# Chapter 2. Divided Cities: Understanding Income Segregation in OECD Metropolitan Areas

Andre Comandon
Michiel Daams
Miquel-Àngel Garcia-López
Paolo Veneri

This chapter provides an assessment of income segregation levels within cities in 12 countries. It also provides an analysis of the characteristics of cities associated with income segregation. Within-city variation in income segregation is measured using a fine-grained method for obtaining spatial entropy indexes based on gridded income data. This measurement approach, applied to the EC-OECD functional urban areas, minimises the biases due to different administrative boundaries and allows robust international comparability. The results may inform public policy in domains connected to urban development, including housing and transport.

## Introduction

The geographical concentration of households with a similar income level, known as spatial income segregation, increasingly shapes how people live their lives within cities. Recent research covering both Europe and the United States shows that the extent to which people live separated according to their level of income has increased during the last few decades (Marcińczak et al., 2016; Massey et al., 2009; Pendall and Hedman, 2015).

Income segregation is a phenomenon that is linked to urban development. As people choose a place to live, subject to their resources constraints, they often tend towards locations where people who are similar to them in terms of culture and socio-economic background live. Recent literature, mostly on US cities, shows that income is one of the dimensions that most explains the clustering of people in separated neighbourhoods (Glaeser and Vigdor, 2012; Logan and Stults, 2011), although there are some recent studies suggesting that race is still important (Sander and Kucheva, 2016). Income segregation can also be a result of free choice. In this case, a certain degree of spatial concentration of people with similar characteristics can be an efficient setting for enhancing social networks. It can also foster positive externalities, especially for those living in the most affluent and highest quality neighbourhoods (Morrison, 2015). Such neighbourhoods will likely have good schools and good teachers, as well as students that share similar values. This mechanism might explain the evidence for the United Kingdom suggesting higher levels of segregation to be associated with higher levels of inequality of individuals, which in turn is driven by higher performance at the top end of the social ladder (Gordon and Monastiriotis, 2006).

While income segregation is neutral in essence, it can, however, become problematic if it affects those that are less advantaged. This can be the case when disadvantages concentrate in space, which can typically be the case for neighbourhoods with low accessibility to jobs and quality services and amenities that also have a poor social environment. Such spatial concentration of disadvantages can be a life-long obstacle to opportunities available for those who live or grew up in such disadvantaged areas (Chetty and Hendren, 2015). Moreover, recent work showed that high spatial segregation might lower the cohesion of a city and as such lower the general well-being there (Novara et al., 2017). This is of increasing policy relevance as during the last couple of decades the processes that give rise to spatial segregation have been spurred by economic globalisation, immigration, and a widening gap between low-skilled and high-skilled jobs (OECD, 2016). If cities are to perform their role as locations for socioeconomic mobility, the local socioeconomic divisions that shape how benefits of life and work in cities are distributed over inhabitants should be better understood.

In response to this, the current paper introduces city-level measures of income segregation that are internationally comparable. The resulting international indicators allow a broadening of the debate on how income segregation and public policies relate. This is important and challenging at the same time because the character of both income segregation and related public policies may vary substantially across countries – and across their cities. What does it mean when segregation is higher in one city than in another? How may this be related to public policy? This paper brings systematic data to further advance on this debate. It contributes to understanding whether lower segregation in cities yields better aggregate outcomes for those living there, whether policy can promote a more inclusive and less segregated urban environment, and at what cost.

Income segregation in cities is investigated by looking at the distributions of income across income-classes and local areas, in a granular way. This granularity is important because spatial scale is crucial in the analysis of segregation. A city with low overall inequality may face deeper within-city divisions than a city with high overall inequality. This can be understood from the character of segregation in two main ways. First, segregation levels may vary with income level. This is addressed in the analysis by measuring segregation levels by income group. This then makes it possible to evaluate whether the average level of segregation in a city is driven by segregation of poorer households or segregation of wealthier households. Second, the geographical scale of segregation is considered by fitting geo-data on income to a fine grid pattern and then aggregating it to same-sized “neighbourhood” areas. Neighbourhood areas of different sizes are analysed to evaluate the appropriate geographical scale to capture income segregation within cities. Since cities come in various shapes and sizes, and so do the income data, the measurement approach is aimed to maximise the international comparability of its outcomes.

The analysis shows that segregation can vary substantially across cities in the same country and that it tends to be higher in cities with average higher household income. For example, some of the most affluent cities in the analysis also have amongst the highest levels of income segregation. While this might be interpreted as income segregation of people within cities being a natural consequence of economic growth and increased prosperity, previous studies suggest that this relationship varies. Cities with similar wealth levels can show levels of segregation that are very different, suggesting that other factors than wealth alone affect the way people cluster in space and the consequent neighbourhood divide. While understanding such divides would require contextual analysis of cities, a sound starting point for understanding segregation is systematic insight into how strongly income segregation varies across cities in different countries. For this reason, this paper assesses income segregation in metropolitan cities in 12 countries. While this analysis is mostly cross-sectional, trends in segregation over time are observed for a subset of countries for which the necessary data are available.

The last part of the chapter studies the determinants of income segregation. An econometric model where the main dependent variable is a measure of income segregation is regressed against measures of city size, different types of urban forms, types of city government and the economy of the city. The results confirm that not only city size but also urban form matter for explaining segregation levels. The main results vary by levels of income. While the level of segregation of the poor seems to be only related to the labour productivity of the city and to the degree of spatial centralisation, the segregation of the rich are related to the city size, the degree of spatial centralisation of the city, the labour productivity and the youth dependency ratio.

The remainder of the paper is organised as follows. The next section introduces the methods used to analyse income segregation, followed by an overview of the underlying data in section three. The fourth section presents the results. The fifth section presents some empirical evidence on the determinants of income segregation. The sixth section offers orientations for policy analysis, and the seventh section concludes.

## Measuring income segregation

Income segregation in cities was assessed through the use of entropy indexes, consistently with the most adopted practices in the literature for the measurement of income segregation (Reardon et al., 2006). The entropy-based measurement approach requires working with fine-scale geographical data. This section provides the details on how income segregation is measured, by highlighting the issues of scale and international comparability.

The entropy measures capture how households at different income levels are spatially distributed within cities. In so doing, this study departs from conventional measures of segregation at the scale of fixed spatial units, such as census tracts or other predefined neighbourhood areas. This study establishes income-data at a 100 m x 100 m grid level (the underlying data and techniques are detailed in Box 2.2 in the next section), and uses these data to measure segregation within spatial units that are (in contrast to administratively defined neighbourhoods) consistent across countries. The consistent units are based on radii of varying length: 0.5 km, 1 km, 2 km, and 4 km. For each radii length, the segregation indexes capture how different from the city’s distribution of income that unit is. The smaller units (0.5 km and 1 km) capture local variations more precisely. It indicates the degree to which people live surrounded by people of similar income levels within their immediate surroundings. The larger radii (2 km and 4 km) effectively smooth the measurement of segregation across larger spaces. That is, the level of segregation within a 4 km radius may be close to a city’s average segregation level. However, there is no theoretical guidance on the optimal radius to measure segregation within a city. Therefore, the radius that best captures segregation in the observed data is established empirically (see Annex 2.A).

The entropy measures also capture how, at the city-level, the degree of segregation may vary for households with different levels of income. Doing so follows earlier work by Monkkonen and Zhang (2014) who compare segregation levels in San Francisco and Hong Kong. Because income data is ordinal, variation is measured as the spread of the distribution over income bins. An adaptation of the method developed by Monkkonen and Zhang (2014) is used to build a data base on entropy-based segregation within each of the observed metropolitan areas. The script was written in Python to integrate with ArcGIS and was modified to both increase its efficiency and be better adapted to comparative work (i.e. dealing with a large sample of cities). The first modification is that it offers the option of dasymetric mapping (See Box 2.2). This insures that only the parts of large sparsely populated areas with residents enter the entropy calculations. The other modification enables us to iterate over all metropolitan areas in a country, allowing the script to run automatically.

