Differences in the college enrollment decision across race.
Lucia, Kathlyn E. ; Baumann, Robert W.
INTRODUCTION
Educational attainment in the United States and several other
developing countries has grown substantially in the past 50 years. Much
of this growth is evident in the college enrollment data, which begins
to rise in the United States around 1980. However, both the percent of
those enrolled in college and the growth rates are not equal across
races/ethnicities. Figure 1 graphs white, black, and Hispanic college
enrollment rates using 2004 data from the National Center for Education
Statistics (NCES). Figure 1 shows that black and Hispanic enrollment
rates are consistently lower than white enrollment rates after 1980.
While whites and blacks have roughly the same upward trend in education
after 1990, Hispanic enrollment rates are considerably more volatile.
After hovering around 30 percent throughout the 1980s, Hispanic
enrollment rates jump to about 35 percent after 1990 and fluctuate
around this figure until the end of the sample frame.
The first attempts to understand the growth in college enrollment
produced a variety of approaches: comparisons of college and high school
wage returns, macroeconomic effects of human capital attainment, and the
effect of changes in the pecuniary costs of college, i.e. tuition and
financial aid. As many of these authors have already discussed, the
importance of their research lies in the substantial percentage of
government budgets devoted to education. The U.S. Department of
Education estimates roughly $900 billion was spent on all levels of
education for the academic year 2004-2005, a majority of which comes
from public sources. These public outlays represent the belief of
governments that education creates positive externalities that all
citizens can enjoy.
We enter this literature by examining the differences in college
enrollment rates across races by focusing on the enrollment decision of
the recent high school graduate. This decision is influenced by several
factors, including tuition, student achievement, high school quality,
and family background characteristics such as household income and
parents' education. We investigate how these factors and others
influence the college attendance decision, and compare these effects
across whites and blacks using data provided by NCES.
In addition to the broad motivation of education research discussed
above, research on racial differences in education provides important
information for colleges and universities. Many post-secondary schools
have special programs to improve minority enrollment in order to
increase diversity. These programs are particularly important for
private institutions, which tend to have lower minority enrollment
because of higher tuition. For public institutions, these programs
combat criticism for under-representing minorities and those with low
incomes relative to their state's population. In addition, there
are several government programs with the goal to increase educational
attainment for those with below average earnings, e.g. subsidized
student loans and Pell grants. Since there is a larger percentage of
minorities in this population, these programs should help decrease the
gap in earnings between whites and other minorities in the long run.
Further, these programs are becoming increasingly more important as the
wage gap between terminal high school and college graduates continues to
grow.
[FIGURE 1 OMITTED]
We compare the black and white college enrollment decision and find
that it should be estimated separately. The evidence comes from
econometric tests, which confirm systematic differences in the
unexplained component of the enrollment decision, and by simply
examining the coefficients of separate estimations. Since blacks and
whites have different responses to the determinants of college
attendance, any conclusions drawn from estimations not taking this
heterogeneity into account are misleading. For example, pooling blacks
and whites into one sample causes results that look similar to the white
model alone since the whites constitute a much larger percentage of the
population. Within race, a further cut of the data by gender is
necessary for blacks, and to a lesser extent also for whites, for the
same reasons listed above.
We find parents' education, high school quality, and student
achievement have the expected positive effect on college enrollment, but
the effects vary greatly across our four race-gender groups.
Improvements in school quality, which we proxy using the percent of
students in a college prep program and whether the school is private,
increase the probability of college enrollment for black males by a
considerably larger amount than any of the other three groups.
Surprisingly, we find no effect of household income or socioeconomic
status for black females, and only a weakly positive income effect for
black males, suggesting the affordability of college does not affect
black enrollment rates after accounting for the rest of the enrollment
decision. However, we are unable to control for variation in tuition
across states because of anonymity concerns of the data, so we do not
assert the absence of a price response stemming from changes in tuition
and/or financial aid for blacks, which is supported in the literature.
As a whole, our results suggest the college enrollment decision,
particularly for blacks, is made long before the senior year of high
school via school quality, parents' education, geographic location,
and other factors correlated with grades and standardized test scores
such as motivation and innate ability. Similar arguments are found in
Taubman (1989) and Kane (1994), though the approaches are different.
Since colleges and universities can only control tuition and financial
aid, our results suggest tuition and/or financial aid breaks will not
expand the supply of black applicants. Rather, these tools are used
competitively for the pool of college-ready blacks. Our results are
somewhat more encouraging for governments who have some degree of
control over school quality, which we find greatly influences the
college enrollment decision for black males.
LITERATURE REVIEW
Because the college attendance decision is influenced by a variety
of individual, school, and geographic factors, the literature on college
choice is extensive. Perhaps the most commonly cited student choice
study is Fuller, Manski, and Wise (1982), which uses an expected utility
setup to arrive at a multinomial logit estimation where respondents
choose one of several post-secondary options. In general, later studies
tended to focus on one aspect of college enrollment decision: tuition,
financial aid, race, school quality, parent's education, and the
public vs. private decision, to name a few.
In the list of above, the effect of rising tuition on enrollment
rates (the price response) has received the most attention in the
literature. Leslie and Brinkman (1987) surveys 25 of these studies and
notes nearly all of them find a negative and statistically significant
relationship between tuition and college enrollment. After standardizing
the results of each work, Leslie and Brinkman find a mean price response
of -0.7 percentage points for every $100 (in 1982-83 dollars) increase
in tuition. Since the enrollment rate in higher education in 1982 was
0.33 percent, the authors conclude that a $100 increase in tuition
decreases college enrollment by 2.1 percentage points. Contrary to these
findings, enrollment rates grew while tuition rose during the early
1980s. Leslie and Brinkman list six potential explanations: 1) tuition
did not rise significantly in real terms; 2) some students matriculated
to cheaper institutions, leaving enrollment rates unaffected; 3)
need-based financial aid grew substantially since 1972; 4) increased
enrollment of women; 5) new student programs and aggressive marketing
strategies; and 6) decreased admission standards widened the applicant
pool.
