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The Welfare Effects of Coordinated School Assignment:
Evidence from the NYC High School Match ∗
Atila Abdulkadiroğlu Nikhil Agarwal Parag A. Pathak †
November 2013
Abstract
Centralized and coordinated school assignment systems are a growing part of recent education
reforms. This paper estimates school demand using student rank order lists submitted
in New York City’s high school assignment system launched in Fall 2003 to study the effects
of coordinating admissions in a single-offer mechanism based on the deferred acceptance
algorithm. Compared to the previous mechanism with multiple offers, a limited number
of choices, and three rounds of offer processing, there is a 7.2 percentage point increase in
matriculation at assigned school in the new mechanism. Student preferences trade off proximity
and school quality, but are substantially heterogeneous. Uncoordinated offers leave
more than a third unassigned after the first round, of which the majority eventually obtain
over-the-counter assignments close to home. The new mechanism assigns students to schools
on average 0.69 miles further away. Even though all else equal students prefer nearby schools,
we estimate that the average student welfare gain from the improved school match is equal
to eight times the disutility from increased travel. Students from across all demographic
groups, boroughs, and baseline achievement categories obtain a more preferred assignment
on average, though the benefit is larger for student groups more likely to be unassigned after
the old mechanism’s first round. These facts imply that allocative changes involving matching
mechanisms need not be zero-sum. However, the gains from coordinating assignment are
larger than from relaxing constraints imposed by the new mechanism’s assignment algorithm.
JEL: C78, D50, D61, I21
Keywords: School Choice, Matching Theory, Deferred Acceptance, Congestion
∗ We thank Neil Dorosin, Jesse Margolis, and Elizabeth Sciabarra for their expertise and for facilitating access to
the data used in this study. A special thanks to Alvin E. Roth for his collaboration, which made this study possible.
Jesse Margolis provided extremely helpful detailed comments. We also thank Josh Angrist, Jerry Hausman, and
Ariel Pakes and seminar participants at the NBER Market Design conference for input. We received excellent
research assistance from Weiwei Hu, Danielle Wedde, and a hardworking team of MIT undergraduates. Pathak
acknowledges support from the National Science Foundation (grant SES-1056325). Abdulkadiroğlu and Pathak
are board members of the Institute for Innovation in Public School Choice, a non-profit that provides technical
assistance to districts on enrollment issues.
† Abdulkadiroğlu: Department of Economics, Duke University, email: atila.abdulkadiroglu@duke.edu. Agarwal:
Cowles Foundation, Yale University and Department of Economics, MIT email: agarwaln@mit.edu. Pathak:
Department of Economics, MIT and NBER, email: ppathak@mit.edu.

1 Introduction
Whether transferring to an out-of-zone public school, applying to a charter, magnet or selective
exam school, or using a voucher to attend a private school, a growing number of families can now
opt out of attending their neighborhood school. As school choice options have proliferated, so
too has the way in which choices are expressed and students are assigned. Ad hoc decentralized
assignment systems where students applied separately to schools with uncoordinated admissions
offers have been replaced with centralized, coordinated single-offer assignment mechanisms in
a number of cities including Denver, London, New Orleans, and New York City. 1 In these
cities, student demand is matched with the school seat supply using algorithms inspired by the
theory of matching markets (Gale and Shapley 1962, Shapley and Scarf 1974, Abdulkadiroğlu
and Sönmez 2003). Changes in assignment protocols are inevitably controversial, however, since
reallocating school seats may result in some students assigned to high quality schools while others
are assigned to less desirable alternatives.
In this paper, we exploit a large-scale policy change in New York City to study the effects
of moving from an uncoordinated assignment system to a coordinated single-offer system on the
allocation of students to schools. Prior to 2003, roughly 80,000 aspiring high school students
applied to five out of more than 600 school programs; they could receive multiple offers and
be placed on wait lists. Students in turn were allowed to accept only one school and one wait
list offer, and the cycle of offers and acceptances repeated two more times. However, a total of
three rounds of offer processing proved insufficient to allocate all students to schools, and more
than 25,000 applicants were assigned to schools not on their original application list through
an administrative “over-the-counter” process. Students initially expressed their preferences on a
common application, but admissions offers were not coordinated across schools, so we refer to
the old mechanism as an uncoordinated mechanism.
In Fall 2003, the system was replaced by a single-offer assignment system, based on the
student-proposing deferred acceptance algorithm for the main round. Applicants were allowed
to rank up to 12 programs for enrollment in 2004-05 and a supplementary round assigned those
unassigned in the main round. Since most students received one offer through the central office,
we refer to this new mechanism as a coordinated mechanism. The Department of Education
(DOE) adopted the new mechanism to provide a greater voice to student’s choices, to utilize
school places more efficiently, and to reduce gaming involved to obtain a school seat (Kerr 2003).
Parents were also provided with additional information on school options through an expanded
set of parent workshops and high school fairs. At the conclusion of the first year, 82% of students
were assigned in the main round and one-third fewer participants were processed in the over-thecounter
round.
This large-scale policy change provides a unique opportunity to investigate the consequences
of centralized and coordinated school assignment. Changes were advertised widely beginning
only in September 2003, and students submitted their preferences in November 2003. This brief
timeline limits the scope for participants to react by moving in response to the new mechanism.
1 A number of U.S. cities are in the process of adopting unified enrollment systems using similar matching
algorithms, including Chicago, Newark, Philadelphia, and Washington DC (Darville 2013).
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Moreover, rich micro-level data from both systems allow us to surmount many of the usual challenges
associated with evaluating allocative aspects of assignment mechanisms. A key strength of
our study is that we observe submitted preferences, round-by-round placements, and subsequent
school enrollment of all students in both the old and new mechanism. Using student preferences
together with detailed information on student and school attributes, we estimate the factors that
account for school demand. The estimated preference distribution is then used to evaluate the
distributional consequences of the new mechanism and to assess mechanism design choices.
The new mechanism is based on the student-proposing deferred acceptance mechanism, where
truth-telling is a weakly dominant strategy for participants (Dubins and Freedman 1981, Roth
1982). This motivates our empirical approach of recovering the preference distribution using
the revealed preferences of students with discrete choice demand models. The richness of our
data allow us to fit models with substantial student heterogeneity and unobserved school effects.
While the incentive properties of the new mechanism motivate treating stated rankings as true
preferences, there are some complications we investigate. First, the new mechanism only allows
participants to rank at most 12 choices. Although 80% of applicants in our sample rank fewer than
12, this constraint interferes with the dominant strategy property of the mechanism for students
who find more than 12 schools acceptable (Abdulkadiroğlu, Pathak, and Roth 2009, Haeringer
and Klijn 2009). Second, it is possible that the sudden adoption of the new mechanism led some
families to use heuristics developed from the old mechanism, despite the DOE’s advice to rank
schools truthfully. 2 For instance, some families might have ranked a “safety” school as their last
choice, even though the new mechanism’s properties make this unnecessary if ranking fewer than
12 choices.
We start with benchmark models that use all ranked choices and assume the ranking is
truthful, before turning to several alternatives. The alternatives are from models that treat only
top choice as the most preferred alternative, that treat only the top three choices as the three
most preferred, that restrict the student sample to those ranking less than 12 schools and treating
their rankings as truthful, and that use all choices other than the last to eliminate a possible
safety-school effect. We also report estimates assuming that stated choices are not necessarily
preferred to unranked schools and from models with different assumptions on the outside option.
We do not directly model strategic choices because we anticipate strategic considerations to be
less important in mechanisms based on deferred acceptance than in other more manipulable
mechanisms. 3
Changes in student assignment due to the coordination of admissions offers can happen
through many channels. First, the new mechanism allows students to rank up to 12 choices,
whereas the old mechanism only allowed for five. Second, the limited number of rounds of
offers and acceptances can lead to coordination failures where students hold on to less preferred
choices waiting to be offered seats at more preferred schools once others decline. With few
rounds of offer processing, this may, in turn, lead to inefficiencies as many are left unassigned,
2 The DOE’s school brochure advised: “You must now rank your 12 choices according to your true preferences”
(DOE 2003).
3 Hastings and Weinstein (2008) report that in Charlotte-Mecklensburg’s highly manipulable immediate acceptance
mechanism, students respond to information on historical odds of assignment. Pathak and Sönmez (2013)
formalize how constrained deferred acceptance is less manipulable than the immediate acceptance mechanism.
2

a phenomenon termed congestion by Roth and Xing (1997). In the old mechanism, the district
simply placed unassigned students to nearby schools in an over-the-counter process, even if they
wanted to go elsewhere. In a centralized single-offer system, school seats can be used effectively,
as the computerized rounds of offers and acceptances minimize coordination issues related to
insufficient offer processing time. Third, in New York’s old mechanism, schools were able to see
the entire rank ordering of applicants, and often advertised they would only consider those who
ranked them first. This property creates strategic pressure on student ranking decisions. Each
of these features of uncoordinated assignment can result in student mismatch.
On the other hand, coordinated assignment may make encourage movement throughout the
district for little benefit. Ravitch (2011), for instance, argues that the elevation of choice in
NYC “destroyed the concept of neighborhood schools” as “children scattered across the city in
response to the lure of new, unknown small schools with catchy names, or were assigned to
schools far from home.” Critics of the new system believed that denying principals’ information
on students’ ranking of the school restricts a principal’s ability to attract “students who want
them most” (Herszenhorn 2004). This logic implies that removing a school’s ability to know
whether they were ranked first could lead fewer of their offered students to enroll. It also may be
in a district’s interest to advantage certain student subgroups to prevent them from leaving the
district (Engberg, Epple, Imbrogno, Sieg, and Zimmer 2010). 4 Providing students with multiple
offers and letting them decide upon receiving offers may make it easier for some students to decide
what school is best for them. 5 Taken together, these points suggest that the new mechanism
may involve a substantial redistribution among students, rather than better assignments for most
students.
The questions we examine are also relevant to other settings where uncoordinated assignment
procedures have been replaced with coordinated ones. For instance, in England, where the 2003
Admissions Code mandated coordination of admissions nationwide, a number of local education
authorities, governing bodies similar to U.S. school districts, adopted common applications and
centralized assignment. The English motivation parallels NYC since authorities wanted to ensure
that “every child within a local authority area would receive one offer of a school place on the same
day. This would eliminate or largely eliminate multiple offers and free up places for parents who
would not otherwise be offered a place” (Pennell, West, and Hind 2006). All 32 London boroughs
coordinated to establish a Pan London Admissions Scheme based on deferred acceptance to make
the admissions system “fairer” and “simpler,” and to “result in more parents getting an offer of
a place for their child at one of their preferred schools earlier and fewer getting no offer at all”
(ALG 2005, Pathak and Sönmez 2013). In 2012, the Recovery School District in New Orleans
also coordinated disparate school application processes within a common application and singleoffer
system, citing the need to eliminate a “frustrating, ad-hoc enrollment process handled at
individual campuses” (Vanacore 2012).
We find compelling evidence that the new mechanism is an improvement relative to the old
one based on offer processing and matriculation patterns. Students are more likely to enroll in
4 Williams (2004) profiles families who had to pay a deposit to reserve a spot in a private or parochial school
while awaiting their school placement in the first year of the new mechanism.
5 Similar arguments for the flexibility provided by multiple offer systems have been raised by critics of the
National Residency Matching Program. See, e.g., Bulow and Levin (2006) and Agarwal (2013).
3

the school they are assigned. In the old mechanism, 18.6% of students matriculated at schools
other than where they were assigned at the end of the match, while in the new mechanism only
11.4% students do. Multiple offers and short rank order lists in the old mechanism advantage
few students, but leave many without offers. Roughly one-fifth of students obtained multiple
offers, but of those who accept a first round offer, more than 70% take their most preferred offer,
suggesting that the majority of the students with multiple offers did not benefit from having
more than one option. Half of applicants obtain no first round offer and 59% of these applicants
are assigned in the over-the-counter process. The take-up rates for over-the-counter students
are similar across mechanisms, but the number of students assigned in that round is three times
larger in the old mechanism. In addition, 8.5% of applicants left the district after assignment in
the old mechanism, while only 6.4% left under the new mechanism.
The most significant difference between assignments under the two mechanisms is the distance
between students and their assigned school. In the old mechanism, students travelled on average
3.36 miles to reach their assigned school. Students travel 0.69 miles further in the new mechanism.
All else equal, students prefer schools that are closer to home according to their preference
rankings in the new mechanism. However, preferences are substantially heterogeneous. Estimates
from models using all ranked choices show that student preferences trade off proximity and school
quality. Asian and white students and those with high baseline scores exhibit greater variance in
their taste for school characteristics, net of distance, than black and Hispanics and those with low
baselines scores, respectively. Students prefer schools with higher math achievement, but high
baseline math students prefer them more. Students prefer schools with fewer subsidized lunch
peers, but students from wealthier neighborhoods prefer them more. Students prefer schools with
more white peers, but white and Asian students are more sensitive to this dimension than blacks
and Hispanics. Variations from the demand model using first choice, top three choices, choices
among those who rank fewer than 12, and dropping last choice show broadly consistent patterns.
This fact together with evidence on both in and out-of-sample model fit reassure us about the
suitability of using the estimated preferences to make statements about student welfare.
The preference estimates suggest that the new mechanism has made it easier for students to
express and obtain a choice they want. Even though school assignments are further away, based
on our estimated distribution of preferences, the amount that students prefer these schools more
than compensates for this difference. Ignoring the greater travel distance, the improvement
associated with the matched school is distance-equivalent of 5.53 miles; net of distance, the
average improvement is 4.79 miles. That is, on average the improved school match is equal to
eight times the disutility from increased travel. Students across demographic groups, boroughs,
baseline achievement levels all obtain a more preferred assignment on average from the new
mechanism. The largest gains are for student groups who were more likely to be unassigned
after the old mechanism’s first round. Given that some students eventually must attend less
desirable schools under any mechanism, the pattern suggests the assignments produced by the
new mechanism were a net improvement for most students and these allocative changes were
not from zero-sum. These gains are also seen whether utility is measured based on assignments
made at the end of the high school match or based on subsequent enrollment.
The reforms of the school choice mechanism in New York City also raise a number of optimal
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design questions that we examine using our preference estimates. As a benchmark, we compute
the utilitarian optimal assignment given resource constraints on the number of school seats. The
new mechanism is 2.85 miles in distance-equivalent utility below this idealized benchmark. Had
the mechanism produced a student-optimal stable matching, average student welfare improves
by an equivalent of 0.11 miles. 6 An ordinally Pareto efficient matching is equivalent to an
improvement of 0.60 miles. Unfortunately, these allocations cannot be implemented without
harming the mechanism’s incentive properties and mechanisms that implement these allocations
as equilibrium outcomes are not known. Nonetheless, the average welfare levels from these
counterfactuals show that any potential gain from relaxing the constraints imposed by the new
mechanism’s algorithm are smaller than those from coordinating assignments.
The literature on school choice is immense and not easily summarized. We share a focus
with papers interested in understanding how choice affects assignment and sorting of students
(Epple and Romano 1998, Urquiola 2005), rather than the competitive effects of choice on student
achievement (Hoxby 2003, Rothstein 2006). We also concentrate our study on allocative
efficiency, rather than effects of choice options on subsequent test scores (Abdulkadiroğlu, Angrist,
Dynarski, Kane, and Pathak 2011, Deming, Hastings, Kane, and Staiger 2011). This study
contributes to a growing theoretical literature on centralized admissions to college (Balinski
and Sönmez 1999) and K-12 public schools (Abdulkadiroğlu and Sönmez 2003). A number
of recent papers use micro data from assignment mechanisms to understand school demand
(Hastings, Kane, and Staiger 2009, He 2012), but these datasets comes from variants of the
Boston mechanism, a mechanism where parents have a strong incentive to rank schools strategically.
Niederle and Roth (2003)’s study of the introduction of a gastroentrology match is an
important precursor, but the rich data we have allow us to examine the consequences of sorting,
quantitatively evaluate student welfare, and assess design choices. Finally, our work complements
theoretical papers investigating other assignment mechanisms using simulated data
(Erdil and Ergin 2008, Kesten 2010, Abdulkadiroğlu, Che, and Yasuda 2012) or those that
use submitted ordinal student preferences to examine theoretical counterfactuals, but not with
empirically-grounded cardinalizations of utility (Abdulkadiroğlu, Pathak, and Roth 2009, Pathak
and Sönmez 2008).
The paper proceeds as follows. Section 2 provides additional details on high school assignment
in New York City. Section 3 describes our data. Section 4 reports on descriptive features of offer
processing in the two mechanisms. In Section 5 we outline our empirical strategy, while Section 6
reports estimates of the distribution of student preferences. Section 7 uses the demand estimates
to compare student welfare across the two mechanisms, while Section 8 quantitatively assesses
tradeoffs in design choices. The last section concludes.
6 Even though the mechanism is based on student-proposing deferred acceptance, the matching is not studentoptimal
because school-side priorities are not strict (Erdil and Ergin 2008, Abdulkadiroğlu, Pathak, and Roth
2009, Kesten 2010, Kesten and Kurino 2012).
5

2 High School Choice in NYC
2.1 School Options
Forms of high school choice have existed in New York City for decades. Before 2002, high
school assignment in New York City featured a hodgepodge of choice options mostly controlled
by borough-wide high school superintendents. Significant admissions power resided with the
schools because they could directly enroll students. Across the city, specific programs existed
within schools, with curricula ranging from the arts to sciences to vocational training. It was not
uncommon for multiple program types to exist within the same school, a feature that continues
today. The set of school programs that developed at the time shaped the set of school options
available in the uncoordinated mechanism. The 2002-03 High School directory describes seven
types of programs, categorized according to their admissions criteria.
At Specialized High Schools, such as Stuyvesant and Bronx Science, there is only one type of
program, which admits students by admissions test performance on the Specialized High Schools
Admissions Test (SHSAT). 7 Audition programs interview students for proficiency in specific
performing or visual arts, music, or dance. Screened programs evaluate students individually
using an assortment of criteria including a student’s 7th grade report card, reading and math
standardized scores, attendance and punctuality, interview, essay or additional diagnostic tests.
Educational Option programs also evaluate students individually, but for half their seats. The
other half is allocated by lottery. Allocation of seats in each half targets a distribution of
student ability: 16 percent of seats should be allocated to high performing readers, 68 percent
to middle performers, and 16 percent to low performers. Unscreened programs admit students
by random lottery, while Zoned programs give priority to students who apply and live in the
geographic zoned area of the high school. Limited Unscreened programs allocate seats randomly,
but give priority to students who attend an information session or visit the school’s exhibit at
high school fairs or open houses conducted each admissions season. We categorize programs
into three main groups: Screened programs which also include Testing and Audition programs,
Unscreened programs, which also include limited Unscreened and Zoned programs, and the rest
are Educational Option programs.
Throughout the last decade, a important component of education reform efforts in NYC
involved closing and opening of new small high schools throughout the city, with roughly 400
students. A big push for these small high schools came as part of the New Century High Schools
Initiative launched by Mayor Bloomberg and Chancellor Klein. Eleven new small high schools
were opened in 2002 and 23 new small schools were opened in 2003, and the peak year of small
high school openings was in 2004 (Abulkadiroğlu, Hu, and Pathak 2013). Most of these schools
are small and have about 100 students per entering class. As a result, the new small high schools
have a relatively small impact on overall enrollment patterns during our study period.
7 Abdulkadiroğlu, Angrist, and Pathak (2013) describe their admissions process in more detail.
6

