Assessing the “Mismatch” Hypothesis:
Differentials in College Graduation Rates by Institutional Selectivity
Sigal Alon
Tel Aviv University
Marta Tienda
Princeton University
Running Header:
Assessing the Mismatch Hypothesis
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We gratefully acknowledge research support from the Mellon Foundation and
institutional support from the Office of Population Research at Princeton University.
Please direct all correspondence to salon1@post.tau.ac.il
June 2004
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Assessing the Mismatch Hypothesis
Assessing the “Mismatch” Hypothesis:
Differentials in College Graduation Rates by Institutional Selectivity
Abstract: This paper evaluates the “mismatch” hypothesis advocated by opponents of
affirmative action, which predicts lower graduation rates for minority students who attend
selective postsecondary institutions compared with those who attend colleges and
universities where their academic credentials are better matched to the institutional
average. Using two nationally representative longitudinal surveys (HS&B and NELS:88)
and a unique survey of students enrolled at selective and highly selective institutions
(C&B), we test the “mismatch” hypothesis by implementing a robust methodology that
jointly considers enrollment in and graduation from selective institutions as interrelated
outcomes. Our findings do not support the “mismatch” hypothesis for black and Hispanic
students who attended college during the 1980s and early 1990s.
Introduction
Waning support for affirmative action during the 1990s challenged the research
community to justify consideration of race as a legitimate factor in college admissions
decisions. Critics of affirmative action allege that treating race and ethnicity as a plus
factor for purposes of admission to selective and highly selective institutions sets up
minorities for failure because they are putatively unprepared to succeed academically
(Graglia 1993; Sowell 2003). Dubbed the “mismatch” hypothesis,1 the basic claim is that
the lower average graduation rates of “affirmative admits” result from a mismatch
between their academic preparation—indicated by their lower standardized college
entrance test scores and high school grades—and the scholastic requirements of the
schools that admitted them by taking race into account (Pell 2003). Presumably,
“mismatched” minority students become demoralized, underperform, and ultimately fail
to graduate (Crawford 2000; Thernstrom and Thernstrom 1999; Lerner and Nagai 2001;
Pell 2003). This logic implies that a better match between the academic credentials of
minority students with the average of institutions they attend will lead to stronger
performance, including higher graduation rates and post-graduate activities (Arkes 1999).
These claims contrast with both common knowledge and empirical research based
on elementary and secondary school students, which demonstrates that, regardless of
prior achievements, students who attend higher tracks and/or better schools make greater
scholastic gains (Gamoran 1987; Gamoran and Berends 1987; Hallinan 1996; 2000;
Entwisle et. al. 1997; Hoffer, 1992; Gamoran and Mare, 1989). Empirical studies have
demonstrated the advantages of placement in higher ability groups with better instruction,
1
less distraction, more time spent on task, more academic role models, and more serious
learning climates (Hallinan 2001). These findings indicate that cognitive skill
development depends crucially on the opportunities for learning that schools afford
(Gamoran 1987). Participation in higher academic tracks and more demanding schools
may have offsetting advantages for disadvantaged students (Hallinan 2001).
Black students’ postsecondary experiences further support this idea. By
demonstrating that for all intervals of the SAT distribution graduation rates of black
students increase as institutional selectivity rises, Bowen and Bok (1998) challenged the
core of the “mismatch” hypothesis. Not only do their findings dispute allegations that
black students can not succeed at selective colleges and universities, but they also
demonstrate a consistent positive association between institutional selectivity and several
post-graduation outcomes, including completion of advanced degrees, earnings, and
overall satisfaction with college experiences (Dworkin 1998). Attending to the same
question, Kane (1998) argues that affirmative action narrows rather than widens gaps in
college retention rates by race because the net relationship between college selectivity
and college graduation rates is positive for all students.
While informative, findings based on comparisons of students attending
institutions that differ in the selectivity of their admissions fall short of demonstrating a
causal link between institutional selectivity and subsequent college outcomes by ignoring
student allocation to selective and nonselective college destinations (Winship and
Morgan, 1999). Because the determinants of attending a selective institution and
graduating from college overlap to a large extent, ignoring students’ institutional
2
assignment can lead to biased inferences about the effect of college selectivity on
graduation resulting from unmeasured influences that are correlated both with
institutional assignment and college graduation. This is particularly important if the
conditional probability of attending selective postsecondary institutions differs for
minority and nonminority populations of varying academic qualifications—that is, if
institutions practice affirmative action. Therefore, testing the mismatch hypothesis
requires joint estimation of the selection regime allocating students to colleges and their
graduation probability. Jointly modeling the graduation outcomes and the institutional
assignment process not only resolves a methodological weakness of prior studies, but
bears important substantive implications for the ongoing debate about affirmative action.
Our evaluation of the “mismatch” hypothesis extends prior research in three
important ways. First, unlike prior studies, we account for the selection bias stemming
from the fact that the allocation of individuals to colleges and universities that differ in
the selectivity of their admissions is endogenous to subsequent academic success. Our
analytical framework—devised to assess the causal link between institutional selectivity
and college graduation—stands to this challenge by combining several statistical methods
that model the allocation regime governing assignment to a selective institution based
both on observable and unobservable student attributes. Specifically, using propensity
score analysis (Rosenbaum and Rubin, 1983) we assess the likelihood of graduation for
groups with similar characteristics and propensity to attend a selective institution. Using a
dummy endogenous variable model (Heckman, 1978), we simultaneously model
enrollment in selective and nonselective institutions on the likelihood of graduation.
3
Second, we compare the experiences of students attending selective and highly
selective institutions using the College and Beyond (C&B) database to national collegebound populations. Analyzing the C&B data allows us to extend our analysis to students
attending the most competitive institutions in the country, which are the main focus of the
controversy about race-sensitive admissions practices. Comparing the experiences of
those students to the national college-bound populations yields a broader perspective on
the selection processes that allocate students to institutions that vary in the
competitiveness of their admissions, and also provides a reliability check on Bowen and
Bok’s (1998) claims for blacks based on the C&B data. This is especially important
because the C&B institutional selectivity spectrum is truncated, which may limit the
generalizability of inferences.
Finally, we compare the educational experiences of the four major ethno-racial
groups. By emphasizing black-white differences, prior analysts neglect the most rapidly
growing segments of the college population, namely Hispanics and Asians (see Bowen
and Bok, 1998; Kane, 1998).2 We pay special attention to Hispanics, whose position in
higher education has been relatively understudied compared with blacks. Although
Hispanics are notorious for their educational underachievement, particularly their
persistent and elevated rate of high school non completion (Fry 2003), understanding
their success in higher education—both who gains admission to and who graduates from
selective institutions—holds promise for the design of policy geared to improve their
standing in postsecondary institutions and beyond. Multi-group comparisons based on
nationally representative data not only situate Hispanics in the broader terrain of higher
4
education, but also validate findings for blacks based on a subset of highly selective
institutions.
In what follows, we elaborate on the testable implications of the “mismatch”
hypothesis and formulate a strategy for evaluating them. After describing the three data
sources used for empirical estimation, we report the statistical results. We find that
conditional on admission, all students who attend selective institutions are more likely to
graduate within six years of enrollment than their counterparts who attended less
selective colleges. We reject the “mismatch” hypothesis for students who enrolled at the
most selective institutions during the late 1980s and early 1990s.
Assessing the "Mismatch Hypothesis"
The controversy about affirmative action in college admissions, and the derivative
“mismatch” hypothesis, is about access to the most selective postsecondary institutions in
the nation. Although many factors determine the selectivity of admissions, two key
indicators are singled out for ranking postsecondary institutions, namely the average SAT
score of freshman classes and the percent of applicants admitted (Barron’s 2003; Bowen
and Bok 1998; Greenberg 2002; U.S. News and World Report 2003). Based on the 1650
institutions listed in the 2003 Barron’s Guide, only 64 institutions, or 3.9 percent, are
classified as “most competitive.” According to Greenberg (2002: 526), the nation’s
twenty-five most highly selective universities offer about 50,000 slots annually. Rising
demand for a relatively fixed number of slots at the most competitive institutions has
certainly fueled growing disapproval of affirmative action in college admissions, but so
5
too has the growing belief that standardized scores on college entrance exams are reliable
criteria for establishing admission cutoffs.3 That minority students typically average
lower scores on standardized college entrance exams is used to justify claims about their
unsuitability to attend selective institutions, where the average SAT score is well above
the minority group average (Arkes 1999; Graglia 1993; Lerner and Nagai 2001; Pell
2003).
