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This essay presents a literature review about residential segregation. Given the vast extension of it, the focus has been on those works that we have considered either more influential or with the potential to define the new trends of this kind of research. We have classified the literature into the following subjects: definitions, measures, causes and consequences. Our main conclusions are that the measurement and description of segregation must be based upon techniques that incorporate spatial factors; it is crucial to use individuals interactions and social dynamics models in order to understand the segregation causes and consequences; it is necessary to consider general equilibrium models, with endogenous location decisions and the interaction of relevant markets to shed light on the segregation consequences upon the society as a whole and to evaluate any policy designed to deal with it. JELCodes: R, R14, R31, R34 y R38.
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Residential Segregation:
A Literature Review
Vicente Royuela
Miguel Vargas
07
Residential Segregation: A Literature Review
Vicente Royuela
and Miguel Vargas
Abstract
This essay presents a literature review about reside ntial segregation. Given the vast ex-
tension of it, the focus has been on those works that we have considered either more influential
or with the potential to define the new trends of this kind of research. We have classified the
literature into the following subjects: definitions, measures, causes and consequences. Our
main conclusions are that the measurement and description of segregation must be based
upon techniques that incorporate spatial factors; it is crucial to use individuals interactions
and social dynamics models in order to understand the segr egation causes and consequences;
it is necessary to consider gener al equilibrium models, with endogenous location decisions
and the interaction of relevant markets to shed light on the segregation consequences upon
the society a s a whole and to evaluate any policy designed to deal with it.
JELCodes: R, R14 , R31, R34 y R38.
Key words: Residential Segregation, Urban Economics.
1 Introduction
The first academic work dealing with residential segregation (RS hereafter) is Park (1926).
Since then, an important quantity of research on this topic has been done. One of the aims
of the present essay is to classify this literature. To see whether it is dedicated to cast a
light on RS defi nition, its measures and both its causes and its consequences. In all these
subjects, both empirical and theoretical research, has been conducted. With regards to the
amount of investigation don e on each one of them, by far the emphasis has been placed on RS
measures, meanwhile the literature’s focus on causes and consequences has been more limited.
Amongst the possible explanations about this fact it is feasible to think of the lack of formal
Grup d’Anlisi Quantitativa Regional, Universitat de Barcelona. vroyuela@ub.edu
Universidad Diego Portales, Chile. miguel.vargas@udp.cl
1
models or econometric techniques and data bases (Bayer et al., 2004a). Nonetheless, during
recent years, some important developments on economic and econometric th eory applied to
social interactions and social dynamics h ave occurred, and have been useful to in corporate
new in dividuals’ behaviour concepts into formal models which have facilitated the empirical
and theoretical analysis of RS (Durlauf and Young, 2001; Meen and Meen, 2003). Because of
these reasons, a new and interesting research avenue has been opened , based on the concepts
previously mentioned , which has allowed to restart the study of this phenomenon putting a
particular emphasis on both its causes and its consequences.
Due to the extensive amount of research , the focus of this essay has been limited to two
subjects. First, to establish a taxonomy of this literature, classifying it in a simple and easy way
in order to allow any economist to be able to understand its basis and th e main facts related to
it. Second, to draw the reader’s attention to the most important new advances of this kind of
investigation, and what the futu re tendencies may be.
According to these aims this essay is organised as follows. The first section is dedicated to RS
definitions. Then, it develops the topic of RS measures which explains the main characteristics
of all the different indices that have been proposed by the literature to identify the level of
segregation of a given urban area. In the next section an analysis of what has been done
concerning the causes of RS is presented. Then, the analysis is focused on the consequences of
RS. Finally, conclusions are presented.
2 RS Definition
The most general RS definition that it is possible to find talks about the level of dispersion of
a particular group in a given geographical area. Park (1926) presents th e very first definition.
He says th at RS is the link that exists between both the social distance and the physical
distance. White (1983) defines RS as the existing distance amongst those areas inhabited by
different social groups. Jargows k y (1996) defines RS as the concentration level of social groups
in given areas of the city. Sabatini et al. (2001) says that RS is the extent of spatial p roximity, or
territorial agglomeration, of households belonging to the same social groups, w here a social group
can be understood in terms of race, age, religion or income. Rodr´ıguez (2001) indicates that RS
corresponds to the level of concentration of different social groups in specific city areas. As one
2
can see, th er e is no consensus on an unique definition of RS. However, the work that arrives
closest to a universal definition is Massey and Denton (1988). In this article RS is presented
as the result of different social phenomena interactions. This id ea relies upon the concept that
urban spatial social structures is inherently multidimensional (Timms , 1971). Specifically, the
RS definition is based on five dimensions: evenness, exposure, clustering, centralisation and
concentration. The main characteristic of this work is the clarity and richness with which RS
has been addressed. Accordingly, it is possible to say that in one way or another all the RS
definitions that have been found in literature are included in these five dimensions. These
elements have made this work one of the most influential in RS literature and not just with
respect to how to define this phenomenon but also with respect to how RS can be measured,
as it will be seen later on. The five Massey and Denton (1988) dimensions definitions are the
following:
Evenness: it refers to the d istribution differences between two groups over geographical
units, as census tracts, inside a city. A minority group will be segregated if it is unevenly
distributed over the geographic units. The evenness will be maximised, and hence the RS
minimised, when every geographic unit has the same proportion of the minority group
that the city as a whole has . For instance, if in the city as a whole the minority group
proportion is 20% in order to have a full evenness, every geographic unit must have also a
minority group pr oportion of 20%.
Exposure: corresponds to the degree of potential contact, or the interaction possib ility,
between a minority group and the remaining population within a geographic area or city.
Although exposure looks similar to evenness, th ey are conceptually different, because th e
latter takes into account the relative size of the groups that are compared.
Concentration: is the amount of relative physical space occupied by a min ority group in
either a given geographical area or city. Those groups that occupy a small part of the total
area will be segregated.
Centralisation: has to do with the degree of pr oximity of the p lace where a minority group
lives to the city centre.
Clustering: is the degree of agglomeration of those areas inhabited by a minority group.
3
It measures the extent at which a minority group lives, u nbalanced, in contiguous areas.
Although it s eems to be similar to Centralisation, they are n ot. The difference rely on the
fact that Concentration exists, for instance, when a minority group lives just in two census
tracts within a city without considering whether these two census tracts are contiguous or
not, as Clustering exists when not only the minority group lives in two census tracts but
when th ese two census tracts are contiguous.
In order to have a clearer picture of the differences that exist between all the dimensions
explained above, figures 1, 2 an d 3 illustrate high and low s egregation situations for each one of
them. Every one of these figures shows the distribution of households within a hypothetical city.
The black squares represent the minority group and the white squares represent the majority
group. Dimensions are arranged in column, so in figure 1 column a represents evenness and
column b r epresents exposure. The upside hypothetical city in every column shows high levels
of segregation meanwhile the downside city shows low levels of segregation, so, following with
figure 1 example, the upside city in column a shows high levels of segregation r elated to even-
ness and the downside one in column a illustr ates a case of low segregation related to th e same
dimension. The column b of figure 1 shows high (up side city) and low (downside city) d egree
of segregation related to exposure measured as isolation. Figure 2 illustr ates concentration in
column a and centralisation in column b”. Fin ally, figure 3 presents th e clustering dimen-
sion. This figure is very useful to clarify the difference between concentration and clusterin g. As
can be appreciated in fi gu re 2 column a concentration arises wh en minority group o ccupies
a small proportion of land within the city, it does not matter if this small areas are contiguous
or they are not, meanwhile, as can be appreciated in figure 3 u pside city, clustering arises when
the minority group live in neighbourhoods that are contiguous.
As it can be seen, this approach widely covers the main possible aspects of RS and it has
not been possible to find in literature a more complete definition than this one. As a matter of
fact, Massey et al. (1996) revisited this multidimensional approach and reconfirmed its validity.
The importance of these resu lts do es not rely just upon the possibility of having a better
understanding of the RS concept, but has allowed for empirical analysis. Within the latter,
economists’ work has been focused, mainly, on the stu dy of even ness and exposure. A possible
explanation for this fact can be, as it is discussed later on, that it is easier to get in dices to
4
Figure 1: High an d Low segregation with evenness and exposure
measure and to study these RS dimens ions than to get indices for the reminding d im ensions.