The analysis also uniquely considers segregation at the income-extremes. Patterns of income segregation often show that the highest levels are among the poorest and wealthiest residents (Reardon et al., 2006). Therefore, it could be so that overall segregation is much lower in one country compared to another, but that the poorest and wealthiest households in the two countries are similarly segregated.1

## Data

Entropy indexes are obtained using data for cities across 12 countries; Australia, Brazil, Canada, Denmark, France, United Kingdom, Ireland, Mexico, the Netherlands, New Zealand, South Africa and the United States. Cities are defined based on the Functional Urban Areas (FUA) defined by the OECD in collaboration with the European Commission (OECD, 2012). The adopted method ensures the maximum comparability in terms of the spatial units of analysis as the same method was followed in all countries. Relying on a consistent definition of cities helps capture the outcomes of the mechanism that drives segregation at the appropriate spatial scale, as the FUA scale encloses the local economic dynamics that shape a city. This is important because if a city’s boundary is considered in a too narrow way (which would be likely for an administrative boundary definition), or at a too high large scale, the level of segregation can be overstated or understated. Specifically, a FUA is a cluster of contiguous local administrative units (i.e. municipalities, ward, census tracts, etc.) composed by a high-density core and a surrounding commuting zone. In this work all FUAs with at least 500 000 inhabitants were selected for the analysis. For simplicity reasons and consistently with OECD (2012), these large FUAs are called metropolitan areas (MA) or cities in the rest of the paper. In the case of Brazil, New Zealand and South Africa, the FUA definition is not available. Therefore, the city boundaries that come closest to the FUA definition is applied in these countries: Metropolitan Regions in Brazil, Metropolitan Municipalities in South Africa.

The measures of city-level segregation draw from census data for most of the countries considered in this work. Data sources in each country are summarised in Table 2.1. Among the main challenges for international comparability is the consistency in the definition of income, income intervals, and scale at which data is available in each country. Countries use different definitions of income and collect income data in varying ways. This requires, in some cases, re-formatting the data provided by each National Statistical Office to maximise the level of cross-country comparability and combining data at different scales. Each country’s definition of income, as well as the number of income classes, and scale are summarised in Table 2.1. Relevant to note is that income data are not available for the same years for all observed countries. Therefore, the most recent income data available are taken into account.2

The assessment of income segregation across cities in different countries requires considering a number of issues that are related to the data available in each country and that might limit the extent to which indicators are fully comparable. The following paragraph discusses such limitations and explains how, when possible, differences in data sources were addressed to maximise comparability.

The first issue is the spatial scale and coverage of income data. Table 2.1 shows how much variation exists in the size, both in terms of area and population, across cities within and across countries. For countries for which different small scale layers of data are available, it is possible to compute segregation indexes at the different scales to gain insight into the importance of consistent boundaries. This allows the degree to which modifiable areal unit problem possibly affects the precision of international comparison of cities to be assessed. This issue is further discussed in Annex 2.A.

Box 2.1. Spatial ordinal entropy index

The Spatial Ordinal Entropy Index can be computed using grid cells data to create local environments or neighbourhoods that are defined at different scales. For example, spatial entropy at a 1 000 m scale takes each grid cell and defines a 1000-meter area surrounding it as the neighbourhood. The outcome values of the Spatial Ordinal Entropy Index are between 0 and 1, and reflect the ratio between the proportion of the population from each income group in this neighbourhood to that in the city. Given the large number of cells that approximate a surface distribution, integrals are used for the calculations as specified by:

where $T$ is the city population and is the population of the neighbourhood, and ${\stackrel{~}{v}}_{p}$ are the entropy for the city and the neighbourhood respectively, with the latter is calculated as follows:

,

where $M$ is the number of income groups and is the cumulative income share in the neighbourhood $p$ for each cell in the surface grid, with ${\stackrel{~}{\pi }}_{pk}$ being the share of the population in income group $k$. The same procedure is applied for each neighbourhood to obtain $v$.

It may be noted that the component of the index, or the raw entropy, has a maximum value equal to the log of the number of income categories (thus, in the case of 10 income categories the maximum value will be (10) = 1). However, regardless of maximum values, the final index is between 0 and 1 because it gives a ratio that captures the relative deviation of the observed segregation from the observed maximum value.

The Spatial Ordinal Entropy Index as a measure of income segregation has several advantages. For instance, it allows considering several income groups instead of only two and it minimises the modifiable areal unit problem by eliminating borders and relying on the surface distribution of individuals.

Box 2.2. Dasymetric mapping and spatial segregation measurement

Dasymetric mapping is the redistribution of a variable (income) that is measured at a certain administrative areas scale so that it follows population density. Using this method to down-scale spatial data is particularly useful for segregation analysis in urban regions that have a large catchment area. In such cities, overall density can be quite low and the geographic sub-units large, and dasymetric mapping allows analysis of segregation beneath the scale of those geographical sub-units.

The benefits are two-fold for the next steps of data processing. The first is the gains in processing time. The surface density approach to calculating entropy indexes draws a grid over the entire area of the urban region, therefore, the more area that can be eliminated because no people live there, the smaller the area for which the procedure needs to estimate surface density (Figure 2.1). Importantly, having a more precise distribution of the population can lead to better estimates at different scales, though not of the level of segregation. For example, at the border of two large adjacent sub-units, the surface density approach would weigh the distribution of population across the border similarly, even if one side happens to have no population within the area estimated. This is particularly relevant for areas where leapfrogging begins to take place.

There is also a caveat to dasymetric mapping. Applying this technique assumes that the distribution of the observed household incomes or income-levels is the same across the entire area considered by the original geographical data on income. Within this area, however, dasymetric mapping, apportions the frequency of household incomes to proportionally with population on a 100 m x 100 m Landscan data grid (i.e. all parts of the area have the same income distribution, the only thing that changes is how many people live there.) Evidence from previous studies shows that within small areas, the assumption of such income homogeneity does not hold (Tarozzi and Deaton, 2009). Therefore it is relevant to note that the resulting estimate of income distributions is no more accurate. But, it does add flexibility to the measurement of local spatial segregation as it transforms the scale of the income data from pre-defined (administrative) neighbourhoods to grid cells, which can be more freely aggregated using the spatial entropy technique.

Regarding the coverage of income data, countries like the United Kingdom and the United States make data available at a small scale for the entire country, making it possible to include all units within the boundaries of cities. However, countries like Canada, France, Mexico and the Netherlands have more limited coverage. There is a trade-off between coverage and accuracy as the units with missing data tend to be larger and contain less information about the location of households of different income. In the cases of Canada, France and the Netherlands, the next smallest administrative units are included in peripheral locations to increase coverage (see Table 2.1, Unit column).

In the cases of Mexican cities, however, data necessary to fill in those gaps are missing. In all cases, the coverage includes most of the population because areas with sparse data are those with the lowest density and overall population (i.e. small peripheral municipalities). The one case that deserves careful consideration is Mexico where available data, on average, cover less than 7% of the total FUA area. This limited coverage is not as much of a concern because data cover most of the urbanised area close to 75% of the total FUA population. Depending on the income distribution of the areas that are not included, this missing data could possibly lead to bias and should be taken into consideration when interpreting the results.