The broad implication of these claims is that Hispanics and blacks enrolled in
institutions with selective and highly selective admissions have a lower probability of
graduating than their counterparts with similar characteristics who attend post secondary
institutions with less selective admission criteria.4 Before developing our analytical
strategy, it is important to distinguish between racial and ethnic graduation probabilities
within institutions and the predictions of the “mismatch” hypothesis, which focus on
same group comparisons between selective and nonselective institutions. Both sources of
inequality are of policy interest, but we are concerned with the latter.
Assessing the “mismatch” hypothesis requires comparing the graduation
likelihood of students attending selective institutions with their same-race counterparts
who attend nonselective schools. However, graduation from a selective institution is
conditional on being admitted, a highly selective process influenced by many observed
and unobserved factors that also influence the likelihood of timely college graduation.5
We use the Counterfactual Account of Causality conceptual and notational framework to
describe the problem (for a review see Winship and Morgan, 1999).
6
Each individual is exposed to one of two destination states, i.e. nonselective vs.
selective colleges, although each individual may be exposed to either state a priori. Each
college destination is characterized by a set of conditions that, upon exposure, affects the
likelihood of college graduation. In this framework, college destination states may be
considered as treatment and control in a quasi-experiment. A key assumption of the
counterfactual framework is that all students have a graduation likelihood in both states:
the one in which they are observed and the one in which they are not observed. A student
attending a nonselective college has an observable outcome in a nonselective college and
an unobservable counterfactual outcome at a selective institution. The causal effect of the
treatment (institutional selectively) on the outcome (graduation) of the ith individual is the
difference between the two potential outcomes in the treatment and control states.
Because only one outcome is observed for each individual, it is not possible to calculate
individual-level casual effects. Considering group differences offers a partial solution.
Analytically, the mismatch hypothesis has two related, but separable components:
(1) group differences in the probability of graduating from institutions that differ in the
selectivity of their admissions; and (2) group differences in the probability of attending a
selective institution. The following two equations formally summarize the model.
Pr( Υ i = 1 | Χ = x i ) = α Τ i + β ′ Χ i + ε i
(1 )
Pr( Τ i* = 1 | Ζ = z i ) = δ ′ Ζ i + ν i
(2)
Let Y be a measure of college graduation of the ith individual; Τi* is a latent
continuous variable denoting institutional selectivity of the ith individual's destination
7
college, where Ti=1 if Τi* ≥ 0 (selective college destination) and Ti=0 if Τi* <0
(nonselective college destination); α is its coefficient; Χ is a vector of observed
attributes that influence college graduation;
β is the vector of their coefficients; and ε is
an error term that captures unobserved factors affecting graduation. The parameter α in
equation (1) is the coefficient of interest for testing the “mismatch” hypothesis: the
hypothesis cannot be rejected when α < 0; that is, if students attending less selective
schools ( Τ = 0 ) are more likely to graduate compared with students attending more
demanding institutions ( Τ = 1 ). However, comparisons between students who attend
colleges that differ in selectivity are prone to bias because of observable and
unobservable differences that govern the selection regime. Because our substantive
interest is in same group comparisons between selective and nonselective institutions, this
equation is estimated separately for each racial-ethnic group.
Equation (2) represents the selection regime that determines assignment into
college destinations, where Ζ is a vector of observed exogenous covariates that allocate
students among postsecondary institutions;
δ is a vector of associated coefficients, and
ν is an error term that captures unobserved influences in the allocation regime. Selection
bias is possible because T and the error term of equation (1), ε , can be correlated in two
different ways (Winship and Morgan, 1999; Heckman and Hotz, 1989). First, when Ζ
(eq.2) and ε are correlated, but ε and ν are uncorrelated, the selection regime is based
on the observable attributes. If students allocated to selective and nonselective institutions
are dissimilar in their observed characteristics, meaningful comparisons are not possible
8
(Slavin, 1990). In the extreme case of no overlap between the groups, graduation
outcomes for students attending selective and nonselective institutional destinations
would differ even had all attended similar type of institution. In this case, some observed
set of factors in Ζ is related to the likelihood of graduation.
A second source of bias arises when ε and ν , the two error terms, are correlated,
which implies selection on unobservable attributes. That is, when unobserved variables
influence both the institutional assignment and the graduation outcome, the errors of the
prediction equations for both outcomes are likely to be correlated, and hence must be
jointly estimated to obtain unbiased estimates (Pindyck and Rubinfeld 1998). Drawing
causal inferences about group-specific effects of institutionsl selectivity on graduation
outcomes requires addressing both types of selection bias.
To assess the bias associated with "selection on the observables" ( Ζ and ε are
correlated), we fit equation (2) by calculating a propensity score for each individual
(Rosenbaum and Rubin 1983). Propensity scores represent the probability that
individuals with observed characteristics Ζ i , are assigned to a selective rather than a
nonselective institution. If the likelihood of attending a selective college is purely a
function of the observables, then conditional on the Z vector, assignment is random with
respect to the graduation outcome. Including the propensity score as a control variable in
the graduation equation (equation 1) removes from both Yi and Ti the component of their
correlation that is due to the assignment process (Winship & Morgan 1999). To assess the
bias stemming from the "selection on the unobservables" ( ε and ν are correlated), we
jointly estimate the likelihood of enrollment at selective institutions (equation 2) and the
9
likelihood of graduation (equation 1). Following Heckman (1978), we fit a dummy
endogenous variable model to obtain unbiased and consistent estimates. Using
appropriate distributional assumptions, this technique estimates error covariances (i.e. the
correlation between ε and v) across equations (Pindyck and Rubinfeld, 1998; Greene,
2000).
Testing the “mismatch” hypothesis once selection is accounted for requires
evidence of lower graduation odds relative to statistically similar group members
attending less demanding schools. That is,
H 0 : Pr( Υi = 1 | Τi = 1, X = xi ) < Pr(Υi = 1 | Τi = 0, X = xi )
(3)
H 1 : Pr(Υi = 1 | Τi = 1, X = xi ) ≥ Pr(Υi = 1 | Τi = 0, X = xi )
(4)
The “mismatch” hypothesis (H0) predicts that Hispanic and black students (as well as
whites and Asians) are less likely to graduate from selective compared with nonselective
institutions, conditional on their propensity to attend a selective institution. The
“mismatch” hypothesis cannot be rejected if counterpart students are more likely to
graduate from less selective schools ( α < 0 in equation (1)). Alternatively, we can reject
the “mismatch” hypothesis (H1) if statistically similar Hispanic and black students are
equally or more likely to graduate from selective compared with nonselective institutions
(when α ≥ 0).
10
Data and Empirical Estimation
To estimate graduation probabilities of students attending selective and highly
selective institutions, we analyze the 1989 cohort of the College and Beyond (C&B)
database. However, because these data represent the experience of a relatively small
share of students attending selective and highly selective four-year institutions, we also
analyze two nationally representative data sets—the High School and Beyond (HS&B)
and the National Educational Longitudinal Survey (NELS:88).
C&B is a restricted-access database constructed by the Andrew W. Mellon
Foundation between 1995 and 1997 (Bowen and Bok 1998: Appendix A). Two strengths
of these data for analyzing graduation rates at selective colleges and universities are the
accurate persistence data derived from college transcripts (rather than students’ selfreports) and the relatively large samples of minority students attending highly selective
institutions. The core of the C&B database is an “institutional data file” consisting of
undergraduate students who enrolled at one of 28 academically selective colleges and
universities in the fall of 1989.6
The institutional file contains information drawn from students’ applications and
transcripts, including race, sex, SAT scores, college grade point average, major field of
study, and importantly, graduation status (outcome and date). Institutional records were
collected for all students who enrolled in the fall of 1989 at all but three of the C&B
institutions.7 Individual student records are linked to several other sources, including a
survey that collected retrospective data, files provided by the College Entrance
Examination Board (CEEB), and data collected by Higher Education Research Institute
11
(HERI) at the UCLA. Limiting the analysis to U.S. residents/citizens with valid racial
and ethnic identities and graduation status, the final sample of 29,018 students includes
23,086 white, 2,260 black, 1,235 Hispanic, and 2,437 Asian origin students.
