# Chapter 3. Income Segregation in Brazilian Cities: The role of vertical neighbourhoods

Ana I. Moreno-Monroy

This chapter investigates the role of vertical neighbourhoods in explaining income segregation at the bottom and top of the income distribution for 100 urban agglomerations in Brazil in 2000 and 2010. Income segregation is measured using rank-order income segregation measures for different neighbourhood definitions and income percentiles. An econometric model of income segregation is fitted for income segregation measures at the bottom and top of the income distribution against a new measure that aims to capture the isolation of apartment dwellers to other type of dwellers. The results show that this measure is significant in explaining the segregation of those at the top of the income distribution but not of those at the bottom.

## Introduction

Income segregation is the uneven distribution of households of different income levels within cities (Reardon and Bischoff, 2011). As such, segregation does not represent a problem to be solved, but rather a manifestation of urban configuration forces at work at each stage of development (Sabatini, 2006). The possible implications of the segregation of affluence (i.e. of those in the top of the income distribution) and poverty (i.e. those at the bottom) in terms of social welfare have been documented in the literature. If present, they operate through channels such as the provision of public goods and amenities (Ross and Yinger, 1999; Cutler and Glaeser, 1997), peer effects on human capital and labour market outcomes (Åslund et al., 2010) and inter-generational effects on social mobility (Chetty et al., 2014). The existing literature on what determines segregation of poverty and affluence is based on studies for a limited number of metropolitan areas, mostly in European or US cities (Musterd et al. 2015). However, existing comprehensive accounts of the segregation of affluence and poverty across the urban hierarchy of a country are so far limited to the case of the United States (Bischoff and Reardon, 2014; Watson, 2009; Coulton et al., 1996).

This chapter studies the residential segregation of household by income levels in Brazilian cities, building on previous work by García-López and Moreno-Monroy (2017). Brazil offers an important case for the study of income segregation, as it is a large, highly urbanised and highly unequal country with a great variety of cities. In 2010, 84% of its population lived in cities, while the ratio of the average income of the richest 10% to the poorest 10% was 40.6. The vertiginous process of urbanisation set off by industrialisation has led to cities where luxurious apartment towers are found side-by-side densely populated favelas. Deep socio-economic changes starting from the 1980s have created more complex urban configurations that go beyond the traditional core-periphery pattern (Sabatini, 2006; Villaça, 2011).

The chapter starts by quantifying the extent of income segregation across Brazilian urban agglomerations in 2000 and 2010. Segregation is measured using a rich database of over 120 000 small areas in 100 urban agglomerations that house over 60% of the urban population of Brazil. In order to compare segregation across cities and over time in a meaningful way, (spatial) rank-ordered measures of income segregation are calculated at the urban agglomeration level. These measures, besides satisfying all the relevant desirable criteria for measures of the kind, use all available information on income distribution, do not confound changes in income segregation with shifts in the income distribution, are not sensitive to a particular choice of income threshold, and can accommodate different neighbourhood definitions (Reardon and O’Sullivan, 2004; Reardon, 2011). They also allow constructing comparable measures of segregation at different points of the income distribution (Reardon and Bischoff, 2011; Chetty et al., 2014). Importantly, the methodological approach is comparable to that used by Bischoff and Reardon (2014) for 117 metropolitan areas in the United States, which allows drawing some relevant parallels between the two cases.

Next, the chapter estimates an econometric model of the determinants of income segregation, including city size, income inequality, demographic and other usual controls (Pendall and Carruthers, 2003; Watson, 2009; Reardon, 2011). Segregation at the top and bottom of the income distribution is then related to a new measure that aims to capture the isolation of apartment dwellers from other type of dwellers. Apartment buildings were seen as a symbol of status when they first appeared in Brazilian cities at the end of the 19th century, and have been since then adopted as a preferred type of housing for the middle and high-income classes (Ficher, 1994). As will be shown, there is a clear spatial correlation between “vertical neighbourhoods” and neighbourhoods where the rich - and not the poor - concentrate in cities of different sizes.

The econometric results show that the exposure of apartment dwellers to other types of dwellers, which clearly decreases as cities grow, has an independent effect on the segregation of affluence and no relationship with the segregation of poverty. This results are in line with the fact that in Brazil, low-rising informal and public housing is more common than cortiços (rooms rented for entire families) in high-rises and public housing in groups of tall isolated buildings (a.k.a. “projects”).

The chapter is structured as follows. After this introduction, the second section outlines the theoretical predictions on segregation. The third section details the data sources and definitions and explains the method for constructing the a-spatial rank-order segregation measures. The fourth section introduces the econometric approach for measuring the determinants of income segregation. Finally, the last section concludes.