However, as Echenique and Fryer (2007) pointed out, there is a feature that makes these two
dimensions interesting to work with: only these two dimensions can take into account the effects
of RS on social interactions.
3 RS measures
As Reardon and Firebaugh (2002) indicates, the first systematic and critic endeavour for doing
a deep analysis on indices and measures of RS is the work presented by Duncan and Duncan
(1955). One of th eir main conclusions is that there is few information of RS indices that is not
contained in the index of dissimilarity. Later on Taeuber and Taeuber (1965) reaches the same
conclusion. One of the main consequences of this was the popularisation of its use. Despite
this conclusion, during a long period of time there was no s uch a thing as a consensus about
one particular way of measuring RS and several different authors based their investigation on
5
Figure 2: High and Low segregation with concentration and centralisation
different RS definitions and different RS measures. For instance, Bell (1954), Farley (1984),
Farley (1977), Lieberson and Carter (1982a) and Lieberson and Carter (1982b) did their research
based on the index of exposure. Coleman et al. (1982) and Zoloth (1976) conducted research
using the variance ratio applied to RS and applied to educational segregation. Thus, during
the 70s and 80s, it was possible to watch an avid discussion with respect to virtues and defects
of RS indices. Some interesting examples of this debate are Cohen et al. (1976); Coleman et al.
(1982); Cortese et al. (1976); Falk et al. (1978); James and Taeuber (1985); Kestenbaum (1980);
Lieberson and Carter (1982b); Morgan (1983); Taeuber and Taeuber (1976); Winship (1977,
1978).
A crucial advance to this discussion was James and Taeub er (1985). This work develops a
set of f ou r criteria whose aim is to evaluate the perf ormance of the different indices of RS. The
four criteria, which indicate how R S indices must react to changes in the groups distribution
between geographical sub areas, are:
6
Figure 3: High and Low segregation with clustering
1. Organisational equivalence: if one geographical sub area is divided into k units, every one
of these new units with the same groups proportion of the original area, RS does not
change. The same happens if k geographical sub areas with the same group proportion
are merged into one single area.
2. Size invariance: if the number of individuals in each group within each geographical sub
area is multiplied by a constant factor RS remains the same.
3. Th e principle of Transfers: if an individual belonging to one group is moved from one
geographical sub area to another, where the proportion of persons of this group is greater
in the sub area of origin than the su b area where the in dividual arr ives to, then RS is
reduced.
4. Composition invariance: if the number of individuals of one group in each geographical
sub area increases by a constant factor and the number and distribution of individuals of
all other groups is unchanged, RS is unchanged.
7
This criteria also demonstrates that indices that are highly correlated in empirical studies
may nonetheless behave very different und er certain circumstances, such as when the population
shares of groups change.
Massey and Denton (1988), using factor analysis classify RS indices according to the five
dimensions th at they proposed. Besides, applying empirical and conceptual criteria they deter-
mine which index is the best for each one of these ve dimensions.
This analysis was carried out for 20 indices, which is a bigger figure than the five indices
analysed by James and Taeuber (1985). Massey and Denton (1988) came to the conclusion that
the most suitable measures for each dimension are respectively: the index of dissimilarity, the
index of exposure, relative concentration, absolute centralisation and spatial proximity. The
remaining in dices that were studied are: Gini, entropy and Atkinson indices for evenness; ration
of correlation for exposur e; delta and absolute concentration for concentration; city centre pro-
portion and relative centralisation for centralisation; and absolute clustering, relative clustering,
interaction and isolation w ith distance adjustment for clustering.
However, this is not the only approach that is possible to find in RS literature. The devel-
opment of geographical information technologies and the spatial statistics have made it possible
to incorporate in an explicit way spatial variables into the analysis.
Including spatial elements responds to a necessity for studying this phenomenon following a
strategy that allows to embrace all of its possible edges. For example, each individual environ-
ment definition has been left out of the analysis which has been focused upon non-spatial aspects
because of this kind of non-spatial approach considers just the equivalent social environment or
some sort of spatial organisation unit such as census tracts concentrating its efforts only on th e
degree to which these spatial organisation units could d iffer amongst in dividuals (Reardon and
O’Sullivan, 2004).
Consequently, a group of indices based on th ese spatial concepts has been proposed to mea-
sure RS. Examples of these m easures are the spatial dissimilarity index, the I of Moran and the
local indicator of spatial autocorrelation LISA. As Massey and Denton (1988) did previously,
Reardon and O’Su llivan (2004) evaluate the spatial indices and as a result they indicate that
those indices with better properties are the index of spatial exposure and the index of spatial
information.
There is another reason to use spatial indices: RS in general has the peculiarity of being
8
sensitive to changes in the geographical scale used, so the higher the level of geographical d isag-
gregation the higher the level of RS that will be reported. For example, let us consider the case
of a chess board where every square is occupied by individuals belonging to two different groups
(one group occupying the white squares and the another one occupying the black squares), the
dissimilarity ind ex will reach its higher value, 1, if the sub geographical unit used to calculate
this index is the square. However, if instead of considering every square as a single sub geo-
graphical unit the board is divided into two half and every one of these two halves is considered
to be a sub geographical unit to calculate the index of dissimilarity, the latter will reach a value
of 0, albeit the ind ividual distr ibution across the boar has not ch an ged at all.
This is one of the problems generated by what has b een called in literature as “The Modifiab le
Areal Unit Problem” (MAUP), and it is known as the scale effect. Heywood (1998) defines
MAUP as the problem that arises due to the imposition of artificial units of spatial r eporting on
a continuous geographical phenomenon resulting in the generation of artificial spatial patterns.
Given the fact that this problem arises when sp atial aspects such as distance, the level of
contact between geographical units, and the extent of local individuals interactions, are not
taken into account, then it seems that a possible solution for this problem is to include these
sort of variables into the measures used. However, Wong (2004) shows that this approach is
not enough to resolve the MAUP: the spatial indices are sensitive to scale as well. For instance,
Krupka (2007) show that the common know ledge about the fact that greter cities are more
segregated tha smaller ones is based on a spurious correlation amongts segregation and city size.
The reason behind this fact is that measur es based upon census tracts data will tend to report
higher values for bigger cities because this kind of cities have more neighbourh oods that are
big enough to contain one or more than one census tract meanwhile smaller ones need to pair
neighbourhoods in order to ll-up a censcus tract. This bias will be reduced at smaller levels of
spatial aggregation.
Consequently, it is important to be careful when comparing the level of RS between the
different cities or between RS measured in different moments for the same city. Moreover, it
is advisable to carry out a multi-scale analysis. Reardon and O’Sullivan (2004) developed a
methodology to compute a RS profile which describes the level of RS at a given scale and the
extent that the RS structure changes when the scale changes also. Although this represents
an interesting strategy in order to deal with this pr ob lem, it has not yet been widely used in
9
literature, s o it is not possible to compare its performance against other kinds of RS measures.
Echenique an d Fryer (2007), propose another app roach to deal with these sort of p roblems
based on social interactions and social n etworks theory: the spectral segregation index (SSI).
The SSI is based upon two premises: rst, a measure of segregation should disaggregate to
the level of individuals, and second, an individual is more segregated the more segregated are
the agents to w hom he interacts w ith . As the authors point out, the SSI has four important
features that give it important advantages over others indices of RS. First, it is invariant to
arbitrary partitions of a city. Second, it allows to investigate how segregated multiple minority
groups are within and between cities. Third, it allows f or analysis of the full distribution of
segregation, allowing researches to move beyond aggregate statistics, which can be misleading.
Fourth, there are inh er ent multiplicative effects captured by SSI which other indices omit given
the f act that it is built based on a social network framework. The main disadvantages of this
index are the following: first, it depen ds on the quality of the information that can be obtained
on social interactions. For instance, in the case of RS, the typical information available is
restricted to the place where the individuals live within a city and not in the way they interact
with one another. Second, it is sensitive to the fraction of individuals in a network who have the
characteristic under study. Third, implementing the SSI can imply a momentous computational
effort.
The next subsection presents conceptual and technical descriptions of the indices mentioned
above classifying them as non-spatial and spatial measur es.
