PATHWAYS TO AN ELITE EDUCATION:
APPLICATION, ADMISSION, AND
MATRICULATION TO NEW YORK CITY’S
SPECIALIZED HIGH SCHOOLS
Sean Patrick Corcoran
(corresponding author)
Steinhardt School of Culture,
教育, and Human
发展
纽约大学
纽约, 纽约 10003
sean.corcoran@nyu.edu
乙. Christine Baker-Smith
Steinhardt School of Culture,
教育, and Human
发展
纽约大学
纽约, 纽约 10003
christine.baker-smith@nyu
.edu
抽象的
New York City’s public specialized high schools have a long
history of offering a rigorous, college preparatory education
to the city’s most academically talented students. Though im-
mensely popular and highly selective, their policy of admitting
students using a single entrance exam has raised questions about
diversity and equity in access. 在本文中, we provide a de-
scriptive analysis of the “pipeline” from middle school to ma-
triculation at a specialized high school, identifying group-level
differences in application, admission, and enrollment. In doing
所以, we highlight potential points of intervention to improve ac-
cess for underrepresented groups. Controlling for other measures
of prior achievement, we find black, Hispanic, low-income, 和
female students are significantly less likely to qualify for admis-
sion to a specialized high school. Differences in application and
matriculation rates also affect the diversity in these schools, 和
we find evidence of middle school “effects” on both application
and admission. Simulated policies that offer admissions using
alternative measures, such as state test scores and grades, 苏格-
gest many more girls, Hispanics, and white students would be
admitted under these alternatives. They would not, 然而, 美联社-
preciably increase the share of offers given to black or low-income
学生.
土井:10.1162/EDFP_a_00220
© 2018 Association for Education Finance and Policy
256
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Sean Patrick Corcoran and E. Christine Baker-Smith
I N T RO D U C T I O N
1 .
New York City’s (NYC’s) elite specialized high schools have a long history of offering
a rigorous, college preparatory education to the city’s most academically talented stu-
凹痕. Stuyvesant High School, the most well-known, was founded in 1904. 布鲁克林
Technical High School and The Bronx High School of Science opened in 1922 和 1938,
分别, and would eventually join Stuyvesant as the city’s most selective public
学校. The specialized high schools are aspired to by many—in a typical year in which
80,000 eighth graders apply to NYC high schools, 25,000 apply to the specialized high
学校, 和 5,000 are accepted.
Although there is mixed evidence on whether already high-achieving students are
better off academically attending an elite high school,1 the intense competition for entry
into the specialized high schools has raised questions about equity in access to them.
Unlike other NYC high schools, the specialized high schools admit students based on a
single entrance exam. Many argue that this policy rewards intense test preparation and
inhibits racial/ethnic and gender diversity at the schools. In the most recent year, 为了
例子, the three largest specialized high schools were predominately Asian (65 每-
分), 白色的 (21 百分), and male (58 百分).2 Others contend that the city has failed
to ensure that advanced students at all middle schools are competitive for admission
(ACORN 1996). Supporters of the test, 另一方面, point to its objectivity and
emphasis on higher-order skills. The admissions policy receives especially strong sup-
port from immigrant families, who view the specialized high schools as an affordable
gateway to educational and labor market success.
Because the entrance exam is the sole criterion for admission, group differences
in test performance are the primary explanation for the lack of gender, 种族, and eth-
nic representation in the specialized high schools. 然而, little is known about how
these gaps relate to other measures of academic achievement, or about the roles ap-
plication behavior, student preferences, and middle school context play in admissions
to the specialized high schools. 在本文中, we provide a descriptive analysis of the
“pipeline” from middle school to matriculation at a NYC specialized high school. In do-
ing so, we address three major questions, highlighting potential points of intervention
to improve access for under-represented groups:
(1) Conditional on prior academic achievement, are there differences in student
propensities to apply, to be admitted, and to matriculate to the specialized high
schools that lead to an over- or underrepresentation of students by race/ethnicity,
性别, family income, or educational need?
(2) To what extent are applicants and admitted students concentrated in the same set
of middle schools? Are there “school effects” on application and admission, condi-
tional on achievement and proximity, that potentially reflect differences in school
supports for specialized high school admissions?
1. 看, 例如, 克拉克 (2010), Abdulkadiro˘glu, Angrist, and Pathak (2014), Dobbie and Fryer (2014), Lucas
and Mbiti (2014), and Rokkanen (2015).
2. Authors’ calculations using the 2014–15 New York City Department of Education Demographic Snapshot (纽约-
CDOE 2014). 在 2012, a coalition of educational and civil rights groups filed a complaint with the U.S. Depart-
ment of Education claiming that the specialized high school exam is racially discriminatory (Treschan et al.
2013). This complaint is currently under review. See also Baker (2012).
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257
Pathways to an Elite Education
(3) How might admissions criteria other than the single entrance exam alter the com-
position of specialized high schools, if at all?
Drawing on individual-level data for nine cohorts of eighth graders participating
in high school admissions between 2004–05 and 2012–13, we address each of these
问题. For question 1, we use sequential logistic models to identify group differ-
ences in application, admission, and matriculation beyond those explained by prior
academic achievement. Controlling for a flexible function of state math and English
language arts (ELA) scores, we find girls and black and Hispanic applicants are sub-
stantially less likely to receive admissions offers than their male and white counterparts,
whereas Asian applicants are much more likely. We further show that these gaps are
attributable to group differences in entrance exam performance unexplained by other
measures of academic performance or student background. 例如, girls score
much lower on the entrance exam than would be predicted by their prior achievement.
The exam, 然而, is not the sole explanation for the race and gender imbalance in
the specialized high schools. 例如, we find high-achieving girls are less likely
to apply to the specialized schools—which are largely STEM (科学, 技术, engi-
neering, mathematics)-focused—and are less likely to accept having received an offer.
Higher-achieving low-income students are also less likely to apply than their nonpoor
同行. Asian students, 另一方面, are substantially more likely to apply
than all other racial/ethnic groups, at all levels of prior achievement, and are more likely
to accept an offer if one is extended.
For question 2, we first show the distribution of applicants and admitted students
across middle schools. We find roughly half of all public school students admitted to the
specialized high schools in 2013 attended one of only twenty-four middle schools (4.5
percent of all middle schools in the city), 和 85 percent attended one of eighty-eight
学校 (16 percent of all middle schools).3 To assess whether this imbalance is due to
sorting or to school influences on the specialized high school “pipeline,” we estimate
middle school “effects” on application and admission, net of student characteristics. 我们
do find systematic differences across schools in these outcomes that are meaningful in
size and suggest opportunities for intervention, but we cannot rule out sorting as an
alternative explanation.
最后, for question 3 we simulate alternative admissions rules that use state test
scores, grades, and attendance as admissions criteria in lieu of the single entrance
考试. Variants of these rules have been proposed by opponents of the single test policy
in NYC, and/or are used by other selective high schools in the United States (Finn and
Hockett 2012; Treschan et al. 2013). We find that awarding admission based on these al-
ternative criteria would have little effect on the average achievement of specialized high
school students, as measured by prior test scores and grades, but would increase diver-
城市. A much larger fraction of female applicants would receive offers than under the
current policy, fewer Asian students would be admitted, and a modestly higher fraction
of white and Hispanic students would receive offers (though Asian and white students
would still be significantly over-represented). The alternative criteria would do little to
reduce the concentration of offers in a few middle schools, and would not appreciably
3. As we show later, this pattern is not due to variability in school size.
258
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Sean Patrick Corcoran and E. Christine Baker-Smith
桌子 1. Specialized High Schools in New York City, 2013
学校 (Founding Year)
Stuyvesant High School (1904)
Brooklyn Technical High School (1922)
The Bronx High School of Science (1938)
Staten Island Technical High School (1988)A
High School of American Studies at
Lehman College (2002)
Students
Ranking
学校
百分比
Ranking
学校
22,636
23,071
19,530
15,187
16,746
83.4
85.0
72.0
56.0
61.7
不. 的
Offers
953
1,957
973
337
161
Percent of
Offers
公认
意思是
SHSAT
Percentile
最小
SHSAT
Percentile
91.6
76.2
83.2
92.9
70.8
98.0
87.5
92.9
93.5
91.5
95.0
82.0
88.0
88.0
87.0
High School for Math, 科学, 和
19,009
70.0
180
66.1
89.7
86.0
Engineering at City College (2002)
Queens H.S. for the Sciences
16,626
61.3
155
63.9
91.6
87.0
at York College (2002)
The Brooklyn Latin School (2006)
全部的
16,699
27,139
61.5
—
383
5,099
42.7
78.1
83.5
90.9
81.0
81.0
Notes: Authors’ calculations using Specialized High School Admissions Test (SHSAT) and High School Admissions Process data
provided by the NYCDOE. See online Appendix tables A.1 and A.2 for detailed counts by year. Only eighth grade test takers are
包括.
