The Depth of the River: Student Matriculation Decisions
and the Black-White College Completion Gap
By
Ethan J. Poskanzer
B.A. Economics and International Relations Syracuse University, 2014
SUBMITTED TO THE SLOAN SCHOOL OF MANAGEMENT IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN MANAGEMENT RESEARCH at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY MAY 2020
©2020 Massachusetts Institute of Technology. All rights reserved.
Signature of Author:__________________________________________________________ Department of Management
May 9, 2020
Certified by: ___________________________________________________________________ Emilio J. Castilla NTU Professor of Management Professor, Work and Organization Studies Thesis Supervisor
Accepted by: __________________________________________________________________ Catherine Tucker Sloan Distinguished Professor of Management Professor, Marketing Faculty Chair, MIT Sloan PhD Program
The Depth of the River: Student Matriculation Decisions
and the Black-White College Completion Gap
by
Ethan J. Poskanzer
Submitted to the Department of Management on May 9, 2020 in Partial fulfillment of the requirements for the Degree of Master of Science in
Management Research ABSTRACT
In the United States, black college students are less likely to graduate than white students, which has lead many to argue that the “climate” at colleges and universities is not conducive to black students’ success. However, another factor may also be important: an insufficient pipeline of college-ready black high school graduates. The process through which students select colleges can lead this insufficient pipeline to be reflected as a black-white completion gap within a given college even if all black and white admitted students are equally likely to complete college. Highly college ready black high school graduates are likely to receive more offers of admission than white peers and are less likely to attend any given college, leading black matriculants at a given college to be less college ready on average than white classmates. With data on the full set of admits and matriculants at a US college, we observe a black-white completion gap with matriculants but estimate that no such gap would occur if every admitted student chose to matriculate. This implies that a completion gap could be generated solely through black and white students’ matriculation decisions and ensuing differences in college readiness.
Thesis Supervisor: Emilio Castilla Title: NTU Professor of Management
In the US, college graduation is associated with important outcomes like higher and more consistent earnings, greater class mobility, access to high status occupations and employers and better health (Card 1999, Delaney & Devereux, 1999, Autor et al., 2008, Torche, 2011, Rivera, 2016, Lawrence, 2017, Gaydosh et al., 2017). College graduation rates vary widely by race, which has implications for social stratification and inequality and in particular, black high school graduates are less likely to obtain a college degree than white peers (Bowen & Bok, 1998, Espenshade & Radford, 2009, Carnevale & Strohl, 2013, Charles et al., 2016). Recent research has demonstrated that this gap is largely a result of differences in college completion rates. While black high school graduates are more likely to enroll in college than comparable white students, they are much less likely to complete college (Eller and DiPrete, 2018).
But why are black students less likely to complete college than white students? A widely held argument is that the environment at colleges and universities, or “climate” is harmful to black students’ academic pursuits. Black students may face biases in college, such as discrimination by instructors or harmful stereotypes about their academic ability (Steele & Aronson, 1995,
Milkman et al. 2015). Additionally, most colleges and universities are predominantly white, and accordingly, black students may struggle to fit in with peer groups, interact with authority figures or integrate into a culture that is unfamiliar and, in some cases, hostile (Bowen & Bok, 1998, Aries & Seider, 2005, Fischer 2007, Steele 2011, Jack, 2016). One black student at an elite institution summarized these experiences by writing “Thriving in the Ivy League means suppressing aspects of your racial identity in order to fit in” (Owens, 2017).
While there are good reasons to believe that the climate at many colleges is harmful to black students, another factor may also be important: an insufficient pipeline of “college ready” black high school graduates. We use “college readiness” to refer to the summation of experiences and resources that influence a student’s probability of success in college before stepping foot on campus, such as socioeconomic background, pre-college schooling quality and extracurricular preparation for higher education. Black students face a number of obstacles that are likely to limit the pipeline of college ready black high school graduates such as discrimination in school, fewer economic resources and lower quality primary and secondary schooling (Rich and
Jennings, 2015, Jennings et al., 2015, Card & Giulino, 2016, DiPrete & Eller, 2018, Chetty et al., 2018, Riddle & Sinclair, 2019).
The process through which high school graduates reach colleges may lead this insufficient pipeline to be reflected as a black-white completion gap within a given college. As a result of diversity and affirmative action policies, black students who are highly college ready are likely to be admitted to more colleges than comparable white students (Espenshade et al., 2004, Arcidiacono et al. 2015). While these programs have been shown to benefit affected students (Alon & Tienda, 2005, Bagde et al., 2013), they may engender a readiness gap within a given school if highly college ready black students are admitted to more colleges than white students and make matriculation decisions or “self-sort” differently, and are less likely to attend any given college
This self-sorting process could generate a student body of black and white students that are not comparable with regards to likelihood of completion before college begins, even if there were no
differences in mean probability of graduation between black and white students in the full set of admits. To the extent that the most college ready black admits, who are likely to be relatively scarce as a result of the insufficient pipeline, are least likely to attend any given college, a “missing top” dynamic will occur. If the most college ready black admits are most likely to select out, the matriculants at a given college will be the least ready black admitted students and a relatively wider range of the readiness distribution of white students.
With data on the full pools of admitted students and matriculants at a US college, this paper tests the relative causes of the completion gap by using selection models to estimate what black-white gap would be observed if every admitted student chose to matriculate. If climate is the operative cause of the completion gap, estimates of the gap will be similar regardless of which admits choose to enroll, as climate should affect all students evenly. However, if the estimate of what gap would be observed if every admit enrolled is less than what is observed in the actual set of matriculants, this would provide evidence that sorting decisions at the point of matriculation play a key role in generating the gap.
In line with prior literature, we observe a completion gap within the matriculants at this college with black students underperforming relative to white students. However, we estimate that no such gap would occur if every admitted student chose to matriculate. While climate is likely to play a role at many colleges, our analysis shows that a college completion gap could be
generated solely through self-sorting at the point of matriculation and independent of climate. This provides evidence that black students who reach the point of admission at any given college may be equally ready for academic success as white students, but that the pipeline of such
students is insufficient. Following Bowen and Bok’s (1999) evocative label for the pathways by which minority students reach colleges, “The Shape of the River”, we show that the number of students who cross those pathways, or the “Depth of the River”, has important implications for inequality in college achievement.
Causes of the College Completion Gap
The common finding that black college students are less likely to graduate than white students has led many to propose that the racial climate at colleges and universities is detrimental to black students. Such a climate can affect academic achievement through negative interactions in the classroom, as instructors may provide less attention to black students (Milkman et al., 2015) or hold stereotypes that black students are less competent than others and treat them differently, which has been argued to lead affected students to disengage with academics (Steele & Aronson, 1995, Steele, 2011). Black students may also face challenges when interacting with classmates. In Aries’ (2008) ethnography of a US college, black students describe experiences in which peers believe them to be less intelligent than others and discount their contributions in the classroom, with some going as far as cutting black students’ statements off. One student described these experiences by saying “people just assume when you’re [a black student] in a classroom setting, you don’t know what’s going on”.