The HS&B and NELS:88 surveys are nationally representative samples of the
1982 and 1992 high school graduation cohorts, respectively, collected by the National
Center for Educational Statistics (NCES). The detailed education histories provided by
these longitudinal surveys make them ideal for studying both the transition to college and
the institutional selectivity of matriculants. In addition to over-samples of blacks and
Hispanics, these surveys include rich information about test scores and academic high
school performance, as well as standard indicators of family background. Transcript data
are available for students who attended college.
Our substantive interest dictates restricting both samples to students who attended
a 4-year postsecondary institution with a valid institutional selectivity ranking. For the
NELS survey, the analysis sample includes the 1992 high school graduation cohort
respondents who were interviewed in the 2000 follow-up. Of the 4,530 eligible students,
3,326 are white, 386 black, 361 Hispanic, and 457 of Asian origin. The comparable
HS&B analysis sample consists of 4,704 students who graduated from high school in
1982 and who were re-interviewed 10 years later. Eligible respondents include 3,260
whites, 644 blacks, 559 Hispanics, and 241 Asians.
Descriptive analyses are weighted to adjust for over-sampling, non-response, and
attrition. Moreover, multivariate analyses are adjusted to account for the clustered survey
design of the data set.8 Flags for missing values are included in all models, but are not
12
reported in the results presented here.9 Appendix A provides detailed definitions and
descriptive statistics of variables analyzed from each dataset.
Variables: The measure of institutional selectivity for the HS&B and
NELS:88 is identified as the mean combined SAT score of entering freshmen in 1982 and
1992, based on the Cooperative Institutional Research Project (CIRP) data. "Selective"
institutions include those whose mean classes SAT scores were above 1050; the
remainder of 4-year institutions are classified as "Nonselective." The mean combined
SAT score of the 1989 entering freshmen exceeded 1050 for all C&B institutions, which
qualify as selective under the CIRP classification. The C&B data defined "Highly
selective" institutions as those where the average combined SAT score of the entering
class was 1300 or higher (Bowen and Bok, 1989, Appendix B).
The graduation equation (equation 1) includes a dummy variable for attending a
selective school and a vector of covariates that are known to influence college persistence
and success (Tinto, 1993); including: social class (parental education and income); ability
(high school class rank, individual SAT scores) to isolate student qualifications from
institutional selectivity; and sex. The enrollment equation (equation 2) and the propensity
score model include covariates known to influence access to selective institutions,
namely: background characteristics (parental education and income, dummy variables
for public high school attendance, home geographic region, athlete status),10 and
academic preparation based on high school class rank and SAT scores (Persell et al.
1992; Davies and Guppy 1997; Hearn 1984; 1990; 1991; Karen 2002; Kingston and
Lewis 1990; Davies and Guppy 1997; Carnevale and Rose 2003). Race and ethnicity
13
dummy variables are included only in pooled models to capture minority students’
possible preferential admission advantage.
Results
Table 1 reveals the diversification of college campuses during the post-Bakke
expansion of affirmative action. The relative share of white students attending selective
institutions declined since the early 1980s, when the HS&B students began their
postsecondary education. Asians witnessed the most substantial gains at selective
institutions, nearly doubling their shares between 1982 and 1992. Despite the rapid
growth of the Hispanic college-age population since 1980 and the aggressive recruitment
of black and Hispanic students by admissions officers from selective colleges and
universities, their shares of the entering cohort rose only slightly during the 1980s.
[Table 1 about here]
At the most competitive institutions included in the C&B sample, the combined
representation of blacks and Hispanics reached 13 percent. Paralleling national trends,
the diversification of the most elite institutions largely reflects the rising Asian presence.
Cross-data comparisons reveal relatively similar shares of black students attending
selective institutions, approximately 6 to 7 percent for NELS and C&B, respectively, but
lower shares of Asian and Hispanic enrollees in selective institutions included in the
C&B data compared with NELS. Most likely this reflects the exclusion of Texas and
California public flagship institutions from the C&B database.
14
Although minority enrollment and graduation from selective postsecondary
institutions increased since 1980, racial and ethnic disparities in graduation rates persist.
Six-year graduation rates are higher, on average, at selective compared with nonselective
institutions, which undermines allegations that lowering admission thresholds to include
more minority students lowers overall graduation rates. Table 2 refutes this claim by
showing that black and Hispanic student graduation rates increased between 1982 and
1992 at both selective and nonselective institutions, even as their relative shares of the
student body rose. Specifically, the graduation rate of black students attending
nonselective schools rose from 26 percent in 1982 to 48 percent in 1992, while black
graduation rates at selective institutions rose 20 percentage points—from 52 to 72 percent
over the decade. The rise in Hispanic graduation rates during this period was more
modest, increasing from 26 to 40 percentage points at nonselective institutions compared
with an increase of only 7 percentage points at the selective institutions.11
[Table 2 about here]
Graduation rates are uniformly higher for selective compared with nonselective
institutions (see “ratio” column), although the graduation gap between selective and
nonselective colleges and universities narrowed over time for all groups. White students’
1982 graduation ratio of 1.5, which indicates that students attending selective schools
were about 50 percent more likely to graduate than their race counterparts attending
nonselective institutions, declined modestly ten years later. For Hispanic students the
graduation ratio between selective and nonselective institutions narrowed more
substantially, falling from 2.4 to 1.7. That graduation rates are higher for the C&B
15
institutions than the selective schools included in the NELS and HS&B samples is
unsurprising given the positive association between institutional selectivity and
graduation rates overall. However, these differences also highlight a limitation of the
C&B data for testing the “mismatch” hypothesis because the truncated distribution of
institutional selectivity greatly restricts variation in both student attributes and graduation
rates.
That said, two findings are noteworthy for the “mismatch” hypothesis. First,
Hispanic and black students’ graduation probabilities are higher at selective compared
with nonselective institutions, contrary to the predictions of the “mismatch” hypothesis.
In fact, it appears that the racial and ethnic graduation gap narrows as institutional
selectivity increases. Second, the graduation gap between selective and nonselective
institutions is greater for blacks and Hispanics than it is for whites in all datasets.
Although these tabular results appear to challenge the “mismatch” hypothesis, this
conclusion is tentative because students attending selective institutions are generally
better prepared academically than their counterparts enrolled in nonselective institutions.
Thus the higher minority graduation rates at selective institutions may simply reflect their
higher average qualifications relative to their group average.
The Mistmatch Regime
To assess the degree of mismatch between students and their postsecondary
institutions, Table 3 reports the deviation of each group SAT and class rank mean from
the institutional tier average.12 The top panel reports the corresponding tier averages to
16
which group-specific means are compared. In both 1982 and 1992, average SAT scores
for white and Asian students were slightly higher than the institutional tier average at
both selective and nonselective institutions. By contrast, and in line with the claims of
mismatch proponents, both black and Hispanic students enrolled in selective institutions
averaged test scores well below the respective institutional tier averages—162 and 112
points lower, respectively, for black and Hispanic HS&B respondents, and 176 and 95
points lower, respectively, for NELS students. However, the deviation of the black and
Hispanic mean SAT scores for the nonselective institutional average was greater still,
about 180 and 115 points for blacks and Hispanic HS&B students, respectively, and 155
and 100 points for blacks and Hispanic NELS students, respectively. Racial and ethnic
disparities in class rank mirror those based on average SAT scores.
[Table 3 About Here]
That black and Hispanic mean SAT scores lag behind institutional averages at
both selective and nonselective institutions would appear to challenge the “mismatch”
hypothesis. Presumably, group-specific disparities in test scores lower the odds that black
and Hispanic students will graduate in six years, yet the tabular differences reveal more
pronounced disparities among students attending nonselective compared with those
attending selective institutions. The C&B results show similar patterns, indicating that
Hispanic students are better matched to their institutions' average academic level than are
blacks, but less well than either whites and Asians. Hispanic students’ mean SAT scores
lag about 83 and 89 points, respectively, behind the tier averages at selective and highly
selective schools, but they are better matched to highly selective institutions than to
17
nonselective institutions based on class rank. Hispanic and black students attending both
selective and nonselective institutions appear to be less well prepared scholastically,
which has direct implications for their persistence in the postsecondary education system
and ultimate graduation. Their different starting lines may be more consequential at the
most selective institutions compared with less selective schools, according to the
“mismatch” hypothesis, because the academic curriculum is more demanding (Bowen
and Bok 1998; Massey, et al. 2002).
