a credible way to isolate the
causal relationship between transferring and time to degree. We also note that transferring itself
may be a response to family or institutional resource constraints, which our empirical estimates
would capture.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

385

INCREASING TIME TO BACCALAUREATE DEGREE

(or other student characteristics) among graduates has changed in such a way
that could cause an increase in time to degree. Note as well that increasing
returns to college will increase time to degree in the aggregate only if the
number of marginal students induced to complete college is large relative to
the effect of rising returns on infra-marginal students.

A second type of explanation for increases in time to degree is changes
on the supply side of the market that reduce per student college resources. If
reductions in resources produce queuing and course enrollment constraints,
time to degree may increase. Resource reductions occur when increases in stu-
dent demand are not accompanied by proportional increases in public funding;
such dilution in resources is particularly likely in the public sector, where state
subsidies are a signiﬁcant component of revenues. Bound and Turner (2007)
examine supply-side adjustments to variation in student demand generated
by changes in cohort size and ﬁnd evidence that neither state appropriations
nor public subsidies fully offset changes in student demand. Moreover, public
colleges and universities adjust to demand increases in somewhat different
ways across the strata of higher education. Top-tier public and private schools
use selectivity in admissions to regulate enrollment, and time to degree likely
is unchanged or even decreases with increased demand. In contrast, enroll-
ment is relatively elastic among less selective public four-year universities and
for community colleges, leading to reductions in resources per student when
increased enrollment is not met with increases in appropriations from public
sources and other non-tuition revenues. Queuing and shortages of courses
may result if students in relatively large cohorts cannot be accommodated
fully, and it is straightforward to see how such institutional barriers lead to
delays in degree progress.

Increases in collegiate demand therefore can affect the supply side of higher
education and the rate of collegiate attainment by reducing resources per
student in the public sector, particularly at open-access four-year institutions
and community colleges. Because these institutions are unable to adjust fully to
demand shocks, the sectors absorbing the bulk of the students will experience a
reduction in resources. The result is increased stratiﬁcation of resources across
the sectors of higher education in the United States, which could produce the
patterns of time to degree shifts we observe in the NLS72 and NELS:88 data.
Finally, as students face increased difﬁculties in paying for college in
the face of limited access to student loans and parental resources, they may
work more, which may directly affect the pace of degree attainment. As col-
lege costs have increased over the past several decades, and with relatively
modest availability of federal aid and limited institutional ﬁnancial aid funds
outside the most afﬂuent colleges and universities, students from low- and
moderate-income families may face considerable borrowing constraints (see,

386

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

e.g., Ellwood and Kane 2000; Belley and Lochner 2007; Lovenheim 2011).7 In
the context of the Becker-Tomes (1979) model of intergenerational transfers,
rising tuition charges and falling family income lead to the expectation that
students will shoulder a higher fraction of college costs. Students will respond
to the increased burden of college ﬁnancing with some combination of reduc-
ing consumption, borrowing more, and working more hours.8 To the extent
that students are induced to work more hours while in college to ﬁnance atten-
dance, academic pursuits may be crowded out by work time, thereby increasing
time to degree.9

Intertemporal choices about course taking and employment also may be
affected by the structure of tuition, with charges by the term rather than by
the course generally increasing the cost of extension of time to degree. When
we split our sample according to the pricing structure of tuition rather than
the quality rank of the institution, we ﬁnd that only modest increases have
occurred at institutions that charge by the term, with the bulk of the increases
occurring at schools that charge by the unit. While the pricing structure has not
changed notably over the past forty years, it is not implausible that the effect
of extended hours of employment on time to degree is somewhat greater at
those institutions, including many less selective publics, where tuition charges
occur by the credit rather than by the semester. However, because tuition
structures are highly correlated with institutional characteristics, it is difﬁcult
to distinguish this explanation in the data.

4. DATA
Student Attributes from the NLS72 and NELS:88 Surveys

The NLS72 and NELS:88 data sets we use contain a rich set of student back-
ground characteristics. The student attributes we analyze are high school math
and reading test percentiles,10 quartile of the student’s high school GPA,

In addition, Brown, Scholz, and Seshadri (2012) show that many students are credit constrained
because their parents do not provide the expected family contribution assumed in ﬁnancial aid
calculations. As tuition rises, such students are likely to be the most affected by ﬁnancial constraints.
See Bound, Lovenheim, and Turner (2010b) for a further discussion of this issue and of the pricing
information.

9. Keane and Wolpin (2001) show that in a forward-looking dynamic model with limited access to
credit, increases in employment while enrolled in school are the expected response to tuition
increases. An alternative reason for students working while in school is that there is a potential
post-graduation return to this employment experience (Light 2001). For example, working for a
professor may teach valuable skills or generate a strong and credible reference letter. However, the
majority of jobs held by college students are in the trade and service sectors of the economy, such
as working as a waiter or waitress (Scott-Clayton 2012). While such jobs may enhance soft skills,
there are likely decreasing marginal returns to work experience in these sectors.

10. The math and reading tests refer to the exams administered by the National Center for Education
Statistics (NCES) that were given to all students in the longitudinal surveys in their senior year
of high school. Because the tests in NLS72 and NELS:88 covered different subject matter, were
of different lengths, and were graded on different scales, we construct the percentile of the score

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

387

INCREASING TIME TO BACCALAUREATE DEGREE

father’s education level, mother’s education level, real parental income lev-
els, gender, and race.11 Appendix A provides a detailed description of the
construction of the analysis data set.

Table 2 presents means of selected observable characteristics for the sample
of respondents who obtain a BA within eight years of cohort high school
graduation in the two surveys overall and for each type of institution. Means
of the full set of variables used in our analysis are shown in appendix table B.1.
Table 2 shows clearly that there has been no aggregate reduction in academic
preparedness among college graduates over time, as measured by math and
reading test percentiles or high school GPA. Indeed, in all sectors except
community colleges, math test percentiles actually increased among college
graduates across cohorts, and in all sectors GPAs increased among graduates.12
The increased demand for higher education that took place across surveys
did not translate into reductions in academic preparation for college among
graduates for two reasons. First, enrollment increases occurred across the
distribution of academic preparation, muting the impact that the increased
demand for higher education had on the average preparedness of college
students. Second, the less prepared students induced to attend college had very
low completion rates, both because they disproportionately attended sectors
in which completion rates are low and because they were not well prepared
for college (Bound, Lovenheim, and Turner 2010a). As a result, despite the
importance of academic ability in explaining cross-sectional variation in time
to degree, changes in academic preparedness among graduates go in the wrong
direction to explain the lengthening of time to degree. Furthermore, tables 2
and B.1 show that both the educational attainment and real income of parents

distribution for each test type and for each survey. The comparison of students in the same test
percentile across surveys is based on the assumption that the distribution of overall achievement did
not change over this time period. This assumption is supported by trends in nationally representative
National Assessment of Education Progess (NAEP) scores. Since the 1970s, mean NAEP scores in
math and English have been essentially unchanged, and the distribution of these scores has changed
little as well (Rampey, Dion, and Donahue 2009).

11. An important demographic variable that we cannot observe in our data is family structure. The
overall likelihood of growing up in a two-parent family declined signiﬁcantly over our period of
observation. For example, Census Bureau tabulations show the proportion of all children living
with two parents falling from 83 percent to 73 percent between 1972 and 1992. Yet because changes
in family structure measured in the CPS among those graduating from college are quite small,
we conclude that changes in this variable cannot be a primary determinant of changes in time to
degree.

12. While we include a measure of high school GPA because this measure provides information
that predicts collegiate attainment beyond test scores, including high school GPA is potentially
problematic because it is often difﬁcult to standardize grading across schools and over time. For
these reasons we did not include high school GPA in our initial analysis; estimates that exclude
high school GPA are shown in Bound, Lovenheim, and Turner (2010b) and are qualitatively similar
to those shown below.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

388

John Bound, Michael F. Lovenheim, and Sarah Turner

e
g
e

l
l

o
C
y
t
i
n
u
m
m
o
C

e
v
i
t
c
e
e
S

y
l
h
g
H
e
t
a
v
i
r
P

e
v
i
t
c
e
e
S
s
s
e
L

e
t
a
v
i
r
P

0
5

p
o
T

i
l

b
u
P

i
l

b
u
P
0
5

p
o
t
–
n
o
N

e
p
m
a
S

l
l

u
F

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

e
b
a
i
r
a
V

5
.
8
5

9
.
5
5

0
.
8
6

4
.
0
6

3
.
4
8

1
.
8
7

2
1
8

6
5
7

1
0
7

9
8
6

9
9
6

0
6
6

0
1
8

2
5
7

3
8
7

0
4
7

0
0
7

4
6
6

3
.
8
6

0
.
5
6

6
.
1
7

0
.
8
6

8
.
0
7

8
.
6
6

l
i
t
n
e
c
r
e
p

t
s
e
t

g
n
d
a
e
R

l
i
t
n
e
c
r
e
p

t
s
e
t

h
t
a
M

0
2
1
.
0

4
2
2
.
0

4
2
3
.
0

1
3
3
.
0

5
8
0
.
0

2
4
3
.
0

6
8
0
.
0

2
6
2
.
0

9
8
1
.
0

7
3
4
.
0

2
7
0
.
0

0
6
0
.
0

4
6
0
.
0

5
9
4
.
0

3
2
6

1
5
1
.
0

0
3
2
.
0

4
3
1
.
0

6
1
4
.
0

9
1
2
.
0

0
7
1
.
0

8
9
2
.
0

4
5
1
.
0

1
8
1
.
0

6
6
1
.
0

0
5
3
.
0

6
1
0
.
0

3
3
0
.
0

8
4
0
.
0

0
5
5
.
0

5
4
5

5
2
1
.
0

8
0
0
.
0

7
4
0
.
0

5
2
2
.
0

9
1
7
.
0

8
2
0
.
0

2
9
7
.
0

6
1
0
.
0

8
8
6
.
0

9
6
0
.
0

1
5
7
.
0

8
8
0
.
0

3
4
0
.
0

3
7
4
.
0

2
6
5

6
3
1
.
0

0
6
0

0
8
0

2
0
4

9
5
4

3
8
0
0

3
3
5
0

2
4
0
0

8
9
3
0

5
4
0
0

4
1
6
0

8
1
0

4
2
0
0

1
4
0
0

0
5
6
0

2
9
3

0
9
0

9
4
0
0

5
3
1

5
9
2
0

1
2
5

7
3
0

8
2
5

2
3
0

4
1
4

3
5
1
0

8
1
5
0

1
4
0

5
5
0

5
0
1

0
1
4

2
2
8

9
9
1

8
2
1

9
2
1
0

4
4
4

9
9
2

6
1
0

0
7
0
0

8
0
2

7
0
7
0

9
4
0

5
6
0

6
0
4

0
8
4
0

4
3
0

4
4
1

6
1
3

6
0
5

3
2
1
.
0

8
3
1
.
0

2
5
4
.
0

7
8
2
.
0

5
4
0
.
0

2
3
1
.
0

4
8
2
.
0

9
3
5
.
0

1
2
1
.
0

0
2
1
.
0

4
3
4
.
0

5
2
3
.
0

5
5
1

2
8
3

2
6
0
0

2
1
6

5
0
1
0

4
9
4

4
6
0
0

3
5
4

7
1
2
.
0

0
9
2
.
0

8
5
0
.
0

5
1
5
.
0

1
7
1
.
0

1
6
3
.
0

8
1
1

8
4
2

3
4
1

2
0
4

1
1
0

8
0
0

0
8
0

3
1
5

2
0
8

4
8
1
0

3
5
0
0

4
2
5

2
5
1

6
4
6

4
8
0
0

6
5
0
0

9
6
0

3
8
4

3
3
7

7
7
1
0

3
9
0
0

1
7
2

1
2
1

8
8
4

6
3
0
0

3
2
0
0

5
3
0

2
4
5

2
5
6

0
5
1

8
5
0
0

8
5
3

1
7
1

0
9
4

9
3
0
0

6
5
0
0

3
7
0

6
3
4

7
9
3

8
3
3

5
6
1
.
0

8
5
1
.
0

5
5
1
.
0

9
4
3
.
0

4
1
0
.
0

8
1
0
.
0

4
9
0
.
0

8
8
4
.
0

9
5
9
,
1

0
5
4
.
0

2
5
0
.
0

0
2
4
.
0

5
5
1
.
0

3
4
5
.
0

8
5
0
.
0

5
5
0
.
0

4
7
0
.
0

3
5
4
.
0

7
3
1
,
4

3
3
1
.
0

6
1
2
.
0

9
3
1
.
0

4
0
4
.
0

7
1
0
.
0

9
1
0
.
0

2
7
0
.
0

3
2
5
.
0

0
5
3
,
4

l
i
t
r
a
u
q

d
n
o
c
e
S

l
i
t
r
a
u
q

t
s
e
w
o
A L
P
G

l
i
t
r
a
u
q

d
r
i
h
T

l
i
t
r
a
u
q

p
o
T

n
o
i
t
a
c
u
d
e

s
’
r
e
h
t
a
F

a
m
o
p
d
S
H
o
N

n
o
i
t
a
c
u
d
e

s
’
r
e
h
t
o
M

e
r
o
m

r
o

A
B

a
m
o
p
d
S
H
o
N

0
0
0
,
5
2
$ < e m o c n i l a t n e r a P 0 0 0 , 0 5 $ >
e
m
o
c
n

a
t
n
e
r
a
P

n
a
s
A

e
r
o
m

r
o

A
B

s
n
o
i
t
a
v
r
e
s
b
o

f
o

r
e
b
m
u
N

e
p
m
a
s

f
o

n
o
i
t
r
o
p
o
r
P

n
a
c

i
r
e
m
A

n
a
c

i
r
f
A

e
a
M

c
n
a
p
s
H

e
p
y
T

o
o
h
c
S
y
b

,
s
r
a
e
Y

t
h
g
E

n
h
t
i

w
s
e
t
a
u
d
a
r
G
e
g
e

l
l

o
C
r
o
f

s
e
b
a
i
r
a
V

8
8
:
S
L
E
N
d
n
a

2
7
S
L
N
d
e
t
c
e
e
S

f
o

s
n
a
e
M

2
e
b
a
T

r
o
f

d
e
s
u

e
r
e
w
s
t
h
g
e
w
p
u
w
o

–

l
l

o
f

h
t
r
u
o
F

.
y
e
v
r
u
s

e
h
t

d
e
d
u
c
n

s
t
h
g
e
w
p
u
w
o

–

l
l

o
f

h
t
f
ﬁ

e
h
t

g
n
s
u

e
d
a
m
e
r
e
w
s
n
o
i
t
a
u
c
a
c
2
7
S
L
N

.
s
e
s
e
h
t
n
e
r
a
p

e
r
a

s
n
o
i
t
a
i
v
e
d

d
r
a
d
n
a
t
S

:
s
e
t
o
N

2
7
S
L
N
e
h
T

.
s
n
o
i
t
a
u
b
a
t

e
t
e
p
m
o
c

r
o
f

1
.
B

e
b
a
t

x
i
d
n
e
p
p
a

e
e
S

.
s
n
o
i
t
a
u
b
a
t

e
h
t

d
e
d
u
c
n

e
r
a

s
p
u
w
o

–

l
l

o
f

e
s
e
h
t

g
n
i
t
a
p
i
c
i
t
r
a
p

e
s
o
h
t

y
l
n
O

.
s
n
o
i
t
a
u
c
l
a
c

y
e
v
r
u
s

8
8
:
S
L
E
N
e
h
t

o
o
h
c
s

h
g
h

t
r
o
h
o
c

f
o

s
r
a
e
y

t
h
g
e

n
h
t
i

w
h
s
n
ﬁ

o
h
w
d
n
a

n
o
i
t
a
u
d
a
r
g

o
o
h
c
s

h
g
h

t
r
o
h
o
c

f
o

s
r
a
e
y

o
w

n
h
t
i

w
e
g
e

l
l

o
c

d
n
e
t
t
a

o
h
w
e
s
o
h
t

o
t

d
e
t
c
i
r
t
s
e
r

e
r
a

s
e
p
m
a
s

8
8
:
S
L
E
N
d
n
a

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

389

.
8
8
:
S
L
E
N
e
h
t

r
o
f
2
9
9
1

e
n
u
J

d
n
a
2
7
S
L
N
e
h
t

r
o
f

2
7
9
1

e
n
u
J

s
a

d
e
n
ﬁ
e
d

n
o
i
t
a
u
d
a
r
g

o
o
h
c
s

h
g
h

t
r
o
h
o
C

.
n
o
i
t
a
u
d
a
r
g

INCREASING TIME TO BACCALAUREATE DEGREE

increased for college graduates. These shifts are in the direction of shortening
time to degree, all else equal.

