the schelling segregation modelweb.yonsei.ac.kr/wcuecon2012/lecslid/2. schelling.pdf ·...

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


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?


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?


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


Initial Allocation


Perturbation: Remove 20, Replace 5


Sorting Equilibria


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


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


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


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


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


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


Dynamics


Model 2



Median tolerance is 2.5:1

Three stable steady states

Initial conditions matter

Integration can be stable at (80,80)


Model 2: Stable Integration

0 20 40 60 80 100 120 1400

20

40

60

80

100

120

140


Model 3



Median tolerance is 2.5:1

Only segregation is stable even though tolerances are high

What happens if entry is restricted to 40?


Model 3: Unstable Integration

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

120

140


Model 4: Entry Barriers

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

120

140


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)


the schelling segregation modelweb.yonsei.ac.kr/wcuecon2012/lecslid/2. schelling.pdf ·...

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