3.1 Non-spatial measures
The index of dissimilarity, D, developed by Jahn et al. (1947) and Duncan and Duncan (1955),
measures the percentage of the group that must change its location from on e neighbourhood to
another in order to reach the percentage of this group within the neighbourhood so th at this
percentage is the s ame percentage in the city as a whole. For instance, if the group of interest
within the city has a participation of 20%, in order to have no RS, in every neighbourhood the
group participation must be 20%. The index value varies between 0 and 1, representing the
minimum and maximu m level of RS respectively.
10
3.1.1 The Duncan index
This index can be obtained from the Lorenz curve. It repr esents the maximum vertical distance
between the Lorenz curve and the diagonal line that represents full evenness. When the group
under study is small compared to the number of geographical sub areas (like the census tract)
the Duncan index is highly affected by the deviation from evenness and it is not sensitive to
redistributions between geographical sub areas wh er e the proportion of the group under study
is below to the same group proportion of the city as a whole. According to this index, just by
moving people belonging to th e group under study from the geographical sub areas where they
are over-represented to geographical s ub areas where they are under-represented can affect the
level of RS (Massey and Denton, 1988).
The functional form of the Duncan index is:
D =
n
X
i=1
t
i
p
i
P
2T P (1 P )
(1)
where t
i
and p
i
are the total population and minority population of areal unit i, and T and P
are the population size an d m inority proportion of the whole city.
3.1.2 Exposure indices
The both basic exposure indices are the index of interaction (xP
y) and the index of isolation
(xP
x). Th ese indices rep resent, respectively, the p robability that an individual belonging to
the group under study has of sh aring a residential area with th e remaining population.
The index of interaction measures specifically the level of exposure that one group has to the
remaining population. On the other hand, the index of isolation measures th e level of exposure
that individuals belonging to the group under stu dy have to themselves.
When there are only two different groups, the result of the addition of these two indices is 1.
Both low levels of interaction and high level of isolation indicate high levels of RS.
Albeit, the Duncan index and the both indices of exposure are correlated empirically, they
differ conceptually because of the latter d epends on the relative size of the two groups that are
being compared, while the former does not. For example, the Duncan ind ex can indicate a low
level of RS for a certain group of the population, but the level of exposure can be low, which
means a high level of RS, if this group has a high total population participation.
The functional form of these indices, interaction and exposure, are the following:
11
xP
y =
n
X
i=1
x
i
X
y
i
t
i
(2)
xP
x =
n
X
i=1
x
i
X
x
i
t
i
(3)
where X is th e total population of the minority group, Y is the total population of the major-
ity group, x
i
, y
i
and t
i
are the minority, majority and total population within the geographical
sub area i.
3.1.3 The Theil index
An important critique that can be done to Massey and Denton (1988) and James and Taeuber
(1985), and consequently to all the indices presented above, is that th ey do not consider RS
measures involving more than two groups within society. Reardon and Firebaugh (2002) deal
with this issue and propose to work with multi-group indices. They derive and evaluate 6
multi-group indices. The criteria used for this evaluation is, basically, the same used by James
and Taeuber (1985), but, they split the principle of the transfers criterion into two criteria,
namely, tr an sfers and exchanges. The reason this is done is because the two group ind ices
respond in a different way to transfers (one way transfers from one sub area i to a sub area j)
and exchanges (two ways trans fers from one sub area i to a s ub area j) when there are more
than two groups. Besides, th ey d efine two decomposability properties that are desirable for RS
indices: the additive organisational decomposability and the additive group decomposability.
The exact description of these new criteria is as follow:
Exchanges: if an individual of a group m in an organisational unit i is exchanged with an
individual of group n from organisational unit j, where the proportion of per sons of grou p
m is greater in unit i than in j an d the proportion of persons of group n is greater in unit
j than in i, RS is reduced.
Additive organisational decomposability: if J organisational units are clustered into K
clusters, then a segregation measure should be dividable into a sum of indepen dent factors
within —and between—clusters components.
Additive group decomposability: if M groups are clustered in N supergroups, then a
12
segregation measure should be dividable into a sum of independent factors within —and
between—supergroups components.
Following this procedure, they concluded that the best index is the Theil index of information.
The Theil index can be interpreted as a measure of the average difference that exists between
different groups’ proportions, with in a geographical sub area, to the s ame groups’ proportions
within the city as a whole.
This ind ex value varies between 0 (when all the geographical sub areas have the same pop-
ulation composition that the city has) and 1 (when every geographical area is inhabited by one
single group).
The functional form of the Theil index is:
H =
1
E
M
X
m=1
π
m
J
X
j=1
t
j
T
r
jm
ln r
jm
(4)
where i and j index the geographical sub areas and m indexes the groups. t
j
is the number
of in dividuals in the geographical sub area j. T is the total number of individuals. π
m
is the
proportion of group m. E is the T heil index of entropy, where E =
P
M
m=1
π
m
ln
1
π
m
. r
jm
reflects the extent to which the group m is disproportionated against as represented within the
geographical sub area j.
3.2 Spatial Measures
3.2.1 The index of relative concentration
The in dex of relative concentration (RCO) measures th e percentage of space occupied by a
group in society compared to th e space occupied by other group in society . This index value
lies between -1 and 1. A level of 0 means that both groups are equally concentrated across the
urban space. If the index reaches a value of -1 implies that the group under study concentration
is exceeded by the other group concentration, meanwhile a score of 1 means the opposite.
The technical description of the in dex of relative concentr ation is as follow:
RCO =
P
n
i=1
x
i
a
i
X
P
n
i=1
y
i
a
i
Y
1
P
n
1
i=1
t
i
a
i
T
1
P
n
i=n
2
t
i
a
i
T
2
1
(5)
13
where the geographical sub areas are sorted by size, from smallest to biggest. a
i
is the land area
of the geographical sub unit i, and n
1
and n
2
corresponds to the rank of the area wher e the sum
of all t
i
from area 1 (smallest in size) up to area n
1
is equal to X, and to the rank of area where
the sum of all t
i
from area n (largest in size) down to area n
2
is equal to X, respectively. X is the
sum of all x
i
(the total minority population), x
i
is the minority population of the geographical
sub area i, and t
i
is the total population of area i. y
i
is the majority population of area i.
T
1
is the sum of all t
i
in area 1 up to area n
1
and T
2
is the sum of all t
i
in area n
2
up to
area n.
3.2.2 The index of absolute centralisation
The index of absolute centralisation (ACE) examines the group under distribution study around
the centre. The index values lies between -1 and 1. Positive values indicate a grou p under study
has a tendency to live close to the city centre, meanwhile negative values im ply the opposite. A
score of 0 means that the group under study has an uniform distribution across the urban area.
The functional form of the index of absolute centralisation is:
ACE =
n
X
i=1
X
i1
A
i
!
n
X
i=1
X
i
A
i1
!
(6)
where the n geographical sub areas are sorted according to their distance to the city centre,
from the closest to the furthest one. X
i
is the cumulative proportion in geographical su b area i
and A
i
is the cu mulative proportion of area of sub unit i.
3.2.3 The index of spatial proximity
The index of spatial proximity (SP ) is the the average of intra-group proximity for the group
under study and the rest of population, weighted by the proportions th at each group represents
of the total population. If the index of spatial proximity equals 1 then there is no differential
clustering between the group under study and the rest of the population. When this index is
greater than 1.0 then members of each group live nearer to one another than to members of the
other group, and if it is less than 1 th en the group under study and the rest of the population
live nearer to members of the other group than to members of their own group.
The functional form of the index is:
14
SP =
(XP
xx
+ Y P
y y
)
T P
tt
(7)
where P
xx
=
P
n
i=1
P
n
j=1
x
i
x
j
c
ij
X
2
, is the average distance between the members of group X.
P
y y
and P
tt
are th e distances between the members of Y and between the total population
respectively, and they can be calculated as P
xx
. Besides, c
ij
= e
d
ij
and d
ij
is the distance
between the individual i and the individual j.
3.2.4 The index of spatial dissimilarity
The index of spatial dissimilarity (D(s)), developed by Won g (1993), modifies the traditional
index of dissimilarity adding information about the relationship between the area and the perime-
ter of the geographical sub unit. Following this procedure it can be incorporated the fact that
the geographical sub unit shape affects the interaction prob ab ility of individuals belonging to
different geographical sub units. Its value lies between 0 and 1. The closer to 1 th e index value
the higher the RS.