Supply-Side Variables

Changes in the supply side of the higher education market may affect the rate
of attainment by shifting the distribution of students among different types of
institutions or by altering the level of resources per student within institutions.
Across the two cohorts, there was a sizable change in where BA recipients ﬁrst
attend college. However, these shifts are on the whole in a direction that
favors a reduction in time to degree. While there is some increase in eventual
graduates entering community colleges, the distribution of initial school types
within the four-year sector shifted toward the more selective public and private
institutions and away from the non–top ﬁfty public institutions. To illustrate,
the share of degrees awarded by highly selective private schools grew from
9.4 percent to 11.3 percent, and the share of degrees awarded by top public
institutions rose from 14.4 percent to 17.5 percent, while the share of degrees
awarded by non–top ﬁfty public universities declined from 44.9 percent to
34.5 percent between the two cohorts. Thus, shifts in the distribution of degree
attainment by sector can explain little of the aggregate time to degree increases
evident in the data.

We proxy for institutional resources using student-faculty ratios,13 which
are calculated from the 1972 Higher Education General Information System
(HEGIS) survey and the 1992 Integrated Postsecondary Education Data System
(IPEDS) survey. Table 3 contains the means and distributions for our sample
of eight-year BA recipients. Overall, student-faculty ratios increased (i.e., per
student resources decreased) across the two cohorts from 25.5 to 29.8. While
these increases occurred throughout the student-faculty ratio distribution, they
are largest among institutions in the highest deciles, pointing to increased
stratiﬁcation of resources over time.

The remaining panels of table 3 show student-faculty ratios by school type.
The increases have been most dramatic in the sectors that experienced the
largest time to degree increases: non–top ﬁfty public schools and community
colleges. In the elite public and private schools, student-faculty ratios actually
decreased. These tabulations present further evidence that resources not only
have declined overall but have become more stratiﬁed over time across higher
education sectors. They also are suggestive of a role for institutional resources
in explaining increasing time to degree.

13.

In particular, we calculate the ratio of nine- and twelve-month faculty members to total student
enrollment.

390

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

Table 3. Undergraduate Student-Faculty Ratios and Expenditures per Student by Initial School Type among
College Graduates

Panel A: Full Sample

Survey Mean

Student-Faculty Ratios Percentile
50th

75th

25th

90th

Median Expenditures Median Subsidy

per Student

NLS72
NELS:88

25.5
29.8

19.4
20.5

23.1
24.9

28.8
32.3

35.0
52.8

$14,318 $15,445

$10,885 $10,160

Panel B: Public Four-Year Non–top 50

Survey Mean

Student-Faculty Ratios Percentile
50th

75th

25th

90th

Median Expenditures Median Subsidy

per Student

NLS72
NELS:88

25.0
27.6

20.7
22.9

23.9
26.5

28.6
31.3

32.7
36.1

$13,172 $11,886

$10,956 $9,378

Panel C: Public Four-Year Top 50

Survey Mean

Student-Faculty Ratios Percentile
50th

75th

25th

90th

Median Expenditures Median Subsidy

per Student

NLS72
NELS:88

23.0
22.2

20.3
20.4

23.0
22.1

24.2
24.6

30.9
26.9

$19,755 $18,515

$17,085 $15,325

Panel D: Private Four-Year Less Selective

Survey Mean

Student-Faculty Ratios Percentile
50th

75th

25th

90th

Median Expenditures Median Subsidy

per Student

NLS72
NELS:88

22.0
23.9

16.1
17.0

18.7
21.1

24.5
26.7

33.5
33.9

$16,576 $18,689

$8,753 $9,048

Panel E: Private Four-Year Highly Selective

Survey Mean

Student-Faculty Ratios Percentile
50th

75th

25th

90th

Median Expenditures Median Subsidy

per Student

NLS72
NELS:88

18.7
18.4

14.3
13.4

18.4
17.4

23.1
23.1

25.0
28.3

$24,996 $34,212

$14,086 $17,450

Panel F: Community College

Survey Mean

Student-Faculty Ratios Percentile
50th

75th

25th

90th

Median Expenditures Median Subsidy

per Student

NLS72
NELS:88

40.9
57.1

28.9
38.9

36.4
55.2

52.0
70.3

65.1
92.2

$6,316 $6,140

$5,153 $5,542

Notes: NLS72 calculations were made using the ﬁfth follow-up weights included in the survey. Fourth
follow-up weights were used for the NELS:88 survey calculations. Only those participating in these
follow-ups are included in the tabulations. Data on faculty, enrollment, expenditures, and revenues
are from the HEGIS/IPEDS surveys from the Department of Education. Median expenditures per
student are for all education-oriented expenditures, which are all operating expenditures minus
expenditures on research, extension services, and hospitals. Per student subsidies are student-
oriented expenditures minus tuition revenue per student. All ﬁnancial ﬁgures are in real 2007
dollars and are deﬂated by the Higher Education Price Index (HEPI).

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

391

INCREASING TIME TO BACCALAUREATE DEGREE

The ﬁnal columns of table 3 show median student-related expenditures
per student and subsidies per student, measured as the difference between
student-related expenditures and net tuition revenues. Median expenditures
per student increased slightly overall, yet this modest gain combines declines
in the public sector with increases in the private sector, most notably among
the most selective private schools, where expenditures increased by about 37
percent. Overall and in the public sector, subsidies per student fell, reﬂecting
declining state support. That tuition also increased at these institutions points
to a shift from public sector funding to student funding of higher education. In
the private sector, by contrast, the subsidy component rose somewhat. These
calculations echo other ﬁndings of a divergence between the public and private
sectors and the more general increased stratiﬁcation in the higher education
market. Kane, Orszag, and Gunter (2003) document how declines in state
appropriations led to declines in spending per student at public schools relative
to private schools, with the ratio of per student funding dropping from about
70 percent in the mid-1970s to about 58 percent in the mid-1990s. In addition,
Hoxby (1997, 2009) shows that tuition, subsidies, and student quality have
stratiﬁed over the past ﬁve decades, with a particularly substantial divergence
among institutions in the top percentiles of selectivity and resources from the
baseline of observation.

While we use student-faculty ratios as a proxy for institutional resources,
we note that this is one among many potential proxies, each of which is an
imperfect total resource measure (Black and Smith 2006). We favor using
student-faculty ratios for several reasons. First, this ratio is likely correlated
with the college’s ability to meet student demand for courses and with quality
of student advising. Second, changes in monetary measures, such as per
student expenditures, confound changes in resources with changes in the
price of those resources. As faculty salaries and research costs have risen in
real terms, one would expect expenditures to have increased. Yet this increase
reﬂects inﬂation in the inputs to higher education, not necessarily a real
resource increase. Student-faculty ratios are measured in the same units in
both periods, which makes them a more consistent measure of institutional
resources across cohorts. However, table 3 shows that expenditures and
student-faculty ratios have largely changed in a similar manner, which
underscores that fact that our empirical ﬁndings are not very sensitive to
which proxy we use for college resources.

5. EMPIRICAL METHODOLOGY AND RESULTS
Changing Student Attributes, Institution Type, and Student-Faculty Ratios

We ﬁrst examine whether changes in observed student background character-
istics, student preparedness for college, and institutional characteristics such

392

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

as institution type and student-faculty ratios can explain the observed shifts
in the time to degree distribution. Appendix table B.2 demonstrates the cross-
sectional relationship in NELS:88 between time to degree and the observable
characteristics in our data. We focus on NELS:88 because our decompositions
implicitly use the cross-sectional relationships from this survey. Consistent
with previous work, we ﬁnd a strong cross-sectional relationship between our
student academic preparation variables and time to degree, suggesting that
more prepared students graduate faster. The estimates also point to an im-
portant role for institutional resources, as proxied by student-faculty ratios, as
well as for initial school type.14

Given these cross-sectional relationships, we examine how changes in ob-
servable precollegiate characteristics of graduates and characteristics of the
universities they attend relate to changes in time to degree. We conduct a
semi-parametric reweighting, following DiNardo, Fortin, and Lemieux (1996),
to decompose the observed change in the distribution of time to degree in or-
der to distinguish the roles of changes in the distribution of observable student
and collegiate attributes. We reweight the NELS:88 time to degree distribution
using NLS72 data on the characteristics of graduates and the ﬁrst postsec-
ondary institution they attend. This calculation leads to a counterfactual time
to degree distribution in which the proportion of graduates with a given char-
acteristic or a given set of characteristics has not changed between the two
surveys. By comparing the observed NELS:88 outcomes and the reweighted
NELS:88 outcomes, we can determine the proportion of the observed change
in the time to degree distribution that is due to changes in the mix of grad-
uates with a given set of attributes. The remainder reﬂects changes in other
determinants of time to degree as well as changes over time in how character-
istics affect time to degree. What we are estimating is the change in time to
degree conditional on various observable characteristics, integrated over the
distribution of characteristics (see Barsky et al. 2002 for a further discussion).
We generate weights by estimating logistic regressions of a dummy variable
equal to 1 if an observation is in the NLS72 cohort on the observable student
, where
characteristics. The weights used in the reweighting analysis are Wi
1−Wi
Wi are the predicted values from the logistic regressions. These weights are
used to generate our counterfactual NELS:88 time to degree distributions.

The validity of our counterfactual calculations (e.g., the time to degree for
those completing college in the 1990s had they been as academically prepared
for college as graduates in the 1970s) depends crucially on the cross-sectional

14. One of the reasons why time to degree may vary across sectors is because of differences in peer
quality. Unfortunately, we are unable to examine peer effects directly with our data, but how peers
affect the timing of degree receipt is an important area for future research.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

393

INCREASING TIME TO BACCALAUREATE DEGREE

association between background characteristics and college outcomes, reﬂect-
ing a causal relationship not seriously inﬂuenced by confounding factors. For
example, we simulate the time to degree distribution under a counterfactual
distribution of test scores and high school GPAs. For this simulation to accu-
rately represent the counterfactual, it must be the case that the cross-sectional
relationship between these academic measures and time to degree reﬂects the
impact of precollegiate academic preparedness on this outcome. Regardless
of whether the reweighting calculation produces the true counterfactual, the
results present a clear accounting framework for assessing the descriptive im-
pact of the change in the composition of students and the institutions they
attend on the timing of degree receipt.

Table 4 presents the results from this decomposition. As shown in panel
A, changes in academic background variables as well as changes in all prec-
ollegiate student attributes predict a downward shift in time to degree across
cohorts, despite the large upward shift observed in the data. For example,
the shift in math, reading, and GPAs among graduates (row 3) predicts a 3.7
percentage point increase in the likelihood of graduating in four years (condi-
tional on graduating in eight years) and a 0.12-year decline in mean time to
degree. This ﬁnding is due to the fact that academic background is a strong
predictor of time to degree, but as shown in table 2, academic preparation for
college among graduates has risen across cohorts. Other changes in this pop-
ulation, such as parental education, also go in the wrong direction to explain
the increase in time to degree. We found that regardless of which variables
we standardized on or how we performed the standardization, changes in
the characteristics of students graduating from college could not explain the
observed increased time to degree.

The other rows of table 4, panel A, show the extent to which measured
changes in the supply side of higher education can provide empirical traction
in explaining time to degree increases. These estimates include student-faculty
ratios as well as institution-type ﬁxed effects in the logistic weighting function,
which means the counterfactual time to degree distribution is the distribu-
tion expected if student-faculty ratios and the initial school type distribution
remained at their 1972 levels while all other variables changed to their 1992
levels. We calculate this counterfactual by taking the difference between the
full counterfactual estimates (row 4) and the estimates that account for only
individual-level attributes (row 2).

These estimates point to a role for supply-side shifts in explaining time to
degree increases. Changes in student-faculty ratios and where graduates attend
college can account for more than 12.4 percent of the overall mean time to
degree increase. In addition, such changes are associated with about 8 percent
of the decline in the proportion of the sample graduating within four years

394

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

Table 4. Decompositions of Time to Degree Distribution Changes by Type of Institution

Panel A: Full Sample

Row

Mean

1 Observed difference (NELS:88 − NLS72)

−13.7

−9.1 −2.3 −1.7

0.32

2 Difference from observable individual characteristics

3 Difference from student academic preparedness

4 Difference from all observables

4.8

3.4

3.7

5.0

3.3

3.5

2.1

2.8

3.1

1.5

2.7

−0.16

−0.10

−0.12

5 Net effect of institutional resources (row 4 − row 2)

−1.1

−1.7 −0.7 −0.4

0.04

Panel B: Non–top 50 Public

Row

Mean

1 Observed difference (NELS:88 − NLS72)

−20.6 −13.6 −3.3 −1.2

0.44

2 Difference from observable individual characteristics

3 Difference from student academic preparedness

4 Difference from all observables

5 Net effect of institutional resources (row 4 − row 2)

1.1

2.4

−2.4

−3.5

3.6

2.6

0.7

4.6

1.6

3.3

3.5

0.6

3.0

−0.12

−0.07

−0.05

−2.9 −1.3 −0.5

0.07

Row

Panel C: Top 50 Public

1 Observed difference (NELS:88 − NLS72)

−13.0

2 Difference from observable individual characteristics

3 Difference from student academic preparedness

4 Difference from all observables

5 Net effect of institutional resources (row 4 − row 2)

3.1

3.4

3.8

0.7

Panel D: Private Less Selective

4.5

1.8

2.4

1.1

Mean

0.2

1.7

1.2

0.07

−0.06

−0.10

−0.09

0.5

4.9

3.7

4.4

−0.5 −0.7 −0.5

−0.03

Row

Mean

1 Observed difference (NELS:88 − NLS72)

−8.7

−2.7 −0.6 −0.01

2 Difference from observable individual characteristics

3 Difference from student academic preparedness

4 Difference from all observables

5 Net effect of institutional resources (row 4 − row 2)

5.8

4.3

6.0

0.2

4.9

3.8

4.9

2.3

1.8

1.2

0.0

1.0

−1.1 −0.2

0.15

0.02

0.07

0.03

0.01

Panel E: Private Highly Selective

Row

1 Observed difference (NELS:88 − NLS72)

2 Difference from observable individual characteristics

3 Difference from student academic preparedness

4 Difference from all observables

7.9

12.7

8.4

13.0

5 Net effect of institutional resources (row 4 − row 2)

0.3

−0.2

Mean

3.7

4.3

1.4 −0.1

2.8

1.2

1.2 −0.1

2.9

0.0

−0.12

−0.01

−0.11

−0.01

0.00

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

395

INCREASING TIME TO BACCALAUREATE DEGREE

Table 4. Continued.