Similar arguments have proposed that negative racial climates exclude black students from the campus community. Most US colleges and universities are predominantly white, and black students may be treated as outsiders or feel out of place on campus (Tinto, 1987, Bowen & Bok 1998, Frankenberg et al., 2019). As minorities, black students may have a harder time forming
friendships (Hasan & Bagde, 2013), finding peers with whom to study (Steele, 2011) or
interacting with authority figures (Jack, 2016). Additionally, black students may feel pressure to “represent” their race to others, which can lead to interactions that feel unnatural or efforts to craft a public persona that is detached from one’s true self (Aries, 2008). Together, these effects are likely to lead to a diminished sense of belonging at college (Walton & Cohen, 2011).
Black primary and secondary school students also face numerous challenges that are likely to limit the pipeline of highly college ready black high school graduates and as a result, black students underperform relative to white peers throughout childhood education (Jencks & Philips, 2010). Black students experience frequent discrimination (Pager & Shephard, 2008), including in the classroom (Riddle & Sinclair, 2019), and are more likely to attend schools that provide poorer preparation for college (Rich and Jennings, 2015, Jennings et al., 2015). Within those schools, high performing black students are less likely to be selected for gifted student programs that can help bridge the gap to higher education (Card & Giulino, 2016).
Black students are also more likely to be from low socioeconomic status backgrounds (Chetty et al., 2018), which is associated with lower college readiness through lower quality primary and secondary education (Roderick et al., 2011, Reardon, 2016) and less exposure to opportunities for supplemental learning (Alexander et al., 2007). Those from low-income families are also more likely to work jobs in adolescence in lieu of focusing on schoolwork or developing
academic skills (Stevens, 2007) and are less likely to believe in the value of education, which can affect persistence through schooling (Hallsten & Pfeffer, 2018). As a result of these inequalities, DiPrete and Eller (2018) find that pre-enrollment differences in socioeconomic and academic
resources are responsible for the majority of variation in college performance between black and white students.
The process through which high school graduates reach colleges can lead the insufficient pipeline of college ready black students to be reflected as differences in black and white students’ relative college readiness before matriculation, and in turn, a completion gap. Many colleges provide preference to underrepresented minorities in admissions (Espenshade et al., 2004, Arcidiacono et al., 2015), which has been shown to benefit affected students (Alon & Tienda, 2005, Bagde et al., 2013) relative to their outcomes if they attended a less selective school. As such, highly college ready black students are likely to be admitted to more colleges than comparable white students as well as more highly ranked colleges and a readiness gap could occur within a given college if highly college ready black students, who are likely to be
relatively uncommon, are most likely to receive offers and least likely to matriculate.
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This pattern is visualized in Figure 1. While the most college ready black and white admitted students to a given college are likely to attend college elsewhere, this pattern is likely to be particularly strong within black students due to differences in their sets of alternative choices. As such, black and white students will self-sort differently into colleges when making matriculation decisions. This can lead to a completion gap even if there is no difference in likelihood of college completion between black and white students who achieve admission to a given college,
of the college readiness distribution, who are likely to be relatively scarce as a result of the limited pipeline, are least likely to matriculate, a “missing top” dynamic will occur with
matriculants at a given college being the least college ready black admitted students and a wider stratum of the readiness distribution of white admits. This can generate a completion gap
independent of climate, as black and white matriculants will not be comparably college ready before enrollment.
The Admissions and Matriculation Process and Testing the Role of Self-Sorting
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Within a given college, the relative roles of climate and self-sorting at the point of matriculation on the completion gap can be determined by the point in the process through which students reach colleges that a black-white gap in probability of college completion occurs in the set of students who could potentially attend that college. Figure 2 shows the expected relationship between the difference in probability of graduation between all admitted students and all matriculants if climate or self-sorting at the point of matriculation were operative. If climate alone drives the completion gap, any estimates of the difference between black and white students’ probability of graduation for all admitted students will be similar to that within the matriculants, as climate should affect all students equally and independent of which admits choose to matriculate.
However, if self-sorting leads to the gap, estimates of the difference in probability of graduation within admitted students will be of smaller magnitude than what occurs in the actual
the gap, and in doing so, imply that the black-white difference in college readiness is greater in the matriculants than in the full set of admits. Even if climate played a role in determining the magnitude of the gap, this pattern would provide evidence that self-sorting at the point of matriculation alone could generate a black-white completion gap.
Research Setting
We use data on the full pools of admitted and matriculated students at a college in the Northeast United States (“The College”) to examine the black-white completion gap. While focusing on a single institution naturally limits generalizability, this setting allows us to observe the stages and selection processes through which applicants to college reach graduation in close detail. In line with prior research, we observe a completion gap between black and white students at The College, with black students underperforming relative to white students.
The College is private, fully residential and relatively small, with roughly 3,500 undergraduate students enrolled at any given time. 92.8% of undergraduates major in the liberal arts, with the remainder in engineering programs. Despite drawing a relatively wealthy student body (54.3% of matriculants come from zip codes with mean incomes above $100,0001), The College attempts to remain affordable by meeting every student’s demonstrated financial need with aid packages. Like many peer schools, The College is predominantly white. 46.6% of matriculants in our sample are white while only 9.6% are black, which is slightly less than the national average (15%) for US undergraduates (Musu-Gillette et al., 2016).
1This calculation excludes students for whom we cannot calculate the mean income in their home zip code. This
includes international students and those from zip codes that are not populous enough for the census to calculate statistics
The College is ranked within the Top 20 of most major college rankings and accordingly, admission is quite competitive. Less than 20% of applicants are admitted and the average admitted student scored above the 95th percentile on the SAT exam. Despite The College’s high ranking, many admitted students still choose to attend even more highly ranked schools. Only 43.5% of admitted students in our sample elected to matriculate, and of those who did not attend, 62.8% attended more highly ranked schools as measured by the US News and World Report Rankings.
The data include the entire populations of 104,577 applicants, 10,187 admits and 4,437
matriculants to The College over a five-year period (2008 – 2012). For all applicants and admits, we observe a range of variables from the college application such as standardized test scores,2 high school grades, class rank, whether a student applied for financial aid, whether the student attended a private high school, status as a legacy or first-generation college student and
demographics such as race and gender.34 For matriculants, we observe academic performance in college in the form of whether a student graduated within The College’s expected timeframe (four academic years) and grades, as well as courses of study and extracurricular involvement.
