School choice procedures: How do they
matter? Theory and evidence from Belgium
Estelle Cantillon
Nicolas Gothelf
Université Libre de Bruxelles
June 2009
Context
– Freedom of choice is a constitutional right in Belgium
– Education policy split along language lines
– School choice has long been unregulated (left to
parents and school principals)
– Concerns about inequity prompted politicians to
regulate school choice
– Poor information about registration process foreclosed some
parents
– Examples of unjustified refusal to register / discrimination
– Unregulated choice seen as one source of heterogeneity in
student performance in PISA (Belgium has highest social
segregation index in Europe after Hungary – Jenkins,
Micklewright and Schnepf, 2008 )
Context - Flanders
– First reform in 2003
– Set a common date to start registrations
– First come, first served
– Only permissible reason for refusal is that the school has
reached capacity
– Second reform in 2006
– Local coordination platforms at the metropolitan area level
– Priorities to siblings, socially disadvantaged kids allowed
through early registration periods
– 2008 reform
– Following popular discontent over long queues in front of
popular schools, new decree allows for distance instead of
time as a tie-breaker (Gent metropolitan area adopted it)
– LOPs allowed to experiment for two years
Context – French-speaking Belgium
– Enrollment decree, 2007
–
–
–
–
Set a common date for the start of registrations
Priorities for siblings
First come, first served otherwise
Result: Long queues → minister resigned
– Social diversity decree, 2008
– Combination of quotas (for borough versus non borough
students, socially disadvantaged kids) and priorities (siblings
over other kids), lottery as a tie-breaker
– Decentralized application procedure
– Result: bubble of multiple registrations leading to
administrative burden, delays, and lots of kids without a
school → minister did not resign but decree dropped
– Current situation: waiting for the new govt
This talk will take as given that
- students’ preferences are a key input to the
assignment decision of students to schools
- capacity is scarce and we cannot give every
student his/her first choice
- students have different priorities at different
schools and these priorities are (largely) set by
law
- Unconditional priorities (e.g. siblings)
- Conditional priorities: quotas for specific categories of
kids, priority up to the quota level
What this talk will focus on
– Even when we have decided to take students’
preferences into account and what priorities they
have at different schools, there still are several
ways in which we can match students to schools
– This talk will
– summarize what we know and do not know about the
properties of these different matching algorithms
– Illustrate, using data from Dutch-speaking preschools in
Brussels, the impact of this choice on outcomes
SCHOOL CHOICE PROCEDURES
Inputs to school choice mechanism
– Preference reports by students over schools (rank
order list, ROL)
– Usually not needed in decentralized procedures
– i1 : s 1 , s 2 , s 7 , s 4 , …
– Quotas and student priorities at each school
– s1(q11, q12, …): i1, i3, i4, i2, …
– School capacities
Output is an assignment of each student to a school
An assignment is feasible if it respects school capacities
and quotas
Three criteria
– Ex-post efficiency
– An assignment is ex-post efficient if there does not exist
another feasible assignment that every student prefers to the
original assignment, and at least one student strictly prefers
to the original assignment
– No justified envy
– There is no student that has a place in a school, whereas
another one who actually has priority over that student at
that school, and prefers that school to the school he’s
assigned to, does not have one.
– Truthful elicitation of preferences
– It is optimal for students to report their true preferences
over schools.
Student-proposing deferred acceptance algorithm
– Students submits their ROLs and schools their priorities
over students (use of a tie-breaker if necessary)
– Step 1: Each student proposes to her first choice. Each
school tentatively assigns its seats to its proposers one at a
time following their priority order. Any remaining
proposer is rejected.
– …
– Step k: Each student who was rejected in the previous step
proposes to her next choice. Each school considers the
students it had tentatively accepted in the previous period
together with the new proposers and accepts tentatively
those with the highest priorities. It rejects other.
– The algorithm terminates when no more requests are
rejected.
School-proposing deferred acceptance algorithm
– Students submits their ROLs and schools their priorities
over students (use of a tie-breaker if necessary)
– Step 1: Each school with capacity qs proposes to the qs
highest ranked students. Each student accepts tentatively
her most preferred schools among those that have offered
her a seat. All other schools are rejected.
– …
– Step k: Each school student that had some of its offers
rejected in the previous period, proposes its remaining
seats to the next students on its priority order. Each
student compares her new offers with the offer she had
tentatively accepted in the previous period and keeps her
preferred school. All other schools are rejected
– The algorithm terminates when no more offers are rejected
or there are no more students to make an offer to.
Students prefer the student-proposing DAA
– 4 kids, 2 schools with 2 seats each
– Student preferences:
School-proposing DAA, first round:
–
–
–
–
Student a:
Student b:
Student c:
Student d:
1
1
1
2
2
2
2
1
– Priorities over students:
– School 1: a d b c
– School 2: b a c d
Student a gets two offers. He rejects
the offer from school 2
Round2: school 2 offers a seat to c
Student-proposing DAA, first round:
Students apply to their first choice
school. School 1 rejects student c
Round 2: Student c applies to
school 2 and is accepted
All kids are better off
12
Top trading cycle
– Step 1: Each student points to her favorite school and each
school points to the student with the highest priority.
