Human capital attainment, university quality, and entry-level wages for college transfer students.
Hilmer, Michael J.
1. Introduction
The U.S. higher education population is highly mobile. Tinto (1987)
finds that roughly 35% of college graduates from the National
Longitudinal Study of the High School Class of 1972 graduate from a
different institution than the one they first attend. Recent evidence
suggests that the percentage of college attendees choosing to transfer
is on the rise. For instance, a U.S. Department of Education survey of
1992 college graduates finds that over half of the roughly 11,000
students interviewed had attended more than one institution during their
college careers (National Center for Education Statistics 1996). Despite
their obvious place in American higher education, very little is known
about college transfer students. The economics of higher education
literature has devoted much attention to the economic returns to college
attendance and the causes and consequences of college dropouts. Within
the vast literature, however, the transfer student has largely been
neglected.
This is particularly regrettable, as transfer students present the
researcher with additional, potentially valuable information that
nontransfers do not. In particular, transfer students will have taken
courses at more than one quality institution. This fact can possibly be
exploited to provide insight into the role of human capital accumulation in determining a student's postgraduation earnings. A common
problem in the economics of higher education literature is that the
well-known positive return to the quality of university from which a
student graduates is predicted by both human capital and screening
theories (for a more detailed discussion, see Weiss 1995). Much of this
confusion may be based on the fact that previous studies have focused
only on graduation quality. While such an approach is accurate for
nontransfers, it is not accurate for transfer students. Transfer
students clearly complete courses at institutions that are of different
qualities. The human capital theory has implications for the pre dicted
returns to initial quality and tenure for transfer students, while the
screening theory does not. Thus, the returns to initial quality and
tenure may be used to generate some idea which model more accurately
describes the role of educational attainment in determining a
student's entry-level earnings.
This study is one of the first to separately examine the economic
returns to college attendance for transfer students. In particular, I
focus on the returns to quality and educational tenure at institutions
other than the one from which a transfer student graduates and ask what
implications such values have for human capital theory. A theoretical
discussion describes how the educational experiences of college transfer
students can be used to address the role of human capital accumulation
in determining a college graduate's entry-level earnings.
Specifically, to be consistent with human capital theory, the quality of
all institutions attended should have positive effects on future
earnings, while the length of time spent at each institution is
uncertain. The longitudinal nature of the data set analyzed allows me to
improve the efficiency of my estimates by employing panel data
techniques. Using random effects generalized least squares (GLS), I find
significant, positive, and statistically similar returns to b oth
initial and graduation quality and insignificant effects for both
initial and graduation tenure. In other words, by finding that both
initial and graduation quality have significant positive effects on
future earnings, the results can be considered consistent with the
predictions of the human capital theory.
2. Theory
To frame the empirical work here, I start by developing a simple
model of college choice. In choosing a college, the prospective student
has thousands of options to consider. This choice set will differ for
each student as it is limited to only those colleges to which he or she
is able to gain admission. Each college presents the student with a
different combination of quality and cost. A college is an efficient
option if no other college offers a higher quality at a lower cost. The
student limits his or her search to these efficient options. From this
efficient set, the student chooses the level of quality and implicitly
the particular university that results in the highest total utility. If
this value exceeds that which could be received in the labor market, the
student chooses to attend the university. If it is less, he or she
forgoes college attendance and enters the labor market directly...
To formalize the student's college choice, assume there are
two distinct periods representing the college and postcollege years. (1)
The student's objective is to maximize the utility he or she
receives from consumption in the two periods. Each student enters the
first period with a fixed amount of family wealth, M, which is allocated
between current consumption, [X.sub.1], and the cost of college
attendance. Let Q represent the quality of university from which the
student graduates and let C represent the cost per unit of quality. (2)
Finally, if the student chooses not to exhaust his or her first period
wealth, he or she saves the remainder, at interest rate r, for use in
the second period.
The student is able to work for k years during the second period. A
student's future earnings will depend on the quality of university
he or she attends. (3) Let f(Q) represent the student's
postgraduation earnings function. In addition to earned income, the
student receives interest payments on any money saved during the first
period. The sum of these two incomes is spent on second-period
consumption, [X.sub.2].
The optimization problem facing the university-bound student is
subject to [Max.sub.[X.sub.1],[X.sub.2],Q] U([X.sub.1], [X.sub.2])
[X.sub.1] + CQ [less than or equal to] M [X.sub.2] = f(Q) * k(1 + r)[M -
C(Q) - [X.sub.1]]. (1)
The solution to this optimization problem yields a familiar system
of Kuhn-Tucker conditions. (4) These conditions indicate that a student
chooses his or her optimal institution by equating the marginal return
to college quality to the marginal cost. As the marginal benefit of
college quality depends on the effect that college quality has on a
student's future earnings, the specification of the earnings
function is of primary importance to a student's decision.