In the years following Leslie and Brinkman, many more college
enrollment studies appear as researchers examine the effect of rising
tuition, financial aid, and other explanations for differences in the
enrollment rate across race, income, and geographic areas. Heller (1997)
updates Leslie and Brinkman, summarizing this later cohort of college
enrollment studies. A large majority of papers in the Heller survey
again find a negative relationship between tuition and college
enrollment at roughly the same magnitude as Leslie and Brinkman. A
selection of the studies reviewed by Heller focuses on variation in
tuition and financial aid sensitivities across race (Behrman et al.,
1992; St. John and Noell, 1989; Jackson, 1989; Heller, 1994). From these
papers, Heller concludes minorities are more sensitive to changes in
tuition and price, and offers three potential explanations: 1) minority
races are more price sensitive because they tend to have a lower family
income; 2) minorities are less willing to make financial sacrifices
because they do not picture themselves as "college material";
and 3) there are different social values of attending college across
races. Other studies find that black college enrollment rates are pulled
in two different directions by increases in the real cost of college and
improvements in black parental education and income levels (Kane, 1994;
Haveman and Wolfe, 1995).
There are several works on the black-white college attendance gap
that find large black and white high school students differ greatly,
Perna (2000) includes measures of social and cultural capital, e.g.
proxies for high school quality and parental involvement, and finds that
these proxies differ between white and non-white students. Perna notes
that one way that lower social and cultural capital can affect the
college attendance decision is through information. For example, black
high school students may have less access to college information. In
fact, Wells and Crain (1994) finds that black students who attend
schools with greater diversity benefit from increased information about
colleges. Freeman (1997) notes that some of these information gaps are
about financing, in particular whether future earnings would offset the
cost of college (tuition and opportunity). Lastly, Hurtado et al. (1997)
uses college preparatory behavior during high school as predictors for
college attendance and academic success, finding significant differences
across race. Taken together, these articles suggest there are many
differences between black and white high school students.
Much of the literature on the impact of school quality on wages and
educational attainment is also relevant here. School quality is
notoriously difficult to quantify. The most common proxies include
student-teacher ratios, per-pupil expenditures, length of school year,
teacher salary, and teacher education. The literature is divided on the
impact of school quality on educational attainment. Eric Hanushek, who
has written a great deal on school quality, argues there is no
systematic relationship between student performance and teacher-pupil
ratio or teacher education (Hanushek 1986, 1996), although he does find
evidence that teacher skill positively impacts student performance on
standardized tests (Hanushek, 1992). David Card and Alan Krueger find
school quality inputs do impact wages and educational attainment, partly
because school quality impacts the marginal benefit of an additional
year of schooling (Card and Krueger, 1992). Card and Krueger (1996)
compares blacks and whites during and after the segregation era and
finds school quality improvements for blacks after segregation ended led
to increases in wages and educational attainment.
Many of the papers listed in the literature review discuss how
omitted variables can bias the results in educational attainment
estimations. For example, it is well-known that the children of
wealthier parents are more likely to attend better schools. Thus, if
school quality is omitted from the model, then the effects of family
background will be biased upward. Alternatively, Card and Krueger (1996)
note that many schools devote extra resources toward remedial programs
to help their weaker students. If student ability is not accounted for,
it can lead to a downward bias on the effect of school resources.
EMPIRICAL MODEL
Broadly speaking, the college enrollment decision is a function of
student characteristics (which includes parental characteristics),
school quality, and affordability. There are several methods already
detailed in the literature to arrive at this reduced-from equation, most
of which use a lifetime utility maximization process that compares wages
from a high school education to wages from a college education. For
example, Becker (1962) provides a simple theoretical basis for human
capital investment decision using a lifetime utility maximization
process that compares wages under several educational outcomes.
Alternatively, the random-utility model (RUM) approach, which splits
utility into observable and unobservable portions, also applies here
(Manski, 1977). RUMs compare the differences between expected utilities
for two or more educational outcomes to arrive at the estimable equation
below.
Following convention in this literature, we assume a linear
relationship between college enrollment and the explanatory variables
mentioned above. Since the college enrollment decision is a binary
outcome, ordinary least squares produces fitted values of enrollment
that are not constrained to [0,1] and heteroskedastic error terms. For
this reason, we use a probit to estimate the above equation, which
produces consistent and efficient estimators and restricts the predicted
dependent variable to [0,1] via the normal cumulative probability
function. The log likelihood function is
l(enroll|x; [beta]) = [summation over (y=1)]{ln[[PHI](x[beta])]} +
[summation over (y=0)]{ln[1 - [PHI](x[beta])]}
where enroll is a (n x 1) vector indicating the dichotomous college
enrollment choice, the regressors detailed above are condensed into the
(n x k) matrix x, [beta] is (k x 1) matrix of estimated parameters, and
[PHI] is the standard normal cumulative distribution function. (1)
We estimate separate models for each race and also each race-gender
group to account for differences in the college enrollment decision
across samples. We use likelihood ratio tests comparing the results of
the pooled and stratified samples to substantiate this belief. Lastly,
we use White's formula to calculate consistent estimates of the
standard errors in case of heteroskedasticity.
NELS:88 DATA
The National Education Longitudinal Study of 1988 (NELS:88)
consists of a nationally representative sample of eighth grade students
in 1988, who were also surveyed in follow-ups in 1990, 1992, 1994, and
2000. During each follow-up, respondents completed a questionnaire and
aptitude tests in math, reading, science, and social science. In
addition, parents/guardians, teachers, and school administrators were
surveyed during some of the successive waves to augment the student
data.
