AA

HOW DOES AN AFFIRMATIVE ACTION BAN CHANGE ADMISSIONS?

EVIDENCE FROM UNIVERSITY OF CALIFORNIA LAW SCHOOLS



Danny Yagan

Harvard University



March 2011







ABSTRACT



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I use 25,000 law school applications from an elite college’ undergraduates to

estimate consequences of the 1996 ban on a¢ rmative action at the University of

California. The ban reduced black admission rates in this sample by approxi-

mately 50%, suggesting that race was decisive in half or more of the admission

o¤ers awarded to pre-ban black applicants. Post-ban admissions o¢ ces could infer

applicant race quite well, and evidence on avoidance behavior challenges standard

models. The e¤ects of a nationwide ban hinge on whether rejected applicants are

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willing to attend lower-ranked schools. Courts can use this paper’ methods when

enforcing the Civil Rights Acts.







A¢ rmative action— awarding admissions preference to underrepresented minorities on the

basis of race— may be the most controversial policy in U.S. higher education. The public is

divided over the practice. The U.S. Supreme Court has indicated it will ban a¢ rmative action

at public universities in the next twenty years, and …ve states have already done so at the

state level. The quantitative importance of a¢ rmative action is unknown because minority

admissions advantages in the cross section do not distinguish between the e¤ects of a¢ rmative

action and the e¤ects of racial di¤erences in potential and other factors the researcher does

not observe. Furthermore the e¤ects of banning a¢ rmative action are ambiguous because

admissions o¢ ces may avoid the ban.

I make progress using 25,000 law school applications to estimate consequences of the largest

a¢ rmative action ban to date: the a¢ rmative action ban at the University of California,

passed by referendum in 1996. The dataset— which I call the Elite Applications to Law

Email: yagan@fas.harvard.edu. I am grateful to Raj Chetty, David Cutler, John Friedman, Roland

Fryer, Edward Glaeser, Claudia Goldin, Joshua Gottlieb, Nathaniel Hilger, Richard Hornbeck, Caroline Hoxby,

Lisa Kahn, Lawrence Katz, Ilyana Kuziemko, Jessica Laird, N. Gregory Mankiw, Je¤rey Miron, Sendhil Mul-

lainathan, Andrei Shleifer, and Matthew Weinzierl for helpful discussions and comments. Michel Kim provided

excellent research assistance. The computations in this paper were run on the Odyssey cluster supported by

the Harvard FAS Sciences Division Research Computing Group, and in particular I am thankful to Christopher

Walker for his support.

School (EALS)— contains all applications submitted to law schools across the country between

1990 and 2006 by 5,300 undergraduates from one elite college. All results are local to this

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sample. Each EALS observation records the applicant’ race, LSAT standardized test score,

undergraduate grade point average, application year, school applied to, and admissions decision.

The EALS may be the best attainable data to estimate the admissions consequences of an

a¢ rmative action ban for two reasons: it contains the necessary information for a di¤erence-

in-di¤erences design, and law school admissions decisions are largely determined by academic

scores and race and thus narrow the scope for selection bias.

I …rst document the strong correlation between race and admission in the cross section at

the …fteen top U.S. law schools that were never subject to an a¢ rmative action ban. Black

applicants enjoy an average admissions advantage over comparably credentialed white appli-

cants equivalent to 1.5 standard deviations of academic strength (a summary measure of LSAT

score and GPA), approximately the di¤erence between a B/B- GPA and an A- GPA. If all

applicants in this sample were subject to the observed admission standards for white applicants,

black admission rates at the average school would fall from 60% to 15%. These correlations

motivate the central question of the paper: given the importance of race in the cross section,

how does an a¢ rmative action ban change admissions?

Aggregate changes in black admission rates mask an obvious and empirically-relevant selec-

tion e¤ect: post-ban black applicants with low academic credentials may have expected rejection

and thus declined to apply, attenuating the observed e¤ect of the ban. The individual-level

EALS allows me to address this by controlling for academic credentials. I do this in two

ways: semi-parametrically by reweighting post-ban applicant pools to resemble pre-ban ap-

plicant pools as in DiNardo, Fortin, and Lemieux (1996), and parametrically using OLS and

probit regressions. I also control for secular trends at non-UC schools. My preferred estimates

are that the ban reduced the black admission rate by 32 percentage points at UC Berkeley and

29 percentage points at UCLA. Under a monotonicity assumption, this means that 56% and

44% of pre-ban black applicants who were admitted to Berkeley and UCLA, respectively, are

predicted to have been rejected had the ban been in e¤ect.

Despite the large decline in admission rates, post-ban black applicants to UC schools con-

tinued to be admitted at substantially higher rates than would be expected based on their

LSAT scores and GPAs. Standard avoidance models suggest the explanation that admissions







2

o¢ ces continued to use racial proxies to give net preference to minorities, but that the racial

proxies were too impure to make it worth their while or even possible to maintain pre-ban black

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admission rates. This avoidance is ine¢ cient from the school’ perspective because it forces the

school inside its race-sighted frontier (Chan and Eyster 2003), can disrupt academic assortative

matching across schools (Epple, Romano, and Sieg 2008), and can be socially ine¢ cient by

discouraging pre-application investments in human capital by students of all races (Fryer and

Loury 2005; Fryer, Loury, and Yuret 2007). Policymakers advocating a¢ rmative action bans,

including President George W. Bush during the 2003 U.S. Supreme Court a¢ rmative action

cases, nevertheless promote ine¢ cient avoidance as the ideal and expected admissions o¢ ce

response.

The inability of post-ban admissions o¢ ces to infer race is the key technological assump-

tion of standard avoidance models, and I investigate its plausibility by quantifying the degree

to which the non-academic determinants of admission— unobserved by the researcher— proxied

for race, under two alternative and straightforward assumptions for the structure of the non-

academic factors. The key to this exercise is that the less noise there is in admissions decisions

conditional on academic variables and race, the more the non-academic factors must have func-

tioned like a pure race variable in order to produce a given black admissions advantage. I show

that in the …rst half of the post-ban sample, Berkeley admissions were conducted as though

the admissions o¢ ce used a single binary non-academic variable that 93% of black applicants

possessed and only 18% of white applicants possessed— suggesting that the admissions o¢ ce

could infer the race of the vast majority of its applicants. For UCLA, the …gures are 88% and

6%. To the extent that the non-academic factors included any relatively race-neutral char-

acteristics like recommendation letter strength, the remaining non-academic factors bene…tted

black applicants all the more completely and exclusively. Admissions o¢ ces in the second

half of the post-ban period were probably equally technologically able to infer applicant race,

though admissions decisions were noisier and less directly informative.

Supporting these estimates, I argue that post-ban applications did indeed signal race despite

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no longer containing a race question. In the elite college’ yearbooks, 82% of black students and

0% of white students list participation in a black-focused extracurricular group— information

that would be on applicants’résumés. Names often signal race. And immediately after the

ban, Berkeley began prompting applicants to use their personal statements to discuss their







3

likely contributions to “the diversity of the entering class”and their backgrounds including “a

personal or family history of cultural, educational, or socioeconomic disadvantage.”

These facts present a puzzle for understanding avoidance behavior: if post-ban admissions

o¢ ces could infer race quite well, why did they allow black admission rates to fall by half?

Standard avoidance models can explain the results if post-ban admissions o¢ ces could not

infer race absolutely perfectly and if non-racial forms of applicant strength were strong enough

substitutes for racial diversity that admissions o¢ ces preferred to allow black admission rates to

plummet rather than sacri…ce marginally more non-racial strength. I highlight an alternative

possibility: admissions o¢ ces may have continued to use race in admissions while being legally

compelled to allow black admission rates to fall. This possibility has received little attention

in the literature because the letter of a¢ rmative action bans regulates the technology used in

admissions, not aggregate outcomes. But courts never observe the technology used in subjective

selection decisions and thus have used racial disparities in aggregate outcomes to enforce other

nondiscrimination laws. If the UC a¢ rmative action ban was enforceable only when admission

rates diverged too markedly across races, optimal admissions o¢ ce behavior is to continue to

practice a¢ rmative action but mildly enough to stay under the radar— contrary to standard

avoidance models and with none of the attendant ine¢ ciencies. The data are inconclusive in

choosing among these models, especially for recent application years.

I conclude with reduced-form simulations of the consequences of a nationwide a¢ rmative

action ban on black enrollment. I …rst replicate the actual pattern of EALS black enrollment

across the top …fteen non-UC schools using the following simulation algorithm: let all students

“apply” to every school and “enroll” at the top school at which they gain admission. Having

validated the algorithm, I use it to show that if all schools react to an a¢ rmative action ban as

Berkeley and UCLA did, schools ranked 1 through 7 would su¤er a reduction in the black share

of enrollees while schools ranked 8 through 15 would enjoy a rise. The reason is that black

applicants who are newly-rejected from top schools are academically strong enough to gain

admission at lower-ranked schools without substantial admissions advantages. Crucially, this

assumes that newly-rejected black applicants will attend lower-ranked schools rather than opt

out of law school altogether— behavior that is unpredictable ex ante. If simulated applicants

instead refuse to attend lower-ranked schools, a nationwide ban is predicted to reduce black

enrollment across the board.







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This paper contributes to a large literature on a¢ rmative action. It provides estimates

of the e¤ect of an a¢ rmative action ban on black admission rates that are robust to the

empirically-relevant concern that low-credentialed black applicants stopped applying because

they could no longer gain admission. The large estimates lend credence to forecasts that

a¢ rmative action will be needed to sustain black representation at elite schools …fteen years

from now when the U.S. Supreme Court may ban it (Krueger, Rothstein, and Turner 2006).

Theoretically the paper presents an intuitive version of standard avoidance models (Chan and

Eyster 2003, Fryer et al. 2007, Epple et al. 2008) that permits straightforward comparison to

alternative mechanisms.

Bans aside, this paper establishes quantitatively large e¤ects of a¢ rmative action. There

was always the possibility that black admissions advantages in the cross section derived sub-

stantially from black applicants having stronger characteristics that the researcher does not

observe, and many laypeople believe that a¢ rmative action only breaks a small number of ties

between otherwise identical applicants. Because UC admissions o¢ ces could legally continue

to admit black applicants who were stronger on characteristics that members of any race could

possess, my results indicate that approximately half of admitted pre-ban black applicants in the

EALS were admitted through the consideration of race. This is an underestimate if post-ban

admissions o¢ ces avoided the ban.

