segregation: the role of race, income and the housing market. alan kirman, greqam,ehess, université...

Segregation: The role of race, income and the housing

market.

Alan Kirman,GREQAM,EHESS, Université d’Aix Marseille lll

Dejan VinkovićIAS Princeton, USA

University of Split, Croatia

Leiden October 2007

A Few Preliminary Comments

• This paper takes a model of such a social and economic phenomenon, segregation, and uses a physical analogy to understand it.

• Economics has used a model based on classical mechanics. Now more mathematics than physics.

• Can different physical models shed light on economic phenomena?

• The problem of intention: the man and the stone.• We can sometimes see structure which we would not have

found without the physical analogy.• This particular problem.

Three steps: racial segregation, income grouping, the housing

market. • First I shall give you a rapid view of

Schelling’s basic model

• Next I will introduce preferences for income group

• Then I will introduce the housing market and some variations on the basic model.

Isaac Newton

« I can calculate the motion of heavenly bodies, but not the madness of people »

« A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it »

Max Planck, A Scientific Autobiography (1949).

What is Schelling’s Basic Model?

• People of two different colours live on a chessboard. There are some free squares.

• Their utility depends on the number of their neighbours who are of their colour. If a strict majority of their neighbours are of the other colour they are unhappy, low utility, high energy in the analogy.

Schelling’s Model: Why is it so famous?

• It is intellectually intriguing, emergence of aggregate phenomenon, difficult to predict from individual behaviour.

• It is about an important social phenomenon, segregation.

• It is easy to explain and play with.

Schelling Model

• position particles randomly• calculate their utility\energy• create the list of particles that want to move

• pick randomly one particle from the list• move it• update the list

?

?

Basic rule: move to the nearest empty spot where the utility increases

Variations to the basic rule: • swapping particles • no limit on moving distance• moving when the utility does not change ("liquid", "solid")

A Physical Analogue

• In the Schelling model utility depends on the number of like and unlike neighbors. In the particle analogue the internal energy depends on the local concentration (number density) of like or unlike particles.

• This analogue is a typical model description of microphysical interactions in dynamical physical systems of gases, liquids, solids, colloids, solutions, etc. Interactions between particles are described with potential energies, which result in inter-particle forces driving particles' dynamics.

The System is not Closed

• The energy lost by a particle is not transferred to other particles, but transmitted out of the system. Similarly, a particle can gain energy from outside the system when an unlike particle moves into the neighborhood and lowers the particle's utility.

• Hence, the system can change its energy only by emitting or absorbing radiation and not by changing its volume or pressure or number of particles.

Minimisation of Energy

• The basic tendency of such a physical system is to minimize its total energy. Here, it can do that only by arranging particles into structures (clusters) that reduce the individual internal energy of as many particles as possible. In other words, interparticle forces induce particles to cluster and the stability of a cluster is determined by this force.

• Hence, all we need to do is to look at the behavior of this force on the surface of a cluster to see if the surface will be stable or if it will undergo deformations and ripping.

A Continuous Version

• Instead of counting the agents around a particular agent take the solid angle around a differential area, dA.

• Take the integral of the energy along the surface and see what shapes minimise it.

• There is a tendency to flatten the surface.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Strict improvement: The role of preferences and spaces. The formation of a solid structure

Evolution with indifferent movers



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Indifference and Unlimited Moves



Periodic Boundaries



Periodic Boundaries and Long Movers



Clusters want to grow to reduce their surface(surface has "energetically unstable" particles)

radius

1

volume

surface

+kinetically favored energetically favored

The income dimension

• Our next project is to examine when people also have preferences for the incomes of their neighbours.

• They could prefer to be with people with similar, lower or higher income.

• One possibility would be lexicographic preferences, colour first then income.

Income preference

“everybody loves the rich”: =number of poor neighbors

Race+income preference

“extremes” avoid each other

The housing market

• The previous remarks suggest that it will be the relative forces of the colour and income preferences that will emerge.

• Now, the next step is to introduce prices of houses and these could be a function of the incomes of those who choose them.

• What sort of clusters will emerge?

Market phenomena and special influences

• It is widely recognised that in determining the allocation of individuals and resources in space many influences such as altruism, social or racial conformity, aspiration to public goods which may be locally provided, play an important role.

• Trying to analyse the housing market without taking this sort of issue into account may result in misleading conclusions, but trying to analyse segregation without dealing with the housing market can be equally misleading.

Housing price utility

I<1 for rich and for poorR<1 for white (they are richer than blacks for whom R=1 !)

Price gradient pressure

I 1

Racial preference

Income preference

Housing price utilityI<1 for richR<1 for white

Liquids and Solids

• Introducing house prices removes the need to allow people to move even if indifferent. The constant changing of house prices induces movement in the system.

• The choice of utility for income is based on empirical results (see e.g. Bayer et al.(2007)) JPE. They show that people refer to live with richer neighbors.

• They also claim that unobserved neighborhood quality has an impact on prices.

BASELINE MODEL

Results

• We observe racial segregation tending towards complete separation

• There is negligible income clustering, there is no tendency for large clusters of similar incomes to form.

• There is no formation of price clusters• Richer agents occupy more expensive

housing.