Table 2.1. Income data sources, the areal unit for the income data, and the number of income bins per country

Country

Census authority

Avg. areal unit population

Avg. area km2

Areal unit definition

Bins

Australia

2010

Australian Bureau of Statistics

134

1.57

Statistical Area level 1

15

Brazil

2010

Instituto Brasileiro de Geografía e Estatística

206

5.18

Setores Censitarios

10

2011, 2016

Statistics Canada – National Household Survey

2007

4.25

Census tract and district

13

Denmark

2013

Dansk Demografisk Database

1674

18.79

Sogne

5

France

2011, 2014

Institut National de la Statistique

et des études économique

1318

5.62

IRIS and commune

11

Ireland

2006

Central Statistics Office

321

0.27

Census enumeration area

9

Ireland

2011

Central Statistics Office

98

0.77

Small area

9

Mexico

2000

Instituto Nacional de Estadística y Geografía (INEGI)

654

0.55

AGEB

12

Netherlands

2008

Statistics Netherlands

1637

2.82

Neighbourhood

5

New Zealand

2001-13

Statistics New Zealand

906

3.07

Mesh block / area unit

6

South Africa

2011

Statistics South Africa

189

1.08

Small Area

12

United Kingdom

2001

Office for National Statistics

109

0.37

Output areas

9

United Kingdom

2011

Office for National Statistics

228

0.35

Output areas

9

United States

2000

US.S. Census Bureau

1693

31.93

Census tract

16

United States

2014

US Census Bureau – ACS

(5-year estimates) (1)

1681

27.63

Census tract

16

Note:

A second issue concerns the way income data are provided by each country, meaning the definition of income and the type of information on its distribution across individuals (see above). The comparisons made here are therefore based on the assumption that income levels correlate strongly across different definitions. In the case of Canada, for example, income data before and after tax are available and highly correlated. Still, all results should be interpreted with a certain level of cautiousness as small differences can come from these changes in collection methodologies.

Another key element for the comparability of this data collection is the number of income bins that are made available by each country. All countries, with the exception of France, Ireland, the Netherlands and the United Kingdom collect data into income bins. Respondents are asked which range of income they fall within rather than a precise value. In the case of France, the results are reported for each decile. In the case of the Netherlands, the census reports how many respondents fall within each of the quantiles of the overall income distribution. For both countries, the data are still based on income and can be used either directly in the case of the Netherlands, or after reformatting in the case of France. Ireland and the United Kingdom do not collect income data. Instead, they use socio-economic classes that function as proxies for income. Those classes have shortcomings as the income range within each class could be high, but the data have the advantage of being ordinal, as for income data.

The range of each income bin is another issue that should be taken into account. The number of bins and the range of income that they represent vary from 6 in New Zealand to 16 in the United States. Fortunately, most countries where income data are available have 10 or more bins and as such offer a comprehensive indication of the income distribution. While there are methods to add further detail to the income data by estimating the entire income distribution, these are not used for this analysis. That is because they add more uncertainty but offer limited improvement since the current data offer considerable variation in income groups.

Furthermore, for those countries for which cities are defined using the FUA definition, the OECD Metropolitan Database provides several measures of socio-economic conditions and well-being that may relate to income segregation. Indicators of household income, an estimation of GDP and labour productivity, and employment rates amongst the working age population are among the variables that have been considered here.

## Results: Segregation across countries

### Entropy across countries

The overall levels of segregation across countries show substantial variation. Figure 2.2 shows the levels of income segregation of metropolitan areas in the different countries considered. The emerging picture is that countries differ in both the average level of metropolitan income segregation and the extent to which such segregation is different across cities. The countries appear to sort into two groups. One includes Brazil, South Africa and the United States, as those countries have considerably higher levels of segregation than the other countries in the sample. In each of the abovementioned countries with relatively high segregation levels, there are also relatively large cross-city differences in segregation levels. In contrast, amongst countries with lower segregation levels, with the exception of Canada and the United Kingdom, city-level differences in the level of income segregation appear limited. Even in countries with a large number of cities (e.g. Canada and Mexico) these differences are limited. Nevertheless, city-level averages may hide significant differences between inner and outer city areas, as those found for a recent study for France (Floch, 2017).

For the United Kingdom and the United States, income segregation is shown for the same cities at two points in time. For the United Kingdom a dramatic increase is observed over 2001-11. This increase comes from a limited number of cities experiencing relative large increases in their segregation levels. More specifically, segregation rose considerably in Leeds, Liverpool, Manchester, and Sheffield. Over the same period, segregation decreased in London and Newcastle. Interestingly, the UK-wide standard deviation for the level of segregation across cities nearly doubled from 0.009 to 0.017. This indicates that over time the variation in segregation levels in UK cities has increased, which is mostly caused by the cities that show the steepest growths and declines in their segregation levels. Noteworthy is that in nearly half of the UK cities segregation increased less than the national average and remained fairly constant.

The United States shows a relatively uniform and modest increase in the variation of segregation across cities between 2010 and 2014. The variation in segregation across cities increased only slightly, as indicated by the standard deviation of segregation levels increasing from 0.017 to 0.018. Over the same period, 28 out of 62 US cities saw an increase in segregation, while 20 saw a decrease. The remaining 22 cities were stable, as changes in their absolute levels of segregation are negligible.

Among all observed cities, cities in Brazil and South Africa have the highest average levels of segregation. This is in line with the association between segregation and relative high overall inequality in these countries. Both countries have among the highest inequality levels in the world as well as histories of segregation (Christopher, 2005; Telles, 2006). This combination of historical segregation and inequality partly explains why the United States, which shares these traits, has higher segregation levels than other OECD countries.

Results for Mexico should be interpreted cautiously especially when compared with other countries. Despite high levels of inequality, segregation in Mexico appears relatively low. Some features of income data in Mexico may partially explain this pattern. While the small area data covers a majority of households in urban areas, there might be some gaps in data collection as surveys likely leave out the most disadvantaged. This possibility is supported by the New Zealand data, which have measured how many household did not answer the underlying survey. These non-response issues suggest that reporting may be lower in low income areas. If a similar systematic underreporting occurred in the case of Mexico, this would result in a possible downward bias. It might also be the case that Mexico has a different pattern of segregation with respect to other countries. Research on specific cities suggest that segregation, especially at the scale of the current analysis, is generally low among low and middle-income households and higher among high income groups (Aguilar and Mateos, 2011). This is consistent with the results discussed in the following paragraphs and suggests that Mexico has a different pattern of spatial clustering of household in space with respect to most countries.

Australia and New Zealand as well as cities in Denmark and the Netherlands have relatively low levels of segregation compared to cities in Canada and in the United States (Figure 2.4). In contrast to the Anglo-Saxon countries,3 these countries have low inequality levels, especially Denmark and the Netherlands. The similar levels of segregation across cities in these three countries suggest that the link between inequality and segregation is not straightforward. While there is a clear positive correlation, a significant degree of variation exists and many other factors could be at play. To better illustrate differences across countries more details are provided in the examination of segregation across income levels and other socio-economic characteristics of cities.

### High segregation in wealthy and productive cities

Income segregation is known for being related to the economic development of cities. Given that due to the rise of economic globalisation wage gaps within cities may have increased, the relationship between segregation and labour productivity is interesting to consider (Cozzi and Impullitti, 2016). As shown in the upper left panel in Figure 2.4, labour productivity coheres with income segregation in a moderately strong way, as could be expected. Similar patterns are observed in Figure 2.4 for the relationship between income segregation and other measures of economic productivity, the estimated GDP at city-level and the average disposable income of households. The correlation between segregation and employment rate is instead weaker.

### Segregation across the income distribution

The average level of income segregation for all income groups may overlook important patterns in segregation. As could be expected, across countries, segregation levels tend to be higher for households with higher income. However, the data also show that at the highest income levels, several countries have seen large decreases in segregation. To explore this further, consider the curves that show segregation levels for each income bin across countries (Figure 2.5). The curves reflect how segregated a specific income group is from the rest of the population. More concretely, the most left data-point on the segregation curve in Figure 2.5 (Panel A) reflects the segregation of households living in Australian cities below the first income threshold relative to the rest of their city’s population. Then, the most right data-point on the same segregation curve shows segregation of households in the highest income bin from other households.4

However, as shown in Figure 2.5, low segregation levels are observed at the lower end of the income distribution.5 Indeed, Reardon et al. (2006) show that for a number of Metropolitan Areas in the United States, the segregation levels at the lowest income levels are higher than for most of the population, but remain much lower than wealthier households. For France, Floch (2017) also finds higher levels of segregation for the highest income group across twelve French metropolises. This evidence suggests two possible explanations. One is that poorer residents might have more diverse spatial configurations than wealthier residents, as their higher segregation levels are nearly constant across all examined countries. On the other hand, scarcer information at the lowest end of the income distribution might cause an underestimation of segregation for low income households.