aStaten Island Technical High School obtained specialized high school status in 2005.
increase the number of offers extended to black students. Admissions rules that set
aside seats for high-achieving students in every middle school—such as a “Top 10%”
rule—would have a larger impact on diversity, but at the cost of reducing the average
achievement of incoming students.4
In the next section, we provide a brief history of specialized high schools in NYC,
and describe their admissions process. In section 3 we describe mechanisms by which
applications and admissions to the specialized schools may be associated with or influ-
enced by student characteristics and the middle schools they attend. 部分 4 描述
our data and empirical methods, and sections 5 通过 7 present our results. 我们骗-
clude with policy implications in section 8.
2 . B AC K G RO U N D — S P E C I A L I Z E D H I G H S C H O O L S I N N E W YO R K C I T Y
There are currently eight specialized high schools in NYC (桌子 1). Stuyvesant High
学校, The Bronx High School of Science (“Bronx Science”), and Brooklyn Technical
中学 (“Brooklyn Tech”) are the oldest, largest, and most well-known (we collec-
tively refer to these as the “Big 3”). The remaining five are smaller, and four of these were
established since 2002. A ninth elite school, the Fiorello H. LaGuardia High School of
音乐 & Art and Performing Arts, does not use an admissions test, but instead requires
an audition or portfolio.5
4. Based on their own simulations and evidence from this study, the NYC Community Service Society put forth
a proposal that would use Common Core–aligned New York State tests to award admission to the specialized
high schools. The proposal also called for seats to be set aside for the top 3 percent of test-takers in each middle
学校, so long as they were above a certain threshold (Treschan 2015).
5. Our analysis is restricted to the exam schools, and thus excludes LaGuardia applications. 尽管如此, 我们的确是
examine enrollment in LaGuardia as a potential destination for students who do not accept their specialized
high school offer.
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259
Pathways to an Elite Education
Admission to the specialized schools is based strictly on the Specialized High School
Admissions Test, or SHSAT, which students can opt to take in the fall of eighth grade.6
On exam day, applicants provide their ranking of up to eight specialized high schools.
SHSAT scores are sorted from highest to lowest and students are assigned, 为了,
to the highest-ranked school on their list with seats available (Abdulkadiro˘glu et al.
2014; Dobbie and Fryer 2014; NYCDOE 2014). 因此, cut scores for admission
vary by school and year depending on the score distribution, student preferences, 和
available seats. Cut scores are not made public, but there is a well-known hierarchy of
selectivity among the Big 3, with Stuyvesant having the highest cut score, 其次是
Bronx Science and Brooklyn Tech (桌子 1; Feinman 2008; Abdulkadiro˘glu et al. 2014).7
Specialized high school admissions are separate from, but run concurrently with,
traditional high school choice. In that process, all eighth graders provide a list of up
to twelve high schools they would like to attend, ranked in order of preference. A cen-
tralized mechanism matches applicants to schools, taking into account preferences,
空间, admissions priorities, and schools’ rankings of students where applicable (Ab-
dulkadiro˘glu, Pathak, and Roth 2009; Bloom, 汤普森, and Unterman 2010; Corco-
ran and Levin 2011). Students who apply to specialized high schools and/or LaGuardia
also participate in the traditional choice process.8 Admissions offers are extended in
the spring, at which point students offered a seat in one of the specialized high schools
(and/or LaGuardia) decide whether to accept or reject the offer. A student may reject,
例如, if they decide their main high school match is preferable to their special-
ized school offer or if they decide to enroll in a private or charter school. Details on
offers and acceptance rates during our study period are provided in table 1 and in a sep-
arate online appendix that can be accessed on Education Finance and Policy’s Web site
在http://www.mitpressjournals.org/doi/suppl/10.1162/EDFP_a_00220.
The SHSAT is a product of the Hecht-Calandra Act, A 1972 state law that sought to
bring greater equity and transparency to admissions.9 Its use, 然而, has been chal-
lenged by advocates and debated for years in local media (Hammack 2010). Two 1990s
reports entitled Secret Apartheid and Secret Apartheid II claimed that specialized high
school admissions perpetuated a de facto racially segregated school system by admit-
ting mostly white and Asian students from a small number of middle schools (ACORN
1996, 1997). Those reports called for greater middle school support to help poor and
minority students prepare for the SHSAT. 最近, the National Association for
the Advancement of Colored People (NAACP) Legal Defense Fund and others filed a
complaint with the U.S. 教育部, claiming that the exclusive use of
the SHSAT for specialized high school admissions is racially discriminatory (Treschan
等人. 2013). Whatever the merits of these arguments, there is little question that the
6. Ninth graders may also take the SHSAT for tenth-grade admission. 在本文中, we focus exclusively on
7.
eighth-grade applicants.
In a few cases, the cut score for admission to the smaller specialized high schools exceeds that of Brooklyn
Tech High School. These schools are much smaller, 然而, and are able to fill up quickly with high-scoring
学生 (桌子 1).
8. According to the Specialized High School Student Handbook (NYCDOE 2014) students must complete a tradi-
tional high school application in order to receive their SHSAT or LaGuardia audition results. This policy is
intended to prevent students from betting entirely on admission to a specialized school.
9. The SHSAT is intended to test for high-level ability and logical reasoning skills, and consists of ninety-five
multiple-choice questions—forty-five for verbal ability and fifty for mathematics.
260
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Sean Patrick Corcoran and E. Christine Baker-Smith
specialized high schools in NYC lack the gender, 种族, and socioeconomic diversity
of the district. In 2014–15, enrollment at the three largest specialized schools was 58
percent male, 86 percent Asian and white, 4 percent black, 和 6 percent Hispanic. 经过
比较, ninth graders citywide were 51 percent male, 26 percent Asian and white,
32 percent black, 和 41 percent Hispanic. At Stuyvesant High School in 2014–15, 仅有的
28 of the school’s 3,296 students were black.10
Although the specialized high schools are immensely popular, there is mixed ev-
idence as to whether attending an elite school has measurable educational benefits
for already high-achieving students. Abdulkadiro˘glu et al. (2014) and Dobbie and Fryer
(2014) used regression discontinuity designs to compare the outcomes of students just
above and below the threshold for admission to exam schools in NYC and Boston. 他们
found little to no effect of exam school admission on Advanced Placement or state test
scores, PSAT or SAT performance or participation, or college enrollment, graduation,
or quality, for students on the margin. 相似地, Lucas and Mbiti (2014) found no ef-
fects of attending an elite high school in Kenya, where students are also admitted via
an entrance exam. 克拉克 (2010), 另一方面, found students had better long-
run outcomes, including university enrollment, when admitted to an elite secondary
school in the United Kingdom. Recent evidence in Rokkanen (2015) using admissions
data from Boston schools suggests the returns to elite high school attendance may be
greater for inframarginal candidates. If true, well-identified regression discontinuity
studies likely underestimate the benefits of attending a selective high school.11 For this
paper we set aside the question of whether elite high schools have value added for stu-
dents beyond their next best alternative, and proceed on the basis that these schools
provide an educational good that many students and their families value.
