University Differences in the Graduation of Minorities in STEM Fields: Evidence from California

Abstract

We examine differences in minority science graduation rates among University of California campuses when racial preferences were in place. Less prepared minorities at higher ranked campuses had lower persistence rates in science and took longer to graduate. We estimate a model of students’ college major choice where net returns of a science major differ across campuses and student preparation. We find less prepared minority students at top ranked campuses would have higher science graduation rates had they attended lower ranked campuses. Better matching of science students to universities by preparation and providing information about students’ prospects in different major-university combinations could increase minority science graduation.

Increasing the number of science, technology, engineering, and math (STEM) majors is seen as one of the key components to keeping the United States competitive in a global economy (Carnevale, Smith, and Melton 2011).¹ In a 2012 report, the President’s Council of Advisors on Science and Technology suggested that the number of STEM majors needed to increase by 34 percent over current rates to meet the demand for STEM professionals. The lack of STEM majors occurs despite STEM majors earning substantially more than other college degrees with the exception of perhaps business (Arcidiacono 2004; Kinsler and Pavan forthcoming; Melguizo and Wolniak 2012) and that the STEM premium has increased over time (Gemici and Wiswall 2014).²

Of particular concern is the lack of representation of minority students.³ Seymour and Hewitt (2000) pointed out that as of 2000 the National Science Foundation alone had spent more than $1.5 billion to increase participation of minorities in the sciences and two programs at the National Institute of Health had invested $675 million in the same endeavor. At college entry, black and Hispanic students exhibit preferences for STEM fields that are similar to those of non-Hispanic white students, yet their probabilities of persisting in these fields are much lower (Anderson and Kim 2006).

While different programs have been implemented with the aim to reduce the current racial disparities in shares of the US workforce with STEM degrees, little is known about the role that colleges play in “producing” STEM degrees, especially for underrepresented minority (URM) groups. An important exception is the study by Griffith (2010), who finds that characteristics of colleges play a key role in the decision of students to remain in a STEM major and obtain a degree in any of these fields. For example, Griffith finds that students at selective colleges with large research expenditures relative to total educational expenditures have lower persistence rates⁴ for students in the sciences.⁵

Understanding disparities across universities in the production of minority (and nonminority) STEM majors may have important implications for the way agencies, such as the National Science Foundation (NSF) and National Institutes of Health (NIH), allocate resources across colleges to increase the representation of minorities in STEM fields. Moreover, studying these differences by types of colleges (e.g., more selective versus less selective) is relevant for assessing whether programs, such as affirmative action, improve minority representation among STEM degree holders, or hinder it by encouraging minority students to attend colleges where success in STEM fields is unlikely.

In this paper, we examine student-level data for students who applied to, were admitted to, enrolled at, and/or graduated with a baccalaureate degree from one of the campuses within the University of California (UC) system during the late 1990s. As described below, we have measures of students’ academic preparation, intended major and, conditional on graduating, their final major, as well as their minority status.⁶ These data reveal that while the proportion of minority students who initially declare a science major is slightly lower than that for nonminorities (33.4 versus 40.0 percent),⁷ only 24.6 percent of these minority students persist and graduate with a science degree in five years, with 33.8 percent graduating with a nonscience degree and 41.6 percent not completing a BA degree at their UC campus in five years. In contrast, 43.9 percent of nonminority students initially in the sciences persist in this field and graduate in five years, 30.1 percent switch majors but graduate, and 26.0 percent do not graduate within five years. The differences by race in persistence in the sciences and overall graduation rates are even starker when judged by on-time graduations (i.e., in four years).

The differences across minorities and nonminorities in persistence in the sciences within the UC system reflect, in part, differences in academic preparation between minority and nonminority students. Students entering with academic credentials (high school GPAs and SAT scores) that are high relative to the campus average are more likely to persist in a science major and graduate with a science degree.⁸ For example, at UC Berkeley, minorities who persisted in the sciences had entering credentials that were 0.682 of a standard deviation higher than those who switched to a major outside of the sciences (0.706 versus 0.024). For nonminority students, the corresponding gap was less than one-third as large, or 0.215 of a standard deviation (1.285 versus 1.070).

But these racial differences in persistence in the sciences also may reflect campus differences in how student academic preparation translates into graduations. Partly as a result of racial preferences in admissions during the time period we examine, minorities and nonminorities were allocated to UC campuses in a very different manner, conditional on the same levels of preparation. For example, as we show in Section I, minority students admitted to UC Berkeley had, on average, worse academic credentials than nonminority students rejected at UC Berkeley and similar academic credentials to the nonminority students who applied to any UC campus (but were not necessarily admitted).

Using our data for minority and nonminority students who first enrolled at one of the UC campuses between 1995 and 1997, we estimate a model of students’ decision to graduate from college with a particular major. The model examines how academic preparation (broadly defined) translates into persistence in the sciences or overall graduation rates and it allows for differences across UC campuses in the returns to graduating with STEM and non-STEM majors to students with differing academic preparations. To account for selective differences in the UC campus in which students enrolled, we employ an estimation strategy developed by Dale and Krueger (2002) and used in Dale and Krueger (2014) that takes advantage of data on where students submitted applications and where they were accepted. Our data allow us to employ this approach, since we have data on all of the UC campuses where students submitted applications as well as where they were accepted or rejected.

Estimates of the choice model reveal that the match between the UC campus a student attends and their academic preparation is especially important in the sciences. Namely, more prepared students have higher estimated net returns from persisting in the sciences at the most selective UC campuses, e.g., UC Berkeley and UCLA, while those with lower levels of preparation have higher net returns to such persistence at the less selective campuses, e.g., UC Santa Cruz and UC Riverside.⁹ In contrast, the higher ranked UC campuses are estimated to have higher net returns to graduating students with nonscience majors than do lower ranked campuses and this advantage holds over almost the entire range of student academic preparation distribution.¹⁰

Based on these differences across campuses in the estimated net returns to persistence in the sciences, we examine the potential for improving graduation rates in the sciences of both minority and nonminority students by reallocating students from their observed campuses to counterfactual ones. We find that minority students at top ranked campuses would, on average, have significantly higher probabilities of graduating in the sciences if they had attended lower ranked campuses. Similar results do not apply for nonminority students. These differences by race are driven by how the two groups were actually distributed across the UC campuses. In contrast to minority students, very few nonminorities with weak academic preparation were admitted to and enrolled at one of the top ranked UC campuses. As a result, we find that redistributing minority students across UC campuses in a similar manner to how nonminority students were allocated would result in sizable increases in science graduation rates, whereas redistributing nonminority students across the UC campuses according to how minority students were allocated would actually lower nonminority science graduation rates.

Given that these potential gains in minority graduation rates in the sciences from reallocating less prepared minority students from higher to lower ranked campuses are sizable, an obvious question arises: why were these gains not realized? Unfortunately, our data do not allow us to provide a definitive answer. Nonetheless, we do attempt to shed some light on the plausibility of several alternative explanations. One possible explanation for why students attend UC campuses at which they are poorly matched is that graduating from a top ranked college, like UC Berkeley or UCLA, yields higher returns in the labor market than graduating from a lower ranked one, like UC Santa Cruz or UC Riverside, regardless of one’s major. Further, it may be the case that majors are more important to future earnings at the less selective campuses than at the more selective campuses. Using data from the Baccalaureate and Beyond study, we find that neither of these explanations receives empirical support. In particular we find that: (i) majoring in the sciences at less selective institutions results in higher wages than majoring in the nonsciences at more selective ones; and (ii) if anything, the wage return to majoring in the sciences relative to the nonsciences increases as college quality increases.

Another possible interpretation of our results is that students are fully informed and are willing to trade off lower probabilities of finishing in the sciences for a degree at a more prestigious institution, despite the large returns to majoring in the sciences. This could occur because of a higher consumption value associated with having a degree from a more prestigious institution. In this case, affirmative action in admissions is welfare-improving for minority students, although it appears to come with the cost of lowering minority representation in the sciences. But the very low science persistence rates of less prepared students, particularly for on-time graduation, suggest an alternative interpretation. Namely, students may be poorly informed about how different STEM fields are from other fields in the demands they place on their students.¹¹ We discuss the evidence of what students know about majoring in the sciences upon entering college in Section IV.

The rest of the paper is organized as follows. In Section I we describe the data and document across-campus differences in science persistence rates and overall graduation rates. In Section II we develop an econometric model of the decision of students to graduate in alternative majors or not graduate when colleges differ in the net returns to students’ academic preparation. Section III presents estimates of the model and counterfactual simulations showing the potential gains in graduating minority students in the sciences by reallocating them across the UC campuses. Finally, in Section IV, we analyze potential explanations for why minority students, in fact, did not attend those campuses that would have increased their chances of graduating in the sciences. Section V concludes the paper.

I. Data and Descriptive Findings

The data we use were obtained from the University of California Office of the President (UCOP) under a California Public Records Act request. These data contain information on applicants, enrollees, and graduates of the UC system.¹² The data are organized by years in which these students would enter as freshmen. Due to confidentiality concerns, some individual-level information was suppressed. In particular, the UCOP data have the following limitations:¹³

1. The data do not provide the exact year in which a student entered as a freshman, but rather a three-year interval.

2. The data provide no information on gender, and race is aggregated into four categories: white, Asian, underrepresented minority (URM), and other.¹⁴

3. Data on individual measures of a student’s academic preparation, such as SAT scores and high school grade point average (GPA), were only provided as categorical variables, rather than the actual scores and GPAs.¹⁵

4. Detailed information on the specific majors that students stated on their college application or graduated in was not provided. Rather, we were provided information on groups of majors: Science (i.e., STEM), humanities, and social science majors.¹⁶ In the following analyses, we aggregated the humanities and social science categories into one, the Nonscience category.

Weighed against these limitations is having access to the universe of students who applied to at least one campus in the UC system and also whether they were accepted or rejected at every UC campus where they submitted an application. Further, while the versions of SAT scores and high school GPA provided to us were categorical variables, the UCOP did provide us with an academic preparation score, S_i, for each student who applied to a UC campus, where this score is a linear combination of the student’s exact high school GPA and SAT scores which we then normalized to have mean zero and standard deviation one in the applicant pool.¹⁷

Our analysis focuses on the choices and outcomes of minority and nonminority students who enrolled at a UC campus during the years 1995 to 1997. During this period, race-conscious admissions were legal at all of California’s public universities. Starting with the entering class of 1998, the UC campuses were subject to a ban on the use of affirmative action in admissions enacted under Proposition 209.¹⁸ While available, we do not use data on the cohorts of students for this later period (i.e., 1998–2005), as there is evidence that the campuses changed their admissions selection criteria in order to conform with Prop 209.¹⁹

A. Enrollments, Majors, and Graduation Rates

We begin by examining the differences across campuses in enrollments, graduation rates, and in a composite measure, or score, of student preparation for both nonminority and minority students. Tabulations are presented in Table 1, with the UC campuses listed according to the US News and World Report rankings as of the fall of 1997.²⁰ Minorities made up 18.5 percent of the entering classes at UC campuses during this period. The three campuses with the highest minority shares are at the two most selective universities (UCLA and UC Berkeley) and the least selective university (UC Riverside). A similar U-shaped pattern was found in national data in Arcidiacono, Khan, and Vigdor (2011), suggesting diversity at the top campuses comes at the expense of diversity of middle-tier institutions.

Table 1—

Enrollments, Graduation Rates, and Student Preparation Scores by UC Campus and Minority Status, 1995–1997

	Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside	UC System
Number of freshmen enrollees
Nonminority	8,073	8,256	7,525	8,638	7,445	8,277	4,511	3,415	56,140
Minority	2,287	2,803	1,081	1,497	1,129	1,845	970	1,156	12,768
Percent minority	22.1	25.4	12.6	14.8	13.2	18.2	17.7	25.3	18.5
Preparation score (S)
Nonminority	1.052	0.743	0.538	0.143	−0.139	−0.162	−0.174	−0.406	0.274
Minority	−0.099	−0.148	−0.103	−0.518	−0.662	−0.813	−0.954	−1.065	−0.464
Difference	1.151	0.891	0.641	0.660	0.522	0.650	0.780	0.659	0.738
Five-year graduation rates (percent)
Nonminority	85.9	83.3	80.4	76.1	68.3	72.5	67.7	63.0	76.1
Minority	68.4	66.0	66.4	54.8	63.2	60.0	60.9	59.2	63.0
Difference	17.6	17.2	14.0	21.3	5.1	12.5	6.7	3.8	13.1
Four-year graduation rates (percent)
Nonminority	56.1	48.2	49.5	37.2	32.7	44.5	45.9	38.9	44.5
Minority	32.5	26.1	32.2	20.1	24.9	27.8	38.4	29.3	28.4
Difference	23.5	22.1	17.3	17.1	7.9	16.8	7.5	9.5	16.0
Percent of enrollees whose initial major = science
Nonminority	44.6	40.3	48.0	43.7	44.6	26.9	24.7	43.6	40.0
Minority	26.0	31.3	46.0	43.6	45.6	27.9	25.8	31.7	33.4
Difference	18.6	9.0	2.0	0.1	−1.0	−0.9	−1.1	11.9	6.6
Percent of five-year graduates whose final major = science
Nonminority	38.4	31.7	41.3	34.3	29.2	16.9	17.6	31.7	31.2
Minority	14.1	16.9	27.2	24.0	19.8	12.8	12.9	14.8	17.2
Difference	24.3	14.8	14.1	10.3	9.4	4.1	4.8	17.0	13.9

Note: See footnote 16 for the definition of the preparation score, S.

Source: Authors’ calculations

We next examine the distribution of academic preparation of minorities and nonminorities at the various campuses. For both nonminority and minority students, the average preparation score generally follow the rankings of the UC campuses. However, preparation scores for minority students are substantially lower than their nonminority counterparts at each campus, with the largest racial gaps occurring at the two top ranked campuses. For example, minority preparation scores were 1.15 and 0.89 standard deviations lower than their nonminority counterparts at UC Berkeley and UCLA, respectively.

In order to further illustrate the large differences in entering credentials between minorities and nonminorities, Figure 1 shows the S distribution for those admitted and rejected by UC Berkeley for both minority and nonminority applicants. The data indicate that, for both racial groups, admits have preparation scores that are, on average, around one standard deviation higher than those whose applications were rejected. However, the median nonminority reject has a preparation score higher than the median minority admit. In fact, the median preparation score for minority admits is at the seventh percentile of the distribution of nonminority admits.

Figure 1.

Distribution of Preparation Score (S) for Applicants to UC Berkeley by Minority and Accept/Reject Status

Note: See footnote 16 for a definition of the preparation score, S.