Since our paper examines the enrollment decision across race, we
stratify the data into white and black samples using the self-reported
race question. While a comparison of other ethnicities is within our
research question (e.g., Hispanic, Asian, etc.), we omit these
individuals because of language and immigration issues that produce
substantial differences in the college enrollment decision. We also drop
respondents whose native language is not English for the same reason. In
addition, we omit those who did not complete a high school diploma or
GED by 1994 for two reasons. First, they were not eligible for
enrollment at a typical two-year or four-year institution in 1994 and
therefore the enrollment rate for this group is zero. Second, the large
majority of the explanatory variables, in particular the student
characteristics, are missing for this sub-sample since they did not
complete high school. Attempts to fill in these data using previous
follow-ups for this sub-sample, e.g. grades from 1992 (sophomore year of
high school for most) or 1988 (eighth grade for most) do not
substantially change the results.
In the NELS:88 data, assuming the respondent did not repeat eighth
grade and completed high school in four years, the expected high school
graduation date is May or June of 1992. Since the second follow-up is
administered in early spring of 1992, we cannot observe college
enrollment status using this follow-up. Therefore, we create a dummy
variable for enrollment in a two-year or a four-year postsecondary
school using data from the third follow-up, which is given in 1994. (2)
For the large majority of our sample, this leaves two years for the
respondent to enroll in a two-year or a four-year postsecondary school.
(3) Although there are respondents who will enroll in college after
1994, their decision to attend college after, say, a spell in the labor
force, is not the same as the college enrollment decision soon after
completing high school. For example, it is likely that the influence of
our explanatory variables, parents' income, grades, standardized
test scores, etc., diminishes as the respondent waits to attend college.
Light (1995) details this 'interrupted schooling' decision and
finds substantial differences between those who return to school after a
spell in the labor force and those who do not. Finally, our sample
restriction of using only recent high school graduates may be
problematic for blacks, who have lower average earnings and may postpone
college for financial reasons. Therefore, our results should only be
interpreted for the college attendance decision of the recent high
school graduate.
The independent variables come from the second follow-up in 1992,
when the vast majority of the respondents were in the second semester of
their senior year. We separate the independent variables into the
following categories: student characteristics, school quality, and
affordability. For some of these variables, we include a variable that
indicates invalid data rather than dropping the observation. This
decision is based on the difference in college enrollment between those
with valid and invalid data for a given variable. If this difference is
negligible, then we omit these observations on the assumption that this
will not create a non-random sample. For example, those that refused to
provide household income data also tended to have below average college
enrollment rates. If refusing to give income data is a signal of low
incomes, then omitting these observations represents a non-random
deletion. We also did a variety of trial-and-error testing to verify
this claim for each of the variables in our model. While inclusion of a
missing data variable limits interpretation of the marginal effects,
this is preferable to creating a non-random sample which potentially
biases all of the estimates. Lastly, we use the NELS:88 population
weights in all calculations to limit the influence of outliers.
The student characteristic variables are race, gender, geographical
location (see appendix for details), high school program, high school
grades in English, math, and science classes, total number of high
school classes in English, math, and science, the standardized score on
the reading, math, and science tests administered by NELS, and each
parent's educational attainment. For high school program, we create
dummy variables for respondents in a general, college prep, vocational,
and special education programs. NELS respondents take tests at each
interview, but the difficulty of the test depends on the
respondent's previous score in that subject. Since scores on these
exams are not directly comparable across respondents, we use the
NELS-created item response theory (IRT) score, which accounts for
varying difficulty levels of each exam and therefore are comparable
across respondents. We create five dummy variables for each IRT score:
one for each quartile, and another for respondents who did not take the
particular exam. (4) Lastly, we construct the following educational
attainment dummy variables for each parent: less than high school
diploma, terminal high school graduates, some college, and college
degree and higher. We also create two dummy variables for missing
educational attainment data for the mother and father to protect against
non-random deletions. (5)
The school quality proxies are whether the school is in an urban
area, private, and the percent of students at the high school in a
college prep program. The urban area control could plausibly be included
in student characteristics, but we include it here since these data
refer to the location of the respondent's school instead of the
household. Other school quality proxies are available in NELS:88, but
they had no explanatory effect in any of our estimations. This finding
is not surprising given the work of Hanushek mentioned earlier.
Our proxies for affordability are household income in 1991 and
socioeconomic status. We create five 1991 total household income dummy
variables: $25,000 and below, between $25,000 to $50,000, between
$50,000 and $75,000, above $75,000, and missing income data, where all
income figures are from the parent/guardian questionnaire and are in
1992 dollars. We also include the NELS:88 socioeconomic status variable,
which is standardized to have a zero mean over the entire sample. This
variable takes into account household income, and the educational
attainment, employment status, and occupation (weighted by the Duncan
socioeconomic index) of each parent. While the overlap of income in
these controls convolutes the interpretation of its marginal effect, we
find that replacing the NELS:88 socioeconomic status variable with its
non-income characteristics do not change our results.
Unfortunately, we are unable to include tuition proxies because of
data restrictions. In order to protect anonymity, the public release
version of NELS:88 only includes the four census regions for
geographical variables, leaving us with the option of using a tuition
proxy that varies only by region, or simply using regional dummy
variables. This omitted variable threatens the consistency of the
estimates if there is a correlation between tuition and any of the
explanatory variables. We do not believe that this correlation is strong
for two reasons. First, while tuition has been shown to have a negative
relationship with college enrollment rates (see the surveys in Leslie
and Brinkman, 1987 and Heller, 1997), it represents only one aspect for
affordability. A second aspect of affordability is household income,
which has considerably more variation and is included in our model.
Second, most of the variation in tuition occurs across and not within
regions. As a test, we estimate a linear least squares model where the
average 1992-93 in-state tuition at public four-year institutions is a
function of only regional dummy variables using state-level data from
the 1993 Digest of Education Statistics. The r-squared for this
regression is 0.55, meaning that 55% of the variation in tuition across
states is accounted for by the region. Given that we include income in
the model and the majority of the variation in income is accounted for
by region, we do not believe that omitting tuition threatens the
consistency of our estimates.
Table 1 presents the sample means. After omitting respondents with
missing values for the variables discussed above, we are left with 820
black and 6,172 white respondents. The differences in sample means
between our black and white samples are consistent with other research.