2.2 Uncoordinated Admissions in 2002-03
Admissions to the Specialized High Schools and the LaGuardia High School of Music & Art and
Performing Arts have been traditionally administered as a separate process from regular high
schools, which did not change with the new mechanism. 8 In 2002-03, nearly 30,000 rising high
schoolers applied for about 5,000 spots at one of the five Specialized High Schools or LaGuardia
by taking the SHSAT in late October and rank them in order of preference.
About 80,000 students who are interested in regular high schools visit schools and attend citywide
high school fairs before submitting their preference in the fall. In 2002-03, students could
apply to at most five regular programs in addition to the Specialized High Schools. Programs
receiving a student’s application were able to see the applicant’s entire preference list, including
where their program was ranked. Programs then decided whom to accept, place on a waiting
list, or reject. Applicants were sent a decision letter from each program they had applied to and
some obtained more than one offer. Students were allowed to accept at most one admission and
one wait-list offer. After receiving responses to the first letters, programs with vacant seats could
make new offers to students from waiting lists. After the second round, students who do not have
a zoned high school are allowed to participate in a supplementary round known as the variable
assignment (VAS) process. In the supplementary round, students could rank up to eight choices,
and students were assigned based on negotiation on seat availability between the enrollment
office and high school superintendents. After replies to the second letter were received, a third
letter with the new offers was sent. New offers did not necessarily go to wait-listed students in
a predetermined order. Remaining unassigned students were assigned their zoned programs or
administratively, when the central office tried to place kids as close to home as possible, ignoring
their preferences. We refer to this final stage as the over the counter round. 9
Three features of this assignment scheme motivated the NYC DOE to abandon it in favor of a
new mechanism. First, there was inadequate time for offers, wait list decisions, and acceptances
to clear the market for school seats. DOE officials reported that in some cases high achieving
students received acceptances from all of the schools they applied to, while many received none
(Herszenhorn 2004). Comments by the Deputy Schools Chancellor summarized the frustration:
“Parents are told a school is full, then in two months, miracles of miracles, seats open up, but
other kids get them. Something is wrong” (Gendar 2000).
Second, some schools awarded priority in admissions to students who ranked them first on
their application form. The high school directory advises that when ranking schools, students
should “... determine what your competition is for a seat in this program” (DOE 2002). This
recommendation puts strategic pressure on ranking decisions. Listing such a school first would
improve the likelihood of an offer at the risk of rejection from other schools, which take rankings
8 The 1972 Hecht-Calandra Act is a New York State law that governs admissions to the original four Specialized
high schools: Stuyvesant, Bronx High School of Science, Brooklyn Technical, and Fiorello H. LaGuardia High
School of Music and Performance Arts. City officials indicated that this law prevents including these schools
within the common application system without an act of the state legislature.
9 Other accounts of New York City’s high school admissions process now refer to the over the counter round
as the the placement of students who did not submit an high school application because they are new to New
York City (Arvidsson, Fruchter, and Mokhtar 2013). Our analysis follows applicants through to assignment and
therefore does not consider students who arrived to the process after the high school match.
7

into account.
Third, a number of schools managed to conceal capacity to fill seats later on with better
students. For example, the Deputy Chancellor stated, “before you might have a situation where a
school was going to take 100 new children for ninth grade, they might have declared only 40 seats,
and then placed the other 60 outside the process” (Herszenhorn 2004). Overall, critics alleged
that the old mechanism disadvantaged low-achieving students, and those without sophisticated
parents (Hemphill and Nauer 2009).
2.3 Coordinated Admissions in 2003-04
The new mechanism was designed with input from economists (see Abdulkadiroğlu, Pathak,
and Roth (2005) and Abdulkadiroğlu, Pathak, and Roth (2009)). When publicizing the new
mechanism, the DOE explained that its goals were to utilize school places more efficiently and
to reduce the gaming involved in obtaining school seats (Kerr 2003). In the first round, students
apply to Specialized High Schools when they take the SHSAT, just as in previous years. Offers
are produced according to a serial dictatorship with priority given by SHSAT scores.
In the main round, students can rank up to twelve regular school programs in their application,
which are due in November. The DOE advised parents: “You must now rank your 12
choices according to your true preferences” because this round is built on Gale and Shapley
(1962)’s student-proposing deferred acceptance algorithm. Schools with programs that prioritize
applicants based on auditions, test scores or other criteria are sent lists of students who ranked
the school, but these lists do not reveal where in the preference lists they were ranked. Schools
return orderings of applicants to the central enrollment office. Schools that prioritize applicants
using geographic or other criteria have those criteria applied by the central office. That office
uses a single lottery to break ties amongst students with the same priority, generating a strict
ordering of students at each school.
Assignment is determined by the student-proposing deferred acceptance algorithm with student
preferences over the schools, school capacities, and school’s strict ordering of students as
parameters. The algorithm is run with all students in February. In this first round, only students
who receive a Specialized High School offer receive a letter indicating their regular school
assignment, and are asked to choose one. After they respond, students that accept an offer are
removed, school capacities are adjusted and the algorithm is re-run with the remaining students.
All students receive a letter notifying them of their assignment or whether they are unassigned
after the main round.
Unassigned students from the main round are provided a list of programs with vacancies
and are asked to rank up to twelve of these programs. In 2003-04, the admissions criteria at
the remaining school seats were ignored in this Supplementary round. Students are ordered by
their random number, and the student-proposing deferred acceptance algorithm is run with this
ordering in place at each school. Students who remain unassigned in the supplementary round
are assigned administratively. These students and any appealing students are processed on a
case-by-case basis in the over the counter round.
8

3 Data and Sample Definitions
The NYC DOE provided us with several data sets for this study each linked by a unique student
identification number: information on student choices and assignments, student demographics,
and October student enrollment. The assignment file is maintained by the Enrollment office
(formerly known as the Office of Student Enrollment and Planning Operations), which runs
high school admissions. For 2002-03, the assignment files records a student’s initial rank order
list, their offers and rejections for each round, whether they participate in the supplementary
round process, and their final assignment at the conclusion of the assignment process as of July
2003. For 2003-04, the assignment files contain students’ choice schools in order of preference,
priority information for each school, and assignments at the end of each of the rounds, and
final assignment as of early August 2004. The student demographic file for both years contains
information on sending school, home address, gender, race, limited English proficiency, special
education status, and performance on 7th grade citywide tests. We use ArcGIS to compute the
road distance between each student and school, and ArcGIS with StreetMap USA to geocode
each student to a census block group corresponding to her address. Though we use road distance,
we also computed subway distance using the Metropolitan Transportation Authority GIS files;
the overall correlation between driving distance and subway commuting distance for all studentprogram
pairs is 0.96. Further details are in the Data Appendix.
Our analysis sample makes two restrictions. First, since we do not have demographic information
for private school applicants, we restrict the analysis to students in NYC’s public middle
schools at baseline. Second, we focus on students who are not assigned to Specialized high schools
because that part of the assignment process did not change with the new mechanism. Most students
prefer a Specialized High School to a regular ones, limiting the potential for interaction
with the main round to differentially influence assignments as the mechanism changed. Given
these restrictions, we have two main analysis files: the mechanism comparison sample and the
demand estimation sample.
The mechanism comparison sample is used for comparisons of the assignment across the
two mechanisms. This sample is the largest set of students assigned through the high school
assignment mechanism to a school that exists as of the time of the printing of the high school
directory. We do not include students assigned to schools which are created afterwards because
we are not able to evaluate the welfare from those assignments using rankings made before
they existed. Any non-private applicant in the OSEPO files who does not opt for their current
school and is assigned is a member of the mechanism comparison sample in 2002-03 and 2003-04.
Columns (1) and (2) of Table 1 summarize student characteristics in the mechanism comparison
samples across years. 3,500 fewer students are involved in the mechanism comparison 2003-04
sample, which is mainly due to the students assigned to schools created after the printing of the
high school directory or to closed schools (as shown in Table B1).
New York City is the nation’s largest school district, and like many urban districts it is majority
low-income and non-white. Nearly three-quarters of students are black or Hispanic, and
about 10% of students are Asian. Brooklyn is home to the largest number of applicants, followed
by Bronx and Queens, which each account for roughly one quarter of students. Manhattan and
9

Staten Island, areas with high private and parochial school penetration, account for a considerably
smaller share of students about 13 and six percent, respectively. Student characteristics of
participants are similar across years, suggesting applicant attributes did not change substantially
as a result of the new mechanism.
The demand sample contains participants in the main round of the new mechanism in the
assignment files. The school choices expressed by this group of students represent the overwhelming
majority of students. Among the set of main round participants, we exclude a small
fraction of students who are classified as the top 2 percent because these students are guaranteed
a school only if they rank it first and this may distort their incentives to rank schools truthfully.
Additional details on the sample restrictions are in the Data appendix. Table 1 also shows that
the student characteristics are similar across the sample used for comparing mechanisms and
demand samples with one exception. The fraction of students who are classified as receiving a
subsidized lunch differs across years because we only have access to subsidized lunch as measured
as of the 2004-05 school year. For this reason, we use census block group family income as a
student demographic.
Data on schools were taken from New York State report card files provided by NYC DOE.
Information on programs come from the official NYC High School Directories made available to
students before the application process. Table 2 summarizes school and program characteristics
across years. There is an increase in the number of schools from 215 to 235, and a corresponding
decrease in the average number of students enrolled per school of about 40 students. This fact is
driven by the replacement of some large schools with smaller schools that took place concurrently
in 2003-04 described above. Despite this increase, there is little change in the average achievement
levels of schools and school demographic composition as measured by report card data. Moreover,
slightly more than half of the teachers are classified as inexperienced – having taught for less
than two years – a pattern which holds for both years.
Students in New York can choose among roughly 600 programs throughout the city. The
menu of program choices is immense, and programs vary substantially in focus, post-graduate
orientation, and educational philosophy. For instance, the Heritage School in Manhattan is an
Educational Option school where the arts play a substantial role in learning, while Townsend
Harris High School in Queens is a Screened program with a rigorous humanities program making
it among the most competitive in the city. Using information from high school directories, we
identify each program’s type, language orientation, and speciality. With the new mechanism,
there are more Unscreened programs and fewer Educational Option programs, a change driven
by the conversion of many Educational Option programs to Unscreened programs, given their
overlapping admissions criteria. We code language-focused programs as Spanish, Asian, or Other,
and categorize program specialities into Arts, Humanities, Math and Science, Vocational, or
Other. Not all programs have specialties, though about 70% fall into one of these classes.
(Details on our classification scheme are in the Data appendix). The menu of language program
offerings or program specialities changes little across years.
Given the sudden announcement of the new mechanism and the similar student attributes
across years, it seems reasonable that there was little scope for participants to react by either
opting out or in to the mechanism. Likewise, it does not appear that there is a large change
10

in the residential locations of students. The distribution of students throughout the city looks
nearly identical to that in the new mechanism, shown in the map in Figure 1. Moreover, though
there are relatively small changes in the set of school options, these mostly involve an increase
in the number of Unscreened programs, and a decrease in the number of Educational Option
programs, and these two program types are similar. These facts together motivate our approach
of using preference estimates from choices expressed in 2003-04 to measure student welfare from
the final assignments in 2002-03, and to attribute those to changes in the assignment mechanism
rather than changes in the attributes of student participants or the menu of school options.
4 Descriptive Evidence on Mechanism Performance
4.1 Distance, Exit, and Matriculation
One of the most important characteristics of a student’s school assignment is how far away it
is. Figure 2 reports the overall distribution of road distance travelled by students in both the
uncoordinated and coordinated mechanism. New York City spans a large geographic range, with
nearly 45 miles separating the southern tip of Staten Island with the northern most points of the
Bronx, and 25 miles traveling from the western edge of Manhattan near Washington Heights to
Far Rockaway at the easternmost tip of Brooklyn. 10 The closest school for a typical student is
0.82 miles from home, and students in the uncoordinated mechanism on average travelled 3.36
miles to their assignment. In the coordinated mechanism, the average distance is 4.05 miles.
The medians also increase from 2.25 to 3.04 miles. The increase in distance due to a coordinated
mechanism is consistent with the pattern in Niederle and Roth (2003)’s study of a new centralized
match in the gastroentrology labor market. Mobility in their study is defined as the percentage
of gastroenterology fellows who change hospitals (or cities or states) after finishing their previous
training (usually in internal medicine) and starting the gastroenterology fellowship. They report
a centralized mechanism is associated with mobility increases at the hospital, city, and state
level.
The increase in distance to assignment suggests that the scope of the market increased under
the coordinated mechanism, but it does not directly imply a statement about welfare. Table 3
presents further information on distance and offer processing under both mechanisms. In the
uncoordinated mechanism, more students obtain their final assignment in the last round than in
the first round. Panel A of the table shows that 36% of students are assigned over the counter,
compared to 35% in the first round. Since 33,894 students obtain one or more first round offers
(shown in Panel B), but only 24,292 students were finalized in the first round, 9,602 students
with a first round offer were finalized as offers were made in subsequent rounds. The processing
of these students took place as schools revised offers based on first round rejections and made
offers anew in the second and third round. However, the large fraction of students assigned in
the over-the-counter round suggests that three rounds were not sufficient to process all students.
Students who are offered earlier are assigned to and enroll at schools that are further away
than students who are assigned in the last round. This fact is unsurprising given that the
10 Table S1 reports on the relationship between road distance and subway distance. With the exception of
Manhattan, the overwhelming majority of students are assigned to a school in the same borough as their residence.
11

DOE’s explicit aim was to find space for over-the-counter students based on their residence.
After receiving an assignment, a student may opt for a private school, leave New York, or even
drop out. Families may switch schools after their final assignments are announced, but before the
school year starts for a number of reasons including moving within the city. In the uncoordinated
mechanism, principals had greater discretion to enroll students and the DOE officials quoted
above alleged that students with sophisticated parents might just show up at a school in the
fall and ask for a place. Based on exit and matriculation patterns, students assigned earlier
appear less satisfied with their assignment than those assigned in earlier rounds. The fraction of
students who exit NYC public schools is 13.5% among over-the-counter placements, which is 5%
greater than the fraction who exit in earlier rounds. More than a quarter of students assigned in
the over-the-counter round who are still in NYC public schools matriculate at schools other than
where they were assigned. By comparison, the take-up of offered assignments is much higher for
those assigned in the first three rounds.
Panel B shows that roughly one-fifth of students obtained multiple offers in the uncoordinated
mechanism. Though not reported in the table, 73% of those with multiple offers receive two offers,
22% of receive three offers, 5% receive four offers, and 64 applicants received offers at all five
of their schools. Since a student can take at most one of these offer, these numbers imply that
there were a total of 17,263 extra offers made. Based on exit and matriculation, students with
multiple offers are more satisfied with their assignment than students with zero or one offer.
These students also travel further to their final assignment or enrolled school.
Table A1 shows that of the students who accept a first round offer, about 71% take their
most preferred ranked offer. This fact implies that the majority of students who had multiple
offers did not necessarily benefit from having more than one option if their top option is their
most preferred. Multiple offers come at the cost of more than half of the applicants receiving
no first round offer. Though not reported, 58% of students without any offer are assigned in
the over-the-counter process. This fact explains why their assigned schools are closer, they are
more likely to exit NYC public schools, and more likely to enroll at a school other than their
assignment than students with one or more offer.
4.2 Offer Processing by Student Characteristics
Students from across all demographic groups, boroughs, and baseline achievement categories
travel further to their assigned school except in Manhattan (shown in Table 10). The increased
distance for the student subgroups are close to the overall average increase in distance of 0.69
miles. High math baseline and SHSAT test takers tend not to travel as far, while black students
and those from the Bronx and Queens travel further.
As we’ve seen, changes in distance are related to the fraction who are assigned in the overthe-counter
process. Table 4 reports the attributes of students across rounds and number of first
round offers compared to the overall population of applicants in the uncoordinated mechanism
(shown in column (1)). Students from Manhattan, those with high math baseline scores, and
those who have taken the SHSAT tend to obtain offers earlier in the uncoordinated admissions
process. They are overrepresented among students either finalized in the first round or who
receive multiple first round offers. For example, 30% of the students who receive multiple first
12

ound offers take the SHSAT compared to 22.4% overall. Students from Staten Island, students
who are white, and those from high income neighborhoods tend to systematically obtain offers
later in the process. Compared to the overall population, these groups are overrepresented in the
over-the-counter round. About a quarter of students in the over-the-counter process are white,
compared to 15% of participants in the overall distribution. The differences in student attributes
across rounds are not as pronounced with the coordinated mechanism. In the over-the-counter
process, 22.8% of students are SHSAT takers compared to 24.6% in the main round and 16.0%
are white compared to 12.6% in the main round. These facts are consistent with coordinated
assignment more equitably distributing school access across rounds for different student groups.
4.3 Mismatch in Over-the-Counter Round
Before turning to estimates of student preferences, we compare the attributes of schools ranked
by students processed in each round to the attributes of the assigned school. This comparison
indicates how students processed in the main, supplementary, and over-the-counter rounds fare
relative to what they wanted according to their choices.
Students who are processed in earlier rounds are assigned to schools that have attributes more
similar to the schools they ranked than students processed in later rounds. Table 5 shows that
for those assigned in the main round, with the exception of distance, ranked schools tend to have
slightly better attributes than assignments in both mechanisms. Ranked schools have higher
English and Math achievement, more four-year college-going, fewer inexperienced teachers, and
higher attendance rates.
For students placed in the supplementary round, assignments are even worse than ranked
schools. In the uncoordinated mechanism, for instance, the gap high math achievement between
ranked and assigned schools is 0.8 percentage points for those assigned in the main round, while
it 2.5 points in the supplementary round. The gap between ranked and assigned alternatives
in teacher experience and subsidized lunch peers also larger in the supplementary round than
in the main round. Since students participate in the supplementary round if did not obtain a
main round assignment, it is not surprising that these students are assigned to schools with less
desirable characteristics.
The most striking pattern in Table 5, however, is for students who are assigned in the overthe-counter
round. We’ve already seen that there are three times more students assigned in this
round in the uncoordinated mechanism and that these students are assigned to schools much
closer to home than those in other rounds. Aside from distance, each over-the-counter student’s
assignment is considerably worse than the schools they ranked. There is a large gap between the
English and Math achievement levels, college-going, teacher experience, subsidized lunch levels,
and attendance of ranked schools compared to assigned ones in the uncoordinated mechanism.
For instance, there is a 6.8 percentage point gap in English achievement between ranked and
assigned schools in the uncoordinated mechanism, which corresponds to a 40% standard deviation
reduction in this measure.
The differences between ranked and assignments are also large in the coordinated mechanism,
though in some cases, they are not as stark. Achievement differences between ranked and assigned
schools are narrower: for English, it’s a 5.0 percentage point gap (compared to 6.8) and for Math,
13

it’s 3.6 vs. 4.3. On the other hand, assigned schools are not as close to home in the coordinated
mechanism, and all else equal, families prefer closer schools. Therefore, it is not possible to
assert whether the over-the-counter process was better or worse in the two mechanisms. What
is clear is that being processed in the over-the-counter round is undesirable for students in both
mechanisms. As a result, a significant fraction of the changes in student welfare will be driven by
the large reduction in the number of students who enter this round in the coordinated mechanism.
5 Measuring Student Preferences
5.1 Student Choices
What makes a families rank particular schools and where do they obtain information about school
options? In surveys, parents state that academic achievement, school and teacher quality are the
most important school characteristics (Schneider, Teske, and Marschall 2002). In NYC, families
obtain information about high schools and programs from many sources. Guidance counselors,
teachers, peers, and other families in the neighborhood all provide input and recommendations.
The official repository of information on high schools is the NYC High School directory, a booklet
that includes information about school size, advanced course offerings, Regents and graduation
performance, as well as the school’s address, and closest bus and subway. The directory also
includes a paragraph description of each program together with a list of extracurricular activities
and sports teams. Families learn about schools at High school fairs that are held on Saturdays
and Sundays in the fall in each borough, from individual school open houses, from online school
guides such as insideschools.org, and from books about high schools such as Hemphill (2007).
Finally, local newspapers such as the New York Post and New York Daily News regularly publish
rankings of high schools, using publicly available information from the New York State Report
Cards.
Even though the school ranking decision involves evaluating many different alternatives, the
aggregate distribution of preferences displays some consistent regularities: students prefer closer
and higher quality schools as measured by student achievement levels, shown in Table 6. 11 The
first row of the table shows that 20% of applicants rank 12 school choices; the majority rank nine
or fewer choices and nearly 90% rank at least three choices. The average student’s top choice
is 4.43 miles away from home. Given that the closest school is on average 0.82 miles away, this
means that students do not simply rank the school closest to home. An average student’s first
choice is nearly 0.40 miles closer than her second choice, and her second choice is about 0.25 miles
closer than her third choice. Even though other school characteristics change with distance, the
distance to ranked school increases monotonically until the 9th choice, which is 5.65 miles away
on average. The distance to the 10-12th choices is lower than the 9th choice, but since less than
half of students rank 10 schools, this may be due to compositional changes.
Lower ranked schools are not only farther away, but they also less desirable on other measures
of school quality. We measure quality using the Regents performance information in the NYC
11 Table A2 provides additional information on school assignments. 31.9% of students receive their top choice,
15.0% receive their second choice, and 2.4% receive a choice ranked 10th, 11th, or 12th. 17.5% of students are
asked to participate in the supplementary round because they are unassigned in the main round.
14