Source: UCOP, years 1995–1997

In a similar vein, Figure 2 compares the distribution of the preparation score (S) for minority admits at UC Berkeley to the corresponding distribution for nonminorities who applied to any UC campuses. The distributions are almost overlapping: randomly drawing from the pool of nonminority applicants to any UC campus would generate preparation scores similar to those of minority admits at UC Berkeley.

Figure 2.

Distribution of Preparation Scores for Minority UC Berkeley Admits and Nonminority UC Applicants

Note: See footnote 16 for a definition of the preparation score, S.

Source: UCOP, years 1995–1997

The large differences in the academic preparation scores of students across campuses appear to track the across-campus differences in graduation rates, regardless of whether one looks at on-time graduation (in four years) or five-year graduation rates. This is true for both minority and nonminority students. At the same time, the racial gaps in graduation rates vary systematically across the UC campuses. Table 1 shows that nonminority students at UC Berkeley have five-year graduation rates that are almost 18 percentage points higher than minority students at UC Berkeley, while the gap at UC Riverside is less than 4 percentage points. Differences in four-year graduation rates are even starker, with 56.1 percent of nonminority students at UC Berkeley graduating in four years compared to only 32.5 percent for minorities.

Finally, a substantial fraction of students intended to major in the sciences when considering the whole UC system: 40 percent for nonminorities and 33.4 percent for minorities.²¹ However, the share of five-year graduates who are science majors is lower and this is especially true for minorities. Only 17.2 percent of minorities who graduate from a UC campus in five years do so in the sciences, which is almost 14 percentage points lower than the corresponding share for nonminorities (31.2 percent).

B. Persistence in the Sciences

Given the low graduation rates in the sciences shown in Table 1, especially for minorities, we take a closer look at the across-campus and across-race differences in the characteristics of students who graduate with STEM majors. Table 2 displays both average preparation scores (top row) and the share of students (second row) for the three completion categories—graduate in the sciences, graduate but not in the sciences, do not graduate—by initial major and race for each campus, using completion status five years after enrollment.

Table 2—

Academic Preparation Scores and Shares of Students Graduating in Five Years (Percent)

Graduation outcome:	Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside	UC System
Minority
Initial major science
In sciences	0.706 26.9	0.300 26.9	0.240 31.2	0.132 22.2	−0.132 22.3	−0.323 24.1	−0.496 18.4	−0.345 19.1	0.131 24.6
In nonsciences	0.024 39.2	0.010 32.7	−0.094 32.8	−0.351 28.1	−0.500 37.9	−0.744 31.9	−0.880 32.4	−0.922 36.9	−0.338 33.8
Did not graduate	0.021 33.9	−0.178 40.4	−0.215 36.0	−0.500 49.7	−0.647 39.8	−0.857 44.0	−1.087 49.2	−0.983 44.0	−0.494 41.6
Initial major nonscience
In sciences	0.740 2.9	0.414 4.0	0.378 6.0	−0.042 5.0	−0.079 4.2	0.089 3.2	−0.298 4.9	−0.493 4.0	0.044 4.1
In nonsciences	0.068 69.1	0.085 69.9	0.200 70.6	−0.497 61.1	−0.470 64.6	−0.444 69.3	−0.677 62.8	−0.964 58.5	−0.353 65.6
Did not graduate	−0.313 28.0	−0.245 26.0	0.066 23.4	−0.729 33.9	−0.520 31.1	−0.562 27.4	−0.770 32.3	−1.108 37.5	−0.614 30.3
Nonminority
Initial major science
In sciences	1.285 57.3	0.930 49.8	0.725 51.3	0.442 42.8	0.178 33.9	0.121 32.8	−0.033 28.2	0.125 33.9	0.668 43.9
In nonsciences	1.070 28.5	0.827 30.8	0.532 26.4	0.183 30.8	−0.064 31.4	−0.089 34.1	−0.164 35.2	−0.196 27.7	0.352 30.1
Did not graduate	0.982 14.2	0.691 19.4	0.423 22.3	0.101 26.5	−0.194 34.7	−0.208 33.2	−0.314 36.6	−0.481 38.3	0.105 26.0
Initial major nonscience
In sciences	1.183 13.4	0.888 10.6	0.592 16.4	0.254 13.2	−0.002 8.7	−0.037 4.7	−0.043 6.6	−0.135 9.2	0.484 10.2
In nonsciences	0.952 72.6	0.695 74.5	0.469 66.5	0.049 64.9	−0.218 62.0	−0.167 69.9	−0.158 62.5	−0.560 54.8	0.213 67.2
Did not graduate	0.706 13.9	0.386 15.0	0.388 17.1	−0.104 21.8	−0.323 29.3	−0.323 25.4	−0.227 31.0	−0.688 36.0	−0.096 22.5

Notes: Table shows the academic preparation scores and shares of students graduating in five years (percent) with science and nonscience majors for freshman entering a UC campus during 1995 to 1997, by initial major, campus, and minority status. For each initial major and graduation status cluster, the top row gives the average preparation score and second row is percentage of enrollees who started in a particular initial major. The preparation score has been standardized to have mean 0 and standard deviation 1 for the applicant pool.

Source: Authors’ calculations

There is significant sorting on academic preparation scores (S) at all UC campuses, with students who graduate in the sciences having higher preparation scores than those who do not, regardless of initial major. The preparation scores for nonminority students in the UC system who persist in the sciences (i.e., start in and graduate with a science major) are, on average, 0.316 of a standard deviation higher than those for students who switch to a nonscience major (0.668 versus 0.352). The corresponding differences are much larger for minority students. Minority students enrolled at one of the UC campuses who persist in the sciences have preparation scores that are, on average, 0.469 of a standard deviation higher than those students who switch out of the sciences and graduate with a nonscience major (0.131 versus −0.338). Moreover, as reflected in the rates of switching from the sciences in Table 1, nonminorities who begin in the sciences are much more likely to graduate with a degree in the sciences than minorities. For example, Table 2 shows that while 57.3 percent nonminorities who start in the sciences at UC Berkeley actually graduate in the sciences, the corresponding rate is less than one-half of that (26.9 percent) for minority students.²² Given that so few minority students switch from nonscience to science majors, it is clear that the initial major is an important determinant of future academic outcomes.

The importance of the initial major also is present in drop-out rates: students who begin in science majors are less likely to graduate in five years than those who begin in a nonscience major. Nonminority students who begin in the sciences are 3.5 percentage points more likely to not finish in any major in five years than are nonminority students who begin in the nonsciences (26.0 versus 22.5 percent). For minority students, the gap in five-year graduation rates between those who initially majored in the sciences versus the nonsciences is much larger at 11.3 percentage points (41.6 versus 30.3 percent). The lower completion rates for initial science majors holds despite those who start out in the sciences having higher academic preparation scores. These results show the importance of the initial major, both in its effect on the student’s final major and on whether the student graduates at all.

An obvious issue with the interpretation of the across-campus and across-major results presented thus far is the potential importance of selection. Graduation rates are likely higher at UC Berkeley than at UC Riverside, for example, because the students at UC Berkeley have better academic preparation. To start to sort out whether higher persistence rates at top campuses are due to better students or the value added of being educated in the sciences at a top ranked campus, we break out our various graduation rates for the quartiles of the preparation score (S) distributions.

In panel C of Table 3 we display the shares of minority and nonminority students in each quartile of the academic preparation index for each of the eight UC campuses. Note the differences in these distributions by race at top ranked campuses compared to the lower ranked ones. While nonminorities enrolled at top ranked campuses like UC Berkeley and UCLA were disproportionately in the top quartile of the preparation score distribution, minorities enrolled in these same campuses are much more equally distributed across the quartiles. Enrollments are the result of students’ decisions to apply to particular campuses and colleges’ admissions decisions. In panels A and B of Table 3 we display the shares of minorities and nonminorities who applied to and were admitted by each of the campuses. As can be seen, the relatively equal distribution across the quartiles of preparation scores of minorities at the top UC campuses holds for both applications and admissions, while the distributions for nonminorities at these same campuses are more skewed to those with higher preparation scores for both of these stages of the process.

Table 3—

Shares of Students by Quartiles of the Preparation Score (S) Distribution

Prep. score (S) quartile	Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside
Panel A. Application
Minority
QI	0.375	0.471	0.425	0.450	0.564	0.566	0.573	0.673
QII	0.264	0.266	0.274	0.269	0.253	0.259	0.241	0.216
QIII	0.218	0.176	0.197	0.193	0.134	0.136	0.134	0.087
QIV	0.143	0.086	0.104	0.089	0.049	0.039	0.051	0.024
Nonminority
QI	0.085	0.136	0.141	0.177	0.256	0.276	0.268	0.350
QII	0.175	0.235	0.250	0.277	0.296	0.336	0.317	0.313
QIII	0.300	0.304	0.304	0.301	0.272	0.265	0.259	0.217
QIV	0.440	0.325	0.305	0.244	0.176	0.123	0.155	0.120
Panel B. Admission
Minority
QI	0.167	0.149	0.145	0.353	0.386	0.454	0.503	0.599
QII	0.284	0.351	0.355	0.311	0.344	0.322	0.278	0.262
QIII	0.301	0.323	0.318	0.230	0.198	0.174	0.159	0.109
QIV	0.247	0.177	0.183	0.106	0.072	0.051	0.061	0.030
Nonminority
QI	0.009	0.012	0.010	0.046	0.097	0.123	0.174	0.254
QII	0.031	0.042	0.072	0.218	0.307	0.379	0.338	0.345
QIII	0.131	0.221	0.379	0.396	0.355	0.340	0.303	0.255
QIV	0.830	0.725	0.539	0.340	0.240	0.158	0.185	0.146
Panel C. Enrollment
Minority
QI	0.250	0.222	0.184	0.470	0.527	0.609	0.630	0.708
QII	0.319	0.385	0.408	0.279	0.302	0.274	0.221	0.208
QIII	0.267	0.296	0.309	0.175	0.136	0.091	0.104	0.071
QIV	0.164	0.098	0.099	0.076	0.035	0.026	0.045	0.014
Nonminority
QI	0.018	0.027	0.021	0.098	0.187	0.194	0.242	0.417
QII	0.050	0.082	0.129	0.324	0.455	0.463	0.380	0.311
QIII	0.182	0.320	0.516	0.404	0.272	0.255	0.271	0.163
QIV	0.750	0.571	0.334	0.174	0.086	0.088	0.107	0.109

Notes: This table shows shares of minority and nonminority students who applied, were admitted, and enrolled at the various UC campuses by quartiles of the preparation score (S) distribution. See footnote 16 for a description of the construction of students’ preparation scores. The quartiles used were derived for the distribution of scores for the pool of all applicants to one or more UC campus during the years 1995–1997.

Source: Authors’ calculations

The matching of relatively less prepared minority students to top UC campuses is, in part, a consequence of the affirmative action policies that prevailed during the period we examine. This policy of using race as well as academic preparation directly manifested itself in campus admissions decisions. For example, comparing the share of minorities admitted to UC Berkeley from the bottom quartile of S with that for nonminorities, minorities were 18.57 [= 0.167/0.009] times more likely to be admitted than nonminorities. Minorities in the bottom quartile were admitted to UC Riverside at a rate 2.35 [= 0.599/0.254] times higher than nonminorities. The tabulations in panel A of Table 3 also suggest that this policy may have affected the racial mix of applications from students with weaker academic backgrounds across the UC campuses, although these effects appear to be smaller than for admissions.²³

We next examine the differences in three alternative graduation rates for four- and five-year graduation outcomes: (i) graduation in the sciences, conditional on beginning in the sciences; (ii) graduation in any major, conditional on beginning in the sciences; and (iii) graduation in any major, conditional on beginning in a nonscience major.²⁴ In Table 4 we display the average values of these various graduation rates for the top two ranked UC campuses (UC Berkeley and UCLA) and for the three lowest ranked campuses (UC Santa Barbara, UC Santa Cruz, and UC Riverside), by preparation score quartiles and initial major for minority and nonminority students, respectively.²⁵ Panel A (B) shows results for minority (nonminority) students, with the first (second) set of columns showing results for four-year (five-year) graduation rates.

Table 4—

Comparison of Unadjusted Four- and Five-Year Graduation Rates (Percent)

			Four-year graduation rate			Five-year graduation rate
Prep score Initial (S) quartiles	Initial major	Final major	Avg. for top 2 campuses	Avg. for bottom 3 campuses	Diff.	Avg. for top 2 campuses	Avg. for bottom 3 campuses	Diff.
Panel A. Minority
QI	Science	Science	0.0	5.1	−5.1**	9.3	13.8	−4.4*
	Science	Any	8.4	16.7	−8.3**	43.9	49.1	−5.2
	Nonscience	Any	20.2	29.6	−9.3**	59.0	58.7	0.3
QII	Science	Science	2.9	13.5	−10.6**	17.5	26.4	−8.9**
	Science	Any	17.3	26.7	−9.4**	59.3	57.6	1.7
	Nonscience	Any	30.2	39.0	−8.7**	67.0	67.2	−0.2
QIII	Science	Science	9.6	21.5	−11.9**	28.9	36.2	−7.3
	Science	Any	19.9	40.8	−20.9**	63.5	69.2	−5.7
	Nonscience	Any	39.6	42.7	−3.2	76.8	68.6	8.2**
QIV	Science	Science	25.9	42.9	−17.0**	52.1	52.4	−0.3
	Science	Any	38.3	64.3	−26.0**	78.3	78.6	−0.3
	Nonscience	Any	53.1	62.1	−9.1	83.9	84.8	−1.0
Panel B. Nonminority
QI	Science	Science	0.0	8.3	−8.3**	17.5	21.0	−3.5
	Science	Any	5.0	23.3	−18.3**	50.0	54.2	−4.2
	Nonscience	Any	23.6	38.3	−14.6**	58.5	63.9	−5.4*
QII	Science	Science	10.3	14.7	−4.3**	28.7	28.5	0.2
	Science	Any	21.5	31.4	−10.0**	67.0	61.3	5.8*
	Nonscience	Any	39.1	46.7	−7.7**	78.8	72.1	6.7**
QIII	Science	Science	20.1	25.1	−5.0**	45.1	39.6	5.5**
	Science	Any	35.4	43.4	−8.0**	78.1	70.2	8.0**
	Nonscience	Any	50.0	51.2	−1.3	83.5	74.6	9.0**
QIV	Science	Science	38.6	34.3	4.3**	58.1	46.6	11.4**
	Science	Any	53.7	60.0	−6.3**	86.1	79.6	6.5**
	Nonscience	Any	61.5	61.2	0.2	88.9	80.1	8.8**

Note: Table shows comparison of unadjusted four- and five-year graduation rates (percent) of minority and nonminority students for different majors at top two ranked UC campuses with the three lowest ranked, by S quartile and initial major.

^***Significant at the 1 percent level.

^**Significant at the 5 percent level.

^*Significant at the 10 percent level.