Before addressing the broader implications of this issue, as outline in our
analytical strategy, we address this question in the most restricted fashion (see footnote
4), by testing whether the larger the gap between students’ credentials and institutionspecific SAT averages, the greater the likelihood that they will not graduate from college.
For this analysis we use the C&B data to fit a probit model to assess the effect of a
student's match to institution-specific averages (in terms of SAT and class rank) on the
likelihood of graduation.13 Subtracting individual students’ achievements from their
institutional averages yields two "match" variables, which we included (along with their
product terms with group membership dummies) in the graduation equation.
Estimating this model separately for selective and highly selective institutions
reveals that students' SAT and class rank matches only predicts graduation at the less
selective institutions, but not at the most selective schools in the country. Not only is the
mismatch problem is more serious at less selective institutions, but more importantly, the
student-institution mismatch has more deleterious outcomes at less selective than at more
18
selective institutions. However, this analysis, which tests the narrow interpretation of the
mismatch hypothesis, ignores the selection regime into institutions of varying selectivity.
Comparisons between academic preparedness of students attending selective and
nonselective institutions underscores the nature of misunderstanding about the
“mismatch” hypothesis. Although minority students average lower test scores and class
rank than whites and Asians, those enrolled in selective colleges are better prepared than
their same-race counterparts who attend nonselective institutions. The “mismatch”
hypothesis is not about racial and ethnic differences in graduation within institutions, but
rather about same group comparisons across institutions that differ in the selectivity of
their admissions. The ultimate question is whether Hispanics and blacks enrolled in
institutions with selective and highly selective admissions have a lower probability of
graduating than their counterparts with similar characteristics who attend institutions
with less selective admission criteria. This is the crux of the controversy about whether
race-sensitive admissions legitimately by-pass criteria of “merit” in the interest of
diversification.
Multivariate Analysis
The multivariate analysis is designed to assess the effect of institutional selectivity
on six-year graduation status (1 = yes, 0 = no) of white, black, Hispanic, and Asian
students for all three surveys. Because the predictions of the “mismatch” hypothesis
focus on same group comparisons attending selective and nonselective institutions,
estimated models are group-specific (except for one general model for the entire
19
population). The strategy is designed to account for both types of selection bias stemming
from the fact that the allocation regime by institutional selectivity is endogenous to
subsequent academic success.
Because there is no perfect model to assess causality in nonexperimental designs,
and because alternative methods may yield different results, our multi-pronged analytical
strategy that builds on different assumptions about underlying relationships affords a
rigorous standard for testing the mismatch hypothesis (Winship and Mare, 1992). The
base model (Model A) is a simple probit that estimates equation (1) ignoring selection.
To assess the bias that is associated with "selection on the observables," we add the
calculated propensity score as a control variable in the graduation equation (equation 1),
effectively "subtracting out" of Yi and Ti the component of their correlation due to the
assignment process (Winship & Morgan 1999; Rosenbaum and Rubin 1983). Model B
reports these results.
Model C assesses possible bias from the "selection on the unobservables" by
jointly estimating the likelihood of enrollment at selective institutions (equation 2) and
the likelihood of graduation (equation 1). We estimate a bivariate probit technique that
fits a dummy endogenous variable model, as suggested by Heckman (1978), to correct for
correlated errors across equations (Pindyck and Rubinfeld, 1998; Greene, 2000). The
estimated ρ (Rho coefficient) reveals the correlation between the error terms ε and v of
equations (1) and (2), and indicates whether the joint estimation is required (i.e. if ε and
v are indeed correlated) or whether two independent binary probit models are "nested" in
the bivariate probit model (when ρ is not statistically different from zero). Because the
20
determinants of college enrollment and graduation overlap to a large extent, identification
is achieved via distributional assumptions (Greene, 2000). For ease of interpretation,
Table 4 reports marginal effects associated with the covariate of theoretical interest,
namely institutional selectivity [the α in equation (1)].14 Appendix Table B reports the
estimated probit coefficients.
Results for the entire HS&B cohort indicate that, regardless of the statistical
method employed, there is a positive and substantial effect of institutional selectivity on
6-year college graduation status, but particularly once the endogeneity of the institutional
allocation regime is modeled to account for both observed and unobserved individual
differences. Nonetheless, the group-specific models disclose race and ethnic variation in
the benefits associated with attending a selective institution in 1982. For white students
the significant ρ coefficient indicates selection on both unobservables and observables,
which makes the simultaneous assessment critical for this group. Specifically, after
controlling for the selection on the unobservables (model C), the effect of attending a
selective school increases white students’ graduation probability by approximately 40
percent. Both the base model that ignores the selection regime altogether and the model
that accounts for selection on the observables with propensity scores greatly
underestimate the benefits of attending a selective institution for white students.
[Table 4 About Here]
The ρ coefficient is not statistically significant for minority groups, suggesting
either absence of selection bias in the allocation of students across institutions, or bias
derived only from observable attributes (thus, obviating the need for joint estimation).
21
Under model B's assumptions (selection bias on the observables), attending a selective
school increases Black, Hispanic and Asian students’ graduation probability by 14, 17
and 30 percent, respectively. Our formal test requires that α ≥ 0 to reject the mismatch
hypothesis, hence these results are sufficient for the cohort of 1982.
Point estimates for the 1992 entering class (NELS:88 data) reveal the same
positive relationship between institutional selectivity and college graduation, although the
marginal effects are smaller compared with the 1982 cohort. The statistically insignificant
ρ coefficient (model C) indicates the absence of selection bias due to unobservables
attributes. Therefore, we focus on Model B, which after correcting for propensity scores,
reveals a positive causal impact of attending a selective institution on college graduation
on the order of 11 percent for the entire 1992 cohort. The group-specific models reveal
that this effect is significant for whites and Asians, but not black and Hispanic students.
For them, the marginal effect is positive and of approximately similar order of magnitude
as the estimates for whites and Asians, but the point estimate not statistically significant.
None of the methods produced a statistically significant positive effect for black students,
while for Hispanics the point estimates based on models A and B approach the
conventional threshold for statistical reliability. This accumulated evidence allows us to
safely reject the "mismatch" hypothesis for whites and Asians, but not for blacks and
Hispanics. However, even for the latter groups the results do not suggest that there is a
merit in the "mismatch" hypothesis, as all the α ≥ 0.
To further test the “mismatch” hypothesis, we direct attention to highly selective
colleges. Not only are these institutions the focus of controversy about race-sensitive
22
admission policies, but elite institutions also are wealthier and have other resources to
support all students they admit, thereby increasing their odds of graduation. In this
respect, an examination of the difference between C&B students who attend elite schools
and those attending less selective college and universities is particularly instructive. On
average, we find a positive causal impact of institutional selectivity on the likelihood of
graduation, regardless of the estimation strategy used. The results for the entire cohort do
not indicate that selection derives from the unobservables, thus Model B, which corrects
for selection on the observables is sufficient.
Group-specific models reveal that these results are dominated by white students'
experiences. The story for minority groups is somewhat different. Neither model A or B
produces a statistically significant effect for institutional selectivity, and the fact the ρ
(model C) is significant ( ρ ≤ .05 ) for Hispanics and Asians only ( ρ ≤ .10 for blacks)
hints that there is selection bias on the unobservables for minority groups. By accounting
for unobserved selection bias, the increased odds of graduation from attending an elite
institution school is discernible—on the order of 13, 22 and 10 percent for Blacks,
Hispanics and Asians, respectively. Thus, the C&B findings also refute the “mismatch”
hypothesis for blacks, as Bowen and Bok (1998) claimed, and our results allow us to
generalize this finding to Hispanics and Asians as well.
Discussion
Our findings from three different datasets provide a robust assessment of the
causal effect on graduation associated with attending selective institutions, conditional on
23
admission and enrollment. The results clearly demonstrate that attending a selective or
highly selective college increases the likelihood of timely graduation, net of initial
differences. The results lend no support for the "mismatch" hypothesis for minority
students who attend selective and highly selective institutions. Nevertheless, differences
in results obtained for the 1982 and 1992 cohorts are noteworthy because they appear to
imply that benefits of attending a selective institution waned during the 1980s. Although
we restricted our analysis to students who enrolled in four-year institutions, most of the
growth in 4-year postsecondary institutions involves those with less selective admission
criteria. Although we cannot ascertain whether these results capture a true trend in this
decade or just sampling variability due to the different stratification schemes used for
these surveys, the robust C&B results for the 1989 cohort corroborate the latter
interpretation.
