Socio-economic groups moving apart: An analysis of recent trends in residential segregation in Australia's main capital cities

We study changes in the spatial distribution and segregation of socio-economic groups in Australia using a new data set with harmonised census data for 1991 and 2011. We find a general increase in residential segregation by education and occupation groups across the major capital cities in Australia. Importantly, these trends cannot be explained in general by changes in the demographic structure of groups and areas but rather by the rise in the over and underrepresentation of groups across areas. In particular, our analysis reveals clear diverging trends in the spatial configura-tion of high and low socio-economic groups as measured by their occupation and education. Whereas high-skilled groups became more concentrated in the inner parts of cities, the low-educated and those working in low-status occupations became increasingly overrepresented in outer areas. This pattern is observed in all five major capital cities, but it is especially marked in Sydney, Melbourne and Brisbane.


| INTRODUCTION
Social and economic transformations in many industrialised countries over the past 50 years have had very asymmetric effects on skill groups, widening inequalities between them. Various factors contributed to the deterioration of the relative position of low-and middleskilled groups including skilled-biased technical change and the rise in returns to skill (Acemoglu, 2002), offshoring and the polarisation of labour markets (Goos, Manning, & Salomons, 2014) and the decline of labour market institutions (Fortin & Lemieux, 1997).
Similar to other Anglo-Saxon countries like the United States and the United Kingdom, since the 1980s, Australia's labour markets have been characterised by an increasing polarisation, with a decline in middle skill and routine jobs, and a sharp increase in the number of casual jobs-from 15% in 1983 to 28% in 2002 (Campbell, 2004)-all of which disproportionally affected the lowskilled members of the workforce (Coelli & Borland, 2016). This shift in the structure of occupations came alongside an increase in the return to skill of the most qualified further contributing to inequalities between skill groups (Keating, 2003). These changes in labour markets were also reflected in housing markets, where the strong rise in housing prices negatively impacted the levels of housing stress and affordability of most vulnerable groups (Yates, 2008). We hypothesise that these compound inequalities have had consequences for the residential sorting of skill groups within Australian cities. This paper aims to study changes in the spatial distribution of education and occupation groups in Australia's major capital cities between 1991 and 2011 and its effect on residential segregation. Between 1991 and 2011, Australia experienced rates of economic growth outperforming most advanced economies (Reserve Bank of Australia, 2010).
However, similar to other advanced industrialised countries, the increase in national and regional incomes over that period disproportionally benefited those at the top (Azpitarte, 2014;Wilkins, 2007). Examining the implications of postindustrial cities for the spatial sorting of skill groups is the primary purpose of this research.
For the analysis, we use the measurement framework proposed by Alonso-Villar & Del Río (2010)-which allows to quantify the segregation of a group in a multigroup context-and measures of overall segregation that are consistent with it (Frankel & Volij, 2011;Silber, 1992;Theil & Finizza, 1971). Importantly for our purpose, this framework permits the analysis of segregation trends within cities while controlling for changes in the demographic structure of those cities. Specifically, it allows decomposition of the overall segregation in terms of the segregation experienced by population subgroups, as well as, the segregation of the geographical units that compose the city. This is critical to identify the groups and areas that became more or less segregated and also to quantify the contribution of demographic changes to segregation trends. We apply these measures to a newly created, harmonised data set based on census data, which allows the comparison of the spatial distribution of skill groups across comparable geographies at different levels in 1991 and 2011.
Our research contributes to previous literature in several ways.
First, it departs from most works on residential segregation by accounting for the residential sorting of all the socio-economic groups simultaneously. This is so because we use multigroup segregation measures instead of binary measures based on pairwise comparisons, which facilitates comparisons among cities whereas considering the socio-economic diversity existing within them. 1 Second, we measure residential segregation in Australia based on education and occupation groups, whereas most studies in this country focus on segregation by ethnicity or country of origin (Edgar, 2014;Jones, Jonhston, Forrest, Charlton, & Manley, 2018). Third, we use detailed local level data on education and occupation. By doing so, our empirical strategy departs from previous investigation on suburbanization of disadvantage in Australia (Pawson & Herath, 2015;Randolph & Holloway, 2005;Randolph & Tice, 2017), which identified disadvantaged areas using an aggregate index that conflates multiple indicators of local disadvantage and was therefore affected by an ecological fallacy (Goldie, Kakuk, & Wood, 2014) as not all individuals living in disadvantaged areas are disadvantaged individuals. 2 Fourth, by looking at the geographical distribution of education and occupation groups, our analysis sheds some light on the underlying factors driving the suburbanisation of disadvantaged in Australian cities and the groups affected by it, thus expanding previous studies, which provide no insight on the socio-economic groups affected by the transformation of cities.
The paper is organised as follows. Section 2 describes the measurement framework, whereas Section 3 describes the new data set and the harmonisation process. In Section 4, we present the empirical findings including the map evidence for major capital cities.