Source: Authors’ calculations

Considering minority five-year graduation rates, those in the bottom two quartiles of the preparation distribution at the top two campuses have significantly lower probabilities of graduating in the sciences, conditional on beginning in the sciences, than do minorities from the bottom two quartiles who attended the bottom three campuses. This result holds even though students at UC Berkeley and UCLA with S scores in the bottom quartile were presumably stronger in other dimensions, e.g., parental education, income, etc., than those in the bottom quartile at the less selective campuses. Note, however, that minorities in the highest quartile of S shows virtually no difference in science persistence rates between the top two and bottom three campuses. Further, results from the third quartile indicate significantly higher graduation probabilities in the nonsciences among those attending the more selective campuses. Looking at nonminorities also shows the top schools being a relatively better match for the top students. Students in the top two quartiles have higher probabilities of persisting in the sciences, and significant positive effects appear in the second quartile for graduating in the nonsciences. As a whole, these results suggest the possibility that (i) less prepared students may have higher graduation probabilities at less selective schools and (ii) this is especially true in the sciences.

The patterns of persistence in science majors and probabilities of graduating in any field displayed in Table 4 are even more striking if we instead examine four-year graduation rates. Regardless of minority status, no student in the bottom quartile at either UC Berkeley or UCLA finished a science degree in four years, conditional on beginning in the sciences. Both minorities and nonminorities in the bottom three quartiles have significantly lower four-year science persistence rates at the top two campuses compared to the bottom three, while, for both groups, students who begin in a science major have significantly lower four-year graduation rates, regardless of their final major, at the top two versus bottom three campuses. For those who begin in the nonsciences in the bottom two quartiles, significantly lower four-year graduation rates also are found at the top two campuses. Finally, no significant differences are present for initial nonscience majors in the top two quartiles for four-year graduation rates, again suggesting that preparation is particularly important in the sciences at top ranked schools.

II. Modeling Student Persistence in College Majors and Graduation

The descriptive statistics in Section IB suggest that the match between students’ academic preparation scores and the ranking of the UC campus may be important, particularly in the sciences. We now propose a model that is flexible enough to capture these matching effects. We model a student’s decision regarding whether to graduate from college and, if they do, their final choice of major. In particular, student i attending college k can choose to major and graduate in a science field, m, or in a nonscience field, h, or choose to not graduate, n. Denote the student’s decision by d_ik, d_ik ∈ {m, h, n}. In what follows, the student’s college, k, is taken as given. But, as noted above, ignoring the choice process governing which campus a student selected may give rise to selection bias in estimating the determinants of their choice of a major to the extent that admission decisions are based on observed and unobserved student characteristics that also may influence their choice of majors and likelihood of graduating from college. We discuss the selection problem in more detail in Section IIB.

We assume that the utility student i derives from graduating with a major in j from college k depends on three components: (i) the net returns she expects to receive from graduating with this major from this college; (ii) the costs of switching one’s major, if the student decides to change from the one with which she started college; and (iii) other factors which we treat as idiosyncratic and stochastic. The net returns from majoring in field j at college k, R_ijk, is just the difference between the expected present value of future benefits, b_ijk, of having this major/college combination, less the costs associated with completing it, c_ijk, i.e., R_ijk = b_ijk − c_ijk.²⁶ In particular, the benefits would include the expected stream of labor market earnings that would accrue to someone with this major-college combination (e.g., an engineering degree from UC Berkeley), where these earnings would be expected to vary with a student’s ability and the quality of training provided by the college.

The costs of completing a degree in field j at campus k depend on the effort a student would need to exert to complete the curriculum in this major at this college, where this effort is likely to vary with i’s academic preparation, the quality of the college, and its students. With respect to switching costs, each student arrives on campus with an initial major, j^int (as with the college she attends, her initial, or intended, major, j^int, is taken as given). The student may remain in and graduate with her initial major or may decide to switch to and graduate with a different major in which case the switching cost, C_ijk, is paid. Finally, we allow for an idiosyncratic taste factor, ϵ_ijk. It follows that the payoff function for graduating with major j at college k is given by

$$U_{ijk}=R_{ijk}-C_{ijk}+{ϵ}_{ijk},$$ (1)

for j ∈ {m, h}. We assume that ϵ_ijk is unknown at the time of the initial college and major decision.²⁷ This shock can be the result of learning about their abilities in particular subjects (Arcidiacono 2004; Stinebrickner and Stinebrickner 2014) or about their tastes for different educational options.

Since discrete choice models depend on differences in payoffs, without loss of generality we normalize the student’s utility of not graduating from college k, denoted as U_ink, to zero. It follows that the major/graduation choice of student i attending college k is made according to

$$d_{ik}=\underset{m,h,n}{\arg \max }\left\{U_{imk},U_{ihk},0\right\}.$$ (2)

A. Net Returns

We assume that the net returns of a particular major/college combination, R_ijk, varies with a student’s academic preparation for major j, which we denote by the index, AI_ij,²⁸ and that these net returns to AI_ij may differ across campuses. In particular, we assume that R_ijk is characterized by the linear function

$$R_{ijk}={\varphi }_{1jk}+{\varphi }_{2jk}A{I}_{ij}.$$ (3)

The specification in (3) allows college-major combinations to differ in their net returns to academic preparation with higher net returns associated with higher values of ϕ_2jk. As noted above, such differences in ϕ_2jk may result from colleges gearing their curriculum in a particular major to students from a particular academic background which, in turn, produce differences in subsequent labor market earnings. Degrees in various majors from different colleges also may produce differing net returns that do not depend on a student’s academic preparation which is reflected in differing values of ϕ_1jk. For example, the curriculum in a particular major and the course requirements that all students have to meet may vary across colleges, resulting in colleges imposing differing effort and time costs to completing the major.

We are interested in how differences in college quality, or selectivity, affect major-specific graduation probabilities for students of differing academic preparation. To see how the specification of the net returns functions in (3) capture such differences, suppose that college A is an elite, selective college (e.g., UC Berkeley or UCLA), while college B is a less selective one (e.g., UC Santa Cruz or UC Riverside). Three cases are illustrated in Figure 3. One possibility is that highly selective colleges (A) have an absolute advantage relative to less selective ones (B) in the net returns that students from any level of academic preparation would receive and that such advantage is true for all majors. This case is illustrated in panel A of Figure 3, where the absolute advantage holds for all majors.

Figure 3.

Differences in Net Returns to Student Academic Preparation (AI) by Major at Selective (A) and Nonselective (B) Colleges

Alternatively, selective colleges may not generate higher net returns for students with all levels of academic preparation in all fields. For example, selective colleges may have an absolute advantage in moving all types of students through its science curriculum, whereas less selective colleges (B) may have an absolute advantage in training students in the humanities. This case is characterized by panels A and B of Figure 3, respectively, in which elite colleges (A) have absolute advantage in getting students through major j, while less selective colleges (B) have an absolute advantage in graduating all students from major j′. This second case might arise if colleges develop faculties and facilities to educate students in some majors, but not others, such as “technology institutes” (e.g., Caltech, Georgia Tech) which focus their curriculum primarily on science and technology fields.

But some colleges may produce higher net returns in some major j for less prepared students, while other colleges produce higher net returns for better prepared students. This case is illustrated in panel C of Figure 3. At first glance, this differences-in-relative-advantage between highly and less selective colleges may account for the evidence presented in Table 4, showing UC Berkeley and UCLA having greater success in graduating better prepared students in science fields than the lowest ranked UC campuses while being much less successful graduating less prepared students in the sciences than the lower ranked campuses. Below, we examine the empirical validity of this explanation, after explicitly accounting for differences in student preparation.

B. Academic Preparation for Majors

We now specify how the student’s major-specific academic preparation index, AI_ij, is constructed. We assume that the various abilities and factors that go into determining a student’s preparation for a particular major can be characterized by a set of characteristics X_i. These characteristics are then rewarded in majors differently. For example, math skills may be rewarded more in the sciences while verbal scores may be more rewarded outside of the sciences. It follows that the academic preparation index for major j ∈ {m, h}, AI_ij, is then given by

$$A{I}_{ij}={\mathbf{X}}_i^{\prime }{\mathbf{\beta }}_j,$$ (4)

where subscripting β by j allows the weights on the various measures of preparation to vary by major.

Our estimation problem is analogous to that in the literature concerning the effects of college quality on graduation and later-life outcomes. In particular, whether a student remains in a major and graduates from a particular college is the result of student decisions that are influenced by the quality of the campus—in our case the campus-specific net returns to graduating with a particular major and the costs of switching a major—and by observed and unobserved dimensions of her academic preparation. The observed measures of academic preparation in X_i includes high school GPA, SAT math and verbal scores, as well as family background measures such as parental income and parental education. We also include indicator variables for minority and Asian as race and ethnicity are correlated with factors such as high school quality, even after controlling for parental education and income.²⁹

To account for the selection effects based on unobservables, we employ the approach used by Dale and Krueger (2002). In particular, we add to our controls dummy variables for whether a student applied to each of the eight UC campuses, dummy variables for whether they were accepted to each of these UC campuses, and some interactions of these variables.³⁰ Because racial preferences affect admissions and application probabilities, we also interact each of these variables with minority status. This sort of approach requires that students not always attend the most highly ranked college to which they were admitted. In Table A5 of the online Appendix, we show that there is a sufficient number of cases where individuals are admitted to pairs of schools and choose to attend the lower ranked of the pair, regardless of which school pairing we are considering. This approach is not without critics,³¹ as the reasons why someone may choose to apply to a top school, be admitted, and then attend a lower ranked school are not obvious and may be correlated with unobserved ability. Hence, in Section IIIC we explore how our results are affected by using different combinations of Dale and Krueger controls as well as not including them at all.

C. Costs of Switching Majors

Finally, we specify the costs of switching majors, C_ijk. We allow these costs depend on a student’s initial major j and academic preparation index for that major, AI_ij, as well as allowing separate effects for family background, B_i, as measured by parental income and education. Further, these effects are allowed to vary by campus, α_3k, with the specification of C_ijk given by

$$C_{ijk}=\{\begin{array}{ll}{\alpha }_{0j}+{\alpha }_{1j}A{I}_{ij}+{\mathbf{\alpha }}_2^{\prime }{\mathbf{B}}_i+{\alpha }_{3k},& \text{if}{j}^{\text{int}}\ne j,\\ 0,& \text{if}{j}^{\text{int}}=j.\end{array}$$ (5)

D. Estimation

We specify the choice-specific utilities to have a nested logit form, allowing the errors to be correlated among the two graduation options, i.e., graduating with a science major (m) and graduating with a nonscience major (_h). In this way we account for shocks after the initial choice of college and major that may influence the value of a student continuing their education, such as a shock to one’s finances or personal situation. Given our assumption regarding the error distribution, the probability of choosing to graduate from school k with major j ∈ {m, h}, conditional on X and B (but not ϵ), is given by

$$p_{ijk}(\mathbf{\theta })=\frac{{\left({\sum }_{j^{\prime }}\exp \left(\frac{u_{i{j}^{\prime }k}}{\rho }\right)\right)}^{\rho -1}\exp \left(\frac{u_{ijk}}{\rho }\right)}{{\left({\sum }_{j^{\prime }}\exp \left(\frac{u_{i{j}^{\prime }k}}{\rho }\right)\right)}^{\rho }+1},$$ (6)

where θ ≡ {α, β, ϕ, ρ} is the full set of parameters to be estimated and u_ijk ≡ U_ijk − ϵ_ijk. ³² The probability of choosing not to graduate from k is then given by³³

$$p_{i0k}(\mathbf{\theta })=\frac{1}{{\left({\sum }_{j^{\prime }}\exp \left(\frac{u_{i{j}^{\prime }k}}{\rho }\right)\right)}^{\rho }+1}.$$ (7)

We estimate separate nested logit models for four- and five-year graduation outcomes.

Note that since β_j is major-specific, we must normalize one ϕ_2jk for each major. We do so by setting the return on both the science and nonscience academic index at UC Berkeley to 1. The estimated β_js then give the returns to the various components of the academic indexes at UC Berkeley in major j. In order to make our results easier to interpret, the remaining ϕ_2jk parameters are estimated relative to UC Berkeley. In particular, we estimate ${\varphi }_{2jk}^{*}$ for the other campuses where ${\varphi }_{2jk}^{*}={\varphi }_{2jk}-1$. Similarly, we estimate the intercept terms for the other campuses relative to UC Berkeley, estimating ${\varphi }_{1jk}^{*}\equiv {\varphi }_{1jk}-{\varphi }_{1jBERK}$.

III. Results

We begin by discussing the five-year graduation results. We present estimates for the net return functions in (3) and some of the components of academic index in (4) for majoring in science and the nonsciences. The estimates of these key parameters are displayed in Table 5.³⁴ The full model includes 156 parameters. The remaining parameters can be found in Tables A6a, A6b, and A6c of the online Appendix.

Table 5—

Nested logit Coefficients for Choice of Final Major Based on Five-Year Graduation Criteria

	Science	Nonscience			Science	Nonscience
Panel A. Net returns function
Campus-specific intercept coefficients (ϕ1jk)				Campus-specific slope coefficients (ϕ2jk)
UCLA	0.252	−1.215**		UCLA × AIij	−0.022	0.097*
	(0.817)	(0.553)			(0.047)	(0.058)
San Diego	2.548**	0.132		San Diego × AIij	−0.147**	−0.087
	(0.813)	(0.558)			(0.045)	(0.055)
Davis	1.948**	0.132		Davis × AIij	−0.117**	−0.088*
	(0.753)	(0.491)			(0.042)	(0.050)
Irvine	3.318**	1.046*		Irvine × AIij	−0.220**	−0.192**
	(0.816)	(0.563)			(0.043)	(0.053)
Santa Barbara	4.400**	1.560**		Santa Barbara × AIij	−0.276**	−0.229**
	(0.842)	(0.610)			(0.042)	(0.050)
Santa Cruz	6.978**	2.131**		Santa Cruz × AIij	−0.472**	−0.353**
	(1.002)	(0.776)			(0.048)	(0.060)
Riverside	5.319**	1.919**		Riverside × AIij	−0.355**	−0.345**
	(0.909)	(0.683)			(0.044)	(0.059)
Panel B. Academic preparation function (AIij)
High school GPA	2.811**	2.076**
	(0.389)	(0.369)
SAT math (thousands)	8.069**	−1.020**
	(0.580)	(0.467)
SAT verbal (thousands)	−1.453**	1.482**
	(0.440)	(0.410)
urm	−0.986**	−0.884**
	(0.255)	(0.229)
Asian	0.146*	−0.131*
	(0.080)	(0.077)
Mean AIj	14.712	8.309
SD AIj	2.694	1.845
Nesting parameter
ρ			0.317** (0.064)
log-likelihood			−59,611

Notes: All campus dummies are measured relative to UC Berkeley (the omitted category). The coefficients on ϕ_1jk and ϕ_2jk for UC Berkeley are normalized to zero and one, respectively. Original scale for SAT math and verbal 200–800. High school GPA is on a four-point scale. Mean AI_j and SD AI_j are calculated from the UC applicant pool.

