Students for Fair Admissions, Inc. v. President and Fellows of Harvard College et al

Filing 450

AMICUS BRIEF filed by Amici Curiae Economists Michael Keane et al., in Support of Students for Fair Admissions . (Attachments: # 1 Exhibit)(Clark, Randall)

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 1 of 24

IN THE UNITED STATES DISTRICT COURT
FOR THE DISTRICT OF MASSACHUSETTS
BOSTON DIVISION

STUDENTS FOR FAIR ADMISSIONS, INC.,
Plaintiff,
v.

Civil Action No. 14-14176 (ADB)

PRESIDENT AND FELLOWS OF
HARVARD COLLEGE,
Defendant.

BRIEF OF ECONOMISTS MICHAEL P. KEANE, HANMING FANG,
YINGYAO HU, GLENN C. LOURY, AND MATTHEW S. SHUM
AS AMICI CURIAE IN SUPPORT OF STUDENTS FOR FAIR ADMISSIONS
Randall B. Clark BBO # 657560
80A West Hollis Road
Hollis, NH 03049
603-801-3039
[e-mail]
C. Boyden Gray*
Andrew R. Varcoe*
Adam R.F. Gustafson*
James R. Conde*
BOYDEN GRAY & ASSOCIATES
801 17th Street NW, Suite 350
Washington, DC 20006
202-955-0620
[e-mail]
* Pro hac vice admission pending

July 30, 2018

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 2 of 24

TABLE OF CONTENTS
TABLE OF CONTENTS ................................................................................................. i
TABLE OF AUTHORITIES ......................................................................................... iii
INTEREST OF AMICI CURIAE ................................................................................... 1
INTRODUCTION AND SUMMARY OF ARGUMENT ............................................... 1
ARGUMENT .................................................................................................................. 3
I.

HARVARD’S PERSONAL-RATING SCORES ARE SIGNIFICANTLY BIASED AGAINST
ASIAN AMERICANS ................................................................................................ 3
A.

Dr. Arcidiacono persuasively shows that Harvard’s personal-rating
scores are biased against Asian Americans ............................................ 3

B.

Dr. Card’s alternative explanation for Asian Americans’ lower
personal-rating scores is unsupported and unpersuasive ...................... 7
1. Dr. Card fails to identify missing data that could explain the racial
disparity in the personal-rating scores .............................................. 8
2. Dr. Card’s claim that Asian Americans perform worse on nonacademic dimensions than whites is wrong and cannot explain the
racial disparity in the personal-rating scores .................................. 10
3. Dr. Card fails to explain the disparity between Harvard’s personalrating scores and alumni personal-rating scores for Asian
Americans .......................................................................................... 11
4. Dr. Card’s claim of selective reasoning is mistaken ........................ 12

II.

DR. ARCIDIACONO CORRECTLY CONCLUDES THAT INTERACTIONS BETWEEN RACE
AND “DISADVANTAGED” STATUS SHOULD BE INCLUDED IN HIS MODEL ................. 14
A.

B.
III.

Ignoring racial disparities in Harvard’s treatment of “disadvantaged”
applicants undercounts the number of Asian Americans who would be
admitted absent discrimination............................................................. 14
Dr. Card errs in arguing for ignoring racial disparities in Harvard’s
treatment of “disadvantaged” applicants .............................................. 15

DR. ARCIDIACONO CORRECTLY CONCLUDES THAT SPECIAL-RECRUITING-CATEGORY
APPLICANTS, WHO ARE NOT SIMILARLY SITUATED TO OTHER APPLICANTS, SHOULD
BE EXCLUDED FROM THE SAMPLE IN HIS MODEL .................................................. 16

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 3 of 24

CONCLUSION............................................................................................................. 19

ii

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 4 of 24

TABLE OF AUTHORITIES
Page(s)