High School directory, which comes from NY state report cards. The fraction of students scoring
an 85 or higher on the English or Math Regents exam decreases going down rank order lists.
The percent of students attending a four year college also decreases as we go down rank order
lists, and the fraction of teachers classified as inexperienced increases. Finally, schools enrolling
a higher share of white and Asian students tend to be ranked higher than schools with smaller
shares of these student groups.
Using requests for individual teachers, Jacob and Lefgren (2007) find that parents in low
income and minority schools value a teacher’s ability to raise student achievement more than in
high income and non-minority schools. This difference across groups motivates our investigation
of ranking behavior by baseline ability and neighborhood income. Both high and low baseline students
prefer schools that are closer to home, but first choices are closer for low baseline students.
High achieving students also tend to rank schools with high English and Math achievement,
relative to low achievers, though both groups place less emphasis on achievement with further
down their preference list. Similarly, students from low income neighborhoods tend to put less
weight on Math and English achievement than students from high income neighborhoods, but
both groups rank higher achieving schools higher. These differences suggest the importance of
allowing for tastes for school achievement to differ by baseline achievement and income groups.
Based on their submitted preferences, all else equal, students prefer attending a school closer
to home. The fact that students in the new mechanism are assigned to schools further from home
might suggest that the new mechanism led to assignments that are worse on average than the
old mechanism. On the other hand, students may prefer schools outside of their neighborhood
because they are a better fit. We must therefore weigh the greater travel distance in the new
mechanism against the attributes of the school. Students do not rank the closest school to their
home and instead trade off school attributes with proximity. Our next task is to quantify how
students evaluate distance relative to school attributes such as size, demographic composition,
and average achievement levels based on their submitted preferences.
5.2 Model and Estimation Strategy
The comparison of the attributes of first choices relative to later choices provides rich information
to identify how a student trades off these features of schools in her preferences. To quantify these
tradeoffs, we work with a random utility model. Let i index students, j index programs, and
let s j denote the school housing program j. We model student i’s indirect utility for program j
using the following specification:
u ij = δ sj + ∑ l
α l z l ix l j + γd ij + ε ij , with
δ sj = x sj β + ξ sj ,
where z i is the vector of student characteristics, x j is a vector of program j’s characteristics, d ij
is distance between student i’s home address and the address of program j, ξ sj is a school-specific
unobserved vertical characteristic, and ε ij captures random fluctuations tastes via draws from an
extreme value type-I distribution with variance normalized to π2
6
. Since students rank programs,
it is natural to specify utility in terms of programs. However, we write the mean utility δ sj only
15

in terms of school attributes since a program’s type and speciality are the only features that do
vary within schools.
This demand specification allows us to exploit the unusually large number of school and
student characteristics and the student rank order lists in the micro data. Each model contains
234 school fixed effects for each of the 235 schools, where one is dropped for our normalization. To
take advantage of these characteristics, we estimate models with a large number of interactions,
where each student characteristic is interacted with each school characteristic, and the logit
functional form provides a parsimonious way to sidestep the need for numerical integration
because we can write the probabilities in closed form. The logit assumption also comes with
the Independence of Irrelevant Alternatives (IIA) property, which implies that if the choice
set changes, the relative likelihood of ranking any two schools does not change. Most of our
counterfactual exercises compare two different allocations by aggregating utilities for two different
assignments. Our aim is to best fit the utilities of students given their observable characteristics.
Unlike applications which relax the IIA property (Berry, Levinsohn, and Pakes 1995, Berry,
Levinsohn, and Pakes 2004), we are not interested in predicting the consequences of changing
prices or attributes for a given individual. In our setting, there are also relatively modest changes
in the set of school options across years.
In our preferred models, we do not explicitly include an outside option and instead normalize,
without loss of generality, the value of δ for an arbitrarily chosen school to zero. This assumption
is motivated by our primary interest in studying the allocation within inside options rather than
substitution outside of the NYC public school system. As we describe below, we also find the
behavioral implications of an outside option in rank order lists that do not rank all 12 alternatives
unappealing. Indeed, the IIA property implies that our estimates would not change had we
observed the actual rank of the outside option.
The demand sample contains rankings of 69,907 participants in 2003-04 over 497 programs
in 235 schools, representing a total of 542,666 school choices. We start by building a likelihood
function assuming that choices are truthful before examining this assumption in detail. This
assumption implies that student i ranks programs in order of the indirect utility she derives from
the programs. We assume that all unranked schools are less preferred to all ranked schools. Let r i
be the rank order list submitted by student i in our demand sample, with |r i | ≤ 12 denoting the
length of the agent’s list and r ik denoting the kth choice. Let θ = (α, γ, δ) denote the parameters
of interest. Given θ and our logit assumption, the likelihood that student i submits rank order
list r i is:
)
L (θ|r i , z i , X, D i ) = Π |r i|
k=1
(u P irik > max u ij |θ, z i , x j , D i
j∈J\∪ l

students ranking programs is much larger than the number of programs, the estimation error in
δ is negligible compared to the error in β due to sample variance in the set of observed schools.
6 Preference Estimates and Model Fit
Our specifications follow other models of school demand and include average school test scores
and racial attributes as characteristics (see, e.g., Hastings, Kane, and Staiger (2005)). There are,
of course, many school features influencing choices that we do not observe. Therefore, unlike
these earlier models, we include additive school fixed effects to capture school-level unobservables.
As we have seen above, the distance to a school is an important dimension accounting for
choices, so all demand models control for distance. We do not include more flexible controls
for distance because it serves as our numeraire relative to which we measure the value of other
school characteristics and a unit for welfare in the counterfactuals. In each specification, we also
include three program type dummies and ten program speciality dummies. 12 The categorization
of programs into specialities is described in the Data appendix.
6.1 Demand Estimates
Table 7 reports estimates for six specifications of our demand model. The first specification has
school effects and 14 additional parameters (program specialty dummies, program type dummies,
distance, and school characteristics). The school characteristics are size of 9th grade, percent
white, attendance rate, percent subsidized lunch, and the Regents math performance. The second
specification adds 34 parameters by interacting school characteristics with student racial
characteristics. The third specification interacts a enrollment, attendance rate, and math performance
with student baseline achievement. The next three specifications include interactions
between all student demographics (gender, race, Special Ed, Limited English Proficient), math
and English baseline achievement, and the school characteristics. We also include dummies for
Spanish, Asian and Other Language Program, interacting these dummies with a student’s LEP
status and whether they are Hispanic or Asian. This model has 349 parameters. We report three
variations of this specification: using only the top ranked school, using only the top three ranked
schools, and using all ranked schools. Since these specifications include many interactions, we
only report a subset of coefficients, and present all of the estimates in Table C1.
All else equal, students prefer schools closer to home. This fact can be seen by the negative
coefficient, -0.31, on distance in the first specification in Table 7. As we add interactions, the
estimate on distance is remarkably stable. Consistent with the patterns in Table 6, the size
of this coefficient relative to the other coefficients also implies that distance has an important
weight on choices relative to other attributes. The estimate of size of 9th grade or percent white
implies that students are willing to travel for larger schools and for schools with more whites.
Students also prefer schools with higher attendance rates, fewer subsidized lunch students, and
higher math performance.
12 The program type dummies are Unscreened, Screened, and Educational Option. The program specialty
dummies are Arts, Humanities/Interdisciplinary, Business/Accounting, Math/Science, Career, Vocational, Government/Law,
Other, Zoned, and General.
17

Many interaction terms in columns (2)-(4) are significantly estimated and have the expected
signs. For instance, students with high baseline math scores tend to prefer schools with higher
attendance rates and high math performance more than those with low baseline scores. The
psuedo-R 2 indicates the fraction of variation in utility we can explain with observables. Though
many of these interaction terms are significantly estimated, they do not lead to a large improvement
the our psuedo-R 2 relative to the model without interactions. The psuedo-R 2 increases
from 0.85 in column (1) to 0.92 in column (4). Thus, after accounting for distance, the school
and program fixed effects, there are still unobserved components of student tastes.
Aside from comparisons with the distance coefficient and the significance levels, the magnitude
of the estimates in Table 7 are hard to directly interpret. We’d like to know, in particular,
about the extent of student-level preference heterogeneity based on the estimates. In Table 8, we
report on some simple summary measures of heterogeneity using the estimates from the model
with interactions between school characteristics and student demographics and school characteristics
and student baseline achievement reported in column (4) of Table 7. For each student
group, we compute the distance-equivalent utility in miles from each school program by substituting
student and school characteristics into our preference estimates. For this calculation,
we ignore the unobserved taste shock, ɛ ij , and normalize the average utility for students in a
category, net of distance, across programs to be zero. The first four columns report the average
value split by quartile, while the last column reports the range from top to bottom quartile.
Relative to the average across all students, Asian and white students are willing to travel
more for schools than black and Hispanics. This fact can be seen in Panel A in column (5), where
the willingness to travel to go from a top to bottom quartile school is a distance-equivalent of
11.00 and 11.93 miles for Asians and whites, while it is 8.56 and 8.40 for blacks and Hispanics,
respectively. Similarly, high math baseline students exhibit greater willingness to travel for
schools than low math baseline students. In a model without student level heterogeneity, the
range across quartiles for rows split by race or by baseline achievement would be identical to the
first row.
The remaining panels of Table 8 report on willingness to travel for quartiles of school attributes.
As before, we compute the distance-equivalent utility in miles, normalizing the mean
utility to zero within student category. High math baseline students exhibit more spread in their
valuation of high-achieving schools than low baseline students. Students from richer neighborhoods
exhibit also more spread in their valuation of the percent of peers obtaining subsidized
lunches. Finally, Asian and white students exhibit greater taste variation in school percent white
than blacks and Hispanics. Each comparison reported here indicates that observable dimensions
of student preference heterogeneity estimated from our demand model are important role in our
welfare calculations.
6.2 Assessing the Behavioral Assumptions
Treating submitted rankings truthful, as in the estimates in the first four columns of Table 7, is
a natural starting point and apparently generates sensible patterns. It is a benchmark because
of the straightforward incentive properties of the mechanism and the advice that the NYC DOE
provides in the 2003-04 High School Directory and in their information and outreach campaign.
18

For instance, the DOE guide advises participants to “rank your twelve selections in order of
your true preferences” with the knowledge that “schools will no longer know your rankings.”
Nonetheless, truthful behavior is a strong assumption worth investigating for a number of reasons.
A first issue is whether students are deliberately ranking schools, given that there may be
substantial frictions involved in evaluating roughly 500 school programs. Kling, Mullainathan,
Shafir, Vermuelen, and Wrobel (2012), for instance, document “comparison frictions” in the
evaluation of different Medicare Part D prescription drug plans. The choice between a vast
number of school programs may be daunting and as a result, some may simply randomly list
choices, especially further down their rank order list. If preferences were generated in this way
by a large fraction of participants, then we’d expect that most of our point estimates to be
imprecisely estimated or have unintuitive patterns, but they do not. Another way to see that
choices matter for participants is to examine enrollment decisions by choice. Table A3 reports
assignment and enrollment decisions for students who are assigned in the main round. The
table shows that 92.7% of students enroll in their assigned choice, and this number varies from
88.4% to 94.5% depending on which choice a student receives. Interestingly, take-up is higher
for students who receive lower ranked choices, while the fraction of students who exit is highest
among students who obtain one of their top three choices. This fact suggests that either families
are indifferent between later choices and simply enroll where they obtain an offer or families have
deliberately investigated later choices and are therefore willing to enroll in lower ranked schools.
If families are more uncertain about lower ranked choices, then using information contained
in all submitted ranks may provide a misleading account of student preferences. The last two
columns of Table 7 present demand estimates using only the top and top three ranked schools.
These smaller samples use only 13% and 36% of the submitted choices, so they discard much of
the data set. Despite this, the coefficient on distance is similar across these two models and the
one using all submitted ranks. Many of the interaction terms have similar signs to column (4),
but as expected, they are estimated less precisely. On balance, the pattern of estimates shows
remarkable consistency.
The second issue with the assumption of truthful preferences is that students can rank at
most 12 programs on school applications. When a student is interested in more than 12 schools,
she has to carefully reduce her choice set down to at most 12 schools. If a student is only
interested in 11 or fewer schools, this constraint in principle should not influence her ranking
behavior (Abdulkadiroğlu, Pathak, and Roth 2009, Haeringer and Klijn 2009). It is a weakly
dominant strategy to add an acceptable school to a rank order list as long as there is room for
additional schools in the application form. However, 20.3% of students in our demand sample
rank 12 schools. Some of these students may drop highly sought-after schools from top of their
choice lists because of this constraint.
To probe how restrictions on number of choices influence our preference estimates, Table A4
report estimates dropping students ranking 12 choices from the sample. Despite the change in
the composition of students, there is little change in our preference estimates. The coefficients
on distance and school main effects are nearly identical with those in column (4), implying that
the 12 choice constraint is unlikely to significantly alter our conclusions.
Another concern with treated submitted rankings as truthful is that parents rank schools
19

using heuristics carried over from the previous system. Despite the theoretical motivation and the
DOE’s advice, parents might still deviate from truth-telling for reasons related to misinformation
or lack of information about the new mechanism. Table A2 shows that students are more likely
to be assigned their last choice than their penultimate choice. This pattern may be caused by
strategic behavior if students apply to schools that they like and, as a safety option, rank a school
in which they have a higher chance of admissions last. However, it may also be fully consistent
with truth-telling. For example, students usually obtain borough priority or zone priority for
schools in their neighborhoods. Ranking these schools improves their likelihood of being assigned
to these schools in case they are rejected by their higher choices. If students consider applying and
commuting to schools further away from their neighborhood for reasons like math and English
achievement, they may as well stop ranking schools below their neighborhood schools once such
considerations no longer justify the cost of commute. This preference pattern would produce the
assignment pattern observed in the data. Column (3) in Table A4 presents estimates dropping
the last choice of applicants; the coefficients on distance and school effects are nearly identical
to column (1), implying that the possibility of strategically ranking safety schools seems unlikely
to alter our conclusions.
Finally, our approach avoids use of rank order lists to identify the value of the outside option
relative to NYC public schools. The primary reason is that it that our counterfactuals exercises
focus on the re-allocation of NYC public schools. However, one may be worried about bias in our
estimates from this assumption. If ranking additional acceptable schools is cognitively costless,
it may be appropriate to assume that unranked schools are worse than the outside option. Two
facts suggest this is not true: the typical student ranks 9 out of 649 programs and 72.9% of
students who are participate in the supplementary round enroll at the school they are assigned
in that round (shown in Table A3). Column (4) of Table A4 reports estimates of models only
using information about the order of choices among ranked alternatives. We assume that when a
student does not rank a school, that fact does not contain any information about their preferences:
the school could either be ranked above an applicant’s top choice or below it. Our models, so
far, treat ranked schools as more preferred than unranked schools. Perhaps unsurprisingly, the
estimates from this model are considerably different than our other specifications. In particular,
the importance of distance and school main effects are not comparable to the other specifications.
The psuedo-R 2 is only 0.60 and the model fit is worse. As a result, the information on what
schools are ranked or not ranked is important for our preference estimates.
Ignoring the outside option does not yield biased estimates if the value of outside option is
unrelated to preferences for inside options or if number of ranked schools is unrelated to the
value of outside option. These assumptions may not be satisfied, so the last column of Table A4
reports estimates with an outside option, where we normalize the value of the outside option to
zero. The IIA assumption implies that estimates should not be sensitive to the specification of
the outside option assumed to be preferred to all unranked schools. Consistent with this, the
estimates are close to those shown in column (1). However, all of the school effects are less than
0, implying that students prefer the outside option (i.e. not a NYC public school) to unranked
schools. This unappealing implication contradicts the high take-up of public schools among our
students.
20

6.3 Model Fit
An important necessary condition for using our preference estimates to make welfare statements
is that they account for main moments of data. Figure 3 plots the predicted market shares
of each program, computed using our preference estimates in column (4) of Table 7, against
the program’s actual market share on a log scale. Market share is defined as the fraction of
students who rank a program anywhere on their rank order list. We compute predicted market
shares by drawing the top 12 programs from the estimated preference distribution 100 times for
each student and taking the average for each program. The figure shows a strong correlation
between the two measures, an encouraging phenomenon likely driven by the presence of school
fixed effects and the large number of student and school interactions. However, this relationship
is not mechanical since the parameters are not estimated by inverting the fraction of students
ranking a program first (Berry 1994). The single set of school fixed effects used to explain the
rankings could have resulted in a poor fit.
Another way to assess within-sample fit is to see what our estimates imply for the aggregate
patterns by rank in Table 6. In Table 9, we use the estimates to compute the distribution of
preferences and aggregate them into cells corresponding to those reported in Table 6. Comparing
the ranked program to the overall distribution of school characteristics, shown in the first column,
the preference estimates capture many features of the distribution of preferences, though the
estimated tradeoffs in school attributes going down rank order lists is sometimes not as steep
as what is observed. For instance, for first choices, school’s fraction high math achievement is
14.9, while it drops to 13.8 for last choices. In the our sample, the corresponding range is 16.7
to 10.4. Relative to the average attributes of schools, the model fit is much closer to the actual
ranked distribution. The average distance to a high school in New York is 12.3 miles away from
home, yet the top ranked school is 4.4 miles away. Moreover, the average percent white in New
York’s schools is 10.8, but first choices are 19.1 white, while we predict them to be 17.4. Each
predictions is closer to the actual properties of ranked schools than the aggregate distribution.
The attributes of the schools ranked and what we predict using our demand estimates are
relatively close, especially for choices from three to ten. There are more significant differences
between the prediction and actual choices for the top two choices. For instance, we predict
that the average first choice is 5.1 miles away, while it is 4.4 miles away in the data. It is
worth noting that a student’s closest school is 0.82 miles away, so our predictions are far better
than a behavioral model where students simply rank their closest school first. The drop in
predictive accuracy for the last three choices is probably driven by changes in the composition of
students who submit long rank order lists. Nonetheless, the model appears to capture the trend
in preferences going down rank order lists.
We next relate our estimated taste parameters to information that we have not used for
estimating the distribution of preferences in an out-of-sample test. In Table 10, we regress
indicators of exit and school matriculation, shown earlier, on our estimates of the observable
components of student i’s utility for her assignment. This is an out-of-sample test because
neither exit or matriculation decisions are used in estimation. Let y i indicate whether a student
exits NYC public schools or does not exit, but enrolls in a school other than her assigned one.
21

We fit equations like:
y i = λû ia + γd ia + z i β + ɛ i ,
where û ia is student i’s expected utility for program assignment a expressed in miles, d ia is the
distance to assigned school, and z i represents the student demographic and baseline achievement
measures in the demand model. Since distance is a key aspect of student preferences, we compare
whether our imputed utility (which uses the submitted rankings) provides additional information
beyond distance for the exit or matriculation decisions, conditional on student attributes.
The estimates in column (1) show that if students obtain greater utility (measured in miles)
for their assignment, they are less likely to exit in the coordinated mechanism. This pattern is
reassuring since the demand estimates come from the main round of the coordinated mechanism,
but we have not used information on the exit decision in estimation. Distance to school has no
additional predictive power for the exit decision beyond the controls for student attributes in
column (2). Matriculation is also negatively related to the utility from assignment in Panel B,
while distance exhibits the opposite pattern. The magnitude of an increase distance is smaller
than the magnitude of an decrease in estimated utility (in miles) on exit.
An even more demanding comparison considers what our estimates imply for data from the
uncoordinated mechanism. This comparison is more demanding because it uses data on preferences
fitted from the coordinated mechanism to look at an out-of-sample decision in the uncoordinated
mechanism for an entirely different student sample. It is reassuring that the relationship
between utility, exit and matriculation is similar those reported using this distinct data from the
uncoordinated mechanism. Just as with the coordinated mechanism, student exit is negatively
related to a student’s utility from their assigned school, and the utility measure has a larger
weight than distance. The magnitude of the estimate for predicting matriculation is similar to
that in the coordinated mechanism. This out-of-sample comparison suggests that our preference
estimates may be suitable for understanding the utility associated with the assignments in the
uncoordinated mechanism.
7 Comparing Mechanisms
7.1 Measuring Welfare
The preference estimates in the last section allow us to compare the assignments produced by the
uncoordinated and coordinated mechanisms, assuming that the preference estimates for students
in the coordinated mechanism are similar to the underlying estimates in the uncoordinated
mechanism. Since we do not observe the same student in both the uncoordinated and coordinated
mechanism, it is necessary to make statements about groups of students rather than particular
individuals.
Consider a group of students with attribute G and a matching µ, which specifies the program
for each student as µ(i), where if student i is unassigned µ(i) = i. Define the average welfare as
a function of parameters θ as
W µ G (θ) = 1 ∑
u
|G| iµ(i) (θ) ,
i∈G
22