Panel F: Community College

Row

Mean

1 Observed difference (NELS:88 − NLS72)

−21.0 −23.6 −12.2 −9.0

0.68

2 Difference from observable individual characteristics

3 Difference from student academic preparedness

4 Difference from all observables

2.1

1.3

4.2

3.0

3.6

5 Net effect of institutional resources (row 4 − row 2)

−0.8

−0.6

4.5

4.1

5.4

0.9

4.8

3.4

6.1

1.3

−0.15

−0.11

−0.14

0.01

Notes: NLS72 calculations were made using the ﬁfth follow-up weights included in the survey.
Fourth follow-up weights were used for the NELS:88 survey calculations. Only those participating
in these follow-ups are included in the regression. School type samples refer to ﬁrst institution
attended. The NLS72 and NELS:88 samples are restricted to those who attend college within two
years of cohort high school graduation and who ﬁnish within eight years of cohort high school
graduation. Cohort high school graduation is deﬁned as June 1972 for the NLS72 sample and
June 1992 for the NELS:88 sample. Data on faculty and enrollment are from the HEGIS/IPEDS sur-
veys from the Department of Education. Row 1: observed difference between NELS:88 − NLS72;
Row 2: observed NELS:88 − predicted outcome assuming the distribution of individual character-
istics is the same in 1992 as in 1972; Row 3: observed NELS:88 − predicted outcome assuming
the math percentile, reading percentile, and GPA quartile distributions are the same in 1992 as
in 1972; Row 4: observed NELS:88 − predicted outcome assuming the distribution of individual
characteristics, math percentiles, reading percentiles, GPA quartiles, student-faculty ratios, and
initial institution types is the same in 1992 as in 1972; Row 5: row 4 − row 2.

and almost 19 percent of the reduced likelihood of graduating within ﬁve
years. Thus while supply-side changes cannot fully account for the increases
in time to degree that we document, reduced institutional resources and shifts
in where students enter the postsecondary system are important factors in
explaining why degree time has elongated.

In the remaining panels of table 4, we perform the reweighting analysis
separately by type of ﬁrst institution. Similar to the results for the full sample,
we ﬁnd that changes in precollegiate academic preparation of college gradu-
ates and in the background characteristics of these graduates more generally
explain none of the increase in time to degree across cohorts within each
type of institution. Table 4 provides a strong rejection of the hypothesis that
changing individual characteristics among college graduates can explain the
extension of time to degree.

Panel B of table 4 points to a signiﬁcant role for student-faculty ratio in-
creases in explaining time to degree increases in the non–top ﬁfty public sector.
Rising student-faculty ratios alone account for 3.5 out of the 20.8 percentage
point drop (16.8 percent) in the share of degree recipients completing within
four years and for 2.8 of the 11.2 percentage point drop (25 percent) in the
share of degree recipients completing within ﬁve years. They also can explain
15.9 percent of the mean time to degree increase in this sector. In no other

396

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

sector do we ﬁnd a role for changes in institutional resources, as proxied by
student-faculty ratios, in explaining changes in time to degree.15

As discussed above, student-faculty ratios are an imperfect proxy for school
resources. To the extent that the resultant measurement error is classical, it
will cause us to understate the effect of institutional resource shifts on time to
degree. To generate estimates of the effect of changing collegiate resources on
time to degree that are less susceptible to such biases, we next turn to a state-
level estimation strategy that uses demand shocks for college as an instrument
for institutional resources.

Institutional “Crowding” Estimates

Given that over 85 percent of students attend college in their state of residence,
we generate exogenous variation in higher education resources using changes
in the number of eighteen-year-olds in each state between 1972 and 1992. As
long as educational subsidies do not completely adjust to these demand shocks,
the demand shifts generate exogenous variation in institutional resources per
student (Bound and Turner 2007). Thus, our analysis is at the state level, as
this is the governmental level of control for public universities and, in turn, the
division used in determining access for in-state tuition and fees. We use as our
key dependent variables the probability of graduating in four years conditional
on graduating in eight years, log time to degree, and time to degree in years.
A potential confounding factor in analyzing the relationship between the
change in time to degree and the eighteen-year-old population is the role of
changing demographic characteristics within each state. For example, if states
that witness an increase in their eighteen-year-old population also experience
an increase in the number of students with low achievement or from groups
with traditionally lower collegiate attainment, and if more college students are
pulled from this group, we would observe a time to degree increase regardless
of the effect of resources per student on this outcome. To address this prob-
lem, we use a two-stage estimator. First, we regress the dependent variable
of interest on the student characteristics described in appendix table B.1, a

15. For community colleges, the correlation between observed resource measures (both student-faculty
ratios and expenditure metrics) is notably weak; as a result, observed resource declines have no
predictive power for explaining elongating time to degree for this sector. Traditional resource
measures at community colleges may be appreciably noisier than those in other sectors of higher
education, given the reliance on part-time faculty and the substantial provision of nondegree credit
services such as federally funded job training. Moreover, students starting at a community college
who receive a BA degree receive at least one-half of their eventual credits from a four-year institution,
and we do not account for these additional potential institutional resource effects. This ﬁnding is
consistent with other work on community colleges, which shows that measured community college
resources do not affect student outcomes (Stange 2012).

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

397

INCREASING TIME TO BACCALAUREATE DEGREE

state-speciﬁc indicator variable, a cohort-speciﬁc dummy (NELS:88 = 1), and
a state-cohort interaction term at the individual level:

ln TTDi j t = α + φ Xi j t + γ j Sj + δt D92 + λ j Sj D92 + εi j t .

We then construct a counterfactual time to degree measure equal to the ex-
pected time to degree in state j if the NELS:88 cohort had the same distribution
of observables as the NLS72 cohort:

ln(TTD)92
j 72

= α + φ Xi j 72 + γ j Sj + δt + λ j Sj .

In cases where the dependent variable is binary, we use a logit speciﬁcation
to estimate the parameters of this regression; otherwise we use ordinary least
squares (OLS). Our goal is to compare the observed NLS72 outcome and the
counterfactual outcome for NELS:88 if observable characteristics of students
had remained unchanged over time.

Second, we take state-level means of the observed outcomes and the coun-

terfactual outcomes and estimate the second stage:

ln(TTD j 72) − ln

(cid:3)

(cid:2)

TTD92
j 72

= α + βd ln(Pj t ) + η j t ,

where dln(Pj t ) is the change in log population of eighteen-year-olds in each
state.

Results are reported in table 5. In the ﬁrst column, the dependent vari-
ables are the changes in actual state-level outcomes that are not regression
adjusted, NELS:88 − NLS72. In the second column, the dependent variables
are the differences between the NELS:88 counterfactual and the actual NLS72
value of the outcome variable. This difference represents the average change
within each state in the outcome variable that is not attributable to changes in
observable background characteristics.

The results are consistent with the hypothesis that time to degree has ex-
panded the most in states where cohort size has increased, in turn reducing
resources per student. In panel A of table 5, which shows results for the full
sample, a 10 percent increase in a state’s eighteen-year-old population de-
creases the likelihood of graduating in four years by 3.17 percent and increases
time to degree by 1.24 percent, or 0.06 years. The estimates are attenuated
somewhat but are qualitatively similar when we control for covariates, as shown
in the second column.

In panel B we present results for the sample of respondents whose ﬁrst
institution is a public non–top ﬁfty school. Because these institutions are more
open access and because their funding is much more tied to state appropria-
tions than private or top public schools, the effect of demand shocks should be

398

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

Table 5. State-Level Estimates of the Effect of Crowding on Multiple Time to Degree Measures: Second-
Stage Estimates

Independent Variable: Change in Log 18-Year-Old Population (1992–72)

Dependent Variable

P(graduate in 4 | graduate in 8)

Log time to degree

Time to degree

Dependent Variable

P(graduate in 4 | graduate in 8)

Log time to degree

Time to degree

Panel A: Full Sample

Actual 92 − Actual 72
Coefﬁcients

Counterfactual 92 − Actual 72
Coefﬁcients

−0.317∗∗
(0.138)

0.124∗∗
(0.046)

0.631∗∗
(0.185)

−0.201
(0.127)

0.078∗
(0.041)

0.436∗∗
(0.174)

Panel B: Public Non–top 50

Actual 92 − Actual 72
Coefﬁcients

Counterfactual 92 − Actual 72
Coefﬁcients

−0.372∗
(0.200)

0.184∗∗
(0.047)

0.943∗∗
(0.276)

−0.269
(0.209)

0.146∗∗
(0.060)

0.768∗∗
(0.301)

Notes: NLS72 calculations were made using the ﬁfth follow-up weights included in the survey. Fourth
follow-up weights were used for the NELS:88 survey calculations. Only those participating in these
follow-ups are included in the regression. All samples include only those who begin college within
two years of cohort high school graduation and obtain a BA within eight years of cohort high school
graduation. Cohort high school graduation is deﬁned as June 1972 for the NLS72 sample and June
1992 for the NELS:88 sample. The public non–top 50 samples refer to initial institution of the
respondent. Robust standard errors are in parentheses.
∗signiﬁcant at 0.10%; ∗∗signiﬁcant at 0.05%

larger in this sector. Results are consistent with that hypothesis: a 10 percent
increase in a state’s population of eighteen-year-olds reduces the probability of
four-year graduation by 3.7 percent and increases time to degree by 1.8 percent,
or 0.09 years. All three estimates are statistically signiﬁcant at either the 10
percent or 5 percent level and are robust to adjusting for changes in observable
characteristics of respondents.16

The results presented in table 5 can be thought of as the reduced form
of the structural model in which cohort size is used as an instrument for re-
sources. The implied ﬁrst-stage regression of student faculty ratios (in logs)

16. When we repeat this analysis for the elite public and private schools and for both private sectors,
we ﬁnd no statistically signiﬁcant evidence that time to degree is inﬂuenced by the size of the
eighteen-year-old population, which is an expected result, as these sectors should be less responsive
to demand shocks because enrollment is less responsive to demand. Similar to our reweighting
results, we ﬁnd no evidence that reductions in resources brought about by crowding extend time to
degree among students beginning at community colleges.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

399

INCREASING TIME TO BACCALAUREATE DEGREE

on cohort size, adjusting for covariates, produces a coefﬁcient of 0.086 (0.051)
for the full sample and 0.143 (0.060) for the non–top ﬁfty public institu-
tions. When multiplied through by the student-faculty ratio changes shown in
table 3, these estimates imply a large role for declining resources in explaining
increased mean time to degree. However, since both the reduced form results
in table 5 and the ﬁrst-stage coefﬁcients are rather imprecisely estimated, they
encompass both large and small effects of changing institutional resources,
and we view these results as suggestive evidence of the importance of resource
declines that supports our decomposition results.

Credit Constraints and Student Labor Supply

Over the past several decades, the number of hours worked by students in-
creased dramatically. Between 1972 and 1992, average weekly hours worked
(unconditional) among those enrolled in college increased by about 2.9 hours,
from 9.5 to 12.4, as measured for eighteen- to twenty-one-year-old college stu-
dents in the October CPS, with a further increase to 13.2 hours per week evident
in 2005. Figure 3 shows trends in work hours for those enrolled in college by
broad type of institution from the CPS. Employment rates among eighteen-
to nineteen-year-old college students rose steadily over the last quarter cen-
tury, particularly in the two-year and four-year public sectors. Moreover, the
share of enrolled students working more than twenty hours per week also in-
creased. These estimates are consistent with several previous studies showing
student work hours increasing, particularly among students enrolled at public
colleges and universities (see, e.g., Riggert et al. 2006; Stern and Nakata 1991;
Fitzpatrick and Turner 2007; Scott-Clayton 2012). Scott-Clayton (2012) does a
number of tabulations suggesting that rising college costs leading to increased
credit constraints are the most plausible explanation for the relative increase
in hours of work for college students in the 1990s.

Consistent with observations from the CPS and with previous work in this
area, the comparison of the NLS72 and NELS:88 cohorts shows that hours
worked rose sharply for students in their ﬁrst year of college.17 For the full
sample, average unconditional weekly hours worked increased from 6.6 to
13.0 hours and increased from 14.9 to 20.5 hours on the intensive margin.
This increase in working behavior occurred differently across initial school
types. For the public non–top ﬁfty sample, average hours increased from 7.3 to
13.5 and from 10.2 to 18.2 hours for students in the sample entering two-year
colleges. In the public top ﬁfty sector, average hours increased from 4.8 to

17. The NELS:88 survey does not allow one to track work histories fully between the 1994 and 2000
follow-ups. Thus we restrict the analysis of working hours in both surveys to those enrolled in
college in the ﬁrst year following high school cohort graduation.

400

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

Figure 3. Employment among Those Enrolled in College by Type of Institution. Source: Data are
from authors’ tabulations using the October CPS. Individual weights are used.

10.6, while average hours rose from 5.6 to 11.8 and from 4.1 to 10.1 in the
less and highly selective private sectors, respectively. We expect the effect of
work hours on time to BA attainment to be increasing in hours of work as
the potential for crowd-out within the time constraint increases, although the
effect of work hours on time to degree likely is magniﬁed outside the most
selective sectors, where the tuition structure imposes a large penalty for less
than full-time enrollment.

Estimating the effect of working while in school on the rate of collegiate
attainment is difﬁcult because the decision to work and the choice of hours of
employment are endogenous.18 That said, it is hard to imagine that increases
of the magnitude seen would not have an impact on time spent on academic
pursuits and therefore on time to degree. To approximate the potential effects
of hours worked on time to degree, consider a student with a time budget of
ﬁfty hours per week available for coursework and employment. With this ﬁxed
budget, increased hours worked necessarily reduce the time available for study.

18. Stinebrickner and Stinebrickner (2003) present evidence from a natural experiment at Berea College
that students who work more do worse academically. See Riggert et al. (2006) for a critical review
of the student employment literature. This review highlights the inherent difﬁculties in identifying
the causal role of student employment on collegiate outcomes.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

401

INCREASING TIME TO BACCALAUREATE DEGREE

One of the key parameters in estimating the effect of labor supply on time to
degree is the extent of crowd-out of school time for work time. Obtaining
credible estimates of this parameter is difﬁcult. However, as Stinebrickner
and Stinebrickner (2003) show using experimental data from Berea College,
reduced form relationships understate (in absolute value) the negative effect
of working time on school time. Thus we infer that the simple correlation
between time spent in school and hours of employment will provide a lower
bound on the extent of crowd-out.