First, black enrollment rates are lower than white enrollment rates.
Second, whites have characteristics that make them more likely to attend
college relative to blacks. For example, whites tend to have better
grades, test scores, and come from households with higher socioeconomic
status.
RESULTS
Table 2 presents the results for the black and white samples. From
these models, we find evidence that the black and white college
enrollment decision should be estimated separately. First, the pseudo
r-squared values indicate a difference in the explanatory power between
the two models: 31.6 percent for the white sample compared to 26.1
percent for the black sample. Second, the likelihood ratio test rejects
the null hypothesis that the black and white estimates are all equal.
While this test is quite restrictive given the number of parameters, we
also run likelihood ratio tests to compare estimates for different
subsets of variables: regional effects, grades, IRT test scores (by
subject), parent's education, school quality controls, and income.
In each of these tests, we reject the null hypothesis at [alpha] = 0.01.
(6) Taken together, these results suggest the college enrollment
decision is systematically different between whites and blacks, and
therefore these models should be estimated separately. Failure to
account for this difference, e.g. estimating a sample that pools blacks
and whites together, is likely to produce misleading results since
blacks constitute a smaller portion of the population. (7)
Further evidence of the differences between the black and white
enrollment decision can be found in the marginal effects. The largest
differences in the marginal effects are in the parental education,
school quality, and affordability controls. In general, we find that the
mother's education has a larger impact than the father's
education for both races. This result does not appear to be tied to the
presence of the mother or the father in home. (8) Comparing races, we
find the effect of mother's education is considerably stronger for
blacks. All else constant, black children from mothers with at least a
high school diploma are at least 16 percent more likely to attend
college compared to black children from mothers who dropped out of high
school. The effect of father's education is also stronger for
blacks, but these estimates are less precise.
Black respondents also are more sensitive to changes in our proxies
for school quality. A one percentage point increase in the number of
students in a college prep program increases the probability of black
enrollment by 0.44 percentage points, which is over six times larger
compared to the white estimate. The effect of attending a private school
is also larger for blacks, but the difference is less pronounced.
For the affordability controls, we find increases in family income
and socioeconomic status have the expected positive effect for the white
sample, but an inconclusive effect for the black sample. While the white
income estimates generally suggest a positive relationship, all of the
black income estimates are negative (relative to income less than
$25,000, which is the omitted category). Although the effect of the
socioeconomic status control is positive, it is statistically
insignificant. (9) Many of the studies that estimate price response find
that blacks are more sensitive to changes in tuition and financial aid
at four-year institutions (e.g., Behrman, Kletzer, McPherson, and
Schapiro, 1992; St. John and Noell, 1989), which is partially caused by
lower incomes. However, income may be insignificant in our model because
black students tend to receive larger financial aid offers compared to
white students. While we cannot contradict the tuition-sensitivity
findings with our model, it is curious that blacks, who have lower mean
earnings than whites, are not responsive to changes in income after
accounting for the rest of the model. In some respects, this result
echoes Kane's sentiment that changes in the educational attainment
of black parents are far more important to black enrollment than changes
in tuition.
We have outlined reasons that blacks and whites must be estimated
separately because of differences in the college enrollment decision.
However, we could follow the same logic and cut the data in other ways,
e.g. by gender, geographic region, high school quality, or any other
characteristic. However, data limitations prevent repeated cuts,
particularly in the black sample where we begin with 820 observations.
After miming many of these subgroup models with a reasonable black
sample size we found that very few of them provided any additional
insight.
The exception is a model separated into race-gender groups. The
impetus for this cut is in the large difference in the gender
coefficients in Table 2. In both samples, females are more likely to
attend college after accounting for the rest of the model, particularly
for the black sample. Tables 3 (white sample) and 4 (black sample)
display estimates for each race-gender group. We find there are fewer
gender differences in the college enrollment decision for the white
sample, which is partially revealed by the smaller female coefficient in
Table 3. Both the white male and white female models have roughly the
same overall explanatory power (about 32 percent), and the coefficients
are largely similar. In addition, while likelihood ratio tests reject a
null hypothesis where all of the white male and white female estimates
are the same, the likelihood ratio tests on subsets of variables fail to
reject at [alpha] = 0.05. The exception is in the IRT scores; white
males have a stronger response to higher IRT math scores, while white
females have a stronger response to reading IRT scores. In sum, we find
little difference between the white male and white female college
attendance decision, which suggests that it is not necessary to separate
the white sample into male and female estimations.
For the black sample, gender differences in the enrollment decision
are considerably larger. First, the overall explanatory power is over
eight percentage points larger for black males. Second, many of the
coefficients are markedly different, which is confirmed using likelihood
ratio tests on several subsets of variables. (10) For example, black
males have a stronger response to both mother's and father's
education compared to black females. In addition, missing father's
education data has a strong negative effect on black female enrollment,
but a positive and insignificant effect on black male enrollment. This
result is likely tied to whether the father is in the household.
However, as stated in footnote 5, including controls for parents not
present in the child's household does not substantially change
this, or any of the other, results.
Black males and black females also have different responses to the
effects of our school quality controls and affordability. While the
effect of the percentage of students in a college prep program is
positive for both samples, it has considerably larger for black males.
Similarly, the probability of enrollment is not affected by income for
either black males or black females, but socioeconomic status has a
positive effect for black males. The same cannot be said for the black
female sample, which has statistically insignificant effects for all of
our affordability proxies. This same variable was positive and
insignificant for the pooled black sample, which is likely the result of
pooling the black male and black female samples, which are nearly the
same size, and pull this estimate in opposite directions.