^***Significant at the 1 percent level.

^** Significant at the 5 percent level.

^*Significant at the 10 percent level.

Estimates for the net returns functions are displayed in panel A of Table 5. Recall that the estimated campus intercepts and slope coefficients for the specification in (3) are measured relative to those for UC Berkeley where the UC Berkeley intercepts are zero and slopes are one. The net returns to academic preparation (the ϕ_2jks) are larger for higher ranked campuses, consistent with higher ranked campuses having a comparative advantage in graduating the better prepared students. This pattern holds for both STEM and non-STEM majors. However, the intercepts (the ϕ_1jks) are higher for the lower ranked campuses, which admits the possibility that lower (higher) ranked campuses having an absolute advantage in graduating the least (most) prepared students. Again, this pattern holds for STEM and non-STEM majors. In order to determine whether this is the case, we must take into account the distribution of the major-specific academic preparation indices, i.e., the AI_ijs.

The coefficient estimates for the academic preparation function in (4) are found in panel B of Table 5. SAT math scores have a strong, positive effect for majoring in science, but a negative effect for majoring in the nonsciences. In contrast, SAT verbal scores are relatively more important for majoring in nonsciences compared to the sciences.³⁵ Finally, the estimates indicate that while a student’s high school GPA is important for both majors, it is relatively more important for science than nonscience.

We use the estimates in panel B to predict the values of AI_ij for all students in the UC applicant pool who applied to a UC campus in the sciences (j = m) or nonsciences (j = h). The mean and standard deviations for these two distributions are displayed immediately below panel B of Table 5. These distributions differ across the two majors. Such differences, especially with respect to the variances, complicate comparisons of the gradients of net returns with respect to student academic preparation across majors. To avoid this problem, we use the standardized version of AI_ij for each major, i.e., $A{I}_{ij}^{*}\equiv \frac{\left(A{I}_{ij}-{\overline{AI}}_j\right)}{sd\left(A{I}_j\right)}$, where ${\overline{AI}}_j$ is the mean of AI_ij taken over the entire UC applicant pool who declared their initial major in the sciences (j = m) and the nonsciences (j = h), respectively. It follows that the gradient of R_jk with respect to $A{I}_{ij}^{*}$ is given by ϕ_2jk · sd(AI_ij). Thus, while the ${\widehat{\varphi }}_{2jk}\mathrm{s}$ are comparable in magnitude across majors, the gradients with respect to $A{I}_{ij}^{*}$ will not be.

Figure 4 plots the net returns to the two majors across the $A{I}_{im}^{*}$ distribution at three campuses: UC Berkeley, UC Santa Cruz, and UC Riverside. In particular, panel A of Figure 4 plots the net returns in the sciences based on graduating in five years, while panel B plots the corresponding returns for nonscience majors. While it appears that UC Berkeley has an absolute advantage over the two lower ranked campuses in net returns of nonscience majors in terms of five-year graduation, at least over a two-standard deviation range of AI*, the same is not the case for science majors. Rather, while UC Berkeley has higher net returns in the sciences for students with above average AI^*s, both UC Santa Cruz and UC Riverside turn out to have higher net returns for students with lower-than-average AI^*s.³⁶ As a result, the matching of students to campuses by academic preparation is much more important in the sciences than for nonscience fields.

Figure 4.

Differences in Net Returns to Students’ Standardized Academic Preparation Index $\left(A{I}_{ij}^{*}\right)$ by Major at Different UC Campuses

We plot these same net returns to graduating in four years for initially majoring in science and nonscience, respectively, in panels C and D of Figure 4. The matching of students with interests in the sciences to campuses is even more important for on-time graduation based on the estimated net returns associated with graduation in four years. As shown in panel C, our estimates imply that students with AI*s at or below one standard deviation above the mean have higher net returns to graduating in four years in the sciences at UC Santa Cruz or UC Riverside than they would have at UC Berkeley. And, our estimated net returns for graduating in four years in the nonsciences are no longer higher at UC Berkeley relative to the two lower ranked campuses, with the crossing point at about one standard deviation above the mean of the applicant pool.

The distributions of net returns to graduation at higher versus lower ranked UC campuses illustrated in Figure 4 also suggest that there are potential gains to graduation rates of minorities in the sciences from reallocating students across the UC campuses by their academic preparation. To see this, consider the location of the average minority student at UC Berkeley initially declared in the sciences. Based on the estimates for the academic preparation function in (4), this student would have an AI^∗ score of −0.04, barely below the mean score in the applicant pool of ${\overline{AI}}_m^{*}=0$, indicating that this student would have a higher net return at either Santa Cruz or UC Riverside.³⁷ In contrast, the average nonminority student at UC Berkeley who initially declared in the sciences has an $A{I}_{im}^{*}$ of 1.30, above the overall mean and in the range where UC Berkeley’s net returns exceed those of the other two schools. In the next section, we examine how reallocating minority and nonminority students in the sciences from top ranked to lower ranked UC campuses would affect graduation rates in the sciences.

A. Potential Gains from Reallocating Students to Counterfactual Campuses

In this section we use our estimates of net returns to forecast how graduation outcomes would change if students at the top two UC campuses (UC Berkeley and UCLA) had instead attended one of the bottom two campuses (UC Santa Cruz and UC Riverside).³⁸ We focus on changes in the probability of: (i) graduating in the sciences, conditional on beginning in the sciences; (ii) graduating in any major, conditional on beginning in the sciences; and (iii) graduating with any major, conditional on beginning in the nonsciences.

Table 6 presents the results for minority students. The first set of rows gives the average across all minority students who attended UC Berkeley (first set of columns) or UCLA (second set of columns) while the next set breaks out the effects by quartile of the preparation score (S). Our model predicts average gains of 4.3 and 7.2 percentage points for persisting in the sciences, on a base of 27.5 percent, from moving from UC Berkeley to UC Santa Cruz and UC Riverside, respectively. The overall gains from moving students in the sciences from UCLA to UC Santa Cruz are relatively small (2.3 percent) and statistically insignificant, but moving minority students from UCLA to UC Riverside produces an increase in science graduation rates of 4.7 percentage points on a base of 27.0 percent. There are almost no significant gains in total graduation rates, regardless of initial major. The one exception is moving students who are initially nonscience majors from UC Berkeley to UC Riverside, which lowers graduation rates for this group by 3.8 percentage points off a base of 69.9 percent.

Table 6—

Gains in Graduations for Minorities in Moving from Higher to Lower Ranked Campuses

Prep. score (S) quartile	Initial major	Final major	Berkeley base grad. rate	Gain from switch to Santa Cruz	Gain from switch to Riverside	UCLA base grad. rate	Gain from switch to Santa Cruz	Gain from switch to Riverside
Overall	Science	Science	27.5	4.3**	7.2**	27.0	2.3	4.7**
	Science	Any	64.6	−1.6	−1.8	60.8	1.6	1.2
	Nonscience	Any	69.9	−2.7	−3.8**	67.7	0.5	−0.6
QI	Science	Science	8.0	11.8**	9.8**	11.9	8.2**	6.5**
	Science	Any	47.4	4.5*	2.8	45.0	8.1**	6.5**
	Nonscience	Any	59.8	0.3	−1.2	56.3	5.0**	3.5
QII	Science	Science	18.1	8.9**	10**	21.6	4.9**	5.9**
	Science	Any	59.9	0.2	−0.6	57.5	3.0*	2.2
	Nonscience	Any	69.6	−2.7	−3.9**	67.3	0.6	−0.6
QIII	Science	Science	30.0	3.7	7.4**	32.1	0.4	4.0*
	Science	Any	67.4	−2.5	−2.5	65.4	−0.4	−0.4
	Nonscience	Any	76.3	−4.6**	−5.4**	75.0	−2.3*	−3.1*
QIV	Science	Science	43.8	−3.5	3.0	44.2	−5.6**	1.1
	Science	Any	74.9	−5.3**	−4.4**	74.3	−4.1**	−3.2*
	Nonscience	Any	81.4	−5.8**	−6.2**	80.9	−4.3**	−4.7**

Note: Table shows estimated gains (losses) in five-year graduations for minorities in moving from higher to lower ranked UC campuses, by quartiles of academic preparation score distribution and initial major (percentage points).

^***Significant at the 1 percent level.

^**Significant at the 5 percent level.

^*Significant at the 10 percent level.

Looking across quartiles of the academic preparation score (S) distribution, one finds that the gains in graduation rates from moving students from top to lower ranked UC campuses vary significantly by quartile, particularly for science graduation rates. As recorded in Table 6, UC Berkeley students in the bottom quartile of the S distribution who begin in the sciences would see their graduation probabilities in the sciences more than double had they attended either UC Santa Cruz or UC Riverside, increasing their graduation rate by 11.8 and 9.8 percentage points, respectively, on a base of 8 percent. At the second quartile, those moving from UC Berkeley to UC Santa Cruz or UC Riverside would see graduation rate increases in the sciences of 8.9 and 10.0 percentage points, respectively, on a base of 18.1 percent. The gains are insignificant for those students in the third and fourth quartile of the S distribution, with the sign flipping for the fourth quartile at UC Santa Cruz.

Similar patterns are observed for moving students from UCLA to the two lowest ranked campuses, though the gains to moving these students to either UC Santa Cruz or UC Riverside are not as large. Moving UCLA students in the bottom quartile who intended to major in the sciences to UC Santa Cruz or UC Riverside would increase science graduation rates by the 8.2 and 6.5 percentage points, respectively, on a base of 11.9 percent, with significant gains in the second quartile as well for both campuses. Those UCLA science students in the fourth quartile of the S distribution, however, would see significantly lower graduation rates by moving to Santa Cruz, dropping 5.6 percentage points off a base of 44.2 percent.

Differences across the quartiles of the academic preparation score, S, in the gains from moving minority students across campuses also are seen for overall graduation rates. Those in the bottom quartile who begin in the sciences at UCLA see significantly higher overall graduation probabilities of moving to UC Santa Cruz or UC Riverside, with increases of 8.1 and 6.5 percentage points, respectively. The effects are not as pronounced for those at UC Berkeley, with only the increases at Santa Cruz significantly positive. For those in the bottom quartile being in the nonsciences, no significant effects are found for those who begin at UC Berkeley, but those who begin at UCLA would see increases of 5.0 and 3.5 percentage points at UC Santa Cruz and UC Riverside, with the latter only significant at the 10 percent level.

For students in the top quartiles of S, our results imply that moving minority students from UC Berkeley or UCLA to lower ranked schools result in significant losses in total graduation rates, particularly for those who begin in the nonsciences. Those in the top quartile who begin in the nonsciences at UC Berkeley see graduation rate decreases of 5.8 and 6.2 percentage points at UC Santa Cruz and UC Riverside, respectively, on a base of 81.4 percent. Similar graduation rate decreases are seen from moving well prepared minority students from UCLA to UC Santa Cruz or UC Riverside.

Table 7 repeats the analysis in Table 6 for nonminority students.³⁹ The overall patterns for nonminority students are very different than those found for minorities. Moving nonminority students to UC Santa Cruz who begin in the sciences at UC Berkeley or UCLA would result in significant decreases in science graduation rates, while moving them to UC Riverside would have no effect. And overall graduation rates, regardless of initial major, would fall significantly by moving these students from the two top ranked UC campuses to the two ranked at the bottom.

Table 7—

Gains in Graduations for Nonminorities in Moving from Higher to Lower Ranked Campuses

Prep. score (S) quartile	Initial major	Final major	Berkeley base grad. rate	Gain from switch to Santa Cruz	Gain from switch to Riverside	UCLA base grad. rate	Gain from switch to Santa Cruz	Gain from switch to Riverside
Overall	Science	Science	56.4	−11.9**	−0.8	50.3	−9.2**	0.6
	Science	Any	84.7	−8.0**	−6.3**	81.4	−6.3**	−4.9**
	Nonscience	Any	86.9	− 6.4**	−6.4**	84.8	−5.1**	−5.3**
QI	Science	Science	16.0	9.8**	9.8**	18.4	5.5**	6.1**
	Science	Any	55.5	2.1	1.0	57.0	3.2*	2.3
	Nonscience	Any	70.6	−3.2*	−4.3**	67.1	0.5	−0.7
QII	Science	Science	30.0	3.1	7.3**	33.3	−0.8	3.7*
	Science	Any	69.8	−3.4**	−3.3**	68.5	−1.6	−1.4
	Nonscience	Any	77.2	−4.7**	−5.5**	75.2	−2.4	−3.2**
QIII	Science	Science	49.0	−7.2**	1.4	45.3	−6.7**	1.6
	Science	Any	80.0	−6.9**	−5.6**	78.2	−5.3**	−4.3**
	Nonscience	Any	84.3	−6.2**	−6.4**	84.2	−5.1*	−5.4**
QIV	Science	Science	58.9	−13.4**	−1.5	54.5	−11.3**	−0.2
	Science	Any	86.3	−8.4**	−6.5**	84.3	−7.3**	−5.6**
	Nonscience	Any	89.3	−6.8**	−6.5**	88.5	−6.1**	−6.0**

Note: Table shows estimated gains (losses) in five-year graduations for nonminorities in moving from higher to lower ranked UC campuses, by quartiles of academic preparation score distribution and initial major (percentage points).

^***Significant at the 1 percent level.

^**Significant at the 5 percent level.

^*Significant at the 10 percent level.

But, while the overall rates are very different across minority and nonminority students, breaking the results out by quartiles shows similar within-quartile patterns for the two groups. The difference is very few nonminorities at UC Berkeley or UCLA are in the bottom two quartiles. Similar to minority students, nonminority students in the bottom quartile who begin in the sciences at UC Berkeley see increased graduation probabilities of 9.8 percentage points at both UC Santa Cruz and UC Riverside on a base of 16 percent. At UCLA, the increases are 5.5 and 6.1 percentage points, respectively, on a base of 18.4 percent.

Breaking out the results by quartile of the preparation score shows that the difference in the overall effects for minorities and nonminorities are being driven by the combination of minority students coming into the top UC campuses with significantly worse academic backgrounds, coupled with the importance of the match between the college and the student. In particular, the top ranked campuses are comparatively better at graduating the most prepared students, with the lower ranked campuses having an absolute advantage in graduating students in the sciences who are at the bottom of the preparation distribution.