| MEASUREMENT FRAMEWORK
We use the framework proposed by Alonso-Villar and Del Río (2010), which allows decomposing the overall segregation of cities in terms of the segregation experienced by the different groups and the segregation of the areas that comprise the city. We study residential segregation from an evenness perspective-that is, the extent to which a group is unequally distributed across locations-as well as a representativeness perspective concerned with the extent to which the representation of groups in each location differs from the representation one would expect given the group's weight in the overall population.
To quantify the segregation of any given group, g, we use two indices: and Φ g = X l n g l N g ln where N g is the size of demographic group g, P represents total population, n g l is the number of individuals from group g in location l, and p l is the population size of location l.
These indices are equal to 0 if the group is evenly distributed across locations, that is, when the group's population share in each location matches its share in the whole population. The higher the degree of unevenness of the group, the higher the value of these indices. The maximum value of D g is 1 − N g P , whereas that of Φ g is ln P N g À Á , which can be higher than 1. The measure D g , proposed by Moir and Selby-Smith (1979) in the binary case and explored by Alonso-Villar and Del Río (2010) in a multigroup context, has a clear interpretation.
It measures the proportion of group g's individuals that would have to move to another location to be evenly distributed across space. Both indices satisfy standard properties in the segregation literature, but whereas Φ g satisfies the Pigou-Dalton transfer principle, D g does not. 3 We use the two measures to assess the sensitivity of our results to the formulation of the index.
The indices D g and Φ g of group's segregation are related to the measures of overall segregation IP and M used in multigroup settings: and M = X g N g P X l n g l N g ln The IP index, proposed by Silber (1992), is a generalisation of the well-known index of dissimilarity to the multigroup case and corrects some of its shortcomings. 4 Consistent with the index D g , the measure IP represents the proportion of individuals that would have to change residential location so that all groups are evenly distributed across locations. The mutual information index, M, first proposed by Theil and Finizza (1971), has also been claimed to be a suitable measure to quantify residential segregation (Kramer & Kramer, 2018 and That is, if the total population is divided into several mutually exclusive groups, overall segregation as measured by IP and M equals the weighted average of the segregation of the groups according to D g and Φ g , respectively, with weights equal to the groups' shares in the population. In addition to its decomposability by population subgroups, the measure M can also be decomposed in terms of locations, which makes it particularly suitable for quantifying the contribution of each spatial unit to overall segregation. Following Alonso-Villar and Del Río (2010) and Frankel and Volij (2011), the index M can be expressed as where Ψ l = X g n g l p l ln n g l =p l N g =P : The index Ψ l quantifies the level of segregation of any area, l, by looking at the level of under and overrepresentation of the different groups in that area. If the share of each demographic group in a location is similar to the one that the group has in the city as a whole, then the value of Ψ l will be close to zero. In contrast, if the groups' representation in that location differs substantially from the one that would be expected given their shares in the city's population, then the area will be characterised by large values of Ψ l . Expression 7 implies that overall segregation is equal to the weighted average of the segregation of its areas as measured by the Ψ l index.