which is the per-student average of the utilitarian welfare criterion for group G. For two different
matchings, µ and µ ′ , corresponding set of students in group G(µ) and G(µ ′ ), the estimate of the
welfare difference between the two matchings is given by:
W µ µ′
G
(θ) − W
G (θ) = 1
|G(µ)|
∑
i∈G(µ)
u iµ(i) (θ) −
1
|G(µ ′ )|
∑
i∈G(µ ′ )
u iµ ′ (i) (θ) .
Notice that the welfare difference depends only on the utility differences between the inside
options at θ. Therefore, when we compare the uncoordinated and coordinated mechanism, we
normalize the utilities so that the mean utility for all students in the coordinated mechanism is
zero.
Furthermore, since no unassigned students are in the welfare samples, it is not necessary to
impute a value to these students. As a result, our comparisons may understate the total welfare
from the the new assignment system because it is only an intensive margin calculation and
does not include the difference in exit rates that we described earlier. We are able to, however,
assess the effects of the non-compliance by students who switched schools post-assignment using
imputed utilities from the October enrollment in the subsequent school year. 13
To operationalize our welfare comparisons, it is necessary to confront the fact that the precise
allocation system used in the old mechanism cannot be easily simulated. To compute the welfare
of the assignment, we need to calculate the utility conditional on a student being assigned to
a given school program. This utility may differ from the utility given only observed student
characteristics because of the unobserved taste term ɛ ij . A student’s submitted ranking reveals
information about unobserved tastes. It is therefore necessary to model and account for this
selection issue in our welfare calculations.
In the coordinated mechanism, we observe the rankings submitted by students. Under the
assumption that these reports are truthful, a program ranked kth yields the kth highest utility.
For students in the coordinated mechanism who submit rank order list r i , we calculate the
expected utility for each ranked choice and each unranked choice by simulating the utility from
the estimated preference distribution, conditional on the relationships implied by the submitted
ranks (see Appendix A for details on this calculation).
The old mechanism’s uncoordinated nature makes the relationship between preferences and
the final assignments less straightforward. Computing the expected utility conditional on the assignments
requires strong assumptions about the old mechanism. Our approach exploits rankings
from the uncoordinated mechanism’s first round. Such data is rarely available for in uncoordinated
mechanisms, but are also difficult to interpret because of incentive properties of the system
under which they were submitted. To avoid asymmetries in the welfare comparisons between
mechanisms, we assume that the ranked school in the old mechanism are reported truthfully and
all unranked schools are less preferred to ranked schools. This assumption is likely provides an
optimistic case for the students that are assigned to a program to which they applied. 14 It is also
safe to assume that students assigned in the supplementary or over-the-counter round do not
13 The data tell us school a student is enrolled in, but not the program. If the assigned school is identical to the
enrolled school, we assume that the enrolled program remains the same. For students switching to new schools,
we use the program-size weighted mean as the utility measure.
14 We also examined an alternative weaker assumption that schools ranked in the uncoordinated mechanism
23

prefer those assignments to ones they applied to since they could have instead applied to those
schools in the main round (and those schools were in fact available). Indeed, Table 5 makes clear
that those schools have less desirable attributes.
For both mechanisms, we compute the expected utility of a program ranked kth by student
i as
[
E u ij
| u (k+1)
i
]
< u ij < u (k−1)
i
, r ik = j
and the expected utility for all unranked schools as
[
]
E u ij | u ij < u (|r i|)
i
, j ∉ ∪{r ik } , (2)
where u (k)
i
is the kth highest value of {u ij } J j=1 and |r i| is the number of ranks submitted by
student i. 15 Using these values, the welfare difference for group G from assignments µ and µ ′ is
W µ G − W µ′
G = 1
|G(µ)|
∑
i∈G(µ)
E[u iµ(i) |r i ] −
1
|G(µ ′ )|
∑
i∈G(µ ′ )
E[u iµ ′ (i)|r i ],
where E[u ij |r i ] denotes the conditional expectations in equations (1) and (2) above.
7.2 Welfare across Mechanisms
Most students are better off under the coordinated mechanism. Figure 4 plots the overall distribution
of student welfare from the two mechanisms. On average, students benefit by a distanceequivalent
utility of 4.79 miles from the new mechanism. There is a bimodal pattern of utility
in the uncoordinated mechanism due to the students who are assigned in the over-the-counter
round. Most of the mass in the first mode shifts rightward in the coordinated mechanism, given
the sharp reduction in the number of over-the-counter students.
Table 11 reports on welfare differences for the same student groups that we reported on offer
processing. For each student group, there is a positive gain from the new mechanism. Across
racial groups, the gains are similar, with whites and Hispanics improving slightly more than
blacks and Hispanics. There are sharper differences across boroughs. Students from Staten
Island, Queens, and the Bronx gain the most, while the smallest gain of any student group in
the table comes from Manhattan residents. Low baseline math students gain more than high
baseline math students or SHSAT test takers.
One aspect of evaluating an assignment system is understanding whether initially bad allocation
systems are undone post-assignment through aftermarket retrading. This view, sometimes
associated with Coase (1960), implies that greater flexibility to switch assignments in the uncoordinated
mechanism could undo the deleterious effects of initial assignments. To examine
this possibility, we also compute the utility associated with the schools students enroll at in
October of the following school year. Compared to assignments, the gains from the coordinated
are better than those that are not ranked, but we did not utilize information on the ordering within ranked
alternatives. Consistent with evidence on the importance of what is ranked vs. unranked, the welfare estimates
under this assumption are similar to those we report.
15 We do not observe applications for some students, and some choices are not available in the main round. In
these cases, we impute the mean utility conditional on observables alone in the welfare calculations.
(1)
24

mechanism measured by enrollment are somewhat smaller, but are still large. For instance, the
average student benefits by a distance-equivalent utility of 3.99 miles, which is 83% of the gain
from assignments. The change in travel distance to enrolled school is also lower than the change
in travel distance to assignment. About 0.3 of the 0.8 miles difference is due to this reduction
in travel distance. Though a smaller gain from enrollment suggests that some of the old mechanism’s
mismatch was undone in its aftermarket, these facts weigh against the argument that
post-market reallocation will undo a large fraction of misallocation.
Comparing the change in utility to the change in distance, it is possible to measure how
much more match-specific utility students obtain from the coordinated mechanism. On average,
the newly assigned school is equal to 5.53 miles of distance-equivalent utility. This implies that
the improved school match is worth about eight times the costs associated with increased travel
distance. The lowest gains are for Manhattan residents, a group which experiences no increase
in travel distance. However, the welfare gains are not solely driven by changes in distance.
For instance, across boroughs, Staten Island pupils only travel 0.34 miles further, but they
experience the largest improvement of any borough at 6.32 miles. This suggests that mismatch
was particularly severe in Staten Island, and is consistent with the substantially larger fraction
of Staten Island residents who are assigned in the over-the-counter round in the uncoordinated
mechanism. The important role of match-specific utility suggests that even if there are not
enough good schools to assign everyone their top choice, preference heterogeneity generates an
important role for matching mechanisms.
The new mechanism has improved measures of equity of assignment. For instance, welfare
gains are larger for low baseline math students than high baseline math students. They are
also higher for special education and limited English proficient students than SHSAT test-takers.
These differences within student groups closely track the rounds in which students were processed
in the uncoordinated mechanism. For instance, substantially more high baseline students were
assigned in the main round of the old mechanism compared to low baseline students. In many
instances, student groups with higher fractions assigned in the over-the-counter round, shown in
column (7), experience the largest gains. This may explain why there is relatively little difference
between students who are either from rich or poor neighborhoods. Wealthier students may have
been more effective at navigating the old mechanism. However, Staten Island residents, many
who are white, experience the largest welfare gains, and Staten Island’s neighborhood income
levels are higher on average than other parts of the city.
We’ve already seen evidence for mismatch among those assigned over-the-counter in Table 5.
Another way to examine the important role of over-the-counter assignments by further disaggregating
students. We estimate a probit of whether a student is assigned over-the-counter on all
student characteristics in the demand model. We also include census tract dummies to account
for neighborhoods that may or may not have local high schools serving as student fallback. Given
the large number of dummies, we are able to forecast whether a student is locally assigned with
a high degree of accuracy. We then use this estimated relationship to compute each student’s
propensity to be assigned over-the-counter in both the uncoordinated and coordinated mechanism.
For each decile of this propensity, we compare the utility from assignment across both
mechanisms. Figure 5 shows that distance to assignment is relatively unchanged across these ten
25

student deciles. However, there is a clear monotonic pattern between over-the-counter propensity
and the welfare improvement, whether comparing utility differences including distance or net of
distance.
The facts clearly illustrate that the reduction in the number of over-the-counter round participants
drive the welfare gains in the coordinated mechanism. But why were so many students
assigned in that round in the old mechanism? There are at least two features of the old mechanism
that could generate this phenomenon. First, students are not able to rank more than five
choices, so large numbers of unassigned indicate that students were not successful at calibrating
their rankings to ensure acceptance at one of their five choices. In the coordinated mechanism,
12.6% of students were assigned to choices 6-12 (shown in Table A2). Second, there are 17,263
“extra” offers in the first round, but only about 10,000 students finalized in the second and third
rounds. This means that many of these extra offers did not percolate through to other students.
Both multiple offers and short rank order lists in the uncoordinated mechanism interact
to generate over-the-counter placements.
8 Evaluating Mechanism Design Features
Many of the new mechanism’s features were intended to address issues created by the old mechanism.
Among the difficulties of the old mechanism its few rounds of offer processing, multiple
offers, and poor student and school incentives. A single-offer mechanism based on the studentproposing
deferred acceptance algorithm coordinates offers and simplifies the student ranking
problem. Is the allocation produced by the new mechanism the best possible one or would alternatives
have further improved overall student welfare? The alternatives we consider hold here
fixed the set of schools and students, but change the allocation mechanism.
The cardinalization of utility implied by our demand model allows us to compute student
welfare maximum, by finding the assignment that maximizes the sum of student utility subject
the feasibility constraints of the assignment. This program corresponds to the utilitarian optimal
assignment ignoring school priorities and can be computed following Shapley and Shubik
(1971). 16 We first draw complete student preference lists randomly conditional on submitted
ranks, taking 1,000 draws from the distribution conditional on the observed ranks. We then
compute the utilitarian optimal assignment for each draw.
With this aggregate welfare maximizing level of utility as our benchmark, the first question
we ask is how does the allocation produced by the current mechanism compares to this maximum.
We compute assignments from the student-proposing deferred acceptance algorithm using
stated preferences and a single tie-breaking rule 1,000 times. To avoid imputing a welfare to
unassigned, if a student in the demand sample is left unassigned, we use their preferences to
mimic NYC’s supplementary round, by assigning them under a serial dictatorship according to
the random ordering of students. Student preferences for this round use the simulated ranks
from the estimated model. Following the computation for the optimal assignment, the welfare
calculation includes the effect of unobservable taste components ɛ ij conditional on their student
16 The utilitarian allocation implies equal weights on students; in quasi-linear problems, such an allocation would
be synonymous with the Pareto efficient allocation, but need not be here.
26

ank (as described in Appendix A).
The first column of Table 12 shows that the allocation produced by the new mechanism is 2.85
miles from the maximum achievable only respecting feasibility. Relative to the difference between
the uncoordinated and coordinated mechanism of 4.79 miles, this contrast implies that further
improvements in the matching mechanism could at best be equal to 59% of gain from coordinating
assignment. The utilitarian optimal assignment is an idealized benchmark, but is unlikely to
be achieved given that it requires a cardinal mechanism and completely ignores the schools’
priorities. There are 208 screened programs in New York City in 2003-04, so implementing
this allocation would involve overriding the preferences of these programs. It is also possible
that students would express different rank orderings under a mechanism that implements the
utilitarian outcome. Therefore, we consider another alternative that does not completely abandon
school priorities.
The student-proposing deferred acceptance (DA) algorithm produces a stable matching,
which cannot be blocked by a student and school. The presence of ties in school’s ranking
of students, however, means that DA does not produce a student-optimal stable matching, even
though it would if all school preferences are strict. However, a number of authors have pointed
out that deferred acceptance cannot be improved upon without sacrificing strategy-proofness for
students (Erdil and Ergin 2008, Abdulkadiroğlu, Pathak, and Roth 2009, Kesten 2010, Kesten
and Kurino 2012).
We quantify the cost of providing straightforward incentives for students by computing a
student-optimal stable assignment that improves the DA assignment by assigning students higher
in their choice lists, while respecting stability for strict school priorities. Such an assignment can
be computed by the stable improvement cycles (SIC) algorithm developed by Erdil and Ergin
(2008), which iteratively finds Pareto improving swaps for students, while still respecting the
stability requirement for underlying weak priority ordering of schools. A total of 2,348 students
in the demand sample can obtain a better assignment in a student-optimal stable matching, and
this corresponds to an average difference of 2.74 miles of equivalent utility with the utilitarian
optimal assignment. The benefit of a student-optimal stable matching corresponds to a difference
of 0.11 miles relative to the current student-proposing deferred acceptance algorithm. The cost
of this change is that the underlying mechanism is not based on a strategy-proof algorithm. 17
Another way to relax the constraints imposed in the algorithm is to abandon stability all
together. While no stable mechanism eliminates strategic maneuvers by schools (Sönmez 1997),
this may not be an issue in markets with many participants (Kojima and Pathak 2009). Stability
may therefore be seen as an incentive constraint on the assignment mechanism to deal with
strategic schools. 18 If a mechanism does not produce a stable outcome, it is possible that schools
benefit by offering students seats outside of the assignment process. Despite the SIC-outcome
being student-optimal stable, it is not Pareto efficient for students. We quantify the cost of
providing school incentives by computing a Pareto efficient assignment that improves upon the
student-optimal stable assignment by assigning students higher in their choice lists. A Pareto
17 Azevedo and Leshno (2011) provide an example where the equilibrium assignment of the stable improvement
cycles mechanism is Pareto inferior to the assignment from deferred acceptance when students are strategic.
18 Balinski and Sönmez (1999) and Abdulkadiroğlu and Sönmez (2003) provide an alternative equity rationale
for stability.
27

efficient assignment can be found by transferring students from their assigned schools to their
higher ranked choices via the Gale’s Top Trading Cycles algorithm (Shapley and Scarf 1974).
Consequently, we calculate a Pareto efficient matching which dominates each student-optimal
stable matching we simulate and estimate students’ utilities from this Pareto efficient matching
in column (3) of Table 12. A total of 10,882 students obtain a more preferred assignment at a
Pareto efficient matching, which is 2.24 miles away for each student from the utilitarian optimal
assignment. Relative to the current mechanism, the cost of limiting the scope for strategizing
by schools (by imposing stability) is 0.50 miles per student. Both the “cost of strategy-proofness
for students” and the “cost of stability” are smaller than the “benefit of coordination” in the new
mechanism.
The finding that changes to the matching algorithm are smaller than changes associated with
coordinating assignment informs a debate in a related auction market design context. Klemperer
(2002) argued that “most of the extensive auction literature is of second-order importance for
practical auction design,” and that “good auction design is mostly good elementary economics.”
Although our conclusion is not as pessimistic for matching market design, our exercises shows
that even if it were possible to implement a student-optimal stable matching or Pareto efficient
matching, coordinating admissions produces larger gains.
9 Conclusion
Changes in NYC’s high school assignment system provide a unique opportunity to study the
effects of centralizing and coordinating school admissions with detailed data on preferences,
assignments, and enrollment from both mechanisms. The new coordinated mechanism is an
improvement relative to the old uncoordinated mechanism on a variety dimensions. Relative to
the uncoordinated mechanism, there is 7.2 percentage point increase in matriculation at assigned
school. Multiple offers and short rank order lists in the uncoordinated mechanism advantage few
students and leave many without first round offers. A large fraction of these unassigned students
are placed in the over-the-counter round to schools with considerably worse characteristics than
what they ranked. The increase in matriculation is driven by the three times reduction in the
number of students assigned in the over-the-counter process in the coordinated mechanism.
Our demand estimates show that Asians, whites, high math baseline and students from high
income neighborhoods are willing to travel further for good schools. While the coordinated
mechanism assigns students 0.69 miles further to their assignments, it’s easier for students to
obtain the schools they want. The benefit of being assigned through the new mechanism is equal
eight times the cost of additional travel according to our preferred estimates. The gains are
positive on average for students from all boroughs, demographic groups, and baseline achievement
categories. Welfare improvements are also seen whether utility is measured based on assignments
made at the end of the high school match or based on subsequent enrollment, suggesting that
post-match re-allocation does little to undo the market’s design.
The new mechanism increased the equity of access to school choices, since students who were
relatively more effective at navigating the uncoordinated mechanism gained less than students
who were more likely to be processed in its over-the-counter round. Though gains are widespread,
28

low math baseline students and those from Queens and Staten Island benefit more than SHSAT
test-takers and students from Manhattan. Since a shortage of good schools implies that some will
inevitably be assigned to less desirable schools, preference heterogeneity generates a significant
role for a good assignment mechanism to generate allocative efficiencies.
Our study of the new mechanism utilizes rankings submitted in its first year. Though we have
examined several variations to the behavioral assumptions underlying our estimation strategy,
it is possible that we’ve underestimated the long run performance of the new mechanism if
participants alter their behavior as they learn more about how to navigate the process. After the
first year, communication and outreach efforts increased via expanded school open houses and
citywide high school fairs. Schools have also gained more experienced with the new process. For
instance, the DOE has reduced the number of students assigned over-the-counter by providing
guidance on yield management, calibrating offers based on expectations of attrition.
The increase in student welfare from the new mechanism illustrates that there are considerable
frictions to exercising choice in poorly designed assignment systems. The 2003 NYC change
took place in an environment where participants already had some familiarity with choice since
both the uncoordinated and coordinated system had a common application. The most important
differences between the two mechanisms involved eliminating multiple offers and allowing
participants to submit longer rank order lists. We found that these features left many assigned
in an over-the-counter process at schools with significantly worse attributes than where they
would prefer to be placed. These effects are relevant for settings where existing choice processes
have been coordinated and streamlined, such as in London and Denver, two cities which recently
adopted new mechanisms based on deferred acceptance.
In other cities, the welfare gains may be even larger since school assignment processes are even
more uncoordinated and decentralized than NYC’s old HS system. For instance, Boston’s charters
only recently established a unified application timeline, but they still retain school-by-school
admissions and offers, and almost no coordination of waitlists and enrollment. With the exception
of Denver and New Orleans, this situation is the norm across district and charter schools.
However, discussions about unifying admissions and coordinating enrollment are currently under
consideration in cities including Boston, Chicago, Newark, Philadelphia, and Washington DC
(Darville 2013, Vaznis 2013). The NYC evidence suggests that students stand much to gain
from making it easier to apply. However, the relative value of policies such as common timelines,
a common application, single vs. multiple offers, sophisticated matching algorithms, and good
information and decision aids remains an open question.
Finally, it’s worth emphasizing that our analysis has focused on the allocative aspects of
school choice and different school assignment procedures. An important question is whether
allocative changes contribute to changes in the productive dimensions of assignment. That is,
do different student assignment protocols affect levels of student achievement post-assignment?
This far more difficult question requires understanding the link between choices and the education
production function, but we hope to examine it further in future work.
29

Table 1. Characteristics of Student Sample
Mechanism Comparison
Demand Estimation
Uncoordinated Coordinated Coordinated
Mechanism Mechanism Mechanism
(1) (2) (3)
Number of Students 70,358 66,921 69,907
Female 49.4% 49.0% 49.0%
Bronx 23.7% 23.3% 23.7%
Brooklyn 31.9% 34.1% 33.3%
Manhattan 12.5% 11.8% 12.0%
Queens 25.0% 24.8% 24.7%
Staten Island 6.9% 6.0% 6.3%
Asian 10.6% 10.9% 10.6%
Black 35.4% 35.7% 35.7%
Hispanic 38.9% 40.4% 40.3%
White 14.7% 12.6% 13.0%
Other 0.4% 0.4% 0.4%
Subsidized Lunch* 54.0% 63.1% 63.7%
Neighborhood Income 38,360 37,855 37,920
Limited English Proficient 13.1% 12.6% 12.6%
Special Education 8.2% 7.9% 7.5%
SHSAT Test-­‐Taker 22.4% 24.3% 23.9%
Notes: Uncoordinated mechanism refers to 2002-­‐03 mechanism and coordinated mechanism refers to the 2003-­‐04 mechanism based on
deferred acceptance. Subsidized lunch not available pre-­‐assignment and comes from enrolled students as of 2004-­‐05 school year.
Neighborhood income is mean census block group family income from the 2000 census. SHSAT stands for Specialized High School Achievement
Test.

Table 2. Descriptive Statistics for Schools and Programs
Uncoordinated Mechanism
Coordinated Mechanism
(1) (2) (3) (4)
A. Schools
Number 215 235
High English Achievement 19.1 (17.3) 19.3 (17.4)
High Math Achievement 10.2 (13.5) 10.0 (13.4)
Percent Attending Four Year College 47.8 (25.2) 47.2 (25.5)
Fraction Inexperienced Teachers 54.7 (26.8) 55.6 (27.4)
Percent Subsidized Lunch 62.5 (23.0) 62.6 (22.9)
Attendance Rate (out of 100) 85.5 (6.0) 85.7 (6.0)
Percent Asian 8.7 (11.4) 8.6 (11.2)
Percent Black 38.5 (24.2) 38.4 (24.1)
Percent Hispanic 41.9 (22.7) 42.1 (22.8)
Percent White 10.9 (16.5) 10.9 (16.4)
B. Programs
Number 612 558
Screened 233 208
Unscreened 63 119
Education Option 316 119
Spanish Language 27 24
Asian Language 10 9
Other Language 6 7
Arts 80 80
Humanities 89 93
Math and Science 53 60
Vocational 55 59
Other Specialties 163 162
Notes: Panel A reports means in column (1) and standard deviations in column (2), unless otherwise noted. Panel B reports counts. Uncoordinated mechanism refers to 2002-­‐
03 mechanism and coordinated mechanism refers to the 2003-­‐04 mechanism based on deferred acceptance. Data appendix presents information on the availability of school
characteristics. High Math and High English achievement is the fraction of student that scored more than 85% on the Math A and English Regents tests in New York State
Report Cards, respectively. Inexperienced teachers are those that have taught for less than two years.