B. Predicted Graduation Rates under Alternative Assignment Rules

The results in the preceding two sections suggest that matching of students to campuses according to their academic preparation matters for graduation rates in the sciences. Moreover, it appears that these gains in the sciences are greater for minorities than nonminorities. As noted, the latter finding is driven by the differences in the way minority and nonminority students were allocated across the UC campuses in a period where racial preferences were present. Our model also allows us to examine how minority graduation rates would have changed under other, i.e., counterfactual, rules of assigning this group to the UC campuses. For example, what would have happened to minority graduation rates had minorities been allocated to universities in the way nonminority students were? Similarly, we can examine how graduation rates for nonminorities would be affected had they been assigned like minorities. Would their science graduation rates fall or rise under this alternative assignment mechanism?

To address these questions, we use our estimates of students’ selection-adjusted graduation probabilities (the $p_{ijk}(\widehat{\mathbf{\theta }})\text{s}$ in (6) and (7)) along with probabilities of students’ being assigned to each of these campuses as a function of their academic preparation indices (the ${\widehat{AI}}_{ij}\text{s}$) in order to assess the magnitudes of the potential gain in minority graduation rates from this counterfactual allocation of students across the UC campuses.

To proceed, we first estimate assignment rules allocating nonminority and minority students, respectively, across the eight UC campuses for each of the two intended majors, using multinomial logits. We assume that the probability of student i in race/ethnic group r (minority or nonminority) being assigned to campus k is the following function of the student’s estimated academic preparation indices, ${\widehat{AI}}_{im}$ and ${\widehat{AI}}_{ih}$, for field of study j ∈ {m, h}:⁴⁰

$$q_{ijkr}\left({\mathbf{\pi }}_{jkr}\right)=\frac{\exp \left({\pi }_{1jkr}+{\pi }_{2jkr}{\widehat{AI}}_{im}+{\pi }_{3jkr}{\widehat{AI}}_{ih}\right)}{{\sum }_k\exp \left({\pi }_{1jkr}+{\pi }_{2jkr}\widehat{A}{I}_{im}+{\pi }_{3jkr}{\widehat{AI}}_{ih}\right)}.$$ (8)

Let N(j, r) denote the set of students of ethnic group r that were enrolled at one of the UC campuses and declared their initial major to be j and let y_ik be an indicator for whether i was enrolled in campus k. Then, we estimate the parameter vectors for these assignment probabilities, ${\widehat{\pi }}_{jkr}\text{s}$, by solving

$${\widehat{\mathbf{\pi }}}_{jr}=\underset{\pi }{\arg \max }\sum _{i\in N(j,r)}\sum _k{y}_{ik}\ln q_{ijkr}\left({\mathbf{\pi }}_{jkr}\right),$$ (9)

where the π_jkrs for UC Riverside are normalized to zero.

We use the estimates obtained in solving (9) to obtain probabilities of being assigned to each UC campus, both under their own assignment rules and under the opposite ethnic group’s assignment rules. The probabilities of the ith member of group r with initial major j being assigned to the kth UC campus is

$$q_{ijkr}\left({\widehat{\mathbf{\pi }}}_{jkr}\right)=\frac{\exp \left({\widehat{\pi }}_{1jkr}+{\widehat{\pi }}_{2jkr}{\widehat{AI}}_{im}+{\widehat{\pi }}_{3jkr}{\widehat{AI}}_{ih}\right)}{{\sum }_k\exp \left({\widehat{\pi }}_{1jkr}+{\widehat{\pi }}_{2jkr}{\widehat{A}}_{im}+{\widehat{\pi }}_{3jkr}{\widehat{AI}}_{ih}\right)},$$ (10)

$$q_{ijkr}\left({\widehat{\mathbf{\pi }}}_{jk{r}^{\prime }}\right)=\frac{\exp \left({\widehat{\pi }}_{1jk{r}^{\prime }}+{\widehat{\pi }}_{2jk{r}^{\prime }}{\widehat{AI}}_{im}+{\widehat{\pi }}_{3jk{r}^{\prime }}{\widehat{AI}}_{ih}\right)}{{\sum }_k\exp \left({\widehat{\pi }}_{1jk{r}^{\prime }}+{\widehat{\pi }}_{2jk{r}^{\prime }}{\widehat{AI}}_{im}+{\widehat{\pi }}_{3jk{r}^{\prime }}{\widehat{AI}}_{ih}\right)},$$ (11)

for assignment rules r and r′, respectively. The difference between $q_{ijkr}\left({\widehat{\mathbf{\pi }}}_{jkr}\right)$ and $q_{ijkr}\left({\widehat{\mathbf{\pi }}}_{jk{r}^{\prime }}\right)$ characterizes how group r’s campus assignments would change had they been assigned like their r′ counterparts with the same academic preparation indices.⁴¹

Panel A of Table 8 shows how minority students would be allocated across the UC campuses, both under the pre-Prop 209 period of our data (baseline) and if they had been allocated as nonminorities in this period (opposite race). Reallocating minority students using the nonminority assignment rules results in a substantial shift out of both UC Berkeley and UCLA and into the four bottom ranked UC campuses. The shifts are slightly different depending on initial major, but the qualitative patterns are the same. Panel B shows the same results for nonminority students under the baseline and if they were allocated across the campuses in the same way that minorities had been (opposite race). Following the latter assignment rule would move nonminority students out of the bottom four campuses and out of UC Davis and into UC Berkeley and UCLA.

Table 8—

Share of Minority and Nonminority Students under Different Assignment Rules (Percent)

Assignment rule	Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside
Panel A. Minority
Initial major science
Baseline	13.9	20.6	11.7	15.3	12.1	12.1	5.9	8.6
Opposite race	2.7	4.6	8.3	14.8	22.1	19.3	14.3	13.8
Initial major nonscience
Baseline	19.9	22.6	6.9	9.9	7.2	15.7	8.5	9.3
Opposite race	2.8	4.5	4.9	11.2	16.5	26.5	19.3	14.4
Panel B. Nonminority
Initial major science
Baseline	16.0	14.8	16.1	16.8	14.8	9.9	5.0	6.6
Opposite race	23.6	29.5	18.3	9.5	9.1	4.9	1.7	3.5
Initial major nonscience
Baseline	13.3	14.6	11.6	14.4	12.3	18.0	10.1	5.7
Opposite race	26.6	33.6	12.4	6.2	5.6	7.9	3.9	3.9

Finally, we use the estimated assignment probabilities to predict how graduation probabilities in particular fields would change under different assignment rules. As in Tables 6 and 7, we focus on changes in the probability of: (i) graduating in the sciences, conditional on beginning in the sciences; (ii) graduating in any major, conditional on beginning in the sciences; and (iii) graduating with any major, conditional on beginning in the nonsciences. In particular, these predicted probabilities for group r, using the assignment rule of group r′, are given by

$$P\left(g,m|m,r,r^{\prime }\right)=\frac{{\sum }_i{\sum }_{k}I(i\in N(m,r))q_{ijkr}\left({\widehat{\mathbf{\pi }}}_{mk{r}^{\prime }}\right)p_{imk}(\widehat{\mathbf{\theta }})}{{\sum }_{i}I(i\in N(m,r))},$$ (12)

$$P\left(g|m,r,r^{\prime }\right)=\frac{{\sum }_i{\sum }_{k}I(i\in N(m,r))q_{iskr}\left({\widehat{\mathbf{\pi }}}_{mk{r}^{\prime }}\right)\left(p_{imk}(\widehat{\mathbf{\theta }})+p_{ihk}(\widehat{\mathbf{\theta }})\right)}{{\sum }_{i}I(i\in N(m,r))},$$ (13)

$$P\left(g|h,r,r^{\prime }\right)=\frac{{\sum }_i{\sum }_{k}I(i\in N(h,r))q_{ihkr}\left({\widehat{\mathbf{\pi }}}_{hk{r}^{\prime }}\right)\left(p_{imk}(\widehat{\mathbf{\theta }})+p_{ihk}(\widehat{\mathbf{\theta }})\right)}{{\sum }_{i}I(i\in N(h,r))},$$ (14)

where I denotes the indicator function, g denotes the event of graduating from college, and where the $p_{ijk}(\widehat{\mathbf{\theta }})\text{s}$ are the predicted probabilities of student i graduating with major j from campus k, using the estimates $\widehat{\mathbf{\theta }}$ in place of θ in equation (6).

Table 9 displays the predictions of our model for how changes in campus assignment rules would affect the graduation rates of minority and nonminority students. For both groups, we first report graduation probabilities using their baseline assignment rules and then report the change when the opposite group’s assignment rules are used. The top set of rows show the overall effects on science graduation rates for those with an initial interest in the science, overall graduation rates for those who are interested in the sciences, and overall graduation rates for those intending not to major in a STEM field. Allocating minorities according to the nonminority assignment rules results in an average increase in science persistence rates of 1.75 percentage points, which is a little over a 7 percent increase on the base rate of 24.6 percent. Smaller, though still statistically significant, graduation gains are predicted for overall graduation rates among the initial science majors at 0.77 percentage points, with no significant changes in graduation rates for minorities with initial nonscience majors.

Table 9—

Counterfactual Change in Graduation Probabilities of Minorities and Nonminorities with Science or Nonscience Major Based on Alternative Assignment Rules to the UC Campuses (Percentage Points)

Prep.score (S) quartile	Initial major	Final major	Minority base	Opposite race change	Nonminority base	Opposite race change
Overall	Science	Science	24.6	1.75**	43.9	−1.10**
	Science	Any	58.2	0.77**	74.1	−0.08
	Nonscience	Any	65.4	0.35	77.5	0.35
QI	Science	Science	13.3	1.82**	21.3	−1.89**
	Science	Any	47.7	1.53**	55.3	−1.20**
	Nonscience	Any	58.4	1.09**	65.6	−0.46
QII	Science	Science	22.7	1.98**	31.6	−1.70**
	Science	Any	57.9	0.83**	64.5	−0.30
	Nonscience	Any	67.5	0.07	72.3	0.39
QIII	Science	Science	32.9	1.68**	43.5	−1.23**
	Science	Any	65.8	0.15	74.6	0.21
	Nonscience	Any	74.4	−0.63*	80.1	0.72**
QIV	Science	Science	44.8	1.06**	56.9	−0.46
	Science	Any	73.5	−0.25	83.8	0.08
	Nonscience	Any	80.0	−0.78**	87.1	0.32**

^***Significant at the 1 percent level.

^**Significant at the 5 percent level.

^*Significant at the 10 percent level.

The next set of rows in Table 9 display the gains and losses in graduation rates by the quartiles of the academic preparation score, S, used earlier in the paper. Predicted gains in science persistence rates for minorities from being assigned according to the nonminority rules are generally higher for those with lower levels of preparation. The bottom quartile also sees higher overall gains in graduation rates as well. In contrast, minorities in the top two quartiles who begin in a nonscience major see significant decreases in their graduation probabilities using the alternative assignment rule.

As the last two columns of Table 9 indicate, nonminority students would experience lower graduation rates in the sciences if they were assigned to UC campuses according to the assignment rules of minorities. Note that, quartile by quartile, the results of reallocating nonminorities according to minority assignment rules would produce changes in graduation rates that are almost always the same magnitude as what would occur for minorities by reassigning them according to nonminority rules, but the changes go in the opposite direction. This is not surprising since, as we have seen in Table 8, the nonminority rules better matched students to schools in the sciences.

Note that these results ignore general equilibrium effects in how preparation translates into outcomes at the different campuses.⁴² General equilibrium effects could arise from two potentially conflicting sources: peer effects and endogenous grading standards. How peer effects would affect our findings would depend on who is in the relevant peer group. On the one hand, if the peer group was the whole student body, then reassigning minority students to lower ranked schools may result in lowering the average preparation level at that school, which could in turn have negative consequences for learning. The flip side of this is that lowering the average preparation level of the student body may result in lowering grading standards which may result in higher graduation probabilities. Further, if the relevant peers for minority students are primarily other minority students, then we may be underestimating the gains from reallocation. In this case, reassigning minority students to lower ranked schools results in average minority preparation rising at all schools. Our results suggest lower ranked campuses would have produced higher graduation rates for many minority students in the sciences who were at the higher ranked campuses. This occurred despite these lower ranked campuses having a less prepared student body, suggesting that increasing the academic preparation of the minority student body at these less selective schools may lead to even further improvements in graduation rates.⁴³ We leave estimation of general equilibrium effects to future work.

C. Robustness Checks

Until now, we have focused on one set of results using a particular specification for the Dale and Krueger controls. We have estimated a number of other specifications with similar qualitative patterns. Here we show how the last set of results, on how minority graduation probabilities would change if they were allocated according to the nonminority rules, varies with alternative specifications of the graduation model. We consider four alternative models:

1. A specification where no Dale and Krueger controls are used. This will likely bias our results in favor of racial preferences due to selection on unobservables.

2. A specification where we interact all Dale and Krueger controls with whether or not one of the parents was a college graduate.

3. A specification where we treat the initial major as the major listed on the application of the UC campus for which the individual eventually enrolled. To the extent that students are aware of cross-university differences in how academic characteristics translate into success in different fields, this may affect their initial choice of major. For example, those who begin at Berkeley at the bottom end of the distribution may be more likely to begin in the nonsciences in the first place.

4. A specification where we allow for a campus-specific adjustment to the slopes and intercepts for minority students to see whether the production technology is different in some manner for this group. This would be the case, for example, if campuses differed in how they supported minority students.

Note that in each of the cases the estimates of academic preparation indices, ${\widehat{AI}}_{ij}$, change as well and we use these new estimates in our reassignments.

Results are presented in Table 10. With the exception of the case where no Dale and Krueger controls are used, the results are quite similar across the different specifications. But, even absent the Dale and Krueger controls, the overall probability of graduating in the sciences conditional on an initial science major is significantly higher for minority students with the removal of racial preferences: a little over one-half of the magnitude in our baseline specification. While all the other specifications show significant graduation gains in the sciences across all quartiles, absent the Dale and Krueger controls the effects are only significant for the bottom two quartiles. This specification also produces significant negative effects on overall graduation rates for initial nonscience majors. Overall, the evidence is robust that reallocating minority students to less selective colleges would increase science graduation rates.⁴⁴

Table 10—

Counterfactual Change in Graduation Probabilities of Minorities with Science or Nonscience Major Based on Nonminority Assignment Rules to the UC Campuses (Percentage Points)

Prep. score (S) quartile	Initial major	Final major	Base model	No Dale-Krueger controls	Dale-Krueger × parent college educated	Altern. major defn.	Campus intercepts & slopes × race
Overall	Science	Science	1.75**	0.90**	1.67**	1.89**	1.82**
	Science	Any	0.77**	−0.47	0.77**	0.61*	1.04*
	Nonscience	Any	0.35	−0.58*	0.39	0.40	0.56
QI	Science	Science	1.82**	1.29**	1.79**	1.95**	1.92**
	Science	Any	1.53**	0.61**	1.55**	1.43**	2.07**
	Nonscience	Any	1.09**	0.33**	1.14**	1.20**	1.56**
QII	Science	Science	1.98**	1.08**	1.89**	2.26**	2.08**
	Science	Any	0.83**	−0.62*	0.83**	0.68*	1.16*
	Nonscience	Any	0.07	−1.04**	0.10	0.09	0.22
QIII	Science	Science	1.68**	0.54	1.55**	1.79**	1.73**
	Science	Any	0.15	−1.36**	0.14	−0.02	0.18
	Nonscience	Any	−0.63*	−1.76**	−0.63*	−0.66**	−0.80
QIV	Science	Science	1.06**	0.02	0.94**	1.02**	1.02
	Science	Any	−0.25	−1.32**	−0.26	−0.33	−0.46
	Nonscience	Any	−0.78**	−1.60**	−0.78**	−0.86**	−1.11**

^***Significant at the 1 percent level.

