Original article

# What happens after enrollment? An analysis of the time path of racial differences in GPA and major choice

Peter Arcidiacono1*, Esteban M Aucejo2 and Ken Spenner3

Author Affiliations

1 Department of Economics, Duke University and NBER, Durham, NC, USA

2 Department of Economics, Duke University, Durham, NC, USA

3 Department of Sociology, Duke University, Durham, NC, USA

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IZA Journal of Labor Economics 2012, 1:5  doi:10.1186/2193-8997-1-5

 Received: 29 May 2012 Accepted: 28 June 2012 Published: 9 October 2012

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

At the private university we analyze, the gap between white and black grade point averages falls by half between the students' freshmen and senior year. This outcome could suggest that affirmative action policies are playing a key role to reduce racial differences. However, this convergence masks two effects. First, the variance of grades given falls across time. Hence, shrinkage in the level of the gap may not imply shrinkage in the class rank gap. Second, grading standards differ across courses in different majors. We show that controlling for these two features virtually eliminates any convergence of black/white grades. In fact, black/white gpa convergence is symptomatic of dramatic shifts by blacks from initial interest in the natural sciences, engineering, and economics to majors in the humanities and social sciences. We show that natural science, engineering, and economics courses are more difficult, associated with higher study times, and have harsher grading standards; all of which translate into students with weaker academic backgrounds being less likely to choose these majors. Indeed, we show that accounting for academic background can fully account for average differences in switching behavior between blacks and whites.

##### Keywords:
Grade inflation; Affirmative action; Major choice; I2; I20; I23

### 1 Introduction

Scholars have known since the Coleman Report in 1966 that the black white educational achievement gap is a robust empirical regularity. Since then, a prolific literature in economics has emerged trying to describe the evolution, causes and consequences of the racial test scores gap in primary and secondary schools. The main findings indicate that African American children enter kindergarten lagging behind their white counterparts, and these differences are likely to persist for the foreseeable future ( Neal [2006]). Cunha et al. ([2006]) argue that schooling raises measured ability, but does not close gaps between children from different racial and economic strata, and if anything widens them. Fryer and Levitt ([2006]), using the Early Childhood Longitudinal Study database, find that by the end of first grade, black children lost the equivalent of almost three months of schooling relative to whites. These trends continue through middle school with both Phillips and Chin ([2004]) and Hanushek and Rivkin ([2006,2009]) documenting increases in the math achievement gap between blacks and whites through the eighth grade.

The divergence in black/white outcomes at early ages is not surprising given disparities in resources between black and white families. It could also be the case that disparities may continue to grow in college due to differences in parental resources, support, and information that also matter for performing well in college. However, the college environment is substantially different in that students are more separated from their families. Hence, it is also possible to expect, by taking students whose academic background is weak due to lack of resources but whose academic potential is strong, that these students perform poorly at first as they acquire the needed skills to succeed and then, with time, catch up. By way of illustration, consider the case of Ph.D. economics programs in the United States. International students, who often have Master's degrees upon entry, typically come in better prepared than their American counterparts, with American students gradually catching up over time. With affirmative action promoting access to those who are otherwise less prepared, it is possible that the beneficiaries of affirmative action may also catch up, at least partially, over the course of their college career.

In this paper, we examine the evolution of racial disparities in college, focusing in particular on students at Duke University. While researchers have documented lower grades for black students in college (see, for example, Betts and Morell [1999]), this is to be expected given differences in college preparation. Here, we are interested in the time path of racial differences. Clearly using data from one highly-selective school may lead to questions about how the results carry over to other environments. Weighed against this, however, is the ability to use within-school variation, ensuring that our results our not driven by grading patterns being different across the different types of schools blacks and whites attend.

An initial glance at data from consecutive cohorts of students who first enrolled in 2001 and 2002 suggests that black students actually show substantial catch up. Namely, for Duke students who completed collegea, Figure 1 shows that differences in grades between black and white students during their first semester were almost half a grade. However, this disparity was reduced by almost fifty percent by the last semester of college.