Most generally, this paper provides a novel tool for enforcing nondiscrimination laws. The

Civil Rights Acts of the 1960s and 1970s prohibit the use of protected traits— race, sex, age,

religion, and nationality— in employment, housing, and other important selection decisions in

the economy. A typical large-scale discrimination case, like the current class action against

Wal-Mart, centers on a disparity in outcomes by a protected trait, such as a black or female

…xed e¤ect in a regression controlling for observable di¤erences across applicants. The case

hinges on whether a court believes the accused …rm when it argues that the observed disparity

was the result of selection on legally-permissible factors that the court does not observe and

that happened to correlate with the protected trait— rather than the use of the protected

trait itself.1 The methods of this paper can be used to inform that judgment by quantifying

how purely the unobserved determinants of selection approximated the protected trait in the

1

The evidentiary standard of proof in discrimination and other civil cases is merely “the preponderance of

the evidence,” so courts simply make a judgment call that a given disparity in outcomes was probably caused

illegally (e.g. Bazemore v. Friday) or not (e.g. EEOC v. Sears, Roebuck & Co.).







5

underlying decisions. For example, consider a bank that approved mortgages at a higher rate

for white applicants than for black applicants with similar credit scores. By exploiting both

the magnitude of this racial disparity and the level of noise conditional on credit score and race,

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one can use this paper’ methods to quantify, under straightforward assumptions, how purely

the non-credit-score factors functioned like a race variable. The more consistently the non-

credit-score factors bene…tted white applicants and not black applicants, the more con…dent a

court can be that the bank used race in its mortgage decisions.

The paper is organized as follows. Section I reviews the UC a¢ rmative action ban, sum-

marizes the data, and discusses their suitability. Section II documents the cross-sectional

correlation between race and admission at elite U.S. law schools. Section III uses a sim-

ple model of a¢ rmative action ban avoidance to guide the empirical analysis. Section IV

estimates the e¤ect of the UC a¢ rmative action ban on black admission rates, investigates

potential avoidance behavior, and discusses implications for modeling avoidance. Section V

simulates consequences of a nationwide a¢ rmative action ban. Section VI concludes.





I Background and Data

I.A A¢ rmative Action in the United States



Universities in several countries practice a¢ rmative action. U.S. universities began using race

in admissions in the 1960s in order to raise black enrollment, and the practice is currently legal

at all private universities and at most public ones. First in 1978 and again in 2003, the U.S.

Supreme Court judged in 5-4 decisions that, in spite of the nondiscrimination provisions of the

Fourteenth Amendment, public universities may use race as an admissions factor in pursuit of

ow

the educational bene…ts that ‡ from a racially diverse student body. But it warned in its

latest decision that it may ban a¢ rmative action around 2028 (Grutter v. Bollinger 2003).

The U.S. Congress has broad powers to do the same at private universities.2

Depending on the poll, approximately 55% of Americans either support (AP-GfK 2009)

or oppose (Quinnipiac 2009) a¢ rmative action, and more favor admissions preferences for low-

income applicants than for minority applicants (Barrett 2003). The administration of President

2

Over the past 50 years, Congress has used its Commerce Clause authority to prohibit racial discrimination

in employment, housing, restaurant and hotel service, and other prominent spheres of the private sector. It

could similarly prohibit the use of race in private university admissions, at least at those that admit out-of-state

applicants as all selective universities do.







6

George W. Bush echoed many opponents when it argued in its formal advisory opinion to Grut-

ter that universities should be forced to achieve diversity only through race-blind recruitment

strategies and admissions factors like “a history of overcoming disadvantage, geographic origin,

socioeconomic status, challenging living or family situations,” among others (United States

2003). Such sentiments have contributed to a¢ rmative action bans in …ve states— California,

Florida, Michigan, Nebraska, and Washington— most adopted by voter referendum.



I.B The A¢ rmative Action Ban at the University of California



On November 5, 1996, California voters approved Proposition 209 to amend the state constitu-

tion to read: “The state shall not discriminate against, or grant preferential treatment to, any

individual or group on the basis of race, sex, color, ethnicity, or national origin in the opera-

tion of public employment, public education, or public contracting.” The ban went into e¤ect

immediately at UC law schools. It is worded as an individual-level mandate: no applicant is

to be preferred to another applicant on the basis of race.

UC administrators strongly opposed the ban and took steps both to comply with the law

and to sustain minority enrollment. As the California political climate began to turn against

a¢ rmative action, the UC president, UC vice-presidents, and the chancellor of each UC campus

united to “unanimously urge, in the strongest possible terms,” the continuation of a¢ rmative

action (University of California 1995). The day after Proposition 209 passed, UC president

Richard Atkinson announced that the new question facing the university was “How do we

establish new paths to diversity consistent with the law?” (Atkinson 1996). UC applications

were amended to declare that race was not a criterion for admission, and the page of the

application form requesting applicant race was diverted to a UC statistical o¢ ce and was not

reported to admissions o¢ ces. Yet schools also instituted new diversity measures. For example

at Berkeley Law, applicants before the ban were given ten unconnected prompts for the personal

statement, two of which referred to diversity or disadvantages. Immediately after the ban and

ever since, those ten short prompts were replaced by a single lengthy one inviting applicants

to discuss how they would “contribute to the diversity of the entering class” and to describe

“any disadvantages that may have adversely a¤ected your past performance or that you have

successfully overcome, including linguistic barriers or a personal or family history of cultural,









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3;4

educational, or socioeconomic disadvantage.”



I.C Data: Elite Applications to Law School (EALS)



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(i) Source. This paper’ primary dataset— which I call the Elite Applications to Law School

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(EALS)— contains con…dential individual-level data on 67% of an elite college’ seniors and

graduates who applied to law schools nationwide between the fall of 1990 and the fall of 2006.

Applications to almost every U.S. law school are submitted through the Law School Admissions

Council, which records application information and admissions decisions for every application

…led. Applicants choose whether to release their data to their colleges’administrators, and I

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obtained and digitized 17 years of a single college’ data. The percentage of applicants releasing

their data ‡uctuated between a low of 58% in 2002 and a high of 77% in 1995. The college is

elite, outside California, and not subject to an a¢ rmative action ban.

(ii) Variables and Sample Restrictions. The data contain six variables for every application:

race, LSAT standardized test score, undergraduate grade point average (GPA), application

year, law school applied to, and admissions decision.5 GPA is reported to two decimal places;

I de-mean GPA by year to account for modest grade in‡ation over time.

The raw data contain 38,200 applications. I use the following protocol to exclude unsuitable

or ancillary records from the analysis. I omit applications missing any of the six variables or

submitted by the 9.6% of applicants who are not listed as white, Asian, black, or Hispanic.6

For each year I create applicant identi…ers by treating as coming from the same applicant those

applications that match on the application-invariant variables, and I exclude the small number

of observations for which this implies that a single applicant submitted two applications to

the same school. 85% of applications survive these elimination procedures. I then keep

only the 78% of these applications that were submitted to UC Berkeley, UCLA, or one of the

3

I have not obtained archived personal statement prompts for UCLA Law, but the current prompt does not

explicitly mention diversity or disadvantages.

4

A¢ rmative action proponents within individual campus administrations do not appear to have been replaced

by a¢ rmative action opponents over time; for example at Berkeley Law, the pre-ban dean served into 2000 and

the dean since 2004 is a renowned a¢ rmative action scholar and proponent.

5

,

LSAT scores for the …rst application year are in a more compact scale than all other years’ and I convert

them to the modern scale using percentile rank. The admissions decision for a small percentage of accepted

students is classi…ed as rejected when the applicant in fact accepted and deferred an admission o¤er. Under-

graduate major, year of college graduation, and state of permanent residence are available in some but not all

years’ raw data. I omit these variables for their incompleteness and, in the case of state residence, also the

di¢ culty in digitizing two-character state abbreviations.

6

, ,

I code “Chicano/Mexican-American” “Hispanic” and “Puerto Rican” as Hispanic.







8

…fteen most-applied-to schools that were never subject to an a¢ rmative action ban.7 The 170

other schools received relatively few applications and are poor control schools for Berkeley and

UCLA because they are less selective. The resulting 17-school EALS sample comprises 25,499

applications submitted by 5,353 applicants.

(iii) Summary Statistics. Table 1 lists summary statistics. The sample is approximately

61% white, 19.5% Asian, 9.5% black, and 10% Hispanic. White and Asian applicants possess

considerably higher LSAT scores and GPAs than black and Hispanic applicants. To describe

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these di¤erences in a compact manner, I condense each applicant’ LSAT and GPA into a

scalar index that I call “academic strength,” which equals the standardized sum (mean zero

and standard deviation one) of standardized LSAT and standardized GPA.8 I show in Section II

that admissions decisions are well-characterized by academic strength. For now, note that the

academic strength of the average white applicant is 1.27 standard deviations higher than that

of the average black applicant and 0.75 standard deviations higher than that of the average

Hispanic applicant.9 28% (1,594) of all applicants applied to UC Berkeley and 14% (777)

applied to UCLA, respectively ranked #7 and #17 nationwide by U.S. News and World Report

in 1998.10

(iv) Data Suitability. The EALS is possibly the best attainable dataset to estimate the

e¤ects of an a¢ rmative action ban on admissions. Most importantly, it contains both ac-

cepted and rejected applications from the categories necessary for a di¤erence-in-di¤erences-in-

di¤erences (DDD) analysis: from minority and non-minority applicants, submitted to treated

and untreated schools, and from before and after a ban. No public dataset contains this

information.

7

I do not include the University of Michigan in the group of …fteen most-applied-to schools because it was

subject to an a¢ rmative action ban during the sample. I do not analyze Michigan as a treatment school

because its bans were e¤ective during the sample only in 2001 and 2006 and I do not have su¢ cient power to

conduct year-by-year di¤erence-in-di¤erences. UC law schools at Davis and Hastings received few applications

in the EALS and similarly do not permit robust inference.

8

That is, I …rst standardize LSAT and GPA to each have mean zero and standard deviation one across EALS

applicants. I then sum the two variables and divide by the standard deviation to obtain a scalar index that has

mean zero and standard deviation one. Kling, Liebman, and Katz (2007) use a similar rescaling in a di¤erent

context.

9

See Appendix Table 1 for more statistics and Appendix Figure 1 for non-parametric density estimates that

illustrate the …rst-order stochastic dominance of black and Hispanic distributions of academic credentials by

white and Asian distributions. Similarly large racial gaps exist within the broader undergraduate population

(i.e. not just those applying to law school) at elite colleges (Bowen and Bok 2000 p.30). The gaps are probably

smaller at unselective colleges where most applicants are admitted and a¢ rmative action in undergraduate

admissions appears to be negligible (Kane 1998).