Immigration and its Role

• Much of the existing analysis concerns the effect of an influx of new population

• In our model we can take account of this by reducing the amount of free space.

• We also have to take account of the phenomenon of « white flight ».

REDUCED EMPTY SPACE

(influx of new people)

Results from reducing space

• Now spatial income segregation emerges• Poor clusters are associated with consistently low

house prices.• Rich clusters experience high variance of prices.• Rich white clusters « avoid » poor black clusters.

Explanation.• The highest prices occur on the boundaries of

clusters.

The speed of price adjustment

• This is an old problem in economics and one which generated a debate over the relevance of « tatonnement » versus « non-tatonnement » processes.

• Here we consider the effect of a long price adjustment before moves take place.

SLOW PRICE CYCLE

Results for speed of price changes

• If prices are kept constant and agents allowed to move then the system « freezes »

• There is a trade-off between speed of price adjustment and evolution of the system

• The system separates into rich and poor clusters with highest prices following racial borders.

• The results are shown for a number of adjustments equal to the total number of agents.

How important is racial preference?

The impact of differences in income between races

• Many of the versions of Schelling’s model involve groups which are symmetric.

• Yet, there are obvious asymmetries particularly in income.

• We examine the effect of such an asymmetry on the allocation of housing.

BLACK MOSTLY POOR

blacks in middle- or upper-income households Currently: ~1/2 In 1960: ~1/5 (Council of Economic Advisors 1998;U.S. Census Bureau 2000)

different apparent behavior of rich whites and rich blacks is not the cause of segregation in this model, but a consequence of it

Results with mostly poor blacks

• Rich whites move into the interior of white clusters.• Poor whites occupy the borders between racial

clusters.• Poor whites also scatter into poor black

neighborhoods. • Rich blacks do not cluster because their clusters are

invaded by poor blacks.• It is race not income that drives segregation. A

contradiction with the flight from poverty explanation.

Another asymmetry

• Blacks are still a small minority in the U.S

• Does this have an effect on segregation?

• One can analyse this by varying the proportion of blacks in the model.

• This allows one to check the assertion that the smaller the minority population the less important is segregation.

BLACK MINORITY “the largest decreases in segregation occurred in metropolitan areas in which blacks made up a small percentage of the neighborhood of the typical white.”(Farley & Frey. 1994. Am.Soc.Rev. 59, 2345)

Results with black minority

• Only rich blacks cluster and there are not enough of them.

• These clusters are broken up by the invasion of poor blacks.

Asymmetric racial tolerance

• It has been argued that whites have become much more tolerant of mixed neighborhoods what effect does this have.

• What happens if, as Patterson asserts, blacks live with blacks because that is what they prefer and race is more important than class?

ASYMMETRIC RACIAL PREFERENCES

If segregation is caused by white preferences for white neighborhoods, then whites will pay relatively more for housing than blacks as segregation rises. This will reduce the relative housing costs of blacks compared to those of whites. If discrimination and/or black preferences for black neighborhoods are the causes of segregation, then blacks will pay relatively more for housing than whites in more segregated cities. This will increase housing costs for blacks relative to whites. (Cutler et al. 1999. J.P.E. 107, 455506)

BLACK MORE TOLERANT WHITE MORE TOLERANT

Results with asymmetric racial preferences

• In this case the less tolerant group clusters strongly and the rich part of that group dominates the cluster.

• Note how the housing price distribution for blacks shifts towards lower prices when blacks are more tolerant.

Variations in the quality of housing

• Although the process is essentially dynamic, all housing stock is not of equal quality.

• Does the existence of such variations affect the allocation of housing?

• An important avenue for future research is to include the evolution of the quality of the housing stock as individuals invest in infrastructure.

PREDEFINED HOUSING QUALITIES

Sethi & Somanathan (2004) J.P.E. 112, 1296

Results for predefined housing qualities

• If there is a predefined division of housing prices and there is a high price for good housing then the segregation is between rich and poor with racial segregation within clusters.

• If the price of good housing is lower then the segregation is essentially racial.

Some empirical evidence

What happened in New York?

• In the 20’s there was a « color line » which moved southwards.

• Several agreements were reached amongst landlords to try to stop this.

• 140th 137th,135th, 131st 129th st.• By 1920 the cluster had reached 110th st.• The proportion of Black Americans.• Streets v. Blocks, For details see Mobius and Mobius

and Rosenblatt who looked at Chicago. There model is related to the one dimensional approach of Matteo Marsili.

Segregation in Chicago

• The evolution of segregated clusters in Chicago is well documented, (See Mobius and Rosenblatt).

• Mobius suggests that the mechanism is more one dimensional than two dimensional, streets rather than blocks.

• We need to study house prices for the appropriate period.

Conclusions

• This model incorporates three causes of segregation racial preference, income preference, housing prices

• Racial segregation is very persistent as long as its utility is non-negligible

• The proposed model is a good “sandbox” for exploring various scenarios and generates testable predictions

•We also explored low racial preferences and poor cities.

•Although this model does not provide “the explanation” for segregation it does allow one to understand some of the mechanisms at work

segregation: the role of race, income and the housing market. alan kirman, greqam,ehess, université...

Documents

solid slide

favored slide

solid structure slide

periodic boundaries

unlimited moves slide

particles utility

number of particles

list of particles