The technical description of the in dex is the following:
D(s) = D
1
2
n
X
i=1
n
X
j=1
w
ij
|z
i
z
j
|
1
2
h
p
i
a
i
+
p
j
a
j
i
max
p
i
a
i
(8)
where D is the index of dissimilarity, w
ij
=
d
ij
P
n
i=1
d
ij
, z
i
is the group under study proportion
within the geographical sub unit i, d
ij
is the length of the common border of geographical s ub
units i an d j, p
i
is the perimeter of th e geographical sub unit i, a
i
is the unit area and max
p
a
is the maximum ratio among perimeter and area.
3.2.5 The I of Moran
The I of Moran (I), developed by Moran (1948), is a measure of spatial autocorrelation, a
concept similar to autocorrelation in time ser ies, but in this case the sp atial lags are the ones
that have information. As a matter of fact the I of Moran functional form corresponds to th e
correlation test Durbin-Watson weighted by the values in the contact matrix, which can be
either the distance among points or 0 and 1, depending on whether the points are contiguous
or not. The null hypothesis is that there is not sp atial autocorrelation. The index value lies
15
between -1 and 1. A value of -1 implies n egative autocorrelation. A value of 1 means positive
autocorrelation and a value of 0 implies a random spatial structure.
The functional form of the I of Moran is:
I =
N
S
0
P
n
i=1
P
m
j=1
c
ij
(x
i
µ)(x
j
µ )
P
n
i=1
(x
i
µ )
2
(9)
where µ is the average value of the variable x, c
ij
are the components of the contact matrix,
N is the number of geographical sub units, and S
0
is a normalisation factor equivalent to the
sum of th e elements of the contact matrix.
3.2.6 The Local Indicator of Spatial Association
The I of Moran is an index that summarises information for a complete urban area. Given the
need of identifying local concentrations of a variable under study, called hot spots in literature,
Anselin (1995) introduced the Local Indicator of Spatial Association (LISA), I
i
, which takes
different values f or each observation. Besides, it allows to visualise local instabilities, such as
deviations from the global structure of spatial association.
I
i
=
x
i
µ
P
n
i=1
(x
i
µ)
2
n
n
X
j=1
c
ij
(x
j
µ ) (10)
where µ is the average value of the variable x, and c
ij
are the components of the contact
matrix.
3.2.7 The spectral segregation index (SSI)
Due to Echenique and Fryer (2007) the spectral segregation index (SSI) measures the connect-
edness of in dividuals of the same group. The theoretical framework on which this index is based
is the social network theory. According to the SSI an individual will be more segregated if the
agents to whom he interacts with are s egregated also, so th e higher the segregation of the agents
he interacts with, th e higher the individual segregation. Hence, the index depends upon the
network of social interactions among individuals in a given grou p. Albeit this index can be
applied to a myriad of situations, for most of them are not necessarily related to the spatial
phenomena, it has been included as a spatial measure because in the case of RS, the interaction
among in dividuals can be modelled as the geographical distance between them. As it was pre-
viously mentioned, and as the same authors point out, this index has interesting characteristics.
16
First, it is invariant to arbitrary partitions of a city, second, it allows for the investigation of
how segregated the multiple minority groups are; and finally, it allows for the analysis of the full
distribution of segregation, allowing researches to go beyond aggregate statistics, which can be
misleading. To calculate the index can be a difficult task because it is highly data d emanding.
The procedure to obtain the SSI, which is a bit longer than those described above, is as
follows. First, let us consider a group of individuals V and a level of interaction, r
vv
0,
between two individu als, v and v
belonging to this group. If there is no interaction r
vv
= 0
otherwise r
vv
> 0. A matrix R is a matrix containing all this interaction information. Let us
now consider a sub group, or race, h. If all the information related to individuals that d o not
belong to h is dropped from R, the matrix B is obtained, which reflects the extent of interaction
between individuals belonging to a same group. Another important feature of this index is
that it can be disaggregated to the level of individuals. Therefore, there will be two kind of
segregation indices: an aggregated index, S
h
(B), and another one for each one of th e individual,
s
h
v
(B). Let us consider a group N
v
of all the individuals of group h connected to individual v,
and then let us consider the groups of all the individuals of group h connected to the members
of N
v
and so on. The resulting set of individuals, with direct or indirect interactions with v,
is called the connected component of B that v belongs to; denote this s et of individuals by
C
v
. The SSI of each connected component will be the largest eigenvalue of the corresponding
irreducible sub-matrix of B. The spectral segregation index, finally, is calculated by taking the
average S SI of each connected component weighted by the size of those connected components.
The individual SSI is obtained by using the eigenvector corresponding to the largest eigenvalue.
4 Causes of S R
Here, it is proposed to classify RS into two groups: endogenous RS and exogenous RS. The
former is a consequence of the interaction of individ uals preferences, restrictions and character-
istics, meanwhile the latter is the result of an external force, that it is not related to individuals
preferences, that sorts people across an urban area. The endogenous RS sources can be classified
into two different kinds: income and willingness-to-live-amongst-peers. Th e former is the most
common and easy to see RS. The latter is the force that drives RS based upon race, religion,
language, or nationality. If the willingness-to-live-amongst-peers is very strong it can be called
17
prejudice. The exogenous RS drivers have been classified into two kind s: as the outcome of a
policy and real estate markets dynamic. Albeit they are different, these f orces are correlated
and interact between one another, which has as a consequence a reinforcing process. Therefore,
dynamic aspects of RS, as migration, are crucial to understand this phenomenon. Besides,
these interactions make it difficult to isolate, empirically, the drivers behind RS, an issue that
is ver y sensitive to policy application. For instance, Bayer et al. (2004b) is the first attempt at
trying to examine the d egree of importance of households characteristics as RS drivers. They
conclude that depending on their r acial background the drivers of the RS that they must face
are different.
4.1 Endogenous RS
As it was mentioned above, endogenous RS arises du e to the interaction between the economic
agents’ preferences, budget restrictions an d characteristics, such as age or h ou sehold size. These
aspects also consider agents’ decisions for the supp ly of housing services. The forces driving this
kind of RS have been sorted into two groups: income and willingness-to-live-amongst-peers. A
description of these two kind of forces is now presented.
4.1.1 Income as a driver of RS
The “Bid-Rent” model provides a simple and clear explanation, from the theoretical point of
view, of the phenomenon of RS based upon income. The decision location across th e city will be
based on the idea that agents must commute from home to th eir work place which is located in
a central business district (CBD) where all economic activities are concentrated. Consequently,
the transport cost becomes an important element at the moment of taking a location decision.
In the canonical examp le, the households of h igher income will choose a location far away from
the CBD because they can pay the higher transport cost that this location decision implies,
meanwhile the household of lower income will choose a location closer to the CBD to avoid
high transport costs. This urb an structure depends on the assumption that land is a superior
go od. This model was developed by Wingo (1961), Alonso (1964), Mills (1967), Muth (1969)
and Evans (1973), and since its first appearance several extensions have been developed. Fujita
(1989); McCann (2001) and Zhang (2002) present detailed explanation of this mod el and its
extensions.
18
The bid, that is the land rent, is all the income left after other goods have been purchased
and the transport cost has been paid. Hence, there will be an inverse relationship between the
distance to the CBD and the land rent per unit of land, which is represented by the negative
sloped bid-rent curve as it can be appreciated in Figure 4. Under the assumption that the
higher th e income the higher the preference for land, the low income hous eholds will have a
steeper bid -rent curve th an the bid-rent curve of higher income households, which means that
low income households will offer a higher bid in areas located close to the CBD than the offer
that household of h igher income will do. If it is assumed that there exist only three kinds of
households with low, middle and high income, the city will present a s patial framework with
an area located close to th e C BD inhabited just by low income household, an area located in
middle of the city inhabited just by middle income households and an area located at the edge
of the city inhabited just by high income households.