Box 2.3. Local taxation and income segregation in France

The organisation of the tax system at the local level might introduce incentives to household to concentrate in different neighbourhoods, with possible consequences on segregation levels. In France, there are four levels of local authorities: regions (NUTS 2), département (NUTS 3), public-establishments of inter-municipal co-operation (PEIC) and municipalities. At the municipal level (inter-municipal authorities and municipalities), four direct taxes are collected: the House Tax (HT), the Property Tax on Built Properties (PTBP) and non-Built Properties (PTNBP) and economics taxes. The HT is due for the principal dwelling and eventual secondary residence, and it is paid annually by owners, renters or occupier free of charge. The PTBP is only due by owners, even if the dwelling is leased. Both HT and PTBP are based on the cadastral locative value of the dwelling. These locative values have been defined in 1970 and they are updated each year by flat rate decided at the central government level. Local authorities are free to decrease or increase the rate of the HT and of the PTBP, but these decisions have an incidence on the setting of tax rates of the PTNBP and the CPT (Corporate Property Tax). In 2011, the average tax rate setting by municipal block is 23.76 for the HT and 19.89 for the PTBP (Direction générale des collectivités locales, 2013). Moreover, some tax rebates and tax ceiling can be applied under certain conditions.

Building on the work by Tiebout (1956), economic theory helps understand the impact of fiscal decentralisation on how heterogeneous agents sort in different municipalities of metropolitan areas.6 If the public goods can be easily substituted by private ones, more affluent people will sort into municipalities with low housing prices and low public good provision. However, if it is not the case, more affluent people will sort into municipalities with high housing prices and high public good provision. Large differences in the taxation rates across municipalities of a metropolitan area might promote the sorting of different income groups in different neighbourhoods, fostering segregation. However, property taxes are set up on housing values. If relatively poor households go in wealthier municipalities by buying small dwellings to avoid taxes and benefit from high local public expenditures that would decrease levels of income segregation. Similarly, wealthy people with a preference for privates’ goods can decide to live in relatively less affluent municipalities if the tax base is lower. This point should be especially considered in France where the tax base correspond to the cadastral rental values (computed in 1970) and no the real rental values.

Across French metropolitan areas, a high and positive correlation (coeff. 0.79) is observed between the heterogeneity in the HT block rate and levels of income segregation (Figure 2.3). Segregation is measured through the spatial entropy index with 2011 income data, while HT heterogeneity is measured through the Gini index of the HT block rate (sum of the inter-municipalities’ rates and the municipalities’ rates) across the different municipalities of each metropolitan area. On average, metropolitan areas with larger differences in HT rates across their municipalities show higher levels of income segregation. This finding might suggest that households are sensitive to the local taxation and sort into cities according to tax rates.

In France, reforms on House Tax are currently in discussions with a possible reduction of the share of contributors. In turn, such reduction might weaken the relationship between HT rates differences and observed income segregation, although further analysis is necessary to shed light on the possible mechanisms underlying such relationship.

Source: Fourrey, K. (2017), Local Taxation Framework and Segregation in France, mimeo.

A deeper interpretation of the assessment of income segregation can benefit from looking at the countries for which additional information at the lower end of the income distribution are available. Australia, which is the only country along with South Africa to include a category for household with no reported income (rather than non-disclosed), has extremely high levels of segregation at the lowest end of the income distribution (see Figure 2.5, Panel A). This case illustrates another important point concerning segregation at the extremes. Sharp peaks at the extremes should be expected when the category is very small. In the case of Australia, very few people have no reported income. If people in this category concentrate in the same area, this will result in high observed segregation. South Africa (Figure 2.5, Panel I), on the other hand, has lower levels of segregation at the lower extreme, consistent with the patterns recorded in some United States cities. However, South Africa has a different set of confounding factors. The category for no income is either the largest or one of the largest for each city, hiding much variation, especially when considering the significance of the informal economy.

A main insight can be drawn from the shape of the curves of segregation depicted in Figure 2.5. While nearly all countries have higher segregation levels at higher income levels, this does not happen everywhere. It also shows that at the highest income levels the cities in some countries (e.g. Brazil and South Africa) have large segregation decreases relative to the segregation of adjacent income-groups with a lower income. An explanation for this is that the highest income groups may include a small absolute number of households. This then leaves open the possibility that the residential locations of a limited number of these households have a strong influence on the group’s overall level of segregation. In other words, even if only a few of the highest-income households are located in areas of low segregation this could affect the group’s observed segregation level. Such situation is likely to occur in Brazil and South Africa, where income levels have risen strongly in the first decade of 2000. In these countries, households who have experienced increases in income may not have moved to areas that are exclusively inhabited by high-income residents. Such residential behaviour may also have contributed to the low segregation level of Mexican cities.

The remaining countries show a diversity of patterns, but also some consistencies. For example, Canada and New Zealand show the lowest segregation at the bottom of the income distribution and then a steadily increase along the income distribution. Australian and French cities, on the other hand, tend to have flatter levels in the middle income categories and steep increases at the very top of the income distribution. The United States, in 2000, falls somewhat in-between with a steady, but steep increase. By 2014, however, the pattern has changed towards a flatter curve increase more similar to the curve for Canada.

There is more variation at the bottom of the income distribution from Canada’s steep decrease to Australia and the United States’ upward curvature. The case of Canada stands out because of the clear difference in pattern between Edmonton and Québec City, and Vancouver. Such differences within country warrant closer examination, though in this case comparing with other countries can prove useful. Some cities (not shown here) in the United States have curves that resemble Vancouver’s rather than the more usual US “U-shaped” curve observed here. It is this kind of comparison this work seeks to encourage.

Figure 2.6 shows how segregation levels compare between the top and bottom 20% income deciles in each country.7 Figure 2.6 shows that in some countries segregation is similar at both ends of the income distribution (e.g. France) and that in other countries segregation is higher at the higher end of the income distribution (e.g. Mexico). Denmark and the Netherlands are the only countries where segregation is higher at the lower end of the income distribution – relative to the level of segregation of higher income groups.8

Most countries show a consistent pattern of upper deciles (‘d9’ representing the highest income group) being considerably more segregated than lower deciles (‘d1’ representing the lowest income group). Ratios between these deciles are for most cities between 0.6 and 0.8. A much lower ratio is observed for Mexico and South Africa, where wealthier income groups tend to be more segregated than lower income groups.9 Lastly, the United States, where segregation is measured at two points in time (2000 and 2014), show stable segregation levels over time (Figure 2.6). This indicates that the level of segregation of the rich relative to the level of segregation of the poor has remained relatively constant. This is interesting since the 2000-14 period includes the Global Financial Crisis, which had a profound impact on housing and urban economies.

## Determinants of income segregation

### Econometric approach

To study the main determinants of income segregation, the following equation is estimated:

(1)

In Equation (1), the main dependent variable is the log of the measure of income segregation (spatial entropy at 1 km scale). The explanatory variables are grouped in four categories and are based on previous empirical and theoretical literature.

First, following recent literature on inequality and city size (e.g. Baum-Snow and Pavan, 2013) the number of inhabitants is included as explanatory variable. Following Pendall and Carruthers (2003), Galster and Cutsinger (2007), and Ahlfeldt and Pietrostefani (2017a, 2017b), city size is defined in terms of city density by adding the city land area as a control variable. Literature shows that density is linked with multiple urban aspects. There is a positive link with productivity (so higher wages), houses prices, rents, services access, and efficiency of public services, which may lead to higher income segregation. Besides, according to Ahlfeldt and Pietrostefani (2017a), an increase in density leads to a decrease in net wages (higher wages but higher value of space) which is compensated by higher amenities. Thus, the impact of an increase of density on income segregation is ambiguous and it depends on how amenities are evaluated by the people, on how public goods can be replaced by private ones. Then, it may be assumed that wealthier households have a willingness to pay for amenities and public services higher than poorer ones, or at least they have the capacity to pay for them, leading to more income segregation.