We caution against comparing across groups because by construction, groupspecific models only permit within group comparisons.15 However, among the C&B
students, the graduation benefit associated with attending elite schools is larger among
Hispanic and black students than among their white and Asian counterparts. The obverse
obtains for the national datasets, but the selectivity tiers are far more heterogeneous. This
is especially evident for the 1982 cohort, where whites enjoy large graduation advantages
from attending selective institutions. Taken together with the weak results for minorities
based on the national sample, our findings suggest that the more selective an institution’s
admission criteria, the larger the graduation advantages minority students can reap from
attending. This finding is not only reassuring, as it supports the conclusions of prior
24
research that ignored selection regimes, but also supports the arguments about the
continued value of race-sensitive admissions that were upheld in the recent Supreme
Court decision.16 Reflecting on Bowen and Bok’s (1998, p.89) appeal, it appears that
selective institutions that attract talented minority students must strive with equal fervor
to do whatever they can to ensure that all those admitted realize their full potential.
Conclusion
In this analysis we sought to test claims that considering Hispanic origin and race
in admissions decisions predestined “affirmative admits” for inevitable failure. Our
results confirmed claims that minority students thrive in selective schools despite their
disadvantaged starting lines (Bowen and Bok 1998; Massey et al 2003). Specifically, the
likelihood of graduation increases as the selectivity of the institution attended rises. These
findings support the notion that students learn more and are more likely to succeed when
they have greater opportunities for learning (Gamoran 1987). In short, institutional
selectivity appears to reflect better learning opportunities via better prepared classmates
or better teachers (Kane 1998). It also could represent the large institutional endowments
and resources that allow for small class sizes and facilitate strong mentoring at the most
competitive schools.17
Support mechanisms are especially important for students from
socioeconomically and academically disadvantaged backgrounds, particularly first
generation college goers, among whom black, but especially Hispanic students are
disproportionately represented (Tinto, 1993). Evidence about interaction with faculty
25
members unequivocally suggests that more contact with professors and others on campus
is conducive for increasing graduation rates (Pascaralla and Terenzini (1978; 1980);
Nettles, 1991; Nettles et. al 1986; Davis, 1991; Von Destinon, 1988; NCES, 1996). Alon
(2003) directly links financial aid to college graduation by showing that financial aid,
grants in particular, helps equalize black and Hispanic minority students’ college success
with that of their white and Asian counterparts.
Nevertheless, our results do not speak to the persistent racial and ethnic
graduation gap within selectivity tiers. Given the immense efforts and ample resources
devoted to attracting and recruiting under-represented minorities to the most selective
colleges and universities, evidence that nontrivial shares of blacks and Hispanic students
leave these institutions without a college diploma is disconcerting. Even more disturbing
are race and ethnic differences in graduation rates among students of comparable
academic ability and socioeconomic background (Bowen and Bok 1998; Small and
Winship 2002; Vars and Bowen 1998).
Racial and ethnic gaps in college graduation rates are of major concern not only
because education serves as a gateway to personal financial success and social standing,
but also because of the shadow that graduation disparities casts on race-sensitive
admission practices. For these reasons, research must continue to explore reasons for
minority students' underperformance in both selective and nonselective institutions.
Striving to increase college access while narrowing graduation gaps is all the more urgent
in light of the changing demographic contours and the dire need to curtail the ethno-racial
divide in life chances. In that respect, our results suggest that applying race-sensitive
26
admission criteria aid in achieving this societal goal. Our findings imply that investing
institutional resources toward goals that promote college success help minority youth
realize their potential.
27
Notes
1
Bowen & Bok use the term “fit” to portray this hypothesis, but we prefer the term “mismatch” because it
succinctly captures the essence of the debate, namely that minority students with lower credentials are
“mismatched” at selective institutions and thus have worse outcomes.
2
Bowen and Bok were aware of this limitation and were directly responsible for ensuring that the collegegoing behavior of Hispanics was studied with the C&B data. This research derives from that effort.
3
This is manifested by the small industry that developed over the past two decades to prepare students,
mainly from middle and upper middle classes, to improve their SAT scores (McDonough, 1994 ).
4
A narrower interpretation of the mismatch hypothesis is that the larger the gap between students’
credentials and institution-specific SAT averages, the greater the likelihood that they will not graduate from
college. This narrowly crafted test of the mismatch hypothesis is incomplete because of several problems.
First is the complexity of students' profiles: a student may score below the institutional SAT mean but
above the institutional class rank mean or she may have another appealing attribute like athletic prowess or
mastery of an instrument. Moreover, it is not clear how large a gap in credentials should be to indicate a
mismatch. In institutions with diverse student bodies, almost all students are "mismatched" one way or
another. However, the most severe drawback to this narrow conception of the mismatch hypothesis is that it
ignores the selection regime into institutions of varying selectivity. Although we assess the narrow test, our
analytical strategy is designed to deal with the broader implications of the mismatch hypothesis.
5
This is one transition in a multi-stage selection process that includes high school graduation and the
decision to continue education after high school. It is necessary to control for prior selection stages so as
not to confound current selection with determinants of prior selections (Camron and Heckman, 1998).
Unfortunately, like most analysts who do not implement full structural models, we are unable to control for
selection prior to high school graduation.
6
Six institutions were excluded from the analysis: four historically black colleges and universities and two
universities that did not provide the detailed information needed to measure the timing of graduation.
7
For most institutions, the C&B data files included the entire entering cohorts. However for some
institutions the data are derived from samples (Bowen and Bok, 1998). In these cases, sample weights are
equal to the inverse of the probability of being sampled. All descriptive statistics presented use appropriate
sample weights so that the results accurately represent the entire entering cohort at each institution. These
weights allow projections to all C&B institutions (but not to the entire postsecondary universe).
8
This correction affects the estimated standard errors and the variance-covariance matrix of the estimators,
but not the estimated coefficients.
9
Using this strategy, a modified zero-order method, we fill all missing data with zeros and add a dummy
variable that takes the value one for missing observations and zero for complete ones. These flags provide a
useful method for testing whether the pattern of missing observations is random with respect to Y. The
modified zero-order strategy is the simplest solution when the proportion of missing data is small
(Anderson, Basilevsky and Hum, 1983). However, as with most remedies for missing data, it does not
completely eliminate its potential biasing effects.
10
The NELS data does not include a measure for athlete status.
11
That Asians’ graduation probability is lower in 1992 than in 1982 may reflect the greater heterogeneity of
the Asian sample in 1992 compared with 1982. The earlier sample includes a higher share of South and
East Asian youth, who are known to have very high rates of academic success. In addition, their high
graduation rate in 1982 may be inflated due to the small sample size, which increases the error of the
estimate.
12
For the C&B we report the percent in the top decile of their class because of the restricted variation on
this item in this data set.
13
This analysis cannot be performed using the nationally representative datasets because of small number of
students attending each institution.
14
For a dummy variable the marginal effect represents the change in the probability associated with a
discrete change in the variable from 0 to 1, holding other variables at their mean (Long, 1997).
28
15
The marginal effects presented in Table 4 summarize the relationship between selective (versus
unselective) college attendance and graduation for each group.
16
Grutter v. Bollinger, 123 S. Ct. 2325 (2003); Gratz v. Bollinger, 123 S. Ct. 2411 (2003).
17
Based on U.S. News and World Report, the highest ranking institutions have the lowest student/faculty
ratio For example, at the top ranking schools the student/Faculty ratio is 6/1, 8/1, and 7/1 at Princeton,
Harvard, and Yale, respectively. At the five selective schools tied for the 47th ranking, the ratio is 12/1,
17/1, 17/1, 19/1, and 11/1 for Pepperdine University, Rensselaer Polytechnic Institute, University of
California at Santa Barbara, University of Texas at Austin, and University of Washington, respectively.
These factors contribute to the ranking formula (U.S. News and World Report, 2003).