Table 3. Offer Processing across Mechanisms
Distance to School (in miles) Exit from NYC Public In NYC Public, but at
Number of Students Assignment Enrollment Schools School Other than
(1) (2) (3) (4) (5)
A. Uncoordinated Mechanism -­‐ By Final Assignment Round
Overall 70,358 3.36 3.50 8.5% 18.6%
First Round 24,292 4.22 4.10 5.2% 9.5%
Second Round 5,861 4.50 4.40 4.8% 11.3%
Third Round 4,461 4.35 4.25 4.9% 14.1%
Supplementary Round 10,170 4.61 4.37 7.8% 25.4%
Over-­‐the-­‐Counter Round 25,574 1.61 2.09 13.5% 27.4%
B. Uncoordinated Mechanism -­‐ By Number of First Round Offers
No Offers 36,464 2.80 3.12 10.4% 24.4%
One Offer 21,328 3.89 3.85 7.1% 13.8%
Many Offers 12,566 4.07 4.03 5.7% 9.8%
C. Coordinated Mechanism -­‐ By Final Assignment Round
Overall 66,921 4.05 3.91 6.4% 11.4%
Main Round 54,577 4.02 3.86 6.1% 9.9%
Supplementary Round 5,201 5.10 4.90 4.8% 10.4%
Over-­‐the-­‐Counter Round 7,143 3.50 3.52 9.6% 23.6%
Notes: Columns (2) -­‐ (5) report means. Uncoordinated mechanism refers to 2002-­‐03 mechanism and coordinated mechanism refers to the 2003-­‐04 mechanism based on deferred
acceptance. Student distance calculated as road distance using ArcGIS. Assignment is the school assigned at the conclusion of the high school assignment process. Enrollment is
the school a student enrolls in October following application. Assigned student exits New York City if they are not enrolled in any NYC public high school in October following
application. Student in NYC Public, but at school other than assigned if enrolled in NYC public high school other than that assigned at end of match. Final assignment round is the
round during which an offer to the final assigned school first made.

Table 4. Offer Processing by Student Characteristics
Coordinated Mechanism
Final Assignment Round
Number of First Round Offers
All First Second Third
Supplementar
y
Over the
Counter None One Many
Main
Supplementa
ry
Over the
Counter
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
Students 70,358 24,292 5,861 4,461 10,170 25,574 36,464 21,328 12,566 54,577 5,201 7,143
Female 49.4 52.1 52.4 51.0 48.9 46.1 47.1 51.4 52.7 49.4 48.8 46.8
Bronx 23.7 24.1 26.0 34.7 33.2 17.1 23.6 24.6 22.6 23.3 20.0 25.3
Brooklyn 31.9 32.6 34.4 30.6 35.9 29.4 29.8 33.8 34.9 34.7 35.0 29.0
Manhattan 12.5 19.3 14.2 13.7 16.6 3.7 8.5 14.7 19.9 11.4 11.2 15.2
Queens 25.0 21.7 24.2 20.3 14.4 33.4 27.0 23.8 21.3 24.1 31.9 25.2
Staten Island 6.9 2.2 1.3 0.8 0.0 16.4 11.1 3.1 1.2 6.5 1.8 5.2
Asian 10.6 10.3 9.7 9.2 4.0 14.0 11.0 10.0 10.6 11.0 10.3 10.5
Black 35.4 38.6 40.0 37.7 45.2 27.1 32.1 38.6 39.6 35.6 40.1 33.5
Hispanic 38.9 40.9 39.4 43.5 46.5 33.0 37.8 39.4 41.2 40.5 41.0 39.1
White 14.7 9.8 10.5 9.3 3.8 25.5 18.6 11.7 8.3 12.6 8.2 16.0
High Baseline Math 24.0 29.4 23.6 30.4 12.3 22.5 19.3 26.9 32.7 24.5 15.5 21.2
Low Baseline Math 22.5 21.1 25.0 19.9 30.8 20.5 23.6 22.4 19.5 20.6 19.6 25.4
Subsidized Lunch* 54.0 57.8 57.9 59.5 57.6 47.0 51.7 55.7 57.5 63.4 59.7 63.4
Bottom Neighborhood
Income Quartile
24.1 27.6 27.5 27.9 38.8 13.4 21.6 26.0 27.9 25.1 23.2 25.7
Top Neighborhood Income
Quartile
25.8 21.9 23.5 21.7 14.4 35.3 29.0 23.7 20.1 24.6 23.8 27.3
Limited English Proficient 13.1 12.4 13.2 12.2 14.8 13.2 14.1 11.8 12.4 12.7 12.3 12.7
Special Education 8.2 6.3 7.8 6.2 10.6 9.5 9.8 6.6 6.2 6.9 0.0 20.8
SHSAT Test‐taker 22.4 27.8 26.6 34.3 15.9 16.8 17.5 26.2 30.0 24.6 22.9 22.8
Notes: Uncoordinated mechanism refers to 2002‐03 mechanism and coordinated mechanism refers to the 2003‐04 mechanism based on deferred acceptance. Final assignment round is the round during which an offer to the final assigned school was accepted.
Subsidized lunch not available pre‐assignment and comes from enrolled students as of 2004‐05 school year. Neighborhood income is median family income from the 2000 census.

Table 5. School Access across Rounds of Offer Processing
Main Round
Supplementary Round
Over-­‐the-­‐Counter Round
Uncoordinated Coordinated
Uncoordinated
Uncoordinated Coordinated
Mechanism Mechanism
Mechanism Coordinated Mechanism
Mechanism Mechanism
Ranked
Ranked
Ranked
Ranked
Ranked
Ranked
Schools Assigned Schools Assigned Schools Assigned Schools Assigned Schools Assigned Schools Assigned
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
Distance (in miles) 4.81 4.29 5.10 4.00 4.87 4.59 5.87 5.17 5.12 1.60 5.33 3.43
High English Achievement 21.0 20.3 22.1 19.1 19.9 15.8 26.5 20.0 24.2 17.4 24.2 19.2
High Math Achievement 12.4 11.6 13.0 10.7 11.8 9.3 16.6 14.2 14.8 10.5 14.3 10.7
Percent Attending Four Year College 49.1 47.1 50.6 48.3 48.6 44.9 54.1 50.1 51.9 46.7 51.7 47.9
Percent Inexperienced Teachers 45.3 45.7 46.6 43.8 46.0 41.5 45.3 36.9 41.8 39.3 47.8 42.1
Percent Subsidized Lunch 59.9 60.5 57.6 56.7 62.0 61.8 53.5 51.0 53.8 50.3 57.2 53.1
Attendance Rate (out of 100) 85.1 84.6 85.7 83.8 85.1 82.2 87.4 83.2 85.8 80.7 86.7 82.9
Notes: Means unless otherwise noted. Analysis restricts the sample to students from the welfare sample with observed assignments. Uncoordinated mechanism refers to the 2002-­‐03 mechanism
and coordinated mechanism refers to the 2003-­‐04 mechanism based on deferred acceptance. Main round in the uncoordinated mechanism corresponds to the first round. Rankings used are
those submitted in the main round of the process. Student distance calculated as road distance using ArcGIS. High English and High Math achievement are the fractions of students scoring over
85% on the English and Math A regents in New York State Report Cards, respectively. Inexperienced teachers are those who have been teaching less than 2 years.

Table 6. School Characteristics by Rank of Student Choice in Coordinated Mechanism
Choice 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th
A. All Students
Students Ranking Choice 69,907 93% 89% 83% 76% 69% 62% 56% 50% 43% 34% 20%
Distance in Miles ‐ Mean 4.43 4.81 5.05 5.21 5.38 5.49 5.59 5.63 5.65 5.58 5.43 5.12
Median 3.51 3.95 4.20 4.37 4.57 4.63 4.72 4.77 4.78 4.71 4.59 4.24
High English Achievement 27.8 25.6 24.3 23.2 22.2 21.4 20.8 20.5 19.9 19.4 19.1 18.6
High Math Achievement 16.7 15.3 14.7 13.9 13.4 12.8 12.4 11.9 11.5 11.1 10.8 10.4
Percent Attending Four Year College 53.7 54.1 52.8 51.7 50.9 50.1 49.3 49.3 49.0 48.3 47.6 47.5
Fraction Inexperienced Teachers 43.0 43.8 45.0 46.2 47.1 48.1 48.7 49.5 49.5 50.2 49.9 49.9
Fraction Subsidized Lunch 51.4 53.4 54.5 56.2 57.4 58.7 59.8 60.6 61.3 61.9 62.7 63.1
Attendance Rate (out of 100) 87.2 86.7 86.4 86.1 85.9 85.7 85.5 85.5 85.2 85.0 84.8 84.5
Percent Asian 13.8 13.7 13.3 12.7 12.2 11.5 11.0 10.6 10.1 9.7 9.5 9.4
Percent Black 32.6 34.3 35.1 36.0 36.7 37.5 38.2 38.4 38.7 38.9 38.9 38.1
Percent Hispanic 34.4 35.2 35.9 37.0 37.9 38.9 39.6 40.2 40.8 41.5 42.2 43.5
Percent White 19.1 16.7 15.7 14.4 13.3 12.2 11.2 10.8 10.4 9.8 9.4 9.0
B. Students with Low Baseline Math Scores
Distance in Miles ‐ Mean 4.1 4.4 4.7 4.9 5.0 5.1 5.2 5.2 5.2 5.1 5.0 4.8
High English Achievement 20.1 19.4 18.7 18.4 18.1 17.9 17.6 17.7 17.4 17.1 16.6 16.6
High Math Achievement 10.9 10.9 10.5 10.1 10.0 9.7 9.6 9.4 9.4 9.1 8.8 8.8
C. Students with High Baseline Math Scores
Distance in Miles ‐ Mean 4.6 5.0 5.2 5.4 5.7 5.9 5.9 6.0 6.1 6.2 5.8 5.3
High English Achievement 39.4 34.0 32.0 29.8 28.0 26.4 25.2 24.6 23.7 22.8 22.5 21.5
High Math Achievement 26.0 21.4 20.5 19.1 18.2 17.3 16.4 15.6 15.2 14.2 13.9 12.8
D. Students from Bottom Neighborhood Income Quartile
Distance in Miles ‐ Mean 4.3 4.5 4.7 4.8 5.0 5.0 5.1 5.1 5.2 5.1 4.9 4.7
High English Achievement 20.5 19.8 19.1 18.8 18.4 17.9 18.0 18.0 17.5 17.1 17.1 16.6
High Math Achievement 11.4 10.9 10.5 10.4 10.1 9.9 10.0 9.9 9.6 9.3 9.1 8.7
E. Students from Top Neighborhood Income Quartile
Distance in Miles ‐ Mean 4.6 5.2 5.5 5.7 5.9 6.1 6.3 6.4 6.6 6.6 6.4 5.9
High English Achievement 35.6 32.0 29.9 28.4 26.5 25.6 24.6 23.9 23.1 22.4 21.6 21.0
High Math Achievement 23.3 20.7 19.6 18.7 17.7 16.8 16.0 15.1 15.0 14.1 13.2 12.7
Notes: Coordinated mechanism refers to the 2003‐04 mechanism based on deferred acceptance. Data appendix provides details on availability on school characteristics. Student distance calculated as road
distance using ArcGIS. High English and High Math achievement are the fractions of students scoring over 85% on the English and Math A regents in New York State Report Cards, respectively. Inexperienced
teachers are those who have been teaching less than 2 years. High baseline math students score above the 75th percentile for 7th grade middle school math, low baseline math students score below the 25th
percentile. Neighborhood income is median family income from the 2000 census.

Table 7. Student Preference Estimates
School Characteristics x Student Demographics
School Characteristics x School Characteristics x Student Baseline Achievement
School Characteristics x Student Baseline
Specifications: School Characteristics Student Race Achievement
All Choices Top Choice Only Top Three Choices
(1) (2) (3) (4) (5) (6)
A. Preference for Distance
Distance (in miles) -­‐0.318*** -­‐0.313*** -­‐0.316*** -­‐0.310*** -­‐0.387*** -­‐0.353***
B. Preference for School Characteristics
Size of 9th Grade (in 100s)
Main effect 0.015*** 0.040*** 0.015*** 0.059*** 0.100*** 0.099***
Baseline Math 0.004*** 0.001** 0.002 0.001
Baseline English -­‐0.006*** -­‐0.003*** -­‐0.009*** -­‐0.005***
Subsidized Lunch* -­‐0.014*** -­‐0.029*** -­‐0.024***
Neighborhood Income (in 1000s) -­‐0.650*** -­‐1.930*** -­‐1.930***
Special Education -­‐0.007*** -­‐0.017*** -­‐0.012***
Percent White
Main effect 0.026*** 0.040*** 0.025*** 0.032*** 0.040*** 0.033***
Asian -­‐0.016*** -­‐0.015*** -­‐0.027*** -­‐0.018***
Black -­‐0.022*** -­‐0.020*** -­‐0.035*** -­‐0.024***
Hispanic -­‐0.011*** -­‐0.009*** -­‐0.016*** -­‐0.010***
Attendance Rate
Main effect 0.055*** 0.103*** 0.062*** 0.075*** 0.131*** 0.117***
Baseline Math 0.012*** 0.010*** 0.017*** 0.015***
Baseline English 0.014*** 0.014*** 0.020*** 0.021***
Subsidized Lunch* 0.000 -­‐0.008*** -­‐0.005***
Neighborhood Income (in 1000s) 6.000*** 8.000*** 7.000***
Percent Subsidized Lunch
Main effect -­‐0.002*** -­‐0.007*** -­‐0.003*** -­‐0.004*** 0.005*** -­‐0.003**
Asian 0.000 -­‐0.001 -­‐0.004*** -­‐0.001
Black 0.002*** 0.001** -­‐0.008*** -­‐0.002***
Hispanic 0.010*** 0.009*** 0.007*** 0.010***
Subsidized Lunch* 0.000 -­‐0.002** -­‐0.001***
Neighborhood Income (in 1000s) -­‐0.722*** -­‐1.000*** -­‐0.736***

Table 7. Student Preference Estimates (cont.)
School Characteristics x Student Demographics
School Characteristics x School Characteristics x Student Baseline Achievement
School Characteristics x Student Baseline
Specifications: School Characteristics Student Race Achievement
All Choices Top Choice Only Top Three Choices
(1) (2) (3) (4) (5) (6)
High Math Achievement
Main effect 0.008*** 0.007*** 0.004*** 0.000 0.001 -­‐0.001
Baseline Math 0.008*** 0.007*** 0.012*** 0.009***
Baseline English 0.005*** 0.005*** 0.006*** 0.005***
Subsidized Lunch* -­‐0.003*** -­‐0.005*** -­‐0.005***
Neighborhood Income (in 1000s) 0.119* -­‐0.712*** -­‐0.242**
Limited English Proficient -­‐0.002*** -­‐0.003* -­‐0.005***
Special Education -­‐0.003*** 0.000 -­‐0.001
Spanish Language Program
Limited English Proficient 5.147*** 5.755*** 5.472***
Limited English Proficient x Hispanic -­‐3.142*** -­‐3.817*** -­‐3.147***
Asian Language Program
Limited English Proficient 3.687*** 4.253*** 4.203***
Limited English Proficient x Asian -­‐2.131*** -­‐3.299*** -­‐2.717***
Other Language Program
Limited English Proficient 2.289*** 2.947*** 2.870***
Program Type Dummies X X X X X X
Program Specialty Dummies X X X X X X
C. Model Diagnostics
Number of ranks 542,666 542,666 542,666 542,666 69,907 197,245
Number of parameters 248 272 280 349 349 349
Log likelihood -­‐2,726,580 -­‐2,714,493 -­‐2,710,042 -­‐2,690,008 -­‐302,141 -­‐906,942
Pseudo R-­‐squared 0.85 0.89 0.89 0.92 0.96 0.95
Fraction of variance explained by school 0.43 0.68 0.42 0.53 0.58 0.60
observables
Notes: Selected coefficients from two-­‐step maximum likelihood estimation of demand system with 69,907 students and submitted ranks over 497 program choices in 235 schools. All parameter estimates in appendix Table C1. Student
distance calculated as road distance using ArcGIS. Dummies for missing school attributes are estimated with separate coefficients. Estimates use all submitted ranks except in columns (4)-­‐(6). Column (1) contains no interactions between
student and school characteristics. Column (2) contains interactions of race dummies with all school characteristics. Column (3) contains interactions of baseline Math and English score with school characteristics. Columns (4)-­‐(6) contain
interactions of gender, race, achievement, special education, limited English proficiency, subsidized lunch, and median 2000 census block group family income with all school characteristics. High Math achievement is the fraction of student
that scored more than 85% on the Math A in New York State Report Cards. Models estimate the utility differences amongst inside options only, with an arbitrarily chosen school's mean utility normalized to zero (this normalization is without
loss of generality). Number of parameters include school fixed effects. Pseudo R-­‐squared is the fraction of variance in utility explained by observables. * significant at 10%; ** significant at 5%; *** significant at 1%

Table 8. Estimated Heterogeneity in Student Preferences
By Quartile
Range from Top to
Bottom Second Third Top Bottom Quartile
(1) (2) (3) (4) (5)
A. By Quartiles of Student Utility Net of Distance
All Students -­‐4.32 -­‐0.85 1.12 4.82 9.14
Asian -­‐5.13 -­‐1.34 1.08 5.87 11.00
Black -­‐4.15 -­‐0.57 1.19 4.41 8.56
Hispanic -­‐3.89 -­‐0.80 1.08 4.50 8.40
White -­‐5.84 -­‐1.16 1.07 6.09 11.93
High Math Baseline -­‐4.97 -­‐1.21 1.14 5.82 10.78
Low Math Baseline -­‐4.19 -­‐0.79 1.14 4.72 8.91
B. By Quartiles of School High Math Achievement
All Students -­‐1.54 -­‐0.30 0.90 2.15 3.69
High Math Baseline -­‐2.30 -­‐0.68 0.85 3.63 5.94
Low Math Baseline -­‐1.52 -­‐0.30 0.91 2.13 3.65
C. By Quartiles of School Percent Subsidized Lunch
All Students 2.23 0.88 -­‐1.00 -­‐1.41 3.64
Bottom Neighborhood Income Quartile 1.50 0.67 -­‐0.54 -­‐0.86 2.36
Top Neighborhood Income Quartile 3.11 1.11 -­‐1.60 -­‐2.12 5.23
D. By Quartiles of School Percent White
All Students -­‐2.04 -­‐0.69 0.73 2.94 4.98
Asian -­‐3.01 -­‐1.30 0.89 4.57 7.57
Black -­‐1.62 -­‐0.43 0.69 2.10 3.72
Hispanic -­‐1.71 -­‐0.42 0.81 2.54 4.25
White -­‐3.44 -­‐1.73 0.44 5.14 8.58
Notes: Each row defines a set of students and each column defines a set of programs based on either a program characteristic or the estimated desirability of the program. Utilities in
distance-­‐equivalent miles based on the estimates reported in column (4) of Table 7. Each cell reports the average normalized utility for the relevant student-­‐school group, where we
normalize the mean utility, net of distance, across programs for each student to zero.

