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American Educational Research
http://aer.sagepub.com/content/50/2/251The online version of this article can be found at:
DOI: 10.3102/0002831212470483
2013 50: 251 originally published online 14 January 2013Am Educ Res JLiliana M. GarcesFields of Study
Understanding the Impact of Affirmative Action Bans in Different Graduate
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Understanding the Impact ofAffirmative Action Bans in Different
Graduate Fields of Study
Liliana M. GarcesGeorge Washington University
This study examines the effects of affirmative action bans in four states(California, Florida, Texas, and Washington) on the enrollment of under-represented students of color within six different graduate fields of study:the natural sciences, engineering, social sciences, business, education, andhumanities. Findings show that affirmative action bans have led to thegreatest reductions in science-related fields of engineering, the natural sci-ences, and the social sciences. These declines pose serious long-term conse-quences for the United States since these fields provide specialized trainingcritical to the nation’s ability to compete effectively in a global market andfor ensuring continued scientific and technological advancement.
KEYWORDS: access, affirmative action, diversity, STEM, graduate studies
The consideration of race as an affirmative factor in higher education ad-missions decisions remains the target of legal challenges and public
debate. A new challenge to the constitutionality of the practice is now beingconsidered by the U.S. Supreme Court in Fisher v. University of Texas, Austin(2011).1 In addition, eight states currently ban the consideration of race inadmissions at public institutions of higher education. Of these, six(Arizona, California, Michigan, Nebraska, Oklahoma, and Washington) im-plemented the bans through voter-approved initiatives or referenda;2 twoothers (Florida and New Hampshire) banned the practice, respectively, byexecutive decision or legislative vote. These bans have been enacted despite
LILIANA M. GARCES, EdD, JD, is an assistant professor in the Graduate School ofEducation and Human Development at the George Washington University, 2134 GStreet NW, Washington, DC 20052; e-mail: [email protected]. Her research, atthe intersection of law and social science fields, works to understand and inform pol-icies that can assist educators and policymakers address racial and ethnic inequities inK–12 and postsecondary education. Her areas of specializations are access and equityin higher education, diversity in higher education, and social science research andthe law.
American Educational Research Journal
April 2013, Vol. 50, No. 2, pp. 251–284
DOI: 10.3102/0002831212470483
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the 2003 U.S. Supreme Court decision in Grutter v. Bollinger—which allowsinstitutions to practice affirmative action under strict limits—because statescan amend their respective constitutions (through state ballot measures, ini-tiatives, or legislation) to prohibit practices that may be permitted under thefederal constitution or federal law.3
In Grutter, the Court emphasized that institutions could consider race ina limited way to obtain the educational benefits of a racially and ethnicallydiverse student body, ‘‘in a society, like our own, in which race unfortu-nately still maters’’ (Grutter, 539 U.S. at 333). The educational benefits ofracial and ethnic diversity are especially important in graduate training,where a diversity of perspectives can foster the innovation necessary totackle complex research problems (Page, 2007), advance scientific inquiry(Espinosa, 2011), and maintain America’s ability to compete effectively ina global market (Committee on Science, Engineering, and Public Policy,2011; Council of Graduate Schools [CGS], 2010). In its decision, the Courtalso acknowledged the broader implications of diversity for our democracy,emphasizing the role of universities and professional schools in providing‘‘the training ground for a large number of our Nation’s leaders’’ (Grutter,539 U.S. at 332). The Court stressed the need for these institutions to beinclusive of individuals of all races and ethnicities so that members of oursociety can have ‘‘confidence in the openness and integrity of the educa-tional institutions that provide this training’’ (Grutter, 539 U.S. at 332). Inthis way, the Court recognized the important role graduate training playsin sustaining the health of our democracy by having a student body thatmore closely reflects the racial/ethnic diversity of the United States (e.g.,Bowen, Kurzweil, Tobin, & Pichler, 2005).
After bans on affirmative action were implemented in California, Florida,Texas, and Washington, selective undergraduate universities experienceda decline in the enrollment of underrepresented students of color (seee.g., Backes, 2012; Hinrichs, 2012; Tienda, Leicht, Sullivan, Maltese, &Lloyd, 2003). Studies also documented declines in racial and ethnic studentbody diversity in the professional fields of law and medicine (Karabel, 1998;Kidder, 2003, in press). A more recent study, upon which this study builds,documented a decline in the representation of students of color across allgraduate studies, outside the fields of law and medicine (Garces, 2012).These declines in graduate students of color are troubling given the alreadylow representation of students of color, relative to their representation in theUnited States, across graduate fields of study. Sixteen percent of the U.S.population is Latino and 12% is African American, but in 2008, each groupmade up only about 4% of all the students enrolled in the natural sciencesand only about 3% of all students enrolled in the field of engineering(National Science Foundation, National Center for Engineering Statistics,2011). Of all the graduate students enrolled in the social sciences, AfricanAmerican and Latino students comprised only about 1% and 7%, respectively
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(National Science Foundation, National Center for Engineering Statistics,2011). Disparities also persist in non–science-related fields, such as thehumanities and education. Of all the doctoral degrees that were awardedin the humanities in 2009, only about 3% and 5%, respectively, were grantedto African Americans and Latinos (National Science Foundation, Division ofScience Resources Statistics, 2010). And Latinos made up only about 6% of alldoctoral recipients in education in 2009 (National Science Foundation,Division of Science Resources Statistics, 2010).4
Our understanding of the impact of affirmative action bans at the grad-uate schools level, however, remains limited. Unlike colleges or universities,graduate admissions practices and requirements can differ substantially byfield of study (Nettles & Millett, 2006). Thus, the effect of affirmative actionbans on the enrollment of students of color may not be the same across allgraduate programs. Specialization in a field of study also defines the doctoralexperience of students (Nettles & Millett, 2006). For these reasons, the con-sequences of any declines in student of color enrollment may be unique byfield of study. In light of national concerns over the underrepresentation ofstudents of color in the fields of science and engineering, and their under-representation in non–science-related fields such as humanities and educa-tion, we need a more nuanced understanding of the impact of thesepolicies within specific graduate fields of study. This more nuanced under-standing should also help inform the ongoing legal and public debatearound race-based affirmative action policies.
To this end, this study examines the impact of affirmative action bans onthe enrollment of students of color in six fields of graduate study: natural sci-ences, engineering, social sciences, business, education, and humanities.5
These fields represent the majority of all graduate students who wereenrolled in 2009 (about 92%) and are a cross-section of graduate academicdisciplines that allow for comparisons of the impact of the bans among sci-ence and non–science-related fields (CGS, 2009). Table 1 outlines the vari-ous majors, within field of study, included in the study. As noted in thetable, the only field in the survey that is not included in the study is the fielddesignated as ‘‘other.’’ Specifically, I examine the bans on affirmative actionin Texas (during Hopwood v. State of Texas, 1996), California (withProposition 209), Washington (with Initiative 200), and Florida (with OneFlorida Initiative) and utilize a quasi-experimental analytic strategy—the dif-ference-in-differences approach—to estimate the causal impact of affirma-tive action bans in these states on the enrollment rates of students of colorwithin each discipline.6
In this analysis, the outcome is the proportion (as opposed to the num-ber) of first-year graduate students who are underrepresented students ofcolor because the overall enrollment of graduate students changes overtime (e.g., Hinrichs, 2012; Howell, 2010). The definition of underrepresentedstudents of color includes students whose self-reported race or ethnicity is
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African American, Latino, and/or Native Americans/Alaska Natives and whoare not considered international students because the determination of ‘‘raceor ethnicity’’ as a factor in admissions presumably does not apply to interna-tional students. Moreover, the admissions and enrollment considerations forinternational students are different than those for domestic students. I do notinclude Asian American/Pacific Islanders students in my definition of‘‘underrepresented’’ students of color because the category is too broadlydefined to allow me to capture the educational disparities that exist withinthe various subgroups included in the category (CARE, 2010; Teranishi,2010). With enrollment as my outcome, I capture the overall impact of the
Table 1
Majors That Make Up Each Field of Study/Discipline Considered in the Study
Natural Sciences Business
Agriculture Accounting
Biological sciences Banking and finance
Chemistry Business administration and management
Computer and information sciences Public administration
Earth, atmospheric, and marine sciences Business, other
Health and Medical Sciences
Mathematical sciences Education
Physics and astronomy Education administration
Natural sciences, other Curriculum and instruction
Early childhood education
Engineering Elementary education
Chemical engineering Evaluation and research
Civil engineering Higher education
Electrical and electronics engineering Secondary education
Industrial engineering Special education
Materials engineering Student counseling and personnel services
Mechanical engineering Education, other
Engineering, other
Humanities
Social Sciences Arts—history, theory, and criticism
Anthropology and archaeology Arts—performance and studio
Economics English language and literature
Political sciences Foreign languages and literatures
Psychology History
Sociology Philosophy
Social sciences, other Humanities and arts, other
Source. CGS/GRE Survey of Graduate Enrollment. The only field in the survey that is notincluded in the study is the field designated as ‘‘Other,’’ which includes six different majors(architecture and environmental design, communications, home economics, library andarchival systems, religion and theology, and all other fields).
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affirmative action bans on applications, admissions, and enrollment, whichmay also reflect changes in financial aid support.