10

Berkeley received the seventh largest number of applications in this sample and UCLA received the thir-

teenth.





9

Second, an analysis based on the EALS is less prone to selection bias than other potential

analyses. The perfect experiment would hold constant the applicant pool and vary only whether

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an a¢ rmative action ban was in place. This is impossible because a school’ applicant pool

is never exogenously assigned. Given that, the EALS is ideal for two reasons. First, I can

control for applicants’ LSAT and GPA, which addresses an obvious and empirically-relevant

selection problem: low-credentialed minorities declining to apply after the ban because they

believe they will no longer be admitted. Second, law school admissions may be the most

formulaic of all university admissions processes and thus narrow the scope for selection on

unobserved determinants of admission. I show in the next section that within school-year-

races, a probit model with only linear terms in LSAT and GPA correctly predicts 89.1% of

admissions decisions. I discuss remaining sources of potential bias in Section IV.A.(iv).





II Race and Admission in the Cross Section

I motivate the rest of the paper by documenting the correlation between race and admission in

the cross-section at elite U.S. law schools. I con…ne the analysis to the …fteen most-applied-to

law schools in the EALS that were never subject to an a¢ rmative action ban, which constitute

the control group for the quasi-experimental analysis below on UC schools. The relationships

presented here are consistent with cross-sectional analyses of undergraduate admissions such as

Kane (1998), Bowen and Bok (2000), and Espenshade, Chung, and Walling (2004).

I …rst demonstrate that elite law school admissions decisions in the EALS can be character-

ized by within-race admission rules in a summary measure of LSAT score and GPA. This is

important because I use this scalar index of academic strength here and throughout the paper.

I …rst estimate a probit regression of admission on standardized LSAT (mean zero and standard

deviation one), standardized GPA, and school-year-race …xed e¤ects using all applications to

non-UC schools.11 Two facts emerge. First, this simple probit correctly predicts 85.4% of

admissions decisions, where an application is predicted to earn an admission o¤er if and only if

its probit forcing variable is greater than zero.12 I vividly demonstrate this predictive power in

Appendix Figure 2 using a color-coded scatterplot of all 23,128 admissions decisions. Second,

11

The probit model is Pr(Admisssion) = ( LSAT LSAT + GP A GP A + str ) where str is the school-year-

race …xed e¤ect.

12

Allowing the coe¢ cients on LSAT and GPA to vary by school-year-race raises this prediction accuracy to

89.1%.







10

the ratio of the coe¢ cients on LSAT and GPA is 0.95, indicating that a one standard deviation

higher LSAT is about as valuable in the admissions cross section as a one standard deviation

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higher GPA. I therefore summarize an applicant’ “academic strength” as the standardized

unweighted sum of standardized LSAT and standardized GPA.13 Figure 1a plots actual and

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probit-…tted admission rates by academic strength, where each application’ academic strength

has been centered by its school-year-race …xed e¤ect.14 The plot shows that admission is a

steeply increasing function of academic strength and that the semi-parametric relationship is

well-approximated by a simple probit that is linear in academic strength.

Figure 1b uses such probit-…tted admission rules in academic strength by race to illustrate

the relationship between race and admission at the average non-UC school.15 I shift admission

rules horizontally by a constant so that the predicted admission probability for white applicants

equals 0.5 at academic strength 0. The …tted admission rules for black and Hispanic appli-

cants are substantially more lenient than those for white and Asian applicants. There are two

particularly illustrative ways to see this. First, comparing the levels of academic strength that

correspond to a 50% admission probability indicates that black applicants have a cross-sectional

admissions advantage over whites equal to 1.53 standard deviations of academic strength, ap-

proximately equivalent to the di¤erence between a B/B- GPA and an A- GPA. For Hispanics,

the cross-sectional advantage is -0.71 standard deviations. Second, for applicants with academic

strength -0.71, white and Asian applicants are 8-9% likely to be admitted, Hispanic applicants

are 50% likely to be admitted, and black applicants are 92% likely to be admitted.

Admissions outcomes would be very di¤erent if all applicants were subjected to the …tted

admission rule for white applicants in Figure 1b: the black admission rate would fall from 60%

to 15% and the Hispanic admission rate would fall from 46% to 27%.16 This means that black

applicants in the EALS were admitted to top U.S. law schools at four times the rate that would

13

See footnote 8 for a more detailed description.

14

Speci…cally I estimate the probit model Pr(Admisssion) = ( a+ str ) where a is the application’ academic

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strength and str is the school-year-race …xed e¤ect. I then “center” each application’ academic strength by

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adding ^ str = ^ to it. This allows me to pool applications across school-year-races when constructing the …gure.

15

Speci…cally I estimate the probit model Pr(Admisssion) = ( 1 a + 2 I Race + 3 aI Race + st ) where a is

academic strength, where I Race is a vector of three indicators for black, Hispanic, and Asian races, and where

st

is the school-year …xed e¤ect. The regression is weighted by school-year so that the estimates refer to the

average non-UC school in the average year.

16

With reference to the equation in the previous footnote, I predict admission for each application using only

st

1 and , while also adding a constant to the probit forcing variable so that the predicted number of admitted

applicants (the sum over all applicants’admission probabilities) equals the actual number. I add this constant

because reducing admissions advantages for black and Hispanic applicants frees up slots in admitted cohorts.







11

prevail under the …tted white admission rule in academic strength, and Hispanic applicants at

1.7 times. These admission rate changes imply that, under the …tted white admission rule in

the EALS, the share of admitted students that are white or Asian would rise from 78% to 91%,

the share that are black would fall from 12.4% to 2.8%, and the share that are Hispanic would

fall from 9.7% to 5.9%. Appendix Figure 3 illustrates these relationships.

These cross-sectional di¤erences in admissions decisions by race are not causal estimates of

the magnitude of a¢ rmative action because minority applicants could possess stronger non-

racial factors than white and Asian applicants of the same academic strength. Nevertheless

the di¤erences motivate the central question of the paper: given the importance of race in the

cross section, how does an a¢ rmative action ban change admissions?





III A Simple Model of A¢ rmative Action Ban

Avoidance

Admissions o¢ ces face a tradeo¤ between admitting the academically strongest applicants and

admitting minority applicants. I use a simple model to characterize optimal admissions o¢ ce

behavior under an a¢ rmative action ban and to guide the empirical analysis to follow. The

analysis yields four key results. (1) The letter of an a¢ rmative action ban raises the price of

admitting minorities by increasing the non-racial strength that must be foregone. (2) A ban

can therefore cause admissions to be ine¢ cient and can even cause minority admission rates

to rise. (3) If a ban instead constrains only aggregate outcomes, an admissions o¢ ce will

e¢ ciently avoid the ban by practicing modest a¢ rmative action, causing minority admission

rates to fall and generating no ine¢ ciency. (4) A weak but testable prediction of ine¢ cient

avoidance is that admissions becomes less responsive to academic credentials after a ban.



III.A s

The Admissions O¢ ce’ Maximization Problem



s

The simplest way to model the admissions o¢ ce’ maximization problem is to cast it as a two-

good consumption problem. I follow the existing literature in considering an applicant pool

where each applicant is either a racial minority or a racial non-minority, the applicant pool is

the same pre-ban and post-ban, and all admitted students matriculate.17 The admissions o¢ ce

17

In a broader model where not all admitted students matriculate, the yield (the percentage of admitted

students who matriculate) may be a relevant margin for understanding admissions o¢ ce behavior. Using

aggregate data covering all applicants to UC law schools, the black yield at UCLA rose a few percentage points





12

has concave preferences over the aggregate academic strength a and the number of minorities

m of admitted cohorts. The admissions o¢ ce faces a binding capacity constraint: it can admit

no more than a …xed number N of applicants and must reject some applicants. The admissions

s

o¢ ce’ problem is then:

max u (a; m) s.t. N (a; m) N

a;m



where N (a; m) is the minimum number of applicants that must be admitted in order to deliver

aggregate strength a and minorities m. N (a; m) is an implicit function of the joint distribution

of race and academic strength in the applicant pool. The admissions o¢ ce faces a tradeo¤

because the admission rule that maximizes academic strength is not the one that maximizes

the number of minorities.

The admissions o¢ ce can admit applicants on the basis of two pieces of information: aca-

demic strength ai and a binary signal Si 2 f0; 1g of minority status. The optimal admission

rule can always be characterized as a “rank-and-yank”rule that admits the N applicants that

have highest rank according to:

ranki = ai + Si



where is chosen to maximize admissions o¢ ce utility.18 This is true because for any number of

admitted minorities, the admissions o¢ ce maximizes aggregate academic strength by adopting

a threshold rule within each race signal whereby the only admitted applicants are minority-

signalled applicants with academic strength above some aS=1 and non-minority-signalled appli-

cants with academic strength above some aS=0 . Rank-and-yank implements any such pair of

threshold rules by setting weight equal to aS=0 aS=1 .



III.B A¢ rmative Action



When a¢ rmative action is not banned, the admissions o¢ ce can legally use a pure signal of

race in admissions decisions. The signal Si of minority status at its disposal is pure in that

Si = 1 if and only if applicant i is a minority.19 Figure 2a illustrates a feasible pair of optimal

relative to the white yield after the ban; at Berkeley it declined in the …rst year of the ban but then recovered

the following year and rose slightly over time. Explicitly modeling yield is unlikely to break the qualititative

results to follow. See Appendix Figure 4 for the data source.

18

The U.S. Supreme Court judged in 2003 that admissions processes that give minorities a set number of

“points”toward admission are unconstitutional while less formulaic consideration of race is not. The distinction

is poorly de…ned but if rank-and-yank were too formulaic, an admissions o¢ ce could make it arbitrarily less so

by adding noise.

19

Admissions o¢ ces typically construct such a signal simply by asking applicants to report their race on the

application form, where dishonest answers are grounds for rejection or rescission of an already-awarded o¤er of



13

admission rules and illustrates its consequences for minority and non-minority applicants. To

de…ne the no-a¢ rmative-action benchmark, let a be the level of academic strength above

which there are exactly N applicants. This is the race-neutral threshold that would maximize

aggregate academic strength and corresponds to a rank-and-yank admission rule with = 0.