3 . T H E O RY : FAC TO R S A F F E C T I N G A P P L I C AT I O N , A D M I S S I O N , A N D
M AT R I C U L AT I O N TO T H E S P E C I A L I Z E D H I G H S C H O O L S
Our empirical analysis follows students as they progress from middle school to en-
rollment in a specialized high school. This pipeline includes several milestones: 这
decision to apply to a specialized school (IE。, taking the SHSAT), the awarding of an
admissions offer, the decision to accept or reject an offer, and ninth-grade enrollment.
We refer to the decision to accept an offer of admission as “matriculation.” Although
there is some attrition between matriculation and ninth-grade enrollment, it is low (较少的
比 4 百分).
In a narrow sense, applying to a NYC specialized high school is relatively costless—
students simply sign up for the SHSAT and give up 2.5 hours on a weekend in October
for the test. 的确, nearly a third of rising ninth graders do so. 尽管如此, a compet-
itive score will, for most, require significant advance preparation, which can increase
10. This fact was captured in a prominent 2012 article in the New York Times that profiled the experience of
an African American girl enrolled at Stuyvesant High School (see Santos 2012). Diversity at the specialized
high schools has declined markedly over the past twenty years as the schools have become more competitive
(Treschan et al. 2013).
11. Related studies include Berkowitz and Hoekstra (2011), who find a positive effect of attending a single elite
private high school on the selectivity of college attended, and Jackson (2010), who finds large effects on exam
performance of attending a selective high school in Trinidad and Tobago. At the postsecondary level, 戴尔
and Krueger (2002) document modest returns to attending an elite college, suggesting most achievement
differences between graduates of elite and less-selective institutions are due to selection.
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261
Pathways to an Elite Education
the explicit and implicit costs of applying. Students who perceive a low likelihood of
success may choose not to make this investment. Curricular appeal may play an impor-
tant role in application behavior, as the specialized high schools emphasize math and
科学. To the extent that girls are less drawn to STEM fields, they may be less willing
to apply (例如, Schneeweis and Zweimüller 2012; Buser, Niederle, and Oosterbeek 2014;
Legewie and DiPrete 2014). As with any school choice, proximity will also influence
students’ willingness to apply to a specialized high school.
Conditional on applying, admission offers are awarded based on SHSAT scores and
students’ ranked preferences. 最后, group differences in offers must be at-
tributable to differences in SHSAT performance or their rankings of the specialized
schools.12 Math and ELA achievement as measured by state tests are strong predictors
of SHSAT performance (as we show later), but the SHSAT may be sensitive to higher-
order skills for which the state test is not. Controlling for other achievement measures,
gaps in SHSAT scores and admissions offers may reflect differences in these skills. 不-
tably, the scaling of the SHSAT has been claimed by some to advantage students with
exceptionally high ability in one content area, such as mathematics, over students with
high ability in both content areas (Feinman 2008). If true, this could influence group
differences in admission, not to mention test-taking strategy. Students’ own efforts in
preparing for the SHSAT will influence their score, and these efforts are likely to be
aided by resources available to them at home or in school.13
最后, at the matriculation stage, students decide whether to accept or reject their
specialized high school offer or to opt for a different public, 私人的, or charter school. 在
理论, students only rank specialized schools they would like to attend, but in practice
may rank all eight, given that there is no cost to do so (they can always turn down an
offer).14 The decision to accept or reject therefore depends on the student’s specific of-
fer and his alternatives. All students applying to specialized high schools participate in
traditional high school choice, and may find they prefer their main high school match.
Presumably, students with access to higher-quality neighborhood schools or opportu-
nities to attend other selective programs are more likely to turn down an offer. Until
2014, the traditional match had a provision that guaranteed admission to an “educa-
tional option” school (traditional schools that sometimes have highly regarded honors
节目) to students scoring in the top 2 percent on the seventh-grade ELA test, 亲-
vided they listed that school as their first choice.
It is easy to see how middle schools might influence the propensity to apply and be
admitted to the specialized high schools. 例如, schools could vary in resources
devoted to counseling or preparing students for the SHSAT. In some middle schools—
such as those with an honors or gifted program—the curriculum may be better aligned
with the SHSAT than in others. Schools can create a culture of high expectations and
12.
It is possible for a student to score high enough to qualify for one of the specialized high schools, but not high
enough to qualify for one on his list. A student in this case would not receive an offer.
13. The district offers a free Specialized High School Institute (SHSI) to low-income sixth graders with sufficiently
high attendance and fifth grade test scores. This 22-month program involves more than 100 meetings during
the summer and on Saturdays at 18 locations throughout the city. Though there has not yet been a formal
evaluation of the SHSI, those who choose to take advantage of its intense preparation plausibly increase their
chances of admission.
14. The average applicant in 2014–15 ranked 5.5 schools on their SHSAT. Forty-three percent ranked all eight, 和
5 percent ranked only one.
262
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Sean Patrick Corcoran and E. Christine Baker-Smith
aspirations to attend the specialized schools, and peers may influence students’ likeli-
hood of applying (Lauen 2007; Langenkamp 2009). As observed in college admissions,
high-achieving students in lower-performing schools may underestimate their odds of
admission to an elite school (Hoxby and Avery 2013). Collectively, these factors could
yield middle school “effects” on the composition of students at each stage of the spe-
cialized high school pipeline.
The next section describes the data we use and our empirical approach.
4 . DATA A N D E M P I R I C A L A P P ROAC H
Our analysis focuses on nine cohorts of eighth graders who participated in high school
admissions between 2004–05 and 2012–13, 关于 80,000 students per year. We rely
primarily on High School Admissions Process (HSAPS) data provided by the NYC De-
partment of Education, which reports whether a student applied to a specialized high
学校 (IE。, took the SHSAT), whether he or she was offered a seat (and to which school),
and whether the offer of admission was accepted. These data include students’ ranked
and matched schools from the traditional choice process, their final assignment, 和
other student information. We also observe SHSAT scores and student rankings of the
specialized high schools for five cohorts (2008–09 through 2012–13).
Using anonymous identifiers, we linked these data to administrative data on stu-
dents’ background and academic history. These include scores on the New York State
tests in math and ELA, race/ethnicity, 性别, 年龄, eligibility for free or reduced-price
午餐, English language learner (ELL) 地位, country of birth and immigration year,
attendance rates, days late, course grades (2008–09 only), special education status,
middle school (called “feeder,” because not all apply from a traditional middle school),
ninth-grade school of record (if a public school), and geocoded residential address. 作为一个
measure of proximity to specialized high schools, we used the Google Maps application
programming interface to calculate travel time via public transportation from students’
feeder schools to each of the specialized high schools.15
Our baseline sample consists of 727,372 eighth graders, and includes applicants
from both public and private feeder schools. Because demographic characteristics are
unavailable for most private school students, the greater part of our analysis focuses on
applicants from public schools, who represent more than 90 percent of the baseline
sample (N= 658,164).
We begin section 5 by showing how the composition of applicants and admitted
students evolves at each stage of the pipeline. This analysis reveals populations that
may be overrepresented or underrepresented at each milestone. To further examine
group differences in application, admission, and matriculation, we estimate sequen-
tial logistic regression models for each outcome. These models are estimated condi-
tional on having reached the previous stage. 例如, our model for admissions
is conditional on application (taking the SHSAT), and our model for matriculation is
conditional on receiving an offer to attend a specialized high school. These models
15. This serves as an approximation of travel time from home. As a robustness check on this measure, we also
calculated travel time via public transportation from every student’s home address to each specialized high
学校, 在 2013 仅有的. As we describe below, our regression models also control for residential neighborhood,
which should also capture differences in proximity.