2 Applicants reported scores from one of three exams: The three-part SAT, the two-part SAT or the ACT. To
facilitate comparisons between tests, we normalized each student’s score by its place in the distribution of all applicants who took the same test within a given year. For interpretability, the modal test (three-part SAT) is reported in descriptive statistics.
3 We omit the four smallest racial categories by membership (Native American, Multi-Racial, Other and Prefer Not
to Respond) from all tables due to space constraints. However, all models control for membership in these groups.
4 Some variables (high school GPA, high school class rank and mean income by zip code) are not available for all
individuals. In these cases, we include a spline variable indicating whether or not that student reported that variable. Students who did not report a variable are coded with a value of 0 in that variable.
These variables are supplemented in a few ways. We calculate the mean income in a student’s home zip code as recorded by the American Community Survey (U.S. Census, 2017) as a measure of socioeconomic status. Additionally, to proxy for high school quality, we include a binary indicator called “High Status High School” that indicates whether a student attended a high school listed in the US News and World Report’s Top 500 US High Schools. Lastly, for a subsample of admits we observe survey responses regarding the number of colleges to which that student applied and were admitted to, as well as the institution they ultimately chose to attend.
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Figure 3 diagrams the process through which high school graduates reach The College. This process is typical of US colleges and resembles that studied at similar institutions (Stevens 2007, Castilla and Rissing 2018). High school graduates apply for admission as either early or regular decision applicants.5 Early decision applicants apply earlier in the year (November of the year before matriculation, as opposed to December for regular decision applicants) and make a commitment to matriculate and withdraw all other applications if they are accepted. The College chooses to admit, reject or push these students to the regular decision pool. From this pool, applicants are then admitted, rejected or added to a waitlist.6
The College selects students to admit on two primary criteria: their likelihood of academic success in college and their potential to contribute to the campus community, such as through
5 Black students are less likely to apply through the early decision pool than white students (.040 vs. .081, z = 3.40,
p < .001). This could reflect two patterns. First, high readiness black students may anticipate being admitted to a wide set of colleges and be reluctant to commit to one early in the process. Second, black students are more likely to be from secondary schools with poorer college advising and may be less informed about the early decision option.
6 Waitlisted students receive a final admission or rejection after The College has information about how many of the
“original” admits chose to matriculate and the number of open seats remaining. We code students that were admitted off the waitlist as admitted.
diverse backgrounds, extracurricular successes or personal characteristics like grit. Admissions officers largely make inferences about these qualities from students’ written applications. Due to resource constraints, The College is only able to offer interviews to a random set of applicants.7 In addition to these criteria, The College has an explicit goal of increasing the number of underrepresented minorities in the student body and considers this when making admissions decisions.
Students who receive an offer of admission then choose whether or not to matriculate. The vast majority of high school graduates apply to multiple colleges (Hoxby, 2009), and given The College’s selectivity, students that were admitted are likely to have other competitive offers of admission. In support of this, the average admitted student in our sample applied to 11.2 colleges and was admitted by 7.2 (65.2%). Many of these offers are likely to be from highly ranked schools or those that are otherwise appealing to students. Students that are most demanded by admissions committees, whether as a result of high qualifications or certain demographic characteristics, such as racial minorities, are likely to be admitted to a wider set of other schools and to choose not to matriculate.
Empirical Design
Our primary measure of college completion is whether or not a student obtained their bachelor’s degree within four academic years. This measure, called “On-Time Graduation”, was chosen because The College considers four years to be the expected timeframe to obtain a bachelor’s degree and students who take longer are likely to have experienced some academic difficulty.
We supplement this analysis by using final cumulative grade point average (GPA) as an alternative measure of academic performance.
At the point of application, students have the option to select a racial identity from the following list: Asian, Black, Hispanic, Multi-Racial, Native American, Other, White and Prefer Not to Respond. The primary independent variable is a binary indicator for whether a student self-identified as black on their application. Indicators for all other groups are included as control variables in all models. As the modal group, white students are the reference category in all multivariate models. While we focus on black students, we expect to observe similar patterns for other groups that are affected similarly by diversity policies, such as Hispanic students. Asian students are not affected by diversity policies in the same way and as such, achievement differences between Asian and other students are outside the scope of this work.
To test the role of self-sorting at the point of matriculation in generating this gap, we estimate selection models that predict college completion within the pool of admitted students while controlling for the estimated probability that a given student chooses to matriculate8. This probability is estimated based on students’ demographic information and indicators of college readiness such as standardized test scores and high school grades. We use bivariate probit
8 All models and analyses exclude students who recruited athletes, as athletes follow a fundamentally different
process to The College than other students. 1.1% of all applicants and 9.2% of all admits are recruited athletes. Athletes are encouraged by coaches to apply to The College while in high school instead or choosing to apply independently, are selected for admission based on athletic talent in addition to academics and are likely to select colleges on different dimensions than other students, such as the quality of their sports team. This omission is unlikely to affect a black white gap, as there is no significant difference between black and white applicants’ probability of being an athlete (.011 vs. .009, z = .117, p = .91)
models9 with selection for this analysis because both the selection (matriculation) and outcome variables (on-time graduation) are binary.
These models estimate what black-white completion gap would be observed if every admitted student chose to matriculate, and in doing so, identify the point in the process through which students reach The College that a black-white gap occurs. This allows us to identify the role of self-sorting in generating the completion gap at The College. If the estimate of what gap would occur if every admitted student chose to matriculate is similar to what is observed in the actual matriculants, this would provide evidence that climate drives the gap. However, if our estimate of what would occur if every admit matriculated is of smaller magnitude that what is observed in the matriculants, this would indicate that self-sorting and ensuing readiness differences can independently generate a completion gap.
Selection models require a variable that satisfies the exclusion restriction to achieve full
identification. This variable must affect an admitted student’s likelihood of matriculation but be uncorrelated with academic performance and accordingly, is included in the selection equation but not the outcome equation. We use distance from a student’s home zip code to The College to fulfill this requirement. This measure is only available for students with a US zip code, and as such, our analysis is restricted these students (82.8% of the sample). Distance to a college has been used similarly as an instrumental variable in a number of other studies (Card, 1995, Kane & Rouse, 1995, Kling, 2001, Carneiro & Lee, 2008, Carneiro et al., 2011). As distance from home
9 The logic behind this model is similar to Heckman’s (1979) selection correction, but instead of estimating selection
and the outcome in two steps, both equations are estimated simultaneously using a full information maximum likelihood framework
to The College increases, a student’s probability of matriculation is likely to decrease, as travel costs increase and students may prefer to attend school closer to home. However, distance from home should not affect a student’s ability to succeed academically. For further analysis on distance’s validity in satisfying the exclusion restriction, see Appendix A.