There exists at least one cycle. Every student in a cycle is
assigned a seat in the school she points to and is removed.
The number of available seats at schools in a cycle is
reduced by one. If this number is equal to zero, the school
is removed
– Step k: Each remaining student points to her favorite
school among those available, and each school points to the
student with the highest priority among those remaining.
Every student in a cycle is assigned a seat in the school she
points to and is removed. The number of available seats at
schools in a cycle is reduced by one. If this number is equal
to zero, the school is removed.
– The algo terminates when all students are assigned a seat.
Comparisons among procedures
Efficiency
No justified
envy
Truthful
preferences
Information
for public
decisions
First come, first
served (enrollment
decree, original GOK
decree)
NO
YES
NO
NO
School-proposing
DAA
(social diversity
decree )
NO
YES
ALMOST
YES if
centralized
Student-proposing
DAA
NO
YES
YES
YES
Top trading Cycle
YES
NO
YES
YES
Comparison among procedures
– There is no procedure that satisfies all three first
criteria (Roth, 1982) → Lawmakers / policymakers
will always need to make an arbitrage
– Student-proposing DAA is not dominated on
efficiency ground by any other envy-free and
strategyproof mechanism (Abdulkaderoglu et al.,
2009)
Current research frontier on school choice
procedures
Current research looks at
– potential enhancements to the student-proposing DAA
– other criteria for evaluating school choice mechanisms
PRELIMINARY EVIDENCE FROM DUTCHSPEAKING PRESCHOOLS IN BRUSSELS
Data
– Preschool population in Dutch-speaking
preschools in Brussels as of 1 October 2008
(10,867 kids, 150 schools, entering class 4079)
– Kid characteristics: age, location, nationality, GOK
status, socioeconomic class of neighborhood,
whether Dutch is spoken at home, school attended
– School characteristics: location, network,
confessional orientation, establishments,
pedagogy
Legal constraints on the mechanisms
Current procedure:
Siblings have priorities over other kids
30% quota for GOK students
45% quota for Dutch native speakers
Priorities and quotas implemented through early
registration periods
– First come, first served as a tie-breaker
– Decentralized
–
–
–
–
New GOK decree allows them to experiment with
distance as a different tie-breaker
Analysis of the current situation – heterogeneity
across schools
Percentage of GOK students and native speakers across
schools
0.8
0.7
% GOK students
0.6
% Dutch @ home
0.5
0.4
0.3
0.2
0.1
0
10% lowest
2
3
4
5
6
7
8
9
10%
highest
Analysis of the current situation – distance to
school
Brussels kids going to preschool in Brussels - closest school
0.35
0.3
whole sample
low socio
0.25
high socio
gok
0.2
Dutch @ home
0.15
0.1
0.05
0
closest
2 to 3
4 to 5
6 to 10
11 to 15
1141 incoming students, 958 outgoing students,
16 to 20
21 to 30
above 30
Generating a counterfactual policy experiment
– LOP Brussels is considering to replace its time
priority with a distance-based tie breaker .
– How will kids be impacted? How will schools be
impacted?
– Main challenge : We do not observe preferences
over schools
Calibrating preferences
Working assumptions:
– Current procedure can be approximated by a studentproposing DAA with socioeconomic status, then distance as
a tie-breaker
– Brussels-based students have preferences over Brussels
schools that depend on their socioeconomic status (top
30%, GOK, other)
uis = α1k distanceis + α2k qualitys + (1- α1k - α2k )εis
They also have an outside option (random utility) and place
the school where they have a sibling first
– Out-of-Brussels students have preferences that take the
form
uis = δ qualitys + (1- δ)εis
Calibrating preferences (continued)
Calibrate these preferences so that predicted
outcome (distribution of ranks of assigned school)
close to actual outcome
α1high = 0.55
α1GOK = 0.70
Weight on ε set to 0.05
α1rest = 0.58
δ = 0.75
Counterfactual 1: From time to distance as a tiebreaker – aggregate results
Counterfactual 1: Distributional aspects
Counterfactual 1: Impact on school population
Proportion of Dutch native speakers - before and after
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10%
lowest
2
3
4
5
simulated "before"
6
7
"after"
actual
8
9
10 %
highest
Impact on school population (cont’d)
Proportion of GOK students before and after, per decile of
schools
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10%
lowest
2
3
4
5
simulated "before"
6
7
"after"
8
actual
9
10 %
highest
Counterfactual 1: Likely long term residential
effects
– Mean median distance to school goes from 1.45
km to 0.9 km
– Mean max distance to school goes from 11.17 km
to 10.54 km
– max distance goes down in 41 schools out of 147
– Min max distance goes from 0.94 km to 0.45 km
Counterfactual 2: School-proposing DAA
CONCLUSIONS
Conclusions
– Even when everything seems to be decided
(priorities, quotas, ….) there are still a lot of non
trivial choices to make
– Very little attention is devoted to these design
choices in legal texts or administrative directives
– Yet some of these choices may have first order
effects on outcomes
– We have shown this with data from Dutchspeaking primary schools in Brussels