Agent-Based Models in Economics and Finance
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Prof. Dr. Thomas Lux
Christian-Albrechts-Universität zu Kiel
Institut für Volkswirtschaftslehre
Lehrstuhl für Geld, Währung und Internationale Finanzmärkte
„Micromotives and Macrobehavior: An Example
of Involuntary Racial Segregation”
It is a common observation that residential segregation between white and black
neighborhoods in the U.S. is highly persistent. In contrast to observed segre-
gation, survey studies found most respondents stating they would rather prefer
to live in a racially mixed area than in a homogeneous one.
One explanation of this divergence is that individuals have a tendency to appear
more tolerant in interviews than they really are. Another explanation is that
social segregation is the involuntary outcome of an uncoordinated residential
choice process which favors a self-organization into uniform neighborhoods.
Example
: assume the pool of potential inhabitants of a neighborhood consists
of 100 whites (W) and 50 blacks (B). Within both groups a similar distribution
of tolerance and racial diversity exists: The most tolerant white (black) indi-
vidual would be willing to accept a maximum ratio of W:B (B:W) of 1:2, i.e.
a two-thirds majority of the other group. The least tolerant individual of each
group would only like to live in a homogeneous environment without individuals
of another color.
One immediately observes that there exist quite a number of configurations in
which a mixed neighborhood could be formed from this heterogeneous pool of
individuals, e.g. with W:B numbers of 25:25, 25:30 etc.
Agent-Based Models in Economics and Finance
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Figure 1: Tolerance levels of W population.Source: Schelling.
Figure 2: Areas of expansion and contraction of W and B populations.
Source: Schelling.
Graphical representation: the distribution of tolerance levels, Prob (tolerance
> x), in the upper panel of Fig. 1 can be translated into a map from W to
B: the tolerance distribution of whites could be transformed into the maximum
number of blacks that a certain number of whites would be willing to tolerate in
their neighborhood, and vice versa for the maximum tolerable number of white
persons from the viewpoint of blacks (Fig. 2).
Acceptable combinations can be identified by the intersection of the areas below
the W and B schedules.
Dynamics
: with W and B schedules as demarcation lines, we can assume the
following plausible dynamic process:
Agent-Based Models in Economics and Finance
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Figure 3: An example with the possibilities of a mixed equilibrium with coex-
istence of both groups.
Source: Schelling.
•
if B or W agents in the area are content with the current racial mix, the
area will attract additional residents from the pertinent group,
•
if the number of residents with the opposite color exceeds the tolerance
level of one group, some members of this group will move out of the area.
Result
: In the above example, this dynamics will
not
converge to a mixed
neighborhood scenario, but will lead to the formation of an all-white or all-
black community.
While this unfortunate result survives for many choices of the population size
and distribution of tolerance levels, the formation of a mixed neighborhood is
not entirely impossible, c.f. Fig. 3.
Note, that even in this scenario (B=100, W=100 with the same distribution
Agent-Based Models in Economics and Finance
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of tolerance levels as above), the outcome is not unique, but there are three
steady states (mixed neighborhood and all black/all white areas). Which one
the dynamics converges to depends on initial conditions.
Exercise
: formulate the above migration process as a system of differential equa-
tions for the change of the number of whites and blacks over time!
Literature:
Schelling, T.,
Micromotives and Macrobehavior
, New York 1978.
More elaborate models of neighborhood formation would have agents themselves
being localized in space, mostly in a lattice structure. Agents would, then, react
to the configuration within their visible neighborhood, e.g. they would move
out of the area of the majority of their direct neighbors is of another color.
Examples of such processes and easy to use computer code for their simulation
can be found in:
Gaylord, R. and L. D’Andria,
Simulating Societies
, New York 1998.