CONCLUSION
The decision to enroll in college is part of a larger lifetime
utility maximization decision. The tradeoff between higher wages after
attending college and the pecuniary and non-pecuniary costs of attending
college is determined by a variety of factors such as tuition, student
characteristics, family background, and high school quality. Much of the
extant literature focuses on the conflicting effects of large increases
in tuition and an increase in parental educational attainment on college
enrollment rates. This literature finds both explanations are relevant,
and in the process has explored other intricacies related to the
enrollment decision including financial aid, the public vs. private
decision, and enrollment differences across race, gender, and income
groups. We enter this debate and argue the college enrollment decision
needs to be estimated separately for whites and blacks, and further
separated into gender for blacks, because of differences in the
unexplained portion of the enrollment decision. Since blacks constitute
roughly 13 percent of the U.S. population (2000 Census), any estimation
that pools both races in the same model will likely have any
black-specific effects washed out by the white sample. This is
particularly important for colleges and universities aiming to increase
black enrollment, and governments wishing to close the income gap
between blacks and whites via the college wage premium.
We find the largest differences between black and white college
enrollment decision in the effects of parents' education, school
quality, and family income. Blacks, particularly males, are much more
likely to attend college if their mother attended college. However,
whites are less responsive to parental education after accounting for
the rest of the model. In addition, blacks, particularly males, benefit
from increases in the quality of the surrounding student body, which we
measure using the percent of students in a college prep program. Lastly,
we show no evidence that affordability impacts the black female
enrollment decision, and only limited evidence that affordability
impacts black males. While our model specification prevents this finding
from contradicting the extant literature on tuition sensitivity, we
conclude that student characteristics and school quality play a larger
role in black enrollment.
As a whole, we hope for improvements in college attendance and
readiness for both races. In many respects, our findings open up many
other research questions such as the causes of racial differences in the
parent-child education correlation, and how affordability affects black
enrollment. By recognizing these differences, decision-makers at
colleges and governments can tailor policies toward specific races, and
in the case of blacks, to specific genders. In addition, it seems likely
that other ethnicities, such as Asians and Hispanics, also have unique
college decision processes, which complicates public policy but may
produce greater results in improving minority college attendance rates.
APPENDIX: CENSUS REGIONS
Region 1: Northeast
Connecticut
Maine
Massachusetts
New Hampshire
New Jersey
New York
Pennsylvania
Rhode Island
Vermont
Region 2: Midwest
Illinois
Indiana
Iowa
Kansas
Michigan
Minnesota
Missouri
Nebraska
North Dakota
Ohio
South Dakota
Wisconsin
Region 3: South
Alabama
Arkansas
Delaware
District of Columbia
Florida
Georgia
Kentucky
Louisiana
Maryland
Mississippi
North Carolina
Oklahoma
South Carolina
Tennessee
Texas
Virginia
West Virginia
Region 4: West
Alaska
Arizona
California
Colorado
Hawaii
Idaho
Montana
Nevada
New Mexico
Oregon
Utah
Washington
Wyoming
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NOTES
(1.) Tobias (2002) argues that the probability of attending college
is sensitive to the distribution and calculates predicted probabilities
that are generalized to the family of student's [t.suv.v]
distributions. Tobias finds that this specification is particularly
important for inferences across race, arguing that the distributions
with larger tails are better fits for black samples. We choose not to
follow his technique because we found no substantial differences between
the probit and logistic models (two special cases of student's
[t.sub.v] distributions), and we could not find evidence of differing
tails across race in our data.
(2.) We define enrollment as attending either a four-or two-year
institution since we do not model college completion (e.g., Light and
Strayer, 2000), and often attending a two-year institution is a stepping
stone to a four-year institution. We also attempted to estimate a
separate "attend a two-year college" decision via a
multinomial logit and multinomial probit approach, but these results did
not provide any additional insight.
(3.) Over 90 percent of our sample graduates in either May or June
1992. We also tried to define enrollment for those who attend a two-year
or a four-year postsecondary school within a certain time frame after
graduation, e.g. six or twelve months, but this produces no substantial
changes. As a comparison, Perna (2000) uses NELS data and restricts
college attendance to the fall after high school graduation.
(4.) As another example of non-random deletion rules, it is
plausible that poor students, who are not likely to go to college, may
refuse to take the test or not take it seriously.
(5.) For example, if the father's educational attainment is
missing, it could be because the father is not active in the
child's life, which could have a negative effect on college
attendance. Alternatively, parents with low educational outcomes may
refuse to answer the question.
(6.) Likelihood ratio tests on subsets of variables require
estimation of a pooled model. We omit those estimates for brevity. With
the exception of father's education, which has statistically
insignificant values for each sample, all other comparisons reject the
null hypothesis at [alpha] = 0.05.
(7.) While we have found that this problem occurs for our sample,
we do not present these results for the sake of brevity.
(8.) We tried several approaches to ensure that this result is not
influenced by differences in the percentage of mothers and/or fathers in
the household, e.g. estimating separate models for two-parent and
single-parent households and adding controls for mothers and fathers not
present in the child's household. These approaches did not change
the underlying result that blacks and whites have different responses to
their mother's and father's education level.
(9.) Since the socioeconomic control includes income, employment,
and the Duncan-weighted occupation, we also estimate a model that
replaces the socioeconomic control with controls for each component of
the index. The black income estimates remain negative and none of the
remaining controls are statistically significant.
(10.) The variables in the model differ because of a lack of
variation in some of the variables within each sample. For example,
there are no black females in our sample in a special education program.
As before, the likelihood ratio tests on subsets of variables are done
using a pooled black sample, with careful attention to the variable
specification.
Kathlyn E. Lucia, University of Washington Department of Economics
Seattle, WA 98195
Robert W. Baumann, College of the Holy Cross Department of
Economics One College Street Worcester, MA 01610 Telephone: (508)
793-3879 Fax: (508) 793-3708
Robert W. Baumann, Corresponding author. We are grateful to Miles
Cahill, John F. O'Connell, Patricia Reagan, John Carter, and the
participants of the 2005 Academic Conference at College of the Holy
Cross for valuable advice.