CASES

Boykin v. Georgia-Pacific Corp.,
706 F.2d 1384 (5th Cir. 1983) ................................................................................ 13
Sobel v. Yeshiva Univ.,
839 F.2d 18 (2d Cir. 1988) ........................................................................................ 8
OTHER MATERIALS
Gregory C. Chow, Tests of Equality Between Sets of Coefficients in Two Linear
Regressions, 28 Econometrica 591 (1960) ........................................................... 18
The Economist, A Lawsuit Reveals How Peculiar Harvard’s Definition of Merit Is
(Jun. 23, 2018) ..................................................................................................... 13
Federal Judicial Ctr. & Nat’l Research Council, Reference Manual on Scientific
Evidence (3rd ed. 2011)................................................................................. 7-9, 15
Bo Hu et al., Pseudo-R2 in Logistic Regression Model,
16 Statistica Sinica 847 (2006) .............................................................................. 8
Daniel McFadden, Quantitative Methods for Analyzing Travel Behaviour of
Individuals: Some Recent Developments (Nov. 22, 1977)..................................... 9

iii

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 5 of 24

INTEREST OF AMICI CURIAE 1
Amici—Dr. Michael P. Keane of the University of New South Wales; Dr.
Hanming Fang of the University of Pennsylvania; Dr. Yingyao Hu of Johns Hopkins
University; Dr. Glenn C. Loury of Brown University; and Dr. Matthew S. Shum of
the California Institute of Technology—are leading economists and econometrics
scholars who have extensively studied and written about discrete choice modeling
and econometrics tools of the kind used by the experts in this case and are
professionally interested in the proper use of such tools. Amici are of the view that
the statistical model used by the plaintiff’s expert in this case is methodologically
sound. Biographies of amici are summarized in Exhibit A to this brief.
INTRODUCTION AND SUMMARY OF ARGUMENT
Amici write to address three central statistical issues.
First, Harvard’s Office of Admissions consistently rates competitive AsianAmerican applicants as having lower “personal ratings.” Students for Fair
Admissions (SFFA) argues that these rating scores are biased against Asian
Americans. Harvard disputes this claim, speculating that unknown, unobservable
data could perhaps explain the remarkable racial disparity in the scores. Our

Counsel for amici curiae state that (1) this brief was authored by counsel for amici
curiae and not by counsel for any party, in whole or in part; (2) no party or counsel
for any party contributed money that was intended to fund preparing or submitting
the brief; and (3) apart from amici curiae and their counsel, no person contributed
money that was intended to fund preparing or submitting the brief. Institutional
affiliations of amici are provided for identification purposes only.

1

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 6 of 24

review of the publicly available expert reports supplied by the parties’ experts—Dr.
Peter Arcidiacono, for the plaintiff, and Dr. David Card, for the defendant—leads us
to agree with Dr. Arcidiacono’s conclusion that the personal rating is biased. The
disparity is striking. For example, Asian-American applicants in the top academic
decile are less likely to receive a high personal-rating score than white applicants in
the top 50%. This remarkable racial disparity does not appear in the personal
ratings given by alumni who actually interview applicants. Dr. Card offers no
plausible, non-discriminatory explanation for this stark disparity.
Second, Dr. Card argues that SFFA should have ignored racial disparities in
how Harvard treats students whom it designates as socio-economically
“disadvantaged.” This argument is unpersuasive. In seeking to explain the effect of
race in admissions, it makes sense to account for how Harvard treats
“disadvantaged” applicants of different races. Failing to account for this disparate
treatment would obscure the magnitude of Harvard’s bias against Asian Americans.
Third, Dr. Card argues that it was unreasonable to exclude applicants in
special recruiting categories—recruited athletes, “legacy” applicants, specially
selected “Dean’s List or Director’s List” applicants, and children of Harvard faculty
and staff—from consideration in Dr. Arcidiacono’s preferred model. We disagree.
The special-category applicants receive personalized attention from Harvard that is
not afforded to others. The unusual treatment afforded to these individuals provides

2

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 7 of 24

a reasonable justification for excluding them from the model. 2
ARGUMENT
I.

HARVARD’S PERSONAL-RATING SCORES ARE SIGNIFICANTLY BIASED AGAINST
ASIAN AMERICANS.
A.

Dr. Arcidiacono persuasively shows that Harvard’s personalrating scores are biased against Asian Americans.