29
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Table 1
Racial and Ethnic Composition of Post-secondary Institutions by Admission Selectivity Tier and Entry Cohort
HS & B, 1982
Tier:
White
Black
Hispanic
Asian
%
Mean SAT
N
Non-selective
C & B, 1989
NELS, 1992
Selective
Non-selective
Selective
Selective
Highly Selective
82.5
11.4
4.4
1.7
85.4
5.3
4.4
4.9
79.4
10.3
6.2
4.1
78.2
6.2
6.0
9.6
82.7
6.9
3.3
7.1
75.4
7.2
5.5
11.8
83.2
918 (171)
3,847
16.8
1082 (174)
857
72.2
911 (167)
3,172
27.9
1083 (162)
1,358
79.2
1185 (149)
22,253
20.8
1333 (122)
6,765
Table 2
Graduation Probabilities by Race, Institutional Selectivity Tier and Entry Cohort
HS & B, 1982
Tier:
NELS, 1992
C & B, 1989
Non-selective
(1)
Selective
(2)
Ratio
(2)/(1)
Non-selective
(1)
Selective
(2)
Ratio
(2)/(1)
Selective
(1)
Highly selective
(2)
Ratio
(2)/(1)
White
Black
Hispanic
Asian
53.4
26.4
25.7
50.9
82.0
51.6
62.1
90.9
1.5
2.0
2.4
1.8
62.5
47.6
40.5
53.6
81.2
71.7
69.0
82.9
1.3
1.5
1.7
1.5
86.5
73.4
81.0
89.2
94.8
85.1
90.6
95.9
1.1
1.2
1.1
1.1
Average
49.0
80.0
1.6
59.3
80.0
1.3
85.0
94.0
1.1
3,847
857
3,172
1,358
22,253
6,765
N
Table 3
The Mismatch Regime: Deviations from Mean Institutional Scholastic Achievement and Class Rank
by Selectivity Tier, Entry Cohort and Race
HS & B, 1982
Tier:
Nonselective
NELS, 1992
Selective
Nonselective
C & B, 1989
Selective
Selective
Highlyselective
1333
(122)
Tier Means:
Tier SAT mean
(s.d.)
930.7
(182.2)
1112.6
(179.3)
912.7
(176.7)
1090.2
(172.0)
1185
(149)
Tier class rank mean
(s.d.)
64.6
(25.47)
78.5
(19.81)
67.4
(23.09)
81.4
(18.32)
63.7
21.8
10.0
21.8
13.5
13.2
1.5
2,680
0.1
580
1.0
2,387
-0.4
939
2.3
17,983
-180.0
-162.3
-155.1
-176.0
-170.7
-9.5
549
-7.0
95
-6.9
298
-3.2
88
-25.3
1,770
-115.2
-112.0
-100.1
-95.1
-83.3
-10.6
467
-3.1
92
-0.1
278
1.5
83
-11.9
861
Asian
SAT mean Deviation
7.4
37.0
-19.3
32.6
49.7
Class rank mean Deviation
N
9.1
151
9.3
90
-5.7
209
4.5
248
2.8
1,639
a
83.8
a
Deviations from Tier Means:
White
SAT mean
Class rank mean
N
Black
SAT mean Deviation
Class rank mean Deviation
N
Hispanic
SAT mean Deviation
Class rank mean Deviation
N
a
For C&B data, classrank represents percent ranked in top decile.
b
The number reported is the deviation from the corresponding tier average percentage in HS top ten percent.
13.3
b
1.0
5,103
b
-154.7
b
-18.9
490
b
-89.0
b
-3.1
374
b
51.1
b
7.1
798
b
Table 4
Group-Specific Marginal Effects (Discrete Change)a of Attending a Selective Institution on 6-Year Graduation Status
HS & B, 1982
NELS, 1992
Model Ab
Model Bc
Model Cd
Probit
Probit with
Control for
Propensity
Score
Bivariate
Probit
Model A
Probit
C & B, 1989
Model B
Model C
Probit with
Control for
Propensity
Score
Bivariate
Probit
Model A
Probit
Model B
Model C
Probit with
Control for
Propensity
Score
Bivariate
Probit
All Students
0.20 **
0.18 **
0.37 **
ρ = -0.37 **
0.11 **
0.11 **
0.04
ρ = 0.12
0.06 **
0.05 **
0.11 **
ρ = -0.25
Group-Specific Models
White
0.19 **
0.17 **
0.40 **
ρ = -0.52 **
0.10 **
0.10 **
0.00
ρ = 0.17
0.06 **
0.05 **
0.10 *
ρ = -0.19
Black
0.12 *
0.14 *
-0.03
ρ = 0.23
0.11
0.11
-0.07
ρ= 0.27
0.05 †
0.03
0.13 *
ρ = -0.24 †
Hispanic
0.17 **
0.17 **
0.14
ρ = 0.04
0.13 †
0.14 †
0.12
ρ= 0.03
0.07 †
0.05
0.22 *
ρ = -0.56 *
Asian
0.31 **
0.30 **
0.37
ρ = -0.15
0.13 **
0.13 **
0.10
ρ= 0.06
0.03
0.01 †
0.10 *
ρ = -0.43 **
Note: Appendix B presents complete results
* P ≤ .05; ** P ≤ .01; † P ≤ .10 (two-tailed: null hypothesis b = 0)
a) For a dummy variable the marginal effect represents the change in the probability associated with a discrete change in the variable from 0 to 1, holding
other variables at their mean (Long, 1997).
b) Model A does not control for nonrandom assignment into selective institutions (the "treatment").
c) Model B controls for students' propensity to attend a selective institution by controling for "propensity scores."
The specification of the model predicting propensity scores is identical to that estimated in the bivariate probit assignment equation (i.e. attending
a selective institution).
d) Model C is a group-specific bivariate probit (dummy endogenous variable model) of enrollment and 6-year graduation status.
Table Appendix A:
Descriptive Statistics of HS&B, NELS:88 and C&B Samples
Data:
College Entry Cohort:
Variable
Definition
Grad6
White
Black
Hisp
Mexican
Puerto Rican
Cuban
Asian
6-year graduation proportion
White, not of Hispanic origin
Black, not of Hispanic origin
Hispanic, regardless of race
Hispanic of Mexican origin
Hispanic of Puerto Rican origin
Hispanic of Cuban origin
Asian or Pacific Islander
0.54
0.83
0.10
0.04
Selective
Tresholds for selective
Parents, B.A.
Parental income
Class rank
SAT
Athlete
Female
Public
South
Midwest
West
a
(Std. Dev.)
NELS
1992
Mean
(Std. Dev.)
C&B
1989
Mean
(Std. Dev.)
0.02
0.65
0.79
0.09
0.06
0.47
0.11
0.42
0.06
0.87
0.81
0.07
0.04
N/A
N/A
N/A
0.08
If attend a selective institution
HS&B and NELS:88: above 1050
C&B: Selective :above 1050; Highly Selective: above 1250
0.17
0.28
0.21
At least one parent with a BA degree
In categories (HS&B:6; NELS:15; C&B:17 )
HS class rank (C&B: in Top 10%)
SAT score
If student was an athlete
Female=1, Male=0
If attend a public HS
If home region in South
If home region in Midwest
If home region in West
0.19
0.10
50.01
960.47
0.12
0.53
0.83
0.29
0.30
0.14
0.22
0.10
55.19 (35.79)
963.25 (192.81)
N/A
0.55
0.75
0.31
0.27
0.15
0.09
0.19
0.55
1217.03 (156.07)
0.12
0.51
0.44
0.26
0.23
0.08
4,530
29,018
Observations
a
HS & B
1982
Mean
C & B: if attend a highly selective institution
0.45
0.13
0.42
4,704
(36.20)
(193.83)
Appendix Table B1: Estimates of 6-Year College Graduation: HS&B 1982 Entry Cohort
All students
White
Black
Hispanic
Asian
Model C
Model C
Model C
Model C
Model C
Model A Model B
Model A Model B
Model A Model B
Model A Model B
Model A Model B
Bivariate Probit Probit
Bivariate Probit Probit
Bivariate Probit Probit
Bivariate Probit Probit
Bivariate Probit
Probit
Control
Control
Control
Control
Control
Propensity
Propensity
Propensity
Propensity
Propensity
Score
(1)
(2)
Score
(1)
(2)
Score
(1)
(2)
Score
(1)
(2)
Score
(1)
(2)
Grad6 Selective
Grad6 Selective
Grad6 Selective
Grad6 Selective
Grad6 Selective
Selective institution
Est. propensity score
Parents, B.A.