Figure 4: Bid rent model
This urban structure can change if there are others elements apart from work, such as
entertainments activities, that generate trips to the CBD, or if the individuals’ preferences
change (Brueckner et al., 1999). For example, it could be possible to split up the high-income
group into two different groups: young high-income and old high-income. The first one could
have preference for accessibility meanwhile the latter could have preferen ce for land in order
19
to accommodate families with more member s. As a consequence, the young high-income group
will choose a location in the closest area to the CBD. This type of residential pattern broadly
represents the urban land allocation in cities with large international finan cial activities, such
as New York, Tokyo, L on don and Paris. T he urban land allocations will be fully reversed if the
income elasticity of d emand for accessibility is greater than the income of demand for space. If
that is the case then high-income earner s will live in the city centre, with middle-income earners
in the immediately adjacent areas, and low -in come earners will be located on the outskirt of
the city (McCann, 2001). However, despite the exact urb an structure, the underlying concept
is the same: if two households are competing for land, it will be ad judged to the household that
offers the highest bid, which generates segregated neighbourhoods according to the households
income.
An alternative approach to explain RS based upon income is the one given by Tiebout (1956)
and his voting-with-your-feet theory. In this model municipalities within an urban area or region
offer different public amenities at different tax rates. Individuals, according to their preferences
for public amenities, will choose a location such that, subject to their budget constrains, their
utility is maximised. This model is based on the following assumptions: consumers are fr ee to
choose where they live and that there are no tr an sport cost, there is complete information, there
are many municipalities to chose from, pu blic amenities do not spill over of benefits/costs from
one municipality to the next, an optimal city size exists, municipalities try to achieve optimal
size, municipalities are rational and try to keep the public bad consumers away. In the end,
affluent households will occupy the municipalities with better public amenities crowding out low
income households because they are able to pay a higher land rent as a way to guarantee the
access to these better public amenities. A good example of this kind of segregation is the one
that arises due to s chool selection by households. As they compete for living in the municipality
with the best school provision, the land price will get higher in those municipalities with better
schools and consequently the households with higher income will live closer to the those schools,
a process that sorts out households across the city according to their income. Benabou (1993)
develops a game theory model which exp lains h ow a process of these characteristics can generate
segregation when local schools are funded by local taxes.
20
4.1.2 The willingness-to-live-amongst-peers as a driver of RS
The bid-rent model has also been used to explain RS driven by willingness-to-live-amongst-
peers, through an extension of it called the border model. In the border models there exists
an area where one group of society looses utility if it lives close to it. For instance, in group 1
the population would loose utility if it lives close to a neighbourhood inhabited by people that
belong to a group 2, i.e. group 2 generates negative externalities on group 1. As a consequence,
the group 1 population would be willing to pay a h igher price in order to get away from this
border, which will change the bid-rent curve slope. The reason explaining the change of the
bid-rent curve slope is that the further the location from the border the higher the land rent will
be. After a certain point the effect of the border will be negligible and, therefore, the bid-rent
curve s lope will be negative again. If the negative effect of living close to the border is high
enough, it will be a derelict piece of land between the two groups, as can be appreciated in
Figure 5.
Figure 5: Border model
The Border models were developed by Bailey (1959) and Rose-Ackerman (1975), (1977),
whom ad op ted th e approach of Stull (1974), which was originally used to explain externalities
amongst producers and households. The Border models work under the assumption that there
is a urban pattern with full RS. This is considered to be as an important weakness of this
approach because RS must be derived endogenously from the model. Alternative approaches
to the classical border model, considering RS as an endogenous result of the model (but that
21
respond to the same logic of the bid-rent m odel), are the local externalities models and the
global externalities models.
Local externalities models were developed by Yinger (1976) and Schnare (1976). The reason
to call these models in this way is due to the fact that they consider that hous eholds are concerned
about the racial composition of their own neighbourhood. Albeit RS arises endogenously in this
model, it is also restrictive because they assume that households do not care about the race of
households that live just a bit furth er away from their neighbourhood’s border.
Global externalities models attributed to Yellin (1974), Papageorgiou (1978a), (1978b),
Kanemoto (1980) and Ando (1981), assume that households are concerned about the race of all
the city’s inhabitants. Specifically, the negative externalities that one group of people su ffer are
the weighted sum of all the other group population that live in the city. The weights considered
in these models comes from a decreasing fun ction of the distance that exists between both group
populations.
All the models mentioned above give an explanation of the process that generates RS when
there is a sector of the population that only wants to live amongst its peers — except the border
model which assumes exogenously the existence of RS —, and its consequences to the urban
structure. The people that belong to this group will suffer a negative externality if they must
live with people belonging to a different type of population, like, for ins tance, a different race.
Besides, all these models belong to bid-rent kind of models. In the first typ e, border model, RS
is exogenous, meanwhile in local and global externalities models it is en dogenous. Despite this
difference the main conclusion of all of them is the same: RS is Pareto-efficient.
As it was mentioned previously, the border model assumes exogenously the existence of RS,
and local and global externalities models consider only the interaction between the group but
not at an individuals’ level. Besides, all these models produce full RS un der any circumstances,
which is an un realistic result since it is empirically possible to obs er ve a certain degree of
interm ingle between groups.
An alternative approach is the one that offers Schelling (1971). Schelling’s model is an
important forerunner of social interaction literature, and agent-based simulation applied to
social sciences. In th is model individuals’ behaviour depends on local interaction with their
neighbours. In particular ind ividuals who have pr eferences about the kind of neighbours they
want to live with, and depending upon those preferen ces they choose a location across the city.
22
Placing pennies and nickels —as a way to represent two different groups living in the same
city—, on a chessboard, Schelling starts his analysis considering a full integrated city (Figure
6.a), then a random perturbation is introduced —two inhabitants of the city are interchanged,
or one inhabitant leaves the city —, as a consequence of this perturbation the individuals that
live in a n eighb ou rhood, or neighbourhoods, that have suffered it, will be in an uncomfortable
situation, and consequently, they will want to move to another neighbourhood, which starts
a process that ends up with high levels, or even full level of RS in the city (Figure 6.b).
This pr ocess depends on a rule th at is previously determined and that specifies individuals’
preferences. Schelling analyses the sys tem beh aviour under two kin d of rules. The firs t one
considers that individuals only want to live amongst peers, hence if th er e is only one different
individual in the neighbourhood, individuals belonging to the majority in this neighbourhood
will be hurt. Consequently, it does not seem to be surprising the fact that the city will end u p in
a high level of RS. However, what is indeed surprising is th at this result is the same even when
individuals have a small preference for living amongst peers. The main conclusion of this model
is, then, that RS is the unique stable equilibrium even when individuals have small preferences
for livin g amongst peers.
Figure 6: Schelling model
The lack of mathematical formalisation of this model is one of the reasons that explains why
it has not been applied in a more general way to the study of SR (Krugman, 1996; Young,
23
1998; Zhang, 2004). Despite the latter, this model has been fundamental for understanding
the social dynamic processes underlying SR. Social d y namics studies individuals’ interaction
at local levels and how these local interactions can p roduce macro social structures. In order
for these macro structures to arise, it is essential to observe the system’s dynamic evolution
because the macro behaviour is the consequence of dynamic and cumulative processes, which
are strongly determined by thresholds.
4.2 Exogenous RS
Within exogenous RS a taxonomy of two groups of drivers has been proposed: those related to
policies w hich either intentionally or unintentionally produce segregation, and real estate mar-
kets’ dynamics. The latter is understood as exogenous to the individuals — who are consu mers
of housing services—point of view.
4.2.1 Public policy as a driver of RS
Either intentionally or unintentionally p ublic policy can generate RS. The former kind of public
policy is known as de jure segregation, which occurs when the law explicitly requir es some kind
of residential exclusion. Examples of de jure RS are the form er European Jewish ghettos, the
Nazi Germany racial laws or the South African and former Rhodesia (now Zimbawe) apartheid.
Christopher (1990) investigates the imp act of apartheid on the levels of RS in South Africa, his
main conclusion is that RS in Sou th Africa r aised markedly during the 20th century reach ing
remarkably high levels as a result of the legislative programmes implemented in order to exclude
black people. Albeit most of these kinds of policies have been prohibited in western societies,
as it has been the case in th e United S tates since the mid 60s or the apartheid since th e early
90s, th eir consequences, as Saff (1995) points out, still have effect on the urban patterns. Falah
(1996) investigates the features of RS in Israeli mixed cities. His conclusions are that as an
outcome of state politics these cities have experienced a continuou s trend of high ind ices of
segregation and that the scope of of both social and economic interactions between the two
communities sharing the s ame urban space remains underdeveloped.