The role of different types of urban forms: monocentric vs. polycentric cities, compact vs. disperse cities, centralised vs. decentralised cities is also considered. These urban forms are related to different spatial distributions of jobs within cities and, as a result, they might be related to different residential location patterns. For example, McMillen (2001) highlights that subcentres in a polycentric city enjoy some of the same agglomeration economies as the CBD (high wages), but offer lower commuting costs and housing prices for suburban workers. Thus, less segregation may be observed in polycentric cities (Garcia-López and Moreno-Monroy, 2016). However, if there is also job segregation, with qualified jobs in the CBD, less qualified jobs in the subcentres and non-qualified jobs elsewhere, polycentric cities might be related to more income segregation.

Based on Pendall and Carruthers (2003), the role of governments within the city is also studied. In this sense, Tiebout (1956) shows that people sort according to their preferences in terms of public goods, which is in part related to their income level. Thus, the more there are intra-city governments (e.g. municipalities), the more they might have preferences for segregation.

As usual, controls for the economy of the city are added. First, labour productivity, which is related to the abovementioned literature on inequality and city size (Baum-Snow and Pavan, 2013), is added. The idea is that higher productivity means higher wages, especially for skilled workers, leading to more relative wage differences between skilled and low skilled workers. This increasing difference in terms of wages may result in more differences in terms of preferences (commuting, public goods, amenities, etc.) and, as a result, more income segregation. It is important to notice that, when controlling for productivity, the density effect is interpreted for a give level of productivity, and vice-versa.

An additional variable for the economy of the city is the employment rate that allows controlling for the situation of the labour market (and the city capacity to integrate low skill workers) and, in general, for the level of development of the city (Pendall and Carruthers, 2003).

Finally, following Pendall and Carruthers (2003), Galster and Cutsinger (2007) and Garcia-López and Moreno-Monroy (2016), controls are included for city demography (youth and old age ratios). The idea is that families in different stages of their live cycle show different preferences that might affect their location patterns. For example, young people with children might compete for better school districts, leading to more income segregation.

Equation (1) is estimated by Ordinary Least Squares (OLS) pooling data for 107 cities in the years circa 2001 and 119 cities in the years circa 2011. The whole set of cities included in the analysis are reported in Table 2.2.

### The role of city size, government, economy and demography

Equation (1) is estimated using gradual specifications in Table 2.3. That is, in the first step log of the city population is included as an explanatory variable in Column 1. Then, in Column 2, the log of the administrative fragmentation index is added, computed as the ratio between the number of local governments and the population in the city. Column 3 includes two variables related to the economy of the city in log form: Labour productivity, measured as the ratio between city GDP and total employment, and employment rate, measured as the percentage of city employment over total labour force. Finally, the log of two demographic variables is also added: the youth dependency ratio, measured as the ratio between the youth population (0–14 years old) over the working age population (15–64 years old), and the old dependency ratio, measured as the ratio between the elderly population (65+ years old) over the working age population (15-64 years old). All these explanatory variables are obtained from the OECD Metropolitan database.10

Results in Table 2.3 show a positive and significant relationship between income segregation and some of the explanatory variables. In particular, the results show that the higher the population, the labour productivity and the youth dependency ratio of a city, the higher its degree of income segregation.

Table 2.2. Countries, cities and years

Country

City

Year

Australia

2010

Calgary, Edmonton, Hamilton, Montreal, Ottawa-Gatineau, Quebec, Toronto, Vancouver, Winnipeg

2011

Denmark

Copenhagen

2013

France

Bordeaux, Grenoble, Lille, Lyon, Marseille, Montpellier, Nantes, Nice, Paris, Rennes, Rouen, Saint-Étienne, Strasbourg, Toulon, Toulouse

2011

Ireland

Dublin

2006 2011

Mexico

Acapulco, Aguascalientes, Centro, Chihuahua, Cuernavaca, Guadalajara, Juárez, León, Mexicali, Ciudad de México, Monterrey, Morelia, Mérida, Puebla, Querétaro, Reynosa, Saltillo, San Luis Potosí, Tampico, Tijuana, Toluca, Torreón, Veracruz

2000

Netherlands

Amsterdam, Eindhoven, Rotterdam, The Hague, Utrecht

2008

United Kingdom

Birmingham, Bradford, Bristol, Cardiff, Leeds, Leicester, Liverpool, London, Manchester, Newcastle, Nottingham, Portsmouth, Sheffield

2001 2011

United States

Akron, Albany, Albuquerque, Atlanta, Austin, Baltimore, Baton Rouge, Birmingham, Boston, Buffalo, Charleston, Charlotte, Chicago, Cincinnati, Clearwater/St Petersburg, Cleveland, Colorado Springs, Columbia, Columbus, Dallas, Dayton, Denver, Des Moines, Detroit, El Paso, Fort Worth, Fresno, Grand Rapids, Harrisburg, Houston, Indianapolis, Jacksonville, Kansas City, Las Vegas, Little Rock, Los Angeles, Louisville, Madison, McAllen, Memphis, Miami, Milwaukee, Minneapolis, Nashville, New Orleans, New York, Norfolk-Portsmouth-Chesapeake-Virginia Beach, Oklahoma City, Omaha, Orlando, Philadelphia, Phoenix, Pittsburgh, Portland, Providence, Raleigh, Richmond, Sacramento/Roseville, Saint Louis, Salt Lake City, San Antonio, San Diego, San Francisco, Seattle, Tampa, Toledo (only 2000 data), Tucson, Tulsa, Washington, Wichita

2000 2014

Table 2.3. Determinants of income segregation (I): City size, government, economy, demography

Dependent variable:

ln(SE 1-km index)

[1]

[2]

[3]

[4]

ln(Population)

0.062a

(0.014)

0.065a

(0.017)

0.052a

(0.014)

0.050b

(0.016)

ln(Fragmentation)

0.012

(0.026)

0.016

(0.026)

0.014

(0.028)

ln(Labour productivity)

0.154b

(0.055)

0.203a

(0.054)

ln(Employment rate)

-0.248

(0.200)

-0.100

(0.240)

ln(Youth dependency ratio)

0.391b

(0.160)

ln(Old age dependency ratio)

0.066

(0.080)

0.725

0.725

0.729

0.735

Note: 226 observations (107 in 2011, 119 in 2011). All regressions include country and year fixed-effects. Robust standard errors in parenthesis clustered by country. a, b and c indicates significant at 1%, 5%, and 10% level respectively.

Source: Elaborations based on national data on income distribution (see Table 2.1) and OECD (2018) OECD Metropolitan Database, http://stats.oecd.org/Index.aspx?Datasetcode=CITIES.

### The role of urban form

In Table 2.4 alternative measures of urban form are tested. The idea is to test the effect of different types of urban spatial structures (e.g. monocentric vs. polycentric cities, compact vs. disperse cities, centralised vs. decentralised cities). Column 1 includes the log of the city land area. By doing so, the coefficient of the city size variable, the city population, can be interpreted in terms of population density (Combes and Gobillon, 2015). Column 2 proves this statement by substituting the population variable by the population density. In both cases, results for the log of population (Column 1) and the log of population density (Column 2) show that a higher population density is also directly related to a higher degree of income segregation.