Figure 1. Evolution of students noncumulative semester GPA open by race at Duke University. Source: CLL.

There are, however, at least two reasons to be skeptical of Figure 1: variance and course selection. With regard to variance, instructors use much less of the grade distribution in upper year coursesb. Indeed, the standard deviation of grades for second-semester seniors is 86% percent of the standard deviation of grades for first-semester freshmen. For convergence to occur, it is therefore important to examine differences in class rank over time rather than GPA levels.

The second concern is course selection. Grading standards differ wildly across majors at Duke (see Johnson [1997,2003]), with similar differences seen across many universities (see Sabot and Wakeman-Linn [1991], Grove and Wasserman [2004], Bar and Zussman [2012] and Koedel [2011]).c In particular, natural science, engineering, and economics classes have average grades that are 8% lower than the average grades in humanities and social science classes. Note that these averages do not take into account selection into courses: average SAT scores of natural science, engineering, and economic majors are over 50 points higher than their humanities and social science counterparts. Although blacks and whites initially have similar interests regarding whether to major in the more strictly graded fields, the patterns of switching result in 68% of blacks choosing humanities and social science majors compared to less than 55% of whitesd. We show that accounting for these two issues can explain virtually all the convergence of black white grades.

Accounting for shrinking grade variances and course selection also explains the convergence in grades for a group where we would expect catch up to not occur: legacies. Legacies at Duke start out behind their white non-legacy counterparts (though not as far back as blacks) with 65% of the gape removed by the end of the senior year. Similar major-switching patterns occur for legacies as well, with large shifts away from the natural sciences, engineering, and economics towards humanities and social sciences. The different grading standards across courses legacies and blacks take, coupled with the tighter variances on the grade distributions of upper year courses, accounts for their catch up to their white non-legacy counterparts.

The convergence of black/white grades is then a symptom of the lack of representation among blacks in the natural sciences, engineering, and economics. Over 54% of black men who express an initial interest in majoring in the natural sciences, engineering, or economics switch to the humanities or social sciences compared to less than 8% of white men. While the similar numbers for females are less dramatic across races, they are nonetheless large: 33% of white women switch out of the natural sciences, engineering, and economics with 51% of black women switching.

These cross-race differences in switching patterns can be fully explained by differences in academic background. We show that natural science, engineering, and economics courses are more difficult, associated with higher study times, and are more harshly graded than their humanities and social science counterparts. These trends are particularly true for students with weaker academic backgrounds resulting in those with relatively weaker academic backgrounds being much less likely to persist in natural science, engineering, and economics majors.f

### 2 The Campus Life and Learning Project Data (CLL)

The data we analyze come from the Campus Life and Learning Project (CLL). The data was collected from surveys of two consecutive cohorts of Duke University students before college and during the first, second and fourth college years. The target population was defined as all undergraduate students in the Trinity College of Arts & Sciences and the Pratt School of Engineering. The sampling design randomly selected about one third of white students, two thirds of Asian students, one third of bi- and multiracial students and all black and Hispanic students. As a result, the final sample (including both cohorts) consists of 1536 students: 602 white, 290 Asian, 340 black, 237 Hispanic and 67 bi- or multiracial students.

Each cohort was surveyed via mail in the summer before initial enrollment at the university; the questionnaire was completed by 1181 students, a 77% response rate. However, response rates declined in the years following enrollment: in the first year of college 71% of students responded to the survey; in the second year 65% and in the third year 59%.g In addition to the information provided by the surveys, the survey asked permission to access their confidential student records. Since the students were given the opportunity to answer yes to this question on each survey, permission was granted at a very high rate: 91% of the sample granted confidential access to their student records. These records include complete college transcripts, major selection, graduation outcomes, test scores (i.e. SAT, ACT), Duke Admission Officers rankings based on high school curriculum, reader rating scores, high school extracurricular activities, and financial aid and support.