Parental income
Class rank
SAT
Black
Hispanic
Asian
0.524** 0.489** 1.121**
(0.060) (0.062) (0.190)
0.552*
(0.242)
0.279** 0.248** 0.234**
(0.046) (0.048) (0.048)
0.046** 0.041** 0.039**
(0.012) (0.012) (0.012)
0.013** 0.012** 0.012**
(0.001) (0.001) (0.001)
0.001** 0.001** 0.001**
(0.000) (0.000) (0.000)
-0.235** -0.281** -0.284**
(0.062) (0.065) (0.063)
-0.234** -0.276** -0.278**
(0.074) (0.077) (0.075)
-0.017 -0.107 -0.124
(0.087) (0.097) (0.090)
0.252**
(0.055)
0.043**
(0.016)
0.008**
(0.002)
0.002**
(0.000)
0.419**
(0.084)
0.413**
(0.089)
0.679**
(0.113)
0.557** 0.496** 1.354**
(0.078) (0.079) (0.192)
0.858**
(0.283)
0.291** 0.248** 0.228**
(0.054) (0.056) (0.057)
0.030+ 0.017
0.014
(0.015) (0.016) (0.016)
0.014** 0.014** 0.013**
(0.001) (0.001) (0.001)
0.001** 0.000
0.000
(0.000) (0.000) (0.000)
0.307*
(0.153)
0.358*
(0.163)
-0.537
(0.532)
0.249** 0.296* 0.338**
(0.064) (0.122) (0.127)
0.082** 0.061* 0.057+
(0.021) (0.030) (0.031)
0.007** 0.011** 0.012**
(0.002) (0.003) (0.003)
0.002** 0.001** 0.002**
(0.000) (0.000) (0.000)
-0.071
(0.465)
0.423*
(0.167)
0.429*
(0.169)
-0.088
(0.653)
0.328** 0.287+ 0.212
0.211
(0.125) (0.161) (0.154) (0.156)
0.057+ -0.053 0.078* 0.078*
(0.031) (0.040) (0.036) (0.036)
0.012** 0.010* 0.008** 0.008*
(0.003) (0.004) (0.003) (0.003)
0.002** 0.003** 0.002** 0.002**
(0.000) (0.000) (0.000) (0.001)
Mexican
-0.090
(0.145)
-0.238
(0.212)
0.387**
(0.132)
Puerto Rican
Female
Athlete
Public
South
Midwest
West
Pseudo R2a
Log pseudo-likelihood
0.103*
(0.045)
0.106*
(0.045)
0.105*
(0.043)
0.033
(0.053)
0.235**
(0.069)
-0.226**
(0.079)
-0.931**
(0.095)
-0.573**
(0.084)
-0.374**
(0.113)
0.036
(0.052)
0.037
(0.049)
0.110
(0.119)
0.217**
(0.083)
-0.236**
(0.091)
-1.051**
(0.118)
-0.515**
(0.089)
-0.412**
(0.152)
0.096
(0.119)
0.099
(0.118)
0.250
(0.190)
-0.269+
(0.154)
-1.080**
(0.175)
-0.697**
(0.195)
-0.155
(0.200)
-0.090
(0.144)
-0.231
(0.214)
0.388**
(0.131)
0.360
(0.870)
1.022** 1.004** 1.258
(0.261) (0.272) (0.848)
0.343
(0.775)
0.211
-0.028 0.049
0.007
0.018
(0.156) (0.199) (0.218) (0.231) (0.231)
0.078* 0.021
0.133* 0.139* 0.137*
(0.036) (0.042) (0.055) (0.056) (0.054)
0.008* 0.009* 0.014** 0.014* 0.014*
(0.004) (0.004) (0.005) (0.006) (0.006)
0.002** 0.002** 0.002** 0.002+ 0.002
(0.001) (0.001) (0.001) (0.001) (0.001)
-0.090
(0.145)
-0.233
(0.211)
0.388**
(0.131)
0.380+
(0.220)
-0.035
(0.064)
0.013+
(0.007)
0.004**
(0.001)
0.270
(0.183)
-0.047
(0.250)
0.329
(0.207)
0.426
(0.333)
-0.042
(0.195)
-0.974**
(0.250)
-1.306**
(0.353)
-0.675*
(0.264)
0.329
(0.207)
0.328
(0.206)
0.178
(0.420)
-0.234
(0.278)
-0.902*
(0.413)
-1.165**
(0.306)
-0.729**
(0.267)
0.15
0.15
0.13
0.13
0.13
0.13
0.15
0.15
0.31
0.31
-2734.08 -2730.93 -4519.37
-1901.66 -1896.23 -3103.15
-378.61 -378.07 -589.47
-322.79 -322.78 -531.32
-107.98 -107.91 -228.34
ρ
-0.37 **
-0.52 **
0.23
0.04
-0.15
Constant
-2.040** -1.748** -1.640** -3.791** -1.831** -1.362** -1.227** -3.950** -2.317** -2.527** -2.463** -3.273** -2.776** -2.811** -2.801** -3.256** -3.754** -3.467** -3.528** -4.201**
Observations
4704
4704
4704
4704
3260
3260
3260
3260
644
644
644
644
559
559
559
559
241
241
241
241
Robust standard errors in parentheses
+ significant at 10%; * significant at 5%; ** significant at 1%
a) The Pseudo R2 is the McFadden's R2, also known as the "likelihood rario index",compares the model with just the intercept to a model with all parameters (Long, 1997).
Appendix Table B2: Estimates of 6-Year College Graduation: NELS 1992 Entry Cohort
All students
White
Black
Hispanic
Asian
Model C
Model C
Model C
Model C
Model C
Model A Model B
Model A Model B
Model A Model B
Model A Model B
Model A Model B
Bivariate Probit Probit
Bivariate Probit Probit
Bivariate Probit Probit
Bivariate Probit Probit
Bivariate Probit
Probit
Control
Control
Control
Control
Control
Propensity
Propensity
Propensity
Propensity
Propensity
Score
(1)
(2)
Score
(1)
(2)
Score
(1)
(2)
Score
(1)
(2)
Score
(1)
(2)
Grad6 Selective
Grad6 Selective
Grad6 Selective
Grad6 Selective
Grad6 Selective
Selective institution
0.314** 0.324** 0.119
(0.055) (0.056) (0.374)
Est. propensity score
-0.346
(0.329)
Parents, B.A.
0.266** 0.289** 0.278**
(0.048) (0.053) (0.052)
Parental income
0.063** 0.068** 0.066**
(0.011) (0.012) (0.012)
Class rank
0.010** 0.011** 0.011**
(0.001) (0.001) (0.001)
SAT
0.001** 0.001** 0.001**
(0.000) (0.000) (0.000)
Black
-0.020 0.029
0.008
(0.078) (0.088) (0.092)
Hispanic
-0.307** -0.273** -0.286**
(0.079) (0.085) (0.091)
Asian
0.084
0.153
0.124
(0.080) (0.107) (0.110)
Mexican
0.210**
(0.052)
0.065**
(0.012)
0.006**
(0.002)
0.003**
(0.000)
0.587**
(0.087)
0.322**
(0.092)
0.608**
(0.083)
0.290** 0.298** -0.001
(0.065) (0.066) (0.533)
-0.248
(0.388)
0.273** 0.287** 0.288**
(0.057) (0.062) (0.063)
0.080** 0.085** 0.086**
(0.013) (0.015) (0.016)
0.011** 0.011** 0.011**
(0.001) (0.001) (0.001)
0.001** 0.001** 0.001**
(0.000) (0.000) (0.000)
0.278
(0.183)
0.279
(0.185)
-0.028
(0.927)
0.196** 0.497** 0.498**
(0.064) (0.181) (0.180)
0.096** 0.048
0.048
(0.016) (0.031) (0.034)
0.004* 0.009* 0.009*
(0.002) (0.004) (0.004)
0.003** 0.001+ 0.001
(0.000) (0.001) (0.001)
-0.171
(3.406)
0.340+
(0.191)
0.351+
(0.192)
-0.268
(0.934)
0.503** -0.033 0.258
0.303
(0.181) (0.224) (0.179) (0.229)
0.051
0.057
0.043
0.040
(0.041) (0.052) (0.033) (0.034)
0.010* 0.010* 0.011** 0.012**
(0.004) (0.005) (0.004) (0.004)
0.002
0.003** 0.000
0.000
(0.003) (0.001) (0.000) (0.001)
Public
South
Midwest
West
0.437** 0.454** 0.336
(0.153) (0.158) (1.315)
-0.381
(0.654)
0.267
0.664** -0.036 -0.020 -0.032
(0.271) (0.212) (0.168) (0.169) (0.174)
0.042
-0.043 0.035
0.035
0.035
(0.036) (0.039) (0.028) (0.028) (0.028)
0.011** 0.010
0.004
0.006
0.005
(0.004) (0.007) (0.004) (0.004) (0.006)
0.000
0.003** 0.002** 0.002** 0.002
(0.001) (0.001) (0.000) (0.001) (0.001)
0.147
(0.155)
0.015
(0.027)
0.013**
(0.004)
0.003**
(0.000)
-0.328* -0.324* -0.328* -0.047
(0.161) (0.164) (0.163) (0.182)
-0.342 -0.332 -0.341 0.212
Puerto Rican
Female
0.295
(1.189)
0.198** 0.198** 0.198**
(0.044) (0.044) (0.044)
0.163** 0.163** 0.164**
(0.052) (0.052) (0.051)
-0.145
(0.091)
-0.200**
(0.067)
-0.064
(0.081)
0.247**
(0.095)
0.488** 0.488** 0.485**
(0.138) (0.138) (0.155)
-0.142
(0.126)
-0.158*
(0.081)
-0.076
(0.093)
0.183
(0.121)
0.241+
(0.139)
-0.037
(0.397)
-0.290
(0.467)
0.075
(0.450)
0.636
(0.711)
0.241+
(0.139)
0.241+
(0.139)
0.241+
(0.137)
0.032
(0.221)
0.016
(0.313)
0.348
(0.336)
0.470
(0.362)
0.242+
(0.137)
0.241+
(0.137)
0.067
(0.274)
-0.567**
(0.202)
0.057
(0.286)
0.264
(0.193)
Pseudo R2
0.13
0.13
0.12
0.12
0.15
0.15
0.10
0.10
0.14
0.14
Log pseudo-likelihood -2516.72 -2516.10 -4652.02
-1824.05 -1823.84 -3378.95
-226.73 -226.73 -384.60
-224.93 -224.89 -375.07
-220.53 -220.37 -460.40
ρ
0.12
0.17
0.27
0.03
0.06
Constant
-2.244** -2.549** -2.415** -5.018** -2.448** -2.684** -2.716** -5.397** -2.302** -2.322* -2.605 -4.789** -1.534** -1.685* -1.560+ -4.426** -2.226** -2.512** -2.305* -4.427**
Observations
4530
4530
4530
4530
3326
3326
3326
3326
386
386
386
386
361
361
361
361
457
457
457
457
Robust standard errors in parentheses
+ significant at 10%; * significant at 5%; ** significant at 1%
a) The Pseudo R2 is the McFadden's R2, also known as the "likelihood rario index",compares the model with just the intercept to a model with all parameters (Long, 1997).