| DATA
We draw on publicly available socio-economic and geocoded data.
Data on education and occupations come from the 1991 and 2011 Basic Community Profiles (BCPs) compiled by the Australian Bureau of Statistics (ABS). 5 These profiles include count data on residents' characteristics at various regional levels. We focus on the population aged 15 and older.
To ensure the comparability of geographies and variables across years, we constructed a harmonised data set that allows meaningful comparisons of the spatial distribution of groups in 1991 and 2011.

| Occupations
Occupations for 1991 were classified using the first edition of the

| Geographical units
We used information on three geographical units: statistical local area (SLA), statistical subdivision (SSD) and SD. Data on the first two were used to identify the two spatial levels employed in the analysis, whereas the latter allowed us to delimit Australia's main capital cities. to match a SLA of 1991 whose territory had been partitioned. In some cases, however, creating a harmonised region also required the amalgamation of SLAs from 1991.
Of the 390 SLAs of 1991, for about 71% (278 SLAs  The increase in segregation is also found when segregation is measured using SSDs rather than SLAs (see Table SB1), which shows the robustness of our findings to the geographical unit of analysis. 10 In 2011, Sydney and Melbourne were the cities with the highest level of segregation in terms of both education and occupation, followed by Brisbane, which had the largest increase over the period.
The IP index indicates that, in 2011, 12.9% (resp. 11.3%) of the population in Sydney would have to relocate for the city to eliminate residential segregation by education (resp. occupation). The lowest segregation values are in Perth (requiring moving 9.6% and 8.5% of its population) and Adelaide (9.7% and 8.9%).

| Segregation of socio-economic groups and locations
We examine the contribution of socio-economic groups and locations to the rise in segregation exploiting the decomposability properties of the IP and M measures. These allow us to evaluate whether the increase in segregation stemmed from changes in the residential patterns of disadvantaged or advantaged groups. Table 3 provides estimates of the residential segregation of each group at the SLA level as measured by the D g and Φ g indices. As discussed in Section 2, these measures are consistent with the measures of overall segregation IP and M, which can be expressed as the weighted average of the D g and Φ g , respectively. Table 3 reveal diverging trends between skill groups.