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Table 1 shows descriptive statistics for the pools of admitted and matriculated students. Of the 10,187 admits, 4,437, or 43.5%, become matriculants. Table 1 also shows statistical tests comparing admits who matriculate with those who do not. Binary variables, such as gender, are tested with z-tests and all other variables are tested with t-tests. The descriptive statistics provide preliminary evidence that matriculants are on average less college ready than those who go elsewhere, as admitted students who choose not to matriculate perform better on measures of college readiness such as SAT scores10 (2239.0 vs. 2191.3, t = 17.3, p < .001), high school GPAs11 (102.0% vs. 98.2%, t = 3.41, p < .001) and high school class ranks (Top 1.9% vs. Top 3.3%, t = 11.9, p < .001)12 than matriculants.
Evidence of Self-Sorting Differences Between Black and White Students
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10 Results are similar (-.085 vs. .902, t = 15.4, p < .001) for the wider, normalized standardized test score variable 11 High school GPA is measured as the percentage of the school’s maximum GPA that a given student achieved.
For example, GPAs of 3.5/4 were coded as .875, or 87.5%. Many schools allow for GPAs greater than one. We were unable to observe the maximum GPA possible for all students. In these cases, we used a K-nearest neighbors model using the student’s GPA and The College’s evaluation of that student’s academic ability to estimate a maximum.
12 Class Rank refers to a student’s place in the ranking of graduates within their high school. Students that ranked
first in a class of 100 have a class rank of .01, or 1/100. This value increases as the student falls in the class rank distribution. Lower nominal values of class rank represent better performance.
Insert Table 2 about here ---
We observe descriptive evidence that the pipeline of highly college ready black high school graduates is limited relative to white high school graduates. Black admits are less college ready as measured by standardized test scores (2033.0 vs. 2258.8, t = 43.8, p <.001) and high school class rank (Top 4.5% vs. Top 2.1%, t = 10.3, p <.001). A similar pattern occurs within the matriculants, as black matriculants are less college ready than white matriculants as measured by standardized test scores (1971.5 vs. 2229.9, t = 32.2, p <.001), high school GPA (96.5% vs. 98.2%, t = 3.0, p =.003) and high school class rank (Top 6.1% vs. Top 2.7%, t = 2.5, p = .01). Figure 4 shows this divide graphically with a histogram of black and white admits sorted by standardized test score. The pipeline of black students the upper tail of the readiness distribution is particularly limited, as only .09% of admits in the top 25% of the range of standardized test scores are black, as compared to 11.4% of all admits. A similar pattern occurs within other indicators of college readiness. Black students represent only 1.0% and 6.3% of admits in the top 25% of high school GPA and class rank, respectively
We also find evidence that black and white students sort differently at the point of matriculation. First, black admits are less likely to matriculate than white admits. 37.0% of black admits
matriculate, as compared to 50.7% of white admits (z = 4.1, p < .001). This pattern is particularly stark within the upper tails of indicators of college readiness. Only 4.3% of black admits in the top 25% of the standardized test distribution chose to enroll, as compared to 33.5% of white admits in the same range. A similar dynamic occurs between black and white students in the
upper tails of high school GPA, in which 2.3% of black admits in the top 25% enroll vs. 38.3% of white admits, and class rank, 25.0% of black admits enroll vs. 49.3% of white admits.
Additionally, while black students are on average less college ready than white students within both admits and matriculants, the gap is wider within matriculants, which implies that
matriculation decisions widen the readiness gap between black and white students. White admits outperform black admits by 225.7 points on the SAT (t = 43.8, p <.001), while white
matriculants outperform black matriculants by 258.4 points (t = 32.2, p <.001). Similarly, white admits perform black admits by 2.4 percentage points of class rank (t = 3.0, p =.003), white matriculants outperform black matriculants by 3.4 percentage points (t = 2.5, p = .01). Lastly, while we observe only a loosely significant difference between the high school GPAs of black and white admits, black matriculants have lower GPAs than white matriculants (95.5% vs. 98.2%, t = 3.0, p = .003).
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Figures 5 and 6 provide further evidence that self-sorting affects the difference in average college readiness between black and white matriculants. Figure 5 shows a histogram of black admits ranked by standardized test score13 and cut by whether or not the student chose to matriculate, while Figure 6 shows the same plot for white admits. The vertical line on each plot
13 Standardized Test Score is used in this, as well as other graphs because it is the observable measure of college
readiness that is reported by most students and is most conducive to comparing students from different secondary schools.
marks where the median matriculant fell in the distribution of all admits by standardized test score. The median black matriculant was at the 34.8th percentile of all black admits, while the median white matriculant was at the 39.4th percentile of white admits. Thus, the median white matriculant is likely to be more college ready relative to the pool of white admits than the relative black matriculant is to the pool of black admits.
Black and white admits are likely to sort differently at the point of matriculation by virtue of having difference choice sets. We observe descriptive evidence of this pattern. Black admits received 7.5 offers of admission on average, while white admits received 6.2 (t = 4.0, p < .001). Black admits also received offers of admission at a higher rate, receiving .731 admissions offers per application sent compared to .642 for white admits (t = 6.1, p <.001). Additionally, black admits were more likely to attend a more highly ranked school per the US News and World Report in that year than white admits (33.1% vs. 30.0%), although the difference is insignificant (t = .9, p = .37). While we are unable to observe the full set of schools to which each student was admitted, this provides some evidence that black admits were more likely to have the option to attend a higher ranked school.
Results
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Table 3 reports results from multivariate models of the processes that connect applicants to The College to graduation. All models in table 3 include the full set of relevant controls and year-level fixed effects. Model 1 is a logistic regression estimating the probability that a given applicant is admitted. College readiness in the form of standardized tests (β =2.133, z = 73.2, p
<.001) 14, high school grades (β =.007, z = 5.4, p <.001) and high school class rank (β = -.186, z = 27.8, p <.001)15 is positively associated with admission. Black applicants (β =3.693, z = 59.4, p <.001) are more likely to be admitted than white applicants, which likely reflects The College’s efforts to increase diversity.
Model 2 estimates the probability that a given admit chooses to matriculate. We find evidence that more college ready admits are less likely to matriculate, as better standardized test scores (β =-.983, z = 19.6, p <.001), high school grades (β = -.028, z = 11.3, p <.001) and high school class ranks (β =.934, Z = 8.2, p <.001) are all negatively associated with matriculation. Black admits are 77% (β = -1.479, z = 14.8, p < .001) times less likely to matriculate than white admits.