Table 9. In-­‐Sample Model Fit
Average in
Ranked Choice
Overall
Distribution 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th
A. All Students
Assignment Observed -­‐ 32% 15% 10% 7% 5% 4% 3% 2% 1% 1% 1% 1%
Distance Observed 12.7 4.4 4.8 5.1 5.2 5.4 5.5 5.6 5.6 5.6 5.6 5.4 5.1
Simulated 5.1 5.2 5.3 5.3 5.4 5.4 5.5 5.5 5.6 5.7 5.7 5.7
High English Achievement
High Math Achievement
Observed 19.3 27.8 25.6 24.3 23.2 22.2 21.4 20.8 20.5 19.9 19.4 19.1 18.6
Simulated 24.8 24.8 24.5 24.3 24.0 23.9 23.7 23.6 23.5 23.5 23.4 23.3
Observed 10.0 16.7 15.3 14.7 13.9 13.4 12.8 12.4 11.9 11.5 11.1 10.8 10.4
Simulated 14.9 15.0 14.7 14.5 14.3 14.2 14.1 14.0 14.0 13.9 13.9 13.8
Percent Attending Four Year
College
Fraction Inexperienced
Teachers
Fraction Subsidized Lunch
Attendance Rate (out of
100)
Observed 47.2 53.7 54.1 52.8 51.7 50.9 50.1 49.3 49.3 49.0 48.3 47.6 47.5
Simulated 52.8 53.1 53.1 53.0 52.9 52.7 52.6 52.5 52.4 52.3 52.2 52.1
Observed 55.6 43.0 43.8 45.0 46.2 47.1 48.1 48.7 49.5 49.5 50.2 49.9 49.9
Simulated 44.9 44.9 45.0 45.1 45.1 45.2 45.3 45.3 45.4 45.4 45.5 45.5
Observed 62.6 51.4 53.4 54.5 56.2 57.4 58.7 59.8 60.6 61.3 61.9 62.7 63.1
Simulated 53.5 53.7 54.0 54.2 54.4 54.6 54.7 54.9 55.0 55.1 55.3 55.4
Observed 85.7 87.2 86.7 86.4 86.1 85.9 85.7 85.5 85.5 85.2 85.0 84.8 84.5
Simulated 86.3 86.3 86.2 86.1 86.1 86.1 86.0 86.0 86.0 86.0 86.0 86.0
Percent Asian Observed 8.6 13.8 13.7 13.3 12.7 12.2 11.5 11.0 10.6 10.1 9.7 9.5 9.4
Simulated 13.0 13.0 13.0 13.0 13.0 13.0 12.9 12.9 12.9 12.9 12.9 12.9
Percent Black Observed 38.4 32.6 34.3 35.1 36.0 36.7 37.5 38.2 38.4 38.7 38.9 38.9 38.1
Simulated 34.5 34.7 34.9 35.1 35.2 35.4 35.5 35.6 35.7 35.8 35.9 35.9
Percent Hispanic Observed 42.1 34.4 35.2 35.9 37.0 37.9 38.9 39.6 40.2 40.8 41.5 42.2 43.5
Simulated 35.1 35.2 35.3 35.5 35.6 35.7 35.7 35.8 35.9 35.9 36.0 36.0
Percent White Observed 10.9 19.1 16.7 15.7 14.4 13.3 12.2 11.2 10.8 10.4 9.8 9.4 9.0
Simulated 17.4 17.1 16.7 16.5 16.2 16.0 15.9 15.7 15.6 15.4 15.3 15.2
B. Students with Low Baseline Math Scores
Distance Observed 12.3 4.1 4.4 4.7 4.9 5.0 5.1 5.2 5.2 5.2 5.1 5.0 4.8
Simulated 5.0 5.1 5.1 5.1 5.2 5.2 5.2 5.3 5.3 5.4 5.4 5.4
High Math Achievement Observed 10.0 10.9 10.9 10.5 10.1 10.0 9.7 9.6 9.4 9.4 9.1 8.8 8.8
Simulated 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.3 10.3
C. Students with High Baseline Math Scores
Distance Observed 13.2 4.6 5.0 5.2 5.4 5.7 5.9 5.9 6.0 6.1 6.2 5.8 5.3
Simulated 5.1 5.2 5.4 5.5 5.5 5.6 5.7 5.8 5.9 5.9 6.0 6.1
High Math Achievement Observed 10.0 26.0 21.4 20.5 19.1 18.2 17.3 16.4 15.6 15.2 14.2 13.9 12.8
Simulated 20.7 20.8 20.0 19.3 18.9 18.6 18.4 18.2 18.1 18.0 17.8 17.7
Notes: Means. Observed characteristics of each choice are from demand sample. Simulated characteristics come from estimated preference distribution corresponding to the model in Table 7 column (4) assuming students rank their top 12 programs.
Missing school characteristics are ommitted from both observed and simulated rows. The average in overall distribution shows average distance to school for all student-­‐shool pairs and other school characteristics are an unweighted average across
programs.

Table 10. Out of Sample Fit for Exit and Matriculation
Coordinated Mechanism Uncoordinated Mechanism
(1) (2) (3) (4)
A. Exit from NYC Public Schools
Utility from Assignment (in miles) -­‐0.0027*** -­‐0.0030***
(0.0002) (0.0002)
Distance from Assignment 0.0001 -­‐0.0026***
(0.0003) (0.0003)
Number of observations 66,921 66,921 70,358 70,358
R-­‐squared 0.0650 0.0623 0.0870 0.0856
B. Enroll in School Other than Assigned
Utility from Assignment (in miles) -­‐0.0130*** -­‐0.0156***
(0.0003) (0.0003)
Distance from Assignment 0.0120*** 0.0009*
(0.0004) (0.0005)
Number of observations 62,656 62,656 64,349 64,349
R-­‐squared 0.0601 0.0392 0.0610 0.0313
Notes: Uncoordinated mechanism refers to 2002-­‐03 mechanism and coordinated mechanism refers to the 2003-­‐04 mechanism based on
deferred acceptance. Exit is indicator that assigned student enrolled in a school outside NYC public system. Enroll in school other than assigned
is an indicator that assigned student enrolled in NYC public high school other than that assigned at end of match. Distance calculated as road
distance using ArcGIS. Utility estimates are come from specification in column (4) of Table 7, projected on observable student and school
characteristics for the mechanism comparison sample in the uncoordinated and coordinated mechanism. Columns (1) and (3) report estimates
of exit and enrollment indicators regressed on utility (in distance units), while columns (2) and (4) report estimates of exit and enrollment
indicators regressed on on distance to assignment. All models include controls for student race, baseline Math, baseline English, no baseline
Math score, no baseline English score, subsidized lunch, neighborhood income (from 2000 census block group median family income), limited
English proficiency, and special education. * significant at 10%; ** significant at 5%; *** significant at 1%

Table 11. Welfare Comparison between Mechanisms
Change in Utility
(in miles)
Change in Distance (in miles)
2002-­‐03 Offer Processing
Assignment Enrollment Assignment Enrollment Main Rounds Supplementary Over-­‐the-­‐Counter
(1) (2) (3) (4) (5) (6) (7)
All Students 4.79 3.99 0.69 0.38 49.2% 14.5% 36.3%
Female 4.45 3.63 0.68 0.37 51.8% 14.3% 33.9%
Asian 4.75 3.75 0.63 0.33 46.6% 5.4% 48.0%
Black 4.57 3.82 0.74 0.45 53.7% 18.4% 27.8%
Hispanic 4.95 4.23 0.66 0.39 51.9% 17.3% 30.8%
White 5.25 3.94 0.56 0.22 33.1% 3.8% 63.1%
Bronx 5.26 4.57 0.93 0.64 53.5% 20.2% 26.2%
Brooklyn 4.79 4.15 0.52 0.33 50.3% 16.2% 33.5%
Manhattan 1.80 1.39 0.00 -­‐0.09 69.9% 19.2% 10.8%
Queens 5.41 4.01 1.13 0.57 43.2% 8.3% 48.5%
Staten Island 6.32 6.20 0.34 0.00 13.5% 0.0% 86.5%
High Baseline Math 3.14 2.12 0.53 0.20 58.5% 7.4% 34.1%
Low Baseline Math 5.25 4.65 0.57 0.33 47.1% 19.8% 33.1%
Subsidized Lunch* 4.52 3.77 0.59 0.31 52.9% 15.4% 31.7%
Bottom Neighborhood Income
4.38 3.96 0.57 0.42 56.4% 23.3% 20.3%
Quartile
Top Neighborhood Income Quartile 4.59 3.36 0.71 0.25 42.2% 8.1% 49.8%
Special Education 5.38 4.40 0.76 0.43 39.2% 18.8% 42.0%
Limited English Proficient 5.68 5.02 0.60 0.38 47.1% 16.3% 36.6%
SHSAT Test-­‐Takers 2.63 1.85 0.55 0.25 62.5% 10.3% 27.2%
Notes: Utilities are in distance units (miles) averaged across students in the mechanism comparison sample in Table 1 using preference estimates in Table 7 column (4). Assignment is the school assigned at the
conclusion of the high school assignment process. Enrollment is the school student enrolls in October following application. 2002-­‐03 offer process reports the fraction of students with row characteristic first offered
school finally assigned in the main round (rounds 1-­‐3), the supplementary round or the over the counter process. Student distance calculated as road distance using ArcGIS. High baseline math students score above
the 75th percentile for 7th grade relative to citywide distribution, while low baseline math students score below the 25th percentile. Subsidized lunch not available pre-­‐assignment and comes from enrolled students
as of 2004-­‐05 school year. Neighborhood income is median census block group family income from the 2000 census.

Table 12. Alternative Mechanisms Relative to Utilitarian Optimal Benchmark
Student-­‐Proposing Student Optimal Ordinal Pareto Efficient
Deferred Acceptance
Matching
Matching
(1) (2) (3)
Utility (in miles) -­‐2.85 -­‐2.74 -­‐2.24
Number of students reassignments
relative to column (1)
2,348 10,882
Notes: Utility from alternative assignments relative to utilitarian optimal assignment computed using actual preferences ignoring all school-­‐side
constraints except capacity. Utility computed using estimates in Table 7 column (4). Mean utility from the utilitarian optimal assignment normalized to
zero. Column (1) is from 500 lottery draws of student-­‐proposing deferred acceptance with single tie-­‐breaking using the demand estimation sample. If
a student is unassigned, we mimic the Supplementary Round by assigning students according to a serial dictatorship using preferences drawn from the
preference distribution estimated in Table 7 column (4). Student optimal matching computed by taking each deferred acceptance assignment and
applying the Erdil-­‐Ergin (2008) stable improvement cycles algorithm to find a student-­‐optimal matching. Ordinal Pareto Efficient Matching computed
by applying Gale's top trading cycles to the economy where the student-­‐optimal matching determine student endowments, followed by the
Abdulkadiroglu-­‐Sonmez (2003) version of top trading cycles with counters.

Figure 1. School Locations and Students by New York City Census Tract in 2002-­‐03 and 2003-­‐04

Figure 2. Distribution of Distance to Assigned School in
Uncoordinated (2002-­‐03) and Coordinated (2003-­‐04) Mechanism
Mean (median) travel distance is 3.36 (2.25) miles in 2002-­‐03 and 4.05 (3.04) miles in 2003-­‐04. Top and bottom 1% are not shown in
figure. Line fit from Gaussian kernel with bandwidth chosen to minimize mean integrated squared error using STATA’s kdensity
command.

Figure 3. Log-­‐Log Plot of Predicted vs. Actual Program Market Shares
Market share means fraction of applicants ranking program anywhere on rank order list. Predicted program market shares based on
preference estimates from the specification in column (4) of Table 6, using 100 draws from our estimates and assuming students
rank their top 12 programs. Each point corresponds to the predicted and actual market share.

Figure 4. Student Welfare from Uncoordinated and Coordinated Mechanism
Distribution of utility (measured in distance units) from assignment based on Table 7 column (4) estimates plotted with mean utility
in 2003-­‐04 normalized to 0. Average difference corresponds to 4.79 miles. Top and bottom 1% are not shown in figure. Line fit
from Gaussian kernel with bandwidth chosen to minimize mean integrated squared error using STATA’s kdensity command.

Figure 5. Change in Student Welfare by Propensity to Assigned
in the Over-­‐the-­‐Counter Round of Uncoordinated Mechanism
Probability of over the counter assignment estimated from probit of over the counter on student census tract dummies and all student characteristics in the
demand model except for distance. If student lives in tract where either all students are assigned over the counter or no students are assigned over the
counter, for forecasting all students from those tracts are coded as over the counter. Each student is assigned to one of ten deciles of probability of over the
counter based on these estimates. Differences across deciles in distance-­‐equivalent utility including distance, distance-­‐equivalent utility net of distance, and
distance are plotted, where preference estimates come from column (4) of Table 7, conditional on submitted rankings. Distance is calculated as road
distance using ArcGIS.

References
Abdulkadiroğlu, A., J. Angrist, and P. Pathak (2013): “The Elite Illusion: Achievement
Effects at Boston and New York Exam Schools,” forthcoming, Econometrica.
Abdulkadiroğlu, A., J. D. Angrist, S. M. Dynarski, T. J. Kane, and P. A. Pathak
(2011): “Accountability and Flexibility in Public Schools: Evidence from Boston’s Charters
and Pilots,” Quarterly Journal of Economics, 126(2), 699–748.
Abdulkadiroğlu, A., Y.-K. Che, and Y. Yasuda (2012): “Expanding Choice in School
Choice,” Working paper, Duke University.
Abdulkadiroğlu, A., P. A. Pathak, and A. E. Roth (2005): “The New York City High
School Match,” American Economic Review, Papers and Proceedings, 95, 364–367.
(2009): “Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning
the New York City High School Match,” American Economic Review, 99(5), 1954–1978.
Abdulkadiroğlu, A., and T. Sönmez (2003): “School Choice: A Mechanism Design Approach,”
American Economic Review, 93, 729–747.
Abulkadiroğlu, A., W. Hu, and P. A. Pathak (2013): “Small High Schools and Student
Achievement: Lottery-Based Evidence from New York City,” NBER Working Paper, 19576.
Agarwal, N. (2013): “An Empirical Model of the Medical Match,” Unpublished working paper,
MIT.
ALG (2005): “Association of London Government, Report to the Leader’s Committee on London
Co-ordinated Admissions (Item 9), May 10,” May 10.
Arvidsson, T. S., N. Fruchter, and C. Mokhtar (2013): “Over the Counter,
Under the Radar: Inequitably Distributing New York City’s Late-Enrolling High
School Students,” Annenberg Institute for School Reform at Brown University, Available
at: http://annenberginstitute.org/publication/over-counter-under-radar-inequitablydistributing-new-york-city%E2%80%99s-late-enrolling-high-sc,
Last accessed: October 2013.
Azevedo, E. M., and J. D. Leshno (2011): “Can we make school choice more efficient? An
example,” Unpublished mimeo, Harvard University.
Balinski, M., and T. Sönmez (1999): “A Tale of Two Mechanisms: Student Placement,”
Journal of Economic Theory, 84, 73–94.
Berry, S. (1994): “Estimating Discrete-Choice Models of Product Differentiation,” Rand Journal
of Economics, 25(2), 242–262.
Berry, S., J. Levinsohn, and A. Pakes (1995): “Automobile Prices in Market Equilibrium:,”
Econometrica, 63(4), 841–890.
48

(2004): “Differentiated Products Demand Systems from a Combination of Micro and
Macro Data: The New Car Market,” Journal of Political Economy, 112(1), 68–105.
Bulow, J., and J. Levin (2006): “Matching and Price Competition,” American Economic
Review, 96, 652–668.
Coase, R. (1960): “The Problem of Social Cost,” Journal of Law and Economics, 3, 1–44.
Darville, S. (2013): “NYC Sitting Out National Move to Tie Charter, District Admissions,”
GothamSchools, September 20, http://gothamschools.org/2013/09/20/nyc-sitting-outnational-move-to-tie-charter-district-admissions/,
Last accessed: September 2013.
Deming, D. J., J. S. Hastings, T. J. Kane, and D. O. Staiger (2011): “School Choice,
School Quality and Postsecondary Attainment,” forthcoming, American Economic Review.
DOE (2002): “Directory of the New York City Public High Schools: 2002-2003,” New York City
Department of Education.
(2003): “Directory of the New York City Public High Schools: 2003-2004,” New York
City Department of Education.
Dubins, L. E., and D. A. Freedman (1981): “Machiavelli and the Gale-Shapley algorithm,”
American Mathematical Monthly, 88, 485–494.
Engberg, J., D. Epple, J. Imbrogno, H. Sieg, and R. Zimmer (2010): “Bounding the
Treatment Effects of Education Programs that Have Lotteried Admission and Selective Attrition,”
Unpublished working paper, University of Pennsylvania.
Epple, D., and R. Romano (1998): “Competition Between Private and Public Schools, Vouchers,
and Peer Group Effects,” American Economic Review, 88(1), 33–62.
Erdil, A., and H. Ergin (2008): “What’s the Matter with Tie-Breaking? Improving Efficiency
in School Choice,” American Economic Review, 98, 669–689.
Gale, D., and L. S. Shapley (1962): “College Admissions and the Stability of Marriage,”
American Mathematical Monthly, 69, 9–15.
Gendar, A. (2000): “Simpler HS Entry Eyed Ed Board Aims to Trim Selection Process, Improve
Schools,” New York Daily News, October 21.
Haeringer, G., and F. Klijn (2009): “Constrained School Choice,” Journal of Economic
Theory, 144, 1921–1947.
Hastings, J., T. J. Kane, and D. O. Staiger (2005): “Parental Preferences and School
Competition: Evidence from a Public School Choice Plan,” NBER Working Paper, 11805.
(2009): “Heterogenous Preferences and the Efficacy of Public School Choice,” Working
paper, Yale University.
49

Hastings, J., and J. M. Weinstein (2008): “Information, School Choice and Academic
Achievement: Evidence from Two Experiments,” Quarterly Journal of Economics, 123(4),
1373–1414.
He, Y. (2012): “Gaming the Boston Mechanism in Beijing,” Unpublished mimeo, Toulouse.
Hemphill, C. (2007): New York City’s Best Public High Schools: A Parent’s Guide, Third
Edition. Teachers College Press.
Hemphill, C., and K. Nauer (2009): “The New Marketplace: How Small-School Reforms
and School Choice have Reshaped New York City’s High Schools,” Center for New York City
Affairs, Milano the New School for Management and Urban Policy.
Herszenhorn, D. M. (2004): “Council Members See Flaws in School-Admissions Plan,” New
York Times, Metropolitan Desk, November 19.
Hoxby, C. (2003): “School Choice and School Productivity (Or, Could School Choice be a
Rising Tide that Lifts All Boats),” in The Economics of School Choice, ed. by C. Hoxby.
Chicago: University of Chicago Press.
Jacob, B., and L. Lefgren (2007): “What Do Parents Value in Education? An Empirical
Investigation of Parents’ Revealed Preferences for Teachers,” Quarterly Journal of Economics,
122(4), 1603–1637.
Kerr, P. (2003): “Parents Perplexed by High School Admissions Rule: Reply,” New York Times,
November 3.
Kesten, O. (2010): “School Choice with Consent,” Quarterly Journal of Economics, 125(3),
1297–1348.
Kesten, O., and M. Kurino (2012): “On the (im)possibility of improving upon the studentproposing
deferred acceptance mechanism,” WZB Discussion Paper SP II 2012-202.
Klemperer, P. (2002): “What Really Matters in Auction Design,” Journal of Economic Perspectives,
16(1), 169–189.
Kling, J. R., S. Mullainathan, E. Shafir, L. C. Vermuelen, and M. V. Wrobel
(2012): “Comparison Friction: Experimental Evidence from Medicare Drug Plans,” Quarterly
Journal of Economics, 127, 199–235.
Kojima, F., and P. A. Pathak (2009): “Incentives and Stability in Large Two-Sided Matching
Markets,” American Economic Review, 99(3), 608–627.
Niederle, M., and A. E. Roth (2003): “Unraveling reduced mobility in a labor market:
Gastroenterology with and without a centralized match,” Journal of Political Economy, 111,
1342–1352.
Pathak, P. A., and T. Sönmez (2008): “Leveling the Playing Field: Sincere and Sophisticated
Players in the Boston Mechanism,” American Economic Review, 98(4), 1636–1652.
50

(2013): “School Admissions Reform in Chicago and England: Comparing Mechanisms
by their Vulnerability to Manipulation,” American Economic Review, 103(1), 80–106.
Pennell, H., A. West, and A. Hind (2006): “Secondary School Admissions in London,”
Centre for Education Research, LSE CLARE Working paper No. 19.
Ravitch, D. (2011): The Death and Life of the Great American School System. Basic Books.
Roth, A. E. (1982): “The Economics of Matching: Stability and Incentives,” Mathematics of
Operations Research, 7, 617–628.
Roth, A. E., and X. Xing (1997): “Turnaround Time and Bottlenecks in Market Clearing: Decentralized
Matching in the Market for Clinical Psychologists,” Journal of Political Economy,
105, 284–329.
Rothstein, J. (2006): “Good Principals or Good Peers: Parental Valuation of School Characteristics,
Tiebout Equilibrium, and the Incentive Effects of Competition Among Jurisdictions,”
American Economic Review, 96(4), 1333–1350.
Schneider, M., P. Teske, and M. Marschall (2002): Choosing Schools: Consumer Choice
and the Quality of American Schools. Princeton University Press.
Shapley, L., and H. Scarf (1974): “On Cores and Indivisibility,” Journal of Mathematical
Economics, 1, 23–28.
Shapley, L., and M. Shubik (1971): “The Assignment Game I: The core,” International
Journal of Game Theory, 1(1), 111–130.
Sönmez, T. (1997): “Manipulation via Capacities in Two-Sided Matching Markets,” Journal of
Economic Theory, 77, 197–204.
Urquiola, M. (2005): “Does school choice lead to sorting? Evidence from Tiebout variation,”
American Economic Review, 95(4), 1310–1326.
Vanacore, A. (2012): “Centralized enrollment in Recovery School District gets first tryout,”
Times-Picayune, New Orleans, April 16.
Vaznis, J. (2013): “Barros Proposes Single Application for City, Charter Schools,” Boston Globe,
Education Desk, June 5.
Williams, J. (2004): “HS delay pinches parents,” New York Daily News, March 25.
51

Table A1. Offer Acceptances among Students who Obtain Multiple First Round Offers in Uncoordinated
Mechanism
Among those Accepting First
Round Offer
Fraction who
Accept No First
Fraction who
Accept First
Accept Offer
Other than
Most Preferred
Number Round Offer Round Offer
Accept Most
Preferred
(1) (2) (3) (4) (5)
Two or more offers 12,508 0.14 0.86 0.71 0.29
Best offer
1 7,096 0.09 0.91 0.75 0.25
2 3,159 0.17 0.83 0.67 0.33
3 1,624 0.23 0.77 0.60 0.40
4 629 0.30 0.70 0.58 0.42
Notes: Table reports the fraction of students who received multiple first round offers in the uncoordinated mechanism in 2002‐03. A
student accepts her most preferred option if assigned to that option at the conclusion of the match. A student accepts first round
offer other than most preferred if assigned to an school ranked below the most preferred offer. A student accepts none of her first
round offers if assigned to a school not offered in the first round at the conclusion of the match.