Columns 3 to 4 test whether there are significant different effects between monocentric and polycentric cities. First, the log of population is interacted with a dummy for polycentric cities (and add also this dummy as explanatory variable) in Column 1. The polycentricity dummy is computed using the OECD variable named Polycentricity. The results show that the positive and significant relationship between population density and income segregation is clearly related to monocentric cities (0.066), whereas is much smaller for polycentric cities (0.001=0.066-0.065). Column 4 splits the overall city population between central city population (computed using OECD variable Population Core) and suburban population (computed using OECD variable Population Hinterland). Results for these variables show that 1) a higher central population is not different between monocentric and polycentric cities and is positively related to higher income segregation levels (0.064); 2) a higher suburban population is positively related to income segregation only in monocentric cities (0.011) whereas is negatively related to income segregation in polycentric cities (-0.056=0.011-0.067). Finally, Column 5 adds an additional interaction between the polycentricity dummy and the labour productivity. This interaction is significant and negative and, in absolute values, higher than the coefficient for monocentric cities. As a result, it seems that cities with higher labour productivity levels are related to higher income segregation levels in monocentric cities (0.255), and to lower income segregation in polycentric cities (-0.044=0.255-0.299).

Columns 6 to 9 analyse the effect of other measures of the spatial configuration of cities. Departing from specification in Column 1, a measure of the degree of spatial concentration, the Theil’s entropy index, is added in Column 6; the average weighted distance to CBD to measure the degree of spatial centralisation in Column 7; and both measures of spatial concentration and decentralisation in Column 8; and, departing from specification in Column 8, the number of city centres (based on the OECD variable Polycentricity) in Column 9. Since the Theil’s concentration index ranges between 0 and 1, with 0 indicating perfect concentration (see Veneri [2015] for further explanations), results for these regressions show that cities with lower (higher) spatial concentration indexes are related to lower (higher) levels of income segregation. Results for the average distance to CBD show that less (more) centralised cities are related to lower (higher) segregation levels. Finally, in line with the results in Columns 3 to 5, a higher (lower) number of city centres (with a minimum of 1 for monocentric cities, and more than 1 for polycentric cities) are related to lower (higher) levels of income segregation. All these results clearly show the important role of the urban form on the degree of income segregation at the city level. Furthermore, they also show significant different relationships between monocentric and polycentric cities, and between less and more spatially concentrated and centralised cities.

Table 2.4. Determinants of income segregation (II): Urban form

Dependent variable:

ln(SE 1-km index)

Land area and population dens

Monocentric

and polycentric cities

Number of centres,

Centralisation and concentration

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

ln(Population)

0.044a

(0.010)

0.066a

(0.014)

0.036b

(0.016)

0.081a

(0.017)

0.075a

(0.018)

0.086a

(0.013)

ln(Pop) x D Poly

-0.065

(0.034)

ln(Central population)

0.064a

(0.009)

0.062a

(0.10)

ln(Central pop) x D Poly

-0.020

(0.022)

0.025

(0.021)

ln(Suburban pop)

0.011a

(0.002)

0.011a

(0.002)

ln(Sub pop) x D Poly

-0.076b

(0.024)

-0.067a

(0.017)

ln(Land area)

0.011

(0.024)

0.055c

(0.026)

0.010

(0.026)

0.008

(0.031)

0.006

(0.030)

0.010

(0.023)

0.021

(0.022)

0.027

(0.025)

0.029

(0.026)

ln(Population density)

0.044a

(0.010)

Theil concentration index

0.118c

(0.058)

0.147b

(0.057)

0.168b

(0.057)

Average distance to CBD

-0.008b

(0.003)

-0.009b

(0.003)

-0.009b

(0.003)

Number of centres

-0.032b

(0.014)

ln(Fragmentation)

0.013

(0.027)

0.013

(0.027)

0.016

(0.028)

0.001

(0.021)

0.000

(0.021)

0.002

(0.013)

0.009

(0.012)

0.010

(0.011)

0.013

(0.012)

ln(Labour productivity)

0.208b

(0.053)

0.208a

(0.053)

0.230a

(0.061)

0.234b

(0.064)

0.255a

(0.057)

0.195a

(0.051)

0.182b

(0.062)

0.214a

(0.044)

0.226b

(0.044)

ln(LProd) X D Poly

-0.299b

(0.128)

ln(Employment rate)

-0.106

(0.243)

-0.106

(0.243)

-0.189

(0.262)

-0.167

(0.259)

-0.144

(0.238)

-0.023

(0.256)

-0.069

(0.237)

-0.075

(0.238)

-0.096

(0.231)

ln(Youth dependency ratio)

0.377c

(0.174)

0.377c

(0.174)

0.367c

(0.165)

0.386c

(0.187)

0.396c

(0.173)

0.373c

(0.192)

0.332c

(0.173)

0.329c

(0.175)

0.332c

(0.166)

ln(Old age depen. ratio)

0.076

(0.097)

0.076

(0.097)

0.078

(0.098)

0.141

(0.097)

0.148

(0.094)

0.038

(0.067)

0.045

(0.075)

0.043

(0.975)

0.043

(0.077)

Dummy Polycentricity

0.885

(0.494)

1.189a

(0.233)

3.844b

(1.268)

0.736

0.736

0.740

0.750

0.752

0.719

0.723

0.725

0.727

Note: 226 observations (107 in 2011, 119 in 2011). All regressions include country and year fixed-effects. Robust standard errors in parenthesis clustered by country. a, b and c indicates significant at 1%, 5%, and 10% level respectively.

Source: Elaborations based on national data on income distribution (see Table 2.1) and OECD (2018) OECD Metropolitan Database, http://stats.oecd.org/Index.aspx?Datasetcode=CITIES.

Finally, in all regressions in Table 2.4 the variables labour productivity and youth dependency ratio keep showing a positive and significant relationship with income segregation. The only exception is the above mentioned interaction of labour productivity and the dummy for polycentric cities (Column 5).

### Different spatial scales

As a robustness check, Equation (1) is estimated using the income segregation measure computed at different spatial scales. This new set of regressions departs from the baseline specification in Table 2.4 Column 9.

Table 2.5 reports results when using a segregation index computed for a spatial scale of 500 meters in Column 1, of 2 000 meters in Column 2, and of 4 000 meters in Column 3. Column 4 uses the a-spatial segregation index computed using the smallest available intracity unit (i.e. municipalities, wards, or census tracts). In all regressions, results are not significantly different from the preferred specification in Table 2.4 Column 9 and show that cities with a higher (lower) population density, degree of spatial concentration and centralisation, labour productivity, and youth dependency ratio are related to higher (lower) levels of income (decrease) income segregation.

Table 2.5. Determinants of income segregation (III): Spatial vs. A-spatial income segregation indices

Dependent variable:

ln(SE 1-km index)

500 m

2 km

4 km

A-Spatial

[1]

[2]

[3]

[4]

ln(Population)

0.080a

(0.020)

0.107a

(0.013)

0.164b

(0.060)

0.080b

(0.026)

ln(Land area)

0.028

(0.028)

0.028

(0.026)

0.025

(0.023)

0.025

(0.028)

Theil concentration index

0.166b

(0.061)

0.175b

(0.056)

0.202b

(0.065)

0.159c

(0.074)

Average distance to CBD

-0.008b

(0.003)

-0.010a

(0.003)

-0.016a

(0.005)

-0.008b

(0.003)

Number of centres

-0.027c

(0.013)

-0.044b

(0.016)

-0.072b

(0.026)

-0.023c

(0.011)

ln(Fragmentation)

0.009

(0.012)

0.020

(0.015)

0.035

(0.027)

0.005

(0.011)

ln(Labour productivity)

0.248a

(0.040)

0.197a

(0.055)

0.152

(0.117)

0.260a

(0.048)

ln(Employment rate)

-0.118

(0.206)

-0.021

(0.256)

-0.033

(0.279)

-0.106

(0.167)

ln(Youth dependency ratio)

0.309c

(0.158)

0.393c

(0.180)

0.365

(0.354)

0.289c

(0.127)

ln(Old age depen. ratio)

0.047

(0.075)

0.039

(0.082)

-0.003

(0.098)

0.058

(0.073)

0.702

0.752

0.765

0.671

Note: 226 observations (107 in 2011, 119 in 2011). All regressions include country and year fixed-effects. Robust standard errors in parenthesis clustered by country. a, b and c indicates significant at 1%, 5%, and 10% level respectively.