We use the American Time Use Survey (ATUS) from 2003 to 2006, which
is linked to the CPS. The ATUS asks respondents about minutes worked
and minutes spent in school (both study time and class time) on the day
of the interview. We use interviews from Monday through Friday only, as
students may allocate their time differently on weekends, and we scale the
time measures to hours per ﬁve-day week. For the population of enrolled
students, we regress total amount of time spent on school on the total amount
of work time and ﬁnd a crowd-out on the order of −0.3.19 Using this estimate,
we measure the extent to which “effective time to degree” has changed, which
is measured as the amount of nonworking time (in months) that it takes
each individual to obtain a baccalaureate degree out of high school. For each
respondent, effective time to degree is calculated as

ttd e
i

= ttdi ∗ (1 − (hi /50) ∗ crowdout),

where crowdout is our ATUS estimate of 0.3. The variable h is hours per
week worked in the ﬁrst year after cohort graduation for NLS72 and NELS:88
respondents. In the above calculation, we assume the average student would
spend ﬁfty hours per week on schooling if she did not work. For example,
out of a ﬁfty-hour week, if a student works twenty hours, she then will have
(1 − (2/5)∗0.3) = 88 percent of her time for study. If we observe that it takes
this student ﬁve years to graduate, we calculate the effective time to degree as
(1 − 0.12) × 5 = 4.4 years.

We estimate an increase in “effective” time to degree from 4.31 to 4.46 years
for the full sample assuming a 0.3 crowd-out, suggesting that increases in time
working can explain 47.4 percent of the observed mean increase in time to
degree across samples of 0.32 years. For students beginning at public non–top
ﬁfty schools, effective time to degree increases by 0.28 years, which is 62.6
percent of the observed mean increase in time to degree in this sector. In the
community college sector, work increases explain 55.7 percent of the increase

19. See Bound, Lovenheim, and Turner (2010b), appendix table B.2, for regression estimates. These

estimates are qualitatively similar when we include weekend hours.

402

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

in mean time to degree. Thus, under plausible and conservative assumptions,
higher student labor supply can explain a large proportion of the observed
mean time to degree increase in our data.

If increased working hours increase time to degree in the less selective
public universities and two-year schools, why have they not also done so at
private colleges and the top ﬁfty public universities? While we do not have a
deﬁnitive answer to this question, we believe there are two plausible explana-
tions for the difference. First, the increases in work were off a smaller base
in these sectors.20 In addition, as discussed above, pricing structures differ
dramatically across sectors, with it being substantially more difﬁcult and ex-
pensive to increase the time to degree in the selective public and private sectors
than it is in the less selective public sector.

Consistent with the interpretation that increased student employment and
the associated extension in time to degree reﬂects constraints in the capacity to
ﬁnance college, we ﬁnd some evidence of a widening difference in time to de-
gree for students from above and below the median of the income distribution.
Rising tuition charges coupled with declines in the availability of federal ﬁnan-
cial aid lead to unambiguous increases in net cost for low-income students,
as little additional ﬁnancial aid is offered by public universities, particularly
outside the most selective few. Over time, as college costs have risen, families
as well as individual students have been expected to shoulder an increasingly
larger portion of the cost of college attendance.

Although our descriptive statistics and decomposition analysis lead to re-
jection of the hypothesis that family economic circumstances among college
graduates worsened, students in the 1992 cohort from below the median
family income level may have faced greater challenges in paying for college.
Figure 4 plots the distribution of time to degree, holding the distribution of
student achievement constant, for graduates above and below the median fam-
ily income in both cohorts. Overall and for students at the public institutions
outside the top ﬁfty, the gap in time to degree grows appreciably between
1972 and 1992 between below-median family income students and their peers
above the median. Notably, among students at public colleges outside the top
ﬁfty, the time path of BA completion across these family income levels was
similar for the 1972 cohort, with about 84 percent of eventual completers from
both income groups ﬁnishing in ﬁve years. For the 1992 cohort, however, a
substantial gap emerged in outcomes by socioeconomic circumstances, with

20. In the top ﬁfty sector, effective time to degree increased by 0.04 years, and it increased by 0.02 years
in the less selective private sector. In the highly selective privates, effective time to degree actually
declined. Thus increased labor supply affected degree length the most in the non–top ﬁfty public
and community college sectors.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

403

INCREASING TIME TO BACCALAUREATE DEGREE

–

p
u
w
o

l
l

o
f

h
t
r
u
o
F

.
y
e
v
r
u
s

e
h
t

d
e
d
u
c
n

s
t
h
g
e
w

–

p
u
w
o

l
l

o
f

h
t
f
ﬁ

e
h
t

g
n
s
u

e
d
a
m
e
r
e
w

s
n
o
i
t
a
u
c
a
c

2
7
S
L
N

.
n
o
i
t
u
t
i
t
s
n

f
o

e
p
y
T

d
n
a

e
m
o
c
n

y
l
i

m
a
F

y
b

e
e
r
g
e
D

o
t

e
m
T

e
r
u
g

404

e
r
a

s
e
p
m
a
s

8
8
S
L
E
N

d
n
a

2
7
S
L
N

e
h
T

.
s
n
o
i
t
a
u
b
a
t

e
h
t

d
e
d
u
c
n

e
r
a

s
p
u
w
o

–

l
l

o
f

e
s
e
h
t

g
n
i
t
a
p
c
i
t
r
a
p

e
s
o
h
t

y
l
n
O

.
s
n
o
i
t
a
u
c
l
a
c

y
e
v
r
u
s

8
8
:
S
L
E
N

e
h
t

r
o
f

d
e
s
u

e
r
e
w

s
t
h
g
e
w

o
o
h
c
s

h
g
h

t
r
o
h
o
C

.
n
o
i
t
a
u
d
a
r
g

o
o
h
c
s

h
g
h

t
r
o
h
o
c

f
o

s
r
a
e
y

t
h
g
e

n
h
t
i

w
h
s
n
ﬁ

o
h
w
d
n
a

n
o
i
t
a
u
d
a
r
g

o
o
h
c
s

h
g
h

t
r
o
h
o
c

f
o

s
r
a
e
y

o
w

n
h
t
i

w
e
g
e

l
l

o
c

d
n
e
t
t
a

o
h
w
e
s
o
h
t

o
t

d
e
t
c
i
r
t
s
e
r

e
p
m
a
s
2
7
S
L
N
e
h
t

0
0
0
5
1
$ n a h t r e t a e r g s a d e n ﬁ e d s i e m o c n i i n a d e M l . e p m a s 8 8 : S L E N e h t r o f 2 9 9 1 e n u J d n a l e p m a s 2 7 S L N e h t r o f 2 7 9 1 e n u J s a d e n ﬁ e d s i n o i t a u d a r g . s r a l l o d l i a n m o n n i l e p m a s 8 8 : S L E N e h t n i 0 0 0 , 0 5 $
n
a
h
t

r
e
t
a
e
r
g

s
a

d
n
a

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

75 percent of high-income degree recipients ﬁnishing in ﬁve years relative to
69 percent of low-income degree recipients.

6. DISCUSSION
The data are clear with respect to the growth in time to degree for BA recipients
over the past three decades. While we focus our analysis on the inter-cohort
comparison afforded by NLS72 and NELS:88, this ﬁnding is reinforced in other
data sets, including the CPS and the National Survey of College Graduates.
Furthermore, it is clear that the rise in time to degree is largely concentrated
among students beginning at non–top ﬁfty ranked public universities and
two-year colleges. Although we are constrained by limited exogenous variation
that would provide sharp identiﬁcation of causal mechanisms, we marshal
substantial proximate evidence for and against three main explanations for
the time to degree increases we observe.

First, we ﬁnd no evidence that changes in student background charac-
teristics or incoming academic preparation can explain these shifts. In fact,
changes in these observables go in the wrong direction to explain time to
degree increases.

Second, our analysis points to the importance of changes in resources on
the supply side of public higher education in explaining time to degree changes.
We present evidence that increases in student-faculty ratios can explain some
of the expansion in time to degree we document, particularly in the non–
top ﬁfty public sector. Furthermore, we ﬁnd that increases in cohort size
within some states led to declines in resources per student at non–top tier
public institutions—schools that could not ration access through selective
admissions. The resulting increased stratiﬁcation in per student resources
within the public sector led to substantial extension of time to degree for
students beginning college at non–top ﬁfty public four-year colleges compared
with only very modest increases for students at top-tier public universities.

Third, we argue that increased student labor supply in response to increases
in direct college costs, plausibly reﬂecting credit constraints that limit the
capacity of students to ﬁnance full-time attendance, is empirically relevant to
explaining increased time to degree. For many students, family economic cir-
cumstances have eroded relative to the cost of college, contributing to the need
to increase employment to cover a greater share of college costs. Consequently,
students in the more recent cohorts are working a signiﬁcantly higher number
of hours while they are in school. Although the magnitude of the effect of
increased employment on degree progress is hard to ascertain with precision,
the direction of the effect is unambiguous, and our calculations suggest that in-
creased working behavior alone can explain about half of the mean increase in
time to degree and almost two-thirds of the increase in the non–top ﬁfty sector.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

405

INCREASING TIME TO BACCALAUREATE DEGREE

The sum total of our evidence points strongly toward the central role of
declines in both personal and institutional resources available to students
in explaining the increases in time to baccalaureate degree in the United
States. That these increases are concentrated among students attending public
colleges and universities outside the most selective few suggests a need for
more attention to how these institutions adjust to budget constraints and
student demand and how students at these colleges ﬁnance higher education.
Moreover, the fact that students from below-median-income families have
experienced the largest increases in time to degree not only supports the
hypothesis that credit constraints limit the rate of collegiate attainment but
also points to substantial distributional consequences, as extended time to
degree has unambiguously large private costs.

While clear evidence in the United States and abroad indicates that the
rate of degree attainment responds to incentives in ﬁnancial aid and tuition
pricing,21 our analysis points to the need for careful consideration of whether
reducing students’ ﬁnancial burdens while enrolled in college would help
reduce time to degree. Our ﬁnding of increased stratiﬁcation in resources
among colleges and universities—both between public and private and within
the public sector—suggests that the attenuation of resources at less selective
public universities in particular limits the rate of degree attainment. To this
end, further work to understand how students, public funders, and colleges
assume the costs of increased time to degree is important to better understand
the social welfare implications of policies designed to reduce time to degree.

We would like to thank Paul Courant, Harry Holzer, Caroline Hoxby, Tom Kane,
and Jeff Smith for comments on an earlier draft of this article; Charlie Brown, John
DiNardo, and Justin McCrary for helpful discussions; and N. E. Barr for editorial
assistance. We also thank Jesse Gregory, Casey Cox, and Hannah Geiser for providing
helpful research support. We have beneﬁted from comments of seminar participants
at NBER, the Society of Labor Economics, the Harris School of Public Policy, the
Brookings Institution, Stanford University, and the University of Michigan. We would
like to acknowledge funding during various stages of this project from the National
Science Foundation, the National Institute of Child Health and Human Development,
the Andrew W. Mellon Foundation, and the Searle Freedom Trust. Much of this
work was completed while Bound was a fellow at the Center for Advanced Study in the
Behavioral Sciences and Lovenheim was a fellow at the Stanford Institute for Economic
Policy Research.

21. Scott-Clayton (2011) presents evidence of increases in four-year degree completion among students
receiving a West Virginia scholarship contingent on completion of a full course load. Garibaldi et al.
(2012) also show that students facing higher tuition are more likely to ﬁnish in four years using
tuition discontinuities at Bocconi University in Italy.

406

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

REFERENCES
Adelman, Clifford. 2004. Principal indicators of student academic histories in postsecondary
education, 1972–2000. Washington, DC: U.S. Department of Education.

Adelman, Clifford. 2006. The toolbox revisited: Paths to degree completion from high school
through college. Washington, DC: U.S. Department of Education.

Autor, David H., Lawrence F. Katz, and Melissa S. Kearney. 2008. Trends in U.S. wage
inequality: Revising the revisionists. Review of Economics and Statistics 90(2): 300–23.

Barsky, Robert, John Bound, Kerwin Koﬁ Charles, and Joseph P. Lupton. 2002. Ac-
counting for the black-white wealth gap: A nonparametric approach. Journal of the
American Statistical Association 97(459): 663–73.

Becker, Gary, and Nigel Tomes. 1979. An equilibrium theory of the distribution of
income and intergenerational mobility. Journal of Political Economy 87(6): 1153–89.

Belley, Philippe, and Lance Lochner. 2007. The changing role of family income and
ability in determining educational achievement. Journal of Human Capital 1(1): 37–89.

Black, Daniel A., and Jeffrey A. Smith. 2006. Estimating the returns to college quality
with multiple proxies for quality. Journal of Labor Economics 24(3): 701–28.

Bound, John, Michael Lovenheim, and Sarah Turner. 2010a. Why have college com-
pletion rates declined? An analysis of changing student preparation and collegiate
resources. American Economic Journal: Applied Economics 2(3): 1–31.

Bound, John, Michael Lovenheim, and Sarah Turner. 2010b. Increasing time to bac-
calaureate degree in the United States. NBER Working Paper No. 15892.

Bound, John, and Sarah Turner. 2007. Cohort crowding: How resources affect colle-
giate attainment. Journal of Public Economics 91(5–6): 877–99.

Bowen, William G., Matthew W. Chingos, and Michael S. McPherson. 2009. Crossing
the line: Completing college at America’s public universities. Princeton, NJ: Princeton
University Press.

Bradburn, Ellen M., Rachel Berger, Xiaojie Li, Katharin Peter, and Kathryn Rooney.
2003. A descriptive summary of 1999–2000 bachelor’s degree recipients 1 year later, with
an analysis of time to degree. Washington, DC: U.S. Department of Education, National
Center for Education Statistics.

Brown, Meta, John Karl Scholz, and Ananth Seshadri. 2012. A new test of borrowing
constraints for education. Review of Economic Studies 79(2): 511–38.

Deming, David, and Susan Dynarski. 2008. The lengthening of childhood. Journal of
Economic Perspectives 22(3): 71–92.

DesJardins, Stephen L., Dennis A. Ahlberg, and Brian P. McCall. 2002. A temporal
investigation of factors related to timely degree completion. Journal of Higher Education
73(5): 555–81.

DesJardins, Stephen L., Dennis A. Ahlberg, and Brian P. McCall. 2006. The effect of
interrupted enrollment on graduation from college: Racial, income and ability differ-
ences. Economics of Education Review 25(6): 575–90.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

407

INCREASING TIME TO BACCALAUREATE DEGREE

DiNardo, John, Nicole M. Fortin, and Thomas Lemieux. 1996. Labor market institutions
and the distribution of wages: 1973–1993, a semi-parametric approach. Econometrica
64(5): 1001–44.

Ehrenberg, Ronald G., and Douglas A. Webber. 2010. Do expenditures other than
instructional expenditures affect graduation and persistence rates in American higher
education? Economics of Education Review 29(6): 947–58.