Table A2. Main Round Assignments in Coordinated Mechanism, by Length of Rank Order List
Length of Rank Order List
Choice Assigned All 1 2 3 4 5 6 7 8 9 10 11 12
Total 69,907 4,597 3,282 4,128 4,622 4,952 4,776 4,406 4,390 4,558 6,135 9,849 14,212
1 31.9% 88.6% 40.7% 35.2% 31.9% 27.9% 28.6% 27.1% 25.7% 25.6% 25.4% 26.2% 25.2%
2 15.0% 39.8% 17.7% 15.1% 14.8% 14.6% 13.7% 13.9% 13.9% 15.2% 14.7% 14.6%
3 10.2% 24.3% 11.6% 11.6% 10.6% 10.0% 10.8% 9.9% 10.4% 10.4% 10.5%
4 7.3% 18.0% 9.3% 8.1% 7.9% 8.0% 7.6% 7.6% 7.8% 8.2%
5 5.4% 12.8% 7.0% 7.0% 6.3% 6.1% 6.6% 6.2% 6.7%
6 3.9% 10.2% 5.7% 4.9% 5.0% 4.9% 4.8% 5.3%
7 2.9% 8.1% 4.3% 4.4% 4.0% 4.1% 4.3%
8 2.0% 5.8% 3.4% 3.3% 2.9% 3.5%
9 1.5% 4.0% 2.8% 2.7% 2.8%
10 1.1% 3.2% 2.3% 2.6%
11 0.8% 2.6% 2.2%
12 0.5% 2.5%
Unassigned 17.5% 11.4% 19.5% 22.8% 23.3% 23.6% 20.9% 20.6% 20.3% 20.1% 16.7% 15.3% 11.6%
Notes: This table reports choices assigned after the main round in coordinated 2003-­‐04 mechanism based on deferred acceptance.

Table A3. Assignment and Enrollment Decisions of Students in Coordinated Mechanism by Rank Order List Length
Length of Rank Order List
All 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th
A. Assignment Offered in Main Round
Number of Students 57,658 4,072 2,641 3,187 3,545 3,782 3,776 3,497 3,499 3,642 5,113 8,340 12,564
Average Rank of Assignment 3.00 1.00 1.49 1.86 2.21 2.53 2.76 3.04 3.20 3.35 3.49 3.60 3.93
Accept Main Round Assignment 92.7% 91.2% 88.5% 88.4% 90.2% 91.2% 92.3% 91.9% 93.0% 93.6% 94.5% 94.6% 94.3%
Enroll at Private High School 2.5% 6.9% 7.4% 6.1% 4.5% 2.9% 2.4% 2.1% 1.9% 1.2% 1.0% 0.7% 1.0%
Remain in Current School 1.2% 1.2% 2.0% 2.3% 1.9% 2.1% 1.4% 1.8% 1.4% 1.2% 0.9% 0.7% 0.6%
Attend Specialized or Alternative School 0.1% 0.0% 0.0% 0.0% 0.0% 0.1% 0.1% 0.2% 0.1% 0.1% 0.2% 0.1% 0.0%
Participate in Supplementary Round 0.3% 0.1% 0.2% 0.2% 0.4% 0.5% 0.6% 0.3% 0.6% 0.3% 0.3% 0.2% 0.3%
B. Students Unassigned after Main Round
Number of Students 12,249 525 641 941 1,077 1,170 1,000 909 891 916 1,022 1,509 1,648
Participate in Supplementary Round 52.6% 26.1% 44.8% 54.0% 54.1% 56.2% 55.6% 55.7% 52.7% 46.5% 43.5% 49.6% 68.2%
Enroll at Supplementary Round Assignment 72.9% 73.0% 85.0% 76.0% 75.5% 77.8% 73.0% 75.9% 74.5% 68.8% 71.7% 69.5% 66.3%
Enroll at Private High School 2.8% 6.7% 6.1% 4.7% 3.5% 3.8% 2.2% 1.7% 1.6% 1.9% 2.2% 1.4% 1.9%
Remaining in Current School 3.2% 6.7% 6.2% 5.6% 5.3% 4.4% 3.2% 3.3% 2.5% 2.0% 1.5% 0.9% 1.8%
Attend Specialized or Alternative School 0.3% 0.8% 0.5% 0.6% 0.2% 0.1% 0.3% 0.3% 0.3% 0.1% 0.2% 0.5% 0.1%
Notes: Assignment and enrollment decisions of students in the demand estimation sample under the coordinated mechanism. Panel A restricts to students that received an assignment in an NYC Public School in the Main Round. Panel B restricts to students that did not
receive an assignment in the Main Round.

Table A4. Preference Estimates from Alternative Specifications
All Drop Lists wth Dropping Last Ranked With Outside
Choices 12 choices Choice Only Option
(1) (2) (3) (4) (5)
A. Preference for Distance
Distance (in miles) -­‐0.310*** -­‐0.317*** -­‐0.302*** -­‐0.024*** -­‐0.304***
B. Preference for Schools -­‐ Main effects
Size of 9th Grade (in 100s) 0.059*** 0.067*** 0.061*** 0.042 0.044***
Percent White 0.032*** 0.032*** 0.029*** 0.001 0.030***
Attendance Rate 0.075*** 0.082*** 0.087*** 0.061 0.053***
Percent Free Lunch -­‐0.004*** -­‐0.004*** -­‐0.004*** 0.005 -­‐0.005***
High Math Achievement 0.000 -­‐0.001 0.002*** 0.003 0.002***
Program Type Dummies X X X X X
Program Specialty Dummies X X X X X
C. Model Diagnostics
Number of ranks 542,666 372,122 472,579 542,666 542,666
Number of parameters 349 349 349 349 350
Log likelihood -­‐2,690,008 -­‐1,818,749 -­‐2,431,624 -­‐753,816 -­‐2,876,073
Pseudo R-­‐squared 0.92 0.92 0.92 0.60 0.86
Fraction of variance explained by school observables 0.53 0.56 0.51 0.15 0.47
Notes: Maximum likelihood estimates from demand systems with variations in the sample of students and alternative behavioral assumptions. All estimates have same controls as in column (4)
of Table 7, which includes interactions with student demographic racial and baseline achievement and school characteristics. Dummies for missing school attributes are estimated with separate
coefficients. The first column treats all choices as truthful, the second column drops students who have ranked 12 schools from the sample, the third column only uses information about relative
comparisons among listed alternatives, assuming that unlisted alternatives are missing at random, and the fourth column drops the last ranked school from each students list. Columns (1) through
(4) estimate utility amongst inside options only, with an arbitrarily chosen school's mean utility normalized to zero (this normalization is without loss of generality). Column (5) adds an outside
option to the model, treating unranked schools as worse than the outside option. Pseudo R-­‐squared in the fraction of variance in utility explained by observables. * significant at 10%; **
significant at 5%; *** significant at 1%

A
Appendix: Simulating Utilities
This appendix explains how we simulate utilities for students given the preference estimates.
Consider a random utility function of the form
u ij = V ij + ε ij ,
where ε ij is distributed as F (ε) = exp (− exp (−ε)) and V ij is known. Suppose we observe
ranking r i = (j 1 , ..., j K ) . We simulate the utilities conditional on the rankings by simulating the
utility of kth choice conditional on the simulated utility of (k − 1)st choice. For the first choice,
draws are simulated unconditionally.
A.1 Ranked Choices
Calculation of probabilities. The probability that ε ij1 is less than ¯s conditional on u ij1 being
the largest in a set J when ε ij1 ≤ ¯s can be written as
P (ε ij1 ≤ ¯s|u ij1 = max u ij ) = P (u ij 1
= max u ij |ε ij1 ≤ ¯s) F (¯s)
P (u ij1 = max u ij )
=
F j1 (¯s) F (¯s)
P (u ij1 = max u ij ) .
The quantities F (¯s) and P (u ij1 = max u ij ) are known. To compute F j1 (¯s), we have
F j1 (¯s) =
=
=
=
∫ ¯s
∏
s=−∞
j∈J\{j 1 }
∫ ¯s
s=−∞
∫ ¯s
s=−∞
∫ ∞
exp(−¯s)
p that V ij +ε ij

The expression for the required probability simplifies to
( (∑
j
P (ε ij1 ≤ ¯s|u ij1 = max u ij ) = exp − exp (−¯s)
exp (V ))
ij)
+ 1 .
exp (V ij1 )
Conditional on all utilities for j ∈ J being less than û. The probability that ε ij1 is less
than ¯s conditional on u ij being less than û for all j ∈ J, and j 1 the largest amongst the remaining
choices is given by Bayes’ Theorem.
{
0 ¯s ≥ û − V ij
P (ε ij1 ≤ ¯s|u ij ≤ û, u ij1 = max u ij ) =
Fij û
1
(¯s) otherwise
Fij û
1
(¯s) = P (u ij 1
= max u ij |u ij ≤ û, ε ij1 ≤ ¯s) P (u ij ≤ û, ε ij1 ≤ ¯s)
P (u ij1 = max u ij |u ij < û) P (u ij ≤ û)
= P (u ij 1
= max u ij |u ij ≤ û, ε ij1 ≤ ¯s) F (¯s)
P (u ij1 = max u ij |u ij ≤ û) F (û − V ij1 ) .
Notice that P (u ij1 = max u ij |u ij ≤ û) is just P (u ij1 = max u ij |u ij ≤ û, ε ij1 ≤ ¯s) evaluated at
¯s = û − V ij . Therefore, we need to compute P (u ij1 = max u ij |u ij ≤ û, ε ij1 ≤ ¯s) . Since the event
u ij1 = max u ij |ε ij1 ≤ ¯s is contained in the event u ij ≤ û, for ¯s ≤ û − V ij1 , we have that
P (u ij1 = max u ij |u ij ≤ û, ε ij1 ≤ ¯s) P (u ij ≤ û) = P (u ij1 = max u ij |ε ij1 ≤ ¯s) . Therefore,
F û
ij 1
(¯s) =
P (u ij1 = max u ij |ε ij1 ≤ ¯s) F (¯s)
P (u ij1 = max u ij |ε ij1 ≤ û − V ij1 ) F (û − V ij1 )
(
∑
j
(exp (− (û − V ij1 )) − exp (−¯s))
exp (V ij)
exp (V ij1 )
= exp
)
F (¯s)
F (û − V ij1 ) .
Inverse CDF. For simulations, we need the inverse cdf function.
(
∑
F ûj
j
1
(¯s) = exp {exp (− (û − V ij1 )) − exp (−¯s)}
exp (V )
ij) F (¯s)
exp (V ij1 ) F (û − V ij1 )
(
(∑
j
= exp {exp (− (û − V ij1 )) − exp (−¯s)}
exp (V ))
ij)
+ 1
exp (V ij1 )
{
(∑
j
⇒ ¯s = − ln exp (− (û − V ij1 )) −
exp (V −1
}
ij)
+ 1)
ln F ûj exp (V ij1 )
1
(¯s)
Clearly, at F ûj 1
(¯s) = 1, ¯s = û − V ij1
as desired.
A.2 Unranked Programs
For a program that wasn’t ranked, we know that the utility for this program is less than all programs
ranked by the student. Let û be the lowest utility from ranked programs. The probability
distribution of ε ij of unranked programs is given by
F û
ij (¯s) =
{
0
F (¯s)
F (û−V ij )
¯s > û − V ij
otherwise .
The value of û can be simulated using the procedure above.
57

B
Appendix: Subway Distances
In New York, high school students who live within 0.5 miles of a school are not eligible for
transportation. If a student lives between 0.5 and 1.5 miles the Metropolitan Transit Authority
provides them with a half-fare student Metrocard that works only for bus transportation. If they
reside 1.5 miles or greater, they obtain full fare transportation with a student Metrocard that
works for subways and buses and is issued by the school transportation office.
Since subway is a common mode of transportation in New York City, this appendix assesses
how the driving distance measure we utilize in the paper differs from commuting distance using
NYC’s subway system. Subway distance is defined as the sum of distance on foot to the student’s
nearest subway station, travel distance on the subway network to a school’s nearest subway
station, and the distance on foot to the school from that station. To compute these distances,
we used ESRI’s ArcGIS software and information on the NYC subway system using GIS files
downloaded from Metropolitan Transit Authority’s website. Details on these sources are in the
Data appendix.
The overall correlation between driving distance and total commuting distance for all studentprogram
pairs is 0.96. A regression of commuting distance on driving distance yields a coefficient
of 0.77. Table S1 provides a summary of the correlations by the student and school borough.
The correlations are higher than 0.84, except for schools in Staten Island, where the subway
system is not quite as extensive as in other boroughs. In fact, it may be that driving distances
are a more accurate measure of travel costs in Staten Island than subway distance.
Panels B and C shows that most students are assigned to schools in their borough in both
the uncoordinated and coordinated mechanism. In both mechanisms, a very small number of
students that do not live in Staten Island travel are assigned to schools there and conversely, only
a small number of students living in Staten Island are assigned to school in a different borough.
58

Table S1. Subway and Driving Distance and Cross-­‐Borough School Assignment
School Borough
Brooklyn Bronx Manhattan Queens Staten Island Total
Student Borough (1) (2) (3) (4) (5) (6)
A. Correlation between Subway and Driving Distance
Brooklyn 0.91 0.90 0.95 0.91 0.92
Bronx 0.93 0.90 0.97 0.91 0.76
Manhattan 0.95 0.96 0.98 0.95 0.76
Queens 0.91 0.91 0.95 0.87 0.85
Staten Island 0.92 0.84 0.85 0.89 0.73
B. Cross-­‐Borough Travel in Uncoordinated Mechanism
Brooklyn 20,877 13 1,073 502 12 22,477
Bronx 41 15,187 1,382 66 1 16,677
Manhattan 42 89 8,604 24 1 8,760
Queens 493 15 586 16,498 0 17,592
Staten Island 13 2 59 4 4,774 4,852
C. Cross-­‐Borough Travel in Coordinated Mechanism
Brooklyn 20,035 39 1,858 846 40 22,818
Bronx 85 13,335 2,049 84 8 15,561
Manhattan 108 238 7,492 52 7 7,897
Queens 584 26 1,028 14,972 9 16,619
Staten Island 37 3 69 4 3,913 4,026
Notes: Panel A reports on the correlation between student-­‐school distance as computed by travel distance and by subway
distance. Subway distance is the sum of distance on foot to the student's nearest subway station, travel distance on the
subway network to a school's nearest subway station, and the distance on foot to the school from that location. Both measures
of distance were computed using ArcGIS. Panels B and C report on the number of students in each borough who are offered a
school in each borough.

C
Appendix: Data
The data for this study come from the NYC Department of Education (DOE), the 2000 US Census,
ArcGIS Business Analyst toolbox and GFTS NYC subway data from the NYC Metropolitan
Transit Authority. These sources provide us with data on students, schools, the rank-order lists
submitted by the students, the assignment of students to schools or the distance between the
students and schools on the road network or the subway system. Students and programs are
uniquely identified by a number that can be used to populate fields and merge across DOE
datasets. We geocode student and school addresses to merge with geo-spatial data.
We also use three samples of students in our analysis: one sample to estimate demand and
the other two to infer the welfare effects of the mechanism change. The welfare samples consists
of public middle schools student that matriculate into NYC Public High Schools in the academic
years 2003-04 and 2004-05. The demand sample consists of public middle school students that
participated in the main round of the mechanism in 2003-04. The demand sample and the welfare
sample from 2003-04 are not nested because students participating in the mechanism may choose
to enroll in a school outside the NYC Public School system whereas others may be assigned to
a public school outside the main assignment process.
C.1 Students
Assignment and Rank Data
Data on the assignment system come from the DOE’s enrollment office. The files indicate the
final assignment of all students in both years in our analysis. We use these assignments as
the basis of our baseline welfare calculations. In addition, the assignment system also provides
separate files that detail the rank orders, applications or processes through which a student is
assigned to a given school.
We use the records from the main round in the new mechanism to obtain the rank order
lists submitted by students and the assignment proposed by the mechanism. A total of 87,355
students participated in the main round.
For the old mechanism, the assignment system provides student choice and decision files for
the main round. The former contains the ranked applications submitted by the students and the
latter provides the decisions of the schools to accept/reject/waitlist the student and the students
response to these offers, if any. A total of 84,272 students participated in the main round.
The old assignment system also contains several files documenting the supplementary variable
assignment process (VAS) round.
Assignment Rounds and Offers in the Old Mechanism
The files in the old mechanism do not directly contain information on how students were assigned
to their programs. However, we are able to determine whether a student applied to a particular
program/school in the main process or the supplementary VAS process. We first append fields
indicating whether a student applied to her assigned program in the main process. We also
append a field indicating whether a student applied to her assigned school in the supplementary
60

VAS process. It turns out that no final assignment appears in both the main and the VAS files.
We therefore categorize the former assignments as main-round assignments and the latter as VAS
assignments. We assume that all other assignments are through the over the counter process.
Based on conversations with DOE officials, students were typically assigned to school closest to
home that had open seats. Our understanding is that most of the students that participated in
the VAS process did not have a default local school. An analysis of the geographic distribution
of our definition of students assigned over the counter is consistent with this fact: many parts of
NYC have no students assigned through the over the counter process.
Finally, we also append the number of offers made to a particular student using a file with
the initial response of schools to the student application.
Assignment Rounds in the New Mechanism
We use the NYC assignment files described above to determine the process through which a
student was assigned a given school.
The assignment files in the new mechanism contain, for every student program pair that
is ranked in either the main round or the supplementary round, two fields indicating whether
the student is eligible for the school and if the student was assigned to that school. A final
assignment is treated as a main-round assignment if it appears as an eligible assignment in the
main round. Assignments that are not made in the main round are treated as a supplementary
round assignment if they appear in the supplementary round files. All other assignments are
treated as over the counter assignments.
Student Characteristics
The records from the NYC Department of Education contain the street address, previous and
current grade, gender, ethnicity and whether the student was enrolled in a public middle school.
Each student is identified by a unique number that allows us to merge these data with additional
data from the NYC DOE on a student’s scores in middle school standardized tests, Limited
English Proficiency status, and Special Education status. A separate file indicates subsidized
lunch status as of the 2004-05 enrollment. If a student is not in that file, we code the student as
not receiving a subsidized lunch.
There are several standardized tests taken by middle school students in NYC. To avoid the
concern that two different tests may not be comparable indicators of student achievement, we
identify the modal standardized tests in math and reading taken by students in our sample. These
are the May tests with codes CTB and TEM respectively. Of the students that did not take
either of these tests in May, at most 10% (

fractions are 7.13% and 12.56%.
Geographic Data
We use the 2000 US Census to obtain block group family income. The addresses of students
and their distance to school were calculated using ArcGIS. Corrections to the addresses, when
necessary, were made using Google Map Tools followed by manual checks and corrections.
The final set of addresses were geocoded using ArcGIS geocoder with the address-set in the
Business Analyst toolbox (ver. 10.0). We first used an exact match to determine if a student’s
address can be geocoded precisely to a rooftop. If the results were unreliable, we coded the
student to the centroid of the zip-code. The vast majority of students were placed at the rooftop
level. The OD Cost matrix tool in the Network Analyst toolbox was used to compute the
distance by road for each student-school pair. The road network is also obtained from Business
Analyst.
Our computation of subway distances assumes that a student first walks to the closest subway
stop, then uses the subway system to travel to the subway stop closest to the school, and finally
walks from the subway to the school. The location of the subway stops is taken from the GTFS
and geodata data on the NYC Metropolitan Transit Authority website. The network analyst
toolbox is used to compute the walking distance and the GTFS data is used to compute the
distance on the subway system between every pair of subway stops.
Merging Student Records
Assignment and other DOE files are matched using the unique student identifier linking these
data. Each eighth-grade non-private middle school student in the Department of Education
records could be merged uniquely with a student in the NYC assignment records. Less than
0.45% of students with known assignments in the records of the NYC assignment system could
not be merged with a student in the DOE records. These students were not included in the
analysis.
C.2 Applicant Sample Construction
Our goal is to consider first-time applicants to the NYC public (unspecialized) high school system
that live in New York City attend a public middle school 8th grade. Below, we described the
procedure used to construct the samples. The selection procedure is also summarized in Table
B1.
Welfare Sample
The welfare samples is constructed from the NYC Department of Education’s records of all
students enrolling in ninth grade at a high school in academic years 2003-04 and 2004-05.
As our choice set in the demand analysis will be restricted to unspecialized, non-charter high
schools in the public school system, we do not include students that matriculated to such schools
in the welfare sample.
62