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263
Pathways to an Elite Education
take the form:
Pr(APit = 1) = logit
Pr(OFit = 1|APit = 1) = logit
Pr(ACit = 1|OFit = 1) = logit
−1(Xitβ + ηt + G(ELAit ) + H(mathit )),
−1(Xitγ + ηt + G(ELAit ) + H(mathit )),
−1(Xitδ + ηt + G(ELAit ) + H(mathit )),
(1)
(2)
(3)
where APit, OFit, and ACit are binary outcomes equal to one if student i applied to a spe-
cialized high school, was admitted, and was accepted, 分别, and equal to zero
否则. Because we are primarily interested in variation in outcomes conditional
on prior achievement, the explanatory variables include cubic functions of student i’s
eighth grade ELA and math scores [G(ELA) and h(math), 分别], allowing for non-
linearities in the relationship between achievement on the state test and these out-
来了. Other student characteristics in X include indicators for gender, race/ethnicity,
特殊需求 (例如, ELL and special education status), and socioeconomic status (eligi-
bility for free and reduced-price lunch). Other controls include a cohort effect (ηt) 和
indicators for the student’s residential neighborhood, to capture effects of proximity to
the specialized high schools and the quality of other nearby school options.16 In models
1 和 2 we include a measure of travel time in minutes from i’s middle school to the
nearest Big 3 specialized high school. In model 3, we instead use travel time to the offered
学校. For ease of interpretation, we report average marginal effects for the explana-
tory variables, rather than logit coefficients.17 These are interpreted as the change in
predicted probability of the outcome, for the average student, given a marginal change
in the explanatory variable (other things held constant).
部分 6 examines variability across middle schools in the propensity to apply and
be admitted to a specialized high school. We first look at the distribution of applicants
and admitted students across middle schools to assess the extent of concentration. 我们
then estimate random effects linear probability models to quantify the school-level vari-
ation in admissions outcomes unexplained by student predictors. These models use
the same controls as models 1 通过 3, including neighborhood indicators and travel
时间, to ensure that the school effects are not capturing effects of proximity.
We defer a description of our simulations of alternative admissions criteria to
部分 7.
5 . T H E P I P E L I N E : A N OV E RV I E W O F A D M I S S I O N S TO N YC ’ S
S P E C I A L I Z E D H I G H S C H O O L S
之间 2005 和 2013, almost one third of students applying to NYC public high
schools took the SHSAT (32 百分), 或大致 25,000 每年. Of those, 19 百分
16. The neighborhood variables are indicators for the thirty-two geographic school districts in NYC. Although these
are not strictly aligned with neighborhoods—and some are larger in area than others—they are more local
than borough of residence. They also correlate with students’ school choice opportunity set, since admissions
preferences are sometimes given to students living in the same geographic district. The HSAPS data do not
report students’ residential district; 反而, we use geocoded home addresses to map each student to his
residential district.
17. Logit coefficients are reported in the online appendix, along with ordinary least squares linear probability
model coefficient estimates.
264
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Sean Patrick Corcoran and E. Christine Baker-Smith
received an offer of admission to a specialized high school. The Big 3 together accounted
为了 74 percent of these offers. 也许令人惊讶, not all students who received an of-
fer matriculated. 的确, 仅有的 73 percent during this period did so. Rates of matricula-
tion varied from a high of 88 百分 (to Stuyvesant) to a low of 27 百分 (to Brooklyn
Latin). Private school students—only 9.5 percent of the baseline sample—represented
14.4 百分, 16.3 百分, 和 11.5 percent of specialized high school applicants, offers,
and matriculants, respectively.18 Taken together, specialized high school students rep-
resented a very select group of eighth graders, 仅与 6.2 percent of the baseline
population receiving offers.
桌子 2 provides descriptive statistics for applicants from public schools at various
stages of the pipeline. In this table, the first column describes all public-school ap-
plicants in the baseline sample; the second describes applicants to specialized high
学校; the third and fourth describe students receiving offers (the latter for Big 3
schools only); and the fifth describes matriculators.
There are notable, if unsurprising, differences in the composition of students at
each stage.19 For example, specialized school applicants scored significantly higher on
state tests than the baseline population—about 0.66 standard deviations (标清) in ELA,
一般, 和 0.74 SD in math. Students receiving a specialized school offer scored
higher still—about 1.5 SD in ELA, 一般, 和 1.7 SD in math. Close to 26 百分
of admitted students scored in the top 2 percent of the ELA exam, which—until a recent
law change—granted them priority admission to certain schools in the traditional high
school matching process.
Girls were slightly overrepresented among applicants (50.7 百分, 相对 49.1 每-
cent of all eighth graders), but underrepresented among admissions and acceptances
(45.6 百分比和 42.3 百分, 分别). Compared with the baseline population,
white and Asian students were overrepresented among applicants, offers, and matric-
ulators. Asian students made up 14.2 percent of eighth graders, 但 29.1 percent of ap-
plicants, 54.0 percent of offers, 和 59.8 percent of matriculators. Black and Hispanic
students made up a combined 71.6 percent of eighth graders, yet only 16.1 的百分比
specialized school offers. Applicants and admitted students were more economically
advantaged and had fewer special educational needs than the population. 尽管如此,
32.6 percent of offers went to students eligible for free meals (compared with 58.6 每-
cent of all eighth graders). As might be expected, only a small share of ELL and special
education students took the SHSAT, and even fewer were offered a seat in a specialized
学校.
桌子 2 also shows the high fraction of immigrant students in NYC public schools,
and the specialized high schools in particular. Almost one in five (17–18 percent) 在
each stage of the admissions process were foreign-born. Chinese and other Far East
Asian immigrants made up 2.3 percent of the baseline population, 但 7.9 的百分比
18. Private school students have been falling as a share of the baseline sample (从 10.7 百分比在 2005 到 7.9
百分比在 2013) and of specialized high school admissions offers (从 17.1 百分比在 2005 到 13.2 百分比在
2013).
19. These differences are consistent with those reported in the descriptive statistics of Dobbie and Fryer (2014)
and Abdulkadiro˘glu, Angrist, and Pathak (2014).
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265
Pathways to an Elite Education
桌子 2. Descriptive Statistics: Eighth-Grade Public School Students Applying to NYC High Schools
Asian
白色的
黑色的
Hispanic
女性
Free-lunch eligible
Reduced-price lunch
ELL
Special education
Foreign born
Chinese spoken at home
English spoken at home
ELA z-score (8th grade)
Math z-score (8th grade)
Top 2% in ELA (7th grade)
Attendance (7th grade)
Borough of residence:
布鲁克林
Manhattan
Queens
Staten Island
Bronx
Charter middle
不. of traditional choices
Travel time to closest Big 3
41.8
Travel time to offered SPHS
LaGuardia H.S. offer
SHSAT percentile
氮
Baseline
Applied to
SPHS
Offered a
SPHS
Offered a
Big 3
公认
SPHS Offer
14.2
13.5
31.9
39.7
49.1
58.6
7.1
11.9
16.1
17.9
5.3
56.6
29.1
18.0
27.3
24.8
50.7
48.0
9.6
3.6
4.3
17.3
12.4
54.5
54.0
29.1
7.4
8.7
45.6
32.6
10.5
0.4
1.2
16.9
28.1
43.8
59.3
26.7
6.4
7.0
45.1
33.8
10.8
0.3
1.1
17.4
32.2
39.6
59.8
24.4
7.1
8.0
42.3
35.5
11.2
0.4
1.2
18.3
32.3
38.5
0.012
0.012
0.660
0.741
1.545
1.666
1.579
1.722
1.521
1.697
2.9
92.4
31.6
11.5
27.5
6.2
23.1
1.2
7.1
—
1.1
—
7.7
95.9
35.6
11.5
30.6
5.9
16.5
2.1
7.4
42.7
—
2.7
49.9
25.8
97.6
32.2
16.3
38.9
6.5
6.1
0.9
6.0
46.8
52.2
6.8
90.5
26.9
97.8
37.0
15.7
40.7
2.1
4.6
0.7
6.0
46.4
54.4
6.9
91.6
24.5
97.7
34.3
14.7
38.1
6.8
6.2
0.8
6.0
46.8
51.5
3.6
91.5
659,464
198,349
37,532
18,995
28,658
Notes: Authors’ calculations using High School Admissions Process (HSAPS) and Specialized High
School Admissions Test (SHSAT) data provided by the NYCDOE, 2004–05 through 2012–13. See the
online appendix for a description of the baseline sample. Includes only students who applied from
a NYC public school. The number of traditional choices refers to the number of schools ranked on
the student’s main high school admissions form (not the specialized high schools). ELA = English
language arts; ELL: English language learner; SPHS = specialized high school.