Source: Elaborations based on national data on income distribution (see Table 2.1) and OECD (2018) OECD Metropolitan Database, http://stats.oecd.org/Index.aspx?Datasetcode=CITIES.

### The poor vs. the rich

Finally, Equation (1) is estimated for different types of population according to their income level. The idea is to test whether the above studied “average” relationships remain as such across the income distribution and, in particular, for the lowest and highest income levels (the poor and the rich).

Table 2.6 reports results for the lowest income levels (the poor) and for the highest income levels (the rich) using the income segregation index computed only for the 10th and 20th percentiles (Columns 1 and 2) and for the 80th and 90th percentiles (Columns 3 and 4) respectively. This new set of results clearly shows that the level of segregation of the poor is only (positively) related to the labour productivity of the city and to the degree of spatial centralisation. On the other hand, the results for the highest income levels are quite similar to the “average” results and show that the segregation of the rich are (positively) related to the city size (population density), the degree of spatial centralisation of the city, the labour productivity and the youth dependency ratio.

Table 2.6. Determinants of income segregation (IV): Poor vs. Rich

Dependent variable:

ln(SE 1-km index)

Poor

Rich

Percentiles:

10th

20th

80th

90th

[1]

[2]

[3]

[4]

ln(Population)

0.079

(0.052)

0.063

(0.059)

0.115b

(0.030)

0.130b

(0.033)

ln(Land area)

-0.016

(0.024)

0.038

(0.045)

0.011

(0.033)

0.002

(0.038)

Theil concentration index

0.235a

(0.102)

0.173

(0.157)

0.064

(0.112)

0.065

(0.130)

Average distance to CBD

-0.010

(0.006)

-0.013a

(0.003)

-0.006c

(0.003)

-0.008b

(0.003)

Number of centres

-0.083

(0.064)

-0.030

(0.033)

-0.025

(0.025)

0.010

(0.018)

ln(Fragmentation)

0.043b

(0.009)

0.010

(0.013)

-0.013

(0.015)

-0.008

(0.014)

ln(Labour productivity)

0.361a

(0.055)

0.403a

(0.077)

0.261a

(0.048)

0.319a

(0.050)

ln(Employment rate)

-0.011

(0.296)

-0.080

(0.180)

-0.040

(0.160)

0.029

(0.163)

ln(Youth dependency ratio)

-0.165

(0.155)

0.002

(0.159)

0.479c

(0.186)

0.527b

(0.186)

ln(Old age depen. ratio)

0.011

(0.130)

-0.010

(0.143)

0.038

(0.067)

0.157

(0.085)

0.762

0.787

0.659

0.749

Note: 226 observations (107 in 2011, 119 in 2011). All regressions include country and year fixed-effects. Robust standard errors in parenthesis clustered by country. a, b and c indicates significant at 1%, 5%, and 10% level respectively.

Source: Elaborations based on national data on income distribution (see Table 2.1) OECD (2018) OECD Metropolitan Database, http://stats.oecd.org/Index.aspx?Datasetcode=CITIES.

## Orientations for policy analysis

Income segregation may come in many varieties. It is the result of the sorting of people in space by some socio-economic or cultural criteria. On the causes of such process there is still much research to be done and the interaction of individual decisions with factors of global, national, and local nature, is likely to play a role. Even the process of economic growth and agglomeration economies generated in cities can be related to segregation. More specifically, income growth at the top of the income distribution can lead to increases in the spatial concentration of wealth – and thus add to segregation (Reardon and Bischoff, 2011). At the same time, however, the relation between income inequality and segregation is not necessarily systematic. An increase in inequality does not necessarily translate to an increase in segregation. Vice versa, changing segregation is not necessarily followed by a change in income inequality.

The functioning of the housing market is inherently connected to the extent to which people live segregated within cities. An obvious connection is that households tend to sort into areas where the other households have a similar income (Nguyen-Hoang and Yinger, 2011). Then, given their budget constraint, households that wish to relocate may be able to consider only houses in a limited range of locations. These are in turn shaped by several factors, including the competition for space between commercial, public, and residential uses (Alonso, 1964). Such competition can result in housing close to a city’s centre, where jobs and services are most accessible and, as a consequence, land is most expensive. Individuals pay higher prices to live in the location with highest accessibility, closest to the CBD. If the cost of commuting is low, however, more individuals could accept a higher distance from the centre and afford larger homes. The above core economic factors are however not sufficient to explain patterns in where the rich and the poor live within cities.

Rich households concentrate within the centre of a city when this city-centre has a higher level of cultural, natural, or consumer amenities than the city’s suburbs, and vice versa (Brueckner et al., 1999). Moreover, although differences in housing prices may be very high across city neighbourhoods, reflecting a certain level of segregation, housing policies may mitigate the segregation of income groups. For example, most US cities include a mix of expensive and cheap housing near their CBD. In addition to discrimination in access to finance, the lack of public transit connecting suburbs to job centres insured that most low income housing would be concentrated in a few central locations (Glaeser, Kahn and Rappaport, 2008). Such processes have long historical shadows. Today, areas of concentrated poverty persist because, among other factors, the high spatial concentration of subsidised housing and unemployed people creates an oversupply of low skilled workers in city centres (Lens, 2014). This case is not specific to the United States, as similar mechanisms can be found in peripheral areas of European cities.

The longevity of buildings is another factor linking income segregation with housing. Most residential buildings have a life span of decades, sometimes centuries. This longevity makes it difficult to replace the housing stock to match the intensity of land use that a location could support, as it effectively fixes the supply of housing in the short run (Di Pasquale and Wheaton, 1996; Glaeser and Gyourko, 2005). Because of this, housing can become more expensive quickly if the demand for its location surges. As a consequence, additional housing units in higher buildings could be developed to drive down housing prices through increasing the housing supply. While this could ensure local affordability of housing and mitigate segregation, this is typically prevented by a city’s existing built structure and the cost of redevelopment. The slow adjustment of the housing market is particularly relevant in cities with rapid population growth, where poorer households may experience increasing barriers to living close to a centre of economic activity – resulting in income segregation.

An example that illustrates the flip side of how segregation may be influenced by building longevity is Tokyo. In Tokyo, land use restrictions and the clustering of affordable housing have led to levels of segregation and housing affordability that are amongst the lowest for metropolitan housing markets of a similar size (Cox and Pavletich, 2015). Until recently, the Japanese government supplied subsidised housing in central, high accessibility locations. While the supply of new subsidised housing has slowed to a trickle, creating long waiting lists, the existing stock maintains a greater degree of income diversity even in the most sought after neighbourhoods (Tiwari and Hasegawa, 2001). In addition to the state’s role in providing affordable housing, another important factor is the role of the state in regulating housing supply. One of the recurrent findings on land use regulation is that stricter regulations drive up housing prices, see Kok, Monkkonen, and Quigley (2014), and increase the level of income segregation (Lens and Monkkonen, 2016). Again, Tokyo stands out as an example of policy intervention which, although not aimed at desegregation, likely contributed to the lower levels of segregation. The Tokyo Metropolitan government used its influence to push the national government to reform its land use legislation and enable greater flexibility, particularly in high density construction (Fujita, 2011). As a result, and in conjunction with Japan’s tradition of shorter lived buildings, Tokyo has only 2% of its buildings pre-dating 1960 and over 30% have been built since 2000. In comparison, in Los Angeles, one of the most expensive housing markets, about 56% of buildings predate 1960 and only about 8% were built after 2000.