Consequently, the work here focuses on the role that college quality
plays on a student's future earnings.
Unfortunately, the student's problem is not necessarily as
simple as specified in Equation 1. Graduation from college is an
uncertain event. Simply gaining admission and enrolling at a particular
institution does not guarantee that a student will one day complete the
requirements for a degree at that institution. On graduation from high
school, neither colleges nor students are certain whether students have
the ability and/or desire to persist to graduation. Thus, it is
reasonable to assume that substantial mismatching exists between
students and first-choice colleges. In a nontransfer world, students who
decide to attend a particular institution must either persist to
graduation at that institution or drop out without receiving a degree.
In a transfer world, students who are initially overmatched and do not
meet the requirements at their first-choice institutions can transfer to
lower-quality institutions rather than dropping out. (5) Likewise,
students who are initially undermatched and far exceed the requi rements
at their first-choice institutions can transfer to higher-quality
institutions.
Consider the difference between the earnings function for a student
who transfers from his or her initial-quality institution to a
different-quality institution. This student will not have one fixed
quality, as specified in Equation 1, but rather he or she will have
different qualities for all institutions attended. Let [Q.sup.G]
represent the quality of university from which the student graduates and
let [Q.sup.T] represent the quality of university from which the student
transfers. In addition to the different qualities, the student will have
different tenures at each of the different institutions. To account for
this, let [[alpha].sup.T] the percentage of total credits spent at the
initial institution. The postgraduation earnings function for a transfer
student is then
f([Q.sup.G], [Q.sup.T], [[alpha].sup.T]), (2)
as presumably the qualities and tenures of all institutions will
affect a student's future earnings.
An important question is how the different qualities and tenures at
each institution affect a student's future earnings. By examining
only the quality of university from which a student graduates, previous
studies (Wales 1973; Solmon and Wachtel 1975; Wise 1975; James et al.
1989; Mueller 1988; Rumberger and Thomas 1993) have implicitly treated
the transfer student's earning function as specified in Equation 1
rather than Equation 2. As such, they have ignored the potentially
important effect that initial quality and tenure may have on
postgraduation earnings.
The additional information to be gained by controlling for a
transfer student's entire educational background may provide
insight into important economic questions. For example, human capital
attainment is a cornerstone of much of the economics of education
literature. According to the human capital theory of Becker (1964), the
oft-cited positive return to a college education (recent examples
include Katz and Murphy 1992, Murphy and Welch 1992, and Kane and Rouse
1995) results from the increased human capital attained through college
attendance. A natural extension of this argument is that students who
attend higher-quality universities accrue higher levels of human capital
and should receive higher wages on graduation (this argument is
supported by Psacharopoulos 1974). Indeed, James et al. (1989),
Rumberger and Thomas (1993), and many others find a positive return to
the quality of university from which a student graduates. If human
capital increases with college quality, then the quality of each
institutio n attended should affect a student's future earnings and
not just the quality of university from which the student graduates.
This observation leads to testable hypotheses about the postgraduation
earnings function of college transfer students.
For demonstration purposes, I will distinguish between three
students who graduate from the same-quality institution: those who
transfer from a lower-quality institution, those who transfer from a
higher-quality institution, and those who do not transfer. Contrasting
the expected returns to quality and tenure for these students will
demonstrate how transfer students might provide additional insight into
the role of human capital accumulation in determining a student's
future earnings.
Consider first the expected return to quality. Human capital theory
implies that higher-quality universities provide higher levels of human
capital. Hence, the return to quality should always be positive, not
only for the graduation institution but for all institutions attended.
In other words, holding graduation quality constant, the higher the
quality of institution initially attended by a transfer student, the
more human capital the student should have accumulated. This should be
true regardless of whether the transfer student increases or decreases
quality. For example, consider students graduating from a university
with a median SAT score (the quality measure used in this analysis) of
1000. A student who transfers up from a college with a median SAT score
of 800 should have accumulated more human capital than a student who
transfers up from a college with a median SAT score of 600. Likewise, a
student transferring down from a college with a median SAT score of 1400
should have accumulated more human capi tal than a student transferring
down from a college with a median SAT score of 1200. Consequently, under
human capital theory, we would expect a positive return to initial
quality ([Q.sup.T] > 0) for transfer students regardless of whether
they transfer up or down in quality.