## Theoretical predictions

The urban economics literature has offered some theoretical explanations for the intra-urban location of households of different levels of income. Earlier models formalise a recurrent pattern in US metropolitan areas, where the rich flee decaying down-towns (or Central Business Districts) in search for larger and cheaper housing in the less populated suburbs (Glaeser, 2008). The seminal monocentric Alonso-Mills-Muth land use model replicates this spatial pattern as long as the willingness to pay for housing more distant from the CBD decreases more slowly for the rich than for the poor. Ultimately, this means that the rich are more willing to sacrifice commuting time, as long as they can have more housing space. The distribution and type of dwellings in which the rich and the poor reside in the US is consistent with this theory. As the level of income increases, so does the preference for detached, single-family dwellings. The supply of new suburban single-unit dwellings for the rich follows its demand, while old multi-family dwellings located in central areas previously occupied by the rich are “filtered down” to those with lower capacity to pay (Brueckner and Rosenthal, 2009).

Furthermore, this standard urban economics model assumes that all intra-urban locations are homogeneous in terms of amenities, including the provision of public infrastructure. While some works for Europe have incorporated central-city amenities to explain the location of the rich near historical centres in European capitals (Brueckner, Thisse, and Zenou, 1999), the assumption of unequal distribution of public infrastructure within urban areas is not been contested since it is not much of an issue in advanced economies. Including a spatial restriction on the provision of public infrastructure to central areas in the standard model can lead to the prediction that the affluent locate in central areas, well-provided areas, whereas the poor locate in under-provided peripheral areas (Griffin and Ford, 1980). A centralised provision of public infrastructure, especially transport infrastructure, also has implications for the supply of housing, since it can lead to segmented housing markets, where formal developers build tall buildings near the CBD, and informal developers build low-rise buildings outside the CBD (Posada and Moreno-Monroy, 2017).

The assumption of constrained provision affects the assumption of job location. Although the monocentric model assumes a unique employment centre, the suburbanisation of the rich in the US context has been accompanied by job suburbanisation. However, under-provision in areas far away from the CBD also can also affect the location decisions of firms, since they also make use and depend on the provision of basic services and infrastructures. If the provision of public infrastructure and amenities is incremental from the historical CBD towards an expanded CBD, both rich households and firms de-concentrate in the proximities of the historical CBD as a result. Under this scenario, the rich would segregate in more dense, vertical neighbourhoods located near the CBD (as opposed to the rich living in single-family houses in the suburbs), while the poor would scatter in low-rise informal constructions around the periphery (Henderson, Regan, and Venables, 2016; Feler and Henderson, 2011). It is likely then that mobility for the rich is spatially constrained to within the expanded CBD area, which is the best served area in the city in terms of jobs, services and infrastructure.

In models that consider the durability of housing stock (Brueckner and Rosenthal, 2009), the prediction that the older hosing stock located near the CBD previously used by the rich filters down to the poor may have restricted validity for the bottom income groups who have tight residential mobility restrictions related to the difficulty of accessing credit for informal workers, the insecurity of tenure and poor definition of property rights that increase permanence in informal plots, on top of the general effect of stagnating real incomes, persistent inequality and stricter regulations to build (Cavalcanti and Da Mata, 2013). The sheer scale of redevelopment in CBDs in Latin American and Brazilian cities, as well as the amount of self-built, self-improved dwellings in areas around the CBD, are testimony of the constrained mobility of the rich within central areas, and the low residential mobility of those at the bottom of the income distribution (Griffin and Ford, 1980).

## Measurement

Segregation at different points of the income distribution is measured by means of the rank-order index of segregation. The sources and processing of the geo-statistical information are detailed in Annex 3.B. The rank-order information theory index captures the ratio of within-unit income rank variation to overall income rank variation (Reardon and Bischoff, 2011). Annex 3.B provides more technical details on the calculation of the indices. These measures use the full distribution of income and are independent of threshold choices (Reardon and Bischoff, 2011). Rank-order indices capture the extent of residential segregation by income levels, as opposed to capturing changes in income levels (resulting from changes in income inequality) even when no residential sorting takes place as a consequence in the change in income levels (Watson, 2009). Besides the a-spatial ( $HA$ ) index, the spatial versions ( $\stackrel{̃}{H}\right)$ of the index are calculated for 100 and 500 meter bandwidths (see Box 3.1 for details). Here results are shown for different points of the distribution: the 10 and 25 percentiles ( $HA\left(0.1\right)$, $HA\left(0.25\right)\right)$, representing the segregation of poverty, and the 75 and 90 percentiles ( , representing the segregation of affluence.