^**Significant at the 5 percent level.

^*Significant at the 10 percent level.

IV. Why Don’t Less Prepared Minorities Go to UC Riverside and Graduate in the Sciences?

The size of the potential gains in graduation rates in the sciences of reallocating less prepared minority students from higher to lower ranked campuses raises an obvious question: why were these gains not realized? A definitive answer to this question is beyond the scope of our data and analysis. But, in this section, we explore some potential reasons why less prepared students who are interested in the sciences choose to attend colleges where success in the sciences is unlikely.

We begin with the argument that the lack minorities graduating in the sciences at top ranked versus lower ranked campuses simply reflects the self-interest of these students. For example, perhaps it is the case that the returns to attending a t op ranked school are high regardless of one’s major, with one’s major only mattering for earnings at lower ranked campuses. In this case, there would be a natural shift away from the sciences at top ranked institutions relative to their lesser ranked counterparts. Our data do not allow us to directly address this possibility, since we do not have information on expected or realized wages of the students in our data. But, in an attempt to shed light on the potential importance of this explanation, we examine the relationship between one’s major and the ranking of one’s college and wages using data from the Baccalaureate and Beyond (B&B) study (National Center for Education Statistics 1993–2003).

Individuals in the B&B received their BA/BS degree during the 1992–1993 academic year.⁴⁵ B&B respondents were interviewed in 1994, 1997, and 2003, respectively, were asked for their major field of study as an undergraduate in the 1994 wave, and, in that and subsequent waves, were asked about their employment and earnings. B&B respondents were asked whether they were currently working and, if so, about their current earnings and hours of work. We use this information to construct hourly wage rates for those who worked.⁴⁶ We use the log of hourly wages as the dependent variable in all of our regressions, using person-years of data only for those years in which respondents reported to have worked. We classified B&B respondents as having STEM or non-STEM majors, using the same classification system as that in the UCOP data. Finally, to characterize the quality or ranking of the college/university from which each B&B respondent graduated, we used the college’s average SAT scores of their entering class of 1990, obtained from the US News and World Report’s 1991 Directory of Colleges and Universities.⁴⁷

The results from a series of log wage regressions using the B&B data are presented in Table 11. The odd-numbered columns show unadjusted wage returns for different combinations of college major and rankings of college, while the even-number columns provide the corresponding estimates that adjust for test scores and background characteristics described in the table footnote. In columns 1 and 2 of Table 11, we present estimates of the returns to graduating with a STEM major. Consistent with the previous literature,⁴⁸ we find sizable wage returns to graduating with a STEM major, varying between 19 percent and 21 percent. Columns 3 and 4 contain estimates of the returns to graduating from college by quartiles of the distribution of the average SAT score of colleges attended. Consistent with the previous literature,⁴⁹ students who graduate from more highly ranked colleges have, on average, higher wages. For example, students who graduate from a college in the highest quartile of the average SAT score distribution earned wages that were almost 14 percent higher than students who graduated from a college in the bottom quartile, while graduates from a college in the second and third quartiles earned 3.76 percent and 9.53 percent more, respectively, than those who graduated from a college in the bottom quartile.

Table 11—

Relationship between log Wages and College/Student Characteristics, for Public Universities: Baccalaureate and Beyond Data

Variable	(1)	(2)	(3)	(4)	(5)	(6)
Regression estimates
STEM	0.2130** (0.0130)	0.1860** (0.0120)			0.1620** (0.0220)	0.1530** (0.0202)
College in QII of Ave. SAT Distn.			0.0376** (0.0125)	0.0232** (0.0116)	0.0242* (0.0135)	0.0174 (0.0126)
College in QIII of Ave. SAT Distn.			0.0953** (0.0136)	0.0838** (0.0126)	0.0635** (0.0151)	0.0682** (0.0139)
College in QIV of Ave. SAT Distn.			0.1390** (0.0166)	0.1150** (0.0155)	0.1050** (0.0187)	0.0951** (0.0173)
STEM × College in QII					0.0418 (0.0336)	0.0224 (0.0302)
STEM × College in QIII					0.0804** (0.0347)	0.0524* (0.0309)
STEM × College in QIV					0.0755* (0.0409)	0.0688* (0.0355)
Observations	13,308	10,074	13,362	10,110	13,308	10,074
R2	0.002	0.387	0.007	0.378	0.025	0.391
Background variables, age and year dummies	No	Yes	No	Yes	No	Yes
Tests of differences in log wages for non-STEM by quality with STEM by quality
non-STEM in QIV – STEM in QIV					−0.237**	−0.222**
non-STEM in QIV – STEM in QIII					−0.201**	−0.179**
non-STEM in QIV – STEM in QII					−0.123**	−0.098**
non-STEM in QIV – STEM in QI					−0.057**	−0.058**
non-STEM in QIII – STEM in QIII					−0.242**	−0.206**
non-STEM in QIII – STEM in QII					−0.164**	−0.125**
non-STEM in QIII – STEM in QI					−0.098**	−0.085**
non-STEM in QII – STEM in QII					−0.204**	−0.176**
non-STEM in QII – STEM in QI					−0.138**	−0.136**
non-STEM in QI – STEM in QI					−0.162**	−0.153**

Notes: We include data from the 1994, 1997, and 2003 waves of the B&B data. The sample includes minority and nonminority men and women who received a baccalaureate degree from a public university in 1993. The B&B sample sizes for underrepresented minorities were not sufficient to reliably estimate wage differences separately by minority status. Colleges in four quartiles based on the average SAT scores of the college in 1994. Students with ACT scores were converted to SAT score-equivalents, using 2005 ACT & SAT Concordance Tables developed by the College Board (College Board 2009). Background variables include: an indicator for Asian and underrepresented minority; SAT score; age; family size; an indicator for private high school; whether the mother and whether the father are high school graduates, college graduates, or have Master’s degrees or more; the log of parental income; log of student income (if an independent student); student listed as a dependent; total financial aid received; indicator for receiving need-based aid in 1992; an indicator for private college; and year dummies. Standard errors in parentheses. The test is of the differences in average log wage estimates between the various STEM (non-STEM) by college quality combinations, with the null that the difference equals zero. The average log wage estimates for each STEM (non-STEM) by college quality group are calculated from the regression coefficients above.

^***Significant at the 1 percent level.

^**Significant at the 5 percent level.

^*Significant at the 10 percent level.

In the final two columns of Table 11, we interact the STEM major and college ranking quartile dummies. We use these coefficients to calculate the differences in average wage returns between graduating with a non-STEM degree from a college ranking in a particular quartile and graduating with a STEM degree from a college of the same or lower rank. These results are found in the bottom half of the table. The first thing to note is that all of these difference in means are negative; wage returns from a non-STEM degree obtained from either highly or more lowly ranked colleges/universities are always less than those from a STEM degree from a comparably or lesser rank institution. These differences are often quite sizable, ranging from 8.5 percent to as much as 23.7 percent larger returns for STEM degrees at comparable or lower ranked colleges. And, finally, all of these differences are statistically significant. In short, graduating from college with a STEM degree trumps graduating from a highly ranked college, at least with respect to wages.⁵⁰

The findings above about wages by major and college quality are subject to the usual concerns about selection bias, given the sorting of students across majors and universities by observed and unobserved characteristics that also affect success later in life. But, taken at face value, they do make it more difficult to attribute the lack of persistence of minority students in the sciences at top ranked colleges to financial choices. That said, it is still possible that students, minority or otherwise, realize other, nonpecuniary, benefits from attending top ranked versus lower ranked campuses, regardless of their major. We cannot dismiss this possible explanation for why less prepared students with interests in the sciences chose to enroll at campuses that appear to lessen their likelihood of actually obtaining a science degree. To the extent that the latter is true, admission policies that give weight to race and academic preparation are likely welfare-enhancing for minorities, even if it results in lower shares of minorities graduating with science degrees.

But, the very low science persistence rates, particularly for on-time graduation, also suggest the possibility that students may be poorly informed about how different STEM fields are from other fields in the demands they place on their students. In the introduction, we cited studies that found differences in grading differences and study times between science and nonscience majors. But are students aware of these differences? Results from Stinebrickner and Stinebrickner (2014) suggest that students are poorly informed about within-school differences in grading standards. Using data from Berea college, these authors show that freshmen are dramatically overconfident about how they will perform in science classes, so much so that even those who persisted in the sciences—and therefore received relatively positive signals—revised their beliefs about expected performance in science classes downward as they progressed through these fields.

The Stinebrickner and Stinebrickner (2014) findings provide a potential explanation for students not persisting in the sciences, regardless of their race. And, the experience they describe would seem more likely to hold for less prepared students and students from more disadvantaged backgrounds, including minorities.⁵¹ Indeed, Arcidiacono et al. (2011) show, for students at Duke University, that it is the least prepared students who are the most overly optimistic as students and underestimate the importance of academic preparation in future grades. When students are ill-informed, racial preferences have the potential to be welfare-decreasing for their beneficiaries. Thus, it would seem that better informing students about their prospects for success in different majors before they make their enrollment decisions would be beneficial, reducing the scope for race-preferential admissions policies being welfare-decreasing for some minorities while still allowing these policies to expand the college choice sets of minorities.

V. Conclusion

In this paper, we examine whether campuses that differ in their selectivity produce different graduation rates in STEM fields. Our key finding is that more selective UC campuses have an advantage over the less selective UC campuses in graduating better prepared students in the sciences, while the less selective campuses have an advantage at graduating less prepared students in the sciences. At the same time, and importantly, we find that the most selective UC campuses had an absolute advantage over less selective ones in graduating students in nonscience fields, regardless of their academic preparation. We examine the consequences of these findings for what would happen to graduation rates of students, minority and nonminority, if they were allocated across the UC campuses in a way that exploits the advantages different campuses have in graduating students with differing backgrounds in the sciences and nonsciences.

The resulting counterfactual distributions indicate that, in a period when racial preferences in admissions were in place, and the less academically prepared at the more selective campuses were disproportionately minorities, minority students with declared interests in the sciences were mismatched across campuses which resulted in lower graduation rates in the sciences, especially four-year graduation rates. Given that many fewer less-prepared nonminority students attended the higher ranked campuses during the era of racial preferences in admissions, we find that these reallocations of students across campuses would have much less effect on the overall science graduation rates of nonminority students.

Our findings and the results from our counterfactual reallocation of students across the UC campuses have implications for at least two policy-related issues. The first concerns what incoming students know, or do not know, about their likely success in different majors at schools of differing selectivity. As we discuss above, our findings, and an emerging literature on success in STEM majors, suggest that there are potential gains to less prepared incoming students, be they minority or nonminority, of “information interventions” about what it takes to be successful in the sciences, especially at elite universities.⁵² Providing students with such information may reduce the likelihood that students with interests in the sciences place themselves in environments where success is less likely.

The second concerns what our results imply and do not imply about affirmative action policies in college admissions. What we have shown is that success in STEM fields at highly selective universities requires stronger precollege academic preparation. That is, there are important dynamic complementarities between early investments in math and science coursework and experiences and success in the sciences at highly selective universities.⁵³ One of the hopes of affirmative action admission policies was that they would mitigate the effects of racial differences in precollege preparation. Our evidence indicates that this does not hold in the sciences, at least given the level of racial preferences observed in our data, although it may hold for the nonsciences. Thus, reducing or eliminating racial preferences in admissions at elite universities may improve science graduation rates among minorities by improving the matches of students to colleges where they are more likely to succeed.

But, in order for more minorities to be competitive in the sciences at elite universities, the pool of minority students with stronger academic precollege preparations must increase, an issue we do not address in this paper as the precollege preparation of minority and nonminority students is taken as given in our analyses. Some scholars have argued that race-based affirmative action plans in college admissions provide minorities the incentives to acquire this preparation.⁵⁴ However, there also is evidence that the science curricula and experiences in the primary and secondary schools which most minorities attend must be improved in order to increase the number of high school minority students who are adequately prepared to succeed in STEM majors at the most selective colleges.⁵⁵ The relative importance of the latter two mechanisms is an issue for future research.

Table A-1:

Classification of Majors at UC Campuses

Science (STEM)	Humanities		Social Science
Aerospace Engineering	American Culture	Naval Architect & Marine En	Anthropology
Biochemistry	Architecture	Nursing	Anthropology-Zoology
Biology	Asian Studies	Performance	Business Administration
Bio-psychology & Cognitive	Creative Writing - Lit	Philosophy	Economics
Cellular & Molecular Biol	Dance	Resid College Lower Div.	Environ Policy & Behavior
Chemical Engineering	Education - Secondary	Spanish	History
Chemistry	Elementary Education	Sport Management & Comm	Organizational Studies
Civil Engineering	English	Theatre	Political Science
Computer Science	Film & Video Studies	Undertermined	Resource Ecology & Managemnt
Electrical Engineering	French		Sociology
Engineering: First Year	General Studies		Women’s Studies
General Biology	German
Industrial & Operations Eng	Graphic Design
Materials Science & Engin	History of Art
Mathematics	Individualized Concentrnt
Mechanical Engineering	Industrial Design
Microbiology	Japanese
Movement Science	L S & A Undeclared
Nuc Eng & Radiol Sciences	Linguistics
Pharmacy	Music Education
Statistics	Music Theatre

Table A-2a:

Unadjusted Shares of Minority Students Graduating in 4 Years with Science or Non-Science Majors, by Campus, S Quartile, and Initial Major (%)^†

Prep. Score (S) Quartile	Initial Major	Final Major	Top 4 UC Campuses				Bottom 4 UC Campuses				All Campuses
			Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside
Q1	Science	Science	0.0**	0.0**	2.7	1.7**	3.1	4.9**	5.3**	5.2**	3.3
	Science	Any	10.6	7.0**	16.2	7.9**	11.2	15.5**	20.5**	15.6**	13.0
	Non-Science	Any	23.3**	17.3**	20.8**	16.8**	25.3**	26.0**	38.0**	28.2**	25.0
Q2	Science	Science	1.3**	3.7**	9.2	2.6**	8.3*	11.7**	18.6**	13.3**	6.9
	Science	Any	27.7	12.1**	19.9	14.0**	18.5	22.1	28.8*	32.7**	19.5
	Non-Science	Any	32.5**	28.6**	33.1	24.4**	35.8	35.2*	48.4**	38.0*	32.5
Q3	Science	Science	11.8**	8.3**	17.8	10.3**	15.5	20.0	10.7	29.8**	13.1
	Science	Any	25.1**	16.6**	36.7	19.9**	28.9	40.0**	39.3	42.6**	26.1
	Non-Science	Any	39.2	39.9	46.1	37.1	41.1	40.2	42.5	51.4	40.6
Q4	Science	Science	29.9	20.6**	29.3	29.7	23.1	47.6*	41.7	33.3	28.2
	Science	Any	40.2**	35.7**	39.7*	36.5**	38.5	61.9**	58.3	77.8**	40.4
	Non-Science	Any	53.8	52.0	59.2	57.5	57.1	44.4	78.1**	57.1	55.2

^†The stars on the estimates in this table indicate the significance of a t-test of the equality of the estimated share of a particular higher-ranked (lower-ranked) UC campus with the average share of bottom four (top four) UC campuses, where the bottom four are UC Irvine, UC Santa Barbara, UC Santa Cruz, and UC Riverside and the top four are UC Berkeley, UCLA, UC San Diego, and UC Davis. For example, the share in the cell Q1-science-science-UC Berkeley (UC Irvine) is compared with the corresponding average share at the bottom (top) four institutions.