matriculators. Rather remarkably, 28.1 percent of students admitted to a specialized
high school spoke Chinese at home.20
数字 1 provides a closer look at the eighth-grade math and ELA achievement of
specialized high school applicants and admitted students in 2013 (both scores are nor-
malized to mean zero, SD one, using all eighth-grade test takers). Panel A shows the
percent of students at each z-score who applied or were admitted to a specialized high
学校, and panel B shows the resulting score distributions for applicants and admit-
ted students. Application and admission rates increase sharply and nonlinearly with
math and ELA scores. 尤其, not all admitted students had exceptional scores on
20. Detailed statistics on country of origin and language spoken at home are provided in Appendix table A.3,
在线提供.
266
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笔记: Includes eighth-grade public school students only. ELA = English language arts.
数字 1. Percent Applying and Receiving Offers to Specialized High Schools by Eighth-Grade Test Scores, and Test Score Distributions of
Applicants and Offers, 2013. A. Percent Applying and Receiving Offers [Above Lefthand Column]. 乙. Test Score Distribution of Applicants and
Offers [Above Righthand Column].
eighth-grade tests, particularly in ELA. Also notable is the nontrivial fraction of high-
achieving students that did not take the SHSAT at all (15–20 percent of students who
scored more than 1 SD above average on state tests).
Compositional differences in applicants, admitted students, and matriculators re-
flect increasingly high-achieving populations and are not necessarily evidence of dif-
ferences in the propensity to apply or be admitted to a specialized school for students
with similar achievement. To identify factors associated with progression through the
specialized school pipeline, we estimated the sequential logistic models described in
部分 4. The marginal effects from these models are shown in table 3.
桌子 3 confirms that student performance on state ELA and math tests is strongly
related to application and admission to the specialized schools, with math achievement
more predictive than ELA. Conditional on achievement, 然而, we observe interest-
ing group differences in the likelihood of application, admission, and matriculation to
the specialized high schools. (All the ones described here are statistically significant at
这 1 percent level or below.) 例如, holding constant prior achievement, 黑色的
students were more likely to apply (经过 2.0 百分点), and more likely to accept
an offer when extended one (经过 9.1 点). Hispanic students were also more likely
to accept an offer (经过 2.9 点) but less likely to apply (经过 3.3 点). 相似地, 低的-
income students were more likely to accept an offer (3.7 点) and less likely to apply
(2.4 点). Asian students, 相比之下, were substantially more likely to apply, at every
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Pathways to an Elite Education
桌子 3. Marginal Effects from Logistic Regression Models for Application, Admission, and Offer Acceptance, 2005–13
Asian
黑色的
Hispanic
女性
Free-lunch eligible
Reduced-price lunch
ELL
Special education
Recent immigrant
Math z-score
ELA z-score
Attendance rate
年龄
Travel time to SPHS
(minutes)
Charter middle
氮
Mean of dep. var.
Pseudo R2
Log-likelihood
Applied to
SPHS
0.1713***
(0.0021)
0.0203***
(0.0019)
−0.0332***
(0.0017)
−0.0272***
(0.0010)
−0.0242***
(0.0011)
0.0033
(0.0019)
−0.0780***
(0.0023)
−0.0528***
(0.0019)
0.0017
(0.0014)
0.1291***
(0.0008)
0.0890***
(0.0008)
0.0068***
(0.0001)
−0.0338***
(0.0010)
−0.0004***
(<0.0001)
0.0699***
(0.0048)
Offered a
SPHS
0.0506***
(0.0020)
−0.0475***
(0.0027)
−0.0576***
(0.0023)
−0.0687***
(0.0013)
−0.0298***
(0.0015)
−0.0168***
(0.0022)
−0.0571***
(0.0073)
0.0188***
(0.0058)
−0.0066***
(0.0017)
0.1347***
(0.0010)
0.1027***
(0.0010)
0.0002
(0.0002)
−0.0142***
(0.0018)
<0.0000
(0.0001)
−0.0266***
(0.0068)
Accepted
SPHS offer
0.1762***
(0.0069)
0.0912***
(0.0118)
0.0291**
(0.0104)
−0.0880***
(0.0050)
0.0368***
(0.0059)
0.0241**
(0.0081)
−0.0276
(0.0450)
−0.0110
(0.0206)
0.0374***
(0.0065)
0.0236***
(0.0043)
−0.0143**
(0.0039)
−0.0007
(0.0008)
−0.0278***
(0.0071)
−0.0006***
(0.0001)
−0.1135**
(0.0319)
Pseudo-
offer
0.0516***
(0.0024)
−0.0564***
(0.0033)
−0.0584***
(0.0028)
−0.0704***
(0.0016)
−0.0349***
(0.0019)
−0.0199***
(0.0027)
−0.0697***
(0.0082)
0.0219***
(0.0066)
−0.0086***
(0.0020)
0.1311***
(0.0012)
0.1075***
(0.0012)
0.0009***
(0.0003)
−0.0124***
(0.0022)
<0.0000
(0.0001)
−0.0341***
(0.0075)
606,925
0.320
0.322
−258195.08
194,338
0.190
0.480
−49117.94
30,579
0.729
0.126
−15610.72
134,630
0.194
0.481
−34343.00
Notes: Logit coefficients reported in online Appendix table A.5. “Pseudo offers” are assigned to applicants based solely
on their SHSAT score, ignoring their ranked preferences for specialized high schools (which could affect their likelihood of
admission); this model is necessarily restricted to 2008–13, the only years in which we observe SHSAT scores. The ELA and
math z-scores enter all logistic models as a cubic function. The average marginal effects reported for ELA and math are
the average effect of a marginal change in the ELA or math score on the outcome, across all students, and thus reflect the
quadratic and cubic terms. ELA = English language arts; ELL: English language learner; SPHS = specialized high school.
Standard errors reported in parentheses.
**p < 0.01; ***p < 0.001.
level of achievement, and were more likely to accept an offer when extended one (by 17.1
and 17.6 percentage points, respectively).
There were large group differences in admissions offers for students with similar
eighth-grade math and ELA achievement. Black and Hispanic students were signifi-
cantly less likely to be admitted (by 4.8 and 5.8 percentage points, respectively) and
free-lunch eligible students were an additional 3.0 points less likely to receive an ad-
mission offer. Asian students were 5.1 percentage points more likely to be admitted to
a specialized high school conditional on their eighth-grade test scores. Each of these
gaps is large on a baseline admissions rate of 19.0 percent.
268
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The gender gap in specialized high school enrollment begins at application, and
grows at the offer and matriculation stages. Holding constant middle school achieve-
ment, girls were 2.7 percentage points less likely to sit for the SHSAT, 6.9 percentage
points less likely to be admitted to a specialized high school (6.1 percentage points for
the Big 3; not shown) and 8.8 percentage points less likely to matriculate when admit-
ted. These gaps are quite large. Indeed, conditional on prior test scores, the gender
gap is larger than both the black–white and Hispanic–white gaps in admission to the
specialized schools.