In the sections that follow, I first outline the literature to which this studycontributes. Next, I describe my research design and findings, which showthat the bans on affirmative action have led to the greatest reductions inthe proportion of enrolled graduate students who are students of color inscience-related fields of engineering, the natural sciences, and the social sci-ences. These findings suggest that affirmative action bans are underminingnational goals to increase access and persistence for students of color in crit-ical fields like science and engineering; institutions in states with affirmativeaction bans may need to reevaluate their admissions policies and implementinnovative outreach and recruitment efforts if they are to address and reversethe impact of these policies. Though the effect is not as great, I also finda decline in student of color enrollment in the humanities. There appearsto be no impact of affirmative action bans on the proportion of graduate stu-dents of color who are enrolled in the field of business. I conclude by out-lining the policy implications of this work and outlining areas for futureresearch.
Background and Context
Studies on the Effect of Affirmative Action Bans in Graduate Education
Most of the research examining the effect of affirmative action bans inhigher education has focused at the undergraduate level, documenting de-clines at selective colleges and universities (see e.g., Backes, 2012;Hinrichs, 2012; Tienda et al., 2003). The few studies that examine the impactof affirmative action bans in graduate studies have also documented declinesin the enrollment rates of students of color. In a study of the enrollment ratesat five selective law schools in California, Texas, and Washington, for exam-ple, Kidder (2003) documented a drop of about 4 percentage points, ornearly two-thirds, in the small enrollment rates of African Americans (from6.5% to 2.25%) and more than a third for Latinos (from 11.8% to 7.4%) afterthe implementation of affirmative action bans in these states. The study com-pared the enrollment rates 5 years after the bans in California and Texas toenrollment rates 4 years before and enrollment rates 3 years after the ban inWashington to enrollment rates 3 years before (see also Kidder, in press). Ina comparison of Black and Chicano students who were admitted at theUniversity of California medical schools between 1996 and 1997, whenProposition 209 banned affirmative action in California, Karabel (1998)showed that the numbers enrolled dropped by 38% and 29%, respectively.These studies followed prior simulation studies that had predicted declinesin enrollment among students of color when race or ethnicity ceased tobe considered in admissions decisions in graduate studies (Cross & Slater,
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1997; Dugan, Baydar, Grady, & Johnson, 1996; Wightman, 1997). These stud-ies, however, are primarily descriptive and do not support causal inferencebecause they do not account for other trends in enrollment.
A more recent study on the impact of the bans across graduate studieswas able to support causal inference (Garces, 2012). That study found thatoutside professional fields of law or medicine, affirmative action bans inTexas, California, Florida, and Washington have reduced the average pro-portion of graduate students who are students of color by about 12.2%(from 9.9% to 8.7%). This study extends this prior work by focusing onthe impact of bans within specific fields of study, as opposed to across allgraduate fields. Unlike colleges or universities, admissions requirementsand processes at the graduate school level can differ substantially by fieldof study, with some fields emphasizing standardized test scores more thanother factors like past work experience (Nettles & Millet, 2006). Becausethe consequences of banning the consideration of race in admissions maydiffer based on the relative weight that is given to standardized test scoresand other factors in admissions processes by field, the impact of the bansmay not be the same across all graduate programs. Understanding theimpact of affirmative action bans within specific fields of study will thus pro-vide a more nuanced understanding of the impact of these policies at thegraduate school level.
Graduate Admissions in Various Fields of Study and Hypotheses
Although literature documenting specific admissions practices in gradu-ate studies is scant, studies have documented the consideration of race orethnicity for historically underrepresented groups in higher education asa substantial factor in admissions practices across various graduate fieldsof study (Attiyeh & Attiyeh, 1997; Dugan et al., 1996). As is the case in under-graduate admissions, standardized test scores are also a main criteria that fac-ulty rely upon to make decisions about graduate admissions (Attiyeh &Attiyeh, 1997; Posselt, 2011; Sternberg & Williams, 1997; Willingham,1974). This traditional measure of academic achievement can disadvantageAfrican American and Latino students, who, as a group, are generally under-represented at higher score percentiles on standardized tests and overrepre-sented at lower percentiles (Bowen & Bok, 1998; Diaz, 1990; Jencks &Phillips, 1998).7 For these reasons, one would anticipate that prohibitingthe consideration of race as a plus factor in admissions may lead to fewerstudents of color being admitted, with a potentially worse impact in fieldswhere the average standardized test scores of enrolled students is higherthan other fields.
Findings from a 2006 survey of the background and experiences of doc-toral students suggest that science-related fields of engineering, physical sci-ences, and social sciences tend to have student bodies with higher
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standardized test scores than those in the humanities or education. Nettlesand Millett (2006) found that for the 9,036 students who participated inthe study and were representative of the graduate student body in thenation, the overall mean quantitative GRE score was highest in engineering(757), ‘‘followed by those in sciences and mathematics (731), social sciences(656), humanities (614), and education (567)’’ (p. 62). The average GRE ana-lytic scores reflected a similar ordering, with the highest mean in science andmathematics (679), followed by engineering (677), social sciences (646),humanities (645), and education (571). Profile information for the fall 2010entering classes in the fields of engineering and education at theUniversity of California, Berkeley, supports this contrast, with the averagequantitative GRE score in engineering at 773, compared to 624 in education(U.S. News and World Report, 2010).8
The effect of affirmative action bans may also differ depending on whatadditional factors are considered in admissions decisions by faculty or in thedecisions of students to apply for admissions in specific fields. The character-istics of the graduate students in the Nettles and Millet (2006) study show thatin less technically focused fields of education (and similarly humanities andbusiness), past work experience may be an important factor that plays intostudents’ decisions to apply to these fields or in faculty’s admissions deci-sions. For the sample of students in the study, the longest time lapsebetween undergraduate and doctoral degrees was in the field of education(an average of nearly 12 years), followed by engineering, humanities andsocial sciences (an average of 3.5 to 4.5 years), and science and mathematics(an average of 2 years). Moreover, on average, the youngest students (anaverage of 25 years old) were in sciences and mathematics, and the oldeststudents (an average of about 35 years old) were in education. A focus onwork experience may balance the salience that is placed on standardizedtest scores and, consequently, mitigate the negative impact of affirmativeaction bans in these fields. For these reasons, as a result of affirmative actionbans, I anticipate a greater decline in the enrollment of underrepresentedstudents of color in science-related fields of engineering, physical sciences,and social sciences than in the humanities, education, or business.
The Affirmative Action Bans Considered in This Study
In this study, I examine the impact of the affirmative action ban that wasimplemented in Texas in 1997 as a result of the Hopwood court opinion andthat remained in place until 2003, when Grutter overruled the decision. In1997, the Texas Attorney General interpreted the decision to apply to bothpublic and private institutions in the state and to extend to admissions deci-sions, financial aid, scholarships, and recruitment and retention practices. Inthis study, however, I do not consider the impact of affirmative action banson private institutions in Texas because the affirmative action bans in the
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other states considered in this study (California, Washington, and Florida)only applied to public institutions. Including private institutions in Texasmay thus bias the results because the characteristics of private institutionsdiffer from those of the public institutions that make up the rest of thesample.
I also investigate the impact of the affirmative action bans on the enroll-ment of graduate students of color in California (with Proposition 209),Washington (with Initiative 200), and Florida (with the One FloridaInitiative). These bans were implemented, respectively, in 1998, 1999, and2000. Although Proposition 209 in California did not take effect until theentering class of 1998, because of the public discussion and attention tothe issue during the time it was being litigated, it arguably affected graduateapplications and enrollment decisions as early as fall 1997. For this reason, inmy main analysis, I anticipate the impact of the ban in California to havestarted in 1997. Results, however, are robust to the choice of either year.In Table 2, I display the years the policy took effect in each state and themain analytic window I use in the study, 1994 to 2003. This analytic windowcovers 3 years before the first ban in Texas and California took effect and 3years after the last ban in Florida was implemented. The year the ban wentinto effect in each state is based on the first cycle of admissions and enroll-ment decisions for which the ban on the consideration of race would haveapplied for fall semester enrollment.
Following the passage of affirmative action bans, each state adopted alter-native strategies that sought to mitigate potential declines in the enrollment ofstudents of color. These strategies included various versions of percentageplans that granted high school seniors automatic admissions to state universi-ties. These policies, however, applied to undergraduate students, not those ingraduate programs. Based on the timing of these alternative strategies and thetime period in this study, my analysis may capture a lag effect of the percent-age plan in Texas. That is, my analysis may include underrepresented studentsof color who may have been admitted to a college in Texas under the Top TenPercent Plan in 1998, graduated within 4 years, and subsequently enrolled ina graduate field of study by 2003. It is also possible that faculty or administra-tors in various fields of study may have engaged in efforts to mitigate thepotential decline in the enrollment of students of color after the bans. Thesepossibilities would attenuate the estimated impact of the bans.
Research Design and Analytic Framework
Research Design
Conceptual analytic strategy: Difference-in-differences. In my analyses, Iused a difference-in-differences estimation strategy, which employsa ‘‘before’’ and ‘‘after’’ comparison to estimate the effect of the affirmative
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Table
2
Years
Th
at
Aff
irm
ati
ve
Acti
on
Ban
san
dP
erc
en
tag
eP
lan
sW
ere
inE
ffect
inE
ach
Key
Sta
te
Anal
ytic
Win
dow
Year
s
Stat
ePolicy
Type
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Texas
Court
deci
sion
XX
XX
XX
X
Perc
enta
ge
pla
n%
%%
%%
%
Cal
iforn
iaPro
posi
tion
209
XX
XX
XX
X
Perc
enta
ge
pla
n%
%%
Was
hin
gto
nIn
itia
tive
200
XX
XX
X
Flo
rida
Flo
rida
One
Initia
tive
XX
X
Perc
enta
ge
pla
n%
%%
%
Sou
rce.