* and ** indicate significance at 10% and 5% level, respectively.

Table A-2b:

Unadjusted Shares of Non-Minority Students Graduating in 4 Years with Science or Non-Science Majors, by Campus, preparation score, and Initial Major (%)^†

Prep. Score (S) Quartile	Initial Major	Final Major	Top 4 UC Campuses				Bottom 4 UC Campuses				All Campuses
			Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside
Q1	Science	Science	0.0**	0.0**	5.3	4.3**	7.0*	7.8**	10.2**	7.6**	7.2
	Science	Any	13.3	0.0**	19.7	14.2**	18.1	20.6**	30.2**	21.4**	20.3
	Non-Science	Any	29.0*	20.1**	26.3*	23.0**	28.4**	38.8**	42.6**	33.9**	33.5
Q2	Science	Science	12.5	9.1*	18.7**	10.9**	12.0	14.3	14.7	15.3	13.3
	Science	Any	26.0	18.8**	32.9**	24.4**	24.2	31.4**	34.2**	28.9	27.5
	Non-Science	Any	41.5	37.6**	46.8	40.1**	36.0**	46.6**	49.1**	42.2	42.8
Q3	Science	Science	24.9	17.6**	24.8	18.0**	20.2	22.3	18.9	36.7**	21.6
	Science	Any	42.7*	31.5**	39.8	31.5**	30.2**	40.9**	43.9**	48.0**	36.2
	Non-Science	Any	50.4	49.7	53.5**	43.1**	39.4**	53.4**	49.2	46.3	48.7
Q4	Science	Science	44.1**	30.8**	42.6**	33.6	37.5	30.6**	32.6	39.5	38.3
	Science	Any	59.0	46.3**	55.6	47.0**	54.3	52.0	59.8	69.3**	53.9
	Non-Science	Any	61.0	61.9*	59.6	55.8	49.8**	65.2*	55.4*	64.3	60.5

^†The stars on the estimates in this table indicate the significance of a t-test of the equality of the share of a particular higher-ranked (lower-ranked) UC campus with the average shares of bottom four (top four) UC campuses, where the bottom four are UC Irvine, UC Santa Barbara, UC Santa Cruz, and UC Riverside and the top four are UC Berkeley, UCLA, UC San Diego, and UC Davis. For example,the share in the cell Q1-science-science-UC Berkeley (UC Irvine) is compared with the corresponding average share at the bottom (top) four institutions.

* and ** indicate significance at 10% and 5% level, respectively.

Table A-3a:

Unadjusted Shares of Minority Students Graduating in 5 Years with Science or Non-Science Majors, by Campus, S Quartile, and Initial Major (%)^†

Prep Score (S) Quartile	Initial Major	Final Major	Top 4 UC Campuses				Bottom 4 UC Campuses				All Campuses
			Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside
Q1	Science	Science	7.1**	10.9	9.5	10.5	12.1	15.8**	12.6	11.8	12.0
	Science	Any	50.6	39.5**	47.3	37.2**	49.6**	50.7**	43.7	50.9**	46.3
	Non-Science	Any	61.5	56.5	62.4	51.5**	62.3*	58.2	60.9	57.8	58.4
Q2	Science	Science	10.7**	20.8	29.1	17.1**	24.4	27.3*	28.8	23.5	22.0
	Science	Any	64.8	56.5	59.7	49.2**	64.9*	53.9	57.6	63.3	58.2
	Non-Science	Any	67.0	66.9	64.1	59.6**	69.4	65.3	70.3	68.3	66.3
Q3	Science	Science	26.2**	30.6	34.3	34.2	36.1	43.6*	17.9*	38.3	32.1
	Science	Any	64.2	63.1*	70.4	65.8	71.1	80.0**	67.9	57.4	66.4
	Non-Science	Any	73.8	79.2**	77.0*	75.9	71.4	68.8*	65.8*	74.3	75.4
Q4	Science	Science	53.7	50.0	56.9	50.0	46.2	61.9	41.7	44.4	52.0
	Science	Any	77.4	79.4	81.0	64.9*	80.8	81.0	66.7	88.9	76.7
	Non-Science	Any	83.5	84.5	77.6	80.0	85.7	85.2	84.4	85.7	83.2

^†The stars on the estimates in this table indicate the significance of a t-test of the equality of the estimated share of a particular higher-ranked (lower-ranked) UC campus with the average share of bottom four (top four) UC campuses, where the bottom four are UC Irvine, UC Santa Barbara, UC Santa Cruz, and UC Riverside and the top four are UC Berkeley, UCLA, UC San Diego, and UC Davis. For example, the share 7.1% (12.1%) in Q1-science-science-UC Berkeley (UC Irvine) is compared with the corresponding average share at the bottom (top) four institutions.

* and ** indicate significance at 10% and 5% level, respectively.

Table A-3b:

Unadjusted Shares of Non-Minority Students Graduating in 5 Years with Science or Non-Science Majors, by Campus, preparation score, and Initial Major (%)^†

Prep. Score (S) Quartile	Initial Major	Final Major	Top 4 UC Campuses				Bottom 4 UC Campuses				All Campuses
			Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside
Q1	Science	Science	20.0	16.0	18.4	22.4	18.7	22.5	21.1	19.8	20.5
	Science	Any	46.7	52.0	46.1	54.8	50.9	56.1	57.9	50.5	53.1
	Non-Science	Any	60.3	57.3*	68.8	66.0	64.8	67.1*	64.1	59.5*	64.0
Q2	Science	Science	24.0	31.5	39.2**	33.3**	30.0**	28.7**	27.5**	29.1**	30.9
	Science	Any	70.8*	64.8	70.7**	70.8**	64.0**	64.3**	60.0**	56.2**	65.2
	Non-Science	Any	82.0**	76.8**	79.0**	77.9**	70.9**	74.2**	70.8**	64.6**	73.8
Q3	Science	Science	43.0	46.2**	46.2**	43.5**	39.5**	37.7**	30.0**	52.3**	43.3
	Science	Any	79.9**	77.2**	75.3**	73.5**	67.7**	72.1*	66.4**	69.7**	73.6
	Non-Science	Any	81.7**	84.6**	82.5**	79.7**	72.1**	78.7**	68.9**	71.8**	79.1
Q4	Science	Science	61.3**	53.5**	62.7**	58.5**	52.4**	48.0**	42.4**	47.1**	57.7
	Science	Any	87.6**	83.9**	84.2**	82.6	81.6*	77.3**	79.5	82.4	84.6
	Non-Science	Any	88.8**	89.0**	86.5**	85.3**	85.1	84.8*	74.3**	80.4**	87.3

^†The stars on the estimates in this table indicate the significance of a t-test of the equality of the share of a particular higher-ranked (lower-ranked) UC campus with the average shares of bottom four (top four) UC campuses, where the bottom four are UC Irvine, UC Santa Barbara, UC Santa Cruz, and UC Riverside and the top four are UC Berkeley, UCLA, UC San Diego, and UC Davis. For example,the share in the cell Q1-science-science-UC Berkeley (UC Irvine) is compared with the corresponding average share at the bottom (top) four institutions.

* and ** indicate significance at 10% and 5% level, respectively.

Table A-4:

Logit Coefficients for Admissions by UC campus^†

	Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside
Minority	3.547** (0.040)	3.334** (0.039)	2.503** (0.048)	3.065** (0.059)	1.337** (0.046)	1.967** (0.049)	1.283** (0.060)	0.915** (0.054)
Minority × Science	−1.391** (0.060)	−0.551** (0.057)	−0.172** (0.071)	0.425** (0.098)	−0.088 (0.075)	−0.318** (0.093)	0.098 (0.112)	−0.290** (0.104)
Preparation Score	2.340** (0.019)	3.029** (0.022)	3.637** (0.028)	3.078** (0.029)	2.685** (0.026)	3.596** (0.034)	2.383** (0.033)	2.173** (0.032)
Minority Non-science Advantage in Prep Score Units	1.516	1.101	0.688	0.996	0.498	0.547	0.538	0.421
Minority Science Advantage in Prep Score Units	0.921	0.919	0.641	1.134	0.465	0.458	0.579	0.288

^†Separate logits were estimated for each campus where the outcome was whether or not the student was admitted and the sample was the set of students who applied to that particular campus. Additional controls included were (i) initial science major, (ii) dummy variables for each parental income category, and (iii) dummy variables for each parental education category. Preparation score is in standard deviation units. Minority non-science advantage is calculated by dividing the coefficient on minority by the coefficient on the preparation score. Minority science advantage is calculated by summing the coefficient on minority and minority times initial science major and dividing by the coefficient on preparation score. Standard errors in parentheses.

* and ** indicate significance at 10% and 5% level, respectively.

Table A-5:

Attendance decisions of minority students admitted to different pairs of UC campuses for pre-Prop 209 period^†

	Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside
Non-Minority
Berkeley	-	72%	84%	88%	89%	89%	90%	84%
UCLA	6118	-	78%	81%	88%	89%	90%	83%
San Diego	4335	5886	-	65%	75%	75%	78%	80%
Davis	3551	2843	4303	-	66%	64%	73%	79%
Irvine	1770	3896	3945	2619	-	62%	72%	81%
Santa Barbara	1483	2380	3489	4103	3698	-	62%	69%
Santa Cruz	1128	727	1472	2614	1083	3740	-	50%
Riverside	639	1364	1627	1123	3502	1571	727	-
Minority
Berkeley	-	53%	77%	82%	82%	86%	88%	83%
UCLA	1739	-	76%	80%	81%	88%	90%	83%
San Diego	821	1170	-	53%	65%	63%	71%	67%
Davis	941	706	459	-	54%	55%	65%	63%
Irvine	412	1151	426	355	-	50%	58%	64%
Santa Barbara	723	1051	618	644	563	-	65%	62%
Santa Cruz	587	384	285	466	210	747	-	45%
Riverside	231	578	234	235	543	454	239	-

^†For Row A, Column B, value of cell is: Above diagonal: If admitted to Campus A and B, percentage of students attending campus A, conditional on attending campus A or B. Below diagonal: Number in race-period group admitted to Campus A and B and attended Campus A or B. (A student admitted to more than two campuses will appear in this count multiple times)

Table A-6a:

Nested Logit Coefficients: Dale-Krueger Controls 5-Year Graduation Criteria

	Coef.	Std. Err.	Coef. × URM	Std. Err.
Science Index
Admitted × Berkeley	0.649**	0.175	0.011	0.247
Admitted × UCLA	0.703**	0.165	−0.147	0.240
Admitted × San Diego	0.563**	0.152	0.049	0.285
Admitted × Davis	0.350	0.228	0.566	0.810
Admitted × Irvine	0.471**	0.231	1.706**	0.711
Admitted × Santa Barbara	0.089	0.265	1.429*	0.800
Admitted × Santa Cruz	0.891	0.854	2.822	2.140
Admitted × Riverside	1.471*	0.870	0.866	2.011
Applied × Berkeley	0.052	0.083	−0.171	0.213
Applied × UCLA	−0.111	0.090	−0.130	0.220
Applied × San Diego	0.198*	0.111	−0.252	0.265
Applied × Davis	0.374*	0.208	−1.232	0.805
Applied × Irvine	−0.498**	0.232	−1.095	0.691
Applied × Santa Barbara	0.102	0.275	−1.440*	0.799
Applied × Santa Cruz	−1.026	0.854	−2.308	2.128
Applied × Riverside	−1.416	0.869	−0.402	2.001
Admitted Top × Rej. Mid.	−0.464*	0.277	0.458	0.732
Admitted Top × Rej. Low	−0.124	0.133	−0.592**	0.285
Applied Top × Rej. Mid.	−0.293	0.239	1.251	0.781
Applied Top × Rej. Low	0.582	0.607	1.571	1.578
Applied Mid × Rej. Mid	0.294	0.937	0.057	1.736
Non-Science Index
Admitted × Berkeley	0.480**	0.164	0.052	0.212
Admitted × UCLA	0.549**	0.161	−0.129	0.202
Admitted × San Diego	0.493**	0.144	0.241	0.235
Admitted × Davis	0.383*	0.201	−0.426	0.547
Admitted × Irvine	0.303	0.207	0.832*	0.488
Admitted × Santa Barbara	−0.200	0.220	0.769	0.523
Admitted × Santa Cruz	0.878	0.741	1.843	1.415
Admitted × Riverside	1.138	0.762	1.446	1.358
Applied × Berkeley	−0.060	0.077	−0.155	0.181
Applied × UCLA	0.089	0.085	−0.213	0.185
Applied × San Diego	0.271**	0.101	−0.447**	0.214
Applied × Davis	0.185	0.180	−0.282	0.538
Applied × Irvine	−0.433**	0.208	−0.219	0.462
Applied × Santa Barbara	0.630**	0.233	−0.878*	0.523
Applied × Santa Cruz	−0.926	0.742	−1.231	1.394
Applied × Riverside	−1.169	0.762	−0.816	1.343
Admitted Top × Rej. Mid.	−0.198	0.250	0.292	0.538
Admitted Top × Rej. Low	−0.139	0.125	−0.501**	0.245
Applied Top × Rej. Mid.	−0.439**	0.210	0.634	0.538
Applied Top × Rej. Low	0.565	0.525	1.255	1.072
Applied Mid × Rej. Mid	−0.101	0.813	0.068	1.284

* and ** indicate significance at 10% and 5% level, respectively.