Several other predictors of application, admission, and matriculation are worth not-
ing. First, students in charter middle schools were much more likely to apply to special-
ized high schools (by 7.0 points), but were less likely to be admitted or to matriculate
conditional on applying. The latter may reflect their opportunity for continued enroll-
ment in their charter school. Second, travel time to the nearest specialized high school
had a weak but statistically significant negative association with application. Students
who would be required to travel farther to their offered specialized high school were also
less likely to accept. We estimate a 1 SD increase in the expected travel time to school
(24.7 minutes) to be associated with a 1.5-point reduction in the likelihood of matricula-
tion, a relatively small effect.21 Third, students offered admissions to both a specialized
high school and LaGuardia High School were much less likely to accept their special-
ized high school offer (by 29 percentage points; not shown in table 3). Fourth, students
who scored in the top 2 percent on the seventh grade ELA exam—and thus were guar-
anteed admission to an “educational option” program if they ranked it first—were also
less likely to matriculate to a specialized high school when offered (by 3.4 points; also
not shown).
These findings, together with observed variation across neighborhoods in the
propensity to apply and matriculate to the specialized high schools, suggest students’
decisions are influenced by their outside options. In online Appendix table A.4, we re-
port the most common destinations for the one in four students who did not accept
their specialized high school offer. Of those who turned down an offer in 2013, 12 per-
cent ended the process with no assignment (suggesting they enrolled in a private school
or public school outside of NYC), 13 percent accepted an offer at LaGuardia High School,
and roughly 52 percent opted to attend one of fifteen other highly regarded high schools
in the city, most prominently Townsend Harris in Queens (15 percent), and Beacon (5.8
percent) and Bard Early College High Schools (5.6 percent) in Manhattan.
Group differences in offers of admission could to some degree be an artifact of appli-
cants’ ranking of the specialized high schools. For example, if girls or free-lunch eligible
students are less likely to rank schools with lower cut scores (ranking Stuyvesant, say,
but not Brooklyn Tech or Brooklyn Latin) they will receive fewer offers of admission
even with comparable scores. To examine this possibility, we used the SHSAT data to
21.
It is likely that much of the effect of proximity on the application and matriculation decisions is absorbed
by the residential neighborhood controls. Thus, the travel time coefficient likely understates the importance
of proximity to these decisions. As a robustness check for our travel time result, we substituted travel time
from students’ homes to their offered school in 2013 (the only year for which we had these data). Indeed, the
coefficient on travel time is larger when using this measure—we estimate a 1 SD increase in travel time to be
associated with a 4.9-point reduction in the likelihood of matriculation. This is a larger effect but still small
relative to the 73 percent acceptance rate.
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Pathways to an Elite Education
Table 4. Gaps in SHSAT Performance Conditional on Eighth Grade Achievement, 2008–13
Asian
Black
Hispanic
Female
Free-lunch eligible
Reduced-price lunch
ELL
SHSAT
(1)
10.704***
(0.445)
−20.518***
(0.471)
−19.684***
(0.474)
−20.329***
(0.290)
−11.416***
(0.328)
−8.553***
(0.535)
−27.862***
(0.858)
Cubic in state math score
Cubic in state ELA score
YES
YES
SHSAT:
Math
(2)
10.258***
(0.263)
−11.898***
(0.278)
−11.145***
(0.280)
−12.577***
(0.171)
−4.428***
(0.194)
−3.005***
(0.316)
−7.609***
(0.508)
YES
YES
SHSAT:
Verbal
(3)
0.445
(0.275)
−8.620***
(0.291)
−8.540***
(0.293)
−7.752***
(0.179)
−6.989***
(0.203)
−5.548***
(0.331)
−20.253***
(0.531)
YES
YES
SHSAT
(high ach)
(4)
17.283***
(0.713)
−28.225***
(0.947)
−26.855***
(0.902)
−22.605***
(0.547)
−14.067***
(0.618)
−9.541***
(0.961)
−26.404***
(2.527)
YES
YES
N
Mean SHSAT
SHSAT SD
R2
137,388
137,388
137,388
44,560
397.3
90.9
199.7
49.2
197.6
50.2
476.2
74.3
0.663
0.598
0.575
0.425
Notes: SHSAT scores are in their original scale score units. The mean and standard deviation
remain roughly constant over this period, at 400 and 90, respectively. The only student controls
not shown in the table are age and enrollment in a universal free meals school (a proxy for low-
income students not already identified by the free and reduced-price lunch variables). ELL: English
language learner. Standard errors reported in parentheses.
***p < 0.001.
directly estimate gaps in exam performance unexplained by achievement on state tests.
For the regressions shown in table 4, we again controlled for a cubic in state ELA and
math scores while estimating differences in SHSAT scores by gender, race/ethnicity,
free/reduced price meal eligibility, and ELL status.22 The main result in column 1 shows
sizable gaps in exam performance between groups, with black and Hispanic students
scoring roughly 20 points (0.22 SD) below white students, Asian students scoring 10
points (0.12 SD) higher, and free-lunch eligible students 11 points (0.13 SD) below non-
poor students. Somewhat remarkably, the gender gap on the SHSAT (20 points, or
0.22 SD) is approximately the same size as the black and Hispanic gaps after condi-
tioning on prior achievement.
Columns 2 and 3 of table 4 split the SHSAT score into its math and verbal sections.
For black, Hispanic, and female students the gap is larger on the math section (0.23–
0.25 SD) than the verbal (0.15–0.17 SD). Asian students outperform in math (0.21 SD)
but not verbal. On the verbal section, girls score 0.15 SD below boys with similar state
test scores, a marked contrast from the raw 0.33 SD gap in favor of girls on the state
test. Column 4 restricts the sample to high-performers, those scoring more than 1 SD
22. SHSAT scores are in their original scale score units rather than z-scores. The mean score and standard devia-
tion remained roughly constant over time, at 400 and 90, respectively.
270
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above the average on the state math and ELA tests, a more relevant range for successful
applicants. Among this population, group differences in SHSAT scores are even larger.
Taken together, the racial/ethnic, gender, and income gaps in specialized high
school admissions do not appear to be artifacts of preference rankings, but reflective
of real differences in SHSAT performance. As an alternative way of looking at this
question, we removed all potential effects of preference rankings by awarding “pseudo-
offers” to the highest-scoring k students each year, where k is equal to the number of
actual seats awarded. In this scenario, no student fails to receive an offer because of her
specific ranking of specialized high schools. As seen in the rightmost column of table 3,
the gaps in offer rates are comparable or larger.
In the next section, we take a closer look at the public middle schools from which
students apply.
6 . M I D D L E S C H O O L S A N D S P E C I A L I Z E D H I G H S C H O O L A D M I S S I O N S
A chief concern of the Secret Apartheid reports of the 1990s (ACORN 1996, 1997) was
that students admitted to specialized high schools were disproportionately drawn from
a small number of the city’s middle schools. For the most part this remains true, a reflec-
tion of the uneven distribution of high-achieving students across NYC middle schools.
For figure 2, we use our baseline population to produce a Lorenz-type curve showing
the distribution of applicants and admitted students across public feeder schools. The
curve plots the cumulative percent of students in a group (e.g., applicants, on the y axis)
that come from a given x percent of feeders (on the x axis), after sorting schools in de-
scending order by their number of students in that group. If schools were identical in
size, a diagonal (45-degree) line would indicate a perfectly even distribution of students
across schools. Because feeder schools vary in size, the baseline Lorenz curve serves as
the benchmark for an even distribution, rather than the diagonal.23
The topmost curves in figure 2 show the distribution of students admitted to spe-
cialized high schools in 2013. In the top panel we see 53 percent of admitted students
applied from only 5 percent of the city’s middle schools.24 By comparison, the largest
5 percent of middle schools enrolled about 20 percent of eighth graders. Eighty-three
percent of admitted students originated from only 15 percent of middle schools, and
nearly half of all middle schools sent few if any students to the exam schools. The dis-
tribution of applicants (those taking the SHSAT) is closer to the baseline distribution—5
percent of middle schools comprise about 27 percent of applicants, and 15 percent of
feeders account for 53 percent of applications.25
23.
24.