Hopw
ood,78
F.3d
932
(5th
Cir.);Cal
.Const
.ar
t.I,
§31;W
ash.Rev.Code
§49.6
0.4
00
(2003);
Fla
.G
overn
or\
prim
es
Exec.
Ord
erN
o.99-2
01
(1999).
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action bans (the first difference), adjusting for secular changes in enrollmentthat could have taken place over the same periods irrespective of the bansthrough comparisons to similar institutions in states not affected by thebans (the second difference). This estimation strategy has been used ina number of important research studies to document the impact of policychanges on education outcomes (Dynarski, 2004; Flores, 2010; Kane, 1998;Long, 2004) and is well suited for estimating the impact of the affirmativeaction bans on the enrollment rate of students of color in graduate programs.As a quasi-experimental method, however, this analytic strategy is neverthe-less limited in its ability to support causal claims, and plausible alternativeexplanations for the findings must be considered and ruled out (Shadish,Cook, & Campbell, 2002).9 As I explain in the following, I implementedthe difference-in-differences estimation strategy in a Tobit multilevel regres-sion framework to account for anomalies in the distribution of my outcomeand address the hierarchical nature of the data (observations nested withininstitutions over time, nested within states).
Data Sets
I analyzed data that had been aggregated, before I received them, up tothe level of academic major from the CGS/GRE Survey of GraduateEnrollment and Degrees, a national survey cosponsored by the Council ofGraduate Schools and Graduate Record Examinations Board. The CGS/GRE Survey includes responses from graduate-level institutions that are rep-resentative of all the graduate programs in the United States, outside the pro-fessional fields of medicine or law; participating institutions grantapproximately 90% of the doctorates awarded each year in the UnitedStates and 75% of the nation’s master’s degrees (CGS, 2009). It is also theonly annual survey that collects enrollment information by race and ethnicityacross 51 distinct fields of study in graduate school; thus, it presents an infor-mative data set for addressing this important policy question across a broadrange of fields. Among other variables, these data also describe whether theinstitution was public or private, its total enrollment size, its Carnegie classi-fication (based on the 200 Carnegie classification system), and the statewhere the institution was located. I merged these data with informationon state demographics and labor market conditions from the U.S. CensusBureau and Bureau of Labor Statistics.
Limitations
This study is contextualized by important limitations of the data. First,the terms under which I was granted access to CGS/GRE Survey requirethe anonymity of the institutions. The removal of the names of the institu-tions presented limitations for my analysis because I was unable to include,and control for, additional specific institutional-level characteristics that may
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have influenced enrollment (e.g., school selectivity, average GRE scores,average tuition, and financial aid) and could have increased the precisionof my estimates. The institutional-level (Carnegie classification) and state-level (demographics and socioeconomic characteristics) control variablesincluded in the analysis, however, helped capture some information thatoverlapped with those characteristics, including school selectivity, which isarguably captured in part by Carnegie Classification. Second, the aggregatenature of the available data makes it more difficult to estimate the levels ofthe outcome with the same precision as with student-level information. As Iexplain in the following, I used a type of weight to account for the varyinglevels of precision with which I could estimate the outcome. Finally, student-level data—particularly at the application, admission, and enrollmentstage—would allow for a more fine-grain and throughout disentangling ofthe impact of the bans in each of these stages. Such data across the broadrange of graduate fields of study covered in this study, however, are notavailable.10 The outcome measure of enrollment nevertheless captures apolicy-relevant impact of affirmative action bans because it allows us tounderstand how these policies are affecting the overall representation of stu-dents of color in graduate fields of study.
Sample
From all of the institutions that responded to the CGS/GRE Survey, I lim-ited my sample to public institutions. I also excluded those that were classi-fied as Historically Black Colleges and Universities; although theseinstitutions have important graduate programs, they may not have re-sponded to bans on affirmative action in a manner comparable to other in-stitutions in the sample because they generally enroll high percentages ofstudents of color. From that subset, I excluded institutions whose reportedfirst-time enrollment values in a particular major were missing for studentsof all races across all years of the analytic window (1994–2003) or acrossa pre-ban or post-ban period for a respective state. In these cases, I assumedthat the institution did not offer the major. Because the original survey instru-ment that each institution received listed all possible majors within a field ofstudy, institutions that did not offer the major may have left enrollment fig-ures in these majors blank. When institutions reported an enrollment num-ber of zero for a certain race but not for other races or ethnicities, Iassumed the institution offered the major but did not have students of thatparticular race or ethnicity enrolled in the program. Finally, I excluded insti-tutions whose total enrollment numbers were not disaggregated by major;these institutions only reported enrollment totals across all majors and fieldsof study offered at the institution.11
After imposing these limitations, I was left with 118 graduate institutionsin the sample: 33 graduate institutions in the four target states that provided
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estimates of the first difference (Texas, California, Washington, and Florida)and 85 institutions in the comparison group that provided the required seconddifference. For this latter ‘‘comparison’’ group, I chose 17 states (Arkansas,Arizona, Colorado, Illinois, Indiana, Kansas, Massachusetts, Maryland, NorthCarolina, New Jersey, New Mexico, Nevada, New York, Ohio, Oklahoma,Pennsylvania, and Virginia) where the breadth of graduate programs, demo-graphic characteristics, levels of educational attainment, and labor marketswere comparable to those in my target states. Of the states that I consideredincluding in my comparison group, I excluded 7 Southern states (Alabama,Georgia, Louisiana, Mississippi, Tennessee, Kentucky, and South Carolina)because the public institutions in these states faced desegregation litigationduring the period of investigation and therefore may not provide an untaintedview of general underlying trends in enrollment. I also did not include thestate of Michigan because of the ongoing litigation on affirmative action inthe state during 2000 to 2003, which may have led individuals or institutionsto respond in a manner that would not reflect general trends in the enrollmentof students of color in graduate school. As I note in the following, my findingsare robust to different compositions of the comparison group.
In Table 3, I present descriptive statistics on selected institutional and statecharacteristics for my sample. First, in the left columns, I provide the numberof public institutions, in total and by Carnegie Classification (i.e., whether theinstitution is ‘‘research extensive,’’ ‘‘research intensive,’’ or ‘‘master’s’’/‘‘special-ized’’). As I show in the table, public institutions that are ‘‘research extensive’’and ‘‘master’s/specialized’’ are represented across all the states with an affir-mative action ban and most states in the comparison group, whereas institu-tions that are ‘‘research intensive’’ are underrepresented in the sample, limitingmy ability to generalize findings to these institutions. In the right columns, Ipresent summary statistics on selected state characteristics. Overall, the statesare fairly comparable across these measures, with some exceptions where thepercentage of the Latino population is substantially lower (Arkansas, Indiana,Maryland, Ohio, and Pennsylvania) or the percentage of the Native Americanpopulation is substantially higher (New Mexico and Oklahoma) than therespective Latino or Native American population in the target states.However, in my statistical analyses, I included covariates that controlled forthese demographic differences.
The number of observations in my data set—that is, each observed propor-tion of first-time underrepresented students of color of all graduate studentswho are enrolled at a particular institution in each of the six fields of interest—across each of the years in my main analytic window, 1994 to 2003, are: naturalsciences (n = 1,060), engineering (n = 634), social sciences (n = 959), business(n = 835), education (n = 935), and humanities (n = 942). By choosing an ana-lytic window that included data from all years between 1994 and 2003, I wasable to maximize the number of observations present in my analytic samplewhile staying close to either side of the policy disruptions (Murnane &
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Table
3
Sele
cte
dS
um
mary
Ch
ara
cte
risti
cs
on
the
Pu
bli
cIn
sti
tuti
on
sin
the
Sam
ple
,an
dS
ele
cte
dS
tate
Ch
ara
cte
risti
cs,
for
Year
2000
Public
Inst
itutions
Char
acte
rist
ics
Stat
eChar
acte
rist
ics
N
Rese
arch
Exte
nsi
ve
Rese
arch
Inte
nsi
ve
Mas
ter’s
or
Speci
aliz
ed
Tota
l
Popula
tion
Perc
enta
ge
White
Perc
enta
ge
Latino
Perc
enta
ge
Bla
ck
Perc
enta
ge
Nat
ive
Am
erica
n
Perc
enta
ge
25
Year
s1
With
Bac
helo
r’s
Degre
e
Unem
plo
ym
ent
Rat
efo
r25-
to34-Y
ear
-
Old
s
United
Stat
esa
155
64
20
71
75.1
12.5
12.3
0.9
24.4
3.7
Sta
tes
wit
hba
ns
Cal
iforn
ia16
70
933,8
71,6
48
59.5
32.4
6.7
1.0
26.6
4.9
Flo
rida
64
11
15,9
82,3
78
78.0
16.8
14.6
0.3
22.3
3.1
Texas
62
04
20,8
51,8
20
71.0
32.0
11.5
0.6
23.2
3.4
Was
hin
gto
n5
20
35,8
94,1
21
81.8
7.5
3.2
1.6
27.7
4.9
Tota
lN
33
15
117
Com
pa
riso
nst
ate
s
Arizo
na
32
10
5,1
30,6
32
75.5
25.3
3.1
5.0
23.5
3.7
Ark
ansa
s1
00
12,6
73,4
00
80.0
3.2
15.7
0.7
16.7
4
Colo
rado
52
12
4,3
01,2
61
82.8
17.1
3.8
1.0
32.7
2.3
Illinois
94
14
12,4
19,2
93
73.5
12.3
15.1
0.2
26.1
4.1
India
na
32
01
6,0
80,4
85
87.5
3.5
8.4
0.3
19.4
2.7
Kan
sas
31
02
2,6
88,4
18
86.1
7.0
5.7
0.9
25.8
2.9
Mas
sach
use
tts
41
03
6,3
49,0
97
84.5
6.8
5.4
0.2
33.2
2.0
Mar
yla
nd
41
03
5,2
96,4
86
64.0
4.3
27.9
0.3
31.4
3.0
North
Car
olina
62
13
8,0
49,3
13
72.1
4.7
21.6
1.2
22.5
2.8
New
Jers
ey
51
22
8,4
14,3
50
72.6
13.3
13.6
0.2
29.8
3.6
New
Mexic
o5
21
21,9
54,5
99
67.8
344.0
32.0
39.6
825.3
3.6
Nevad
a1
10
02,4
95,5
29
73.6
524.4
57.3
41.2
220.8
3.7
(con
tin
ued
)
263 at AERA on March 21, 2014http://aerj.aera.netDownloaded from
Table
3(c
on
tin
ued
)
Public
Inst
itutions
Char
acte
rist
ics
Stat
eChar
acte
rist
ics
N
Rese
arch
Exte
nsi
ve
Rese
arch
Inte
nsi
ve
Mas
ter’s
or
Speci
aliz
ed
Tota
l
Popula
tion
Perc
enta
ge
White
Perc
enta
ge
Latino
Perc
enta
ge
Bla
ck
Perc
enta
ge
Nat
ive
Am
erica
n
Perc
enta
ge
25
Year
s1
With
Bac
helo
r’s
Degre
e
Unem
plo
ym
ent
Rat
efo
r25-
to34-Y
ear
-
Old
s
New
York
75
02
18,9
76,4
57
67.9
15.1
15.9
0.4
27.4
4.5
Ohio
83
41
11,3
53,1
40
85.0
1.9
11.5
0.2
21.1
4.0
Okla
hom
a1
00
13,4
50,6
54
76.2
5.2
7.6
7.9
20.3
3.4
Pennsy
lvan
ia13
31
912,2
81,0
54
85.4
3.2
10.0
0.1
22.4
3.9
Virgin
ia7
42
17,0
78,5
15
72.3
4.7
19.6
0.3
29.5
2.2
Tota
lN
85
34
14
37
Nofin
stitutions1
18
49
15
54
Sou
rce.