An admissions o¢ ce practicing a¢ rmative action chooses > 0 and thus adopts a threshold

admission rule for minorities at aS=1 and a separate threshold for non-minorities at aS=0 ,

with aS=0 aS=1 = . Relative to the no-a¢ rmative-action benchmark, the admissions o¢ ce

practicing a¢ rmative action admits extra minorities (highlighted in checkered green) and rejects

extra non-minorities (highlighted in solid black). Figure 2c illustrates the a¢ rmative action

budget set in (m; a) space for the simple case of uniform distributions of academic strength

within each race, where the range of weights 2 [0; 1) traces out the budget constraint.20



III.C Ine¢ cient Avoidance



The letter of an a¢ rmative action ban prohibits the admissions o¢ ce from using a pure signal

of race in admissions decisions but allows it to use race-blind factors that correlate imperfectly

with race, such as whether an applicant has a history of overcoming cultural and socioeconomic

disadvantages. I model this as fraction pm of minorities and fraction pn of non-minorities

possessing the binary signal Si , with pm pn 1

AA

M RTm;a (pm pn )2



The higher price puts the ine¢ cient avoidance budget set in the interior of the a¢ rmative action

budget set, illustrated in Figure 2c. As in any two-good consumption problem when the price of

one good rises, changes in the consumption bundle hinge on income and substitution e¤ects and

are indeterminate when utility is unspeci…ed. The “standard” avoidance models mentioned

s

in the previous paragraph put structure on the admissions o¢ ce’ preferences and thereby

generate speci…c directional predictions, illustrated in the …gure.21 However, the admissions

s

o¢ ce’ preferences are not knowable a priori.



III.D Alternative Responses and a Testable Prediction



Figure 2c also depicts two alternative responses to an a¢ rmative action ban that keep the ad-

missions o¢ ce on its race-sighted frontier. First, the admissions o¢ ce could abandon its prefer-

ences for admitting minorities and maximize only the academic strength of the admitted cohort,

landing the admissions o¢ ce at point F where admitted minorities falls and aggregate academic

strength rises. Second, enforcement frictions may allow an admissions o¢ ce that can still infer

race to e¢ ciently avoid a ban. A¢ rmative action bans are intended to constrain individual

decisions, but admissions decisions are subjective and courts cannot observe the technology

used. Similar to enforcement of other nondiscrimination laws discussed in Section IV.B.(ii),

courts may instead impose a de facto constraint on the black admissions advantage over com-

parable non-minorities— or, equivalently, the total number of admitted minorities— under the

belief that the admissions o¢ ce is probably violating the law if it exceeds the constraint. This

s

constraint creates a kink in the admissions o¢ ce’ budget constraint, and the optimal response

of the admissions o¢ ce is to continue practicing a¢ rmative action, only more modestly than

21

In Chan and Eyster (2003), a and m enter separably and linearly. Under this and technology restrictions,

the admissions o¢ ce may respond to a ban by deliberately introducing white noise— an implicit racial proxy

when minorities are concentrated at lower levels of the academic strength distribution— into admissions decisions

and generate outcomes like points B and C in the …gure but not Gi¤en point E. Fryer, Loury, and Yuret (2007)

allow the admissions o¢ ce to use explicit racial proxies and assume a …xed exogenous constraint on admitted

minorities, landing the post-ban admissions o¢ ce at point D.





15

before the ban. This lands the admissions o¢ ce at a point like G where admitted minorities

falls and aggregate academic strength rises.

Figure 2d illustrates a unique testable prediction of ine¢ cient avoidance that does not

require impractically precise measurement of (m; a) bundles. Only under ine¢ cient avoidance

does the admissions o¢ ce abandon threshold admission rules in academic strength for each

race. Admission rules thus “‡atten”only under ine¢ cient avoidance. The caveat is that this

prediction need not hold if the admissions o¢ ce in reality values more than aggregate academic

strength and minorities. For example, if all other goods (e.g. recommendation letter strength

or non-racial forms of diversity) are a substitute for racial diversity, admission rules in academic

strength could ‡atten even if the admissions o¢ ce does not ine¢ ciently avoid the ban and thus

stays on its race-sighted frontier. Similarly, if racial diversity is valued more than all other

goods, an admissions o¢ ce could respond to a ban by replacing admissions weight on all other

goods with weight on an impure racial proxy. This would put the admissions o¢ ce inside

its race-sighted frontier and would ‡atten admission rules in all other goods (which I do not

observe) but not necessarily in academic strength.





IV Results

IV.A Black Admission Rates



I con…ne the main analysis to black admission rates and present estimates for Hispanics in

the appendix because Hispanic admissions are considerably noisier and generate imprecise es-

timates.

(i) Raw Admission Rate Changes. Aggregate data provided by the UC system on the

universe of applicants to Berkeley and UCLA law schools reveal that black admission rates at

both schools dropped by over half in the …rst year after the ban but then converged toward

white admission rates. See Appendix Figure 4 for the time series. Crucially, the aggregate data

contain no information on applicants’credentials so they cannot be used to identify the e¤ect

of the ban on admission rates for a constant sample of applicants. Changes in applicant pool

composition are a particularly serious concern because the black share of the applicant pool at

each school declined by about 45% in the two years after the ban. This is to be expected: if the

ban reduced the black admissions advantage, black applicants who anticipated rejection may

have declined to apply, and indeed in unreported results I …nd at marginal signi…cance levels



16

that less-credentialed black EALS applicants were substantially less likely to apply after the

ban.22 Post-minus-pre changes in aggregate black admission rates could therefore substantially

underestimate the e¤ect of the ban. I use the EALS to control for such compositional changes.

(ii) Semi-parametric DDD. I estimate the e¤ect of the a¢ rmative action ban on black

admission rates at UC schools using a di¤erence-in-di¤erences-in-di¤erences (DDD) design. For

each UC school, I …rst estimate the impact of the UC a¢ rmative action ban on black admission

rates as the post-minus-pre change in black admission rates at the UC school, controlling for

changes in white admission rates at that school and for changes in the black-white admission

rate di¤erential at non-UC schools:



(1) DDD black;s = black;s;post black;s;pre white;s;post white;s;pre



[( black;~ s;post black;~ s;pre ) ( white;~ s;post white;~ s;pre )]





where is a reweighted admission rate, s denotes a UC school, and ~ s denotes non-UC schools.

Note that this statistic mechanically overestimates the magnitude of the e¤ect of the ban on

black admission rates because a decline in black admission rates opens up space in the admitted

cohort for more members of all races. The bias is relatively small because non-minorities

dominate the applicant pool. Correcting for this would require imputing admission to students

on the margin until the open spaces were …lled. For simplicity I do not attempt such a

correction in these semi-parametric estimates, but I do make the correction in the parametric

DDD analysis below.

In computing each admission rate , I control for changes in the academic strength of ap-

plicants. Applying the widely-used DiNardo, Fortin, and Lemieux (1996) method, I account

for these changes semi-parametrically by reweighting post-ban applications within each school

and race to match the academic strength distribution of pre-ban applications. For each race r

and school s, I compute the terciles of academic strength among pre-ban applications.23 Then

for each time period T , I weight applications so that each pre-ban-de…ned tercile of academic

22

Admissions decisions are explained very well by LSAT, GPA, and race, but application decisions are not.

Simple OLS regressions predict admission at Berkeley and UCLA with r2 of .44 to .50 (Appendix Table 3,

columns 4 and 6). The same speci…cation predicts the decision to apply to Berkeley and UCLA with r2 of

.02 to .03. The reason is that applicants choose among similarly-ranked schools based on geographical, legal

specialty, and other preferences that I do not observe. I consequently have little power to analyze the e¤ect of

the ban on application decisions, such as whether the ban reduced application rates among high-credentialed

black students— the focus of Card and Krueger (2005), who …nd little or no e¤ect of a¢ rmative action bans on

the college application behavior of high-SAT-scoring minorities in California and Texas.

23

Quartiles yield very similar results. I use terciles because some bin counts are small.





17

24

strength receives equal weight when computing admission rate r;s;T . Each computed admis-

sion rate r;s;T is then an estimate of the admission rate that pre-ban applicants of race r at

school s would have experienced if they had applied in period T .

Figure 3 displays the results. Each panel plots a time series of black and white admission

rates. I am unable to display the time series annually because of small sample sizes: in several

post-ban years at individual UC schools, black students did not apply from every academic

strength bin. I instead plot admission rates in two pre-ban time periods (1990-1992 and

1993-1995) and two post-ban time periods (1996-2000 and 2001-2006).

Figure 3a shows that, at non-UC schools, there was almost no change over time in the

di¤erence between black and white admission rates. Figure 3b shows that, at UC Berkeley, the

black admission rate rose between 1990-1992 and 1993-1995 almost exactly as much as the white

admission rate did, lending credence to the parallel trends assumption of this DDD analysis.

Between 1993-1995 and 1996-2000, the black admission rate fell from 64% to 33% and did not

recover 2001-2006 relative to the white admission rate. Pooling pre-ban and post-ban years

as in equation (1), the DDD estimate of the e¤ect of the a¢ rmative action ban on the black

admission rate at UC Berkeley is -30 percentage points. If one makes the mild monotonicity

assumption that the ban would not have caused any rejected pre-ban black applicants to have

been admitted, this DDD estimate and the pre-ban black admission rate of 57% suggests that

53% of black applicants who were admitted to UC Berkeley before the ban would have been

rejected had the ban been in e¤ect.25 These DDD calculations are shown in Appendix Table

2. Figure 3c shows similar results at UCLA, with a DDD estimate of -41 percentage points.

The pre-ban black admission rate was 65%, so this suggests that 63% of black applicants who

were admitted to UCLA before the ban would have been rejected had the ban been in e¤ect.26

These changes are much larger than those at any non-UC school so the empirical p-values are 0,

indicating that the UC a¢ rmative action ban statistically signi…cantly reduced black admission

24

I use this particular reweighting strategy because empirically at individual non-UC schools, black admission

rates at a given tercile of the black applicant distribution track white admission rates at the same tercile of the

white distribution. Reweighting instead across races and schools on academic strength levels would produce

censored control-group changes because admissions standards vary considerably across races and schools and

admission rates are con…ned to the range [0,1].

25

This assumption does not strictly hold if admissions became more or less responsive to academic credentials,

which I investigate in the next subsection. Any such changes mean that an even greater number of admitted

pre-ban black applicants are predicted to have been rejected under the ban.

26

Appendix Figure 5 repeats Figure 3 for Hispanics. Broadly speaking, Hispanic admission rates display

smaller but still substantial post-minus-pre changes in admission rates, though for Berkeley the observed decline

is larger in later years.