Models 3 and 4 estimate admitted students’ choice sets when deciding whether or not to
matriculate at The College. Model 3 estimates the probability that a given student attends a more highly ranked school. We observe evidence that readiness affects a student’s choices, as better standardized test scores (β =2.311, z = 20.0, p <.001), high school grades (β =.019, z = 7.5, p <.001) and high school class rank (β =-.105, z = 7.0, p <.001) are positively associated with attending a higher ranked school. Black admits are 3.40 times (β =1.223, z = 11.8, p < .001) more likely to attend a higher ranked college than comparable white students, which provides evidence that black admits are also more likely to have the option to attend a more highly ranked school.
14 The beta on standardized test score refers to the effect of a one standard deviation increase in standardized test
score within each individual test
Model 4 estimates a Poisson regression of the number of admissions offers that a given student receives. College readiness as measured by standardized test scores (β =.070, Z = 3.4, p <.001) and high school class rank (β =-.113, Z = 2.9, p <.01) is positively associated with number of admissions received. Model 4 estimates that black admits receive .19 (z = 4.9, p < .001) more offers of admission than comparable white students, with the number of applications sent
controlled. Together, Models 3 and 4 indicate that black students have choice sets at the point of matriculation that are likely to be associated with a lower probability of selecting to matriculate at The College than comparable white students.
--- Insert Table 4 about here ---
Table 4 reports estimates of academic performance within the matriculants. Prior research would lead to the expectation that white students will outperform black students. Model 5 estimates the probability that a given student graduates within four years, or “on-time”. High school GPA is positively associated with on-time graduation (β = .026, z = 3.7, p <.001) and class rank is loosely associated with on-time graduation (β = .033, z = 3.6, p = .08). In line with prior work, we estimate that black matriculants are 49% (β = -.676, z = 2.7, p < .01) less likely to graduate on-time than comparable white matriculants. Additionally, distance from a student’s home to The College, which is used to satisfy the exclusion restriction in later selection models, is uncorrelated with on-time graduation.
Model 6 supplements our analysis of graduation rates by estimating academic achievement in the form of cumulative college GPA. College readiness as measured by standardized test scores (β = .130, t = 14.7, p < .001), high school grades (β = .003, t = 5.5, p < .001) and high school class
ranks (β = -.011, t = 6.4, p < .001) are all associated with better grades in college. Once again in line with prior research, we estimate that black matriculants underperform white matriculants by .194 grade points. This represents a sizable gap, as 91.8% of matriculants in our sample recorded final college GPAs between 3.0 and 4.0. Distance from a student’s home to The College is once again unrelated to academic achievement (β = -.002, t = .5, p =.539).
--- Insert Table 5 about here ---
Table 5 reports results from bivariate probit models with selection that estimate academic performance within the pool of admitted students while controlling for a given admitted student’s probability of choosing to matriculate. These models estimate two equations
simultaneously: a selection equation that estimates probability of matriculation and an outcome equation that estimates probability of on time graduation while controlling for the probability of matriculation.
Model 7 estimates on-time graduation rates within the pool of admitted students while
controlling for a given student’s estimated probability of matriculation. The coefficient on the indicator variable for black students is positive (β =.042) and insignificant (z = .4, p = .690), and as such, we estimate that no black-white gap would be observed if every admitted student chose to matriculate. This provides evidence that all admitted students are equally likely to graduate, but that differences in self-sorting at the point of matriculation between black and white students,
and in particular highly college ready black students’ low probability of matriculation, generate differences in pre-college readiness that contribute to the completion gap16.
Model 8 reports results from an identical regression to Model 7 using cumulative college GPA as the dependent variable. In this case, we estimate that black students would outperform white students by .104 grade points if every admitted student chose to matriculate (t = 4.2, p < .001). This figure is substantial and represents 32.5% of the standard deviation of all final GPAs in the sample. Overall, this result provides further evidence that self-sorting engenders meaningful differences between black and white matriculants.
--- Insert Figure 7 about here ---
Figure 7 shows the difference between the completion gap in the matriculants and our estimate of what would be observed if every admit matriculation for on-time graduation rate and GPA. For both measures of academic performance, models that control for probability of matriculation estimate a smaller, or even reversed difference between black and white students.
Robustness
In this section we report results from a supplementary analysis designed to test the robustness of the finding that differences in self-sorting at the point of matriculation lead to a completion gap. To check the selection models’ robustness, this analysis must fulfill two criteria. First, since the
16 Appendix B reports results from a Heckman two-step model of the same equations. This model estimates that
white students outperform black students on grade point average within the pool of admits, but the point estimate is 38.7% smaller than what is observed in the matriculants.
main result considers the transition from an admitted student to a matriculant, this analysis must incorporate data on both admits and matriculants. Second, since we find that differences in black and white admits’ matriculation decisions lead to a gap, the analysis must be conditional on comparable self-sorting decisions by black and white admits.
To conduct this analysis, we isolate a subset of the admitted students in which black and white students are comparably college ready and matriculate in similar numbers. To identify this subset, we first ranked every admitted student by their standardized test score. The lowest performing admitted student received a value of zero and the highest performing admitted student received a value of 10,187, which is the number of admits in the sample. This ranking allows us to identify an area of the sample in which students are comparably college ready. While standardized test score is an imperfect measure of readiness, it is our best proxy as it is strongly linked to academic performance and allows to make direct comparisons for as many students in the sample as possible.
--- Insert Figure 8 about here ---
We then limit the data to matriculants, as we only observe academic performance for this group. While the data is limited to matriculants, students remain ranked and distributed by their test score in the pool of admits, meaning students are ranked by their readiness relative to the full pool of admits. Additionally, while only black and white students are shown, students are ranked by their test scores relative to all admits. Figure 8 shows distribution of matriculants ranked by
test score and cut by race. Black and white matriculants clearly occupy largely separate spaces of this distribution.
We are able to identify one area of the distribution in which black and white admits choose to matriculate in similar numbers, which is roughly bounded by the solid lines in Figure 8. That black and white students matriculate in similar numbers within this subset indicates that
differences in college readiness are minimized in this group. Accordingly, we expect to estimate no differences in academic performance between black and white students in this subset.
--- Insert Figure 9 about here ---
Figure 9 shows a subset of Figure 8 focused on the area of the distribution with comparable numbers of black and white matriculants. To identify the exact subset within which to conduct the supplementary analysis, we identified the range of 100 admitted students in the test score distribution with a minimal difference between the number of black and white students. The range centered on the 1100th place in the distribution of admits has an identical number of black and white matriculants and is used as the centerpoint of the subset.
To obtain additional statistical power, we then expand the boundaries of the subset evenly until the subset contained at least 100 black or white students.17 This process leads to a 400 student-wide subset with boundaries at the 900th and 1300th students in the original distribution, which is demarcated by the dotted lines in Figure 9. This subset represents 1.9% of the full sample and
17 At sizes greater than 2200 (21.6% of the data), the subsets become asymmetric. Since the centerpoint is at the
1100th student in the distribution, there are no more students to pull to the left of the centerpoint and we can only
contains 62 black matriculants and 53 white matriculants, which is a much closer ratio than in the full pool of matriculants, in which white students outnumber black students 4.77 to 1.