Ellwood, David, and Thomas Kane. 2000. Who is getting a college education? Family
background and the growing gaps in enrollment. In Securing the future, edited by
Sheldon Danziger and Jane Waldfogel, pp. 283–64. New York: Russell Sage.

Fitzpatrick, Maria D., and Sarah E. Turner. 2007. Blurring the boundary: Changes in
collegiate participation and the transition to adulthood. In The price of independence,
edited by Sheldon Danziger and Cecilia E. Rouse, pp. 107–38. New York: Russell Sage.

Flores-Lagunes, Alfonso, and Audrey Light. 2010. Interpreting degree effects in the
returns to education. Journal of Human Resources 45(2): 439–67.

Garibaldi, Pietro, Francesco Giavazzi, Andrea Ichino, and Enrico Rettore. 2012. College
cost and time to complete a degree: Evidence from tuition discontinuities. Review of
Economics and Statistics 94(3): 699–711.

Goldrick-Rab, Sara. 2006. Following their every move: An investigation of social-class
differences in college transfer. Sociology of Education 79(1): 61–79.

Goldrick-Rab, Sara, and Fabian T. Pfeffer. 2009. Beyond access: Explaining sociological
differences in college transfer. Sociology of Education 82(2): 101–25.

Horn, Laura, Paula R. Knepper, and Alexander C. McCormick. 1996. A descriptive
summary of 1992–93 bachelor’s degree recipients: One year later, with an essay on
time to degree. Washington, DC: U.S. Department of Education, National Center for
Education Statistics.

Hoxby, Caroline. 1997. How the changing market structure of U.S. higher education
explains college tuition. NBER Working Paper No. 6323.

Hoxby, Caroline. 2009. The changing selectivity of American colleges. Journal of Eco-
nomic Perspectives 23(4): 95–118.

Ishitani, Terry T. 2006. Studying attrition and degree completion behavior among
ﬁrst-generation college students in the United States. Journal of Higher Education 77(5):
861–85.

Kane, Thomas, Peter Orszag, and David Gunter. 2003. State ﬁscal constraints and
higher education spending: The role of Medicaid and the business cycle. Urban-
Brookings Tax Policy Center Discussion Paper No. 11.

Keane, Michael, and Kenneth Wolpin. 2001. The effect of parental transfers and bor-
rowing constraints on educational attainment. International Economic Review 42(4):
1051–103.

Light, Audrey. 2001. In-school work experience and the returns to schooling. Journal
of Labor Economics 19(1): 65–93.

408

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

Lovenheim, Michael. 2011. The effect of liquid housing wealth on college enrollment.
Journal of Labor Economics 29(4): 741–71.

McCormick, Alexander C. 2003. Swirling and double-dipping: New patterns of stu-
dent attendance and their implications for higher education. New Directions in Higher
Education 2003(121): 13–24.

National Center for Education Statistics (NCES). 2006. Table 129. SAT score averages
of college-bound seniors, by state or jurisdiction: Selected years, 1987–88 through
2004–05. Digest of education statistics 2005. Washington, DC: U.S. Department of
Education.

Rampey, Bobby D., Gloria S. Dion, and Patricia L. Donahue. 2009. NAEP 2008 trends in
academic progress. NCES 2009-479. Washington, DC: U.S. Department of Education.

Riggert, Steven C., Mike Boyle, Joseph M. Petrosko, Daniel Ash, and Carolyn Rude-
Parkins. 2006. Student employment and higher education: Empiricism and contradic-
tion. Review of Educational Research 76(1): 63–92.

Royston, Patrick. 2004. Multiple imputation of missing values. Stata Journal 4(3):
227–41.

Scott-Clayton, Judith. 2011. On money and motivation: A quasi-experimental analysis
of ﬁnancial incentives for college achievement. Journal of Human Resources 46(3): 614–
46.

Scott-Clayton, Judith. 2012. What explains rising labor supply among U.S. undergrad-
uates? National Tax Journal 65(1): 181–210.

Stange, Kevin. 2012. Ability sorting and the importance of college quality to student
achievement: Evidence from community colleges. Education Finance and Policy 7(1):
74–105.

Stern, David, and Yoshi-Fumi Nakata. 1991. Paid employment among U.S. college
students: Trends, effects and possible causes. Journal of Higher Education 62(1): 25–
43.

Stinebrickner, Ralph, and Todd Stinebrickner. 2003. Working during school and aca-
demic performance. Journal of Labor Economics 21(2): 449–72.

Turner, Sarah. 2004. Going to college and ﬁnishing college: Explaining different ed-
ucational outcomes. In College choices: The economics of where to go, and how to pay for
it, edited by Caroline Hoxby, pp. 13–62. Chicago, IL: University of Chicago Press for
NBER.

U.S. News and World Report. 2005. America’s best colleges and universities. U.S. News
and World Report, 29 August.

Van Buuren, Stef, Hendriek C. Boshuizen, and Dick L. Knook. 1999. Multiple impu-
tation of missing blood pressure covariates in survival analysis. Statistics in Medicine
18(6): 681–94.

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

409

INCREASING TIME TO BACCALAUREATE DEGREE

APPENDIX A: TECHNICAL APPENDIX
1. NLS72 AND NELS:88 DATA
Time to Degree and Degree Completion

Time to degree and degree completion are calculated using NLS72 and
NELS:88 survey responses from the ﬁrst through ﬁfth follow-ups in NLS72
and the fourth follow-up in NELS:88. The NLS72 study participants were se-
niors in high school in the spring of 1972. Following the base year interview,
participant follow-up surveys were administered in 1973, 1974, 1976, 1979,
and 1986 (for a subsample), with questions covering collegiate participation
and degree attainment. In addition, the Department of Education collected
detailed high school records and postsecondary transcripts.

The NELS:88 survey started with students who were in the eighth grade
in 1988 (high school class of 1992) and conducted follow-up surveys with
participants in 1990, 1992, 1994, and 2000. Similar to the NLS72 sur-
vey, NELS:88 contains high school records and collegiate transcripts as
well as a host of background information that may be relevant to time to
degree.

Although degrees can be awarded throughout a year, we calculate time
to degree as the number of months between high school cohort gradua-
tion and the month of BA receipt. Cohort high school graduation is de-
ﬁned as June 1972 for the NLS72 sample and June 1992 for the NELS:88
sample.

Because the NELS:88 survey is composed of eighth graders from 1988 and
the NLS72 survey follows twelfth graders from the class of 1972, the NELS:88
survey contains more students who graduate high school after their cohort’s
high school graduation. In our base sample, 1.3 percent of respondents in
NLS72 and 4.4 percent of respondents in NELS:88 ﬁnish high school after
June of their respective cohort graduation year. However, looking only at
eight-year BA recipients, 0.3 percent and 0.6 percent, respectively, in NLS72
and NELS:88 did not ﬁnish high school on time. It therefore is unlikely that
the larger preponderance of late high school graduates in the NELS:88 survey
biases our time to degree calculations.

Table A.1 contains variable names and deﬁnitions used to deﬁne the sample
and to calculate time to degree and degree completion in both the NLS72 and
NELS:88 surveys.

School Type and Collegiate Start Dates

We deﬁne enrollment as those who start at an academic institution within
two years of cohort high school graduation. Academic institutions are all
four-year schools and public two-year schools. We exclude private two-year

410

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

Table A.1. Variable Names and Deﬁnitions for Calculation of Time to Degree and Degree Completion in
NLS72 and NELS:88

Variable Name

Variable Deﬁnition

Follow-Up

Panel A: NLS72

Fq2

Edatt86

Fq3b

Fq3a

Tq48ea

Tq48eb

Tq48ec

Ft76ea

Ft76eb

Ft76ec

High school completion dummy

Educational attainment as of 1986

High school graduation year

High school graduation month

BA completion dummy as of 10/1/1976

Month BA received as of third follow-up

Year BA received as of third follow-up

BA completion as of fourth follow-up

Month BA received as of fourth follow-up

Year BA received as of fourth follow-up

Fi19b1ey–Fi19b4ey

Year ended most recent school attended, ﬁrst through

fourth time

Fi19b1em–Fi19b4em

Month ended most recent school attended, ﬁrst through

fourth time

Fi19h

Fi19i

Course of study in most recent school attended

Completed requirements in most recent school attended

Fi20b1ey–Fi20b4ey

Year ended second most recent school attended,

ﬁrst through fourth time

Fi20b1em–Fi20b4em

Month ended second most recent school attended,

ﬁrst through fourth time

Fi19h

Fi19i

Course of study in second most recent school attended

Completed requirements in second most recent school attended

Panel B: NELS:88

1–5

Variable Name

Variable Deﬁnition

Follow-Up

F4hsgradt

High school graduation date

F4ed1

F4edgr1

F4ed2

F4edgr2

F4ed3

F4edgr3

F4ed4

F4edgr4

F4ed5

F4edgr5

F4ed6

F4edgr6

Degree receipt date–ﬁrst degree received

Degree type received–ﬁrst degree

Degree receipt date–second degree received

Degree type received–second degree

Degree receipt date–third degree received

Degree type received–third degree

Degree receipt date–fourth degree received

Degree type received–fourth degree

Degree receipt date–ﬁfth degree received

Degree type received–ﬁfth degree

Degree receipt date–sixth degree received

Degree type received–sixth degree

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

411

INCREASING TIME TO BACCALAUREATE DEGREE

schools because they typically are not oriented toward allowing students to
obtain a BA after graduation.

College transcript data and self-reported enrollment records from the ﬁrst
through fourth follow-up surveys for the NLS72 survey and from NCES-
aggregated responses in the NELS:88 survey are used to deﬁne the type of
institution of initial collegiate enrollment. We use the transcript for the ﬁrst
post–high school institution attended by respondents in the transcript ﬁles to
assign ﬁrst institution attended for most respondents. In the cases in which
there are multiple ﬁrst transcripts from different institutions on the same
date, we assign each student to the school at which she took the most credits
during the ﬁrst semester. Some students report attending college within two
years of their cohort’s high school graduation but do not have any transcripts.
In NLS72, 6.8 percent of the sample reporting attendance do not have tran-
scripts, and in NELS:88, 8.2 percent of the sample falls into this category. For
these respondents, we use the ﬁrst institution reported by them in the survey
ﬁles.

In the NLS72 survey, we begin by determining the year in which a stu-
dent ﬁrst enrolls in an academic postsecondary institution, where academic
is deﬁned as granting at least an associate’s degree or BA. In each follow-up,
students were asked about colleges they attended (up to three) in each year
since the previous survey. The ﬁrst college attended is identiﬁed from the en-
try the ﬁrst time a student reports attending an academic institution, and we
record the institutional identiﬁer (FICE code) either directly from transcript
ﬁles or from the student survey responses about which institution he or she
attended. We then merge institutional-level information that contains pub-
lic/private status, two-year/four-year identiﬁers, and collegiate rankings and
classify the respondent’s initial institution accordingly.

In the NELS:88 survey, we use a similar methodology to identify each re-
spondent’s initial institution. The NCES has constructed variables that identify
ﬁrst institution attended in the transcript ﬁles (the ref variables). We use the
transcript-based NCES-constructed institutional identiﬁer (unitid) code when
it is available. For those who report college attendance and the sector of ﬁrst
attendance but are not assigned a transcript-based ﬁrst institution identiﬁer
by NCES, we use the NCES-constructed variables that report individual enroll-
ment histories from the survey data that identify ﬁrst institution of enrollment
(unitid) and ﬁrst institution type (f4efsect).

For students with postsecondary experience preceding high school gradu-
ation, we use the ﬁrst start date and institution after high school graduation
taken from the postsecondary transcript ﬁles. For all other students in the
NELS:88 survey, ﬁrst start date is identiﬁed by f4efmy, which is the NCES-
constructed date of ﬁrst postsecondary attendance.

412

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

A list of the top ﬁfty public schools from the 2005 U.S. News and World
Report rankings as well as the top sixty-ﬁve private schools and the top ﬁfty
liberal arts colleges plus the U.S. Armed Services Academies, which constitute
the highly selective private schools, is shown in table A.2.

Background Characteristics

Math and Reading Tests

In both surveys, tests of academic achievement were administered to students
in the senior year. The NLS72 exam was administered as a sixty-nine-minute
test book with sections on vocabulary, picture numbers (associative memory),
reading, letter groups, mathematics, and mosaic comparisons. Each section
was ﬁfteen minutes (except for the mosaic comparison, which was nine min-
utes). We use the reported scaled math score (scmatsc) test score measure in
NLS72.

The NELS:88 cognitive test batteries were administered in each of the ﬁrst
three waves, with sections on reading, math, science, and social studies. The
tests were eighty-ﬁve minutes and consisted of 116 questions, 40 of which
were on math and 21 of which were on reading comprehension. Unlike the
NLS72 exams, the NELS:88 tests covered more material and tested more skills.
Further, because the NELS:88 tests were given in subsequent waves, students
were given harder or easier tests in the ﬁrst and second follow-ups, depending
on their scores in the previous wave, to guard against ﬂoor and ceiling effects.
We use the math and reading item response theory (IRT) theta scores (f22xmth
and f22xrd) from the second follow-up as the base measure of test scores. These
scores are psychometric evaluation scores of each student’s ability that account
for the difﬁculty of the exam.

Because the tests in NLS72 and NELS:88 covered different subject matter,
were of different lengths, and were graded on different scales, the scores are
not directly comparable across surveys. Instead, we construct the percentile of
the score distribution for each survey among all high school graduates on each
exam. The comparison of students in the same test percentile across surveys
is based on the assumption that overall achievement did not change over this
time period. This assumption is supported by the observation that there is
little change in the overall level of test scores on the nationally representative
NAEP over our period of observation. Similarly, examination of time trends
in standard college entrance exams such as the SAT provides little support for
the proposition that achievement declined appreciably over the interval. For
the SAT, the ratio of test takers to high school graduates increased from 33
percent to 42 percent, while mean math scores declined from 509 to 501 over
the 1972–92 interval (NCES 2006).