In addition to the different-quality levels themselves, the lengths
of time a student spends at different-quality institutions should affect
his or her human capital accumulation. Predicting the expected return to
tenure is not straightforward, however. To see why, consider a transfer
student who increases quality from his or her initial institution
([Q.sup.G] > [Q.sup.T]). As a first pass, one might predict that
according to human capital theory such a student would be accumulating
less human capital than a student who attended the graduation university
continuously without transferring. It then would follow that the longer
the student spent at the initial, lower-quality institution, the less
human capital he or she would accumulate. Contrast this to a transfer
student who decreases quality from his or her initial institution
([Q.sup.G] < [Q.sup.T]). According to simple human capital theory,
such a student would be accumulating more human capital than
nontransfers, and the longer the student spends at the in itial,
higher-quality institution, the higher the accumulation. Thus, to be
consistent with simple human capital theory, one might simply expect a
positive return to the length of time spent at initial institutions for
transfer students who decrease quality and a negative return to the
length of time spent at initial institutions for transfer students who
increase quality.
This simple interpretation ignores the important role that learning
plays in human capital accumulation, however. If indeed students
transfer because of an initial mismatching between their ability and/or
motivation and that required at their initial institution, then the
tenure at their initial institution may not have had uniform effects on
human capital accumulation. The reason for this is that effective
learning might depend on the quality of the match between a particular
student and his or her classmates at a given school. As an example,
consider a student who is far overmatched at his or her initial school.
Being toward the bottom of the class, the level and pace of instruction
might be high and fast enough to preclude effective learning. If so, the
student might actually lag so far behind his or her classmates that he
or she is able to learn less than if he or she were in a class with less
talented peers even though that class would be taught at a lower level
and slower pace. In such a case, transfer ring down to a lower-quality
institution might actually facilitate better learning and more human
capital accumulation. Under such a scenario, the simple predictions
outlined previously would be inaccurate. Therefore, without being able
to isolate the specific effects of classroom learning, the predicted
effects of tenure at initial and graduation institutions is uncertain.
(6)
3. Empirical Model
The empirical work here attempts to test the predictions of the
theoretical discussion by estimating wage functions for a sample of
college graduates. To motivate the empirical work, I start by writing a
general form of the wage function to be estimated. A student's
future earnings are assumed to be a function of his or her experiences
during college as well as individual and family background
characteristics that may affect his or her productivity level. Let the
student's future earnings be
[Y.sub.i] = Y([Z.sub.i], [A.sub.i], [J.sub.i], [P.sub.i]), (3)
where [Y.sub.i] is the log annual earnings of student i, [Z.sub.i]
is a vector of individual and family background characteristics,
[A.sub.i] is a vector representing i's academic performance in
college, [J.sub.i] is the postgraduation job market experience of i, and
[P.sub.i] is a vector of variables representing the attendance path i
followed while pursuing his or her degree.
Several aspects of a student's educational path are observable to a potential employer. As demonstrated in Equation 2, a transfer
student will have some combination of initial and graduation quality as
well as some percentage of time spent at his or her initial institution.
To account for these values, the student's educational path is
considered:
[P.sub.i] = P([Q.sup.G.sub.i],[Q.sup.T.sub.i][[alpha].sup.T.sub.i]), (4)
where [Q.sup.G.sub.i] is the quality of university from which i
graduates, [Q.sup.T.sub.i] is the quality of university from which i
transfers, and [[alpha].sup.T.sub.i] is the percentage of total credits
i spends at initial institutions before transferring to the
degree-granting institution. (7)
A general form of the wage function to be estimated is thus
[Y.sub.i] = [B.sub.0] + [B.sub.1][Q.sup.G.sub.i] +
[B.sub.2][Q.sup.T.sub.i] + [B.sub.3][[alpha].sup.T.sub.i] +
[delta][Z.sub.i] + [eta][A.sub.i] + [gamma][J.sub.i] +
[[epsilon].sub.i], (5)
where the variables are defined as previously and [[epsilon].sub.i]
is a normally distributed error term. Parameters to be estimated are
[B.sub.1], [B.sub.2], [B.sub.3], [delta], [eta], and [gamma]. Moreover,
to test the predictions of the theoretical model (i.e., [B.sub.1] > 0
and [B.sub.2] > 0), I want to estimate Equation 5 for the subset of
four-year transfer students only, as they are the only subset for which
both quality measures are available. (8)
The data set I analyze in this study has postgraduate earnings for
multiple years. Therefore, I can improve the efficiency of my estimates
by analyzing a panel data set. My estimating equation is then
[Y.sub.i] = [B.sub.0] + [B.sub.1][Q.sup.G.sub.i] +
[B.sub.2][Q.sup.T.sub.i] + [B.sub.3][[alpha].sup.T.sub.i] +
[delta][Z.sub.it] + [eta][A.sub.it] + [gamma][J.sub.it] + [u.sub.t]
[[epsilon].sub.it], (6)
The dependent variable is the logarithm of annual earnings of
individual i in time period t(t = 1994, 1997). The constant vectors
[Q.sup.G.sub.i], [Q.sup.T.sub.i], [[alpha].sup.T.sub.i], and [A.sub.i]
are as defined previously, and the panel variables [Z.sub.it] and
[J.sub.it] are vectors of time-specific individual and family background
characteristics and postgraduation job market experience of i in time
period t. The error term in Equation 6 has two components, [u.sub.i] and
[[epsilon].sub.it], both of which have zero mean. The component
[u.sub.i] is individual specific and time invariant and generates
correlation over time across the observations of a given individual.