CG
S/G
RE
Surv
ey
of
Gra
duat
eEnro
llm
ent
and
Degre
es,
U.S
.Censu
sBure
auAm
erica
nCom
munity
Surv
ey,
and
Bure
auof
Labor
Stat
istics
Geogra
phic
Pro
file
ofEm
plo
ym
entan
dU
nem
plo
ym
ent.
a Tota
lnum
berofpublic
inst
itutions
and
sele
cted
inst
itutional
char
acte
rist
ics
incl
ude
inst
itutions
that
resp
onded
toth
eCG
SSu
rvey
and
incl
udes
inst
itutions
inal
lst
ates,
exce
ptth
ose
that
are
excl
uded
inth
esa
mple
(Ala
bam
a,G
eorg
ia,Lo
uis
iana,
Mic
hig
an,M
issi
ssip
pi,
Tenness
ee,K
entu
cky,an
dSo
uth
Car
olina)
.In
stitutional
type
cate
gories
are
bas
ed
on
2000
Car
negie
Cla
ssific
atio
ns.
‘‘Rese
arch
Exte
nsi
ve’’
inst
itutions
incl
ude
inst
itutions
com
mitte
dto
gra
duat
eedu-
cation
thro
ugh
the
doct
ora
tean
dth
ose
that
awar
ded
50
or
more
doct
ora
ldegre
es
per
year
acro
ssat
leas
t15
dis
ciplines,
where
as‘‘R
ese
arch
Inte
nsi
ve’’
incl
ude
those
that
awar
ded
atle
ast
10
doct
ora
ldegre
es
per
year
acro
ss3
or
more
dis
ciplines,
or
atle
ast
20
doct
ora
ldegre
es
per
year
overa
ll.
‘‘Mas
ter’s’’i
ncl
udes
inst
itutions
com
mitte
dto
gra
duat
eeduca
tion
thro
ugh
the
mas
ter’s
degre
ean
d‘‘S
peci
aliz
ed’’
offers
degre
es
rangin
gfr
om
the
bac
helo
r’s
toth
edoct
ora
tean
dty
pic
ally
awar
da
maj
ority
ofdegre
es
ina
single
field
.
264 at AERA on March 21, 2014http://aerj.aera.netDownloaded from
Willett, 2010), capturing at least 3 years of data before the implementation of thefirst ban in Texas and 3 years of data after the last ban in Florida. As I note in thefollowing, my findings are robust to different time periods.
Analytic Strategy
Tobit regression analysis. To model the impact of the affirmative actionbans on the enrollment of students of color, I employed Tobit regression anal-ysis. I chose this technique because exploratory analyses confirmed that thedistributional properties of my outcome did not satisfy the usual normal-theory assumptions required by ordinary least squares (OLS) regressionmethods. For instance, the values of my outcome had a positively skewed dis-tribution and were truncated in the lower tail at a value of zero while retaininga disproportionate number of zero values. It was not surprising that the out-come distribution contained many zero values as students of color are highlyunderrepresented in these graduate programs. In many cases, the distributionof a skewed variable can be rendered more symmetric by a log or logit trans-formation (Ramsey & Schafer, 2002). In my case, however, such transforma-tions did not succeed because they could not separate from each other themany zero values that existed at the low end of the distribution.
To model outcomes with these distributional properties, researchers haveused Tobit regression analysis (e.g., Grogan-Kaylor & Otis, 2007; Jacobs &O’Brien, 1998). The approach, developed originally by Tobin (1958), isa hybrid of Probit and OLS regression analysis. In the higher education con-text, for instance, the method has been used to analyze the determinants ofout-of-state enrollments, where the outcome, percentage of enrollment, wasalso truncated in the lower tail at values of zero (Mixon & Hsing, 1994). Forcomparison purposes, I also replicate my main results using OLS regressionanalysis, though these estimates should be considered biased because any dif-ferences in the enrollment rates of students of color in fields where student ofcolor enrollment can be higher or lower are averaged with differences in fieldswhere enrollment can only remain at zero or be larger.
Statistical Model Specification
What is the impact of the statewide affirmative action bans in Texas,California, Washington, and Florida on the enrollment of underrepresentedstudents of color within any of six selected fields of study—the natural sci-ences, engineering, social sciences, business, education, and humanities—atpublic institutions in these states? To address this question, I fitted the fol-lowing multilevel Tobit regression model:
SoCENRLdjt 5 b0 1 b1ðBANstÞ1 b2Xjt 1 b3Wt
1 d0Ss 1 a0Yy 1 ðedjt 1 ujÞ;ð1Þ
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where: SoCENRL is the proportion of students of color who are enrolled ina particular discipline (d) at a given institution (j) in a given year (t);12 BAN isa dichotomous question predictor that equals 1 when a ban on affirmativeaction took effect in a particular year and subsequent years and 0 for prioryears; X represents selected time-varying institutional-level covariates, suchas total institutional size and Carnegie Classification (research extensive orresearch intensive/master’s/specialized); W represents selected time-varyingstate characteristics, such as state-level racial demographics (percentagepopulation White, Black, Latino, Native American, and Asian American),state-level educational attainment (the percentage of the population that is25 years and older with a bachelor’s degree), and state-level economic indi-cators, such as the unemployment rate of the population that was eligible forgraduate study (25–34 year olds); S indicates a vector of state dichotomies todistinguish among the 21 states and to control for all time-invariant differen-ces, both observed and unobserved, among the states; Y represents yeardichotomies to distinguish among the chronological years to which my sum-maries apply and to account for average differences in the outcome amongthe 10 chronological years spanned by my data, which include yearsbetween 1994 and 2003; and Edjt 1 uj represents the sum of a hypothesizedtime-level and an institutional-level population residual.13 An estimate ofparameter b1 is the difference-in-differences estimate of the effect of affirma-tive action bans on the enrollment rates of graduate students of color ina specific field of study.
I also fitted augmented versions of this basic statistical model in which Ireplaced the year fixed effects with state-specific time trends, in order toallow for trends in enrollment over time to differ by state. The model spec-ification for this augmented model was:
SoCENRLdjt 5 b0 1 b1ðBANstÞ1 b2cyearstj 1 b3Xjt 1 b4Wt 1 d0Ss
1 nsScyear 1 ðedjt 1 ujÞ;ð2Þ
where cyear represents a continuous-year variable (coded so that 1994 = 1,1995 = 2, 1996 = 3, etc.); and Scyear represents a full set of two-way interac-tions between each state dummy and a continuous predictor representingthe linear effect of year.14
Weighting
I incorporated two types of weights into my Tobit regression analyses.The first were a set of inverse variance-based weights to account for differ-ences in the level of precision with which the values of my outcome, whichwere proportions, were known.15 This had the effect of ensuring that obser-vations whose proportions were known more precisely counted moreheavily in the estimation (e.g., Afifi, Clark, & May, 2004). I also used a second
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type of weight to account for the fact that my data were aggregated to thelevel of academic major and that graduate enrollment differed at various in-stitutions. This second type of sampling weights ensured that institutionswith a larger number of first-time enrolled students within a field of studywere weighted more heavily in the model-fitting than those with a smallernumber of first-time enrolled students.16 I then multiplied the two types ofweights together prior to including them in the analysis.