Table 3.1 shows the average value of $HA$, $HA\left(0.1\right)$, $HA\left(0.25\right)$, $HA\left(0.75\right)$ and $HA\left(0.9\right)$ across the 100 urban agglomerations for 2000 and 2010, as well as the values for cities in four urban population quantiles. Evidently, the level of income segregation increases with city size. The value of $HA=0.179$ for a 100 meter buffer for the urban agglomerations in the top size quantile (with populations ranging between 845 000 and 19.5 million) in Table 3.1 may be compared the value of 0.138 found by Monkkonen and Zhang (2014) for Hong Kong in 2001 using the same methodology and bandwidth. This evidence is consistent with the fact that although the inequality level in Hong Kong is high (the Gini index in 2001 was 0.49), it is much higher in large Brazilian metropolises (the Gini index was 0.59 in 2000 in the 10 largest cities).

Box 3.1. Spatial segregation measures

The spatial rank-order segregation indices $\stackrel{̃}{H}$ rely on surface-based smooth density approximations that allow adjusting for the spatial extend of local neighbourhoods, instead of relying on ad hoc boundaries (Reardon and O’Sullivan, 2004). The R package seg is used to calculate these indexes (Hong, O’Sullivan, and Sadahiro, 2014). A plausible population density surface is obtained using interpolation techniques. Basically, the package converts the discrete block-level data to a population density surface (implicitly assuming that the population of the census sector is uniformly distributed inside the sector), and approximates the true distribution with a Gaussian kernel density estimator. The value of the kernel bandwidth is varied between 100 to 500 meters. A simple inverse distance function is used to calculate the weight of each point.

It is important to notice, however, that spatial measures reflect the assumptions made on interpolation, which may not best reflect the actual connectivity between places. For instance, enumeration areas are often defined based on existing natural and man-made barriers, such as roads and rivers. For Brazilian cities, the average enumeration area falls within a radius of 100 to 500 meters, so in principle a-spatial measures and spatial measures at this spatial range should be more or less equivalent. The difference is that spatial measures in a way “blur” existing delimitations between areas that may correspond to actual barriers, and in this way are likely to under-estimate the actual level of separation between two places. On the other hand, it is possible that by taking into account that neighbourhoods extent beyond administrative boundaries, spatial measures correct for a possible upward bias in a-spatial measures of segregation. As the extent each of these cases applies is unknown, results using both types of measures are presented.

Table 3.1. Mean rank-order index by population quantile, 2000 and 2010

Index

All cities (N=100)

Q1

Q2

Q3

Q4

HA, 2000

0.144

0.115

0.127

0.142

0.191

HA, 2010

0.137

0.104

0.129

0.130

0.187

2000

HA (0.1)

0.080

0.070

0.075

0.078

0.097

HA (0.25)

0.087

0.071

0.075

0.088

0.112

HA (0.75)

0.201

0.161

0.176

0.195

0.272

HA (0.9)

0.249

0.201

0.220

0.242

0.332

2010

HA (0.1)

0.095

0.087

0.088

0.091

0.115

HA (0.25)

0.083

0.056

0.081

0.079

0.116

HA (0.75)

0.189

0.146

0.174

0.176

0.258

HA (0.9)

0.245

0.190

0.230

0.232

0.326

Source: Elaborations based IBGE (2017) Demographic Census Universe Data (Dados do Universo, Censo Demográfico), ftp://ftp.ibge.gov.br/Censos/ and IBGE (2017) Digital Network (Malhas Digitais, Setores Censitarios), https://mapas.ibge.gov.br/bases-e-referenciais/bases-cartograficas/malhas-digitais.html.

Somewhat surprisingly, the average value of $HA$ for 2010 is smaller than the value of 0.148 reported in Bischoff and Reardon (2014) for 117 metropolitan areas in the United States using the same methodology, even though the inequality level in Brazil is much higher: the average Gini in Brazil in 2000 was 0.57, compared to 0.4 in the United States. This may be due to the fact that the poorer experience higher levels of segregation in US metropolitan areas. Indeed, Bischoff and Reardon (2014) report average values of 0.146 and 0.163 for the segregation of poverty index for 2000 and 2010 respectively, while for Brazil the values are 0.08 and 0.096. In contrast, Bischoff and Reardon (2014) report values of 0.185 and 0.2 for the segregation of affluence in 2000 and 2010, while the mean values for Brazil are 0.249 and 0.245. Note that the much higher segregation of affluence is particularly salient in the largest cities.