Because of this correlation, ordinary least squares (OLS) estimation of
this equation is inefficient, and the OLS standard errors are
inconsistent. I therefore estimate this model using a random effects GLS
technique that incorporates this error structure into the estimation.
(9) Specifically, random effects GLS estimation utilizes the corr
elation over time for a given individual in the estimation of the
standard errors.
4. Data
The data analyzed in this study are drawn from a relatively new
longitudinal study conducted by the U.S. Department of Education. The
Baccalaureate and Beyond (B&B; National Center for Education
Statistics 1996) survey tracks the experiences of a cohort of recent
college graduates who received the baccalaureate degree during the
1992-1993 academic year and were first interviewed as part of the
National Postsecondary Student Aid Study. The base year survey
interviewed roughly 10,000 students and collected extensive information
on student's postsecondary educational and labor market
experiences, including detailed financial aid information. The first
follow-up was conducted in April 1994 and collected detailed information
on the student's postgraduate education and early postbaccalaureate
labor market experiences. The second follow-up took place in April 1997
and collected postgraduate education and labor market information
similar to the previous follow-up.
This sampling design makes the B&B ideal for examining the
economic returns to college attendance, as such studies require
information on several different aspects of a student's college
experiences, including field of study, college performance, and the
institution attended. Further, because it derives from an initial sample
of college graduates, it provides far larger sample sizes than
alternative data sets that derive from initial samples of high school
graduates. (10) This is because, in general, only about half of all high
school graduates ever attend a four-year college, and among those
four-year college attendees, less than half tend to persist to
graduation.
The dependent variable in my earnings functions is the logarithm of
annual earnings. I impose the restriction that annual earnings must be
greater than $5000 and less than $500,000. Table 1 contains detailed
information on the control variables used in this analysis. The
university quality measure is the median SAT score of entering freshmen
at a particular institution as reported in Barron's Profiles of
American Colleges (1994). The independent variables of interest are
binary measures for college major, which are collapsed into seven
categories: business, engineering, science, social science, humanities,
education, and other major. I use these broad aggregated major
categories to avoid small sample sizes associated with more detailed
classifications. (11)
The control variables include continuous measures for age at
bachelor's degree graduation in 1993, family income in 1991
(measured in dollars), and the student's SAT score. (12) I also
include binary variables for race/ethnicity (black, Hispanic, other),
gender, marital status, completion of a postgraduate degree, part-time school enrollment, and a control for imputation of the SAT score from
ACT data. The models also include indicators for missing values of the
continuous variables, in which case the continuous variable is set to
zero for that observation. The panel data models also include a year
dummy for 1997.
Table 2 presents descriptive statistics for 1994 and 1997 annual
earnings and work experience and college qualities and tenures. The
first two columns present values for the focus groups of this study:
four-year transfers who increase quality and four-year transfers who
decrease quality, respectively. For comparison purposes, the final two
columns present values for nontransfers and two-year transfers. (13)
Allowing for modest inflation, average earnings for this sample of
college graduates appear to be consistent with national data. According
to the 1990 census of population and housing, the average annual
earnings of 18- to 24-year-old college graduates employed year-round
full-time in 1990 were $23,430 for males and $20,229 for females (U.S.
Bureau of the Census 1992). (14) Comparing across attendance paths
suggests little difference between the groups in both 1994 and 1997.
Specifically, the average annual earnings of the four groups are within
roughly $1000 of each other in both sampled years. Additional ly, in
both years, four-year transfers who decrease quality have the highest
average earnings, while nontransfers have the lowest. Finally, it does
not appear that the differences in average earnings are due strictly to
differences in work experience, as all four groups average nearly the
same work experience.