Public policies that unintentionally have as a result RS are those policies which aim is
not to produce any kind of exclusion or RS, but either throu gh their use or as a side effect
of their use, RS can arise. Weiher (1989) us ing examples taken from ju risprud en ce argues
24
that the federal court policy in the United States has reinforced devices which support inter-
jurisdictional RS. The idea behind this argument is that policy developments have shifted RS
from the neighbourhood to the jurisdictional level throu gh two ways: first, reinforcing and
encouraging the use of exclusionary powers on the part of predominantly white and well-off
municipalities, and second, changing the nature of the in formation available to people making
location decisions. The central hypothesis is that this change in segregation mechanisms should
generate a change in geographic patterns of RS. Using Census data fr om Los Angeles and the
Cook Counties, the conclusion is that this shift has taken place, and that is in these counties
that RS occurs by race, educational attainment and occupation and have come to organise the
areas by cities rather than n eighb ou rhoods over the period of 1960-1980.
Other examples of public policies that can generate RS are: zoning and public housing. As
Berry (2001) indicates zoning regulations most commonly used as exclusionary devices include
bans on multifamily housing and a variety of minimum building standards such as lot size and
width, b uilding size, density, etc. Albeit restrictions like these do not explicitly exclude specific
people or groups of people, they effectively establish minimum limits on the cost of housing,
which can generate RS. Besides, given the correlation amongst race and income, RS based on
income would generate racial segregation.
According to Sugrue (1962) the Federal government in the United State since the end of
the Second World War and until 1960 implemented two strategies to deal with the lack of
housing: to build housing for the working class and to finance mortgages through the Federal
Housing Administration. As Jackson (1985) points out, almost all these loans went to white
households in white neighbourhoods. The latter combined with white demand to exclude black
people, avoided the construction of public housing in white neighbourhoods. Thus, Jacobs (1962)
indicates that th e bleak architecture of public hou sing also isolates their resid ents and blocks
out social interactions.
The C hilean public hou sing policy is also an interesting case of how a public policy can
produ ce, as a side effect, RS. The reason is that Santiago, the capital of Chile, is one of the
most segregated cities in Latin America, despite the fact that Chile is the country with the
highest income per pers on of Latin Amer ica. The chapter 3 of the present dissertation develops
an empirical study of the RS drivers in Santiago. One of the main results is that the public
housing policy is the most important d river of segregation. The mechanism behind this fact
25
work s as follow: as a way to reduce the shortage of affordable housing, the Chilean government
bought cheap land in the outskirts of the cities to build the public housing projects. Households
must apply for a subsidy to buy these affordable dwellings. However, once the hou seholds have
won this subsidy they cann ot buy a house in any place, but they are forced to buy it in a
particular neighbourhood of these public housing projects. As a result the government, albeit
has been successful in reducing the lack of affordable housing, h as created ghettos of low income
households in the outskirts of the city.
Given the consequences of RS, governments must be very careful in order to design and to
implement policies that can be generate segregation, particularly when this segregation is based
on income which is one that has the worst effects on individuals’ well-being, as is going to be
discussed later on.
4.2.2 Real Estate Markets Dynamics as a driver of RS
According to Meen et al. (2005), one of the most important elements to understand the processes
behind RS is to look at the local Real Estate Markets Dynamics an d how they can change the
neighbourhoods’ structure. The underlying mechanism is the filtering process. Hoyt (1939) is the
first research that talks about this phenomenon. The idea behind this concept, as Hoyt points
out, is that the wealthier households w ill tend to move towards new real estate developments,
mainly in suburb of the cities, then, as an outcome, old neighbourhoods will be occupied by
progressively lower-income residents.
Yates and Wood (2005) indicate that there are three kinds of filtering processes that literature
has identified: by income, price and quality. The processes that are relevant to this section are
those related to price an d quality.
The filtering by pr ice arises when the dwellings’ physical characteristics remain the same but
either demand or su pply movements generate h igher or lower ground prices. As a consequen ce
of these movements either relatives or real prices would change, depending on whether these
variations are local or generalised. Bond and Coulson (1989), Brueckner (1977) and Little
(1976) pr ovide examples of how the filtering process can describe changes of neighbourhoods’
composition as a result of dwellings’ relative prices changes.
The filtering by quality has to do with the phenomenon in which the housing services provided
by on e p articular dwelling decrease du e to physical deterioration, or they increase because the
26
dwelling has experimented physical improvements.
These processes are influenced by the owners’ maintenance decisions, and these maintenance
decisions are, in turn, determined by the extent of the filtering by the price process (Yates and
Wood, 2005).
Through these two kinds of ltering processes is possible that some neighbourhoods tend
to polarise, changing from a mixed composition to one w ith inhabitants belonging just to one
socio-economic grou p, and therefore RS will arise (Galster, 2001; Grigsby et al., 1987; Vandell,
1995).
Consequently, if either the dwellings’ quality is im proved or the ground price increases, the
supply of low price housing services is going to be dropped from the market and they will be
replaced by higher price housing services. T his process is called gentrification, and the opposite,
i.e. when high price housing ser v ices are replaced by low price ones, is called deprivation, which
implies a deterioration of the neighbourhood.
An interesting feature of these two processes, gentrification and deprivation, is that they are
cumulative. For instance, once a gentrification process has started it will put pressure on the
price of housing services, which, in turn, will give incentive to improve the dwelling’s quality,
which will put pressure on the housing services price again and so on. Another important
element, related to the latter, is the existence of non-linearities and thresholds. Therefore, before
any of these two process start, gentrification or deprivation, they must reach a given threshold,
such as a certain price level, like it is depicted in figure 7. Hence, only when gentrification rate
passes this th reshold, the local area, or neighb ou rhood, will take off or it will go into decline.
This could generate situations such that dwellings’ prices in a given area can take off meanwhile
in a contiguous neighbourhood they present just little changes. This kin d of relationships have
been investigated by Galster (2002), Meen and Meen (2003) and Meen et al. (2005).
Yates and Wood (2005) test this behaviour for Sydney Housing Market. Their main conclu-
sion is that low rent housing is characterised by a growing polarisation, and that the cumulative
dynamics reinforce this polarisation. In this manner, a locality with low proportion of low rent
dwellings has a higher probability of having future reductions of this kind of hou ses. Meen et al.
(2005) perform a similar analysis f or England and their conclusions are not different from those
of Yates and Wood (2005).
Finally, it is important to say th at albeit deprivation and segregation seem to be a similar
27
Figure 7: Relationship between dwellings prices and gentrification
concept they are not. As Meen et al. (2005) indicate that in an extreme case all the geographical
units within a city can have a high level of deprivation, in such a case there will be no segregation
because RS has to do with the dispersion of deprivation across the city.
5 Consequences of RS
The discussion abou t RS consequences is still open. During years the literature has been fo-
cused upon negative consequences of RS on households’ well-being. However, most recently
two important results have been found. Firstly, it has been shown that RS can have, at least in
the short term, positive consequences. Secondly, and mainly after the Moving to Opportunity
experiment in the USA, a group of new investigations have indicated that RS has almost neg-
ligible effects upon households well-being. Thus, RS consequences literature has been classified
into three groups: positive, negative and no consequences.
5.1 Positive consequences of RS
RS has, in th e short run, positive effects mainly when is based upon nationality or language. For
example, if in a city there is a Chinese community, a new comer that speaks only Chinese will
have an easier chance of getting a job due to the existence of this community. A similar situa-
tion can arise with Hispanic communities, independ ently of the particular nationality of the new
comers. Namely, RS can have positive effects through social capital formation and networking.
Following the approach of individual-based models of social capital formation, —by Glaeser et al.
(2002), Alesina and LaFerrara (2000), Portes (1998) and Portes and Landolt (2000)—Molina et
28
al. (2002) identify three transmission mechanisms that link RS and individual-level of ou tcomes.
The firs t one is positive inter generational effects accruing from parental social capital in the
form of expanded social networks and access to an array of inter generational weak ties. Second,
income and labour effects accruing from individual membership in local groups, associations
and networks. Third, political effects through a more effective neighbourhood voice. Segregated
neighbourhoods can start collective action easier than nonsegregated neighbourhoods by mo-
bilising ethnic or cultural ties. A further discussion on the RS positive effects, particularly on
migrants, can be foun d in Bosswick et al. (2007).
Another potential source of welfare related to RS is the labour market matching. Bayer et al.