Table 3.1 also shows that the value of the index is relatively stable across the size distribution, with the exception of the last quantile, where it shows a significant increase. Unlike the United States, where the average level of segregation increased by 9% between 2000 and 2009, the average level of income segregation in Brazilian cities decreased between 2000 and 2010 by 5%. This result is in line with a fall in the level of income inequality in Brazil between 2000 and 2010. This trend is also verified with respect to the segregation of affluence in all quantiles except the second. However, the segregation of poverty increased by 20%.

## The relationship between vertical neighbourhoods and income segregation

### A measure of exposure in vertical neighbourhoods

A question arising from the preliminary evidence is: what can explain the high levels of segregation of affluence? Because the rank-order information theory is an index that captures clustering in space, a high level of segregation means that the neighbourhoods where the affluent reside are the most coherent of all neighbourhoods in the city (Louf and Barthelemy, 2016). In other words, the affluent are not scattered across the city, but clustered in a small number of areas. As shown below, many of these areas can be characterised as “vertical neighbourhoods”, because they contain a relatively high share of apartment buildings, as opposed to other types of housing units. The hypothesis is that an over-representation of the affluent in these vertical neighbourhoods partly explains their high levels of spatial concentration, because relatively small areas contain a high count of “stacked” affluent residents.

Unfortunately, the available data does not contain information on the place of residency of heads of household by income categories, but it does contain information on the type of building residents live in. Figure 2.1 to Figure 2.3show the percentage of high-income heads of household (i.e. those earning more than 15 minimum wages a month), the percentage of low-income heads of household (i.e. those earning one minimum wage or less a month) and the percentage of residents living in apartments for a large city (Rio de Janeiro), a medium sized city (Fortaleza) and a small city (Vitoria da Conquista).

It is evident that many vertical neighbourhoods (i.e. those with a high share of residents living in apartments) coincide with neighbourhoods with a high percentage of affluent heads of household. Table 3.2 shows the 90th decile of the share of households residing in apartment buildings (i.e. the cut-off for defining a “vertical neighbourhood”), the share of high-income and the share of low heads of household residing in vertical neighbourhoods.

Table 3.2. Share of low income and high income heads of household residing in vertical neighbourhoods

Urban agglomeration

Vertical neighbourhood (%)

Percentage of high income

Percentage of low income

Rio de Janeiro

97.28

28.14

2.11

Fortaleza

53.02

45.82

2.37

Vitoria da Conquista

8.8

41.45

2.27

Note: Vertical neighbourhood (%) is the 90th percentile of the share of households in apartments.

Source: Elaborations based on IBGE Censo Demográfico 2000, “Dados do universo”, ftp://ftp.ibge.gov.br/Censos/Censo_Demografico_2000/.

Vertical neighbourhoods seem to become more coherent as cities grow in size: in some areas of Rio de Janeiro, residents are virtually surrounded by apartment buildings, as 97% of more of households live in apartments. Interestingly, these areas concentrate 28% of the high-income households in Rio de Janeiro (i.e. 135 399 households), and only 2% of the low-income households (i.e. 8 445 households), meaning that vertical neighbourhoods host 16 times more high-income than low-income heads of household. Vertical neighbourhoods in smaller cities like Fortaleza and Vitoria become less coherent (i.e. apartment buildings and other types of dwellings are more mixed), but still those with a relatively high proportion of apartment dwellers contain a larger percentage of higher income heads of household.

To capture concentration in vertical neighbourhoods more formally, the following measure of exposure of residents living in apartment buildings $b$ to residents living in other types of dwellings $a$ is proposed:

${M}^{ab}=\frac{1}{{N}_{a}}\sum ^{j}{t}_{aj}{r}_{bj}$

where ${r}_{bj}=\frac{{t}_{bj}/{t}_{j}}{{T}_{b}/T}$ is the representation of apartment dwellers in each local area $j$, equal to the share of apartment dwellers in the area over the share of apartment dwellers in the city, ${t}_{aj}$ is the proportion of residents in other type of dwellings in area $j$ and ${N}_{a}$ is the total number of residents in other types of dwellings in the city. If ${M}^{ab}=1$, the spatial co-location of building dwellers and other type of dwellers is random. If ${M}^{ab}>1$, building dwellers and other types of dwellers co-locate or “attract” each other, whereas ${M}^{ab}<1$ indicates the opposite, i.e., that apartment building dwellers “repel” other type of dwellers. The minimum value of the index is zero, which indicates that apartment dwellers and other types of dwellers are never present in the same area (Louf and Barthelemy 2016).