Figures on
The groups with lower education levels (i.e., those with a certificate or with no postschool qualification) became more segregated as their    The segregation level of areas that are 70 km far from the centre was not very different from that of areas located within a 5-to 10-km ring.
To further investigate the relationship between segregation and location, we estimated the following ordinary least squares (OLS) econometric model that allows the identification of nonlinear relationships between segregation and distance to the city centre: where LSeg l is the measure of local segregation in area l, Dist l denotes the distance from the city centre, and ε l is an i.i.d. error term. The model also controls for differences across cities using five dummy variables (one for each city) that are included in the vector X l and take value 1 when the area belongs to the city and 0 otherwise.
Ordinary OLS regression models may yield biased and inefficient estimations in the presence of spatial dependence in the data (Martin, 1974). Thus, in addition to OLS models, we also estimated spatial lag and spatial error models that account for spatial correlation in the data (Anselin, 1988;Anselin, Syabri, & Kho, 2006). The spatial lag model incorporates a spatially laggeddependent variable on the right-hand side of the equation, ρWLSeg , where ρ is the parameter of spatial autocorrelation and W is a matrix of spatial weights. The spatial error model allows for correlation in the error term of the model, which is assumed to be ε = λWε+u, where λ is a parameter capturing the extent of autocorrelation, W is the spatial weight matrix, and u is a vector of i.i.d. errors. Table 4 shows the estimation results from the three models for 1991 and 2011. Models were estimated using the D g and Φ g indices of local segregation yielding very similar results, so only the results for  Table 1  To evaluate the contribution of demographic changes to segregation trends, we turn to counterfactual analysis. We focus on the measure M, which has the advantage of being decomposable in terms of both the segregation of groups and regions-Equations 6 and 7.
To evaluate the role of demographic and segregation factors, we undertake two counterfactual analyses because, when moving from 1991 to 2011, we can follow two paths depending on whether we first change the groups' sizes or the groups' segregation levels. These two paths lead to the following decompositions: Notes: ** and * denote coefficient significantly different from 0 with 1% and 5% confidence level, respectively. Standard errors are reported in parentheses. Abbreviation: OLS, ordinary least squares.
Decomposition 10 breaks down the change in overall segregation in two components: one that results from the difference between overall segregation in 2011 and overall segregation in the counterfactual assuming groups' shares as in 1991 and groups' segregation as in 2011 (labelled demographic factor) and a second component given by the difference between overall segregation in that counterfactual and the actual overall segregation in 1991 (labelled groups' segregation factor). In the decomposition given by (11), the demographic factor is given by the difference between overall segregation in the counterfactual (with groups' shares as in 2011 and groups' segregation as in 1991) and overall segregation in 1991, whereas the groups' segregation factor is the difference between overall segregation in 2011 and overall segregation in the counterfactual. The contribution of demography (resp. groups' segregation) to the change in overall segregation between 1991 and 2011 is defined as the mean of the two demographic (resp. groups' segregation) factors divided by the total change.
To explore whether the change in overall segregation between 1991 and 2011 stems from changes in the group composition of the SLAs (segregation factor) or in the shares these areas account for (demographic factor), we also build two counterfactual distributions: one in which we keep unaltered the SLAs' shares whereas the composition of each area moves from that in 1991 to that in 2011; and another in which the representation of the groups within each SLA is the factor that remains unchanged whereas the areas' shares change. Table 5 provides the results of the decompositions by groups and regions. Changes in the relative size of education groups unambiguously contributed to the increase in residential segregation by education (the demography factor contributes positively to explain the change, which ranges between 113% and 233% depending on the city). The sharp increase in the prevalence of highly educated individuals who tend to be more unevenly distributed than other groups (as shown in Table 3) certainly lies behind this result. If segregation levels of education groups were as in 1991 and their demographic shares as in 2011 (M (seg = 91; pop = 11) ), the M index would have increased much more than it actually did, which indicates that changes in the groups' segregation levels between 1991 and 2011 contributed to prevent the rise in overall segregation. The decline in the unevenness of the most educated is a factor clearly pushing in that direction.
In contrast, the value of the counterfactual M (seg = 11; pop = 91) is greater than M 91 , suggesting a positive contribution of groups' segregation to the increase in overall segregation, likely reflecting the increase in the segregation of low-educated groups documented above. As mentioned earlier, the contribution of a factor to the change in overall segregation was calculated as the mean contribution of the factor in the two counterfactual analyses. In the case of the segregation factor, this average turns out to be negative, reflecting the larger magnitude of the negative contribution of the segregation factor in one of the decompositions.
The analysis thus suggests that although individuals with bachelor's degrees experienced a decrease in segregation, as shown in Section 4.1, this highly segregated group grew so much during this period that it made overall segregation rise. This effect was reinforced by the rise in the unevenness of those with low education.
If we look instead at residential segregation by occupation, we find that in Sydney, Melbourne and Brisbane, segregation increased mainly because occupation groups became more unevenly distributed across regions (although changes in the groups' sizes played also a role). Thus, for example, in Sydney, 83.4% of the change came from changes in the groups' segregation levels and 16.6% from demographic changes.
The reason why segregation by occupation increased in all the cities over the period was that individuals working in middle and bottom occupations were more unevenly distributed in 2011 than they were in 1991 (as shown in Table 3