Table A-6b:

Nested Logit Coefficients: Remaining Academic Index Coeff. (AI_ij) and Intercept for 5-Year Graduation Rates

	Science	Non-Science
Academic Index Coefficients
ln(Par. Income)	0.395** (0.087)	0.463** (0.084)
ln(Par. Income Missing)	4.004** (0.903)	4.766** (0.869)
ln(Par. Income Capped)	−0.056 (0.095)	−0.074 (0.089)
Par. Educ: Some College	−0.164* (0.099)	−0.038 (0.091)
Par. Educ: 4 Year Grad	0.223** (0.110)	0.369** (0.104)
Par. Educ: Post Grad	0.637** (0.149)	0.684** (0.142)
Overall Intercept of the Campus Specific Intercepts
Intercept	−13.983** (1.469)	−5.143** (1.159)

* and ** indicate significance at 10% and 5% level, respectively.

Table A-6c:

Nested Logit: Switching Cost Coefficients 5-year Graduation Criteria

Coefficients Switching Cost:
STEM Intercept	1.567** (0.431)
Non STEM Intercept	1.740** (0.338)
STEM × AIim	−0.061** (0.026)
Non STEM × AIih	0.001 (0.030)
ln(Par. Income)	0.067** (0.022)
ln(Par. Income Missing)	0.766** (0.231)
ln(Par. Income Capped)	0.042 (0.036)
Par. Educ: Some College	0.055 (0.043)
Par. Educ: 4 Year Grad	0.072* (0.040)
Par. Educ: Post Grad	0.024 (0.040)
URM	−0.055 (0.046)
Asian	−0.138** (0.029)
UCLA	−0.385** (0.062)
San Diego	0.014 (0.041)
Davis	−0.183** (0.042)
Irvine	−0.313** (0.044)
Santa Barbara	−0.210** (0.051)
Santa Cruz	0.060 (0.055)
Riverside	−0.294** (0.065)

* and ** indicate significance at 10% and 5% level, respectively.

Table A-7:

Nested Logit Coefficients for Choice of Final Major based on 4-year Graduation Criteria

	Science	Non Science			Science	Non Science
Panel A: Net Returns Function:
Campus-Specific Intercept Coefficients (ϕ1jk):				Campus-Specific Slope Coefficients (ϕ2jk):
UCLA	−0.362 (0.935)	−1.972** (0.381)		UCLA × AIij	0.005 (0.059)	0.334** (0.081)
San Diego	3.69** (0.821)	−0.214 (0.356)		San Diego × AIij	−0.203** (0.048)	0.011 (0.071)
Davis	2.991** (0.816)	−0.361 (0.323)		Davis×AIij	−0.203** (0.048)	−0.050 (0.065)
Irvine	3.064** (0.856)	0.089 (0.339)		Irvine × Alij	−0.192** (0.051)	−0.078 (0.072)
Santa Barbara	5.366** (0.832)	0.458 (0.327)		Santa Barbara × Alij	−0.326** (0.047)	−0.069 (0.064)
Santa Cruz	8.406** (0.923)	2.109** (0.432)		Santa Cruz × Alij	−0.537** (0.048)	−0.409** (0.066)
Riverside	5.727** (0.866)	0.904** (0.367)		Riverside × AIij	−0.325** (0.048)	−0.158** (0.077)
Panel B: Academic Preparation Function (Alj):
HS GPA	2.114** (0.154)	1.020** (0.111)
SAT Math	9.469** (0.559)	−1.01** (0.231)
SAT Verbal	0.009** (0.340)	2.417** (0.271)
URM	−1.136** (0.218)	−0.851** (0.128)
Asian	0.048 (0.053)	−0.275** (0.041)
Nesting parameter
ρ			0.407** (0.083)
Log-Likelihood			−54,670

All campus dummies are measured relative to UC Berkeley (the omitted category). The coefficients on ϕ_1jk and ϕ_2jk for UC Berkeley are normalized to zero and one, respectively.

* and ** indicate significance at 10% and 5% level, respectively.

Table A-8a:

Nested Logit Coefficients: Dale-Krueger Controls 4-year Graduation Criteria

	Coef.	Std. Err.	Coef. × URM	Std. Err.
Science Index
Admitted × Berkeley	0.440**	0.088	0.305	0.258
Admitted × UCLA	0.357**	0.082	0.438	0.276
Admitted × San Diego	0.187*	0.095	−0.101	0.329
Admitted × Davis	0.139	0.204	−0.419	0.923
Admitted × Irvine	0.651**	0.221	1.126	0.849
Admitted × Santa Barbara	0.144	0.278	0.909	1.031
Admitted × Santa Cruz	0.431	0.887	19.267	53.033
Admitted × Riverside	0.382	0.878	7.633	35.189
Applied × Berkeley	−0.096	0.059	−0.317	0.242
Applied × UCLA	−0.205**	0.067	−0.543**	0.266
Applied × San Diego	−0.159*	0.087	0.264	0.315
Applied × Davis	0.059	0.200	0.386	0.919
Applied × Irvine	−0.724**	0.221	−0.699	0.844
Applied × Santa Barbara	−0.267	0.277	−0.746	1.027
Applied × Santa Cruz	−0.729	0.888	−19.059	53.033
Applied × Riverside	−0.443	0.878	−7.267	35.188
Admitted Top x Rej. Mid.	−0.503**	0.236	1.305	0.967
Admitted Top × Rej. Low	0.076	0.094	−0.364	0.276
Applied Top × Rej. Mid.	0.155	0.225	−0.025	0.988
Applied Top × Rej. Low	0.249	0.655	−1.025	1.788
Applied Mid × Rej. Mid	−0.222	0.936	9.900	35.182
Non-Science Index
Admitted × Berkeley	0.093	0.061	0.117	0.121
Admitted × UCLA	0.181**	0.063	0.160	0.117
Admitted × San Diego	0.100*	0.057	0.076	0.138
Admitted × Davis	0.039	0.103	0.327	0.373
Admitted × Irvine	0.091	0.112	1.002**	0.336
Admitted × Santa Barbara	−0.124	0.124	1.022**	0.375
Admitted × Santa Cruz	0.882*	0.470	−0.095	0.930
Admitted × Riverside	0.365	0.467	−0.375	0.912
Applied × Berkeley	−0.095**	0.038	−0.064	0.106
Applied × UCLA	0.051	0.043	−0.240**	0.112
Applied × San Diego	−0.014	0.048	0.011	0.126
Applied × Davis	0.009	0.098	−0.351	0.369
Applied × Irvine	−0.262**	0.113	−0.738**	0.327
Applied × Santa Barbara	0.321**	0.125	−0.998**	0.372
Applied × Santa Cruz	−1.033**	0.473	0.436	0.927
Applied × Riverside	−0.515	0.467	0.699	0.911
Admitted Top × Rej. Mid.	−0.075	0.140	0.642*	0.376
Admitted Top × Rej. Low	0.005	0.060	−0.242*	0.132
Applied Top × Rej. Mid.	−0.208*	0.114	0.303	0.368
Applied Top × Rej. Low	0.350	0.324	0.166	0.736
Applied Mid × Rej. Mid	−0.175	0.504	−0.680	0.836

* and ** indicate significance at 10% and 5% level, respectively.

Table A-8b:

Nested Logit Coefficients: Remaining Academic Index Coeff. (A_lj) and Intercept for 4-Year Graduation Rates

	Science	Non-Science
Academic Index Coefficients
ln(Par. Income )	0.202** (0.044)	0.296** (0.035)
ln(Par. Income Missing)	2.314** (0.474)	3.287** (0.384)
ln(Par. Income Capped)	0.028 (0.061)	−0.006 (0.042)
Par. Educ: Some College	−0.111 (0.077)	0.035 (0.051)
Par. Educ: 4 Year Grad	0.026 (0.072)	0.132** (0.049)
Par. Educ: Post Grad	0.225** (0.074)	0.239** (0.053)
Overall Intercept of the Campus Specific Intercepts
Intercept	−16.005** (0.998)	−4.743** (0.570)

* and ** indicate significance at 10% and 5% level, respectively.

Table A-8c:

Nested Logit: Switching Cost Coefficients 4-year Graduation Criteria

Coefficients Switching Cost:
STEM Intercept	1.910** (0.422)
Non STEM Intercept	1.912** (0.258)
STEM × AIij	−0.056** (0.028)
Non STEM × AIij	−0.050 (0.045)
ln(Par. Income)	0.090** (0.032)
ln(Par. Income Missing)	0.993** (0.339)
ln(Par. Income Capped)	0.036 (0.049)
Par. Educ: Some College	−0.040 (0.063)
Par. Educ: 4 Year Grad	−0.039 (0.058)
Par. Educ: Post Grad	−0.070 (0.057)
URM	0.022 (0.069)
Asian	−0.090** (0.040)
UCLA	−0.636** (0.050)
San Diego	0.034 (0.057)
Davis	−0.211** (0.056)
Irvine	−0.295** (0.061)
Santa Barbara	−0.110 (0.071)
Santa Cruz	0.095 (0.074)
Riverside	−0.315** (0.084)

* and ** indicate significance at 10% and 5% level, respectively.

Table A-9:

Estimated Percentages of Minority Students who would have Higher Graduation Probabilities if they had been at a Different (Counterfactual) UC Campus (%)

Counterfactual Campus:
Campus Enrolled at:	UC Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside
Graduating with Science Major, Conditional on Initial Major = Science:
Berkeley	—	100	100	100	91	100	72	94
UCLA	0	—	100	100	74	99	70	90
San Diego	0	0	—	0	0	42	29	31
Davis	0	0	100	—	41	96	72	85
Irvine	1	14	100	63	—	100	83	100
Santa Barbara	0	0	23	2	0	—	67	44
Santa Cruz	2	6	20	8	6	25	—	21
Riverside	0	1	30	5	0	51	69	—
Graduating with Any Major, Conditional on Initial Major = Science:
Berkeley	—	0	39	34	29	44	33	28
UCLA	100	—	94	94	70	77	57	55
San Diego	77	8	—	44	30	50	36	26
Davis	44	0	65	—	60	78	66	59
Irvine	52	15	48	48	—	99	63	46
Santa Barbara	25	6	15	16	0	—	67	40
Santa Cruz	18	10	16	16	14	24	—	6
Riverside	41	17	37	38	42	62	93	—
Graduating with Any Major, Conditional on Initial Major = Non-Science:
Berkeley	—	0	0	0	11	37	23	14
UCLA	100	—	49	48	57	74	48	38
San Diego	100	59	—	9	67	91	40	24
Davis	100	21	97	—	90	98	77	67
Irvine	89	25	13	12	—	100	52	21
Santa Barbara	37	8	2	2	0	—	7	1
Santa Cruz	58	20	20	19	35	93	—	0
Riverside	72	29	33	33	64	100	100	—

Results based on criteria of graduating in 5 years or less. Calculated using the model estimates to get predicted graduation probabilities at both the actual and counterfactual campuses. Entries show the share students who would have higher graduation probabilities at the counterfactual campus.

Table A-10:

Estimated Proportions of Non-Minority Students who would have Higher Graduation Probabilities if they had been at a Different (Counterfactual) UC Campus (%)

Counterfactual Campus
Campus Enrolled at:	UC Berkeley	UCLA	San Diego	Davis	Irvine	Santa Barbara	Santa Cruz	Riverside
Graduating with Science Major, Conditional on Initial Major = Science:
Berkeley	—	58	100	100	28	67	7	35
UCLA	28	—	100	100	37	81	10	51
San Diego	0	0	—	0	0	5	2	4
Davis	0	0	100	—	3	66	18	43
Irvine	12	43	100	92	—	100	49	91
Santa Barbara	0	1	58	9	0	—	22	20
Santa Cruz	11	21	58	34	25	64	—	57
Riverside	12	21	72	35	9	89	39	—
Graduating with Any Major, Conditional on Initial Major = Science:
Berkeley	—	0	4	2	1	2	1	1
UCLA	100	—	36	33	7	10	4	4
San Diego	93	54	—	45	2	6	3	2
Davis	89	36	66	—	8	20	10	7
Irvine	75	40	82	78	—	95	31	22
Santa Barbara	64	41	55	56	14	—	23	4
Santa Cruz	54	37	50	50	47	62	—	26
Riverside	59	43	60	58	60	83	61	—
Graduating with Any Major, Conditional on Initial Major = Non-Science:
Berkeley	—	0	0	0	0	2	1	0
UCLA	100	—	7	7	8	13	5	3
San Diego	100	92	—	61	10	37	4	2
Davis	100	82	65	—	33	65	13	7
Irvine	97	46	40	38	—	100	26	6
Santa Barbara	85	44	17	17	0	—	1	0
Santa Cruz	94	60	59	59	80	100	—	2
Riverside	84	43	50	49	78	100	97	—

Results based on criteria of graduating in 5 years or less. Calculated using the model estimates to get predicted graduation probabilities at both the actual and counterfactual campuses. Entries show the share students who would have higher graduation probabilities at the counterfactual campus.

Table A-11:

Counterfactual Change in Graduation Probabilities of Non-Minority Students with Science or Non-Science Majors Using Minority Assignment Rules to the UC Campuses (Percentage Points)

Prep. Score (S) Quartile	Initial Major	Final Major	Base Model	No Dale- Krueger Controls	Dale- Krueger ×Parent College Educated	Altern. Major Defn.	Campus Intercepts & Slopes × Race
Overall	Science	Science	−1.10**	−0.47*	−1.03**	−1.29**	−0.95**
	Science	Any	−0.08	1.04**	−0.07	0.04	−0.15
	Non-Science	Any	0.35	1.45**	0.36	0.38	0.19
Q1	Science	Science	−1.89**	−1.20**	−1.80**	−2.08**	−1.95**
	Science	Any	−1.20**	0.58	−1.19**	−0.98**	−1.21**
	Non-Science	Any	−0.46	1.08**	−0.49	−0.54	−0.57
Q2	Science	Science	−1.70**	−0.81**	−1.58**	−1.90**	−1.72**
	Science	Any	−0.30	1.40**	−0.28	−0.12	−0.44
	Non-Science	Any	0.39	1.79**	0.39	0.39	0.18
Q3	Science	Science	−1.23**	−0.38	−1.14**	−1.38**	−1.09**
	Science	Any	0.21	1.37**	0.22	0.32	0.11
	Non-Science	Any	0.72**	1.73**	0.74**	0.77**	0.53
Q4	Science	Science	−0.46	−0.18	−0.43	−0.69**	−0.13
	Science	Any	0.08	0.65**	0.08	0.11	0.06
	Non-Science	Any	0.32**	0.93**	0.34**	0.40**	0.20

* and ** denote that the change is statistically significant at 10% or 5% level, respectively.