To support its argument that Harvard discriminates against Asian
Americans in the admissions process, SFFA relies on a logistic regression model by
Professor Peter Arcidiacono, based on his review of six years of admissions data. See
Expert Report of Peter S. Arcidiacono, Doc. 415-1, Ex. A (Arcidiacono Report). To
ascertain the effect of race on admissions, the model controls for applicant
characteristics correlated with Harvard’s admission decisions, including academic
performance, extracurricular activity, teacher and school-counselor
recommendations, and alumni-interview ratings. See id. at 62 (Model 5). Using his
model, Dr. Arcidiacono finds clear evidence of bias against Asian Americans. See id.
at 65. His methodology and findings are sound.
Importantly, Dr. Arcidiacono’s preferred model excludes Harvard’s “personal
rating” because, he argues, the personal-rating scores are tainted with racial bias

Amici also agree that it was reasonable for Dr. Arcidiacono to pool data for all six
years together, instead of annually. This brief does not further address that issue,
which seems to make little difference to the result.

2

3

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 8 of 24

against Asian Americans. 3 This is sound. If these scores are biased, then a model
that controls for such scores would mask the true effect of race on admission
decisions. Id. at 19. As Harvard’s expert, Professor David Card, concedes, “it is a
well-accepted practice to exclude variables from a regression model that may
themselves be directly influenced by the variable of interest (here, race).” Report of
David Card, Doc. 419-33, Ex. 33 at 10 (Card Report).
This issue is critical. The inclusion or exclusion of the personal rating has the
largest effect of any modeling decision on the estimated degree of discrimination
against Asian-American applicants. Rebuttal Report of David Card, Doc. 419-37,
Ex. 37 at 55, Ex. 13 (Card Rebuttal). If the personal rating is biased, then all of the
sensitivity analyses performed by Dr. Card to confirm that there is no evidence of
discrimination are invalid, for they all include the personal rating. Id. at 53–64.
Dr. Arcidiacono examines whether non-racial factors can explain Asian
Americans’ lower personal-rating scores. He reasonably concludes that they cannot.
See Arcidiacono Report 55. If Harvard treated Asian Americans as it treats whites,
his model predicts that Asian-American applicants’ probability of receiving a high
personal score “would have increased by over three percentage points, reflecting a

It appears that Harvard provides no objective standards for how to determine this
opaque rating. Arcidiacono Report 37–38. Admissions officers have testified that
they seek applicants with a “positive personality,” including “character traits” such
as “likeability, helpfulness, courage and kindness” and whether the applicant is an
“attractive person to be with,” is “widely respected,” is a “good person,” and has good
“human qualities.” See SFFA SMF, Doc. 414 ¶ 90; Harvard SMF, Doc. 420 ¶ 60.
3

4

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 9 of 24

20% increase[d] chance of receiving a 2 or better.” Id. at 57; see id. at 5, 20, 36, 38
(further discussing significance of rating scale of 1 to 6 (lowest being best)).
Several highly suspect patterns in the observed data support the conclusion
that Harvard’s personal-rating scores are biased against Asian Americans.
First, Asian-American applicants to Harvard are highly competitive relative
to other applicants in all observable academic and non-academic measures that
affect admission decisions except Harvard’s personal rating. On the whole, AsianAmerican applicants clearly outperform other applicants in the academic measures.
Arcidiacono Report 36–37. As to non-academic measures, Asian Americans have
scores similar to whites’ scores, and generally higher than African Americans’ and
Hispanics’ scores, with two exceptions: the athletic rating (which is not correlated
with a significantly increased chance of admission outside the special category of
recruited athletes) and the personal rating. Id. at 37; see Rebuttal Expert Report of
Peter S. Arcidiacono, Doc. 415-2, Ex. B at 29, Table 3.1N (Arcidiacono Rebuttal).
Second, applicants with stronger academic ratings tend to have higher nonacademic ratings across all dimensions, regardless of race. Arcidiacono Report 47–
48. But for the personal rating, this correlation is exceptionally weak for AsianAmerican applicants. Inexplicably, the most academically competitive Asian
Americans do much worse in Harvard’s personal-rating score than do academically
similar applicants of other races. Id. at 49–50. As is shown in Figure 1 below, AsianAmerican applicants in the very top academic decile (the top 10%) are less likely to
receive a good personal-rating score (2 or lower, lowest being best) than whites in

5

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 10 of 24

the top five deciles (the top 50%), Hispanics in the top six deciles (the top 60%), and
African Americans in the top eight deciles (the top 80%). This striking pattern is not
replicated in other measures used by the Office of Admissions: the academic rating,
extracurricular rating, alumni personal rating, teacher letter scores, and highschool counselor scores. In other words, personal-rating scores make the topperforming Asian-American applicants less competitive while making other topperforming applicants more competitive. This matters, because only applicants that
have a 2 or better on both the personal-rating and the academic-rating scores are
likely to gain admission. Arcidiacono Report App’x A Table A.8.