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

413

INCREASING TIME TO BACCALAUREATE DEGREE

s
l
o
o
h
c
S

e
t
a
v
i
r
P
e
v
i
t
c
e
e
S

y
l
h
g
H

s
t
r
A

a
r
e
b
i
L

0
5

p
o
T

s
l
o
o
h
c
S

e
t
a
v
i
r
P
5
6

p
o
T

s
l
o
o
h
c
S

i
l

b
u
P
0
5

p
o
T

s
g
n
k
n
a
R

t
r
o
p
e
R
d
l
r
o

W
d
n
a

s
w
e
N

S
U
5
0
0
2

e
h
t

m
o
r
f

s
e
g
e

l
l

o
C
s
t
r
A

a
r
e
b
L

0
5

p
o
T

d
n
a

,
s
o
o
h
c
S
e
t
a
v
i
r
P
5
6

p
o
T

,
s
o
o
h
c
S
c
i
l

b
u
P

0
5

p
o
T

2
A
e
b
a
T

414

e
g
e

l
l

o
C
e
r
o
m
h
t
r
a
w
S

e
g
e

l
l

o
C
y
r
u
b
e
d
d
M

e
g
e

l
l

o
C
a
n
o
m
o
P

e
g
e

l
l

o
C
n
o
d
w
o
B

e
g
e

l
l

o
C
n
o
t
e
l
r
a
C

e
g
e

l
l

o
C
n
o
s
d
i
v
a
D

e
g
e

l
l

o
C
d
r
o
f
r
e
v
a
H

a
n
n
e
K
c
M

–
t
n
o
m
e
r
a
C

y
t
i
s
r
e
v
i
n
U
n
a
y
e
s
e
W

e
g
e

l
l

o
C
y
e
s
e

l
l

e
W

e
g
e

l
l

o
C

l
l

e
n
n
i
r

e
g
e

l
l

o
C
d
d
u
M
y
e
v
r
a
H

e
e
L

d
n
a

n
o
t
g
n
h
s
a
W

e
g
e

l
l

o
C
r
a
s
s
a
V

e
g
e

l
l

o
C
n
o
t
l
i

m
a
H

y
t
i
s
r
e
v
i
n
U
e
t
a
g
o
C

e
g
e

l
l

o
C
n

i
l
r
e
b
O

e
g
e

l
l

o
C
y
b
o
C

e
g
e

l
l

o
C
r

w
a
M
n
y
r
B

e
g
e

l
l

o
C
s
e
t
a
B

e
g
e

l
l

o
C
o
d
a
r
o
o
C

e
g
e

l
l

o
C
r
e
t
s
e
a
c
a
M

e
g
e

l
l

o
C
s
p
p
i
r
c
S

e
g
e

l
l

o
C
h
t
i

m
S

e
g
e

l
l

o
C
t
s
r
e
h
m
A

e
g
e

l
l

o
C
s
m
a

i
l
l
i

y
t
i
s
r
e
v
i
n
U
n
a
i
t
s
i
r
h
C
s
a
x
e
T

a
s
u
T

f
o

y
t
i
s
r
e
v
i
n
U

n
o
t
y
a
D

f
o

y
t
i
s
r
e
v
i
n
U

e
x
e
r
D

y
g
o
o
n
h
c
e
T

f
o

e
t
u
t
i
t
s
n

s
o
n

i
l
l
I

o
g
e
D
n
a
S

f
o

y
t
i
s
r
e
v
i
n
U

y
t
i
s
r
e
v
i
n
U
c
i
l

o
h
t
a
C

y
t
i
s
r
e
v
i
n
U
a
o
y
o
L

c
ﬁ
i
c
a
P

e
h
t

f
o

y
t
i
s
r
e
v
i
n
U

o
c
s
i
c
n
a
r
F

n
a
S

f
o

.
v
i
n
U

o
o
h
c
S
w
e
N

y
t
i
s
r
e
v
i
n
U
n
r
e
t
s
a
e
h
t
r
o
N

y
t
i
s
r
e
v
i
n
U

l
l

a
H
n
o
t
e
S

s
a
m
o
h
T

.
t
S

f
o

y
t
i
s
r
e
v
i
n
U

e
g
e

l
l

o
C
h
t
u
o
m

t
r
a
D

y
t
i
s
r
e
v
i
n
U
a
b
m
u
o
C

.
h
c
e
T

f
o

e
t
u
t
i
t
s
n

a
n
r
o
f
i
l

a
C

a
n
a
v
l
y
s
n
n
e
P

f
o

y
t
i
s
r
e
v
i
n
U

y
t
i
s
r
e
v
i
n
U
n
o
t
e
c
n
i
r
P

y
t
i
s
r
e
v
i
n
U
d
r
a
v
r
a
H

y
t
i
s
r
e
v
i
n
U
e
a
Y

y
t
i
s
r
e
v
i
n
U
d
r
o
f
n
a
t
S

y
t
i
s
r
e
v
i
n
U
e
k
u
D

T
I
M

l
l
i

s
e
e
g
n
A

r
o
b
r
A

n
n
A
–
n
a
g
h
c
M

a
n
g
r
i
V

s
o
L
–
a
n
r
o
f
i
l

a
C

y
e
e
k
r
e
B
–
a
n
r
o
f
i
l

a
C

e
p
a
h
C
–
a
n

i
l

o
r
a
C
h
t
r
o
N

f
o

y
t
i
s
r
e
v
i
n
U

f
o

y
t
i
s
r
e
v
i
n
U

f
o

y
t
i
s
r
e
v
i
n
U

f
o

y
t
i
s
r
e
v
i
n
U

f
o

y
t
i
s
r
e
v
i
n
U

n
o
s
d
a
M
–
n
s
n
o
c
s
W

o
g
e
D
n
a
S
–
a
n
r
o
f
i
l

a
C

s
o
n

i
l
l
I

f
o

y
t
i
s
r
e
v
i
n
U

f
o

y
t
i
s
r
e
v
i
n
U

f
o

y
t
i
s
r
e
v
i
n
U

y
g
o
o
n
h
c
e
T

f
o

e
t
u
t
i
t
s
n

a
g
r
o
e
G

y
r
a
M
d
n
a
m
a

i
l
l
i

f
o

e
g
e

l
l

o
C

s
u
o
L

.
t
S

f
o

.
v
i
n
U
n
o
t
g
n
h
s
a
W

y
t
i
s
r
e
v
i
n
U
n
r
e
t
s
e
w
h
t
r
o
N

y
t
i
s
r
e
v
i
n
U
s
n
k
p
o
H
s
n
h
o
J

o
g
a
c
i
h
C

f
o

y
t
i
s
r
e
v
i
n
U

y
t
i
s
r
e
v
i
n
U
e
m
a
D
e
r
t
o
N

y
t
i
s
r
e
v
i
n
U

t
l
i

b
r
e
d
n
a
V

y
t
i
s
r
e
v
i
n
U
y
r
o
m
E

y
t
i
s
r
e
v
i
n
U
e
c
i
R

y
t
i
s
r
e
v
i
n
U
n
w
o
r
B

y
t
i
s
r
e
v
i
n
U

l
l

e
n
r
o
C

y
t
i
s
r
e
v
i
n
U
n
o

l
l

e
M
e
g
e
n
r
a
C

a
n
r
o
f
i
l

a
C
n
r
e
h
t
u
o
S

f
o

.
v
i
n
U

y
t
i
s
r
e
v
i
n
U
n
w
o
t
e
g
r
o
e
G

y
t
i
s
r
e
v
i
n
U

t
s
e
r
o
F

e
k
a
W

y
t
i
s
r
e
v
i
n
U
s
t
f
u
T

a
r
a
b
r
a
B
a
t
n
a
S
–
a
n
r
o
f
i
l

a
C

s
i
v
a
D
–
a
n
r
o
f
i
l

a
C

e
n
i
v
r
I
–
a
n
r
o
f
i
l

a
C

f
o

y
t
i
s
r
e
v
i
n
U

f
o

y
t
i
s
r
e
v
i
n
U

f
o

y
t
i
s
r
e
v
i
n
U

y
t
i
s
r
e
v
i
n
U
e
t
a
t
S
a
n
a
v
l
y
s
n
n
e
P

n
i
t
s
u
A
–
s
a
x
e
T

f
o

y
t
i
s
r
e
v
i
n
U

n
o
t
g
n
h
s
a
W

f
o

y
t
i
s
r
e
v
i
n
U

a
d
i
r
o
F

f
o

y
t
i
s
r
e
v
i
n
U

k
r
a
P

e
g
e

l
l

o
C
–
d
n
a
l
y
r
a
M

f
o

y
t
i
s
r
e
v
i
n
U

k
c
i
w
s
n
u
r
B
w
e
N
–
y
t
i
s
r
e
v
i
n
U
s
r
e
g
t
u
R

a
g
r
o
e
G

f
o

y
t
i
s
r
e
v
i
n
U

a
w
o

f
o

y
t
i
s
r
e
v
i
n
U

)
o
h
O

(

y
t
i
s
r
e
v
i
n
U

m
a
M

y
t
i
s
r
e
v
i
n
U
e
t
a
t
S
o
h
O

y
t
i
s
r
e
v
i
n
U
e
u
d
r
u
P

n
o
i
t
a
t
S
e
g
e

l
l

o
C
–
M
&
A

s
a
x
e
T

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

y
t
i
s
r
e
v
i
n
U
s
e
d
n
a
r
B

t
u
c
i
t
c
e
n
n
o
C

f
o

y
t
i
s
r
e
v
i
n
U

John Bound, Michael F. Lovenheim, and Sarah Turner

s
s
o
r
C
y
l
o
H
e
h
t

f
o

e
g
e

l
l

o
C

e
g
e

l
l

o
C
e
k
o
y
l
o
H

.
t

y
t
i
s
r
e
v
i
n
U

l
l

e
n
k
c
u
B

e
g
e

l
l

o
C
d
r
a
n
r
a
B

e
g
e

l
l

o
C
n
o
y
n
e
K

e
g
e

l
l

o
C

a
t
n
e
d
i
c
c
O

e
g
e

l
l

o
C
e
t
t
e
y
a
f
a
L

y
t
i
s
r
e
v
i
n
U
n
a
m
r
u
F

e
g
e

l
l

o
C
d
r
a
B

e
g
e

l
l

o
C
n
a
m

t
i
h
W

e
g
e

l
l

o
C
y
t
i
n
i
r
T

e
g
e

l
l

o
C
n
o
n
U

d
n
o
m
h
c
i
R

f
o

y
t
i
s
r
e
v
i
n
U

e
g
e

l
l

o
C
e
e
n
a
w
e
S

e
g
e

l
l

o
C
t
u
c
i
t
c
e
n
n
o
C

l
l

a
h
s
r
a
M
d
n
a

i
l

k
n
a
r
F

e
g
e

l
l

o
C
n
o
s
n
k
c
i
D

e
g
e

l
l

o
C
e
r
o
m
d
k
S

e
g
e

l
l

o
C
g
r
u
b
s
y
t
t
e
G

y
t
i
s
r
e
v
i
n
U
w
u
a
P
e
D

e
g
e

l
l

o
C
s
e
d
o
h
R

e
g
e

l
l

o
C
r
e
z
t
i
P

e
g
e

l
l

o
C
d
e
e
R

e
g
e

l
l

o
C
e
r
t
n
e
C

e
v
r
e
s
e
R
n
r
e
t
s
e
W
e
s
a
C

y
t
i
s
r
e
v
i
n
U
k
r
o
Y
w
e
N

e
g
e

l
l

o
C
n
o
t
s
o
B

c
i
n
h
c
e
t
y
l
o
P

r
e
a
e
s
s
n
e
R

y
t
i
s
r
e
v
i
n
U
a
v
i
h
s
e
Y

.
v
i
n
U
n
o
t
g
n
h
s
a
W
e
g
r
o
e
G

y
t
i
s
r
e
v
i
n
U
e
n
d
r
e
p
p
e
P

y
t
i
s
r
e
v
i
n
U
e
s
u
c
a
r
y
S

c
i
n
h
c
e
t
y
l
o
P

r
e
t
s
e
c
r
o
W

y
t
i
s
r
e
v
i
n
U
n
o
t
s
o
B

r
e
t
s
e
h
c
o
R

f
o

.
v
i
n
U

y
t
i
s
r
e
v
i
n
U
h
g
h
e
L

y
t
i
s
r
e
v
i
n
U
e
n
a
u
T

s
e
i
t
i
C
n
w
T
–
a
t
o
s
e
n
n
M

f
o

y
t
i
s
r
e
v
i
n
U

h
g
r
u
b
s
t
t
i
P

f
o

y
t
i
s
r
e
v
i
n
U

e
r
a
w
a
e
D

f
o

y
t
i
s
r
e
v
i
n
U

z
u
r
C
a
t
n
a
S
–
a
n
r
o
f
i
l

a
C

r
e
d
u
o
B
–
o
d
a
r
o
o
C

f
o

y
t
i
s
r
e
v
i
n
U

f
o

y
t
i
s
r
e
v
i
n
U

e
d
s
r
e
v
i
R
–
a
n
r
o
f
i
l

a
C

f
o

y
t
i
s
r
e
v
i
n
U

y
t
i
s
r
e
v
i
n
U
e
t
a
t
S
a
w
o

.
h
c
e
T

a
n
g
r
i
V

y
t
i
s
r
e
v
i
n
U
e
t
a
t
S
n
a
g
h
c
M

n
o
t
m
a
h
g
n
B
t
a

Y
N
U
S

y
t
i
s
r
e
v
i
n
U
n
o
s
m
e
C

y
t
i
s
r
e
v
i
n
U
a
n
a
d
n

y
t
i
s
r
e
v
i
n
U
e
t
a
t
S
a
n

i
l

o
r
a
C
h
t
r
o
N

.
v
i
n
U

t
s
d
o
h
t
e
M
n
r
e
h
t
u
o
S

y
t
i
s
r
e
v
i
n
U
g
n
u
o
Y
m
a
h
g
i
r
B

y
t
i
s
r
e
v
i
n
U
m
a
h
d
r
o
F

y
t
i
s
r
e
v
i
n
U
k
r
a
C

y
g
o
o
n
h
c
e
T

f
o

.
t
s
n

s
n
e
v
e
t
S

y
t
i
s
r
e
v
i
n
U
s
u
o
L

.
t
S

y
t
i
s
r
e
v
i
n
U

r
o
l
y
a
B

y
t
i
s
r
e
v
i
n
U
n
a
c
i
r
e
m
A

y
t
i
s
r
e
v
i
n
U
d
r
a
w
o
H

y
t
i
s
r
e
v
i
n
U
e
t
t
e
u
q
r
a
M

r
e
v
n
e
D

f
o

y
t
i
s
r
e
v
i
n
U

l
l
i
v
x
o
n
K
–
e
e
s
s
e
n
n
e
T

f
o

y
t
i
s
r
e
v
i
n
U

s
a
s
n
a
K

f
o

y
t
i
s
r
e
v
i
n
U

y
t
i
s
r
e
v
i
n
U
n
r
u
b
u
A

t
n
o
m
r
e
V

f
o

y
t
i
s
r
e
v
i
n
U

a
n
o
z
i
r
A

f
o

y
t
i
s
r
e
v
i
n
U

y
t
i
s
r
e
v
i
n
U
o
h
O

t
s
r
e
h
m
A
–
s
t
t
e
s
u
h
c
a
s
s
a
M

f
o

y
t
i
s
r
e
v
i
n
U

a
b
m
u
o
C
–
i
r
u
o
s
s
M

f
o

y
t
i
s
r
e
v
i
n
U

n
o
c
n
L
–
a
k
s
a
r
b
e
N

f
o

y
t
i
s
r
e
v
i
n
U

e
r
i
h
s
p
m
a
H
w
e
N

f
o

y
t
i
s
r
e
v
i
n
U

m
a
M

f
o

y
t
i
s
r
e
v
i
n
U

a
m
a
b
a
A

f
o

y
t
i
s
r
e
v
i
n
U

d
e
t
s

i
l

e
r
a

s
o
o
h
c
s

e
s
a
c

h
c
i
h
w

,
s
e
i
t

y
n
a
m

e
d
u
c
n

s
g
n
k
n
a
r

e
h
T

.
g
n
k
n
a
r

t
r
o
p
e
R

d
l
r
o
W

d
n
a

s
w
e
N

S
U

e
h
t

r
a
e
p
p
a

y
e
h
t

r
e
d
r
o

e
h
t

d
e
t
s

i
l

e
r
a

s
o
o
h
c
S

:
s
e
t
o
N

d
e
m
r
A

S
U

r
u
o
f

e
h
t

s
e
d
u
l
c
n

o
s
a

y
r
o
g
e
t
a
c

o
o
h
c
s

e
t
a
v
i
r
p

e
v
i
t
c
e
e
s

y
l
h
g
h

e
h
T

.
r
e
n
n
a
m
e
m
a
s

e
h
t

k
n
a
r

n
h
t
i

s
o
o
h
c
s

s
t
s

i
l

e
b
a
t

s
h
T

.
k
n
a
r

n
h
t
i

y
l
l

a
c
i
t
e
b
a
h
p
a

.
y
m
e
d
a
c
A

d
r
a
u
G

t
s
a
o
C

S
U
d
n
a

,
t
n
o
P

t
s
e
W

t
a

y
m
e
d
a
c
A

y
r
a
t
i
l
i

S
U

,
y
m
e
d
a
c
A

e
c
r
o
F

r
i
A

S
U

,
y
m
e
d
a
c
A

a
v
a
N

S
U

:
s
e
m
e
d
a
c
A

s
e
c

i
v
r
e
S

.
s
e
t
a
t
S
d
e
t
i
n
U
e
h
t

s
e
i
t
i
s
r
e
v
i
n
u

d
n
a

s
e
g
e

l
l

o
c

f
o

s
g
n
k
n
a
r

t
r
o
p
e
R
d
l
r
o
W
d
n
a

s
w
e
N

S
U
5
0
0
2
:
e
c
r
u
o
S

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

415

INCREASING TIME TO BACCALAUREATE DEGREE

In the multiple imputation of missing variables in the NELS:88 survey,
we use IRT theta test scores from the ﬁrst follow-up for math and reading
(f12xmth and f12xrd) and from the base year for math and reading (by2xmth
and by2xrd). The NCES scales the IRT theta scores to a common metric across
years. The imputed math and reading test scores from the senior year in each
survey are used to construct the test percentiles used in the main analysis.