18

rates at UC schools.

(iii) Parametric DDD. I now generate my preferred estimates of the e¤ect of the a¢ rmation

action ban on black admission rates at UC schools, using a parametric DDD design that mirrors

the semi-parametric one above. For UC Berkeley and separately for UCLA, I estimate probit

and OLS models of the form:



Race Race UC P ost

(2) Pr (Admissionist ) = ( 1 Xi + 2 Ii + 3 Xi Ii + 4 Xi Is + 5 Xi It



Race U C Race P ost Race U C Race P ost

+ 6 Ii Is + 7 Ii It + 8 Xi Ii Is + 9 Xi Ii It

U C P ost Race U C P ost

+ 10 Xi Is It + 11 Ii Is It + st )





s

where Admissionist is an indicator for whether applicant {’ application to law school s in

year t earned an o¤er of admission; Xi is a vector containing LSAT score and separately

undergraduate GPA; IiRace is a vector of three race indicators (IiBlack , IiHispanic , and IiAsian );

U

Is C is an indicator for whether school s is the UC school being analyzed; ItP ost is an indicator

for whether application year t lies after the ban; and st is a school-year indicator.27;28 The

coe¢ cient on IiBlack Is C ItP ost is the DDD estimate of the e¤ect of the a¢ rmative action ban

U





on the black admissions advantage over whites with comparable credentials; I scale this to an

admission rate e¤ect below. Because some non-UC schools received more applications than

others, I weight applications so that each school carries equal weight in each time period (pre-

ban and post-ban) in the regressions. I cluster standard errors at the applicant level.

Table 2 displays the results in percentage point units. Column 4 contains my preferred

estimates: the probit marginal e¤ect averaged over the pre-ban black applicants to the UC

school. This speci…cation indicates that the ban reduced the black admissions advantage over

comparably-credentialed whites by 46 percentage points at UC Berkeley and 42 percentage

points at UCLA. The t-statistics are over eight and four, respectively. Column 6 shows that

the marginal e¤ect for an applicant with LSAT and GPA equal to the mean of pre-ban black

applicants at each school was -60 percentage points at Berkeley and -62 percentage points at

UCLA, highlighting how the ban meant the di¤erence between admission and rejection for

27

Considering the school-year indicators, this model includes the full set of two-way and three-way interactions

among the key variables to control for secular trends. Similar to the semi-parametric analysis, for OLS

s s

speci…cations I bin each applicant i’ LSAT and GPA into deciles of each variable’ distribution among pre-ban

s

applicants of i’ race to school s. See footnote 24 for the rationale.

28

Note that this probit speci…cation does not su¤er from the incidental parameters problem because the

asymptotics are over applicants (per school type and time period) and not over school-years which is the

dimension of the …xed e¤ects.





19

marginal black candidates.29;30

Table 3 displays the admission rate that pre-ban black applicants from each UC school

are predicted to have experienced had the ban been e¤ect. For each UC school, I use the

estimated pre-ban coe¢ cients and the UC-school-speci…c post-ban coe¢ cients from equation

(2) to predict the admission probability of each pre-ban applicant.31 I also add a constant to the

probit forcing variable so that the predicted number of admitted applicants (the sum over all

applicants’admission probabilities) equals the actual number. This correction is useful because

a reduction in minority admission rates frees up slots in the admitted cohort and thus permits

admissions to become somewhat less selective overall, and this is the main reason I prefer these

parametric estimates to the semi-parametric ones. Standard errors are non-parametrically

bootstrapped.32

Column 4 shows that the ban reduced black admission rates by 32 percentage points at

UC Berkeley and 29 percentage points at UCLA with t-statistics over 5 and 2.5, respectively.

Column 5 shows that under the monotonicity assumption that the ban would not have caused

any rejected pre-ban black applicants to be accepted, these estimates suggest that 56% of black

applicants who were admitted to UC Berkeley before the ban would have been rejected had

the ban been in e¤ect. For UCLA, the estimate is 44%. These declines were somewhat larger

in the …rst half of the post-ban period than in the second half. The values in column 2 can

be used to calculate that black admission rates under post-ban regimes were still 2.2 to 4.1

times higher than the admission rate that would have prevailed if all pre-ban applicants had

been subject to the pre-ban white admission coe¢ cients. This advantage motivates the next

subsection’ investigation into possible avoidance behavior.33

s

29

Appendix Table 3 presents simple OLS regressions by school type and time period of admission on race,

LSAT, UGPA, and year …xed e¤ects— and thus with no interaction terms. By comparing coe¢ cients in the

…rst row of columns 2-7, one can obtain similar estimates of the change in the black admissions advantage.

30

Appendix Table 4 repeats the speci…cation in Table 2 but divides the post-ban indicator into two— one

indicator for applications submitted in the …rst half of the post-ban period (1996-2000) and another for appli-

cations submitted in the second half (2001-2006)— in order to parallel analysis of admission rule ‡ atness below.

Appendix Table 5 repeats Table 2 and Appendix Table 4 for Hispanics.

31

Algebraically for column 2, I predict admission for all pre-ban applicants using only coe¢ cients 1 and 4 .

For column 4, I use all coe¢ cients except 5 , 7 , and 9 . For columns 6 and 8, I estimate equation (2) except

)

with the post-ban indicator split into two: one for years 1996-2000 (“early post-ban” and the other for years

).

2001-2006 (“late post-ban” For column 6, I then use all coe¢ cients except 5 , 7 , and 9 and the elements

of coe¢ cient vectors 10 and 11 applicable to the late post-ban. I do the same for column 8, except omitting

those applicable to the early post-ban.

32

I draw 25,499 applications (the total number in the sample) with replacement, use this sample to compute

each estimate, repeat the previous two steps 199 times, and compute the standard deviation of each estimate.

33

I make the comparison to pre-ban white admissions standards rather than the post-ban ones because

avoidance can a¤ect both black and white admissions standards.





20

(iv) Potential Bias. The identifying assumption in this DDD design is that any post-minus-

pre di¤erences in the unobserved strength of black applicants relative to white applicants are

not local to UC applicants. Recall from Section II that EALS admissions decisions are largely

determined by observed variables, which narrows the scope for selection bias. Nevertheless I

discuss two possible sources of bias that push in opposite directions. First, black applicants with

relatively low levels of non-academic credentials (e.g. leadership experience) may have selected

out of the UC applicant pool. The reason is that for any given level of academic strength,

post-ban black applicants may have needed stronger non-academic credentials than pre-ban

black applicants to be competitive. This means that the DDD estimates may underestimate

the magnitude of the e¤ect of the ban on black admission rates.

Second, black applicants with a high desire for same-race interactions or for black-friendly

law schools may have declined to apply after the ban, and this characteristic may have been

correlated with leadership experience. I use 287 yearbook entries of black students from the

elite college to estimate the correlation between participation in black-focused extracurricular

s

groups and leadership experience in the college’ black population. I detail the data collection

procedure in Appendix B. Controlling for total extracurricular participation and across several

speci…cations, participation in an additional black-focused group is statistically signi…cantly

associated with additional leadership positions. Thus if black-focused group participation

is a proxy for desire for same-race interactions in school, post-ban black applicants to UC

schools may have had systematically weaker leadership credentials, which means that the DDD

estimates may overestimate the magnitude of the e¤ect of the ban on black admission rates.

These potential sources of bias push in opposite directions.



IV.B Did the UC Ine¢ ciently Avoid the Ban?



Table 3 showed that despite the large decline in black admission rates, post-ban black admis-

sion rates were still two-to-four times the rate that would prevail under the observed pre-ban

admissions standards for whites. Admissions o¢ ce avoidance is a key candidate explanation.

I …rst test for evidence of the ine¢ cient avoidance predicted by standard models. I then ask

whether the key assumption driving ine¢ cient avoidance is supported by the data.

(i) Did Admission Rules Flatten After the Ban? I explained in Section III.D that admission

rule ‡attening (a decline in the responsiveness of admission to academic strength) is a possible







21

outcome of ine¢ cient avoidance. I now present the time series of admission rule ‡atness at UC

Berkeley, UCLA, and non-UC schools. For each of these three groups and in each time period

considered, I estimate the probit regression:



Race

(3) Pr (Admissionist ) = ( 1 ai + 2 Ii + st )





where ai is academic strength, IiRace is a vector of three race indicators (black, Hispanic, and

Asian), and st is a school-year indicator.34 1 measures the average sensitivity of admission to

1 1

academic strength across races, and I de…ne admission rule ‡atness as (:9) = 1, where

is the inverse standard normal CDF. This scaling is arbitrary but visually intuitive: ‡atness is

s

the standard deviations of academic strength needed to raise one’ admission probability from

50% to 90%, illustrated in Figure 4a.

Figure 4b plots ‡atness over time at UC Berkeley, UCLA, and non-UC schools. I divide

the sample into six time periods: two pre-ban (1990-1992 and 1993-1995), two “early”post-ban

(1996-1998 and 1999-2000), and two “late”post-ban (2001-2003 and 2004-2006).35 Admission

rule ‡atness at the average non-UC school changed little over time. At Berkeley, ‡atness was

roughly constant through the pre-ban and early post-ban periods but rose in the late post-ban

period. UCLA shows a similar patter except with a trend of declining ‡atness in the pre-ban

and early post-ban periods. DDD estimates of the change in the responsiveness of admission to

U

academic characteristics (the coe¢ cient on Xi Is C ItP ost from equation 2) con…rm that admission

rules did not ‡atten signi…cantly relative to the mean non-UC school until the late post-ban,

with the signi…cance being marginal at UCLA.36 Considering the full distribution of ‡atness

s atness change from

changes across non-UC schools, empirical p-values indicate that Berkeley’ ‡

s

pre-ban to late post-ban was marginally signi…cant (p = 0:13) and UCLA’ was not signi…cant

(p = 0:60). From early post-ban to late post-ban, the empirical p-values are 0:26 for Berkeley

and 0:20 for UCLA.

In Section IV.C.(ii) I discuss explanations for and implications of possible ‡attening in later

years. For now it su¢ ces to note that there is no evidence of ‡attening in the several years

immediately following the ban, in spite of the fact from Table 3 that black admission rates in

the early post-ban period were substantially higher than the rate that would prevail under the

34

I weight each school equally when estimating the average admission rule at non-UC schools.

35

I can plot more data points here than I did in Figure 3 because this analysis is less data-demanding.