### Appendix: drop-out bias and non-response bias

The Registrar's Office data provided information on students who were not enrolled at the end semester in each survey year. Non-enrollment might occur for multiple reasons including academic or disciplinary probation, medical or personal leave of absence, dismissal or voluntary (including a small number of transfers) or involuntary withdrawal. Fewer than one percent of students (n=12) were not enrolled at the end of the first year; about three percent by the end of the second year (n=48) and just over five percent (n=81) by the end of the senior year. We combined all of these reasons and tested for differences in selected admissions file information of those enrolled versus not enrolled at the end of each survey year. The test variables included racial ethnic group, SAT verbal and mathematics score, high school rank (where available), overall admission rating (a composite of five different measures), parental education, financial aid applicant, public-private non-religious-private religious high school and US citizenship. Of over 40 statistical tests, only two produced significant differences (with p-value less than 0.05): (1). At the end of the first year, dropouts had SAT-verbal scores of 734 versus 680 for non-dropouts; (2). by the end of the fourth year, those who had left college had an overall admissions rating of 46.0 (on a 0-60 scale) while those in college had an average rating of 49.7. No other differences were significant. We conclude that our data contain very little drop-out bias.

We conducted similar tests for respondents versus non-respondents for each wave for the same variable set plus college major (in 4 categories: engineering, natural science/mathematics, social science, humanities), whether or not the student was a legacy admission, and GPA in the semester previous to the survey semester. Seven variables show no significant differences or only a few small sporadic differences (one wave but not others), including racial ethnic category, high school rank, admissions rating, legacy, citizenship, financial aid applicant, and major group. However, several other variables show more systematic differences:

· Non-respondents at every wave have lower SAT scores (math: 9-15 points lower, roughly one-tenth to one-fifth of a standard deviation; verbal: 18-22 points lower, roughly one-third of a standard deviation).

· Non-respondents have slightly better educated parents at waves one and three, but not waves two and four.

· Non-respondents at every wave are less likely to be from a public high school and somewhat more likely to be from a private (non-religious) high school.

· Non-respondents have somewhat lower GPA in the previous semester compared with respondents (by about one-quarter of a letter grade).

These differences are somewhat inconsistent in that they include lower SAT and GPA for non-respondents, but higher parental education and private (more expensive) high schools. In general, the non-response bias is largest in the pre-college wave and smaller in the in-college waves even though the largest response rates are in the pre-college wave. In general, we judge the non-response bias as relatively minor on most variables and perhaps modest on SAT measures.

### Endnotes

1Graduation rates are quite high at Duke University, with 96% of the students finishing their studies.

2Grove and Waserman [2004] show similar trends in grades for a large private university in the northeast. Moreover, data of four years college graduates from the NLSY97 also shows that students GPA increase in upper years of college while their standard deviation decreases. More specifically, mean GPA increased from 3.18 to 3.33, while their standard deviation decreased form 0.574 to 0.481 between the freshman and senior years.

3For instance, Koedel ([2011]) shows that the grades awarded by education departments are substantially higher than the grades awarded by all other academic departments. The classroom level average GPAs in the education departments are 0.5 to 0.8 grade points higher than in other department groups.

4The high proportion of students that switch major can be explained by students learning about their ability and preferences in the first few years of college. Stange ([2012]) finds that uncertainty about college completion and final major is empirically important. Similarly, Stinebrickner and Stinebrickner ([2011a]) show that students learning about academic matters plays a particularly prominent role in educational decisions.

5Based on comparing non-cumulative semester GPA.

6Stinebrickner and Stinebrickner ([2011b]) show that, in Berea College, the proportion of students who reported that math/science is their most likely major is higher than the proportion for any other major. However, by the second semester of the third year in college, the proportion of students who reported that math/science is the most likely major decreased by 45%. In this regard, they highlight the potential importance of policies at younger ages that lead students to enter college better prepared to study math or science.

7In the appendix we discuss the patterns of non-response and attrition.