Share Receiving a 2 or Better in the Personal Rating Score
50.00%
45.00%
40.00%
35.00%
30.00%
25.00%
20.00%
15.00%
10.00%
5.00%
0.00%

Top 10% 10 to 20% 20 to 30% 30 to 40% 40 to 50% 50 to 60% 60 to 70% 70 to 80% 80 to 90% 90 to 100%

Academic Decile
African American

Hispanic

White

Asian American

Figure 1: Data Taken from Arcidiacono Report 49, Table 5.6

Relatedly, the personal-rating scores are suspiciously sorted by race. “In every
academic decile, African Americans have the highest share [of applicants] scoring a
2 or better on the personal rating, followed by Hispanics, then whites, then Asian

6

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 11 of 24

Americans.” Id. at 49 (emphasis added). 4 This racial pattern—not present for other
ratings—strongly suggests that Harvard puts significant weight on race in
assigning personal ratings.
Third, this disparity does not appear in the separate personal ratings given
by alumni who interview Asian-American applicants. Notably, Admissions Office
staff—unlike alumni—meet with only a very small fraction of applicants. 5 Although
there is also “some racial disparity in the alumni personal rating, it is less than half
of the disparity” in the Harvard personal rating. Arcidiacono Report 50. In sum, the
evidence strongly suggests that the Harvard personal ratings are racially biased.
B.

Dr. Card’s alternative explanation for Asian Americans’ lower
personal-rating scores is unsupported and unpersuasive.

To defend Harvard’s personal ratings against compelling evidence of bias, Dr.
Card invokes the possibility of “omitted-variable bias.” Card Report 70. In essence,
he speculates that something other than race could cause the apparent racial bias
in these ratings. Dr. Card suggests that unspecified “missing data” that are not
observed in any of the summary statistics could explain away this apparent bias. Id.
Dr. Card’s appeal to unknown missing data is unpersuasive. When
“alternative explanations” are “less plausible than the proposed causal link,” they
do not rebut an inference of causality. Federal Judicial Ctr. & Nat’l Research

The only exception to the pattern is shown in the “80 to 90%” decile in Figure 1
(above), in which whites do a bit worse than Asian Americans. See id. Table 5.6.

4

Harvard staff interviews only 2.2% of all applicants, and only 1.2% of all AsianAmerican applicants. Arcidiacono Rebuttal 66.
5

7

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 12 of 24

Council, Reference Manual on Scientific Evidence 221 (3rd ed. 2011) (Reference
Manual). Under accepted econometric practice, an objection of omitted-variable bias
should be accepted only when it is shown that the missing variable (1) “is a
determinant” of the outcome and (2) also correlates with race, “and thus is likely to
cause a demonstrable, rather than an assumed, [omitted-variable] bias.” Sobel v.
Yeshiva Univ., 839 F.2d 18, 36 (2d Cir. 1988). Here, it is unreasonable to infer that
“missing data” could be causing the racial disparities in personal-rating scores. No
plausible, non-discriminatory reason explains why Harvard rates Asian-American
applicants as less personally appealing than applicants in other racial groups.
1. Dr. Card fails to identify missing data that could explain the
racial disparity in the personal-rating scores.
At first, Dr. Card asserted that the regression model finding bias in
Harvard’s personal rating is “poorly fitted” (has a low “McFadden” R2 value). Card
Report 69–70. 6 If true, this would be an important criticism. “Fit” essentially
measures how well the model’s predictions explain the actual personal-rating
scores. The less the model explains the actual scores, the more plausible it is that
the model is ignoring an alternative explanation for the scores.
Generally, R2 “measures the percentage of variation in the dependent variable
[the personal-rating scores] that is accounted for by all the explanatory variables.”
Reference Manual 345. Typical linear models used to predict continuous outcomes
(outcomes that can take any numerical value) use a standard R2 statistic. Different
R2 statistics with different technical definitions can be used in logistic regression
(logit) models used to predict discrete outcomes (e.g., admission vs. rejection), like
the one used in this case. See Bo Hu et al., Pseudo-R2 in Logistic Regression Model,
16 Statistica Sinica 847, 847–48 (2006). Good R2 values in logit models are lower
than in linear models, simply because discrete outcomes are less predictable than
continuous outcomes.
6