| Which groups are located where?
To further shed light on the changes in the spatial distribution of low and high skill groups, we examine the degree of over and underrepresentation of the groups across SLAs. To show the level of representation of any group g in location l, we use the location quotient, r g,l = n g l =N g p l =P , which compares the size of the group in location l with that in the overall population and constitutes the main building block of the index Φ g (see Section 2). We distinguish five levels of representation based on the quintiles of the distribution of r g,l in 1991 computed at city level pooling information on all groups (education or occupation) and SLAs. 16 A group is very underrepresented in a given SLA if r g,l ≤ P 20 , underrepresented if P 20 < r g,l ≤ P 40, represented at the expected level if P 40 < r g,l ≤ P 60, overrepresented if P 60 < r g,l ≤ P 80 , and very overrepresented if r g,l > P 80 .

| CONCLUSIONS
Over the past two decades, Australia has not only witnessed economic growth but also a rise in income inequality (Australian Council of Social Services, 2015). The economic gains of the country during this buoyant period have benefited more those at the top of the income distribution, which has had important consequences in terms of poverty (Azpitarte, 2014), especially for those with low education attainments (Wilkins, 2007). Vulnerability in one dimension usually involves difficulties in others, which explains why Australian lower income households are four (five) times more likely to face precarious housing (employment) than higher income households (Beer, Bentley, & Bake, 2016). Income inequality among individuals tends to translate into spatial inequalities, especially if advantaged and disadvantaged groups locate in differentiated neighbourhoods (Hunter, 2003) and public intervention is limited (Randolph & Tice, 2017).
Using information from a newly created data set on individuals' occupation and education, this paper has documented an increase in residential segregation by socio-economic status in Australian major Unlike most scholarship on socio-spatial inequalities within Australian cities (Pawson & Herath, 2015;Randolph & Tice, 2017), this paper has paid attention to the concentration of not only the bottom social group but also the top and middle ones. Living in a low socio-economic neighbourhood reduces individuals' opportunities and development, whether it is due to a lower school quality, higher exposure to crime or weaker job networks (Rothwell & Massey, 2015). The concentration of social advantage may foster inequalities even further because human capital externalities and access to desirable amenities are likely to occur in places where highly educated individuals are overrepresented (Diamond, 2016). The clustering of skill advantage may have important consequences for not only the low-skill groups but also the middle-skill groups.
Measuring overall segregation using multigroup indices that account for the simultaneous concentration of all the groups (low-, high-, and middle-skill groups) has allowed us to provide a summary statistic of the phenomenon's magnitude. Quantifying the extent of segregation for each group separately has permitted us to show from which group "isolation" comes. In addition, our counterfactual analysis has allowed us to explore whether the rise in segregation was the result of demographic changes or instead the consequence of skill groups moving apart more intensively.
Our research has shown that segregation is not only a pervasive phenomenon (requiring that between 8.5% and 12.9% of individuals in a city change their residential location to remove segregation) but also one that has intensified over this period. The increase in residential segregation is particular intense when looking at education, with a rise of about 50% or above in Sydney, Melbourne, Perth and Brisbane and of roughly 35% in Adelaide.
Our analysis has also revealed that the rise in segregation by occupation groups cannot be explained by demographic changes but rather by an intensification of the over and underrepresentation of groups across locations. Regarding education, we have shown that whereas the highly educated groups are in general the most unevenly distributed in space, the rise in segregation was mostly driven by an increasing segregation of the low-skill groups and the growth of the highly skilled. Isolation of high social groups being higher than that of low social groups is a pattern also detected in North American and European cities (Bischoff & Reardon, 2014;Marci nczak, Musterd, van Ham, & Tammaru, 2016) for other socio-economic indicators.
The analysis given here indicates that whereas the least skilled Randolph & Tice, 2017), although our analysis has moved beyond documenting the spatial patterns of the various skill groups.
14 For the harmonised SLAs that resulted from the amalgamation of SLAs, the distance was computed as the weighted average of the distances to the city centre from each of the centroids using the size of the SLA as weights.