Other factors might certainly influence early postgraduate
earnings. For instance, there is a wide disparity in the average quality
of university from which students graduate. On average, four-year
transfers who increase quality graduate from the highest-quality
universities, while four-year transfers who decrease quality graduate
from the lowest. Given the positive relationship between quality and
earnings (James et al. 1989; Rumberger and Thomas 1993), the higher
average graduation quality for four-year transfers who increase quality
may help explain why they receive higher average earnings than
nontransfers. The difference between transfer and graduation quality for
the two groups of four-year transfers is potentially revealing. As
mentioned previously, a probable reason that a student chooses to
transfer is a mismatching between his or her ability and/or motivation
and the quality of institution initially attended. The entries in Table
2 suggest that this is indeed correct. Four-year transfers who decrea se
quality graduate from institutions that average roughly 115 SAT points
lower in quality than those they started at, while those who increase
quality graduate from institutions that average roughly 100 SAT points
higher in quality. Not surprisingly, students who transfer take longer
to graduate than nontransfers. This may explain why nontransfers have
more postgraduation work experience by the time of the final survey.
Finally, four-year transfers who increase quality have the shortest
average tenures at initial institutions, while two-year transfers have
the longest. This latter fact corresponds to conventional wisdom that
community college attendees are likely to work and take smaller course
loads while attending. (15) This may help explain why, despite
graduating from lower average-quality universities, two-year transfers
have higher average entry-level earnings than nontransfers.
Turning to the values reflecting postsecondary experiences
presented in Table 3, the only difference in average grades across the
different attendance groups is that transfers who increase quality
receive grades that average nearly .2 points (on a four-point scale)
higher. This could be due to the fact that such students were presumably
"overqualified" at their initial institutions, and therefore,
having faced less competition, they likely received higher grades before
transferring. In addition, there is a noticeable difference in college
major choices, which may help account for the observed difference in
average annual earnings. Four-year transfers who increase quality are by
far the most likely to major in engineering. Studies of returns to
college major have frequently documented that engineers observe the
highest return to their degrees, which may provide additional
explanation of their increased annual earnings in this sample. Likewise,
nontransfers and downward transfers disproportionately choose relat
ively low-paying social science majors, which may help explain why they
are the two groups with the lowest average earnings. All three groups
who initially attended four-year colleges are more likely than two-year
transfers to have received postgraduate degrees by the date of the last
interview. Finally, comparing individual and family background
characteristics suggests that both two- and four-year transfers are more
likely than nontransfers to be female. At the same time, four-year
transfers who decrease quality and nontransfers are more likely to be
black, while two-year transfers are more likely than the remaining
groups to be Hispanic.
An important question for the current study is what factors might
influence a student's decision to transfer. Comparing the entries
in Table 3 across attendance paths for college graduates provides some
insight into this question. Four-year transfers who increase quality
have the lowest high school grades and test scores but the highest
college grades (from Table 2) of all graduates who never attend a
two-year college. This provides additional support for the mismatching
story by suggesting that students who transfer up are those who have
worse records on high school graduation but perform better at their
initial institutions. Conversely, students who transfer down have better
high school records but perform worse at their initial institutions than
students who transfer up. Two-year transfers provide a different story.
Those students have the lowest average family incomes and high school
grades but the highest average test scores of all college graduates.
This suggests that two-year transfers are primarily tw o types of
students: (i) those who lack the financial resources to attend a
four-year college for four years and (ii) those who are of high ability
but perform poorly in high school and attend a two-year college to
improve their academic records.
5. Results
The empirical work presented here focuses on estimating the wage
functions given in Equations 5 and 6. Table 4 presents random effects
GLS log annual earnings estimates. (16) The first column groups all
graduates together without distinguishing between nontransfers and
transfers and is included for the sake of comparing this sample with
previous samples. This specification suggests that results for the
current sample are consistent with previous findings. Specifically, for
this sample, increasing graduation quality by 100 SAT points increases
annual earnings by roughly 3.5%, which is similar to the estimates in
James et al. (1989), Rumberger and Thomas (1993), and so on. A problem
with the estimates in column 1 and with previous research using that
specification is that it requires the estimated coefficients to be
constant across attendance paths. To allow for cross-path differences,
the final four columns estimate the returns to graduation quality
separately for each of the attendance paths described previou sly. These
results suggest that the return to graduation quality differs relatively
little across attendance paths, as they all suggest that the return is
somewhere between 2.5% and 3.5%.
As discussed previously, however, the econometric specification in
Table 4 is likely inaccurate for university transfers, as it does not
consider the effect of initial quality. Results from the correct
specification (Eqn. 6) are presented in Table 5. The three columns in
Table 5 present different possible specifications for university
transfers. According to Equation 6, the most complete specification is
presented in column 3. Before discussing the results, it is useful to
recall the predictions from the previous theoretical discussion. To be
consistent with human capital theory, both transfer and graduation
quality should have significant positive effects on future earnings,
while the effects of attendance tenure are uncertain. The random effects
GLS estimates in column 3 suggest that the return to initial and
graduation quality are both positive and statistically significant.