Appendix Table B3: Estimates of 6-Year College Graduation: C&B 1989 Entry Cohort
All students
White
Black
Hispanic
Asian
Model A Model B
Model A Model B
Model A Model B
Model A Model B
Model A Model B
Model C
Model C
Model C
Model C
Model C
Bivariate Probit Probit
Bivariate Probit Probit
Bivariate Probit Probit
Bivariate Probit Probit
Bivariate Probit
Probit
Control
Control
Control
Control
Control
Propensity
Propensity
Propensity
Propensity
Propensity
Score
(1)
(2)
Score
(1)
(2)
Score
(1)
(2)
Score
(1)
(2)
Score
(1)
(2)
Grad6 Selective
Grad6 Selective
Grad6 Selective
Grad6 Selective
Grad6 Selective
Selective institution
Est. propensity score
Parents, B.A.
Parental income
Class rank - top 10%
SAT
Black
Hispanic
Asian
Female
Athlete
Public
South
Midwest
West
Pseudo R2a
Log pseudo-likelihood
0.347** 0.278*
(0.097) (0.112)
0.381+
(0.197)
0.174** 0.172**
(0.023) (0.024)
0.003** 0.003**
(0.001) (0.001)
0.258** 0.238**
(0.047) (0.049)
0.056** 0.026
(0.016) (0.021)
-0.256** -0.318**
(0.070) (0.076)
-0.099 -0.154*
(0.073) (0.073)
0.092
0.079
(0.080) (0.083)
0.108** 0.108**
(0.038) (0.037)
0.684**
(0.230)
0.169**
(0.024)
0.003**
(0.001)
0.231**
(0.054)
0.019
(0.032)
-0.330**
(0.076)
-0.164*
(0.076)
0.077
(0.084)
0.106**
(0.037)
0.381** 0.333** 0.642*
(0.105) (0.121) (0.281)
0.269
(0.233)
-0.021 0.179** 0.174** 0.172**
(0.055) (0.034) (0.035) (0.036)
0.001
0.003** 0.003** 0.003**
(0.001) (0.001) (0.001) (0.001)
0.340** 0.235** 0.224** 0.220**
(0.117) (0.057) (0.060) (0.063)
0.464** 0.051** 0.030
0.023
(0.060) (0.015) (0.024) (0.036)
0.915**
(0.156)
0.636**
(0.158)
0.081
(0.119)
0.087* 0.087* 0.086*
(0.043) (0.042) (0.042)
0.517
(0.425)
0.014
(0.095)
0.560*
(0.258)
-0.171
(0.243)
0.664*
(0.286)
0.163+
(0.089)
0.108
(0.096)
0.496+
(0.275)
0.044
0.248** 0.251**
(0.063) (0.054) (0.055)
0.002
0.003
0.003
(0.001) (0.002) (0.002)
0.300* 0.310** 0.261**
(0.120) (0.068) (0.074)
0.481** 0.080** 0.042
(0.064) (0.024) (0.028)
0.481*
(0.207)
0.339*
(0.152)
0.208
(0.168)
0.754**
(0.271)
0.246** -0.118 0.012
0.051
(0.053) (0.085) (0.089) (0.094)
0.003
0.000
0.005** 0.006**
(0.002) (0.002) (0.002) (0.002)
0.270** 0.564** 0.293** 0.180
(0.075) (0.107) (0.099) (0.111)
0.050
0.361** 0.009
-0.053
(0.031) (0.076) (0.056) (0.059)
0.168** 0.175** 0.167**
(0.053) (0.052) (0.053)
0.516
(0.431)
0.010
(0.107)
0.567*
(0.263)
-0.145
(0.236)
0.669*
(0.289)
1.085**
(0.319)
0.208
(0.181)
0.054
(0.201)
0.686*
(0.272)
0.073
0.012
0.041
0.029
(0.086) (0.132) (0.132) (0.136)
0.006** -0.004 0.001
0.001
(0.002) (0.003) (0.002) (0.002)
0.122
0.457* 0.437** 0.378**
(0.140) (0.196) (0.112) (0.099)
-0.081 0.398** 0.126** 0.065
(0.065) (0.059) (0.038) (0.047)
0.210** 0.218** 0.201**
(0.080) (0.079) (0.076)
0.525
(0.402)
-0.080
(0.078)
0.427
(0.298)
-0.300
(0.338)
0.734+
(0.402)
0.161
(0.098)
0.293
(0.429)
0.025
(0.118)
0.348
(0.322)
-0.274
(0.341)
0.492
(0.407)
0.168+
(0.095)
0.778**
(0.147)
0.023
(0.136)
0.001
(0.002)
0.349**
(0.109)
0.045
(0.052)
0.010
(0.205)
-0.003+
(0.002)
0.417*
(0.199)
0.570**
(0.096)
0.163+
(0.094)
0.510
(0.511)
0.104
(0.083)
0.625**
(0.219)
-0.195
(0.241)
0.657**
(0.204)
0.05
0.05
0.04
0.04
0.05
0.05
0.04
0.05
0.07
0.08
-10359.1 -10344.5 -20984.3
-7951.6 -7946.2 -16228.1
-1185.1 -1183.4 -1931.9
-521.1 -517.8 -1028.9
-674.9 -666.9 -1649.0
ρ
-0.25
-0.19
-0.24 †
-0.56 *
-0.43 **
Constant
-0.044 0.284
0.366
-7.148** 0.009
0.245
0.324
-7.432** -0.591* -0.278 -0.339 -4.903** 0.308
0.839
1.089
-5.573** -0.737 -0.093 0.134
-8.575**
Observations
29018
29018
29018
29018
23086
23086
23086
23086
2260
2260
2260
2260
1235
1235
1235
1235
2437
2424
2437
2437
Robust standard errors in parentheses
+ significant at 10%; * significant at 5%; ** significant at 1%
a) The Pseudo R2 is the McFadden's R2, also known as the "likelihood rario index",compares the model with just the intercept to a model with all parameters (Long, 1997).