The average value of ${M}^{ab}$ across the 100 urban agglomerations is 0.61, indicating that apartment dwellers and other types of dwellers tend to repel each other. Figure 2.4 plots the ${M}^{ab}$ index for the 100 urban agglomerations against urban population levels in 2000. Given the preliminary evidence, the correlation between ${M}^{ab}$ and the segregation of affluence is expected to be negative, indicating that cities where apartment dwellers weakly co-locate with other types of dwellers are also cities where the affluent segregate more intensively. This correlation is not expected to be significant for the segregation of poverty.

Evidently, the repulsion of apartment dwellers increases as cities get larger. This suggest that larger cities have more coherent neighbourhoods by type of dwelling, in the sense of having more areas where apartment buildings are the dominant type of dwelling, and where consequently apartment dwellers do not co-locate with other types of dwellers.

### Econometric specification

An equation relating the level of income segregation to (lagged) levels of urban population, inequality levels and other determinants can be expressed as:

$Se{g}_{i,t}=\alpha +{\delta }_{1}UrbPo{p}_{i,t-1}+{\delta }_{2}Ine{q}_{i,t-1}+{\mathbf{x}}_{\mathbf{i},\mathbf{t}-1}^{\mathbf{\text{'}}}\mathbf{\beta }+{\eta }_{i}+{\epsilon }_{i,t}$

where $Se{g}_{i,t}$ is the $HA$ a-spatial or $\stackrel{̃}{H}$ spatial rank-order information theory index for different bandwidths in city $i$ in $t=2010$, $UrbPo{p}_{i,t-1}$ is the natural log of the urban population in 2000, $Ine{q}_{i,t-1}$ is an inequality index in 2000, $\mathbf{x}$ is a matrix of controls, ${\eta }_{i}$ is a city-specific time invariant effect and ${\epsilon }_{i,t}$ is an error term. ${M}_{i,t-1}^{ab}$, the index of concentration in vertical neighbourhoods in 2000 defined previously, is included in $\mathbf{x}$. Following previous studies (Pendall and Carruthers, 2003; Cutler and Glaeser, 1997; Reardon and Bischoff, 2011; Monkkonen, 2012), controls are included for city size (population in logs), share of population with a university degree, share of employment in tertiary industry, percentage of renters, percentage of residents living in areas classified as slums, and number of homicides per 100 000 inhabitants. The percentage of migrants living in the city for 1-5 years, the percentage of the population under 25 and the percentage of the population over 55 are also included as demographic controls.

The proposed regression is informative about the correlation between the exposure of apartment dwellers and the levels of segregation at different points of the income distribution, controlling for other relevant factors such as urban size and inequality. The aim of the regressions is to confirm whether the exposure of apartment dwellers has an independent relationship with segregation (of poverty or affluence), or if its effect dissipates once other controls are included.

Further interpretation of the estimated coefficients is limited because the regression suffers from possible omitted variable and reversed causality biases. The effect of the latter may be somewhat mitigated by the use of lagged controls, but given the high persistence of segregation, it is likely that this bias, if present, persists. In the case of omitted variables, note that the error term will pick up any time-variant and time-invariant omitted variables. A natural omitted variable candidate is the lag of the segregation index, which has been included in previous specifications as a regressor (Monkkonen, 2012). However, including this lag is problematic because given the strong persistence of segregation, as past values of segregation are likely to be correlated with η and other unobserved covariates, affecting the consistence of the estimated parameters.

### Results

Table 3.3 shows the results for the cross-section estimation for average income segregation, the segregation of poverty and the segregation of affluence. Annex Table 3.C.1 and Annex Table 3.C.2 in Annex 2.C show the results for the same specification using the spatial index for other neighbourhood definitions

The negative relationship between the measure of isolation of apartment dwellers and income segregation is significant for the segregation of affluence, and not for the segregation of poverty. Interestingly, this relationship holds once controls for city size and the homicide rates are introduced, suggesting that vertical neighbourhoods may have an independent effect on segregation.

As expected, the relationship between urban size and income segregation is in principle confirmed for all types of segregation: larger urban sizes are associated with higher levels of income segregation, and higher levels of segregation of poverty and segregation of affluence (Cutler and Glaeser, 1997; Reardon and Bischoff, 2011; Telles, 1995). The point estimate of urban size is higher for the segregation of affluence, a result that holds regardless of the neighbourhood definition (see Annex Table 3.C.1 and Annex Table 3.C.2 in Annex 2.C).

Regarding the relationship between income inequality and income segregation, in line with previous studies (Reardon and Bischoff, 2011; Telles, 1995), there seems to be a positive and significant relationship between inequality levels and average income segregation levels, and the segregation of affluence. However, this result is not confirmed for the segregation of poverty as measured by the HA index for the 10 percentile, regardless of the neighbourhood definition used. These results hold when an alternative measure of inequality (the Gini coefficient) is used.

