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The Schelling Segregation Model
Rajiv Sethi
Yonsei University, August 2012
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 1 / 21
Main Reading
Schelling, Thomas C. (1978). Micromotives and Macrobehavior, Chapter 4
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 2 / 21
Patterns of Association
Patterns of association in cities, campuses, clubs, etc.:
arise from decentralized, uncoordinated choices
interacting with policy initiatives
What determines such patterns of association?
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 3 / 21
Underlying Preferences
What does the extent of observed segregation
tell us about underlying preferences
and discrimination in housing and lending markets?
Imagine a world with no discrimination
and no racial income disparities
and tolerant preferences over racial composition
and decentralized, uncoordinated location decisions
How much segregation would we observe?
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 4 / 21
The Schelling Model
Two types of households located on a grid
Demands: more than a third of neighbors in own-group
Initial locations: perfect integration
Perturbation: random removal and partial replacement
Dynamics: Sequential movement to acceptable locations
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 5 / 21
Initial Allocation
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 6 / 21
Perturbation: Remove 20, Replace 5
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 7 / 21
Sorting Equilibria
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 8 / 21
Stability of Segregation
“People who have to choose between polarized extremes ... will oftenchoose in a way that reinforces the polarization. Doing so is no evidencethat they prefer segregation, only that, if segregation exists and they haveto choose between exclusive association, people elect like rather thanunlike environments”
Schelling, 1978
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 9 / 21
The Bounded Neighborhood Model
Single neighborhood
No capacity constraint
Free entry and exit
Preference heterogeneity: linear tolerance schedules
Dynamics: Least tolerant exist first, most tolerant enter first
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 10 / 21
Model 1
100 whites, 50 blacks
Tolerance ranges from 2:1 to zero (both groups)
Median tolerance it 1:1
Which allocations are “tolerable”?
Which are stable (no entry or exit)?
Example: At (50, 25) whites enter, blacks exit
Example: At (10, 20) whites exit, blacks enter
Example: At (10,10) both enter
Example: At (80,40) both exit
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 11 / 21
Tolerance Schedule: Whites
0 10 20 30 40 50 60 70 80 90 1000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Whites
Tole
rance
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 12 / 21
Tolerance Schedule: Blacks
0 5 10 15 20 25 30 35 40 45 500
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Blacks
Tole
rance
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 13 / 21
Model 1: Unstable Integration
0 10 20 30 40 50 60 70 80 90 1000
5
10
15
20
25
30
35
40
45
50
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 14 / 21
Dynamics
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 15 / 21
Model 2
100 whites, 100 blacks
Tolerance ranges from 5:1 to zero (both groups)
Median tolerance is 2.5:1
Three stable steady states
Initial conditions matter
Integration can be stable at (80,80)
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 16 / 21
Model 2: Stable Integration
0 20 40 60 80 100 120 1400
20
40
60
80
100
120
140
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 17 / 21
Model 3
100 whites, 50 blacks
Tolerance ranges from 5:1 to zero (both groups)
Median tolerance is 2.5:1
Only segregation is stable even though tolerances are high
What happens if entry is restricted to 40?
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 18 / 21
Model 3: Unstable Integration
0 10 20 30 40 50 60 70 80 90 1000
20
40
60
80
100
120
140
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Model 4: Entry Barriers
0 10 20 30 40 50 60 70 80 90 1000
20
40
60
80
100
120
140
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 20 / 21
Conclusions
Eventual outcome sensitive to initial conditions
Segregated allocation are stable even if there exists a stableintegrated allocation (see model 2)
Caps on entry can sustain integration
Less tolerance can result in more integration (compare models 3 and4, assuming intolerance rather than entry barriers)
Sethi (Barnard/Columbia & SFI) Schelling Segregation Model Yonsei, August 2012 21 / 21
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