TABLE 1. Weighted Sample Means
Variable Name Blacks Whites
Enrolled in a post-secondary institution 0.621 0.723
Student Characteristics
Female 0.512 0.491
Northeast Region 0.160 0.225
Midwest Region 0.134 0.341
South Region 0.656 0.284
West Region 0.050 0.150
High School Program--General 0.453 0.413
High School Program--College Prep 0.389 0.477
High School Program--Vocational 0.151 0.105
High School Program--Special Education 0.007 0.005
At Least 'B' Average Grades in English 0.123 0.343
Missing English Grades 0.010 0.005
At Least 'B' Average Grades in Math 0.093 0.260
Missing Math Grades 0.015 0.008
At Least 'B' Average Grades in Science 0.128 0.294
Missing Science Grades 0.005 0.004
# of High School English Classes 3.971 4.045
# of High School Math Classes 3.076 3.195
# of High School Science Classes 2.751 2.978
IRT Reading Test Score--Lowest Quartile 0.306 0.127
IRT Reading Test Score--2nd Quartile 0.270 0.189
IRT Reading Test Score--3rd Quartile 0.196 0.257
IRT Reading Test Score--Highest Quartile 0.098 0.290
Missing IRT Reading Test Score 0.130 0.137
IRT Math Test Score--Lowest Quartile 0.444 0.250
IRT Math Test Score--2nd Quartile 0.271 0.195
IRT Math Test Score--3rd Quartile 0.191 0.249
IRT Math Test Score--Highest Quartile 0.094 0.306
Missing IRT Math Test Score 0.131 0.137
IRT Science Test Score--Lowest Quartile 0.409 0.113
IRT Science Test Score--2nd Quartile 0.232 0.195
IRT Science Test Score--3rd Quartile 0.158 0.249
IRT Science Test Score--Highest Quartile 0.064 0.306
Missing IRT Reading Test Score 0.137 0.137
Fanzily Background Characteristics
Mother's education--less than HS diploma 0.153 0.075
Mother's education--terminal HS diploma 0.465 0.482
Mother's education--some college 0.088 0.100
Mother's education--college graduate 0.192 0.254
Mother's education--missing 0.102 0.089
Father's education--less than HS diploma 0.132 0.086
Father's education--terminal HS diploma 0.397 0.395
Father's education--some college 0.082 0.083
Father's education--college graduate 0.164 0.318
Father's education--missing 0.225 0.118
Urban 0.729 0.643
School Quality Controls
Private school 0.064 0.100
% of students at HS in college prep program 0.410 0.503
Affordability
Income less than $25,000 0.451 0.179
Income between $25,000 and $49,999 0.270 0.329
Income between $50,000 and $74,999 0.121 0.208
Income at least $75,000 0.046 0.139
Missing Income 0.112 0.145
Socioeconomic status -0.283 0.189
TABLE 2. Enrollment Probit Results for White and Black Samples
Variable White Sample
Student Characteristics dF/dx z-stat
Female 0.0476 * 3.31 *
Midwest Region 0.0376 * 2.05 *
South Region 0.0166 0.87
West Region 0.0261 1.12
High School Program--College Prep 0.1132 * 7.22 *
High School Program--Vocational -0.0432 * -2.24 *
High School Program--Special Education -0.1873 * -1.82 *
At Least 'B' Average Grades in English 0.1157 * 6.26 *
Missing English Grades -0.1542 -1.23
At Least 'B' Average Grades in Math -0.0168 -0.80
Missing Math Grades 0.0944 * 1.88 *
At Least 'B' Average Grades in Science -0.0090 -0.45
Missing Science Grades 0.0358 0.45
# of High School English Classes 0.0208 * 2.45 *
# of High School Math Classes 0.0482 * 5.46 *
# of High School Science Classes 0.0608 * 6.82 *
IRT Reading Test Score--2nd Quartile 0.0035 0.16
IRT Reading Test Score--3rd Quartile 0.0331 1.38
IRT Reading Test Score--Highest Quartile 0.0505 * 1.80 *
IRT Math Test Score--2nd Quartile 0.0581 * 2.57 *
IRT Math Test Score--3rd Quartile 0.1010 * 3.99 *
IRT Math Test Score--Highest Quartile 0.1358 * 4.22 *
IRT Science Test Score--2nd Quartile -0.0201 -0.91
IRT Science Test Score--3rd Quartile -0.0228 -0.89
IRT Science Test Score--Highest Quartile -0.0503 -1.58
Missing IRT Test Scores 0.0654 * 2.66 *
Family Background Characteristics
Mother's education--terminal HS diploma 0.0504 * 2.13 *
Mother's education--some college 0.0250 0.77
Mother's education--college graduate 0.0319 1.04
Mother's education--missing 0.0627 * 2.04 *
Father's education--terminal HS diploma -0.0071 -0.34
Father's education--some college -0.0018 -0.06
Father's education--college graduate 0.0132 0.48
Father's education--missing -0.0280 -0.97
School Quality Controls
Urban 0.0100 0.70
Private school 0.0474 * 1.75 *
% of students at HS in college prep program 0.0007 * 2.46 *
Affordability
Income between $25,000 and $49,999 0.0184 1.08
Income between $50,000 and $74,999 0.0480 * 2.21 *
Income at least $75,000 0.0465 * 1.69 *
Missing Income -0.0259 -1.18
Socioeconomic status 0.1238 * 8.07 *
pseudo r-squared 0.3163
N 6,172
Variable Black Sample
Student Characteristics dF/dx z-stat
Female 0.1017 * 2.30 *
Midwest Region 0.0691 0.84
South Region 0.0058 0.08
West Region 0.1317 1.15
High School Program--College Prep 0.1295 * 2.59 *
High School Program--Vocational -0.2050 * -3.08 *
High School Program--Special Education 0.0349 0.16
At Least 'B' Average Grades in English -0.0287 -0.30
Missing English Grades 0.1921 1.06
At Least 'B' Average Grades in Math 0.1346 1.32
Missing Math Grades -0.1414 -0.68
At Least 'B' Average Grades in Science -0.0706 -0.81
Missing Science Grades -0.0839 -0.28
# of High School English Classes 0.0456 * 1.68 *
# of High School Math Classes -0.0003 -0.01
# of High School Science Classes 0.0545 * 1.84 *
IRT Reading Test Score--2nd Quartile 0.0892 1.57
IRT Reading Test Score--3rd Quartile 0.1400 * 1.84 *
IRT Reading Test Score--Highest Quartile 0.0457 0.39