We then estimate academic performance in this subset. To obtain confidence that any results are not the result of idiosyncrasies in the composition of this particular group, we gradually expand the subset’s boundaries by 50 places in the test score distribution on both sides and estimate academic performance within each progressively larger subset. The boundaries of the largest subset (7.9% of the full sample) are marked with thick black lines in Figure 9. As the boundaries expand, then subset begins to resemble the full sample with regards to differences in black and white students’ matriculation patterns. As a result, as the boundaries expand we expect estimates of the black white gap in performance in the subset to converge towards what is observed in the full sample.
--- Insert Table 6 about here ---
Table 6 reports results from models estimating the probability of on-time graduation in the progressively larger subsets. In each subset, the estimate of the black white gap in college completion is of a lower magnitude than what is observed in the full population of matriculants (.676). Additionally, for subsets wider than 1.9% of the data (400 students), we estimate that black students outperform white students or that the difference is very close to zero, although all estimates are insignificant.
That we observe a smaller or insignificant gap between black and white students in a subset in which self-sorting can be ruled out provides support that matriculation decisions affect the
completion gap. As this analytic strategy necessitates a small sample, statistical power is a
concern. However, that all five models show a point estimate of a smaller magnitude than what is observed in the full sample provides confidence that this result is not merely a function of
insignificant power.
--- Insert Figure 10 about here ---
Figure 10 graphically reports estimates of the completion gap across a wider range of subsets. The point estimate of the black-white gap from the full dataset (.676) is plotted with a dotted horizontal line. The X axis shows the subset’s width expressed as the portion of the full dataset included and the Y axis shows the estimate of the gap in that subset. Similar to results reported in Table 6,18 estimates close to the area with similar sorting by black and white students show a smaller gap between black and white students than what is observed in the full sample. As the subset expands, estimates of the gap converge toward the estimate in the full sample.
--- Insert Table 7 about here ---
--- Insert Figure 11 about here ---
Table 7 and Figure 11 report results from an identical analysis using cumulative GPA as the dependent variable. These results provide very limited support for the effect of matriculation decisions on the GPA gap. Table 7 shows estimates of cumulative GPA in the same subsets as
18 These models are similar to Model 5, although two control variables are removed. High Status High School is
removed due to insufficient variation within the subset and distance from the college is removed due to its insignificant relationship with academic performance
models shown in Table 6. Within these subsets, we estimate a slightly smaller GPA gap between black and white students than is observed in the full set of matriculants (.197), but a significant gap between black and white students remains in each model.
Figure 11 shows the point estimate of the black white GPA on a wider range of subsets as is done in Figure 9. The dotted line shows the estimate of the black white gap from the full sample. We estimate a slightly smaller gap between black and white students in the area in which self-sorting differences can be ruled out, but a significant gap remains. Thus, the supplementary analysis provides evidence that self-sorting at the point of matriculation affects the completion gap but only very limited evidence that the same process affects the GPA gap.
Discussion
Black high school graduates in the United States are significantly less likely to obtain college degrees than white peers, which has implications for inequality, as college graduation is associated with important outcomes like higher earnings and greater economic mobility. Prior research has shown that this gap is largely the result of differences in degree completion rates within black and white students who attend college, which has led many to conclude that the climate at colleges and universities is detrimental to black students’ academic pursuits.
We use data on the full set of admitted and matriculated students at a single college to show that an insufficient pipeline of college ready black high school graduates could also explain the completion gap. Additionally, we observe some evidence that the same process generates a black-white gap in grade point average within this college. To do this, we use selection models to
estimate that no black-white completion gap would be observed if every admitted student chose to matriculate. This provides evidence that the difference between black and white students’ likelihood of college completion is greater within the matriculants than the admits, and as such, self-sorting at the point of matriculation engenders meaningful differences in college readiness and can generate a completion gap independent of climate.
While focusing on a single college allows us to examine the process by which applicants to college reach graduation in close detail, doing so limits generalizability. In particular, our
findings are limited to institutions within the relative scope of The College’s status. A key factor in the pattern that we observe is that black students receive more offers of admission on average than white students and are more likely to attend a higher ranked school, likely as a result of affirmative action policies. However, Bowen & Bok (1998) estimate that only 20 – 25% of US colleges are able to enact affirmative action policies, as others are simply not selective enough to differentiate between groups and accept most applicants. Given The College’s selectivity, any student that is admitted is likely to attend a school in that 20 – 25%, and such, this pattern is likely to be limited to that group.
Additionally, while The College is very highly ranked, it is not at the absolute top of the status distribution. That black students are less likely to matriculate could be the result of two patterns at the level of the eco-system of comparable colleges. Due to an insufficient supply of college ready black students, those that are highly college ready may be linearly “pushed up” the ranking hierarchy and attend more highly ranked schools than comparable white peers. If this is the case, we would not expect to observe differences in matriculation decisions at the very highest ranked
schools, as there would be no higher ranked school for the most college ready black admits to attend. Alternatively, a small group of highly ready black students may be admitted to a large number of schools. If these individuals are distributed in their matriculation decisions, even the top schools may see a large portion of highly ready black admits attend elsewhere relative to comparable white admits. Due to our focus on one school, we are unable to observe the
ecological dynamics of students’ matriculation decisions. This would be an interesting area for future research.
That we estimate that no college completion gap would occur if every admit chose to matriculate has important implications for inequality in higher education. First, this provides evidence that pre-enrollment differences in college readiness play a key role in racial differences in college achievement. We show that a black-white college completion gap can be generated solely through self-sorting at the point of matriculation and ensuing differences in college readiness. This finding highlights the gradual pace of policies designed to mitigate deep seated inequalities. While affirmative action policies make progress and improve outcomes for affected students, they impact students at a relatively late stage in their educational career and are unable to fully resolve inequalities generated long before students reach college.
Additionally, our results provide evidence that all admitted students to The College are equally likely to graduate on time, even if the decision to admit a student was based on an affirmative action policy. This finding contradicts arguments that affirmative action policies place minorities in academic environments in which they are underprepared or are unlikely to succeed relative to others (Sander & Taylor, 2012). Rather, our analysis indicates that differences in matriculation
patterns engender a gap by comparing dissimilar subsets of the distributions of black and white students. Thus, we find no evidence that policies designed to increase diversity in the student body generate academic inequality.