Table 3.3. OLS regression results for equation in levels

(1)

(2)

(3)

(4)

(5)

HA 2010

HA (0.1)

HA (0.25)

HA (0.75)

HA (0.9)

Urban population (ln)

0.0147***

0.00993***

0.00982***

0.0217***

0.0295***

(0.00248)

(0.00288)

(0.00340)

(0.00351)

(0.00456)

Theil inequality index

0.123***

-0.0175

0.154***

0.152**

0.216***

(0.0379)

(0.0731)

(0.0514)

(0.0636)

(0.0774)

Mab

-0.0385*

-0.0208

-0.0218

-0.0592*

-0.0886**

(0.0227)

(0.0166)

(0.0180)

(0.0339)

(0.0380)

Percentage in slums

0.142***

-0.0277

0.143*

0.170**

0.219**

(0.0468)

(0.0519)

(0.0799)

(0.0665)

(0.0884)

Percentage of renters

0.111*

0.0838

0.0624

0.222**

0.301***

(0.0627)

(0.104)

(0.0865)

(0.0931)

(0.0906)

Percentage in tertiary employment

0.121***

0.156***

0.0375

0.190***

0.0856

(0.0321)

(0.0530)

(0.0563)

(0.0573)

(0.0666)

Percentage with a university degree

0.00177

-0.00526**

0.000761

0.00131

-0.00276

(0.00208)

(0.00240)

(0.00279)

(0.00339)

(0.00399)

Percentage of population under 25

-0.0123

0.532*

-0.170

0.0200

-0.297

(0.122)

(0.277)

(0.181)

(0.216)

(0.248)

Percentage of population over 55

-0.387

0.514

-0.441

-0.504

-1.083***

(0.237)

(0.416)

(0.288)

(0.381)

(0.406)

Percentage of homicides

8.51e-05**

1.64e-05

5.39e-05

0.000127**

0.000189***

(4.24e-05)

(4.61e-05)

(6.42e-05)

(5.76e-05)

(6.33e-05)

Observations

100

100

100

100

100

R-squared

0.790

0.487

0.592

0.761

0.774

Note: Robust standard errors in parentheses. Constant term included but not reported.

*** p<0.01, ** p<0.05, * p<0.1.

Source: Elaborations based IBGE (2017) Demographic Census Universe Data (Dados do Universo, Censo Demográfico), ftp://ftp.ibge.gov.br/Censos/ and IBGE (2017) Digital Network (Malhas Digitais, Setores Censitarios), https://mapas.ibge.gov.br/bases-e-referenciais/bases-cartograficas/malhas-digitais.html.

The results in Table 2.3 indicate a positive and significant relationship between the percentage of residents in slum areas and homicide rates and the segregation of affluence. Interestingly, these partial correlations are not significant for the segregation of poverty. However, unlike the results discussed previously, this result is sensitive to the definition of neighbourhood: the point estimate becomes statistically not significant when using the spatial indices (see Annex Table 3.C.1 and Annex Table 3.C.2 in Annex 3.C). A similar result is obtained for the share of tertiary employment, which turns statistically insignificant once the definition of neighbourhood is changed. In any case, as evidenced by the R-square coefficients, the specified model is rather powerful in explaining average segregation levels and the segregation of affluence, but fails to capture more than half of the variation in the segregation of poverty across cities (and actually less when using spatial indices).

## Discussion and Conclusions

The study of income segregation for 100 urban agglomerations in Brazil in 2000 and 2010 using the rank-order (spatial) information theory index has revealed interesting patterns. Income segregation increases with city size, especially after a certain size threshold. The econometric analysis shows that a measure of the co-location of apartment dwellers to other types of dwellers is indeed negatively correlated with the segregation of affluence. Neighbourhoods that go through a process of “verticalisation” disproportionally attract the rich, and not the poor. The causes or behavioural consequences of the concentration of groups of households of similar high levels of income in vertical dwellings are relevant topics for further research. A clear result emerging from the analysis is the positive relationship between segregation and income levels. The affluent experience the highest levels of segregation, regardless of the size of the urban area.

The results of this chapter make sense in the context of the measurement of the measure of segregation chosen, and the observed distribution of those at the bottom part of the income distribution. The rank-order information theory index is a measure of spatial clustering by income category, and as such, captures the observed spatial concentration of the rich in a handful of neighbourhoods, as well as the fact that the poorest are scattered in many different areas across the city. Thus, average levels of income segregation are not necessarily informative about the degree of residential segregation experienced by those at the bottom part of the income distribution.