8Note that the median student for each race is changing by year.

9Note that the median student is changing across years.

10See Bar et al. ([2009]) for an analysis of Cornell's program, with Bar et al. ([2012]) developing a theoretical model of how students change their course-taking behavior in response to programs such as this one.

11In principle there is a lower bound on grades. In practice, very few F's are given suggesting that censoring at the bottom end of the distribution is not an issue.

12The formula of the inverse Mill's ratio is given by

13Comparing junior class rank to freshmen class rank still shows a small legacy improvement even after controlling for course selection. However, course selection clearly matters as the gains would be much larger without these adjustments. Overall, the legacy estimates are less stable than the estimates for African Americans. This may be a result of having a smaller number of legacies (175).

14For each ranking category, we created the dummy variables by choosing splits such that a significant fraction received both a high and low ranking. For achievement, recommendations, personal qualities and the essay a high ranking was above 3.5, above 3.75, above 3.7, and above 3.7 respectively. The student needed to receive a 5 to obtain the high ranking on curriculum.

15It is important to highlight that the negative coefficient on SAT is not given by a mechanical result (i.e. students at the top of the distribution initially having less room to move up in later years). This result only implies that SAT is more correlated with the freshman class rank than the senior or the sophomore ones.

16The total sample size of this table (which only includes black and white students) is 663.

17Uncertainty is captured by individuals responding to the expected major question with “Do not know”.

18The proportion of students that reported “Do not know” is 30%.

19The National Longitudinal Survey of Freshmen, which follows a cohort of first-time freshman at 28 selective colleges and universities, shows a similar pattern in major persistence.

20The total number of grades in humanities/social science for non black (black) considering all years is 18535 (5340) while in natural sci/engineering/economics is 13100 (2530).

21Similarly, Bar and Zussman ([2012]) shows that humanities courses at the College of Arts and Sciences of an elite university in the United States provide higher grades than natural sciences ones.

22The intervals are: 0 hours per week, less than 1 hour, 1 to 5 hours, 11 to 15 hours, 16 or more.

23We use the same set of dummy variables as in Table 7.

24Stinebrickner and Stinebrickner ([2004]) find similar results. They show that males study half an hour less per day than females.

25Babcock ([2010]), Babcock and Marks ([2011]) and Stinebrickner and Stinebrickner ([2008]) also show large differences in study time across majors. Babcock ([2010]) provides evidence that harsher grade distributions result are associated with more study time.

26If economics were classified as social science, then there would be a slight decrease in the the study time for engineering and natural sciences relative to humanities, social sciences, and economics. However, the coefficient would remain statistically significant.

27Given that so little switching occurs in the opposite direction (i.e. from humanities or social sciences to natural sciences or economics), we only focus on switches away from natural sciences and economics.

28The higher proportion of females relative to males leaving sciences is an empirical regularity that has been analyzed in Carrell et al. ([2010]). They show that professor gender affects female students' propensity to persist in the sciences.

29If (instead) economics is classified as a social science, the coefficient on female and black will fall slightly but they will remain statistically significant.

30The other reasons were: 1) Academic interests and values have changed since arriving at Duke, 2) Career interests have changed since arriving at Duke, 3) Career values have changed since arriving at Duke, 4) Lack of pre-professional learning opportunities available (e.g., internships, research opporutnities, and 5) Other .

### Competing interests

The IZA Journal of Labor Economics is committed to the IZA Guiding Principles of Research Integrity. The authors declare that they have observed these principles.

### Acknowledgments

We thank Nathan Martin, Todd Stinebrickner, and seminar participants at Stanford Education school for comments. The Campus Life and Learning data were collected by A. Y. Bryant, Claudia Buchmann and Kenneth Spenner, Principal Investigators, with support provided by the Andrew W. Mellon Foundation and Duke University. They bear no responsibility for conclusions, recommendations and opinions found in this paper. Partial funding was provided by Project SEAPHE.

Responsible Editor: Pierre Cahuc

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