(2005) find evidence supporting the hypothesis that social interactions within neighbourhoods
amongst individuals of similar characteristics are a significant factor behind the labour market
behaviour and and they are used by people as a device to nd jobs. Hence, RS generate
specialized n eighb ou rhoods and such kind of neighb ou rhoods seem to be a fertile source of job
matching through th e use of n eighb ou rs, friends and acquaintances (Cheshire, 2007).
Cheshire (2007) indicates also that segregated neighbourhoods can provide consumption
benefits because households of similar incomes, tastes or age tend to consume similar goods and
services, and they require similar amenities.
Luttmer (2005) tests the hypothesis that individuals welfare depends not just upon their
own income, but also on their neighbours income, that is to say individuals care about their
relative in come. Using a sample of 10,000 individuals, he fi nds that loosing $2,000 of income
makes people feel as worse as their neighbour gaining $2,000. Furthermore, he does not find a
significant effect about the neighb ou rhood overall inequality, so what lower the income welfare
is havin g an income lower than the the neighbourhood average. Consequently, households can
derive more utility if they live amongst households of similar or even lower in come than theirs
own income.
5.2 Negative consequences of RS
Literature has identified that RS has effects on joblessness, academic performance, premature
parenthood, health, births out of wedlock, drug abuse, criminality and poverty (Dawkins et
al., 2005; Charles et al., 2004; Clapp an d Ross, 2004; LaVeist, 2003; Dosh, 2003; Burton, 2003;
Yinger, 2001; Massey, 2001; Madden, 2001; Wilson and Hammer, 2001; Logan and Messner,
29
1987; Burnell, 1988; King and Mieszkowski, 1973). Amongst this investigation the following
present some interesting results: Bayer et al. (2004a); Benabou (1996); Borjas (1995); Cutler
and Glaeser (1997) and Nechyba (1999). The latter presents a recapitulation of what social
science has done to s tudy the neighbourhoods and peer effects on individuals. According to this
work a wealth of evidence exists ind icating that RS perpetuates income inequality.
Cutler and Glaeser (1997) raises the q uestion whether racial RS would have positive effects
based on the idea that positive spillovers can exist as an outcome of the interaction between
low income and high income individuals that belong to the same race, and due to segregation,
share the same neighbourhood. After examining academic performance, joblessness and prema-
ture parenthood for the Afro-American population in the United States (cities with more than
100,000 inhabitants and more than 10,000 Afro-American inhabitants) the conclusion is that the
members of households with these characteristics living in h ighly segregated localities exhibit
worse ou tcomes than those that do not.
Borjas (1995) develops a theoretical model to enquire about the consequences of RS and
then he uses it to perform an empirical analysis of this phenomenon. The result of this empirical
analysis is that there is an ethnic spillover: ethnic groups with low income tend to live clustered
in low income neighbourhoods, and the neighbourhood’s effect influences negatively the inter-
generational mobility.
Bayer et al. (2004a) is the first attempt for testing the hypothesis that RS reduces the
minorities public goods’ consumption. Using a detailed data base from the S an Francisco Bay
area, they found enough evidence to support this hypothesis.
Benabou (1996) builds a theoretical general equ ilibrium model in order to analyse the RS
consequences on both efficiency and equity. According to this investigation, little differences
in education tech nologies, endowments, preferences, income or access to the capital market can
drive higher levels of RS, and RS, in turn, make education and income inequalities pervasive
between generations, albeit this is not necessarily true for the level of wealth, i.e. a population
can get r icher but th e income distribution remains the same.
1
1
This would be the case of Chile, a country that in last decade has become the richest country in Latin
America (14,000 USD per person PPP) but its income distribution has not changed (a Ginni index of 0,56) and
that exhibits also high levels of RS.
30
Anas (2002) develops a general equilibrium model in order to understand the RS effects on
individuals well-being and on labour, land and goods markets behaviour . The analysis considers
an urban space with a city centre and suburbs, and the economic activities can be performed
in both city ends. The results depend on the degree of prejudices that the white population
has against the Afr o American population. As white prejudice incr eases the percentage of city
centre residents who are b lack, the percentage of suburban resid ents who are white increases
and the price of land rent falls in the city centre. As the city land becomes cheaper relative
to suburban land, suburban labour becomes cheaper relative to city labour, and city product
becomes cheaper relative to subu rban product. These relative price changes cause labour supply
to the city centre to increase and the suburbs to decrease. City centre output incr eases while
suburban output decreases, but total output falls. An interesting finding of the Anas’ model
is that white p rejudice increases the utility level of blacks because city centre land rents fall
relative to city centre and suburban wages.
As it can be appreciated, there is not d issent about the characteristics of the negative conse-
quences of RS. However, some interesting questions have not been addressed yet. For instance,
an interesting issu e to research empirically is the extent that RS can affect the society as a
whole and not just h ow it can have effects on the segregated population.
5.3 No consequences
As Goering et al. (2003) point out, a major difficulty to research on RS consequences is th e fact
that researchers are restricted to cross-sectional, non-experimental data, which makes almost
impossible to separate the effect of personal factors affecting choice of neighbourhood from
impacts of neighbourhood. Hence, there exists a direction of causation problem that has not
been yet settled (Cheshire, 2007). The Moving to Opportunity experiment in USA, due to the
way it was designed, has been an unprecedented chance to deal with this problem. After more
than 10 years since the programme began, a significant amount of investigations that have been
done to analyse the MT O results have reached to the conclusion that segregation has almost no
consequences upon households well-being. A discussion about these findings is provided in this
section. However, in order to h ave a better picture, first, a description of the MTO programme
is presented.
31
5.3.1 The Moving to Opportunity Experiment
The Moving to Opportunity programme (MTO hereafter) aim has been twofold: to relieve the
problems that segregated households must deal with, and to provide scientific evidence about the
benefits that policies oriented to achieve mixed communities can generate. I n order to achieve
this aim, the p rogramme focuses on enablin g low-income households with children to move from
high-poverty inner city neighbourhoods to middle-class n eighb ou rhoods.
The programme was u ndertaken by the U.S. Department of Housing and Urban Development
(HUD hereafter), which implemented a controlled experimental design to try to overcome the
problem of separating the impact of per sonal factors affecting choice of neighbourhood from the
effects of neighbourhood and the direction of causation. Neighbourhoods were defined as census
tracts. To be eligible households must live in a public or assisted housing in a neighbourhood
with 40 percent or more of residents below the poverty line in 1989, to have at least one child
under 18, not to be behind in rental payments, all households members had to be named on
their current lease and no household member should have a criminal background.
Eligible participants were randomly assigned, as a way to ensure that will not be systematic
differences, to one of the following three groups:
The experimental group, which received vouchers usable only in tracts with less than 10
percent poverty, along with couns elling assistance in order to find a unit.
A comparison group, which received r egular vouchers with no special restrictions or coun-
selling.
An in-place control grou p, which would continue to receive p roject-based assistance.
The MTO programme was rst implemented in Baltimore, Boston, Chicago, Los An geles
and New York. The random assignment started up in late 1994 in Boston and concluded in late
1998 in Los Angeles.
5.3.2 Empirical findings on MTO programme and other studies upon neighbour-
hood effects
The firs t findin gs, summarised in Goering and Feins (2003), were promising: after two years,
indications of children behaviour, health and educational performance imp rovements, compared
32
to the control group, would be observed. These improvements were more marked in the boys
case. Nevertheless, incomes and other labour market indicators showed no a better outcome
relative to the other groups. Durlauf (2004), comparing 25 studies published between 1982
and 2003, concludes there is a significant neighbourhood effect, although he is aware about the
identification problems.
Longer term follow-up studies overtake that results. Kling and Liebman (2004), usin g data
for the five cities, examine indicators of educational performance, mental and physical health,
and behaviour . For none of th ese indicators they found any significant overall differences between
the treatment and comparison groups compared to the control group. K ling et al. (2005) separate
young males and females. They found that for both boys and girls during the first two years
after moving, p roperty arrest fell, but this reduction was not statistically significant. For boys
this figure changes and after the second year it rises significantly compared to the control group.
Overall, males in treatment and comparison grou p show worse results regarding behaviour and
porperty crime than those of the control group, but for both sexes combined there was no
significant reduction because the differences for boys and girls balanced out (Cheshire, 2007).