Further, the estimated coefficients for a 100-SAT-point increase in
quality are both roughly 1.8% (a simple t-test suggests that thos e
returns are not statistically different from each other). The fact that
both the transfer and the graduation SAT coefficient estimates are
positive and significant could then be interpreted as consistent with
human capital theory. Further, the insignificant estimated effects of
attendance tenure are not surprising given the unclear predicted
effects. Hence, it appears that the results presented in this paper are
consistent with the human capital theory of educational attainment.
6. Conclusion
This paper examines the returns to quality and educational tenure
for university transfer students. The results suggest that both transfer
and graduation quality have significant positive effects on the
postgraduation earnings of all university transfer students regardless
of whether they increase or decrease quality. Further, the effects of
tenure at initial institutions are estimated to be statistically
insignificant. Such evidence is consistent with human capital theory,
which predicts positive returns to quality for all institutions attended
and uncertain returns to tenure at those different institutions.
Table 1
Descriptions of Variables Used in Analysis
Multiyear variables
Annual earnings Continuous variable representing
the student's self-reported annual
earnings at the time of the 1994
and 1997 interviews.
Work experience Continuous variable representing
the student's self-reported years
of work experience at the time of
the 1994 and 1997 interviews.
Still attending Binary dummy variable indicating
whether the student was attending
college part time while continuing
to work full time at the time of
the 1994 and 1997 interviews.
Postgraduate degree Binary dummy variables indicating
whether the student had received
an advanced degree by the 1994
and 1997 interview dates.
Constant variables Graduation Continuous variable representing
SAT, transfer SAT the median SAT score of entering
freshmen in 1996 at the university
from which the student graduated
and at the last university
attended before transferring,
respectively. Imputed (using
Astin 1971) for institutions
reporting only average ACT scores.
% Credits pretransfer Continuous variables representing
the percentage of credits the
student completed at institutions
other than the student's
graduation institution. Calculated
from official transcripts.
College GPA Continuous variable representing a
student's college grade-point
average. Calculated from official
transcripts.
Business, engineering, Binary dummy variables indicating
science, social science, the major field in which the
education, humanities, other student received his or her
major bachelor's degree.
Male, white, black, Hispanic, Binary dummy variables indicating
other race, married the student's sex and ethnicity
and whether the student was
married at the time of the 1994
and 1997 interviews.
Age at graduation Continuous variable indicating the
student's age at college
graduation.
Family income Continuous variable representing
the total family income from the
1991 calendar year.
Table 2
Descriptive Statistics for Dependent and Transfer Control Variables
Four-Year Transfers
Increase Quality Decrease Quality
Labor market characteristics
1997 annual earnings 33,716.17 34,140.41
(16,581.36) (19,366.50)
1997 work experience 3.5199 3.5529
(1.0335) (1.0527)
1994 annual earnings 24,290.90 24,592.51
(13,706.32) (10,948.38)
1994 work experience .9065 .9664
(.4007) (.4163)
College characteristics
Graduation SAT 1013.56 911.2
(105.26) (99.88)
Transfer SAT 916.64 1026.11
(93.97) (107.58)
% Credits pretransfer .2668 .323 1
(.2230) (.2361)
Observations 873 709
Nontransfers Two-Year Transfers
Labor market characteristics
1997 annual earnings 33,083.94 33,328.46
(18,949.43) (17,912.06)
1997 work experience 3.4781 3.5864
(1.0180) (.9830)
1994 annual earnings 23,547.24 23,580.26
(20,680.66) (18,313.99)
1994 work experience .8731 .9163
(.3830) (.4214)
College characteristics
Graduation SAT 990.16 960.70
(125.63) (103.75)
Transfer SAT -- --
-- --
% Credits pretransfer -- .2760
-- (.2173)
Observations 2830 1270
Standard deviations, where applicable, are in parentheses. Persons with
missing values for a variable are excluded from the calculation of those
means.
Table 3
Descriptive Statistics for Other Independent Variables
Four-Year Transfers
Increase Quality Decrease Quality
Personal college experiences
Still attending .1924 .2200
Postgraduate degree .1123 .1227
Age of graduation 25.8305 27.2257
(6.6032) (7.9589)
College GPA 2.9678 3.1746
(.6658) (.6350)
Major
Business .1306 .1410
Engineering .0664 .0564
Science .0928 .1044
Social Science .1764 .1354
Other Major .3036 .2807
Humanities .0859 .0874
Education .1443 .1946
Individual and family
characteristics
Male .4456 .4457
White .8843 .8858
Black .0378 .0564
Hispanic .0424 .0296
Other race .0355 .0282
Family income 44,192.89 37,254.66
(50,189.66) (42,613.38)
Observations 873 709
Nontransfers Two-Year Transfers
Personal college experiences
Still attending .1760 .1969
Postgraduate degree .1205 .0969
Age of graduation 23.0099 25.7969
(4.5041) (6.5863)
College GPA 2.9457 2.9474
(.6009) (.6802)
Major
Business .1343 .1685
Engineering .0922 .0819
Science .1088 .0811
Social Science .1739 .1362
Other Major .2399 .2622
Humanities .0961 .0709
Education .1548 .1992
Individual and family
characteristics
Male .4710 .4299
White .8678 .8872
Black .0576 .0446
Hispanic .0332 .0339
Other race .0413 .0441
Family income 49,831.51 36,386.27
(51,484.10) (39,390.72)
Observations 2830 1270
Standard deviations, where applicable, are in parentheses. Persons with
missing values for a variable are excluded from the calculation of those
means.
