School choice procedures: How do they matter? Theory and evidence from Belgium

Estelle CantillonNicolas Gothelf

Université Libre de BruxellesJune 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: s1, s2, s7, s4, …

– 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 schoolAn 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:

– Student a: 1 2– Student b: 1 2– Student c: 1 2– Student d: 2 1

– Priorities over students:– School 1: a d b c– School 2: b a c d

School-proposing DAA, first round: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

12

Round 2: Student c applies to school 2 and is accepted

All kids are better off

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 DUTCH-SPEAKING 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

Analysis of the current situation – distance to school

1141 incoming students, 958 outgoing students,

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 student-

proposing 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

α1rest = 0.58

δ = 0.75

Weight on ε set to 0.05

Counterfactual 1: From time to distance as a tie-breaker – aggregate results

Counterfactual 1: Distributional aspects

Counterfactual 1: Impact on school population

Impact on school population (cont’d)

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 Dutch-speaking primary schools in Brussels