Sensitivity Analyses
In each phase of my analyses, I also conducted sensitivity analyses. First,I examined whether my main findings were robust to the use of a differentyear for ban implementation in California, using 1998 instead of 1997.Although the affirmative action ban implemented in California did nottake effect until the class of 1998 entered graduate school, because of thepublic discussion and attention to the issue during the time it was being lit-igated, I anticipated the ban to have affected applications and enrollment de-cisions as early as the fall of 1997. Thus, it was important to consider whethermy findings were robust to the choice of implementation year.
In a second set of sensitivity analyses, I modified the analytic windowaround the year of the bans, within which I fitted my statistical models(1994–2003). For a narrow analytic window, I selected the years 1996 to2002 to allow for at least 1 year before the implementation of the first affir-mative action ban in Texas and California and 1 year after the implementa-tion of the last affirmative action ban in Florida. These sensitivity analyseshelped me to determine whether the impact of the ban may have beenmore immediate than anticipated under my main analytic window. I alsoselected a broader analytic window, 1992 to 2005, allowing for 5 yearsbefore the implementation of the first ban in Texas and California and 5years after the last ban in Florida. This analysis allowed me to determinewhether the impact of the bans on student of color enrollment continuedor was larger in magnitude than under my main analytic window.
In a third and final set of sensitivity analyses, I tested whether my resultswere robust to different compositions of the comparison group of states byrefitting my principal statistical models with both a broader and a narrowerselection of comparison states. In the broader group, I included all the statesin the United States, with the exception of the 8 states that I excluded fromall analyses because of the ongoing litigation related to desegregation oraffirmative action at the time. My choice of this broader group of comparisonstates allowed me to see whether trends in the selected group of comparisonstates did reflect national trends in enrollment. My choice of the narrowersample of comparison states was based on the possibility that state-to-statestudent mobility into neighboring states may have influenced enrollmentin the chosen group of comparison states. That is, it is possible that because
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of an affirmative action ban in a particular state, students may have chosen toenroll at institutions in nearby states without a ban, thereby elevating enroll-ments artificially in the chosen comparison group. If so, I assumed that stu-dents may have chosen to enroll in states that were close in geographicproximity. Thus, I selected a subset of the 17 comparison states in themain analysis—including only 10 states—that were closest in terms ofbreadth of graduate programs as well as other demographic and educationalattainment characteristics, but not as close in geographic proximity as thosein the main comparison group (Illinois, Indiana, Massachusetts, Maryland,North Carolina, New Jersey, New York, Ohio, Pennsylvania, and Virginia).
Findings
Overall, I estimated that the percentage of students of color enrolleddeclined after the bans on affirmative action by about 2 percentage pointsin each of four of fields of study—natural sciences (1.5 percentage points),engineering (1.6 percentage points), and social sciences (1.9 percentagepoints)—and by about 1 percentage point in the humanities (1.2 percentagepoints). The impact in education (2 percentage points) is only marginally sta-tistically significant, while consistently across models, there appears to be noimpact in the field of business. In all my analyses, the results using Tobit andOLS regression methods were similar in magnitude and consistent in direc-tion. Thus, for the sake of simplicity, I report only the Tobit results in all sub-sequent tables. In the following, I discuss how I arrived at these finalestimates, which I then convert into overall percentage declines to betterconvey the magnitude of the declines in each field.
To obtain the estimates of the average effect of the affirmative action banson the enrollment rates of graduate students of color by field of study, I fitteda taxonomy of models, which I present in Table 4. In Panel A, I present the re-sults of fitting the statistical model in Equation 1, my basic model specification,without a state-specific year trend. In Panel A(1), I present the unweighted re-sults, while in Panel A(2), I show the weighted results. Here, similar to the find-ings in the analysis for all fields, in the weighted analysis, the enrollment ratesdrop in magnitude in the fields of the natural sciences and engineering, suggest-ing that in these fields of study larger institutions may have experienced a lowerdrop in the enrollment of students of color than did smaller institutions. By con-trast, it appears that in the humanities, larger institutions may have experienceda larger decline in the enrollment rates of students of color than smaller onessince in the weighted analysis the negative effect of the bans is larger in mag-nitude and becomes statistically significant.17
In Panel B, I show the results of fitting the statistical model in Equation 2,my augmented model with a state-specific year trend, and compare the find-ings from the unweighted and weighted analyses, respectively. By allowingthe year trend to differ by state (assuming a linear trend), the negative impact
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Table
4
Main
Fin
din
gs,
by
Fie
ldo
fS
tud
ya
Fie
ldofSt
udy
Nat
ura
lSc
ience
sEngin
eering
Soci
alSc
ience
sBusi
ness
Educa
tion
Hum
anitie
s(1
)(2
)(3
)(4
)(5
)(6
)
A.N
ost
ate-s
peci
fic
tim
etrend
1.U
nw
eig
hte
dBAN
–0.0
18~
–0.0
20*
0.0
07
0.0
09
–0.0
15
–0.0
04
(0.0
11)
(0.0
09)
(0.0
11)
(0.0
11)
(0.0
11)
(0.0
13)
2.W
eig
hte
dBAN
–0.0
02
–0.0
06~
–0.0
01
–0.0
05
0.0
09
–0.0
12*
(0.0
04)
(0.0
04)
(0.0
06)
(0.0
05)
(0.0
07)
(0.0
05)
B.St
ate-s
peci
fic
tim
etrend
1.U
nw
eig
hte
dBAN
–0.0
40*
–0.0
23~
0.0
13
0.0
25
–0.0
30~
–0.0
19
(0.0
16)
(0.0
13)
(0.0
16)
(0.0
17)
(0.0
17)
(0.0
21)
2.W
eig
hte
dBAN
–0.0
15**
–0.0
16**
–0.0
19*
0.0
04
–0.0
20~
–0.0
19**
(0.0
06)
(0.0
05)
(0.0
09)
(0.0
07)
(0.0
11)
(0.0
07)
Num
ber
ofobse
rvat
ions
1,0
60
634
959
934
935
942
Left-c
enso
red
143
96
88
99
60
145
Unce
nso
red
917
538
871
835
875
797
Num
ber
ofin
stitutions
116
68
105
103
102
103
Fin
alM
odelb
Pan
elB(2
)Pan
elB(2
)Pan
elB(2
)Pan
elB(2
)Pan
elB(2
)Pan
elA(2
)
Note
.St
andar
derr
ors
inpar
enth
ese
s.a A
vera
ge
effect
ofaf
firm
ativ
eac
tion
ban
son
the
avera
ge
enro
llm
entofgra
duat
est
udents
ofco
lorby
field
ofst
udy,fr
om
fitted
regre
ssio
nm
odels
withoutan
dw
ith
stat
e-s
peci
fic
tim
etrends,
unw
eig
hte
d,an
dw
eig
hte
dto
adju
stfo
rth
epre
cisi
on
ofin
stitutional
sum
mar
yin
form
atio
nan
dth
esi
zeoffirs
t-tim
eenro
llm
entin
eac
hfield
ofst
udy,fo
rth
em
ain
anal
ytic
win
dow
(1994–2003)
and
all17
com
par
ison
stat
es.
bFin
alm
odelse
lect
ed
from
resu
lts
ofgoodness
-of-fitte
sts
com
par
ing
the
chan
ge
in2
2LL
betw
een
fitted
models
inPan
elA(2
)an
dth
ose
inPan
el
B(2
).All
models
incl
ude
stat
efixed
effect
san
da
full
setofin
stitutional
-an
dst
ate-levelco
var
iate
s;in
stitutional
-levelco
var
iate
sin
clude
wheth
er
the
inst
itution
isre
sear
chexte
nsi
ve
(vs.
rese
arch
inte
nsi
ve
or
mas
ter’s/
speci
aliz
ed);
stat
e-levelco
var
iate
sin
clude
perc
enta
ge
of
popula
tion
by
race
(White,
Bla
ck,
Nat
ive
Am
erica
n,
Latino,
Asi
an),
perc
enta
ge
of
popula
tion
with
abac
helo
r’s
degre
e,
and
perc
enta
ge
of
25-
to34-y
ear
-old
sunem
plo
yed.
Models
without
ast
ate-s
peci
fic
year
trend
incl
ude
year
fixed
effect
s;m
odels
with
stat
e-s
peci
fic
year
trend
do
not
incl
ude
year
fixed
effect
sto
avoid
collin
ear
ity.All
models
acco
untfo
rth
ecl
ust
ering
ofobse
rvat
ions
within
inst
itution
over
tim
e(w
ith
inst
itutional
ran-
dom
effect
s)an
dw
ithin
stat
e(w
ith
stat
efixed
effect
s).The
17
com
par
ison
stat
es
incl
ude
Ark
ansa
s,Arizo
na,
Colo
rado,Illinois
,In
dia
na,
Kan
sas,
Mas
sach
use
tts,
Mar
yla
nd,N
orth
Car
olina,
New
Jers
ey,N
ew
Mexic
o,N
evad
a,N
ew
York
,O
hio
,O
kla
hom
a,Pennsy
lvan
ia,an
dVirgin
ia.
~p
\.1
0.*p
\.0
5.**p
\.0
1.
269 at AERA on March 21, 2014http://aerj.aera.netDownloaded from
of the bans on the enrollment rates of students of color is larger in magnitudein three of the six fields: the natural sciences, engineering, and humanities(compare Panels A[1] and B[1] and Panels A[2] and B[2]). The estimatesdrop in magnitude once the results are weighted in the natural sciences,engineering, and education, suggesting, again, that—in these fields—largerinstitutions may have experienced a lower decline in the enrollment of stu-dents of color than did smaller institutions. Finally, a statistically significantimpact in the social sciences emerges once I weight the analyses and allowthe year trend to differ by state.