High School GPA

In the NLS72 survey, the NCES provides a measure of the high school GPA:
imptaver. This variable is constructed by the NCES using high school tran-
scripts and is on a 1–13 scale.

In NELS:88, we use the F2rgpa variable, which is the NCES-constructed

measure of high school GPA as of the last year of high school attended.

Because these GPA variables are on different scales and are potentially
calculated in different ways, we calculate the quartile of the high school GPA
for each student in the data, separately for each sample. These quartiles are
constructed using the full sample, not just the sample of college completers.

Parental Education

We obtain student-reported measures of father’s and mother’s education sep-
arately. In the NLS72 survey, we have three different measures of this variable.
For mother’s education we use the variables cmoed, bq90b, and fq78b. For
father’s education we use the variables cfaed, bq90a, and fq78a. If there are
disagreements across measures, fq78b and fq78a take precedence.

In the NELS:88 survey, we also use student reports of father’s education
(bys34a) and mother’s education (bys34b). For the multiple imputation model,
we include parent self-reports of their own education from the base year and
second follow-up parental surveys. In the base year parent survey, we combine
information on whether the respondent and his or her spouse is the father
or mother (byp1a1 and byp1a2) with reported self (byp30) and spouse (byp31)
educational attainment. A similar methodology is used for the second follow-
up parent survey, using f2p1a and f2p1b to identify the gender of the respondent
and the spouse, respectively, and f2p101a and f2p101b to identify educational
attainment of the respondent and the spouse, respectively. The base year
and second follow-up parental education information are aggregated into two
variables, father’s education and mother’s education, used in the multiple
imputation model.

Parental Income Levels

The parental income variables are bq93 for NLS72 and f2p74 for NELS:88.
The former is reported by the student, while the latter is reported by the

416

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

parents. Unfortunately, NLS72 does not contain a parent-reported measure
and the NELS:88 survey does not contain a student-reported measure, so
these variables are the most closely aligned parental income measures across
the two surveys.

Rather than asking directly for parental income levels, the NELS:88 and
NLS72 surveys ask for income ranges from respondents. Because we are inter-
ested in measuring parents’ ability to ﬁnance college, the variable of interest
is the real income level, not one’s place in the income distribution. We thus
align the income blocks across the two surveys using the consumer price in-
dex. In NLS72, we construct the following measured income groups: less than
$3,000, $3,000–$6,000, $6,000–$7,500, $7,500–$10,500, $10,500–$15,000, and greater than $15,000. In NELS:88, we create the following corresponding
real income blocks: less than $10,000, $10,000–$20,000, $20,000–$25,000, $25,000–$35,000, $35,000–$50,000, and greater than $50,000. Across sur-
veys, the six income groups are comparable in real terms.

Race

Race is measured in the NLS72 survey using crace and race86. The latter is
used if the former is blank due to nonresponse. In the NELS:88 survey, race
is measured using the race variable available in the data ﬁles.

2. PROCEDURES TO HANDLE MISSING DATA
Multiple Imputation

There is a considerable amount of missing data in the NLS72 and NELS:88
surveys. Table A.3 presents the number of unweighted missing observations
by variable and survey. These observations are not missing completely at
random; respondents who have no math test scores have lower time to degree
conditional on ﬁnishing.

Casewise deletion of missing observations will therefore cause a bias in
the calculation of the base trends we are seeking to explain in this analysis. To
deal with this problem, we use the multiple imputation by chained equation
(MICE) algorithm developed by Van Buuren, Boshuizen, and Knook (1999)
that is implemented through the Stata module ICE (see Royston 2004 for a
detailed discussion of ICE).

MICE is implemented by ﬁrst deﬁning the set of predictor variables
(x1 . . . xk) and the set of variables with missing values to be imputed: math
test scores, reading test scores, high school GPA, father’s education, mother’s
education, and parental income levels (y1 . . . y6). The MICE algorithm imple-
mented by ICE ﬁrst randomly ﬁlls in all missing values from the posterior

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

417

INCREASING TIME TO BACCALAUREATE DEGREE

Table A.3. Number of Imputed Observations by Survey and Variable (Unweighted)

Number of Imputed Observations

Variable

Math test score

Reading test score

High school GPA

Mother’s education

Father’s education

Parent income

Total

NLS72

1,197

688

979

4,350

NELS:88

690

1,220

520

540

520

4,140

Notes: Observation counts include only those respondents who enroll in college
within two years of cohort high school graduation at a four-year institution
or a non-private two-year college and who graduate within eight years. Per
the restricted data license agreement with the National Center for Education
Statistics, all unweighted NELS:88 sample sizes are rounded to the nearest
10.

distribution of each variable. Then, for each variable with missing data, yi ,
STATA runs a regression (or ordered logit) of yi on y∼i and x1 . . . xk and calcu-
lates expected values from these regressions for all missing data points. The
expected values then replace the randomly assigned values for the missing
data points. A sequence of regressions for each yi is a cycle, and this process
is repeated for ten cycles, replacing the missing values with the new expected
values from each regression in each cycle. The imputed values after ten cycles
constitute one imputed data set, and this process is repeated ﬁve different
times to generate ﬁve imputed data sets.

There are two important speciﬁcations in implementing MICE: determi-
nation of the predictor variables and determination of the imputation models.
Because of the different structure of the two surveys, different variables are
used in the imputation procedure across surveys. In both surveys we include
dummy variables for cumulative time to degree from four to eight years,
dummy variables for initial school type, interactions between these variables,
an indicator for college attendance within two years of cohort high school
graduation, and race and gender indicators.

Due to the structure of the NELS:88 survey, there is more background
information with which to impute missing data. We use eighth- and tenth-
grade math test scores, parental reports of their education from the base year
and second follow-up parent surveys, and parental reports of their income level
from the base year parent survey. The deﬁnitions of the variables used in the
imputation models are discussed in the preceding section.

418

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

Because the math and reading test scores are continuous variables, we use
OLS regressions to impute these variables. Mother’s and father’s education,
GPA, and income, however, are categorical variables. Because of the ordered
nature of these variables, we use ordered logits to impute the missing values
of these variables. While these model choices are reasonably arbitrary, they are
used only to draw ranges of plausible estimates of missing data.

The multiple imputation procedure creates ﬁve different data sets, each
with different imputed values for the missing observations. All reported statis-
tics and results in our analysis are averages across data sets. In other words,
we conduct each analysis separately for each data set and average the ﬁnal
result. The average of ﬁnal results is what is reported in the article’s tables and
ﬁgures.

Dropped Observations and Missing Transcript Data

The base sample in this analysis consists of all respondents who graduate high
school, attend college within two years of their cohort’s high school graduation,
and obtain a BA within eight years of their cohort’s high school graduation.
We further restrict the sample to exclude those whose only enrollment over
this time period is at a private two-year institution, as these schools are pre-
dominantly professional without a BA track. Table A.4 presents information
on the number of observations that are dropped by survey and the reason
for dropping the observation. For example, in NLS72 168 respondents are
dropped because they are not high school graduates, whereas in NELS:88 720
are dropped for this reason. The apparently higher dropout rate in NELS:88
is because the universe of students is all those enrolled in the eighth grade in
1988, whereas the universe in NLS72 consists of all those enrolled in twelfth
grade in 1972.

In the NLS72 survey, 63 observations are dropped because they report
attending college but provide no information on either the type of institution or
the date they ﬁrst began attending this institution; in NELS:88, 50 respondents
do not provide this information. In addition, 200 observations were dropped
because they were not in all four waves of the NELS:88 survey. In other
words, they have a sample weight of zero. Furthermore, in NELS:88, 4,140
observations are dropped because they do not earn a BA within eight years,
and 2,868 observations are dropped in NLS72 for this reason.

Of potential concern in constructing our sample is the exclusion of those
beginning college more than two years after high school cohort graduation. We
exclude these observations because we are interested in the truncated, eight-
year time to degree distribution. These statistics have a different interpretation
for a student who began college directly after high school than for a student
who began college, for instance, ﬁve years after high school. In NLS72, 889

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

419

INCREASING TIME TO BACCALAUREATE DEGREE

Table A.4. Number of Dropped Observations by Category (Unweighted)

Sample Change

NLS72

Dropped
Observations

Remaining
Observations

Original Base: Fifth follow-up sample

High school dropouts

Missing initial school information

Never attended college

Time between HS and college > 2 years

College dropout

168

4,503

889

2,868

NELS:88

12,841

12,673

12,610

8,107

7,218

4,350

Sample Change

Original base: Fourth follow-up sample

High school dropouts

Observations not in all 4 waves

Missing initial school information

Never attended college

Time between HS and college > 2 years

College dropout

Dropped
Observations

Remaining
Observations

720

200

1,920

970

4,140

12,140

11,420

11,220

11,170

9,250

8,280

4,140

Notes: Per the restricted data license agreement with the National Center
for Education Statistics, all unweighted NELS:88 sample sizes are rounded
to the nearest 10.

respondents attend college more than two years after their cohort’s high school
graduation, and in NELS:88, 970 do so. Given the similarity of these numbers,
shifts in when students began attending college cannot account for the trends
in time to degree reported in the main text.

420

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

John Bound, Michael F. Lovenheim, and Sarah Turner

e
g
e

l
l

o
C
y
t
i
n
u
m
m
o
C

e
v
i
t
c
e
e
S

y
l
h
g
H
e
t
a
v
i
r
P

e
v
i
t
c
e
e
S

s
s
e
L

e
t
a
v
i
r
P

0
5

p
o
T

i
l

b
u
P

i
l

b
u
P
0
5

p
o
T
–
n
o
N

e
p
m
a
S

l
l

u
F

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

e
b
a
i
r
a
V

0
2
1
.
0

4
2
2
.
0

4
2
3
.
0

1
3
3
.
0

5
.
8
5

9
.
5
5

0
3
2
.
0

4
3
1
.
0

6
1
4
.
0

9
1
2
.
0

0
.
4
6

4
.
0
6

7
1
1
.
7
5

9
9
8
.
0
4

3
5
9
.
3

8
5
0
.
0

4
2
6
.
3

4
2
1
.
0

8
0
0
.
0

7
4
0
.
0

5
2
2
.
0

9
1
7
.
0

3
.
4
8

1
.
8
7

5
3
4
.
8
1

3
5
8
.
2

0
7
0
.
0

0
6
0
0

0
8
0

2
0
4

9
5
4
0

2
1
8

6
5
7

3
7
7
8
1

8
7
8

7
1
1

9
4
0

5
3
1

5
9
2

1
2
5
0

1
0
7

9
8
6

9
5
8

3
2

7
8
0
3

5
5
0
0

8
2
1
0

9
2
1

4
4
4

9
9
2
0

9
9
6

0
6
6

6
1
0

9
6
0

8
0
2

7
0
7

0
1
8

2
5
7

9
4
0

5
6
0

6
0
4
0

0
8
4

3
8
7

9
3
7

4
3
0

4
4
1

6
1
3

7
0
5

0
0
7

4
6
6

3
2
1
.
0

8
3
1
.
0

2
5
4
.
0

7
8
2
.
0

3
.
8
6

9
.
4
6

5
4
0
.
0

2
3
1
.
0

4
8
2
.
0

9
3
5
.
0

6
.
1
7

0
.
8
6

1
2
1
.
0

0
2
1
.
0

4
3
4
.
0

5
2
3
.
0

l
i
t
r
a
u
q

A
P
G

t
s
e
w
o
L

l
i
t
r
a
u
q

A
P
G
d
n
o
c
e
S

l
i
t
r
a
u
q

A
P
G
d
r
i
h
T

l
i
t
r
a
u
q

A
P
G
p
o
T

7
.
0
7

8
.
6
6

l
i
t
n
e
c
r
e
p

t
s
e
t

g
n
d
a
e
R

l
i
t
n
e
c
r
e
p

t
s
e
t

h
t
a
M

8
8
0

2
2

7
3
2

2
2

4
7
9

2
2

2
6
5

7
2

3
9
9
.
4
2

7
0
8
.
9
2

8
3
5
.
5
2

o
i
t
a
r

y
t
l
u
c
a
f
–
t
n
e
d
u
t
S

2
2
0
3

4
7
0

8
8
0
3

0
6
0
0

3
1
1
3

4
4
1
0

0
9
2

6
3
0

1
9
1
.
3

3
8
0
.
0

6
7
2
.
3

2
5
0
.
0

2
7
1
.
3

9
9
0
.
0

)
o
i
t
a
r

y
t
l
u
c
a
f
–
t
n
e
d
u
t
s
(
n
L

o
i
t
a
r

F
/
S
g
n
s
s
M

e
p
y
T

o
o
h
c
S
y
b

,
s
r
a
e
Y

t
h
g
E

n
h
t
i

w
s
e
t
a
u
d
a
r
G
e
g
e

l
l

o
C
r
o
f

s
e
b
a
i
r
a
V

8
8
:
S
L
E
N
d
n
a

2
7
S
L
N

f
o

s
n
a
e
M

1
B
e
b
a
T

5
8
0
.
0

5
1
3
.
0

8
5
2
.
0

1
7
1
.
0

0
7
1
.
0

1
6
2
.
0

2
7
2
.
0

5
7
1
.
0

3
2
1
.
0

8
2
0
.
0

0
7
0
.
0

9
0
1
.
0

1
1
3
.
0

2
8
4
.
0

3
8
0

3
4
1
0

1
4
2

8
8
1
0

5
4
3

7
3
0

4
1
2
0

1
2
2

5
7
2

3
5
2
0

5
5
1

6
2
2
0

7
3
2

3
2
2
0

9
5
1
0

2
6
0

9
6
1

9
5
1

7
3
2

5
7
3
0

5
0
1

0
0
2

2
8
2

2
1
2

4
6
0

7
1
2

6
6
2

8
5
2

5
9
1

7
1
2
.
0

1
3
2
.
0

2
6
2
.
0

2
7
1
.
0

8
1
1
.
0

5
4
3
.
0

5
7
1
.
0

9
9
1
.
0

3
1
1
.
0

8
6
1
.
0

8
5
0
.
0

8
0
2
.
0

9
1
2
.
0

9
4
2
.
0

6
6
2
.
0

9
4
4
.
0

4
4
1
.
0

6
8
1
.
0

4
9
0
.
0

6
2
1
.
0

1
7
1
.
0

1
2
2
.
0

8
4
2
.
0

9
9
1
.
0

2
6
1
.
0

e
t
a
v
i
r
p

e
v
i
t
c
e
e
s

y
l
h
g
H

e
t
a
v
i
r
p

e
v
i
t
c
e
e
s

s
s
e
L

c
i
l

b
u
p

0
5

p
o
t
–
n
o
N

e
p
y
t

o
o
h
c
s

a
i
t
i
n

i
l

b
u
p
0
5

p
o
T

e
g
e

l
l

o
c

y
t
i
n
u
m
m
o
C

o
o
h
c
s

e
t
a
u
d
a
r
G

e
g
e

l
l

o
c

e
m
o
S

A
B

a
m
o
p
d
S
H

a
m
o
p
d
S
H
o
N

n
o
i
t
a
c
u
d
e

s
’
r
e
h
t
a
F

D
o
w
n
o
a
d
e
d

f
r
o
m
h

t
t

:
/
/

d
i
r
e
c
t
.