The dispersed distribution of the poorest in cities of different sizes is consistent with the process of informal land occupation through scattered settlements, as well as with the low percentage of households in the bottom part of the income distribution that benefit from social housing, and the existence of height limitations in social housing in Brazil. These differences may be behind the puzzling lower levels of segregation of poverty in Brazil vis-à-vis the levels reported for metropolitan areas in the United States.

The results in this chapter highlight the fact that specific policy interventions against the segregation of the poor, such as punctual slum upgrading programmes, may have little impact on city-wide levels of income segregation. In this sense, income segregation levels as such should not be seen as a policy objective on its own right, but as an indicator of deeper spatial processes at work. The results also call for a conscientious analysis of policy interventions aiming at concentrating those at the bottom part of the income distribution in large vertical neighbourhoods, as they can become a source of increasing segregation of poverty.

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Annex 3.A. Data and geoprocessing

The urban agglomeration-level measures of segregation use information on the income distribution information at the census sector (setor censitario) level from the 2000 and 2010 Population Census micro-data, freely distributed by the Brazilian Institute of Geography and Statistics (IBGE). The census sector unit is equivalent to enumeration areas defined for surveying purposes. Each unit contains on average 400 households. The individual unit of analysis is the head of household (i.e. a person responsible for the household who is older than 10 years old) categorised as belonging to one of nine ordered income categories. Income is defined as the level of nominal monthly income from work or other sources measured in minimum wages (m.w.).

Most urban agglomerations extent beyond the boundaries of a single municipality, and may include peri-urban areas and small towns that fall under the influence of a nearby urban centre. Besides the definition of 68 metropolitan regions, there is no official consistent definition of city boundaries from the Census. The grouping of municipalities by Da Mata et al. (2007) is used to define 123 urban agglomerations in 2000 and 2010. Urban agglomerations include metropolitan regions, non-metropolitan urban agglomerations (resulting from conurbation), and sub-regional urban centres. IBGE freely distributes the digital networks containing the boundaries of the enumeration areas for 2000 and 2010. The geoprocessing was done in the R statistical environment using the maptools, sp, rgdal, rgeos and cleangeo packages. After excluding census sectors classified as rural, there are 104 885 urban census sectors in 2000 hosting 88 302 526 inhabitants and 158 897 urban census sectors hosting 105 188 834 inhabitants in 2010. Restricting the urban population to 90 000 inhabitants in 2000 leads to a final sample of 100 urban agglomerations.

Annex 3.B. Formal definition of the rank-order information theory index of segregation

Let $p$ denote percentile ranks in a given income distribution. The pair-wise information theory index $H$ is defined as:

$H\left(p\right)=1-\sum ^{j}\frac{{t}_{j}{E}_{j}\left(p\right)}{TE\left(p\right)}$

where ${t}_{j}$ is the population in the local environment $j$, $T$ is the total population in the urban area, and $E$ is the entropy of the total population given by $E\left(p\right)=plo{g}_{2}\frac{1}{p}+\left(1-p\right)lo{g}_{2}\frac{1}{\left(1-p\right)}$. The rank-order information theory index is defined as:

$H=2\mathrm{l}\mathrm{n}2{\int }_{0}^{1}E\left(p\right)H\left(p\right)dp$

Following Reardon (2011) and Reardon and Bischoff (2011), the function $\stackrel{̃}{H}\left(p\right)$ is estimated in the following way. First, the pair-wise spatial index $\stackrel{̃}{{H}_{k}}$ is calculated for those above and below each $k-1$ income threshold for each census sector. Then WLS regression of the $k-1$ values of the segregation measures against the cumulative proportions of the population with incomes equal to or below $k$, ${p}_{k}$, and the necessary terms to find the best fitting polynomial is fitted. Finally, the vector of estimated coefficients is multiplied by a vector of scalars for the second-degree polynomial case, as detailed in Reardon (2011). Once the income profile for each urban agglomeration has been obtained - that is, the curve describing the relationship between $H$ and the percentage of individuals in each income category- it is possible to define a measure of segregation as experienced by a given income percentile (Reardon and Bischoff, 2011).