Lastly, our findings provide evidence that black students who achieve admission to a selective college are equally likely to obtain a degree as white students, but that a limited supply of black students reach this point. Achieving admission to selective college is the culmination of a life-long human capital acquisition process that requires great academic and extracurricular accomplishment, and we find that an insufficient number of black high school graduates cross this threshold for equality in college graduation outcomes to be achieved. As such, inequality in colleges’ outputs is closely related to inequalities generated well before students step foot on campus. Our results imply that for a single college, increasing the rate at which black admits choose to matriculate could alleviate racial inequality. At the society level, we find evidence that increasing the number of college ready black high school graduates would reduce inequality in college attainment.
References:
Alexander, Karl L., Doris R. Entwisle, and Linda Steffel Olson. "Lasting consequences of the summer learning gap." American Sociological Review 72.2 (2007): 167-180.
Alon, Sigal, and Marta Tienda. "Assessing the “mismatch” hypothesis: Differences in college graduation rates by institutional selectivity." Sociology of education 78.4 (2005): 294-315.
Alon, Sigal, and Marta Tienda. "Diversity, opportunity, and the shifting meritocracy in higher education." American
Sociological Review 72.4 (2007): 487-511.
Arcidiacono, Peter, Michael Lovenheim, and Maria Zhu. "Affirmative action in undergraduate education." Annu.
Rev. Econ. 7.1 (2015): 487-518.
Aries, Elizabeth. Race and class matters at an elite college. Temple University Press, 2008.
Aries, Elizabeth, and Maynard Seider. "The interactive relationship between class identity and the college experience: The case of lower income students." Qualitative Sociology28.4 (2005): 419-443.
Autor, David H., Lawrence F. Katz, and Melissa S. Kearney. "Trends in US wage inequality: Revising the revisionists." The Review of economics and statistics 90.2 (2008): 300-323.
Bagde, Surendrakumar, Dennis Epple, and Lowell Taylor. "Does affirmative action work? Caste, gender, college quality, and academic success in India." American Economic Review106.6 (2016): 1495-1521.
Bowen, William G., and Derek Bok. The Shape of the River. Long-Term Consequences of Considering Race in
College and University Admissions. Princeton University Press, California/Princeton Fulfillment Services, 1445
Lower Ferry Road, Ewing, NJ 08618, 1998.
Bowen, William G., Matthew M. Chingos, and Michael S. McPherson. 2009. Crossing the Finish Line: Completing College at America’s Public Universities. Princeton, NJ: Princeton University Press.
Card, David. "The causal effect of education on earnings." Handbook of labor economics. Vol. 3. Elsevier, 1999. 1801-1863.
Card, David, and Laura Giuliano. "Universal screening increases the representation of low-income and minority students in gifted education." Proceedings of the National Academy of Sciences 113.48 (2016): 13678-13683. Carneiro, Pedro, and Sokbae Lee. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality." Journal of Econometrics 149.2 (2009): 191-208.
Carneiro, Pedro, James J. Heckman, and Edward J. Vytlacil. "Estimating marginal returns to education." American
Economic Review 101.6 (2011): 2754-81.
Carnevale, Anthony P., and Jeff Strohl. "Separate & Unequal How Higher Education Reinforces the Intergenerational Reproduction of White Racial Privilege." (2013).
Castilla, Emilio J., and Ben A. Rissing. "Best in Class: The Returns on Application Endorsements in Higher Education." Administrative Science Quarterly 64.1 (2019): 230-270.
Chan, Tak Wing, and John H. Goldthorpe. "Class and status: The conceptual distinction and its empirical relevance." American sociological review 72.4 (2007): 512-532.
Charles, C. Z., Fischer, M. J., Mooney, M. A., & Massey, D. S. (2016). Taming the river: Negotiating the academic,
financial, and social currents in selective colleges and universities (Vol. 51). Princeton University Press.
Chetty, Raj, et al. Race and economic opportunity in the United States: An intergenerational perspective. No. w24441. National Bureau of Economic Research, 2018.
Ciocca Eller, Christina, and Thomas A. DiPrete. "The Paradox of Persistence: Explaining the Black-White Gap in Bachelor’s Degree Completion." American Sociological Review 83.6 (2018): 1171-1214.
Delaney, Judith M., and Paul J. Devereux. "More education, less volatility? The effect of education on earnings volatility over the life cycle." Journal of Labor Economics 37.1 (2019): 101-137.
Espenshade, Thomas J., Chang Y. Chung, and Joan L. Walling. "Admission preferences for minority students, athletes, and legacies at elite universities." Social Science Quarterly 85.5 (2004): 1422-1446.
Espenshade, Thomas J., and Alexandria Walton Radford. No longer separate, not yet equal: Race and class in elite
college admission and campus life. Princeton University Press, 2013.
Fairlie, Robert W., Florian Hoffmann, and Philip Oreopoulos. "A community college instructor like me: Race and ethnicity interactions in the classroom." American Economic Review104.8 (2014): 2567-91.
Fischer, Mary J. 2007. “Settling into Campus Life: Differences by Race/Ethnicity in College Involvement and Outcomes.” Journal of Higher Education 78(2): 125-61.
Frankenberg, Erica, et al. "Harming our Common Future: America's Segregated Schools 65 Years after Brown." (2019).
Gaydosh, Lauren, et al. "College completion predicts lower depression but higher metabolic syndrome among disadvantaged minorities in young adulthood." Proceedings of the National Academy of Sciences 115.1 (2018): 109-114.
Greenwald, Bruce C. "Adverse selection in the labour market." The Review of Economic Studies 53.3 (1986): 325-347.
Hällsten, Martin, and Fabian T. Pfeffer. "Grand advantage: family wealth and grandchildren’s educational achievement in Sweden." American Sociological Review 82.2 (2017): 328-360.
Jack, Anthony Abraham. "(No) harm in asking: Class, acquired cultural capital, and academic engagement at an elite university." Sociology of Education 89.1 (2016): 1-19.
Jencks, Christopher, and Meredith Phillips, eds. The black-white test score gap. Brookings Institution Press, 2011. Jennings, Jennifer L., David Deming, Christopher Jencks, Maya Lopuch, and Beth E. Schueler. 2015. “Do Differences in School Quality Matter More Than We Thought? New Evidence on Educational Opportunity in the TwentyFirst Century.” Sociology of Education 88(1):56–82.
Lawrence, Elizabeth M. "Why do college graduates behave more healthfully than those who are less educated?." Journal of health and social behavior 58.3 (2017): 291-306.
Milkman, Katherine L., Modupe Akinola, and Dolly Chugh. "What happens before? A field experiment exploring how pay and representation differentially shape bias on the pathway into organizations." Journal of Applied
Psychology 100.6 (2015): 1678.
Musu-Gillette, Lauren, et al. "Status and Trends in the Education of Racial and Ethnic Groups 2016. NCES 2016-007." National Center for Education Statistics (2016).