Because of the importance of adjusting for the varying levels of precisionwith which I can estimate enrollment rates, and for the size of the enrollmentin each field, I prefer the estimates of the impact of the ban on the enrollmentof students of color from the fitted models in Panels A(2) and B(2) rather thanPanels A(1) and B(1). To select the most parsimonious model, I conductedgoodness-of-fit tests that compared the change in negative 2 likelihood (–2LL)deviance statistic in the weighted models that included a state-specific timetrends and those that did not. The results of these tests indicated that inclusionof the state-specific year trend improved the prediction of the impact of thebans in all the fields of study, except in the humanities.18
Sensitivity Analyses
In Table 5, I present the results of my sensitivity analyses of the pre-ferred models from each field, fitted using my weighted approach. Again,for the sake of simplicity, I do not report the results from my OLS analyses,which were similar in magnitude and consistent in direction to the resultsobtained in the Tobit regression analyses across all fitted models. For easeof comparison, in Panel A, I summarize the final results of the main analysis,employing the analytic window that extended from 1994 to 2003 and usedthe 17 selected comparison states. In Panel B, I present results for when Iestimated the policy change in California to begin in 1998 rather than1997. Here, the results are consistent across fields, except in the social scien-ces, where the negative impact is slightly larger in magnitude.
In Panel C, I display the results for different analytic windows: (1) a nar-row analytic window, 1996 to 2002, which covered at least 1 year before thefirst affirmative action bans took effect in Texas and California and 1 yearafter the last ban in Florida, and (2) a broad window, 1992 to 2005, whichincluded 5 years before the implementation of the first ban in Texas andCalifornia and 5 years after the last ban in Florida. With a narrow analyticwindow, the estimated effect of the bans on the enrollment of students ofcolor remains negative and of relatively similar magnitude as that in themain analysis in the natural sciences, engineering, and social sciences,though not in the fields of education and the humanities, where it loses itsstatistical significance. This change may be expected when analyses are
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Table
5
Sen
sit
ivit
yA
naly
ses
a
Nat
ura
lSc
ience
sEngin
eering
Soci
alSc
ience
sBusi
ness
Educa
tion
Hum
anitie
s
(1)
(2)
(3)
(4)
(5)
(6)
A.M
ain
resu
lts—
anal
ytic
Win
dow
1994–2003
and
17
Com
par
ison
Stat
es
BAN
–0.0
15**
–0.0
16**
–0.0
19*
0.0
04
–0.0
20~
–0.0
12*
(0.0
06)
(0.0
05)
(0.0
09)
(0.0
07)
(0.0
11)
(0.0
05)
Num
ber
ofobse
rvat
ions
1,0
60
634
959
934
935
942
Left-c
enso
red
143
96
88
99
60
145
Unce
nso
red
917
538
871
835
875
797
Num
ber
ofin
stitutions
116
68
105
103
102
103
B.Cal
iforn
iapolicy
chan
ge
in1998
(inst
ead
of1997)
BAN
–0.0
15**
–0.0
16**
–0.0
24**
0.0
03
–0.0
20~
–0.0
11*
(0.0
06)
(0.0
05)
(0.0
09)
(0.0
07)
(0.0
12)
(0.0
05)
Num
ber
ofobse
rvat
ions
1,0
60
634
959
934
935
942
Left-c
enso
red
143
96
88
99
60
145
Unce
nso
red
917
538
871
835
875
797
Num
ber
ofin
stitutions
116
68
105
103
102
103
C.D
iffe
rentan
alytic
win
dow
s
1.N
arro
wan
alytic
win
dow
(1996–2002)
BAN
–0.0
14*
–0.0
13*
–0.0
19~
0.0
04
–0.0
13
–0.0
05
(0.0
07)
(0.0
06)
(0.0
10)
(0.0
09)
(0.0
13)
(0.0
06)
Num
ber
ofobse
rvat
ions
741
441
668
651
651
654
Left-c
enso
red
104
66
60
74
42
95
Unce
nso
red
637
375
608
577
609
559
(con
tin
ued
)
271 at AERA on March 21, 2014http://aerj.aera.netDownloaded from
Table
5(c
on
tin
ued
)
Nat
ura
lSc
ience
sEngin
eering
Soci
alSc
ience
sBusi
ness
Educa
tion
Hum
anitie
s
(1)
(2)
(3)
(4)
(5)
(6)
Num
ber
ofin
stitutions
116
68
105
103
102
103
2.Bro
adan
alytic
win
dow
(1992–2005)
BAN
–0.0
16***
–0.0
11**
–0.0
26***
–0.0
01
–0.0
21*
–0.0
11*
(0.0
04)
(0.0
04)
(0.0
07)
(0.0
06)
(0.0
09)
(0.0
05)
Num
ber
ofobse
rvat
ions
1,4
79
890
1,3
41
1,3
05
1,3
01
1,3
17
Left-c
enso
red
200
134
116
138
81
205
Unce
nso
red
1,2
79
756
1,2
25
1,1
67
1,2
20
1,1
12
Num
ber
ofin
stitutions
116
68
105
103
102
103
D.D
iffe
rentsa
mple
ofco
mpar
ison
stat
es
1.Bro
adsa
mple
ofco
mpar
ison
stat
es
(all
U.S
.st
ates,
with
excl
usi
ons)
BAN
–0.0
15**
–0.0
16**
–0.0
18*
0.0
04
–0.0
18~
–0.0
12**
(0.0
05)
(0.0
05)
(0.0
08)
(0.0
07)
(0.0
11)
(0.0
04)
Num
ber
ofobse
rvat
ions
1,3
33
807
1,1
98
1,2
21
1,2
32
1,2
01
Left-c
enso
red
184
160
144
175
101
224
Unce
nso
red
1,1
49
647
1,0
44
1,0
46
1,1
35
977
Num
ber
ofin
stitutions
147
88
136
138
138
132
2.N
arro
wsa
mple
ofco
mpar
ison
stat
es
(10
com
par
ison
stat
es)
BAN
–0.0
15**
–0.0
16**
–0.0
22*
0.0
01
–0.0
22~
–0.0
19*
(0.0
06)
(0.0
06)
(0.0
09)
(0.0
07)
(0.0
12)
(0.0
08)
(con
tin
ued
)
272 at AERA on March 21, 2014http://aerj.aera.netDownloaded from
Table
5(c
on
tin
ued
)
Nat
ura
lSc
ience
sEngin
eering
Soci
alSc
ience
sBusi
ness
Educa
tion
Hum
anitie
s
(1)
(2)
(3)
(4)
(5)
(6)
Num
ber
ofobse
rvat
ions
878
509
784
769
778
785
Left-c
enso
red
107
78
61
78
56
111
Unce
nso
red
771
431
723
691
722
674
Num
ber
ofin
stitutions
97
55
87
86
86
87
Note
.St
andar
derr
ors
inpar
enth
ese
s.The
models
for
hum
anitie
sdo
notin
clude
stat
e-s
peci
fic
tim
etrend.All
models
incl
ude
stat
efixed
effect
san
da
full
setofin
stitutional
-an
dst
ate-levelco
var
iate
s;in
stitutional
-levelco
var
iate
sin
clude
wheth
erin
stitution
isre
sear
chexte
nsi
ve
(vs.
rese
arch
inte
nsi
ve
orm
aste
r’s/
speci
aliz
ed);
stat
e-levelco
var
iate
sin
clude
perc
enta
ge
ofpopula
tion
by
race
(White,Bla
ck,N
ativ
eAm
erica
n,La
tino,Asi
an),
perc
enta
ge
ofpopula
tion
with
abac
helo
r’sdegre
e,an
dperc
enta
ge
of25-to
34-y
ear
-old
sunem
plo
yed.M
odels
with
ast
ate-s
peci
fic
year
trend
do
notin
clude
year
fixed
effect
sto
avoid
collin
ear
ity
with
stat
e-s
peci
fic
year
trend.M
odels
withouta
stat
e-s
peci
fic
year
trend
(hum
anitie
s)in
clude
year
fixed
effect
s.All
models
acco
untfo
rth
ecl
ust
ering
ofobse
rvat
ions
within
inst
itution
overtim
e(w
ith
inst
itutional
random
effect
s)an
dw
ithin
stat
e(w
ith
stat
efixed
effect
s).
The
17
com
par
ison
stat
es
inm
ain
anal
ysi
sin
clude
Ark
ansa
s,Arizo
na,
Colo
rado,
Illinois
,In
dia
na,
Kan
sas,
Mas
sach
use
tts,
Mar
yla
nd,
North
Car
olina,
New
Jers
ey,
New
Mexic
o,
Nevad
a,N
ew
York
,O
hio
,O
kla
hom
a,Pennsy
lvan
ia,
and
Virgin
ia.
Excl
uded
stat
es
inbro
adsa
mple
of
com
par
ison
stat
es
incl
ude
Ala
bam
a,G
eorg
ia,Lo
uis
iana,
Mic
hig
an,M
issi
ssip
pi,
Tenness
ee,K
entu
cky,an
dSo
uth
Car
olina.