8

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 13 of 24

But this criticism is mistaken. Dr. Arcidiacono’s model is an “excellent fit” by
accepted academic standards. As the classic reference by the Nobel-Prize-winning
econometrician Daniel McFadden explains, “values of 0.2 to 0.4” for the “McFadden”
R2 statistic are considered “an excellent fit.” Daniel McFadden, Quantitative
Methods for Analyzing Travel Behaviour of Individuals: Some Recent Developments
35 n.** (Nov. 22, 1977), https://bit.ly/2JyWFCX. The R2 value that Dr. Card claims
is a “poor” fit is 0.28, well “within the range characterizing an ‘excellent’ fit.”
Arcidiacono Rebuttal 23.
Dr. Card’s rebuttal report abandons his original criticism and states that Dr.
Arcidiacono “misses the broader point.” Card Rebuttal 20. Dr. Card’s “broader
point” is that “even a model that has a relatively” good fit “may suffer from omitted
variable bias in estimating the effect of Asian-American ethnicity” on the personal
ratings. Id. (emphasis added). This is theoretically true, but it does not advance a
plausible non-discriminatory explanation for the racial disparity in scores.
In this case, context makes clear that missing data are very unlikely to be
causing the disparity. 7 It is not apparent what other data could be missing; Dr.
Card provides no plausible hypothesis as to what data could be missing. He notes
that “the model is missing an assessment of the applicant’s personal essay” and
support letters “from figures like research supervisors or extracurricular

As explained in the Reference Manual on Scientific Evidence, “the inference that
one makes from a particular value of R2 will depend, of necessity, on the context of
the particular issues under study and the particular dataset that is being analyzed.”
Reference Manual 314 n.31.
7

9

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 14 of 24

instructors.” Id. at 21. But the suggestion that these materials could explain the
racial bias in the personal-rating scores is not reasonable. It requires accepting
without evidence that Asian Americans write less compelling essays than other
applicants, even though Asian Americans’ verbal SAT scores are generally on par
with whites’ scores and higher than the scores of applicants of other races. See
Arcidiacono Report 33. It would require accepting without evidence that Asian
Americans, who have the highest extracurricular-rating scores of any racial group,
have less compelling extracurricular-instructor recommendations than other
applicants. Id. at 36, Table 4.1. If Dr. Card “has any support for why AsianAmerican applicants have weaker personal qualities than other racial groups, he
does not provide it.” Arcidiacono Rebuttal 25 n.12.
2. Dr. Card’s claim that Asian Americans perform worse on
non-academic dimensions than whites is wrong and cannot
explain the racial disparity in the personal-rating scores.
Dr. Card argues that it is plausible that unobservable omitted variables
explain the observed disparity in the personal-rating scores because, he claims,
Asian-American applicants tend to do worse than whites in observable nonacademic dimensions. See Card Rebuttal 27, 30–31. Dr. Card argues that given this
asserted racial disparity in non-academic ratings, “it is entirely plausible that the
unexplained gap in the personal rating reflects differences in unobservable factors
that are missing from the personal ratings regression, rather than racial bias
against Asian-American applicants.” Id. at 27.

10

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 15 of 24

This argument is not persuasive. Contrary to Dr. Card’s assertion, AsianAmerican applicants do better than white applicants in the non-academic index.
Arcidiacono Rebuttal 29, Table 3.1 (panel 4). Dr. Card is able to argue otherwise
only because he includes applicants in certain special recruiting categories —
“athletes, children of faculty and staff, applicants who are on Dean’s List or
Director’s List, and legacies”— in his comparison. Card Rebuttal 30–31. 8 This
biases the non-academic index. Special-category applicants are much more
competitive in non-academic dimensions (e.g., athletic ratings) than all other
applicants. And Asian Americans are significantly underrepresented in this
category. Arcidiacono Report 21–22, 34 & App’x B, Table B.3.2. Including the
special-category applicants in the comparison therefore creates the misleading
impression that regular white applicants do better than regular Asian-American
applicants, when the opposite is true. Arcidiacono Rebuttal 29, Table 3.1 (panel 4).
3. Dr. Card fails to explain the disparity between Harvard’s
personal-rating scores and alumni personal-rating scores
for Asian Americans.
Unlike Harvard’s admissions staff, Harvard alumni do not score AsianAmerican applicants significantly lower than non-Asian-American applicants on the
Dr. Card also attempts to support his argument by referencing broader “academic
literature” “outside the Harvard data” that purports to show that “Asian-American
high school students apply to selective universities at higher rates than students
from other ethnic groups, even after controlling for whether or not a student is
qualified on key academic dimensions.” Id. at 33. But whatever selection effects
apply more generally, this cannot explain the disparity among similarly-situated
applicants. Asian-American applicants to Harvard receive worse personal ratings
than applicants in other groups even though they have stronger academic ratings
and similar or stronger non-academic ratings.
8