Owens, Ernest. “A Black Face in a White Space: My Four Years at Penn.” Philadelphia Magazine (2017) https://www.phillymag.com/news/2017/08/26/black-students-university-pennsylvania/
Pager, Devah, and Hana Shepherd. "The sociology of discrimination: Racial discrimination in employment, housing, credit, and consumer markets." Annu. Rev. Sociol 34 (2008): 181-209.
Reardon, Sean F. "School segregation and racial academic achievement gaps." RSF: The Russell Sage Foundation
Journal of the Social Sciences 2.5 (2016): 34-57.
Rich, Peter M., and Jennifer L. Jennings. 2015. “Choice, Information, and Constrained Options: School Transfers in a Stratified Educational System.” American Sociological Review 80(5):1069–98.
Riddle, Travis, and Stacey Sinclair. "Racial disparities in school-based disciplinary actions are associated with county-level rates of racial bias." Proceedings of the National Academy of Sciences 116.17 (2019): 8255-8260. Rivera, Lauren A. Pedigree: How elite students get elite jobs. Princeton University Press, 2016.
Roderick, Melissa, Vanessa Coca, and Jenny Nagaoka. "Potholes on the road to college: High school effects in shaping urban students’ participation in college application, four-year college enrollment, and college
match." Sociology of Education 84.3 (2011): 178-211.
Sander, Richard, and Stuart Taylor Jr. Mismatch: How Affirmative Action Hurts Students It S Intended to Help, and
Sauder, Michael, and Ryon Lancaster. "Do rankings matter? The effects of US News & World Report rankings on the admissions process of law schools." Law & Society Review 40.1 (2006): 105-134.
Steele, Claude M. Whistling Vivaldi: And other clues to how stereotypes affect us (issues of our time). WW Norton & Company, 2011.
Steele, Claude M., and Joshua Aronson. "Stereotype threat and the intellectual test performance of African Americans." Journal of personality and social psychology 69.5 (1995): 797.
Stevens, Mitchell L. Creating a class. Harvard University Press, 2009.
Tinto, Vincent. Leaving college: Rethinking the causes and cures of student attrition. University of Chicago Press, 5801 S. Ellis Avenue, Chicago, IL 60637, 1987.
Torche, Florencia. "Is a college degree still the great equalizer? Intergenerational mobility across levels of schooling in the United States." American Journal of Sociology117.3 (2011): 763-807.
U.S. Census Bureau (2017). 2013-2017 American Community Survey 5-Year Estimates
Walton, Gregory M., and Geoffrey L. Cohen. "A brief social-belonging intervention improves academic and health outcomes of minority students." Science 331.6023 (2011): 1447-1451.
Figure 1:
Sorting Differences Between Black and White Admitted Students and the Ensuing College Readiness Gap
Figure 2:
Figure 3:
Table 1:
Table 2:
Figure 4:
Histogram of Black and White Admitted Students Ranked by Standardized Test Score (n = 5,203)
Figure 5:
Histogram of Black Admitted Students That Do and Do Not Matriculate Ranked by Standardized Test Score
Figure 6:
Histogram of White Admitted Students That Do and Do Not Matriculate Ranked by Standardized Test Score
Table 3:
Table 4:
Table 5:
Estimates of Academic Performance Within The Pool of Admits Controlling For Probability of Matriculation (With Selection)
Figure 7:
Point Estimates of the Completion Gap With and Without Controlling For Selection (Probability of Matriculation)
Figure 8:
Histogram of Black and White Admitted Students by Place in Standardized Test Score Distribution of All Admitted Students With Cutoffs for Area with Similar Numbers of Black and
White Matriculants (n = 5,203)
Figure 9:
Histogram of Black and White Matriculants by Place in the Distribution of Standardized Test Scores for All Admits Within the Area With Similar White and Black Matriculants
Table 6:
Estimates of the Black White College Completion Gap Within Progressively Larger Subsets of the Area With Comparable Black and White Matriculants
Figure 10:
Logit Coefficient Estimates of the Black White Completion Gap Within Progressively Larger Subsets
Table 7:
Estimates of the Black White College GPA Gap Within Progressively Larger Subsets of the Area With Comparable Black and White Matriculants
Figure 11:
APPENDIX
Appendix A: Use of Distance from Home to College to Satisfy the Exclusion Restriction in Selection Models
Our main analysis uses selection models to estimate the black white completion gap when a student’s probability of matriculation is controlled. To achieve full identification, selection models require a variable to satisfy the exclusion restriction. The requirements of such a variable are similar to those of a valid instrumental variable: the variable should affect the probability of selection, in this case deciding to matriculate, but not the outcome variable, or academic performance. As such, this variable is included in the selection equation but not the outcome equation.
We use the distance from a student’s home to The College (hereforth, “Distance”) to satisfy the exclusion restriction. Distance is likely to have a strong effect on selection, with greater distances likely to negatively affect a student’s probability of matriculation. Students may prefer to live near home or in a familiar area and students with homes near to The College will have lower travel costs. Additionally, we expect that distance will have no significant
relationship with academic performance. Students who have been admitted to The College are all of high academic quality, and being near home is unlikely to provide any direct academic
advantages. Additionally, to our knowledge, distance is not factored into admissions decisions.
We measure distance as the Haversine Distance in miles between the center of a student’s reported home zip code and the center of The College’s zip code. Haversine Distance is a
curvature. Distance is right-skewed, and as such, we use the natural logarithm in all models. Figure A1 shows a histogram of the distribution of logged distance for all admitted students. The distribution remains bimodal, as a large proportion of the admitted students are from either the east or west coasts of the US.
To satisfy the exclusion restriction, distance must affect the decision to matriculate at The College conditional on admission and be uncorrelated with academic performance. To test this, we performed Wald and Likelihood-Ratio hypothesis tests of the effect of distance on probability of matriculation and academic performance as measured by on-time graduation and GPA. The Wald Test evaluates whether distance adds explanatory power in a single model, while the Likelihood Ratio Test requires estimating models with and without distance and testing whether including distance improves the model’s fit. Results are presented in Table A1.
Model A1 reports results from a regression predicting probability of matriculation. This is the same model as Model 2, and as a result, coefficients other than distance are not reported in the appendix. Model A1 estimates that distance decreases a student’s probability of matriculation (β = -.1319, z = 6.50, p < .001). This estimate implies that a one standard deviation increase in distance decreases probability of matriculation by 13.4%. The Wald test indicates that distance increases the explanatory power of the model (chi2 = 42.27, p <.001) and the Likelihood-Ratio test estimates that distance improves the model’s fit (chi2 = 42.65, p <.001). This provides strong evidence that distance is related to probability of matriculation.