IRT Math Test Score--2nd Quartile 0.0433 0.72
IRT Math Test Score--3rd Quartile 0.1772 * 2.01 *
IRT Math Test Score--Highest Quartile 0.2891 * 2.41 *
IRT Science Test Score--2nd Quartile -0.0516 -0.86
IRT Science Test Score--3rd Quartile -0.1785 * -1.90 *
IRT Science Test Score--Highest Quartile -0.0168 -0.12
Missing IRT Test Scores 0.1244 * 1.94 *
Family Background Characteristics
Mother's education--terminal HS diploma 0.1717 * 2.76 *
Mother's education--some college 0.1645 * 1.97 *
Mother's education--college graduate 0.2122 * 2.58 *
Mother's education--missing 0.0833 0.97
Father's education--terminal HS diploma 0.0377 0.58
Father's education--some college 0.0477 0.44
Father's education--college graduate 0.0839 0.91
Father's education--missing -0.0447 -0.57
School Quality Controls
Urban -0.0005 -0.01
Private school 0.1089 1.13
% of students at HS in college prep program 0.0044 * 4.08 *
Affordability
Income between $25,000 and $49,999 -0.1320 * -2.10 *
Income between $50,000 and $74,999 -0.0070 -0.08
Income at least $75,000 -0.1172 -0.88
Missing Income 0.0780 1.15
Socioeconomic status 0.0564 1.35
pseudo r-squared 0.2608
N 820
* Marginal effects in bold are statistically significant at
a minimum of ten percent.
TABLE 3. Enrollment Probit Results for White Male and White
Female Samples
Variable White Males
Student Characteristics dF/dx z-stat
Midwest Region 0.0194 0.68
South Region -0.0034 -0.11
West Region 0.0220 -0.60
High School Program--College Prep 0.1242 * 5.15 *
High School Program--Vocational -0.0646 * -2.16 *
High School Program--Special Education -0.1495 -1.12
At Least 'B' Average Grades in English 0.0835 * 2.71 *
Missing English Grades -0.2341 -1.23
At Least 'B' Average Grades in Math -0.0090 -0.27
Missing Math Grades 0.0683 0.92
At Least 'B' Average Grades in Science 0.0066 0.20
Missing Science Grades 0.0654 0.66
# of High School English Classes 0.0215 1.53
# of High School Math Classes 0.0395 * 3.08 *
# of High School Science Classes 0.0792 * 6.23 *
IRT Reading Test Score--2nd Quartile -0.0149 -0.45
IRT Reading Test Score--3rd Quartile 0.0183 0.51
IRT Reading Test Score--Highest Quartile 0.0359 0.85
IRT Math Test Score--2nd Quartile 0.0708 * 1.98 *
IRT Math Test Score--3rd Quartile 0.1347 * 3.58 *
IRT Math Test Score--Highest Quartile 0.1326 * 2.74 *
IRT Science Test Score--2nd Quartile -0.0439 -1.13
IRT Science Test Score--3rd Quartile -0.0487 -1.14
IRT Science Test Score--Highest Quartile -0.0437 -0.90
Missing IRT Test Scores 0.0440 1.11
Family Background Characteristics
Mother's education--terminal HS diploma 0.0588 1.41
Mother's education--some college -0.0038 -0.07
Mother's education--college graduate 0.0406 0.82
Mother's education--missing 0.0441 0.84
Father's education--terminal HS diploma -0.0106 -0.32
Father's education--some college 0.0248 0.54
Father's education--college graduate 0.0519 1.25
Father's education--missing -0.0563 -1.19
School Quality Controls
Urban 0.0086 0.41
Private school 0.0429 1.07
% of students at HS in college prep program 0.0005 1.05
Affordability
Income between $25,000 and $49,999 0.0041 0.16
Income between $50,000 and $74,999 0.0399 1.24
Income at least $75,000 0.0481 1.19
Missing Income -0.0527 -1.53
Socioeconomic status 0.1341 * 5.97 *
pseudo r-squared 0.3207
N 3,038
Variable White Females
Student Characteristics dF/dx z-stat
Midwest Region 0.0513 * 2.27 *
South Region 0.0323 1.39
West Region 0.0302 1.07
High School Program--College Prep 0.1109 * 5.70 *
High School Program--Vocational -0.0249 -1.03
High School Program--Special Education -0.2125 -1.31
At Least 'B' Average Grades in English 0.1324 * 6.13 *
Missing English Grades -0.0229 -0.17
At Least 'B' Average Grades in Math -0.0190 -0.77
Missing Math Grades 0.1234 * 2.25 *
At Least 'B' Average Grades in Science -0.0177 -0.73
Missing Science Grades -0.0083 -0.06
# of High School English Classes 0.0208 * 2.08 *
# of High School Math Classes 0.0572 * 5.12 *
# of High School Science Classes 0.0438 * 3.74 *
IRT Reading Test Score--2nd Quartile 0.0420 * 1.66 *
IRT Reading Test Score--3rd Quartile 0.0698 * 2.58 *
IRT Reading Test Score--Highest Quartile 0.0833 * 2.59 *
IRT Math Test Score--2nd Quartile 0.0354 1.34
IRT Math Test Score--3rd Quartile 0.0486 1.59
IRT Math Test Score--Highest Quartile 0.128 * 3.31 *
IRT Science Test Score--2nd Quartile -0.0027 -0.11
IRT Science Test Score--3rd Quartile 0.0037 0.13
IRT Science Test Score--Highest Quartile -0.0727 * -1.73
Missing IRT Test Scores 0.0876 * 3.02 *
Family Background Characteristics
Mother's education--terminal HS diploma 0.0398 1.49
Mother's education--some college 0.0500 1.39
Mother's education--college graduate 0.0175 0.45
Mother's education--missing 0.0817 * 2.35 *
Father's education--terminal HS diploma 0.0018 0.09
Father's education--some college -0.0194 -0.48
Father's education--college graduate -0.0206 -0.58
Father's education--missing -0.0087 -0.25
School Quality Controls
Urban 0.0140 0.76
Private school 0.0543 1.59
% of students at HS in college prep program 0.0009 * 2.59 *
Affordability
Income between $25,000 and $49,999 0.0332 1.56
Income between $50,000 and $74,999 0.0546 * 2.02 *
Income at least $75,000 0.0384 1.06
Missing Income -0.0073 -0.27
Socioeconomic status 0.1087 * 5.53 *
pseudo r-squared 0.3233
N 3,134
* Marginal effects in bold are statistically significant at
a minimum of ten percent.