In other words, if specialized high school applicants and admitted students were distributed across middle
schools in the same way as the baseline population, their curves would look the same as the baseline. In
addition to enrollment differences across feeder schools, differences in the propensity to move to the private
sector for high school will affect the shape of the baseline Lorenz curve. (Students who intend to move to
private schools and do not begin the public high school admission process are not included in our baseline
sample.)
In 2013, 45 percent of all specialized high school offers to public school students went to students in only 20
middle schools (out of a total of 536 feeder schools in the baseline sample).
25. Though not shown here, we looked for changes over time in the concentration of applicants and admitted
students between 2005 and 2013; the Lorenz curves in these years were nearly identical. If anything, the dis-
tribution of admitted students was more concentrated in 2013 than in earlier years.
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Pathways to an Elite Education
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Notes: Excludes special education, home school, and alternative feeder schools. Includes a total of 536 feeder schools and 178 ZIP
codes with at least one student in the baseline sample in 2013. SPHS = specialized high school.
Figure 2. Feeder School and ZIP Code Representation Among Specialized High School Applicants and Admitted Students, 2013.
The bottom panel in figure 2 repeats this analysis for residential ZIP codes, to see
whether the concentration observed in figure 1 is an artifact of residential sorting by
ability. Here the distribution of applicants and admitted students is less concentrated.
This is partly due to the smaller number of ZIP codes than feeders. That said, sorting
by academic ability across middle schools appears more pervasive in NYC than sorting
by ability across residential neighborhoods.
A closer look at specialized high school admits by feeder school reveals a large ma-
jority of admitted students were already attending highly selective middle school pro-
grams. Among offers to students in the top 30 sending schools (which account for 56
percent of offers), 58 percent attended citywide or district gifted and talented programs
that require a test for admission, and another 31 percent attended middle schools that
272
Sean Patrick Corcoran and E. Christine Baker-Smith
screen applicants based on test scores or other criteria. Only 13 percent were from un-
screened programs (all in Queens).
As a more formal test for middle school effects, we use random effects linear prob-
ability models (LPMs) to quantify the between-school variation in outcomes not ex-
plained by student-level predictors.26 In some cases, these middle school “effects” were
sizable. For instance, we find a 1 SD difference in feeder effects is associated with a 9-
percentage point difference in the propensity to apply to the specialized high schools,
implying that similar students attending different schools have meaningful differences
in application rates. On the admissions margin, a 1 SD difference in feeder school ef-
fects is associated with a 2.2-point difference in admission rates, or a 1.2-point difference
in admission to the Big 3. These are fairly large differences given the overall offer rate
of 19 percent. They appear to be driven by earlier cohorts, however, as this estimate is
closer to zero in more recent years. For SHSAT scores, a 1 SD difference in feeder ef-
fects is associated with an 8.7 point (a 0.095 SD) higher SHSAT score.27 We find the
SD of feeder school effects on matriculation to be near zero.
In sum, there do appear to be middle school effects on the pathway to specialized
high school admissions, particularly on the application margin. Middle school effects
on admissions are also meaningful in size. Although we cannot rule out the possibil-
ity that these effects are due to sorting on student characteristics not accounted for by
the models, they suggest that opportunities may exist to identify schools where applica-
tion and admission to the specialized high schools lag behind (or surpass) others with
similar populations.
7 . S I M U L AT I N G T H E E F F E C T S O F A LT E R N AT I V E A D M I S S I O N S C R I T E R I A
Critics of the SHSAT as the sole factor in admission have argued that more holistic
criteria—like those used in some other highly selective U.S. high schools—would in-
crease access to and diversity in the city’s specialized high schools (Finn and Hockett
2012; Treschan et al. 2013). We simulated how the composition of students in the spe-
cialized high schools would change, if at all, under alternative admissions policies. We
focused this analysis on the 2009 applications cycle, the one year for which we have
data on course grades, which are often proposed as potential admissions criteria.
We considered seven alternative admissions policies, described in table 5. All use
some index of state test scores, course grades, and attendance to award offers. Rule 6
further forces proportional representation by borough,28 and Rule 7 (a “Top 10%” rule)
gives priority to students whose average test scores and math and English course grades
are among the top 10 percent in their middle school. For each simulation, we fix the
number of public school students admitted to the actual value in 2009 (4,324). Only
26. Coefficients from the LPM versions of our table 3 models are provided in the online appendix. In LPM models
with fixed school effects, we can reject the null hypothesis that the fixed effects are jointly zero for each outcome
(application, admission, admission to a “big 3,” matriculation). We use a random effects model to quantify
between-school variation, since fixed effects would overstate this variation (due to small samples for some
middle schools).
27. These models control for eighth-grade ELA and math scores which are also potentially affected by middle
school quality. As an alternative, we controlled for students fifth grade (pre-middle school) scores, which re-
duced the size of the feeder school effects somewhat, to 7.6 points for a 1 SD increase.
28. This is similar to a proposal made to the City Council in 2014 (see Shepard 2014).
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Table 5. Simulated Admissions Rules
Rule 1
Applicants are ranked by the average of their seventh-grade math and ELA z-scores, and admitted in order, beginning with the
highest average, until all seats are filled. (Seventh-grade scores are the most recent available at the time of application.)
Rule 2
Applicants are ranked by the average of their seventh-grade math and ELA z-scores, and their seventh-grade math and English
grades (also z-scores), and admitted in order, beginning with the highest average, until all seats are filled.
Rule 3
The same as Rule 2, except that course grades are weighted, with honors/ accelerated classes weighted by a factor of 1.25 prior
to standardization. Students are admitted in order, beginning with the highest average, until all seats are filled.
Rule 4
Applicants are ranked by the average of their seventh-grade math and ELA z-scores, and their seventh-grade math, English, social
studies, and science grades (also z-scores), and admitted in order, beginning with the highest average, until all seats are filled.
As in Rule 3, honors courses are given additional weight.
Rule 5
The same as Rule 3, but the student’s z-score for seventh-grade attendance is also included in the average. Students are
admitted in order, beginning with the highest average, until all seats are filled.
Rule 6
The same as Rule 3, but proportional representation by borough is enforced (Brooklyn 31.8%, Manhattan 11.3%, Queens 27.6%,
Staten Island 6.1%, and Bronx 23.3%, mirroring the distribution of applicants). Within-borough students are admitted in order,
beginning with the highest average, until all seats are filled.
Rule 7
“Top 10%” Rule: all students in the top 10% of their feeder school by the measure in Rule 3 are eligible for admission. If the
number of eligible applicants exceeds the number of available seats, eligible (top 10%) students are admitted in order,
beginning with the highest average, until all seats are filled.
Notes: In the event of ties at the threshold for admission, students at the threshold are offered seats at random. (In practice, ties only occur
under Rule 1.) ELA = English language arts.
applicants—those who expressed an interest in attending a specialized school—were
at risk for admission. We repeated this analysis using the full population, in essence
removing the effect of differential application rates. The results were similar, and
are available in the online appendix.
Table 6 summarizes the simulations, showing how the composition of students
admitted to specialized high schools would differ under these alternative rules. The
first column provides descriptive statistics for the students actually admitted in 2009,
and the remaining columns show the change in student characteristics under the seven
alternatives. Under all but the Top 10% simulation, the mean ELA and math score of
admitted students would be at least as high as the mean for those actually admitted.
This is partly by construction, because all the simulations make some use of math and
ELA scores. Mean course grades and attendance rates under the alternatives are also
as high as (or higher than) those observed among actual admitted students. Mean test
performance on the SHSAT, however, would fall considerably, from 0.33 SD (Rules 1–2)
to as much as 0.73 SD (Rule 7).