36

See columns 3 and 7 of Appendix Table 6 for these estimates. See the notes to that table for how the

s attening dovetailed a stated policy change.

nature of Berkeley’ ‡





22

observed pre-ban admissions standards for whites.

(ii) Could Post-ban Admissions O¢ ces Still Infer Race? The key technological assumption

of the standard model that generates ine¢ cient avoidance is that a ban prevents admissions

o¢ ces from identifying the race of their applicants and thus from being able to e¢ ciently target

preference to minorities. I now investigate whether the correlation between race and the non-

academic determinants of admission is informative about whether post-ban admissions o¢ ces

could infer race. For simplicity I con…ne the analysis to white and black applicants.

Any set of admissions decisions can be understood as a rank-and-yank admissions process:



(4) ranki = ai + ei



where ai is academic strength, ei is an index of everything else (the “non-academic” determi-

nants of admission, considered as a whole), and the N applicants with the highest ranki are

admitted. Applicants admitted with low ai had high ei . The non-academic index ei includes

the e¤ect of non-academic variables used to admit black applicants (either a pure race variable

or impure racial proxies), as well as non-academic variables that the admissions o¢ ce values for

reasons other than their correlation with race such as recommendation letter strength. I as the

researcher do not observe ranki or ei and instead observe only academic strength ai , the pure

race indicator Iiblack , and the admissions decision. I therefore assume one of two distributional

forms for ei jIiblack , …t it to the data, and use this parameterized distribution to place a structural

s

lower bound on the ability of the admissions o¢ ce’ ability to infer race.

A simple intuition drives the results. De…ne the “black advantage” as the amount of aca-

demic strength that I observe black status to be worth in admissions conditional on academic

strength; visually, this is the average horizontal distance that separates black and white admis-

sion rules in academic strength (e.g. 1.5 standard deviations in Figure 1b). The larger the

black advantage and the lower the admissions noise conditional on ai and Iiblack , the more the

non-academic variables as a whole ei functioned like a pure race variable and thus the more we

know the admissions o¢ ce was able to infer race. While a large black advantage and low noise

imply that the admissions o¢ ce could infer race quite well, a small black advantage combined

with high noise is uninformative about the ability to infer race. The reason is that the latter

admissions process is consistent with the use of a very impure racial proxy, as well as with

the use of a pure race variable together with intrinsically-valued variables like recommendation





23

strength. Thus the magnitudes of the black advantage and noise place a lower bound on the

s

admissions o¢ ce’ ability to infer race. See Appendix Figure 6 for a visual discussion.

This intuition is manifested in my parameterization procedure. After specifying a distribu-

tional form for ei jIiblack , for each UC school and time period I …nd the unique parameterization

that— when drawing ei for all applicants, simulating admissions according the rank-and-yank

process of equation (4), and estimating the following probit regression:



black black

(5) Pr (Admissionit ) = ( 1 ai + 2 Ii + 3 ai Ii + t)





— generates the same coe¢ cients as when the regression is …tted to the actual data.37 This is

equivalent to …nding the unique parameterization of ei jIiblack that reproduces the actual black

advantage and admissions noise for each race. Noise in white admissions decisions is re‡ected

in low 1. Noise in black admissions is re‡ected in low 1 + 3. The black advantage—

the standard deviations of academic strength that being black is observed to be worth in the

average year— is large when 2 is large.38 Appendix Table 7 reports these key values for each

UC school and time period.

I …rst assume ei jIiblack is distributed normally with ei jIiblack ? ai , and then I repeat the

process assuming a Bernoulli distribution. The normality assumption corresponds to the

probit functional form that Figure 1a showed closely approximates semi-parametric within-

race admission rules at top law schools, while the Bernoulli structure facilitates comparison

to the pure race variable available to pre-ban admissions o¢ ces. Because the errors around

a probit forcing variable are distributed standard-normally, equation (5) can be rearranged to

characterize admissions as the rank-and-yank process:

8

1

AA

M RTm;a (pm pn )2









Appendix B: Elite College Yearbook Data

A research assistant compiled a dataset of academic and extracurricular characteristics of

s

black and white students listed in the elite college’ yearbooks. Without being informed of the

s

data’ purpose, the research assistant used only pictures and names to subjectively identify as

many black students as possible in the classes 1991, 1998, and 2004. He identi…ed 287 black

students. He then identi…ed 271 white students by beginning at a randomly chosen student in

each yearbook and searching for white-looking students in regular intervals of printed pictures.

For each selected student, the research assistant used the student-provided information listed in

the yearbook to code …ve variables: whether the student was awarded a GPA-based academic

distinction, the number of total leadership positions she held in extracurricular groups, the

number of groups explicitly dedicated to black issues or culture (“black-focused groups” of )

which she was a member, and the number of leadership positions she held in black-focused

groups.







Appendix C: Algorithm for Finding the Best-…t Bernoulli Values

Let N denote the actual number of applicants admitted at a given school in a given time

period. I use the following algorithm to …nd the unique triplet f ; pw ; pb g that best-…ts the

pattern of actual admissions at the given school and in the given time period. (1) Pool

applicants across years and non-parametrically estimate the density of applicants of each race

at increments of 0.0001 standard deviations of academic strength, using an Epanechnikov kernel

with Silverman bandwidth. (2) For every f ; pw ; pb g permutation at increments of 0.04 for

and 0.01 for pw and pb , draw Si for each race at each level of academic strength, admit the

top N applicants, estimate equation 5 using these simulated admissions decisions to compute

the simulated black advantage and noise for each race for this triplet, and compute the sum

of squared deviations between each of these three simulated values and the actual observed

values listed in Appendix Table 7. (3) Repeat step 2 for the subset of the state space with

sum of squared deviations near zero, using increments of 0.001 for and 0.0025 for pw and pb .

(4) Choose the triplet that produces the sum of squared deviations closest to zero, which in

practice is always less than 0.01. Note that I do not have an analytical result that exactly one

triplet f ; pw ; pb g reproduces the observed admission rules and thus produces a sum of squared

deviations equal to zero, but I always …nd existence and uniqueness in practice. Also note that

I do not consider values of greater than 3; in practice, values of greater than 2.25 produce

strongly counterfactual admission rules.

The particular values of , pw , and pb arrived at depend on the joint distribution of race,

academic strength, and admission in the applicant pool, but qualitative claims can guide in-

tuition for why a particular triplet f ; pw ; pb g reproduces the observed black advantage, white

admission rule noise, and black admission rule noise. A black advantage is generated when the

non-academic variables distinguish between the races and when the non-academic variables are

important in admissions. Thus the larger the black advantage, the larger the di¤erence pw pb

or is. Noise in admissions decisions conditional on race and academic strength is generated

when the non-academic variables di¤er within race and when the non-academic variables are

important in admissions. Thus the larger the noise is for race r, the closer to 0.5 pr is or the

larger is.

To aid visualization, note that the Bernoulli structure produces admission rules that are

step-functions in academic strength, each with three steps. There is a -standard-deviation-

wide range of academic strength in which white applicants are admitted with probability pw and

black applicants are admitted with probability pb . Applicants with academic strength below

this range are admitted with probability zero. Applicants with academic strength above this

range are admitted with probability one. For a given triplet f ; pw ; pb g, exactly one location of

this range in the academic strength distribution is consistent with N applicants being admitted.

APPENDIX FIGURE 1

Distribution of Academic Characteristics By Applicant Race









Notes – This figure displays the distribution of academic characteristics by race among EALS applicants. The sample is

confined to the 94% of EALS applicants who applied to one of the seventeen schools used in the paper. LSAT is the

standardized test score used in law school admissions and ranges from 120 to 180. Undergraduate grade point average is the

cumulative undergraduate GPA on a 4.0 scale. “Academic strength” is a scalar index of the strength of an applicant’s

academic credentials and is constructed as follows. Following Kling, Liebman, and Katz (2007), I first standardize LSAT

and GPA to each have mean zero and standard deviation one across EALS applicants. I then sum the two variables and

divide by the standard deviation to obtain an academic strength index that has mean zero and standard deviation one. See the

next figure and Figure 1a for a demonstration that admission rules can be well-approximated by a univariate probit in

academic strength. Each density is estimated non-parametrically using an Epanechnikov kernel with Silverman bandwidth.

These distributions of academic credentials by race are qualitatively similar to those of undergraduate applicants, such as the

distribution of SAT scores by race among applicants to five selective U.S. colleges (Bowen and Bok 2000 p.20).

APPENDIX FIGURE 2

Scatterplot of 23,128 Admissions Decisions at Non-UC Schools









Notes – This figure is best viewed in color. It plots standardized LSAT score (mean zero and standard deviation one),

standardized GPA, and actual admissions decision for all 23,128 applications to the fifteen most-applied-to non-UC schools.

Each application’s LSAT has been centered by its school-year-race fixed effect from a probit regression of admission on

LSAT and GPA. That is, I estimate Pr Admisssion    LSAT LSAT   GPA GPA   str where  str is the school-year-race

LSAT

fixed effect and then use “centered LSAT” for the plot equal to LSAT   str / . The centering is necessary because

selectivity varies by school-year-race. Overlaid on the plot is the best-fit admission threshold line, with slope equal to the

LSAT GPA

ratio of the LSAT and GPA coefficients from the probit regression:  / . Applications above and to the right of the

line have a predicted admission probability of more than 50% while those below and to the left do not. The best-fit

admission threshold line correctly predicts 85.4% of admissions decisions. The slope of the best-fit line is nearly one,

indicating that a one standard deviation higher LSAT is about as valuable in the admissions cross section as a one standard

deviation higher GPA. I therefore summarize an application’s LSAT and GPA with the scalar index “academic strength,”

equal to the standardized sum (mean zero and standard deviation one) of standardized LSAT and standardized GPA. Figure

1a plots raw admission rates versus this academic strength variable, centered by its school-year-race fixed effect, and

overlays the univariate probit fit.

APPENDIX FIGURE 3

Race and Admission in the Cross Section









Notes – This figure characterizes race and admission in the cross section at the average non-UC school in the average

application year in the EALS. The left half of Panel A displays the density of applicants by academic strength and race.