Sele
cted
gro
up
of
10
com
par
ison
stat
es
incl
ude
Illinois
,In
dia
na,
Mas
sach
use
tts,
Mar
yla
nd,N
orth
Car
olina,
New
Jers
ey,
New
York
,O
hio
,Pennsy
lvan
iaan
dVirgin
ia.
a Avera
ge
effect
of
affirm
ativ
eac
tion
ban
son
gra
duat
est
udent
of
colo
renro
llm
ent
by
field
of
study
for
fitted
models
with
stat
e-s
peci
fic
tim
etrends
(exce
ptfo
rfield
ofhum
anitie
s,w
hic
hdid
notin
clude
stat
e-s
peci
fic
tim
etrends)
,w
eig
hte
dto
adju
stfo
rth
ele
velofpre
cisi
on
ofin
form
a-
tion
and
size
offield
ofst
udy
~p
\.1
0.*p
\.0
5.**p
\.0
1.
273 at AERA on March 21, 2014http://aerj.aera.netDownloaded from
conducted in a narrower analytic window, which reduces my statisticalpower to detect the effect of the bans automatically. These results also indi-cate that it may have taken longer for the bans on affirmative action to havehad an impact in the fields of education and the humanities. With a broadanalytic window, the estimated effect also remains negative and of similarmagnitude across fields, with a slightly larger negative effect in the field ofsocial sciences, an additional 1 percentage point drop.
My main results are also robust to the different compositions of the com-parison group: (1) a broader sample of all states in the United States with the8 excluded states and (2) a subset of the selected group of comparison states.As I show in Table 5, the results in Panels D(1) and D(2) are about the sameas those in Panel A. The consistency of my findings with the different com-positions of the comparison states suggests that the selected 17 states in themain analysis reflected national trends in graduate enrollment. With a narrowsample of comparison states, the negative impact of the bans is slightly largerin magnitude in all fields except the natural sciences and engineering. Theseresults support the possibility that students in non–science-related fields mayhave chosen to enroll in geographically close-by states without a ban.
Understanding the Magnitude of These Declines
To better understand the magnitude of these results and allow for com-parisons across fields, I convert the estimated percentage point declines dis-cussed previously into an overall percentage decline in each field.19 Forinstance, in engineering, the average percentage of all graduate studentsenrolled who were students of color across all target states in the sample—-before affirmative action bans were implemented—was about 6.2%. Theestimated 1.6 percentage point drop from my analyses thus representsa drop in student of color enrollment to about 4.6%. Expressed as a fractionof the initial value, this represents a 26% (or over a fourth) decline in studentof color enrollment in engineering.20 Similarly, the decline in the natural sci-ences is about 19% (from 7.8% to 6.3%). In the social sciences, the decline isabout 15.7% (from 12.1% to 10.2%) and in the humanities is about 11.8%(from 10.2% to 9%). Figure 1 illustrates these findings.
In terms of individual students, these declines confirm an average of 12fewer underrepresented students of color in engineering in total across thesestates, an average of about 21 fewer students of color in the natural sciences,an average of 10 fewer students of color in the social sciences, and an aver-age of 8 fewer students of color in the humanities. These numbers reflect thelow representation of underrepresented students of color in most of thesefields. Before affirmative action bans, for example, of all the studentsenrolled across all four states in the field of engineering (about 648), onlyabout 40 students were underrepresented students of color. Of all the stu-dents enrolled in the natural sciences (about 1,270), only about 100 students
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were underrepresented students of color. Given the already minimal repre-sentation of students of color in these fields, even a small numerical declinecan have important consequences for the educational experiences of all stu-dents in these programs.
Conclusion and Implications
Past studies have shown that the enrollment rates of students of color atselective undergraduate institutions, in the professions of law and medicine,and across graduate studies, have declined following the implementation ofaffirmative action bans. This study builds on this work by examining theimpact of the affirmative action bans in Texas, California, Florida, andWashington within various graduate fields of study. Results show that afterthe implementation of affirmative action bans, the greatest declines in theproportion of enrolled graduate students who are students of color tookplace in the fields of engineering (26%), natural sciences (19%), and thesocial sciences (15.2%)—fields where students of color are already themost underrepresented—with a slightly lower decline in the humanities(11.8%). There is no impact of the bans on the enrollment rates of underrep-resented students of color in the field of business and education, where theimpact was only marginally statistically significant.
Do These Reductions Matter?
These results represent meaningful reductions in graduate fields of study,particularly in STEM (science, technology, engineering, and mathematics)
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
Engineering Natural Sciences Social Sciences Humani�es
Enro
lled
Stud
ents
of C
olor
pre-bans post-bans
7.8%
6.3%6.2%
4.6%
12.1%
10.2% 10.2%
9%
Figure 1. Findings for the impact of affirmative action bans by field of study.
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fields, where a difference of a few graduate students of color in the classroomcan have important consequences for the experiences of all students. Thesocial and cultural climate in science-related fields like STEM is one of theleading barriers to the persistence of women of color in STEM career trajecto-ries (Ong, Wright, Espinosa, & Orfield, 2011). A large survey study of womenof color in STEM graduate programs (Brown, 1994, 2000) revealed that isola-tion, racism, and being racially/ethnically identifiable, among other climatefactors, present more difficulty for the persistence of women of color thanstructural factors, such as financial aid or the composition of the faculty.Thus, a decline of a few students of color in a field like engineering canmake it remarkably more challenging for students of color to persist throughtheir program.
Racial and ethnic diversity in the student body has educational value forall students. Thus, a less racially and ethnically diverse student body de-prives students across all races and ethnicities of these benefits, such asenhanced critical and complex thinking skills (Gurin, 1999; Gurin, Dey,Hurtado, & Gurin, 2002; Pascarella, Bohr, Nora, & Terenzini, 1996),improved cross-racial understanding and cultural awareness (Milem, 1992,1994), civic engagement (Bowen & Bok, 1997; Chang, Astin, & Kim,2004), and cross-cultural workforce competencies and leadership skills(Jayakumar, 2008).21 In many graduate fields of study, these benefits are crit-ical for understanding the issues being researched, preparing individuals foreffective professional practice in multiracial settings, and fostering creativityand innovation through the embrace of multiple perspectives (see e.g.,Harvey & Allard, 2011; Page 2007).
These are also meaningful declines for institutional outreach, recruit-ment, and support efforts. In graduate studies, the racial and ethnic charac-teristics of the student body can play an important role in the decisions ofstudents of color to apply or enroll in a field of study. This is because thepresence of students of color can help other students of color feel more wel-come at an institution; and if none or only a few students of color areenrolled, students risk the possibility of being ‘‘tokenized’’ in the classroom(Chang, Eagan, Lin, & Hurtado, 2009; Steele, 1997; Taylor & Antony, 2000).Thus, in science-related fields, where students of color are already severelyunderrepresented, a drop of one or two students of color can have negativelong-term consequences on the decision of other students of color to applyor enroll in these fields. These challenges can make institutional efforts thatattempt to mitigate the negative impact of not being able to consider race inadmissions, through their outreach and recruitment efforts, more difficult.
These declines can also have long-term effects on faculty diversity inthese fields since doctoral training and graduate degree acquisition feedinto faculty positions. In STEM fields, faculty play a critical role in influencingthe decisions of students to attend graduate school, choose a particular pro-gram, and pursue a STEM career (e.g., Gasman et al., 2009; Ong, 2002; Sader,
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2007). Faculty perspectives and research trajectories also have long-lastingeffects on the scientific inquiry (Espinosa, 2011). Declines in the numberof students of color who can become future faculty members in science-related fields thus have long-term consequences for the learning experiencesof students and the types of research studies that are conducted.
Differences by Field of Study and Implications for Institutions and Future
Research
Given that students of color are generally underrepresented at higherscore percentiles on standardized tests and generally overrepresented atlower percentiles (see e.g., Bowen & Bok, 1998; Diaz, 1990), it is not surpris-ing that the impact of affirmative action bans is greater in science-relatedfields like engineering (26%), natural sciences (17%), and social sciences(15.2%), compared to the humanities (11.8%) or education (where theimpact is not statistically significant). This is because the overall mean scorefor standardized tests like the GRE, particularly in the quantitative portion ofthe test, is generally higher in these fields than in the humanities and educa-tion fields. Moreover, as I noted in the hypothesis section, the general char-acteristics of graduate students in less technically focused fields of education(and similarly humanities) suggest that past work experience may be animportant factor that plays into students’ decisions to pursue study in thesefields or in faculty’s admissions decisions. These other factors may thus bal-ance the negative impact of affirmative action bans in these fields.
The higher mean standardized test scores in science-related fields arethe result of a combination of factors, including the characteristics of stu-dents who self-select into these fields (in the application or enrollment stage)as well as the factors that faculty may consider in admissions processes.Although the outcome measure of enrollment allows us to understandhow these policies are affecting the overall representation of students ofcolor in various graduate fields of study, the available data do not allowme to disentangle the impact at these various stages. Future research mayconsider the impact of affirmative action bans on these series of eventsand provide a more thorough understanding of the effect of these policieson the decisions of students to apply to and, if admitted, enroll in a particularprogram as well as in the admissions decisions by faculty, administrators, orother institutional actors.
The decline in the field of engineering, over a fourth, is almost as largeas the declines in the enrollment of students of color in the professional fieldof law as a result of affirmative action bans (nearly two-thirds for AfricanAmericans and a third for Latinos) (Kidder, 2003). As in the field of law,which provides the training for many of the future leaders of our nation,these fields provide students with specialized training critical to the nation’sability to compete in a globalized market and for ensuring continued
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scientific and technological advancement. Declines in racial and ethnic stu-dent body diversity in science-related fields like engineering and the naturalsciences pose serious long-term consequences for our nation. Future studiesshould examine how changes in the social climate as a result of these de-clines, or as a result of the implementation of affirmative action bans, affectthe persistence of students of color in these fields, as well as institutional out-reach, recruitment, and support efforts. We also need a better understandingof the long-term consequences of these declines for faculty diversity in STEMfields, where mentorship and role models, including faculty, serve as a vitalelement in the persistence of students of color (Brown, 1994, 2000).