i
t
.

e
d
u
e
d
p
a
r
t
i
c
e
–
p
d

f
/

7
4
3
7
5
1
6
8
9
3
4
9
e
d
p
_
a
_
0
0
0
7
4
p
d

b
y
g
u
e
s
t

o
n
0
7
S
e
p
e
m
b
e
r
2
0
2
3

421

INCREASING TIME TO BACCALAUREATE DEGREE

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

8
8
:
S
L
E
N

2
7
S
L
N

e
b
a
i
r
a
V

n
o
i
t
a
c
u
d
e

s
’
r
e
h
t
o
M

6
8
0
.
0

9
5
3
.
0

3
9
2
.
0

9
6
1
.
0

3
9
0
.
0

3
3
0
.
0

2
6
0
.
0

4
9
0
.
0

0
4
1
.
0

5
3
2
.
0

7
3
4
.
0

2
7
0
.
0

0
6
0
.
0

4
6
0
.
0

5
0
8
.
0

4
5
1
.
0

5
0
4
.
0

0
6
2
.
0

5
0
1
.
0

5
7
0
.
0

1
3
0
.
0

6
6
0
.
0

9
6
0
.
0

7
9
1
.
0

7
8
2
.
0

0
5
3
.
0

6
1
0
.
0

3
3
0
.
0

8
4
0
.
0

3
0
9
.
0

5
9
4
.
0

0
5
5
.
0

3
2
6

5
4
5

6
1
0
.
0

9
6
0
.
0

7
2
2
.
0

5
6
3
.

2
2
3
.

3
2
0
.
0

5
1
0
.
0

0
3
0
.
0

7
4
0
.
0

4
3
1
.
0

1
5
7
.
0

8
8
0
.
0

3
4
0
.
0

3
4
0
.

7
2
8
.

3
7
4
.
0

2
6
5

2
4
0

7
3
2

4
2
3

1
3
2

6
6
1
0

9
0
0

0
2
0

6
1
0

5
9
0
0

7
4
2
0

4
1
6
0

8
1
0

4
2
0

1
4
0
0

7
1
9

2
3
0

0
1
3

4
4
2

4
6
2

0
5
1
0

4
3
0

0
7
0

8
4
0

1
1
1
0

2
2
2
0

5
1
5
0

1
4
0

5
5
0

5
0
1
0

9
9
7

8
1
1

1
4
3

3
9
2

6
9
1

2
5
0
0

2
2
0

1
5
0

0
7
0

1
6
1
0

4
9
2
0

2
0
4
0

1
1
0

8
0
0

0
8
0
0

1
0
9

3
5
0

8
9
1

6
2
2

7
7
2

7
4
2
0

8
2
0

9
4
0

5
7
0

4
5
0
0

8
4
1
0

6
4
6

4
8
0

6
5
0

9
6
0
0

0
9
7

3
9
0
0

9
2
3
0

6
0
3
0

5
9
1

6
7
0

2
2
0

9
3
0
0

9
5
0
0

4
2
1

7
6
2

8
8
4
0

6
3
0

3
2
0

5
3
0

6
0
9
0

8
5
0

4
9
2

0
9
2

4
1
2

4
4
1

1
3
0

2
8
0
0

8
5
0
0

1
2
1

8
1
2

0
9
4
0

9
3
0

6
5
0

3
7
0

2
3
8
0

5
6
1
.
0

6
0
4
.
0

2
7
2
.
0

8
1
1
.
0

0
4
0
.
0

8
2
0
.
0

5
5
0
.
0

3
7
0
.
0

1
3
2
.
0

5
6
2
.
0

9
4
3
.
0

4
1
0
.
0

8
1
0
.
0

4
9
0
.
0

4
7
8
.
0

2
5
0
.
0

6
6
2
.
0

3
6
2
.
0

5
4
2
.
0

5
7
1
.
0

0
3
0
.
0

3
6
0
.
0

2
6
0
.
0

2
0
1
.
0

0
0
2
.
0

3
4
5
.
0

8
5
0
.
0

5
5
0
.
0

4
7
0
.
0

3
1
8
.
0

3
3
1
.
0

7
6
3
.
0

4
8
2
.
0

3
5
1
.
0

3
6
0
.
0

5
2
0
.
0

0
5
0
.
0

4
6
0
.
0

6
8
1
.
0

2
7
2
.
0

4
0
4
.
0

7
1
0
.
0

9
1
0
.
0

2
7
0
.
0

2
9
8
.
0

0
5
6

0
1
4

3
1
5

3
8
4

2
4
5

6
3
4

8
8
4
.
0

3
5
4
.
0

3
2
5
.
0

o
o
h
c
s

e
t
a
u
d
a
r
G

e
g
e

l
l

o
c

e
m
o
S

A
B

0
0
0
,
0
2
/
0
0
0
,
6
$ 0 0 0 , 5 2 / 0 0 5 , 7 $

0
0
0
,
5
3
/
0
0
5
,
0
1
$ 0 0 0 , 0 5 / 0 0 0 , 5 1 $

+
0
0
0
,
0
5
/
+
0
0
0
,
5
1
$ 0 0 0 , 0 1 < / 0 0 0 , 3 $ < e m o c n i l a t n e r a P i y t i c n h t e / e c a R n a s A i i l a m o p d S H o N l a m o p d S H i n a c i r e m A n a c i r f A e t i h W l e a M i c n a p s H i 2 9 3 2 2 8 2 0 8 3 3 7 2 5 6 7 9 3 , 1 9 5 9 , 1 7 3 1 , 4 0 5 3 , 4 s n o i t a v r e s b o f o r e b m u N e g e l l o C y t i n u m m o C e v i t c e e S l i y l h g H e t a v i r P l e v i t c e e S s s e L e t a v i r P 0 5 p o T c i l b u P c i l b u P 0 5 p o T – n o N l e p m a S l l u F . d e u n i t n o C . . 1 B e b a T l 422 y l n O . s n o i t a u c l a c l y e v r u s : 8 8 S L E N e h t r o f d e s u e r e w s t h g e w p u w o i - l l o f h t r u o F . y e v r u s e h t n i d e d u c n l i i s t h g e w p u w o - l l o f h t f ﬁ e h t i g n s u e d a m e r e w s n o i t a u c l a c l 2 7 S L N : s e t o N t r o h o c f o s r a e y o w t n h t i i w e g e l l o c d n e t t a o h w e s o h t o t d e t c i r t s e r e r a l s e p m a s 8 8 : S L E N d n a 2 7 S L N e h T l . s n o i t a u b a t e h t n i d e d u l c n i e r a s p u w o - l l o f e s e h t n i g n i t a p c i t r a p i e s o h t l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / / 7 4 3 7 5 1 6 8 9 3 4 9 e d p _ a _ 0 0 0 7 4 p d . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 . 8 8 : S L E N e h t r o f 2 9 9 1 e n u J d n a 2 7 S L N e h t r o f 2 7 9 1 e n u J s a d e n ﬁ e d s i n o i t a u d a r g l o o h c s h g h i t r o h o C . n o i t a u d a r g l o o h c s h g h i . s y e v r u s 2 7 S L N d n a 8 8 : S L E N e h t m o r f s n o i t a u b a t l ’ s r o h t u A : e c r u o S John Bound, Michael F. Lovenheim, and Sarah Turner Table B.2. OLS Estimates of the Relationship between Student and Institutional Characteristics and Time to Degree among NELS:88 Graduates Dependent Variable Sample 50 Public Public Selective Selective College Full Non–Top Top 50 Private Less Private Highly Two- Year Ln(student-faculty ratio) Missing student-faculty ratio Math test percentile Reading test percentile Second GPA percentile Third GPA percentile Top GPA percentile 0.163∗∗ (0.078) 0.160 (0.272) 0.487∗∗ (0.153) 1.387∗∗ (0.513) −0.003∗∗ −0.003 (0.003) (0.002) 0.001 (0.001) 0.002 (0.002) 0.347 (0.265) 0.941 (0.829) −0.001 (0.003) −0.003 (0.003) 0.016 (0.107) −0.046 (0.365) −0.002 (0.003) −0.001 (0.003) −0.411 (0.280) −0.325 (0.323) −1.726∗∗ −0.256 (0.593) (0.680) −0.663∗∗ −0.656∗∗ −1.757∗∗ −0.341 (0.559) (0.242) (0.286) (0.639) −0.850∗∗ −0.709∗∗ −1.876∗∗ −0.578 (0.571) (0.238) (0.266) (0.627) −0.050 (0.145) −0.371 (0.526) −0.007 (0.154) 0.161 (0.674) −0.010∗∗ −0.006 (0.005) (0.003) 0.0004 (0.002) 0.006∗∗ (0.003) −0.680 (0.715) −0.537 (0.645) −0.710 (0.642) −0.240 (0.306) −0.685∗∗ (0.304) −1.063∗∗ (0.333) 0.784 (0.659) −0.092 (0.390) l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / Parent income $6,000/20,000 Parent income $7,500/25,000 Parent income $10,500/35,000 Parent income $15,000/50,000 0.035 (0.180) 0.107 (0.170) 0.098 (0.161) 0.158 (0.158) Parent income $15,000+/50,000+ 0.027 (0.153) Father HS diploma Father some college Father BA Father graduate school Mother HS diploma Mother some college Mother BA Mother graduate school Asian 0.312 (0.318) 0.480 (0.312) 0.358 (0.341) 0.588∗ (0.315) 0.375 (0.294) 0.113 (0.207) −0.067 (0.219) 0.031 (0.247) −0.141 (0.354) −0.259 (0.318) −0.124 (0.359) −0.102 (0.340) −0.216 (0.249) 0.001 (0.234) −0.054 (0.243) −0.020 (0.235) −0.297 (0.392) 0.116 (0.414) −0.112 (0.380) −0.301 (0.369) −0.442∗∗ −0.308 (0.499) (0.219) −0.214 (0.239) −0.618 (0.424) −0.251 (0.324) −0.110 (0.285) 0.057 (0.312) 0.167 (0.315) 0.114 (0.302) −0.045 (0.258) −0.002 (0.212) −0.043 (0.189) −0.265 (0.183) −0.236 (0.163) −0.227 (0.147) −0.233 (0.164) −0.110 (0.196) −0.103 (0.169) −0.020 (0.189) −0.206 (0.196) 0.060 (0.107) −0.371∗∗ −0.123 (0.247) (0.160) −0.481∗ −0.380 (0.451) (0.259) 0.056 (0.226) −0.311 (0.264) −0.393 (0.449) −0.266 (0.213) 0.079 (0.219) −0.255 (0.251) 0.022 (0.208) 0.033 (0.240) 0.137 (0.234) 0.004 (0.555) 0.117 (0.539) 0.168 (0.528) 0.177 (0.519) −0.433∗ −0.355 (0.264) (0.316) −0.155 (0.260) 0.332∗∗ −0.113 (0.124) (0.129) 0.249 (0.218) −0.035 (0.074) 0.151 (0.376) −0.112 (0.337) −0.200 (0.365) −0.300 (0.365) −0.589∗ (0.328) −0.489 (0.342) −0.547∗ (0.314) −0.126 (0.294) −0.071 (0.323) 0.155 (0.351) 0.051 (0.362) 0.033 (0.308) / / / / 7 4 3 7 5 1 6 8 9 3 4 9 e d p _ a _ 0 0 0 7 4 p d . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 423 INCREASING TIME TO BACCALAUREATE DEGREE Table B.2. Continued. Dependent Variable Full Non–Top Sample 50 Public Top 50 Public Private Less Private Highly Selective Selective College Two- Year Hispanic Black Male Top 50 public Less selective private Highly selective private Two-year college Constant 0.267∗ (0.138) 0.141 (0.123) 0.169∗∗ (0.050) −0.149∗∗ (0.071) −0.475∗∗ (0.064) −0.533∗∗ (0.082) 0.429∗∗ (0.096) 5.695∗∗ (0.461) 0.526∗ (0.300) 0.253∗ (0.151) 0.211∗∗ (0.084) 0.067 (0.156) 0.318 (0.233) 0.262∗∗ (0.094) 0.435∗∗ (0.173) 0.262 (0.227) 0.254∗∗ (0.095) 0.150 (0.170) −0.167 (0.149) 0.075 (0.083) −0.232 (0.185) 0.024 (0.400) −0.029 (0.132) 3.693∗∗ (0.759) 5.889∗∗ (1.200) 5.221∗∗ (0.734) 6.318∗∗ (0.870) 6.859∗∗ (0.744) Notes: Fourth follow-up weights were used for the calculations. Only those participating in this follow- up are included in the regression. All samples include only those who begin college within two years of cohort high school graduation and obtain a BA within eight years of cohort high school graduation. Cohort high school graduation is deﬁned as June 1992 for the NELS:88 sample. All school types refer to the initial institution of the respondent. Standard errors clustered at the primary sampling unit (HS) level are in parentheses. ∗signiﬁcant at 10%; ∗∗signiﬁcant at 5% Source: Authors’ calculations as described in the text from the NELS:88 survey. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / / 7 4 3 7 5 1 6 8 9 3 4 9 e d p _ a _ 0 0 0 7 4 p d . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 424 INCREASING TIME TO image

Download pdf