Annex Table 3.C.1. : OLS regression results for 100 meter bandwidth spatial rank-order index

(1)

(2)

(3)

(4)

(5)

Urban population (ln)

0.0149***

0.00717*

0.0114*

0.0204***

0.0262***

(0.00347)

(0.00367)

(0.00582)

(0.00473)

(0.00732)

Theil inequality index

0.126*

0.0477

0.121

0.188**

0.293**

(0.0663)

(0.0959)

(0.0957)

(0.0916)

(0.133)

Mab

-0.0520

-0.0525**

-0.0280

-0.0823*

-0.134**

(0.0338)

(0.0230)

(0.0410)

(0.0429)

(0.0578)

Percentage in slums

0.216**

-0.0366

0.317

0.247**

0.298*

(0.0846)

(0.0704)

(0.232)

(0.102)

(0.175)

Percentage of renters

0.273**

0.102

0.385

0.272**

0.415***

(0.121)

(0.133)

(0.320)

(0.117)

(0.156)

Percentage in tertiary employment

0.0996

0.112

-0.121

0.224***

0.115

(0.0778)

(0.0741)

(0.210)

(0.0810)

(0.114)

Percentage with a university degree

0.000357

-0.00444

0.00301

-0.00173

-0.0102*

(0.00349)

(0.00298)

(0.00715)

(0.00442)

(0.00578)

Percentage of population under 25

-0.114

0.141

0.323

-0.457

-0.942**

(0.261)

(0.350)

(0.573)

(0.298)

(0.423)

Percentage of population over 55

-0.704*

0.0490

-0.440

-1.067**

-2.266***

(0.416)

(0.455)

(0.749)

(0.482)

(0.664)

Percentage of homicides

0.000230**

2.88e-05

0.000343

0.000197**

0.000371***

(9.15e-05)

(7.26e-05)

(0.000258)

(9.14e-05)

(0.000107)

Observations

100

100

100

100

100

R-squared

0.589

0.263

0.288

0.660

0.573

Note: Robust standard errors in parentheses. Constant term included but not reported.

*** p<0.01, * p<0.05, * p<0.1.

Source: Elaborations based IBGE (2017) Demographic Census Universe Data (Dados do Universo, Censo Demográfico), ftp://ftp.ibge.gov.br/Censos/ and IBGE (2017) Digital Network (Malhas Digitais, Setores Censitarios), https://mapas.ibge.gov.br/bases-e-referenciais/bases-cartograficas/malhas-digitais.html.

Annex Table 3.C.2. OLS regression results for 500 meter bandwidth spatial rank-order index

(1)

(2)

(3)

(4)

(5)

Urban population (ln)

0.0100***

0.00492*

0.00634**

0.0162***

0.0244***

(0.00236)

(0.00274)

(0.00298)

(0.00317)

(0.00460)

Theil inequality index

0.0637

0.0592

0.0668

0.0932

0.166**

(0.0399)

u(0.0400)

(0.0513)

(0.0569)

(0.0718)

Mab

-0.0430*

-0.0175

-0.0325*

-0.0585*

-0.0889**

(0.0218)

(0.0163)

(0.0168)

(0.0320)

(0.0397)

Percentage in slums

0.0551

-0.0258

0.0451

0.0776

0.118

(0.0449)

(0.0441)

(0.0462)

(0.0674)

(0.0996)

Percentage of renters

0.0752

-0.0659

0.0480

0.137

0.195**

(0.0613)

(0.0558)

(0.0636)

(0.0864)

(0.0943)

Percentage in tertiary employment

0.106***

0.0518

0.0689*

0.151***

0.0844

(0.0344)

(0.0400)

(0.0406)

(0.0522)

(0.0650)

Percentage with a university degree

0.00259

-0.00249

-0.00110

0.00409

0.000107

(0.00215)

(0.00232)

(0.00276)

(0.00333)

(0.00409)

Percentage of population under 25

0.0158

0.222

0.00656

-0.0442

-0.333

(0.130)

(0.134)

(0.162)

(0.196)

(0.226)

Percentage of population over 55

-0.201

0.229

0.0281

-0.469

-1.031***

(0.244)

(0.250)

(0.283)

(0.347)

(0.383)

Percentage of homicides

1.75e-05

-6.09e-08

-4.03e-05

7.21e-05

0.000124**

(4.12e-05)

(3.70e-05)

(4.23e-05)

(5.53e-05)

(6.20e-05)

Observations

100

100

100

100

100

R-squared

0.694

0.384

0.421

0.702

0.707

Note: Robust standard errors in parentheses. Constant term included but not reported.

*** p<0.01, ** p<0.05, * p<0.1.

Source: Elaborations based IBGE (2017) Demographic Census Universe Data (Dados do Universo, Censo Demográfico), ftp://ftp.ibge.gov.br/Censos/ and IBGE (2017) Digital Network (Malhas Digitais, Setores Censitarios), https://mapas.ibge.gov.br/bases-e-referenciais/bases-cartograficas/malhas-digitais.html.