The case of Tokyo illustrates the importance of political structures for segregation. If it were not for the changes in land use regulation and proactive investments in affordable housing, Tokyo could have experienced recurring housing crises. More broadly, housing is an important component of welfare systems, regardless of their orientation (Kemeny, 2001). The state influences the structure of housing markets, in particular the balance between owner-occupied and rental housing. The funding strategies of countries can lead to imbalanced housing systems where the dominance of one housing type constrains the choices of those that do not have access to it. This is the case in the Netherlands where social housing sector is sizeable (Elsinga et al., 2008) and Southern Europe where home ownership stunts the rental market (Arbaci, 2008). In Spain, lower segregation levels often hide different forms of marginalisation that operate through the housing market (Arbaci, 2008). The above examples illustrate that political environments both influence the drivers of income segregation as well as how it is conceived. This underlines that international comparative research on income segregation can be highly beneficial as it may help to expose country-specific blind spots and may highlight a range of policy solutions from across the globe.

## Discussion

This chapter has provided an assessment of income segregation within cities by maximising the comparability across countries. In the twelve observed countries, within-city segregation of households with different income-levels varies considerably across cities – even within cities. This finding suggests that region-specific factors might shape income segregation. The results also suggest that in several cities households at the extremes of the income distribution, the most and least affluent households, have the largest influence on segregation outcomes. In some cities segregation is driven by poorer rather than richer households, and vice versa. It is shown that income segregation is positively associated with the average household income in cities. A certain variation was observed between the income groups of the 2nd and 8th income deciles – those adjacent to the income groups at the extremes of the income distribution.

The econometric results show that: city size matters, as bigger and denser cities are related to income higher segregation levels; economy matters, as cities with higher labour productivity levels are related to higher income segregation levels; demography matters, as higher proportions of elderly population are related to higher income segregation levels.

The econometric results also show that urban form matters. First, income segregation levels related to bigger and denser cities are smaller in polycentric cities than in monocentric ones. Second, bigger central cities are related to higher income segregation levels, both in monocentric and polycentric cities. Third, while higher suburban population are related to higher income segregation levels in monocentric cities, it is related to lower income segregation levels in polycentric cities. Moreover, while a higher labour productivity is related to higher income segregation levels in monocentric cities, the opposite relationship is found for polycentric cities. In fact, less spatially concentrated and centralised cities are positively related to a lower degree of income segregation. Finally, the econometric results show that income levels matter: Labour productivity and the degree of spatial decentralisation of the city are related to income segregation levels of the poor and the rich. Other above mentioned determinants are only related to the segregation level of the rich.

With regards to improving the methods for studying segregation, more work could be done to take advantage of the strengths of individual country databases (e.g. New Zealand's consistent temporal data). This can help to test some of the assumptions made in comparing countries that use different methods of collection and lead to better tools to mitigate the influence of these differences in data collection.

More systematic explorations into methods for extrapolating entire income distributions from available data appear necessary. Using the highest detailed data that countries make available (e.g. Australia, where nearly the entire income distribution is included) allows to evaluate some of the assumptions built into methods of extrapolation and to make decisions about whether uncertainty of the precision of income extrapolation methods is worth increases in coverage.

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Annex 2.A. The appropriate spatial scale of entropy measurement

Income data are not available on a fine spatial scale for all observed countries. Therefore, the extent to which variation in the scale of income data impacts results for entropy measures at different spatial scales was assessed in order to select the appropriate spatial entropy measure (as these are calculated at varying scales from 500 m to 4 000 m): for the main analysis.

Uniquely within the study area, New Zealand provides data at the very fine level of the mesh block, a unit that is smaller than any of the other units used in other country. The census also makes available data at the area unit (AU) level, which corresponds more closely to the scale of the units used in other countries. Therefore the cities in this country lend themselves well for evaluating the appropriate spatial scale of entropy measures.

The smaller scale data inflate the segregation index in a relative sense (the segregation index value becomes three times as large), but that this inflation is modest in an absolute sense (it increases from 0.04, when income data for common-sized AU-level subareas in cities are used, to 0.125 when the more fine-scale mesh areas are used). This means that as the common-sized areas are consistently used in the analysis, possible variation in the results due to the scale of the underlying data is mitigated, as the level of those data is kept relatively constant. This gives confidence that the results in the main analysis are comparable across cities and countries, as it applies data at the common-sized level.

Moreover, the spatial entropy indexes are found to minimise the sensitivity of results to the spatial scale. Again comparing segregation indexes at the two scales in New Zealand, the 500 m scale indexes are 0.018 apart and less than 0.008 at the 1 000 m scale. This gives confidence that the results for spatial entropy indexes are minimally sensitive to the spatial scale of the underlying data. Therefore the spatial indexes are used to evaluate differences across the cities in the observed countries. Specifically, in the main analysis the 1 000 m scale based spatial entropy index is used because it seems to be the one that is least sensitive to scale. The entropy indexes at the larger scales, 2 000 and 4 000 metres provide a different kind of information. They extend beyond what most people would consider as the size of a neighbourhood. These measures are more relevant to evaluating the structure of the city rather than draw conclusions about the experience of residents in their immediate environment.

## Notes

← 1. A lack of information on income-extremes is an issue for studying the spatial distribution of affluent households, especially in countries, such as Canada and New Zealand, where some cities have a sizeable proportion of the population above the highest threshold leading to substantial missing information. The lack of detail about the lower end of the income distribution is unfortunate, especially because it concerns a group of people who might be targeted by a specific policy. In many cases, the first income category includes a wide variety of households with very low incomes, sometimes as much as 15% of the population is included in that first category. The lack of information about the lowest and highest income residents tends to distort the picture for the overall segregation levels in cities because these tend to be the most segregated populations.

← 2. As a result, time-stamps of the observed income data varies across the observed countries from 2008 to 2014, with exception of Mexico (2001).

← 3. Some caution is necessary in the interpretation of results for Anglo-Saxon countries. Anglo-Saxon countries tend to have higher socio-economic inequality levels and generally more liberal form of welfare state (Esping Andersen, 1990). This generalization does not hold empirically, except for Australia, Canada, New Zealand, the United Kingdom and the United States all have very similar income inequality levels, as measured by the Gini coefficient, and do not differ markedly from other European countries (OECD (2015) Income Distribution Database). Australia and New Zealand’s lower levels, as well as the compact distribution of Australian cities around the mean, point to the possibility of these two countries having different structure from other Anglo-Saxon countries. This is consistent with research on ethnic segregation, which shows that cities in Oceanian countries are less segregated than the rest of the Anglo-Saxon world (Johnston, Poulsen, and Forrest, 2007).

← 4. Unfortunately, in most countries the bin for ‘no income’ does not exist and nor does the bin that would include all income above the highest threshold and is as such not comparable across countries. Due to this lack of data the segregation of households at the lower and upper tails of the income distribution remains unobserved for most countries (Australia is an exception as it has a ‘no-income’ bin.

← 5. This holds even when rank-order entropy, a method designed to retrieve the entire income distribution, is used.

← 6. See for instance the review in: Brülhart M., et al. (2015).

← 7. This approach is chosen to minimize the influence of data at the extremes and because all countries have data available at the least between the 20th and 80th percentiles, making the data more comparable. Cut-offs are chosen by calculating the distance between the chosen deciles and the percentiles that correspond to each income bin. So, for example, if there is an income bin that represents 8% of the population and the next two bring the cumulative population to 15% and 26% respectively, the first is chosen as the first decile and the second as the second decile.

← 8. However, consider that due to the lack of data for these countries on the upper and lower ends of the income distribution segregation at the ‘true’ extremes of income-classes remains unmeasured.

← 9. Unfortunately, the Mexican census did not include an income survey in the 2010 iteration. It would be informative to test whether, as income rose in Mexico, particularly in the half of the income distribution, segregation increased in the middle, pushing segregation at the lower end higher in a process of revisualization (i.e. as middle income households move to areas with higher quality amenities, poorer areas become gradually poorer). As noted, this process does not appear to have taken place in Mexico and South Africa would provide a good comparative case since the two countries are at similar income levels.

← 10.