Specifically, I pool all years within each school-race, estimate each school-race’s density non-parametrically using an

Epanechnikov kernel with Silverman bandwidth, shift each school’s distributions horizontally by a constant so that the white

mode lies at academic strength 0, and then average densities across schools. See the previous figure for the definition of

academic strength. The right half of Panel A plots the average probit-fitted admission rule by race, controlling for

school-year fixed effects and weighting each school-year equally. I shift the admission rules horizontally by a constant so

that the predicted admission probability for whites equals 0.5 at academic strength 0. Panel B displays the simulated

consequences in the EALS of subjecting all applicants to the estimated admission rule for white applicants from Panel A. In

predicting admission, I add a constant to the probit forcing variable so that the predicted number of admitted applicants (the

sum over all applicants’ admission probabilities) equals the actual number. The left half of Panel B displays the

consequences for admission rates by race. The right half illustrates the consequences for the racial composition of admitted

EALS applicants at the average school. I stress that this figure portrays only the correlation between race and admission in

the cross section and not necessarily the causal impact of affirmative action.

APPENDIX FIGURE 4

Raw Nationwide Admissions at UC Law Schools









Notes – These graphs use aggregate data reported by the University of California to plot the time series of overall application

and admission rates by race at UC Berkeley and UCLA law schools. Application year is indexed by the fall of the

application year. These aggregate data contain no information on the academic strength of applicants so they cannot be used

to understand whether the post-ban convergence in black and white admission rates is due to affirmative action or to

selection out of the applicant pool by low-credentialed black applicants who update their beliefs on whether they will gain

admission. Applicant race is collected on application forms; after the ban, the page of the form containing applicant race was

diverted to a UC statistical office and was not reported to admissions offices. I accessed these data on August 27, 2009, from

the website of the University of California Office the President:

http://www.ucop.edu/acadadv/datamgmt/graddata/lawnos.pdf. They are no longer available online but they are available

from the author.

APPENDIX FIGURE 5

Time Series of Admission Rates: Hispanics vs. Whites

DFL-Reweighted on Academic Strength









Notes – This figure replicates Figure 3 for Hispanics. See the notes to that figure for definitions.

APPENDIX FIGURE 6

The Black Advantage, Noise, and the Ability to Infer Race









Notes – This figure illustrates the kinds of admission rules that are informative about an admissions office’s ability to infer

race. Each panel displays a pair of hypothetical black and white admission rules, with equal flatness for simplicity. The

“black advantage” is the amount of academic strength that horizontally separates the white and black admission rules. Noise

conditional on academic strength and race is manifested as flat admission rules. In Panel A, the black advantage is so large

and the noise so low that the non-academic variables as a whole must have correlated strongly with race. If they had not, the

only way the admissions office could have generated a large black advantage was to place a large admissions weight on the

non-academic variables, which would have produced counterfactually flat admission rules. Panel A’s admission rules

therefore indicate that the admissions office could infer race quite well. Panel D illustrates the opposite case of a small black

advantage and high noise; here, the non-academic variables as a whole correlated weakly with race. These admission rules

tell us little about the admissions office’s ability to infer race because the weak correlation could have been generated by

failures to proxy for race (in which case the admissions office could not infer race well) or by a pure race variable used in

conjunction with variables like recommendation letter strength that the admissions office intrinsically values and that may

correlate weakly with race. Panels B and C display intermediate cases which are intermediately informative about the

admissions office’s ability to infer race.

APPENDIX TABLE 1

Application Behavior and Applicant Characteristics in the EALS





A. Application Behavior in the Full EALS Dataset, 1990-2006

Applications per applicant 5.7

Applications per applicant who applied to UC Berkeley or UCLA 7.8

Percent of applications sent to schools ranked 1-10 59%

Percent of applications sent to schools ranked 11-20 20%

Percent of applicants who applied to UC Berkeley 28%

Percent of applicants who applied to UCLA 14%





B. Applications and Applicants in the 17-School EALS Sample Used in the Paper

Applications 25,499

Applicants 5,353

Applications and applicants to UC Berkeley 1,594

Applications and applicants to UCLA 777





C. Mean Applicant Characteristics in the 17-School EALS Sample Used in the Paper and Nationwide

EALS

(sd in parentheses) Nationwide

LSAT 166.2 151.5

(6.7)

GPA 3.43 3.16

(0.33)

White 60.8% 70.9%

Asian 19.4% 7.7%

Black 9.7% 12.4%

Hispanic 10.1% 9.1%

Post-ban 54.8%



Notes - Panel A lists statistics on the application behavior of EALS applicants, using all complete observations (32,627 applications

from 5,692 applicants). The rankings refer to the rankings from the 1998 issue of U.S. News and World Report's "America's Best

Graduate Schools", which ranked UC Berkeley seventh and UCLA seventeenth out of 174 law schools. Panel B lists statistics on

applications submitted to the seventeen schools used in the paper and on the 94% of EALS applicants who submitted at least one

those applications. These schools are UC Berkeley, UCLA, and the fifteen most-applied-to schools that were never subject to an

affirmative action ban; among these, Berkeley received the seventh highest number of EALS applications and UCLA the thirteenth.

Panel C lists mean applicant characteristics. The "EALS" column lists statistics for EALS applicants who applied to at least one of

the seventeen schools used in the paper. The "Nationwide" column lists statistics for all U.S. law school applicants in application

year 2000-2001, the closest available year to the midpoint of the EALS sample. LSAT is the standardized test score used in law

school admissions and ranges from 120 to 180. Undergraduate grade point average is the cumulative undergraduate GPA on a 4.0

scale. Academic strength is a scalar index of the strength of an applicant's academic credentials and is constructed as follows. I

first standardize LSAT and GPA to each have mean zero and standard deviation one across EALS applicants; I then sum the two

variables and divide by the standard deviation to obtain an academic strength index that has mean zero and standard deviation one.

See Figure 1a and Appendix Figure 2 for a demonstration that admissions decisions are well-characterized by a univariate probit in

academic strength. Post-ban is an indicator for the applicant applying to law school in application year 1996-1997 or later. The

9.6% of EALS applicants who do not report race or list their race as American Indian/Alaskan Native, Canadian Aboriginal, or Other

are omitted from EALS statistics in this table and all analyses. The corresponding 7.9% of U.S. applicants are omitted from the U.S.

applicant race percentages as well.

APPENDIX TABLE 2

Semi-Parametric DDD Estimates of the Effect of the Ban on Black Admission Rates

DFL-Reweighted on Academic Strength







Admission Rates at Non-UC Schools

Pre-ban Post-ban Difference (pp)

White 40.6% 46.1% 5.5

Black 61.2% 63.0% 1.9

Difference (pp) 20.6 16.9 -3.6





Admission Rates at UC Berkeley

Pre-ban Post-ban Difference (pp)

White 31.0% 33.9% 2.9

Black 56.7% 26.0% -30.6

Difference (pp) 25.7 -7.9 -33.6



DDD estimate (percentage points): -29.9

DDD estimate, as % of pre-ban black admission rate: -52.8%





Admission Rates at UCLA

Pre-ban Post-ban Difference (pp)

White 48.0% 60.1% 12.2

Black 64.5% 32.4% -32.1

Difference (pp) 16.6 -27.7 -44.3



DDD estimate (percentage points): -40.7

DDD estimate, as % of pre-ban black admission rate: -63.0%



Notes - This table constructs semi-parametric difference-in-differences-in-differences estimates of the change

in black admission rates at UC law schools. Each pre-ban admission rate is an actual admission rate. Each

post-ban admission rate is a reweighted estimate of the admission rate that pre-ban applicants of each race

and school are predicted to have experienced after the ban. See the notes to Figure 3 for details on how this

reweighting was done and why it is essential. The differences in the DDD are between pre-ban and post-ban

periods, UC and non-UC schools, and black and white races. The non-UC schools are the fifteen most-

applied-to schools in the EALS that were never subject to an affirmative action ban. This DDD mechanically

overestimates the magnitude of the effect of the ban on black admission rates because a decline in black

admission rates opens up space in the admitted cohort for more members of all races; I adjust for this

parametrically in Table 3. Under the monotonicity assumption that the ban would not have caused any

rejected pre-ban black applicants to be accepted, the DDD estimate as a percentage of the pre-ban black

admission rate represents the percentage of admitted pre-ban blacks at each school that are predicted to

have been rejected had the ban been in effect.

APPENDIX TABLE 3

Race and Admission by School and Time Period





Dependent Variable: Admission

Non-UC Non-UC UC Berkeley UCLA

All Years Pre-ban Post-ban Pre-ban Post-ban Pre-ban Post-ban

(pp) (pp) (pp) (pp) (pp) (pp) (pp)

(1) (2) (3) (4) (5) (6) (7)



Black 60.0 64.2 56.4 77.4 31.9 64.7 19.0

(1.5) (2.0) (2.0) (5.5) (4.8) (7.6) (7.9)



Hispanic 25.9 27.0 24.8 48.0 21.1 30.2 3.1

(1.5) (2.5) (1.8) (6.0) (3.9) (8.4) (5.4)



Asian 2.2 4.1 -0.1 8.2 2.6 8.1 3.3

(1.0) (1.4) (1.4) (3.4) (3.1) (4.5) (4.2)



LSAT (mean=0, sd=1) 24.0 22.8 25.2 24.2 17.5 28.1 28.9

(0.5) (0.7) (0.6) (1.7) (1.4) (2.2) (2.0)



GPA (mean=0, sd=1) 21.5 23.4 19.9 22.3 21.6 20.2 19.3

(0.6) (0.8) (0.9) (1.9) (1.6) (2.4) (2.1)



N (applications) 23,128 9,922 13,206 651 943 347 430

Clusters (applicants) 5,254 2,374 2,880 651 943 347 430

R-squared 0.447 0.444 0.450 0.441 0.363 0.497 0.525



Notes - This table reports coefficient estimates in percentage point units from OLS regressions of

admission on race, LSAT score, undergraduate GPA, and school-year fixed effects. The non-UC schools

are the fifteen most-applied-to schools in the EALS that were never subject to an affirmative action ban.

LSAT and GPA are each standardized across all EALS applicants to have mean zero and standard

deviation one. Some schools received more applications than others so I weight applications by school in

columns 1-3. Standard errors are clustered at the applicant level.

