School Choice: An Experimental Approach

Jong Min Kim

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Introduction

Reputation buildingTo enter a high school in Korea,

Entrance Exam Lottery

Equalization policy

Introduction

Many-to-one matching problem Student – School Intern – Hospital Worker – Firm

Questions

1. Reputation building of schools – whether the students choose the school considering the reputation of school and their own level of academic achievements

2. Equalization effect – to examine the equalization policy would mix the students with different quality and thus result in narrowed gap between schools

Experimental Design

Subjects Undergraduate and Graduate students in the

Experimental Economics seminar during the fall of 2007 (Study 1)

Students from YKGA (Yale Korean Graduate Student Association) and students of Seoul National University (Study 2)

Experimental Design

4 boxes (schools) &16 players (students) in two cities, 4 positions in each box

Each player is randomly assigned one integer (level of academic achievements) from 1 to 16 choose box assigned

The average value of integers of the participants assigned to each box (Bj), and the number of players who chose each box were announced. Each player assigned to Box j earned Bj points.

Experimental Design

City 1 rules If k (more than 4) players choose Box J, the 4 players with the highest

Vi out of the k players are assigned to Box j. If 4 players choose Box J, these 4 players are assigned to Box j. If less than 4 players choose Box j, they are assigned to Box j. The remaining positions are filled randomly from players who do not get

their choice.

City 2 rules If k (more than 2) players choose Box J, the 2 players with the highest

Vi out of the k players are assigned to Box j. If 2 players choose Box J, these 2 players are assigned to Box j. If less than 2 players choose Box j, they are assigned to Box j. The remaining positions are filled randomly from players who do not get

their choice.

Results

City 1

02468

10121416

1 2 3 4 5 6 7 8 9 10

Round

Poin

ts

City 2

02468

10121416

1 2 3 4 5 6 7 8 9 10

RoundPo

ints

Persistence in Reputation/Ranking

Results

Persistence in Reputation/Ranking

Round 1 2 3 4 5 6 7 8 9 10 Avg Std.DAvg6-10

Std.D6-10

Black - - 1 1 1 1 1 1 1 1 1.00 0.00 1.00 0.00

Green - - 2 3 3 2 2 2 2 2 2.25 0.46 2.00 0.00

Purple - - 3 4 4 4 3 4 4 3 3.63 0.52 3.60 0.55

Red - - 4 2 2 3 4 3 3 4 3.13 0.83 3.40 0.55

Round 1 2 3 4 5 6 7 8 9 10 Avg Std.DAvg6-10

Std.D6-10

Blue 1 1 1 2 2 1 1 1 2 1 1.30 0.48 1.20 0.45

Yellow 2 2 4 3 4 4 3 2 4 4 3.20 0.92 3.40 0.89

Brown 3 3 3 4 3 3 2 3 1 2 2.70 0.82 2.20 0.84

Orange 4 4 2 1 1 2 4 4 3 3 2.80 1.23 3.20 0.84

Results Equalization Effect (round 6 to round 10)