Long-term cohort studies offer an alternative approach to isolate the effect of neighbourhood
upon househ olds opportunities. Or eopoulos (2003) and Bolster et al. (2007) are, according
to Cheshire (2007), two of the most convincing of these cohort stud ies. Oreopoulos (2003),
using a Canadian s ample which tracts individ uals over 30 years, conclud es that neighbourhood
characteristics in w hich an individual was born has no statistically significant impact upon either
long-term labour market outcomes or prosperity. Bolster et al. (2007) using a panel data for
Britain follow individuals for ten years. They nd no evidence s upporting the hypothesis that
the original place of resid ence has effect upon labour market success.
5.3.3 Critiques to the MTO programme
The MTO programme has received also some critiques. For instance, Stal and Zuberi (2010) have
indicated that one of the main MTO programme prob lems is that it does not include community
involvement, besides it could be improved if it had consider ed programmes and policies to get a
better social, physical and economic integration of high poverty neighbourhoods into the city.
The most important critique to the MTO programme has been mad e by Clampet-Lundquist
and Massey (2008). These authors, based on their conceptual analysis and empirical investi-
33
gation, claim that the MTO p rogramme d esign and implementation suffer of several problems
that work against the detection of neighbou rhood effects. First, due to the fact that in America
non-poor black neighbourhoods are not equivalent to non-poor white neighbourhoods in terms
of resources, and because the most of MTO households participant move into a segregated neigh-
bourh ood instead of doing it into a integrated one, these households were exposed to a limited
range of resources and opportunities.
Second, because househ olds randomly allocated housing vouch er were not required to use
them, selectivity pollutes the study design: amongst those families assigned to be experimental
subjects, selection into the category of whom complied with the experimental treatment and
moved to a low -poverty neighbourhood was non-random. Furthermore, as African-Americans
are reluctant to enter white neighbourhoods for fear of ostracism and harassment, the decision
of choosing residen ce in an integrated versus a segregated non-poor neighbourhood was also
non-random.
Third, since to remain in the neighbourhood was not compulsory, there was an important
quantity of families that moved out of low-poverty neighbourhoods back to poor settings, there-
fore, experimental subjects accumulated little time living in low-poverty neighbou rhoods.
The main conclusion of Clampet-Lundquist and Massey (2008) is that the MTO programme
cannot refute the existence of neighbourhood effects, but the authors cannot nd evidence in
favour of them either. Besides, the auth ors point out that if the MTO programme data are used
to investigate upon n eighbourhood effects, researchers must be aware of if the voucher offer was
accepted and u sed, if households considered in the programme go to a segregated or integrated
neighbourhood and how long households remain living in a low-poverty neighbourhood.
6 Final remarks
Since the literature on RS is vast, the focus of the present essay is on those aspects that have
been considered either the most influential or those that have the potential to determine future
trends of RS research. The literature has been classified according to the following four subjects:
RS definition, measures, causes and consequences.
With regards to definition without a doubt Massey and Denton (1988) is the most complete
and widely accepted. Th is definition considers RS as a multidimensional phenomenon based on
34
the following dimensions: evenness, exposure, concentration, centralisation and clustering. This
multidimensional definition has been useful to determine the most suitable indices to measure
RS. Every dimension can be measured using different indices; however, according to Massey
and Denton (1988) the best dimensions for them are the following: dissimilarity index, exposure
index, index of relative concentration, index of absolute centralisation and index of spatial
proximity, respectively. Despite their utility, these ind ices suffer of two problems. First, they
wer e not designed to consider the case where more than two groups must be compared. Reardon
and Firebaugh (2002) deal with this problem and posit the Theil index as the best to measure
RS under these circumstances. Second, they are highly sensitive to the geographical scale used,
i.e. the level of RS will depend on the degree of geographical disaggregation. The latter makes
necessary to use spatial measures, multi-scale measures or measures based on social interactions
and networks.
The causes can be either endogenous or exogenous. Amongst the endogenous causes the
income, through the land and d welling prices, and the desire for living amongst peers have been
identified as the main drivers of RS. With regards to exogenous causes de jure RS, like the
former South African apartheid, and some public policies side effects, like the case of some public
housing policies, are the main drivers.
Regarding consequences, there is not such a thing as a consensus. Th e earlier investigations
have claimed that consequences can be either positive or negative. They are positive in the
short term when are, mainly, linked to the migrants’ formation of so cial capital and networking.
Amongst negative consequences the most relevant are the effects on joblessness, health, academic
performance, criminality, births ou t of wedlo ck, premature parenthood, perpetuation of poverty
and bad income distribution. However, new findings, mainly due to the Moving to Opportunity
programme data because it was carefully designed as an experiment, h ave shown that RS has al-
most negligible effects on households well-being. The intuition behind this argument relies upon
the fact that the negative consequences observed in segregated population are linked to those
factors that make households to choose a neighbourhood instead of any kin d of neighbourhood
effect. Still some critiques have been formulated to this app roach. The main ones say that the
programme has failed in assigning the treatment group in a random way, and that an important
amount of families returned to poor areas, which implies that they were exposed to a better
living conditions just for a short time. Consequently, MTO data cannot refute the existence of
35
neighbourhood effects. Hence, if RS h as any sort of effects upon households well-being is still
an open question and it is still a subject of debate.
The former discu ssion is the result, amongst other things, of the identification problems that
exist when one wants to measure the neighbourhood effect. The latter implies that the causation
between s egregation and income inequality has not been determined.
In general, the RS consequences have been studied with respect to their effects on the
segregated population. However, in the case that RS h as effectively impact on individuals, its
impacts could expand to the rest of the pop ulation. For example, the existence of low skilled
labour, as a consequence of the bad academic performance of the segregated population, would
affect negatively the economic growth rate. Besides, given these effects th at RS has on the
economy as a whole, conducting research on this issue would give a positive foundation to
control segregation instead of giving a normative one.
If this negative effect on economic performance is combined with the negative externalities
that one group of the population would generate on another one, or with the desire for living
amongst peers, it is possible to conclude that there is a trade-off and, consequently, th at there
must be an optimum level of segregation, different from 0 but also different from full segregation.
Characterising this optimal RS is something that has not be done yet, and it is a task with
important policy implications.
This is a discussion that is still open. As a matter of fact, there is plenty of research to be
done, especially due to the development of new econometric techniques that allow to deal with
the problems of specification and identification, like the omission of relevant variables, errors of
measure, selection bias and simultaneity, that arise when empirical research on this phenomenon
is performed .
It is also important to take into account the individuals’ interactions as key element in order
to un derstand aggregated population’s behaviour, as RS. There is evidence about the fact that
households’ characteristics, besides race and income, can generate interactions patterns that
could have as an outcome RS. Thus, to use m odels of social dynamics to fully und er stand the
forces behind RS becomes an important issu e. It is also important to consider models where the
characteristics of the neighbourhoods and the characteristics of the individuals living in these
neighbourhoods are endogenous, as a way to analyse the consequences of RS and to evaluate
public policies.
36
These theoretical concepts, related to social dynamics, can be also applied to the empirical
analysis of causes and consequences of RS, due to the development of categorical dependent
variable models that incorporate the individuals’ interaction as explanatory variables. Durlauf
and Young (2001) give a detailed descrip tion of these models, Blume and Durlauf (2001) explain
how to introduce individuals’ interactions into these discrete choice m odels. Meen and Meen
(2003) show how to apply these models to the study of housing markets and RS and provide
three reasons to base this procedure: fir st, because housing markets are particularly sens itive to
the presence of externalities; second, because housing markets are characterised by the existence
of non-linearities and multiple equilibria; and finally, because these models allow for the analysis
of policies oriented to affect individuals interactions instead of just private incentives.
An striking issue related to RS r esearch is a s ort of a divorce between the theoretical def-
initions and the empirical analysis. As a matter of fact, most of the empirical studies have
been done based on Duncan and Exposure indices. The latter h as been done without a strong
theoretical foundation. The most plausible explanation is the fact th at these indices are of easy
calculation and that there are several historical ser ies for d ifferent cities, which facilitate the
result comparison. Notw ith standing, this fact has methodological implications as well, because
the r esearch that has been conducted enquires only of two of the RS dimensions, namely even-
ness and exposure. Thus, to identify causes and consequences of every RS dimensions is an
outstanding task.
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