11

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 16 of 24

personal rating. Dr. Card attempts to explain the disparity by pointing out that the
ratings are “based on different sources.” Card Report 74. He assumes, dubiously,
that the paper materials considered by Harvard are more reliable indicators of
whether a person is (for example) “likeable” than in-person interviews. Id. But
again, he never explains how personal essays could reveal a trove of “missing data”
justifying the assertion that Asian Americans are less appealing than other
applicants, nor does he explain how Asian Americans could manage to conceal
negative personal attributes during in-person alumni interviews while revealing
them in their carefully composed application materials. Dr. Card’s reliance on
unsupported assumptions is scientifically unsound.
4. Dr. Card’s claim of selective reasoning is mistaken.
Finally, Dr. Card argues that SFFA’s expert has engaged in inappropriately
selective reasoning. Asian Americans perform slightly better in Harvard’s academic
and extracurricular rating scores than one would expect based on measured data
(like SAT scores), and Dr. Arcidiacono suggests that this modest “gap” could be
attributable to missing data. Card Rebuttal, 22. In Dr. Card’s view, if Dr.
Arcidiacono is willing to draw such an inference in favor of Asian Americans, he
must also agree that “missing data” explains the racial disparity disfavoring Asian
Americans in the personal-rating scores. Id.
This argument is premised on a false dichotomy. It makes sense to infer that
missing data may explain the gap favoring Asian Americans in the academic and
extracurricular rating scores relative to their test scores, because Asian Americans

12

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 17 of 24

objectively outperform all other applicants in academic and extracurricular
measures. Arcidiacono Rebuttal 26. It does not make sense to infer that missing
data explains away the much starker racial disparity, disfavoring Asian Americans,
in the subjective personal-rating scores, because no observable data justifies that
inference. (African Americans, Hispanics, and whites do not significantly
outperform Asian Americans in other non-academic rating scores. See supra at 10.)
Moreover, the academic and extracurricular rating scores cannot easily be used to
mask or manifest racial bias, and thus it is reasonable to infer that the gap in the
academic and extracurricular ratings truly reflects missing data in the model, not
manipulation or racial stereotyping. 9 By contrast, the personal-rating score, like
similarly “subjective, standardless” rating methods used by employers, is “a
convenient mechanism for discrimination.” Boykin v. Georgia-Pacific Corp.,
706 F.2d 1384, 1390 (5th Cir. 1983).
In sum, Dr. Card’s report does not provide any plausible explanation for the
racial disparities in the personal-rating scores. Dr. Card’s decision to control for
biased factors like “parents’ occupations and the disputed personal rating” is
“statistically rather like saying that once you correct for racial bias, Harvard is not
racially biased.” The Economist, A Lawsuit Reveals How Peculiar Harvard’s
Definition of Merit Is (Jun. 23, 2018), https://econ.st/2MmJeYx.

For example, one can objectively verify that an applicant not only has high math
SAT scores but won a math or science competition, or that she not only plays the
violin in a school orchestra but plays first violin in an award-winning youth
orchestra outside of school.
9

13

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 18 of 24

II.

DR. ARCIDIACONO CORRECTLY CONCLUDES THAT INTERACTIONS BETWEEN
RACE AND “DISADVANTAGED” STATUS SHOULD BE INCLUDED IN HIS MODEL.
A.

Ignoring racial disparities in Harvard’s treatment of
“disadvantaged” applicants undercounts the number of Asian
Americans who would be admitted absent discrimination.