Table 4
Random Effects GLS Log Earnings Estimates by Attendance Path
Four-Year Transfers
All Students Increase Quality Decrease Quality
Graduation SAT/100 .0335 ** .0350 ** .0226
(.0044) (.0124) (.0148)
[R.sup.2] .3134 .3625 .3043
Observations 9681 1489 1213
Nontransfers Two-Year Transfers
Graduation SAT/100 .0396 ** .0279 **
(.0061) (.0100)
[R.sup.2] .3181 .3126
Observations 4791 2188
Dependent variable is the logarithm of a student's annual earnings at
the time of the 1994 and 1997 interviews. Standard errors are in
parentheses. Regressions also include family income, age at receipt of
bachelor's degree, and dummy variables indicating sex, race (white
omitted), marital status, graduate degree attainment, part-time
attendance, graduation SAT score imputed, and dummy variables that are
equal to one if values for a variable are missing (in which case those
variables are set to zero).
** Significant at the 5% level.
Table 5
Random Effects GLS Log Earnings Estimates for Four-Year Transfers
1 2 3
Graduation SAT/100 .0260 ** .0221 ** .0187 *
(.0085) (.0088) (.0099)
Transfer SAT/100 -- .0143 * .0178 *
-- (.0084) (.0097)
% Credits pretransfer -- -- -.0385
-- -- (.0499)
% Credits pretransfer * transfer up -- -- .0396
-- -- (.0580)
[R.sup.2] .3241 .3257 .3259
Observations 2702 2702 2702
Dependent variable is the logarithm of a student's annual earnings at
the time of the 1994 and 1997 interviews. Standard error are in
parantheses. Regressions also include family income, age at receipt of
bachelor's degree, and dummy variables indicating sex, race (white
omitted), martical status, graduate degree attainment, part-time
attendance, graduation and transfer SAT score imputed, and dummy
variables that are equal to one if values for a variable are missing (in
which case those variables are set to zero).
(*), (**) Significant at the 10% and 5% levels, respectively.
Received April 2000; accepted August 2001.
(1.) This model is being developed for the purpose of framing the
empirical work presented here. Thus, it is convenient to assume that the
student's attendance decision is static during the first period. It
is recognized that this decision may actually be dynamic in nature, as
the student must decide each year whether to continue at his or her
current institution or to transfer to a different institution. Expanding
the model to reflect such possible dynamics does not change the basic
results in which I am interested. For an example of a dynamic model, see
Altonji (1993).
(2.) Attendance costs should be increasing in quality for two
reasons. First, higher-quality institutions tend to charge higher fees.
Second, because of the small number of high-quality universities, a
student will have to move from home to attend one, so that the
opportunity cost of attendance will be higher. The data set used in this
analysis allows us to test this proposition as follows. Net costs are
calculated as the difference between the self-reported total attendance
costs (tuition, books, mom and board, and living expenses) and total
financial aid (loans, scholarships, and so on) for each student during
the 1982-1983 academic year. The average net costs for students by
quartiles of university quality are $1915.94, $3320.33, $3688.33, and
$4471.61. Moreover, a regression with net costs at the dependent
variable indicates that university quality has a significantly positive
effect on attendance costs. Specifically, a one-unit increase in the
mean SAT score of entering freshmen increases attendance cost s by
$8.55.
(3.) This is not a trivial assumption. However, empirical evidence
abounds that graduation quality has a positive effect on future
earnings. For example, see Wales (1973), Solmon and Wachtel (1975), Wise
(1975), Mueller (t988), James et al. (1989), and Rumberger and Thomas
(1993).
(4.) A complete discussion of the model is available from the
author on request.
(5.) The concept that students may start attending a particular
college to see whether they have the ability and/or desire to complete
the requirements of a degree is often referred to as the "option
value" of college attendance. For a detailed discussion, see Comay,
Melnick, and Pollatschek (1973); Manski (1989); and Altonji (1993).