TABLE 4. Enrollment Probit Results for Black Male and Black
Female Samples
Variable Black Males
Student Characteristics dF/dx z-stat
Midwest Region -0.0710 -0.58
South Region -0.0410 -0.42
West Region 0.1551 0.78
High School Program--College Prep 0.0846 1.05
High School Program--Vocational -0.428 * -4.14 *
High School Program--Special Education -0.2353 -0.78
At Least 'B' Average Grades in English -0.1542 -0.77
Missing English Grades -0.1215 -0.33
At Least 'B' Average Grades in Math 0.2053 1.06
Missing Math Grades 0.2048 0.73
At Least 'B' Average Grades in Science -0.0686 -0.43
Missing Science Grades 0.0577 0.16
# of High School English Classes 0.0215 0.44
# of High School Math Classes 0.0484 1.19
# of High School Science Classes 0.0630 1.50
IRT Reading Test Score--2nd Quartile 0.1456 * 1.69 *
IRT Reading Test Score--3rd Quartile 0.1824 1.58
IRT Reading Test Score--Highest Quartile 0.0126 0.06
IRT Math Test Score--2nd Quartile -0.1400 -1.39
IRT Math Test Score--3rd Quartile -- --
IRT Math Test Score--Highest Quartile -- --
IRT Math Test Score--3rd & 4th Quartiles 0.0195 0.14
IRT Science Test Score--2nd Quartile -0.0530 -0.59
IRT Science Test Score--3rd Quartile -0.0344 -0.28
IRT Science Test Score--Highest Quartile 0.1715 0.82
Missing IRT Test Scores 0.0106 0.10
Family Background Characteristics
Mother's education--terminal HS diploma 0.2086 * 1.87 *
Mother's education--some college 0.2435 * 1.69 *
Mother's education--college graduate 0.2346 * 1.66 *
Mother's education--missing 0.0507 0.34
Father's education--terminal HS diploma 0.1980 * 1.84 *
Father's education--some college 0.1693 1.18
Father's education--college graduate 0.1639 1.22
Father's education--missing 0.1658 1.41
School Quality Controls
Urban 0.2996 * 1.88 *
Private school -0.0453 -0.58
% of students at HS in college prep program 0.0070 * 4.16 *
Affordability
Income between $25,000 and $49,999 -0.1543 * -1.74 *
Income between $50,000 and $74,999 0.0528 0.45
Income at least $75,000 -0.1895 -0.96
Missing Income 0.1306 1.30
Socioeconomic status 0.1249 * 1.83 *
pseudo r-.squared 0.3349
N 376
Variable Black Females
Student Characteristics dF/dx z-stat
Midwest Region 0.1677 * 1.99 *
South Region 0.0420 0.49
West Region 0.1154 1.03
High School Program--College Prep 0.1257 * 2.22 *
High School Program--Vocational -0.0045 -0.06
High School Program--Special Education -- --
At Least 'B' Average Grades in English 0.0563 0.65
Missing English Grades 0.2253 * 1.69 *
At Least 'B' Average Grades in Math 0.1044 1.08
Missing Math Grades -- --
At Least 'B' Average Grades in Science -0.0171 -0.22
Missing Science Grades -- --
# of High School English Classes 0.0711 * 2.11 *
# of High School Math Classes -0.1062 -0.23
# of High School Science Classes 0.0615 * 1.77 *
IRT Reading Test Score--2nd Quartile 0.0435 0.65
IRT Reading Test Score--3rd Quartile 0.0218 * 1.69 *
IRT Reading Test Score--Highest Quartile -0.0570 1.08
IRT Math Test Score--2nd Quartile 0.1359 * 2.11 *
IRT Math Test Score--3rd Quartile 0.1700 * 2.04 *
IRT Math Test Score--Highest Quartile 0.1908 * 1.71 *
IRT Math Test Score--3rd & 4th Quartiles -- --
fIRT Science Test Score--2nd Quartile -- --
IRT Science Test Score--3rd Quartile -- --
IRT Science Test Score--Highest Quartile 0.0841 0.63
Missing IRT Test Scores 0.2043 * 3.25 *
Family Background Characteristics
Mother's education--terminal HS diploma 0.1419 * 2.07 *
Mother's education--some college 0.1198 1.27
Mother's education--college graduate 0.1318 1.39
Mother's education--missing 0.0376 0.38
Father's education--terminal HS diploma -0.0610 -0.79
Father's education--some college 0.0350 0.24
Father's education--college graduate 0.1445 1.47
Father's education--missing -0.1571 * -1.69 *
School Quality Controls
Urban 0.0149 0.24
Private school 0.1065 1.16
% of students at HS in college prep program 0.0017 1.47
Affordability
Income between $25,000 and $49,999 -0.0715 -0.97
Income between $50,000 and $74,999 -0.0538 -0.48
Income at least $75,000 -0.0116 -0.08
Missing Income 0.0476 0.56
Socioeconomic status 0.0168 0.37
pseudo r-.squared 0.2514
N 444
* Marginal effects in bold are statistically significant at a
minimum of ten percent.