In general, “disadvantaged” applicants are more likely to gain admission to
Harvard than other applicants. See Arcidiacono Report 34. 10 But for AfricanAmerican applicants, “there is no added benefit from being disadvantaged,” id. at
64; for Hispanic applicants, the preference from disadvantaged status is quite
modest. Id. This disparate treatment of disadvantaged students can reasonably be
explained as follows: Harvard already gives such strong preferences to AfricanAmerican and Hispanic applicants in other ratings, such as the personal and overall
rating scores, that it sees no need to grant a significant additional preference to
disadvantaged members of these groups. See id.; Arcidiacono Rebuttal 20-21.
This disparity has important technical consequences for how Harvard’s
admission process should be modeled for purposes of determining the presence or
absence of discrimination against Asian Americans. Ignoring the fact that AfricanAmerican and Hispanic applicants get little or no admission preference from being
disadvantaged “weakens the effect of disadvantage as an explanatory term.”
Arcidiacono Rebuttal 20. And “because more Asian-American applicants than white
applicants are disadvantaged, the weaker [perceived] effect of disadvantaged status

Socio-economically “disadvantaged” status is assigned by the Office of
Admissions “based on information they receive about the high school, neighborhood,
or other facts volunteered by the applicant.” Id.
10

14

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 19 of 24

in turn . . . [tends] to conceal the magnitude of discrimination against AsianAmericans.” Id. at 20–21. Unless the statistical model accounts for the racial
disparity in Harvard’s treatment of disadvantaged applicants, the model will
underestimate the rate at which Asian Americans should have been admitted
(absent racial discrimination) relative to whites. Id. at 20. Hence, the model will
underestimate the degree of discrimination against Asian Americans.
The universally accepted solution to this problem is to add an “interaction
term” to the statistical model. Here, this means an additional variable that accounts
for the effect of disadvantaged status in admissions as it differs by race. See
Reference Manual 316–17. 11 As the Reference Manual on Scientific Evidence
admonishes, “[i]t is especially important to account for interaction terms that could
affect the determination of discrimination; failure to do so may lead to false
conclusions concerning discrimination.” Id. at 317. Indeed, a failure to control for
this racial disparity in the model would lead to erroneous conclusions, significantly
undercounting the number of Asian Americans who would be admitted relative to
whites. Dr. Arcidiacono reasonably and correctly accounts in his model for the racial
disparities in how Harvard treats disadvantaged students.
B.

Dr. Card errs in arguing for ignoring racial disparities in
Harvard’s treatment of “disadvantaged” applicants.

Arguing that Dr. Arcidiacono should have ignored these racial disparities, Dr.
Card states that “[s]ince there are hundreds of potential interactions one could add
An interaction term “is the product of two other variables that are included in the
multiple regression model.” Id. at 316.
11

15

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 20 of 24

to the model, and it is not computationally feasible to include them all, it is unclear
why” Dr. Arcidiacono chose to add this interaction. Card Report 49. Dr. Card
suggests that this choice was not “guided by a clear . . . methodological goal.” Id.
This suggestion is not persuasive.
Ignoring the effect of race on the effect of disadvantaged status would lead to
erroneous predictions for the explanatory variable of interest: race. In a model that
seeks to explain the effect of race on admissions, it is methodologically appropriate
to control for racial disparities. Indeed, Dr. Card agrees with this principle. He
acknowledges that “an interaction between race and disadvantaged status” should
be added “if the effect of being disadvantaged is different for Asian-American and
White applicants.” Card Report 49. But he has no explanation for why disparities
should be ignored when the effect of being disadvantaged is different for African
Americans and Hispanics, as compared against Asian Americans and whites. No
such explanation exists. See Arcidiacono Rebuttal 20–21.
III.