APPENDIX TABLE 4

Parametric DDD Estimates of the Effect of the Ban on the Black Admissions Advantage

Pre-ban vs. Early Post-ban vs. Late Post-ban





Dependent Variable: Admission

Probit Probit

(avgerage marginal (marginal effect at pre-

OLS effect) ban average)

(pp) (pp) (pp) (pp) (pp) (pp)

(1) (2) (3) (4) (5) (6)



A. Berkeley

Black × Early post-ban -45.8 -38.0 -43.1 -42.7 -60.4 -60.6

(8.2) (8.7) (6.0) (6.8) (9.3) (9.3)

Black × Late post-ban -41.0 -34.8 -48.3 -46.5 -61.1 -61.1

(7.2) (7.9) (4.9) (5.5) (9.4) (9.3)



Nat'l trends differenced out x x x



N (applications) 1,594 24,722 1,594 24,722 1,594 24,722

Clusters (applicants) 1,594 5,324 1,594 5,324 1,594 5,324





B. UCLA

Black × Early post-ban -38.8 -31.6 -29.6 -28.0 -49.5 -47.4

(14.8) (15.0) (16.9) (18.1) (25.2) (27.7)

Black × Late post-ban -47.7 -42.0 -48.5 -46.0 -66.2 -65.1

(12.7) (12.7) (8.9) (9.5) (12.0) (12.6)



Nat'l trends differenced out x x x



N (applications) 777 23,905 777 23,905 777 23,905

Clusters (applicants) 777 5,300 777 5,300 777 5,300



Notes - This table replicates Table 2, except the post-ban indicator is now split into an indicator for the first half of the post-

ban period (1996-2000, "early post-ban") and an indicator for the second half (2001-2006, "late post-ban"). See the notes

to Table 2 for definitions and specifications.

APPENDIX TABLE 5

Parametric DDD Estimates of the Effect of the Ban on the Hispanic Admissions Advantage

Pre-ban vs. Post-ban and Pre-ban vs. Early Post-ban vs. Late Post-ban





Dependent Variable: Admission

Probit Probit

(avgerage marginal (marginal effect at pre-

OLS effect) ban average)

(pp) (pp) (pp) (pp) (pp) (pp)

(1) (2) (3) (4) (5) (6)



A. Pre-ban vs. Post-ban: Berkeley

Hispanic × Post-ban -18.7 -15.3 -27.8 -29.2 -29.9 -31.1

(6.9) (6.9) (6.1) (6.1) (7.7) (7.4)



Nat'l trends differenced out x x x



N (applications) 1,594 24,722 1,594 24,722 1,594 24,722

Clusters (applicants) 1,594 5,324 1,594 5,324 1,594 5,324





B. Pre-ban vs. Post-ban: UCLA

Hispanic × Post-ban -26.3 -22.4 -27.9 -27.3 -29.5 -29.6

(9.1) (9.1) (8.1) (8.4) (9.9) (9.9)



Nat'l trends differenced out x x x



N (applications) 777 23,905 777 23,905 777 23,905

Clusters (applicants) 777 5,300 777 5,300 777 5,300





C. Pre-ban vs. Early Post-ban vs. Late Post-ban: Berkeley

Hispanic × Early post-ban -10.2 -10.1 -17.4 -22.1 -21.9 -26.0

(9.0) (9.1) (9.3) (9.3) (10.8) (9.8)

Hispanic × Late post-ban -21.7 -16.5 -30.4 -31.3 -30.9 -32.2

(7.2) (7.3) (6.0) (6.1) (7.7) (7.4)



Nat'l trends differenced out x x x



N (applications) 1,594 24,722 1,594 24,722 1,594 24,722

Clusters (applicants) 1,594 5,324 1,594 5,324 1,594 5,324





D. Pre-ban vs. Early Post-ban vs. Late Post-ban: UCLA

Hispanic × Early post-ban -18.9 -19.4 -20.9 -21.7 -24.4 -25.3

(10.6) (10.6) (12.6) (13.3) (13.3) (13.9)

Hispanic × Late post-ban -29.9 -24.8 -30.0 -29.4 -30.9 -31.2

(10.3) (10.0) (8.4) (8.8) (9.9) (9.9)



Nat'l trends differenced out x x x



N (applications) 777 23,905 777 23,905 777 23,905

Clusters (applicants) 777 5,300 777 5,300 777 5,300



Notes - Panels A and B replicate Table 2 for Hispanics. Panels C and D replicate Appendix Table 4 for Hispanics. See

the notes to those tables for details.

APPENDIX TABLE 6

Effect of the Ban on Admissions Sensitivity to Academic Credentials

Pre-ban vs. Early post-ban and Late post-ban





Dependent Variable: Admission

Berkeley UCLA

(1) (2) (3) (4) (5) (6) (7) (8)



A. Coefficient Estimates

Early post-ban -0.212 -0.222 1.136 1.039

× Academic strength (0.265) (0.287) (0.598) (0.612)



Late post-ban -0.813 -0.885 -0.516 -0.622

× Academic strength (0.248) (0.261) (0.364) (0.370)



Early post-ban × GPA 0.391 0.519 0.825 0.873

(0.244) (0.254) (0.419) (0.424)



Early post-ban × LSAT -0.401 -0.517 0.400 0.215

(0.180) (0.195) (0.420) (0.418)



Late post-ban × GPA 0.003 0.161 -0.569 -0.519

(0.204) (0.214) (0.243) (0.246)



Late post-ban × LSAT -0.738 -0.945 0.090 -0.113

(0.164) (0.174) (0.335) (0.338)



National trends differenced out x x x x



N (applications) 1,594 1,594 24,722 24,722 777 777 23,905 23,905

Clusters (applicants) 1,594 1,594 5,324 5,324 777 777 5,300 5,300





B. Implied Admission Rule Flatness

Implied flatness

Pre-ban 0.549 0.547 0.503 0.510

Early post-ban 0.604 0.607 0.339 0.347

Late post-ban 0.851 0.923 0.662 0.763



Difference: Early post vs. pre 0.055 0.060 -0.164 -0.163



Difference: Late post vs. pre 0.302 0.376 0.159 0.253



Notes - This table presents coefficient estimates on academic credentials from the DD and DDD probit regressions underlying

columns 3 and 4 of Table 2, which is equation (2) in the text. See the notes to that table for details. The only difference in the

specifications is that in the odd-numbered columns, GPA and LSAT are replaced by academic strength. See Table 1 for the

definition of academic strength. Statistics in Panel A are raw probit coefficients and represent the effect of a unit increase of the row

variable on the probit forcing variable. Statistics in Panel B are in units of admission rule flatness, equal to the standard deviations of

academic strength needed to raise one's admission probability from 50% to 90%; see the notes to Figure 4a for an illustration and

Section IV.B.(i) for the simple algebraic expression. Note that column 4 of Panel A shows that Berkeley's flattening was driven by

admissions decisions becoming less responsive to LSAT scores and that this change began in the early post-ban period. This result

dovetails a stated policy change. In 1997 UC Berkeley began to bin applicants' LSAT scores into intervals and reported to the

admissions committee only the interval and not the actual score, which mechanically added noise to the score (source: 1998

Berkeley Law press release, http://berkeley.edu/news/media/releases/98legacy/08-17-1998.html, last accessed February 28, 2011).

APPENDIX TABLE 7

Black Advantage and Admission Rule Flatness at UC Schools over Time





White Admission Black Admission

Statistic: Black Advantage Rule Flatness Rule Flatness

(1) (2) (3)



A. Pre-ban (1990-1995)

Berkeley 1.93 0.46 0.61

UCLA 1.55 0.31 0.57





B. Early Post-ban (1996-2000)

Berkeley 0.97 0.61 0.42

UCLA 0.66 0.23 0.38





C. Late Post-ban (2001-2006)

Berkeley 0.69 0.75 1.01

UCLA 0.32 0.47 1.19



Notes - For each UC school and time period, this table lists the three inputs to the corresponding row in Table

4. The units are standard deviations of academic strength. Each row's values derive from restricting the

sample to black and white applicants to the given UC school in the given time period and estimating equation

(5): a probit regression of admission on academic strength, a black indicator, the interation of academic

strength and the black indicator, and year fixed effects. The "black advantage" is the average amount of

academic strength that being black is observed to be worth in admissions, conditional on academic strength.

This is simply the average horizontal distance that separates the black and white admission rules in academic

strength. See Section IV.B.(ii) for the analytic formula. White admission rule flatness is defined as in Figure 4a

and is the standard deviations of academic strength needed to raise a white applicant's admission probability

from 50% to 90%. It equals Φ-1(.9)/β1 , where β1 is the coefficient on academic strength in equation (5).

Flatness is defined similarly for black applicants and equals Φ-1(.9)/(β1 +β3 ), where β3 is the coefficient on the

interaction of academic strength and the black indicator in equation (5). These values correspond to the means

and variances of the parameterized normal distributions for ei|Iiblack listed in the text.

APPENDIX TABLE 8

Race, College Leadership, and Law School Outcomes in the Cross Section





Graduation Bar Passage

Dependent Variable: College Law School (avg. marginal (avg. marginal

Leadership GPA Graduation effect) Bar Passage effect)

(# positions) (sd) (pp) (pp) (pp) (pp)

(1) (2) (3) (4) (5) (6)



Black 0.381 -1.116 0.14 0.05 -5.22 -5.33

(0.082) (0.100) (1.77) (2.10) (2.94) (3.42)



N 558 1,450 1,974 1,974 1,974 1,974



Mean of Dep. Var. 0.914 0.062 96.54 96.54 89.56 89.56

SD of Dep. Var. 0.981 0.947 18.29 18.29 30.59 30.59



Notes - This table uses yearbook entries from the elite college and the Law School Admissions Council Bar Passage Study to

inform discussion of the strength of unobservable variables across races in the EALS. Column 1 uses self-reported data from

a sample of entries from three years of the elite college's yearbooks, detailed in Appendix B. It reports a coefficient estimate

from a regression of the number of college leadership positions on a black indicator, an indicator for a GPA-based honor, and

year dummies. Leadership positions is censored at three because of outliers; the coefficient is slightly larger without

censoring. Columns 2-6 use the Law School Admissions Council Bar Passage Study sample of 2,003 black or white

matriculants in the fall 1991 entering classes at top-50 U.S. law schools. The Law School Admissions Council normalized law

school GPA to have mean zero and standard deviation one within law schools. In an attempt to adjust GPA by law school

quality, they then added a constant to each law school's standardized GPAs equal to the school's mean deviation of

standardized GPA from expected GPA using a pooled regression of law school GPA on LSAT and undergraduate GPA. Law

school graduates must pass a state bar exam before they can practice law. Each regression in columns 2-6 includes three

covariates: a black indicator, LSAT, and undergraduate GPA. The data do not contain the undergraduate school attended.

Marginal effects reported in columns 4 and 6 are averaged over black matriculants. The LSAC BPS data can be accessed at

http://www2.law.ucla.edu/sander/Systemic/Data.htm or through a request to LSAC at

http://www.lsac.org/LSACResources/Research/RR/Wightman-LSAC-98.asp.