Of the 92,623 eighth grade students matriculating into ninth grade at a NYC public school
in 2002-03, 11,790 (12.73%) students went to a private middle school and were dropped. Another
8,051 (8.69%) of students were not included in the analysis because their assignment was
unknown, or because they matriculated at either a specialized high school or a charter school.
Finally, we exclude students in schools that were closed (no assignments in the new system).
In 2003-04, about 1.3% students had also participated in the old mechanism, presumably
because these students repeated eighth grade. These students were considered a part of the
2002-03 sample and only their 2002-03 assignment into high school is considered in our analysis.
We also drop private middle school students and those not assigned to public school. These
fractions were similar to the 2002-03 numbers, at 12.21% and 8.13% respectively. We also drop
students that were assigned to new schools.
These selections into the sample leave us with 70,358 students in 2002-03 and 66,921 students
in 2003-04. Students that may have been assigned to a high school program through a process
other than the main round are included in these samples.
Demand Sample
This sample is sourced from the NYC Assignment system’s records on the participants in the
main round of the mechanism. As discussed in the text, we use only data only from the main
round of the mechanism as this round has the most desirable incentive properties.
We do not want to exclude students on the basis of final assignment to avoid selecting on the
choice to leave the public school system. In order to most closely match the construction of the
welfare sample, we select the demand sample only on characteristics that can be considered as
exogenous at the time of participation.
Since we focus on first-time applicants in eighth grade, we exclude 747 students that were
part of the 2002-03 files, and 5,311 students that were ninth graders. Presumably, these students
were held back in eighth or ninth grade. This leaves us with a sample of 81,297 eighth grade
students.
Of the eighth-grade participants, 9,301 or 11.44% of students were from private middle schools
and were dropped. We also excluded students designated as belonging to the top 2% of their
middle school class as they are prioritized at education option schools, creating incentives to
misreport their preferences. These are 2.5% of the non-private eighth grade population.
A total of 216 students did not rank any public schools in our sample. After excluding these
students, a total of 69,907 students remain in the sample we will use for the demand analysis.
C.3 Programs/Schools
NYC Department of Education School Report Cards
The school characteristics were taken from the report card files provided by the NYC Department
of Education. These data provide information on a school’s enrollment statistics, racial
composition of student body, attendance rates, suspensions, teacher numbers and experience,
and Regents Math and English performance of the graduating class. A unique identifier for each
school allows these data to be merged with data from our other sources.
63

There were significant differences in the file formats and field names across the years. To
keep the school characteristics constant across years, we use the data from the 2003-04 report
cards as the primary source. Except for data on the math and reading achievement, variable
descriptions were comparable across years. For these comparable variables, we used the 2002-03
data only when the 2003-04 data were not available. The coverage of the characteristics for the
sample of schools is enumerated in Table B2.
Assignment System and DOE files
Assignment data contain a list of all school programs in the public school system along with
an identifier for the associated high school. The department of education provided a separate
file with data on the school addresses and identifiers that allow a merge with the assignment
system database. A second identifier can be used to merge these data with other fields in the
department of education records described above.
Across the two years, the high school identifiers in the files were inconsistent for a small
number of schools in our sample. These were matched by name and address of the school. One
school moved from Brooklyn to Manhattan and was investigated to ensure that the records were
appropriately matched.
Program Characteristics
Program characteristics are taken from the DOE’s High School Directory, which is made available
to students before the application process. Reliable data on program types was not available
in 2002-03. For that year, the program types were imputed from the 2003-04 program types if
the program was present in both years. Otherwise, the program was categorized as a general
program.
There were a very large number of program types. These were aggregated into fewer broad
categories. The items in the list below are the aggregated categories that include all of the
subcategories as described by the data.
1. Arts: Dance, Instrument Performance, Musical Theater, Performing and Visual, Performing
Arts, Theater, Theater Tech, Visual Arts, Vocal Performance.
2. Humanities/Interdisciplinary: Education, Humanities/Interdisciplinary.
3. Business/Accounting: Accounting, Business, Business Law, Computer Business, Finance,
International Business, Marketing, Travel Business.
4. Math/Science: Engineering, Engineering – Aerospace, Engineering – Electrical, Environmental,
Math and Science, Science and Math.
5. Career: Architecture, Computer Tech, Computerized Mech, Cosmetology, Journalism, Veterinary,
Vision Care Technology.
6. Vocational: Auto, Aviation, Clerical, Construction, Electrical Construction, Health, Heating,
Hospitality, Plumbing, Transportation.
64

7. Government/law: Law, Law Enforcement, Law and Social Justice, Public Service.
8. Other: Communication, Expeditionary, Preservation, Sports.
9. Zoned
10. General: General, Unknown.
Finally, some programs adopt a language of instruction other than English. We categorized
the languages into Spanish, English, Asian Languages and Other.
C.4 School Sample Construction
We consider the assignment of eighth grade students in NYC public middle schools into public
high schools that are not charters, specialized or parochial. Our analysis uses two school sample,
one for each year in our analysis.
To construct these samples, we started with the set of schools and programs in the assignment
records. For the analysis of rank data, we added the set of school programs that were ranked by
any student in our demand sample. This initial set consists of 743 (301) programs (schools) in
2002-03 and 677 (293) programs (schools) in 2003-04.
In 2003-04, this list contained 62 parochial school programs. We verified that each of the 130
students matriculating to these school programs were private middle-schoolers. These schools
were dropped from the analysis because private middle-schoolers are not in population of interest.
Subsequently, we dropped all charter and specialized high school programs and other school
programs which do not have assignments and were not ranked by any student in our sample.
A total of 9 continuing student programs accepted students only from their associated middle
school. Since these programs cannot be chosen by students that were not in that school in
eighth grade, we combine these programs with a generic program (e.g., unscreened, English, general/humanities/math).
Rank order lists for students that ranked both the continuing students
only program and the associated program were modified as described below.
Finally, we dropped new and closed schools from the analysis. Closed schools were ones that
admitted students in 2002-03, but not in 2003-04. The set of new schools was collected from
a separate DOE directory of new schools. These schools were not well advertised and very few
students ranked them, making calculations with those schools unreliable.
The number of schools and programs at each stage of our selection procedure is also summarized
in Table B2.
C.5 Program Capacities
Program capacities are not provided separately in the data files. We have estimated program
capacities from the actual match files and students’ final assignments. The capacity of each
program is initially set to zero. If a student in our demand sample is assigned a program at the
end of the assignment process, the capacity of the program is increased by one. Otherwise, if
the student is assigned a program in the main round the capacity of the program is increased
65

y one. Finally, if a student is not assigned in the main round and assigned a program in the
supplementary round, the capacity of the program is increased by one.
Education Option programs are divided into six buckets: High Select, High Random, Middle
Select, Middle Random, Low Select and Low Random. The bucket capacities are calculated as
above by taking into account the category of the assigned student. For example, if a student of
High category is assigned an Education Option program, then the capacity of a High bucket is
increased by one. If the current capacity of the High Select bucket is less than or equal to that of
High Random, then the capacity of the High Select bucket is increased, otherwise the capacity
of the High Random bucket is increased.
C.6 Program Priorities
The type of a program determines how students are priority-ordered for the program. The
data contains a list of all programs with program-specific information, including type, building
number, street address etc. When students have the same priority, the tie is broken randomly.
The random numbers are generated by computer during our simulations.
The assignment data contains the following fields that determine a student’s priority order at
programs. Priority group is a number assigned by the NYC Department of Education depending
on students’ home addresses and location of programs etc. High school rank is a number assigned
by each program. This may reflect an student’s ranking among all applicants to an Education
Option program, or whether a student attended the information session of an limited unscreened
program, etc. These fields are provided for every student at every program that the student
ranked. Students applying to Educational Option programs are placed into one of three categories
based on their score on the 7th grade reading test: top 16 percent (high), middle 68 percent
(middle), and bottom 16 percent (low). Student categories in the assignment data.
Unscreened programs order students based on their random numbers only. Limited unscreened
and formerly zoned programs order students first by priority group, and random number
within priority group. Screened programs order students by priority group, then by high school
rank. Each Education Option program orders all applicants for each of six buckets, High Select,
High Random, Middle Select, Middle Random, Low Select and Low Random. A high bucket
orders high category students first, then middle category students, then low category students.
A middle bucket orders middle category students first, then high category students, then low
category students. A low bucket orders low category students first, then high category students,
then middle category students. A select bucket orders students within each category by priority
order, then by high school rank. A random bucket orders students within each category by
priority order.
C.7 Miscellaneous Issues
Modifications to the rank order list
1. Some students ranked a program that were either charter schools or specialized high schools
in the main round. These programs are not in the sample of schools we consider and were
likely ranked by the students in error. In such cases, programs were removed from the rank
66

order lists and rank orders lists were made contiguous where all programs ranked below a
program not in the sample were moved up in the rank order lists. These programs were
observed a total of 795 times in the data. Thirty students ranked only charter or specialized
programs.
2. The rank order lists of students that ranked continuing student program were modified as
follows: First, the lists of all students that ranked only the continuing student program
were modified so that the student ranked the associated generic program instead. When
students ranked both the generic program and the associated continuing student program,
the list was modified so that only the associated program was ranked, and at the highest of
the two ranked positions. All programs ranked at positions below the lower ranked of the
two programs were moved up by one. A total of 46 students ranked both the continuing
program and the generic program we mapped the continuing program to. In 17 cases, these
ranks were not consecutive.
67

Table B1. Student Sample Selection
Mechanism Comparison
Demand Estimation
Uncoordinated Coordinated Coordinated
(1) (2) (3)
Number in the NYC DOE student file 100,669 97,569
Number of students in the rank data 87,355
Excluding students in both 2002-­‐03 and 2003-­‐04 files from 2003-­‐04 96,275 86,608
Excluding ninth grade students 92,623 89,062 81,297
Excluding private middle school students 80,833 78,183 71,996
Excluding students with addresses outside the five boroughs 80,725 78,089 71,916
Total number of students with known assignments to sample schools 75,515 73,989
Excluding students attending specialized high schools 72,725 70,992
Excluding students attending charter schools 72,681 70,886
Excluding students in closed and new new schools 70,358 66,921
Excluding top 2% students 70,123
Excluding students that did not rank any sample schools 69,907
Notes: Uncoordinated mechanism refers to 2002-­‐03 mechanism and coordinated mechanism refers to the 2003-­‐04 mechanism based on deferred acceptance. A student has invalid census
information if address is missing, cannot be geocoded or places the student outside of New York City. A distance observation is invalid if it is missing or is greater than 65 miles.

Table B2. Construction of School Sample
Uncoordinated Mechanism
Coordinated Mechanism
Programs Schools Programs Schools
(1) (2) (3) (4)
Programs where NYC public school students assigned 743 301 669 293
Adding additional programs ranked by students 677 294
Excluding parochial schools 681 239 677 294
Excluding specialized schools 669 232 665 287
Excluding charter schools 667 230 663 285
Excluding programs with no assignments or ranking 637 225 648 284
Combining continuing education programs 637 225 639 284
Excluding new and closed schools 612 215 558 235
Programs/schools ranked by students in sample 497 234
Notes: Uncoordinated mechanism refers to 2002-­‐03 mechanism and coordinated mechanism refers to the 2003-­‐04 mechanism based on deferred acceptance. 13 continuining student
programs were merged with a generic program at host school. Parochial schools in 2002-­‐03 only have private middle school students assigned to them and are not ranked by students in
the demand sample.

Table B3. Coverage of School Characteristics
2002‐03 2003‐04 Both Years
(1) (2) (3)
Total number of schools in the sample 215 234 215
Size of 9th grade 196 199 189
Race 196 199 189
Attendance Rate 196 199 189
Percent Subsidized Lunch 196 198 189
Percent of teachers less than 2 years experience 219 223 212
High Math Achievement 198 200 191
High English Achievement 180 177 173
Percent Attending College 171 167 165
Notes: Uncoordinated mechanism refers to 2002‐03 mechanism and coordinated mechanism refers to the mechanism
based on deferred acceptance used in 2003‐04. Table reports the fraction of schools with the characteristics from New
York State Report cards.

Table C1. All Coefficients from Student Preference Estimates
School Characteristics x
School Characteristics x Student Demographics
School Characteristics x Student Baseline
School Characteristics x Student Baseline Achievement
Specifications: School Characteristics Student Race
Achievement
All Choices Top Choice Only Top Three Choices
(1) (2) (3) (4) (5) (6)
A. Preference for Distance
Distance -­‐0.318*** -­‐0.313*** -­‐0.316*** -­‐0.310*** -­‐0.387*** -­‐0.353***
B. Preference for School Characteristics
Size of 9th grade (in 100s)
Main effect 0.015*** 0.040*** 0.015*** 0.059*** 0.100*** 0.099***
Female -­‐0.007*** -­‐0.009*** -­‐0.008***
Asian 0.019*** 0.016*** 0.052*** 0.034***
Black -­‐0.040*** -­‐0.038*** -­‐0.042*** -­‐0.044***
Hispanic -­‐0.018*** -­‐0.019*** -­‐0.016*** -­‐0.021***
Baseline Math 0.004*** 0.001** 0.002 0.001
Baseline English -­‐0.006*** -­‐0.003*** -­‐0.009*** -­‐0.005***
No Baseline Math Score -­‐0.027*** -­‐0.010*** -­‐0.033*** -­‐0.019***
No Baseline English Score 0.035*** 0.008*** 0.027*** 0.015***
Subsidized Lunch -­‐0.014*** -­‐0.029*** -­‐0.024***
Neighborhood Income (in 1000s) -­‐0.650*** -­‐1.930*** -­‐1.930***
Limited English Proficient 0.007*** 0.018*** 0.016***
Special Education -­‐0.007*** -­‐0.017*** -­‐0.012***
Percent White
Main effect 0.026*** 0.040*** 0.025*** 0.032*** 0.040*** 0.033***
Female -­‐0.001** -­‐0.001 0.000
Asian -­‐0.016*** -­‐0.015*** -­‐0.027*** -­‐0.018***
Black -­‐0.022*** -­‐0.020*** -­‐0.035*** -­‐0.024***
Hispanic -­‐0.011*** -­‐0.009*** -­‐0.016*** -­‐0.010***
Baseline Math 0.001*** 0.000* 0.000 0.000
Baseline English 0.002*** 0.002*** 0.005*** 0.003***
No Baseline Math Score -­‐0.002*** 0.000 -­‐0.003 -­‐0.001
No Baseline English Score 0.004*** 0.000 0.004* 0.000
Subsidized Lunch 0.001*** 0.003*** 0.002***
Neighborhood Income (in 1000s) 0.911*** 2.000*** 1.000***
Limited English Proficient 0.000 0.000 0.001
Special Education 0.001 0.006*** 0.003***

Table C1. All Coefficients from Student Preference Estimates (cont.)
School Characteristics x
School Characteristics x Student Demographics
School Characteristics x Student Baseline
School Characteristics x Student Baseline Achievement
Specifications: School Characteristics Student Race
Achievement
All Choices Top Choice Only Top Three Choices
(1) (2) (3) (4) (5) (6)
B. Preference for School Characteristics (cont.)
Attendance Rate
Main effect 0.055*** 0.103*** 0.062*** 0.075*** 0.131*** 0.117***
Female 0.002** 0.009*** 0.005***
Asian 0.013*** 0.016*** 0.076*** 0.039***
Black -­‐0.053*** -­‐0.036*** -­‐0.040*** -­‐0.046***
Hispanic -­‐0.053*** -­‐0.037*** -­‐0.040*** -­‐0.047***
Baseline Math 0.012*** 0.010*** 0.017*** 0.015***
Baseline English 0.014*** 0.014*** 0.020*** 0.021***
No Baseline Math Score -­‐0.024*** -­‐0.016*** -­‐0.046*** -­‐0.026***
No Baseline English Score 0.010*** -­‐0.004** 0.009* 0.000
Subsidized Lunch 0.000 -­‐0.008*** -­‐0.005***
Neighborhood Income (in 1000s) 6.000*** 8.000*** 7.000***
Limited English Proficient 0.006*** 0.014*** 0.012***
Special Education 0.004*** -­‐0.008* 0.005*
Percent Subsidized Lunch
Main effect -­‐0.002*** -­‐0.007*** -­‐0.003*** -­‐0.004*** 0.005*** -­‐0.003**
Female -­‐0.001*** 0.000 0.000
Asian 0.000 -­‐0.001 -­‐0.004*** -­‐0.001
Black 0.002*** 0.001** -­‐0.008*** -­‐0.002***
Hispanic 0.010*** 0.009*** 0.007*** 0.010***
Baseline Math -­‐0.001*** -­‐0.001*** 0.000 -­‐0.001**
Baseline English -­‐0.001*** -­‐0.001*** -­‐0.001* -­‐0.001**
No Baseline Math Score -­‐0.001 0.001** 0.000 0.002
No Baseline English Score 0.005*** 0.002*** 0.005*** 0.003***
Subsidized Lunch 0.000 -­‐0.002** -­‐0.001***
Neighborhood Income (in 1000s) -­‐0.722*** -­‐1.000*** -­‐0.736***
Limited English Proficient 0.000 0.003*** 0.002***
Special Education 0.001*** -­‐0.001 0.001

Table C1. All Coefficients from Student Preference Estimates (cont.)
School Characteristics x
School Characteristics x Student Demographics
School Characteristics x Student Baseline
School Characteristics x Student Baseline Achievement
Specifications: School Characteristics Student Race
Achievement
All Choices Top Choice Only Top Three Choices
(1) (2) (3) (4) (5) (6)
B. Preference for School Characteristics (cont.)
High Math Achievement
Main effect 0.008*** 0.007*** 0.004*** 0.000 0.001 -­‐0.001
Female 0.002*** 0.002*** 0.003***
Asian 0.009*** 0.010*** 0.014*** 0.013***
Black -­‐0.004*** 0.000 0.005*** 0.002**
Hispanic -­‐0.001* 0.004*** 0.009*** 0.007***
Baseline Math 0.008*** 0.007*** 0.012*** 0.009***
Baseline English 0.005*** 0.005*** 0.006*** 0.005***
No Baseline Math Score 0.000 0.001 0.008*** 0.002**
No Baseline English Score 0.002*** 0.000 -­‐0.005*** 0.000
Subsidized Lunch -­‐0.003*** -­‐0.005*** -­‐0.005***
Neighborhood Income (in 1000s) 0.119* -­‐0.712*** -­‐0.242**
Limited English Proficient -­‐0.002*** -­‐0.003* -­‐0.005***
Special Education -­‐0.003*** 0.000 -­‐0.001
Spanish Language Program 5.147*** 5.755*** 5.472***
Limited English Proficiency -­‐3.142*** -­‐3.817*** -­‐3.147***
Limited English Proficiency x Hispanic
Asian Language Program 3.687*** 4.253*** 4.203***
Limited English Proficiency -­‐2.131*** -­‐3.299*** -­‐2.717***
Limited English Proficiency x Asian
Other Language Program 2.289*** 2.947*** 2.870***
Limited English Proficiency
Program Type Dummies X X X X X X
Program Specialty Dummies X X X X X X

Table C1. All Coefficients from Student Preference Estimates (cont.)
School Characteristics x
School Characteristics x
Student Baseline
School Characteristics x Student Demographics
School Characteristics x Student Baseline Achievement
Specifications: School Characteristics Student Race
Achievement
All Choices Top Choice Only Top Three Choices
(1) (2) (3) (4) (5) (6)
C. Model Diagnostics
Number of ranks 542,666 542,666 542,666 542,666 69,907 197,245
Number of parameters 248 272 280 349 349 349
Log likelihood -­‐2,726,580 -­‐2,714,493 -­‐2,710,042 -­‐2,690,008 -­‐302,141 -­‐906,942
Variance within students 4.93 4.98 5.00 5.62 8.96 7.43
Variance between students 4.68 8.23 7.79 12.26 32.85 23.48
Pseudo R-­‐squared 0.85 0.00 0.89 0.00 0.89 0.91
Fraction of variance explained by
school observables
0.43 0.00 0.68 0.00 0.42 0.63
Notes: This table reports all parameter estimates corresponding to Table 6. Maximum likelihood estimates from demand systems with 69,907 students and submitted ranks over 497 program choices
in 234 schools. Estimates use all submitted ranks except in columns (4)-­‐(6). Column (1) contains no interactions between student and school characteristics. Column (2) contains interactions of race
dummies with all school characteristics. Column (3) contains interactions of Math and English score with all school characteristics. Columns (4)-­‐(6) contain interactions of gender, race, achievement,
special education, limited English proficiency, subsidized lunch, and median 2000 census block group family income with all school characteristics. Number of parameters correspond to parameters
outside of delta. Fraction of variance explained by school observables is R-­‐squared of projection of mean utility on school attributes. * significant at 10%; ** significant at 5%; *** significant at 1%