Banning race as a plus-factor in admissions in graduate fields of studyalso has consequences that should motivate educators to reconsider their ad-missions practices and consider additional factors that would contribute toa racially and ethnically diverse student body, such as diverse experiences,potential to contribute to research, community involvement or service,research activity on and off campus, and creativity in problem solving.Moreover, standardized test scores should be considered in light of familycircumstances (parental educational levels and socioeconomic status) orother contextual factors (existing community resources, geographic loca-tion) that have been shown to be highly correlated with performance onstandardized tests like the GRE (Educational Testing Service, 2011). In fact,given the limited predictive validity of the GRE, the Educational TestingService discourages use of a GRE score as the sole or best indicator ofachievement and academic ability (Educational Testing Service, 2011).Graduate programs should revise their practices to follow these recommen-dations by placing little emphasis on—or altogether eliminate—GRE scores,not only as a factor in admissions, but also in determining research assistant-ships and other forms of financial support.
As institutions struggle to increase the representation of students of colorin graduate programs, particularly in STEM fields, the findings from this studysuggest that bans on affirmative action are inhibiting these efforts, causing de-clines in the enrollment of students of color in fields that are critical to the eco-nomic competitiveness of the United States and where students of color arealready severely underrepresented. Graduate education programs will needto rise to the challenge and adopt innovative outreach and recruitment prac-tices and adopt admissions criteria to help reverse this trend.
Notes
This research was funded by a Spencer Foundation Fellowship for Research Relatedto Education. The views contained herein are not necessarily those of the SpencerFoundation. I am indebted to the Council of Graduate Schools (CGS) and to Kenneth E.Redd, former director of research and policy analysis at CGS, for providing the data forthis study and for answering my questions. I am grateful to Bridget Terry Long, John B.Willett, and Richard J. Murnane for their helpful feedback on an early version of this
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article. Special thanks to Ann Ishimaru, Cynthia Gordon, Sola Takahashi, Amanda Taylor,and Mara Tieken for their invaluable comments and support. This article also benefittedfrom the constructive feedback of two anonymous reviewers.
1The Court heard oral argument in the case on October 10, 2012, and a decision isexpected by June 2013. Although the constitutional challenge in Fisher only applies tothe consideration of race in admissions at public institutions, another federal law, knownas Title VI, extends the same constitutional requirements to any educational institution thataccepts federal money. This means that the decision would apply, as a practical matter, tovirtually every college and university in the country, including private universities.
2In November 2012, the Sixth Circuit Court of Appeals struck down the state ballotmeasure in Michigan (Proposal 2) as unconstitutional on the grounds that it violated theequal protection clause of the 14th amendment to the U.S. Constitution (see Coalitionto Defend Affirmative Action v. Regents of the University of Michigan, 2012). The rulingcame after the Ninth Circuit Court of Appeals upheld the constitutionality of a similar banon affirmative action in California, Proposition 209 (see Coalition to Defend AffirmativeAction v. Brown, 2012).
3Individual universities can also ban the practice through university policy. TheUniversity of Georgia, for example, banned affirmative action in 2002.
4The disparities in the field of education do not appear as great for African Americansas they made up about 12% of all doctoral recipients in this field in 2009 (National ScienceFoundation, Division of Science Resource Statistics, 2010).
5I use the terms field of study and discipline interchangeably and use them to refer tothe broad area of study that encompasses various ‘‘majors,’’ ‘‘departments,’’ or ‘‘programs.’’Thus, the field of study or discipline of engineering casts a broader net than the specific‘‘major’’ of mechanical engineering or the specific engineering ‘‘program’’ or ‘‘department’’at a particular institution.
6I do not include the affirmative action bans in Arizona, Nebraska, or Michigan in myanalyses because at the time I conducted this study, their implementation had been toorecent (2010, 2008, and 2006, respectively) to determine their impact.
7These differences are not necessarily indicative of innate intelligence or potential forachievement. As research by the Educational Testing Service (ETS), which created theGraduate Record Exam (GRE), has shown, GRE performance is strongly correlated withfamily income and background (Pennock-Roman & Educational Testing Service, 1994).The predictive validity of the GRE for graduate student success is also limited (ETS,2011). Moreover, factors such as ‘‘stereotype threat,’’ or the anxiety or stress triggered bythe fear that one might fulfill a relevant stereotype, can also contribute to the underperform-ance of African American and Latino students in standardized testing (Steele, 1997).
8By contrast, the highest verbal GRE score mean was in the humanities (669), fol-lowed by social sciences (601), sciences and mathematics (575), engineering (562), andeducation (556). The authors speculate that this ordering is not surprising given the natureof the work in each field and suggest that the lower scores in education may reflect diver-sity of interests in the field and demographic diversity such as age and race (Nettles &Millett, 2006).
9A true scientific experiment, however, would be nearly impossible in light of the eth-ical implications for the students whose educational opportunities could potentially beinequitably altered through participation.
10An ideal project would collect student-level information at each of these threestages directly from all of the institutions considered in this study. However, the feasibilityof collecting such information is questionable, particularly given the controversial politicalclimate surrounding affirmative action in which institutions face the threat of litigationwith the mere appearance that they are considering race in their admissions policies(e.g., Miksch, 2008). Collecting the information is also particularly challenging in the con-text of graduate studies because admissions processes are not centralized across differentfields of studies and programs, as they may be in undergraduate studies.
11Before any sample restrictions, my beginning sample size in the four target statesand selected comparison group included a total of 374 institutions: 91 in my four targetstates and 283 in the comparison group. By excluding private institutions and those thatwere classified as Historically Black Colleges and Universities, I eliminated a total of
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188 institutions: 41 in my four target states and 147 in the comparison group. From theremaining 186 institutions, I eliminated a total of 38 institutions (6 in my target statesand 32 in the comparison group) by excluding institutions whose reported first-timeenrollment values in a particular major were missing for students of all races across allyears of the analytic window or across a pre-ban or post-ban period for a respective state.From the remaining 148 institutions, I excluded a total of 30 institutions (11 in my targetstates and 19 in the comparison states) whose reported first-time enrollment values werenot disaggregated by major or field of study. These institutions do not differ from thoseincluded in the study on important characteristics.
12The GSE survey provided the number of students, by race and ethnicity, who werefirst-time enrolled in a major. Thus, to calculate my outcome, I added the number of stu-dents across the different majors that made up the field of study.
13This specification of the multilevel model uses a combination of fixed and randomeffects to account for the nesting of observations at the state and institutional levels(Murnane & Willett, 2010). The presence of the state fixed effects in the model accountsfor the lack of independence among observations within a state (i.e., the nesting of obser-vations within a state); the presence of the institutional random effects accounts for theclustering of observations within an institution, over time.
14Model 2 does not include a full set of year dummies in order to avoid collinearitywith the continuous variable cyear.
15Because of the aggregate-level nature of my data—where each observation isa combination of different observations, such as different underlying number of majorsand number of students who make up a particular field of study at an institution—eachobservation had a different level of precision, or variability. The variance-based weightswere inversely proportional to the variance of each observation (w = 1/y 3 (1 2 y)).
16Here, the weights were equal to the total number of first-time enrolled studentswithin a field of study at a given institution in a given year.
17By contrast, in the weighted analysis, the effect becomes negligent in the social sci-ences and positive in the field of education, though in these two fields the impact was notstatistically significant in models that did not allow the year trend to differ by state.
18The difference in 22LL in the field of natural sciences (52.94), engineering (26.08),the social sciences (36.12), business (80.82), and education (48.02) were all greater thanthe respective critical value from a chi-square distribution at an alpha level of 5% andthe respective degrees of freedom. Thus, I rejected the null hypotheses that the parame-ters associated with the state-specific year trend were simultaneously zero in the popula-tion. The difference in 22LL in the humanities (25.91) was less than the critical value froma chi-square distribution at an alpha level of 5% and 41 degrees of freedom (56.95); thus,in this case, I could not reject the null hypothesis and concluded that the state-specific yeartrend did not help better predict the effect of affirmative action bans in this field.
19To obtain the overall percentage decline, I first estimated the proportion of under-represented students of color who were enrolled within each field across all the targetstates in the sample before any of the bans were implemented in each target state(1994–1996 in Texas and California, 1994–1998 in Washington, and 1994–2000 inFlorida). I did not include years when the bans on affirmative action were in effectbecause enrollment in those years would presumably already reflect the negative impactof the bans and, as such, would bias the overall average. From this figure, I then sub-tracted the estimated impact of the ban.
20A drop from 6.2% to 4.6% can be expressed in two ways: (1) as a drop of 1.6 per-centage points or (2) as a drop of about 26%. The first approach expresses the change asa stand-alone unit that denotes the arithmetic difference between the two percentages.The second approach expresses the change as a fraction of the initial value—that is,a drop to 4.6% from an initial value of 6.2 is a drop by a fraction of .046/.062 = .742; ex-pressed as a percentage, this is a drop of about 26%. In this study, I adopt the latterapproach to express the change because it allows for better comparisons of the impactof the bans across fields as the baseline percentage of student of color enrollment is dif-ferent in each field.
21For a more in-depth discussion of the documented educational benefits of racialand ethnic diversity, see Milem (2003) and Orfield, Frankenberg, and Garces (2008).
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Manuscript received May 8, 2012Final revision received October 12, 2012
Accepted October 25, 2012
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