City 1

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

4th3rd2nd1st

City 2

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

4th3rd2nd1st

Results

Equalization Effect

City 1

0

2

4

6

8

10

12

14

16

18

1 2 3 4 5 6 7 8 9 10

City 2

0

2

4

6

8

10

12

14

16

18

1 2 3 4 5 6 7 8 9 10

Results

Equalization Effect

Round 1 2 3 4 5 6 7 8 9 10

1st 10.25 12 9.75 11.25 12 13 12 11.25 11 12.5

2nd 9.75 9.25 9 11 11.5 10.5 7.75 9 10.75 10

3rd 8 8.75 8.25 6.25 5.5 7.25 7.5 7.75 6.75 5.75

4th 6 4 7 5.5 5 3.25 6.75 6 5.5 5.75

Range 4.25 8.00 2.75 5.75 7.00 9.75 5.25 5.25 5.50 6.75

StD 1.93 3.32 1.17 3.05 3.76 4.22 2.37 2.21 2.79 3.34

Round 1 2 3 4 5 6 7 8 9 10

1st - - 14.5 14.5 14.5 14.5 13 13.25 14.25 14.5

2nd - - 7.5 7.25 7 8.5 10.75 10 10 10.25

3rd - - 6.75 6.5 6.75 6.5 5.75 6.75 6.5 5.25

4th - - 5.25 5.75 5.75 4.5 4.5 4 3.75 4

Range - - 9.25 8.75 8.75 10 8.5 9.25 7.75 10.5

Std.D - - 4.11 4.05 4.04 4.32 4.04 4.01 3.88 4.83

Results

Equalization Effect (round 7 to round 10)

City 1

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17

City 2

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8 9 10 1112 13 14 1516 17

Results – Study 2

Persistence in Reputation/Ranking

City 1

02468

10121416

1 2 3 4 5 6 7 8 9 10Round

Poin

ts

City 2

02468

10121416

1 2 3 4 5 6 7 8 9 10

Round

Poin

ts

Results –Study 2

Persistence in Reputation/Ranking

Round 1 2 3 4 5 6 7 8 9 10 Avg Std.DAvg6-10

Std.D6-10

Green 1 2 1 2 1 1 1 1 1 1 1.20 0.42 1.00 0.00

Red 1 1 2 4 4 3 3 4 4 3 2.90 1.20 3.40 0.55

Black 3 4 3 1 2 4 4 2 2 2 2.70 1.06 2.80 1.10

Purple 4 3 4 3 3 2 2 3 3 4 3.10 0.74 2.80 0.84

Round 1 2 3 4 5 6 7 8 9 10 Avg Std.DAvg6-10

Std.D6-10

Blue 1 1 1 3 4 4 4 4 4 1 2.70 1.42 3.40 1.34

Yellow 2 3 4 2 1 1 3 3 2 4 2.50 1.02 2.60 1.14

Orange 3 2 2 1 2 3 1 1 3 2 2.00 0.77 2.00 1.00

Brown 4 4 3 4 3 2 2 2 1 3 2.80 0.98 2.00 0.71

Equalization Effect (round 6 to round 10)

City 1

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

4th3rd2nd1st

City 2

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

4th3rd2nd1st

Results –Study 2

Equalization Effect

City 1

0

2

4

6

8

10

12

14

16

18

1 2 3 4 5 6 7 8 9 10

City 2

02468

1012141618

1 2 3 4 5 6 7 8 9 10

Results –Study 2

Equalization Effect

Round 1 2 3 4 5 6 7 8 9 10

1st 10.5 13 12.25 10.75 14.5 12.75 14.5 11.5 13.75 14

2nd 10.5 9.75 9.25 9 7 8.75 7.5 8.5 7.75 9

3rd 9.5 8.5 8.25 7.5 6.5 8.25 6.5 7.25 6.25 6.75

4th 3.5 2.75 4.25 6.75 6 4.25 5.5 6.75 6.25 4.25

Range 7.00 10.25 8.00 4.00 8.50 8.50 9.00 4.75 7.50 9.75

StD 3.37 4.28 3.30 1.77 4.02 3.48 4.08 2.13 3.57 4.15

Round 1 2 3 4 5 6 7 8 9 10

1st 11.25 13 12.75 9.75 10 11.5 10 11.5 10 8.75

2nd 7.75 8.5 11 9.75 9 7.75 9.5 8.75 9.5 8.5

3rd 7.5 6.25 6.75 9 7.5 7.5 7.75 7.25 8.75 8.5

4th 7.5 6.25 3.5 5.5 7.5 7.25 6.75 6.5 5.75 8.25

Range 3.75 6.75 9.25 4.25 2.50 4.25 3.25 5.00 4.25 0.50

StD 1.84 3.18 4.18 2.03 1.22 2.01 1.51 2.21 1.90 0.20

Results –Study 2

Equalization Effect (round 7 to round 10)

City 1

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17

City 2

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8 9 10 1112 13 14 1516 17

Results –Study 2

Thank you!