(6.) One might be able to attempt to isolate this effect if more
detailed information on a student's performance in different
classes at the different institutions were available. For instance,
having detailed data on grades received at different institutions might
be helpful as per the previous discussion, as grades of A at a
lower-quality institution might actually imply more human capital
accumulation than grades of C or D at a higher-quality institution.
Unfortunately, the B&B survey collects only an overall grade-point
average instead of grades received at different institutions. The survey
does report major-specific and overall grade point average (GPA), but
controlling for the difference between the two does not provide any
additional information, which is not surprising, as it is not totally
clear at which institutions students would have taken their different
types of courses.
(7.) Transfer students can attend more than one different
institution before transferring to their ultimate university. Four-year
transfers in this sample attended an average of 1.36 before
transferring, while two-year college graduates attended an average of
1.44 before transferring. To account for this, different formulations of
the initial quality measure were tried (i.e., average previous quality,
time-weighted average perviout quality, and so on). The results did not
differ significantly for any of the specifications.
(8.) I would obviously like to be able to estimate the function for
community college transfers. Unfortenately, most community colleges have
open-door policies and therefore do not require applicants to take
standardized qualifying exams. As such, no comparable measure of initial
quality is available for such students.
(9.) Since some individuals contribute earnings in 1997 but not
1994, my panel is unbalanced.
(10.) Prominent alternative data sets are the High School and
Beyond (HSB) and the National Longitudinal Study of the High School
Class of 1972 (NLS-72). The HSB is a nationally representative
longitudinal survey of 12,000 students who were high school seniors and
nearly 15,000 students who were high school sophomores in 1980 (National
Center for Education Statistics 1987). Among HSB seniors, only 1941 had
received a baccalaureate degree by their last follow-up (1986), while
among HSB sophomores, only 3304 bad received a baccalaureate degree by
their last follow-up (1992). The NLS-72 is a nationally representative
sample of students who were seniors in high school a decade earlier
(National Center for Education Statistics 1980). Of the 12,841 students
participating in all follow-ups, 4417 had received at least a
bachelor's degree by 1986. Because of data limitations, the numbers
of students in each sample that can actually be examined are much
smaller. For example, Grogger and Eide's (1995) sample of HSB stud
ents consists of 1087 college graduates, while James et al.'s
(1989) sample of NLS-72 students contains only 2280 (1241 male) college
graduates.
(11.) These broad classifications are consistent with those used in
previous work (e.g., Grogger and Eide 1995). A detailed description of
the specific B&B-defined fields included in each broad category is
available on request.
(12.) The family income data come from financial aid application
information, if available. Otherwise, the data come from one of the
following sources: the parent interview, the student interview, the Pell file, or the student loan file. The SAT score is taken from data
supplied by Educational Testing Service (ETS), who administers the SAT,
and if those data are unavailable, it was taken from records at the
student's college; if either of these methods failed to provide SAT
data, then student self-reports were used. If an ACT score is available
but an SAT score is not, then an SAT score was imputed from the ACT
score using the scale provided in Astin (1971).
(13.) There are a small number of students who start at a four-year
college, transfer to a two-year college, then transfer back to a
four-year college. Because these few students generally spent very
little time at their initial four-year institution and more time at the
two-year institution, I classify these students as two-year transfers.
(14.) Among college graduates in this sample, the average annual
earnings for males is $23,638.63, while the annual eamings for females
is $20,917.88.
(15.) Within the sample, two-year transfers averaged nearly
one-half year more pregraduation work experience than four-year
transfers and nearly one full year more than nontransfers.
(16.) A common concern with this type of analysis is the potential
for self-selection bias. For example, future earnings for four-year
transfers who decrease quality are observed only for students who
actually chose that path and not for students who chose other paths.
Possible corrections for this type of empirical problem include
instrumental variables (IV) and Lee (1983)-type 2 stage selection
models. As is often the case in such situations, however, for the
current problem it is difficult to find either appropriate instruments
or first-stage identifying variables for the decision to transfer up or
down. A possible cause of this difficulty is that, as mentioned
previously, students primarily seem to choose to transfer because of
student/ school mismatching and that many of the covariates included in
the empirical analysis likely account for this factor. Hence, in this
instance, it does not seem that selection bias is a significant concern.
Results of corrections that were tried are available on request.
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Michael J. Hilmer *
* Department of Applied and Agricultural Economics, Virginia Polytechnic and State University, Blacksburg, VA 24602-0401, USA; E-mail
mhilmer@vt.edu.
Special thanks go to Eric Eide, Dan Goldhaber, Mark Showalter,
seminar participants at the Comell Higher Education Research Institute,
and two anonymous referees. The usual disclaimers apply.