The simulated admissions rules do alter the gender and racial/ethnic mix of admit-
ted students. When a combination of state test scores, grades, and attendance is used
in place of the SHSAT, a significantly higher fraction of offers would be extended to
girls (an increase of 9 to 13 points under Rules 1–6). In fact, the gender gap would shift
dramatically in favor of girls with the use of grades and state tests. At the same time,
the fraction of offers extended to Asian students would drop 4 to 13 points, and the
fraction extended to whites would rise 2 to 4 points. (Asians and whites would remain
overrepresented among offers, relative to baseline). The fraction of offers to black and
Hispanic students would rise modestly in Rules 1–6 (0–4 and 3–11 points, respectively),
274
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Table 6. Changes in Composition of Specialized High Schools Under Alternative Admissions Rules
Actual Offers
Change from Actual Offers in 2009
in 2009
Rule 1
Rule 2
Rule 3
Rule 4
Rule 5
Rule 6
Rule 7
53.6
29.2
7.7
9.4
46.1
30.6
1.421
1.701
93.1
91.3
533.8
97.7
100
75.7
23
−8.8
+2.3
+2.0
+4.2
+9.3
−0.2
+0.301
+0.232
+0.1
+0.8
−30.0
−0.2
−37.9
−26.6
+4
−6.5
+3.3
+0.1
+3.1
+13.1
−0.1
+0.176
+0.171
+2.0
+2.8
−31.0
+0.0
−38.8
−27.4
+1
−6.5
+3.5
−0.6
+3.5
+11.3
+0.0
+0.082
+0.048
+1.0
+2.0
−38.6
−0.1
−43.8
−31.4
−5
−6.0
+3.1
−1.3
+4.1
+10.8
+0.7
−0.057
−0.112
+0.5
+1.7
−48.0
−0.2
−49.0
−36.2
−7
−4.3
+2.0
−0.8
+2.9
+11.5
+0.5
+0.079
+0.050
+1.1
+2.1
−37.1
+0.3
−42.9
−30.6
−5
−12.7
−1.7
+3.5
+10.6
+12.8
+4.5
+0.057
−0.023
+0.4
+1.2
−46.7
−0.2
−47.1
−33.7
−1
−15.9
−9.4
+12.7
+12.4
+14.1
+12.0
−0.027
−0.123
+0.3
+0.7
−65.3
−0.5
−57.7
−43.3
+34
Asian
White
Black
Hispanic
Female
Free-lunch eligible
ELA z-score (grade 7)
Math z-score (grade 7)
Math grade (0–100)
English grade (0–100)
SHSAT score
Attendance rate
Received an offer in 2009
Received a Big 3 offer in 2009
No. of schools representing
50% of offers
No. of schools representing
81
+13
+0
−26
−38
−26
+2
+96
85% of offers
Notes: Only students who applied for specialized high school admission (took the SHSAT) in 2009 are included in admissions simulations.
See table 5 for descriptions of each admissions rule.
though they would remain significantly underrepresented. In fact, under Rules 2–5, the
percent of offers extended to black students would decline from current levels.
Perhaps surprisingly, Rules 1–6 have little to no effect on the concentration of spe-
cialized high school offers in a minority of feeder schools (evident in figure 2). The
bottom two rows of table 6 report the number of middle schools that constitute the first
50 and 85 percent of offers, after sorting schools in descending order by offer counts.
Of Rules 1–6, only Rules 1–2 would reduce the concentration of offers (slightly). The
others increase the clustering of offers into a smaller number of middle schools. Even
Rule 6, which enforces borough proportionality, retains a high level of concentration.
Rule 7 (Top 10%) has the most dramatic effect on the concentration and demograph-
ics of specialized high school offers. When giving admissions priority to applicants in
the top 10 percent of each middle school, the racial/ethnic distribution would be closer
to baseline, and a higher fraction of offers would be extended to low-income students.
This assignment rule comes, however, at the cost of lower average achievement on state
tests (and the SHSAT).
These simulations only approximate the potential effect of these rules on the com-
position of specialized high schools, for several reasons. First, they do not address the
general equilibrium implications of a rule change. We took the applicant pool and its
prior performance (e.g., test scores and grades) as given; it is likely both would change
under a new regime. A new rule would likely affect the composition of students who
apply, by incentivizing applicants to shift their emphasis away from SHSAT prepara-
tion and toward course grades and state tests. A rule with set-asides for top students
in each school could also lead to mobility between schools, as was found under the
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Pathways to an Elite Education
Top 10% plan in Texas (Cullen, Long, and Reback 2013). Second, our simulations omit
private school students, who constitute a meaningful share of applicants but lack the
performance measures used in these rules. (Many public school applicants also lack
data on these measures, highlighting a potential barrier to implementation.) Third,
our simulations do not consider qualitative admissions criteria often proposed, such
as recommendations, essays, or interviews. Finally, they are uninformative about un-
measured qualities of students—such as higher-order thinking skills or the ability to
succeed in a competitive admissions process—that the SHSAT is intended to measure.
To the extent the SHSAT is capturing skills that existing performance measures do not,
our simulations ignore an important dimension of selectivity. More evidence is needed
on this question.
8 . D I S C U S S I O N
This paper provides a descriptive look at the pipeline from NYC public middle schools to
matriculation at the city’s elite specialized high schools. A remarkably high proportion
of eighth graders aspire to attend one of these schools, but only a fraction is admitted. A
comparison of mean characteristics confirms admitted students are a highly select pop-
ulation on multiple dimensions, including state test scores and course grades. They are
a somewhat more economically advantaged group than the wider population, although
nearly a third is eligible for free meals, and almost one in five was born outside of the
United States.
The SHSAT does appear to be a barrier to diversity in the specialized schools.
Among applicants with similar track records on state tests, black, Hispanic, and low-
income students are significantly less likely to score high enough on the SHSAT to
receive an offer of admission. Asian and white students, on the other hand, are substan-
tially more likely to receive an offer. Girls score nearly a quarter of a standard deviation
lower than boys on the SHSAT for the same level of prior achievement, and underper-
form on both the mathematics and verbal sections of the test. Simulated policies that
offer admission using alternative measures, such as state test scores, grades, and atten-
dance, suggest that many more girls, Hispanics, and whites would be admitted under
these alternatives. They would not, however, appreciably increase the share of offers
given to black or low-income students, nor reduce the high concentration of offers in a
small number of middle schools.
Our findings offer several important insights. First, measures of academic perfor-
mance beyond the SHSAT are strong predictors of admission to the specialized high
schools. Admissions policies that rely on state test scores and course grades would
admit many of the same students now admitted, and—although improving the repre-
sentation of some groups (especially girls)—would not dramatically change the demo-
graphic composition of the specialized high schools. Behavioral responses to any new
policy would likely limit its impact even further. Second, although measures such as
test scores, grades, and attendance are strongly predictive of current admission, there
are large group differences that remain unexplained. The difference may be higher-
order skills that are not adequately captured in other achievement measures, or simply
differences in test preparation. This remains an important open question for future
research.
276
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Sean Patrick Corcoran and E. Christine Baker-Smith
Finally, we identified several potential points of intervention to improve access to
the specialized high schools. First, a nontrivial share of high-achieving students does
not sit for the SHSAT at all. This may reflect a lack of interest, a lack of resources
for test preparation, or a poor understanding of their odds of admission. We found a
significant middle school effect on the propensity to apply for the specialized schools,
suggesting schools may influence this behavior.29 Second, girls and Hispanic and low-
income students are less likely to apply for admission than their prior achievement
would predict, and girls are much less likely to accept an offer when extended one. The
latter may reflect preferences to some degree, but, given the prominent role specialized
schools play in STEM education in NYC, a better understanding of this phenomenon
is needed. Lastly, echoing the Secret Apartheid studies of the 1990s, we find that stu-
dents admitted to the exam schools originate from a remarkably small number of the
city’s middle schools. Although middle schools matter, this result appears more than
anything to reflect the highly uneven distribution of high-achieving students across
schools.
ACKNOWLEDGMENTS
We would like to thank Lori Nathanson, Jim Kemple, and Leanna Stiefel for helpful comments,
and NYU Steinhardt for providing seed funding for this project.
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