DR. ARCIDIACONO CORRECTLY CONCLUDES THAT SPECIAL-RECRUITINGCATEGORY APPLICANTS, WHO ARE NOT SIMILARLY SITUATED TO OTHER
APPLICANTS, SHOULD BE EXCLUDED FROM THE SAMPLE IN HIS MODEL.
Dr. Arcidiacono’s preferred model is based on a sample of applicants that

excludes applicants in special recruiting categories—“athletes, children of faculty
and staff, applicants who are on Dean’s List or Director’s List, and legacies.”
Arcidiacono Report 22. Applicants in these categories have a substantially increased
chance of admission. Id. at 21–22, 34. The general admission rate is roughly 6%, but
recruited athletes have an admission rate of 86%, legacy applicants have an

16

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 21 of 24

admission rate of 33.6%, and children and faculty of staff have an admission rate of
47.7%. Id. at 21–22. 12 Dr. Arcidiacono appropriately excludes these special-category
applicants from the main sample to allow for a comparison of “similarly-situated
candidates.” Arcidiacono Report 22.
Dr. Card disputes this sampling choice. He argues that “these applicants are
not considered in a separate admission process.” Card Rebuttal 50. Thus, he claims,
their exclusion is methodologically unsound, as “exclusion of this large and
relatively well-qualified group of applicants from the admissions model removes
important information about how Harvard balances the many characteristics it
considers in its decision process, and thus, makes the model less reliable.” Id. at 48.
This methodological dispute is not merely academic. There is no evidence of racial
bias against (the relatively few) Asian Americans in the sample of special-category
applicants; so excluding them, Dr. Card argues, is akin to “stacking the deck in
favor of finding bias.” Id. at 51.
Dr. Card concedes, however, that excluding special-category applicants from
the sample is methodologically appropriate if “evidence outside the data” supports
the claim that Harvard is discriminating only against applicants other than specialcategory applicants. Id. Without such evidence, he claims, there is no “logical reason
to assume” that discrimination is limited to applicants in the larger pool. Id.
Dr. Arcidiacono has the better argument on this issue.

These applicants constitute less than 5% of the applicant sample, but roughly
one-third of admittees. Card Report App’x A, Table A.4.
12

17

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 22 of 24

First, under standard econometric practice, recruited applicants should be
pooled together with regular applicants only if statistical tests show that the
admissions process is “identical . . . for [the] two groups.” Gregory C. Chow, Tests of
Equality Between Sets of Coefficients in Two Linear Regressions, 28 Econometrica
591, 591 (1960). 13 Dr. Card makes no attempt to meet this burden.
Second, there is sound evidence that Asian-American (and other) applicants
in the special recruiting categories are in fact treated differently than typical
applicants. For example, special-category applicants (both the Asian-American
subset and the entire group) receive staff interviews at a much higher rate than
other applicants. Arcidiacono Rebuttal 66–67; see id. at 66, Table 7.3N. The
admission rate for special-category applicants is remarkably higher than the rate
for other applicants, and there are relatively few Asian Americans among the
special-category applicants. Arcidiacono Report 21–22, 34 & App’x B, Table B.3.2.
The personalized treatment afforded special-category applicants provides a logical
reason to think that Asian Americans in that group are less likely to suffer from
stereotyping and implicit bias than are other Asian-American applicants, and
provides a sound justification for excluding special-category applicants from the
sample.

In linear models, one could use a “Chow test” for pooling, while in logit models
one could do a likelihood ratio test.
13

18

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 23 of 24

CONCLUSION
For the foregoing reasons, the Court should conclude (1) that Harvard’s
personal-rating scores are biased against Asian Americans, (2) that Dr.
Arcidiacono’s statistical model correctly accounts for racial disparities in how
Harvard treats “disadvantaged” students, and (3) that it was reasonable to exclude
applicants in special recruiting categories from the sample studied in the model.
Respectfully submitted,
/s/ Randall B. Clark
Randall B. Clark BBO # 657560
80A West Hollis Road
Hollis, NH 03049
603-801-3039
[e-mail]
C. Boyden Gray*
Andrew R. Varcoe*
Adam R.F. Gustafson*
James R. Conde*
BOYDEN GRAY & ASSOCIATES
801 17th Street NW, Suite 350
202-955-0620
Washington, DC 20006
[e-mail]
[e-mail]
[e-mail]
[e-mail]
Counsel for Amici Curiae
* Pro hac vice admission pending

July 30, 2018
19

Case 1:14-cv-14176-ADB Document 450 Filed 07/30/18 Page 24 of 24

CERTIFICATE OF SERVICE
I hereby certify that this document filed through the CM/ECF system will be
sent electronically to the registered participants as identified on the Notice of
Electronic Filing.
/s/ Randall B. Clark
Randall B. Clark