Income segregation in France: a geographical decomposition across and within urban areas

ABSTRACT This article sets out the first comprehensive analysis of income segregation in France across the whole urban–rural continuum. Segregation is broken down by urban areas, their size and the types of municipalities (central/suburban/exurban/rural). A significant part of the segregation is due to differences across urban areas. Moreover, regression analyses show that non-negligible levels of segregation are observed in small urban areas. Finally, disparities between exurban and central/suburban areas have increased sharply, particularly in small urban areas. These results suggest it is necessary to reconsider the view that segregation is limited to Paris, and they call for a new design of anti-segregation policies.


INTRODUCTION
Socio-economic segregation refers to the separation of populations into different neighbourhoods, according to their socio-economic characteristics (income, job, etc.).A high level of segregation means a concentration of poverty in certain neighbourhoods and of high-income households in other neighbourhoods.This geographical clustering of households with common features has important normative consequences through the presence of contextual effects.Several papers suggest that residence in a ghetto could be beneficial, in the short term: poverty and ethnic density may foster the formation of group-specific networks, provide access to employment opportunities (Cutler et al., 2008).However, in the long run, the cost of segregation is high because of the difficulty of expanding beyond these networks (spatial mismatch in the labour market; Mortensen & Vishwanath, 1994) or because of the existence of negative peer effects, and a restrained access to public goods (Lavy et al., 2011).
Consequently, segregation is on the political agenda of many countries and an abundant literature has focused on interpreting the rise and fall of residential segregation, and income segregation in particular.For the most part, this literature has studied the evolution of segregation in metropolitan areas only (Logan et al., 2018;Reardon et al., 2018).However, some studies have begun to decompose metropolitan areas geographically and distinguish between the macro-and micro-components of segregation (Lee et al., 2008;Reardon et al., 2008).As shown by Lichter et al. (2015), a macro-breakdown of segregation of the central city and suburbs is not sufficient.Residential segregation is largely place specific and most of the segregation might be micro, that is, within suburban places, within exurban places or within central cities.Another strand of the literature goes beyond the geographical delimitations of metropolitan areas and proposes a comprehensive measure of segregation across the rural-urban continuum (Logan & Burdick-Will, 2017).Lichter et al. (2007) focus specifically on rural, non-metropolitan areas: segregation in rural and small-town America rises as the share of non-white minorities rises and this 'reinforces the need to broaden the spatial scale of segregation beyond its traditional focus on metropolitan cities or suburban places ' (p. 563).
Our objective in this paper is to propose the first integrated study on the entire urban-suburban-exurban-rural continuum of income segregation in France.So far, we are aware of only three large-scale studies dealing with income segregation in France (Floch, 2017;Quillian & Lagrange, 2016;Vincent et al., 2015).These three papers focus on the largest French urban areas (UAs) and therefore offer only a partial view on income segregation as they calculate the levels of segregation for a few metropolitan areas, but not for the whole country.This has several limitations.First, they disregard segregation in small and mediumsized UAs.However, a recent literature provides evidence of a recent increase in the social divide in French mediumsized UAs (see Courtioux & Maury, 2020, for school segregation; or INSEE, 2014, for the rise of inequality) suggesting that segregation in these areas may be worth investigating.
Second, the literature on income segregation in France ignores the level of segregation across UAs (either big or small).They only consider segregation within these areas (i.e., Paris, Lyon or Marseille taken separately).Outside France, few studies focus on difference in segregation levels across geographical areas (Gradin et al., 2015;Johnston et al., 2006).However, total segregation results from the sum of within-UA segregation (the extent to which local income distributions differ from the distribution in the whole metropolitan area) and between-UA segregation (the extent to which metropolitan income distributions differ from the national distribution).Moreover, between-UA segregation is of crucial importance as metropolitan areas are not static in terms of population.Every year, some households migrate within a metropolitan area or to another metropolitan area.The annual residential mobility rates in 2014 in France was 11.3% (CGET, 2018), and approximately a quarter of this is mobility outside the metropolitan area (i.e., about 3%).As a result, residential mobility choices may lead to selection across UAs.The evolution of segregation in a given area may thus be correlated with segregation observed in another area and the two cannot be considered separately.It is therefore essential to take the broadest possible approachmeasuring segregation across the whole countryand detail its various constituent parts.Therefore, we decompose segregation and measure the contribution of different geographical areas and/or types of UAs to national segregation.
Finally, the existing literature largely disregards the role of exurban areas (i.e., outer fringes of urban units).The reason why such a substantial part of the population is excluded is twofold: first, segregation in sparsely urbanised areas is often considered low.However, some studies suggest that significant segregation phenomena may be at work in exurban areas (Charmes, 2009).In recent decades, there has been significant residential mobility of middleand high-income households from city centres or suburbs to exurban areas (Goffette-Nagot & Schaeffer, 2011).These populations have been inclined to cluster in certain towns of urban fringes.The second reason is technical: measuring segregation in sparsely populated areas requires statistical adjustments.In exurban zones, the basic geographical units for measuring segregation are generally also small in population, which leads to small-unit bias concerns that results in an overestimation of segregation.We correct for this small-unit sample bias to compare the level of segregation in rural areas with those observed in more densely populated zones.
We work with exhaustive data provided by French public administrations, from 1999 to 2015, at the land register unit (LRU) level with a 100% coverage of the population.We use rank-order segregation indices: the mutual information index for different income percentiles and the rank-order information theory index.The rankorder information theory index provides a complete synthetic view of segregation over the whole income distribution.The use of mutual information indexes for different income percentiles makes it possible to focus on certain income profiles (the poorest 10% or 20%, the 50% median, and the richest 10% or 20%).These indexes are strongly decomposable: we exploit this property to break down between-UAs and within-UAs segregation components.We also decompose segregation according to the size of UA (small, medium-sized, large areas) and the 'urban type' (UT) of the municipality (central city/suburbs/exurban areas).
Our most striking results are as follows.
(1) Between 1999 and 2015, across the whole of France, segregation increased slightly, particularly for the poorest (bottom 10% income) and richest households (top 10%).(2) A significant part of segregation is actually between-UAs (i.e., the 'macro' component of segregation) and has therefore never been taken into account into previous studies dealing only with within-UAs segregation.Though remaining high, the macro-components of segregation have significantly decreased since 1999: the observed increase in total segregation is mainly local.(3) Segregation, when measured by an index of all income percentiles, is higher in Paris than in small UAs.However, this result is mainly a consequence of the segregation of the richest (which is very high in Paris).If we focus on bottom 10% of households, segregation is surprisingly higher in medium-sized UAs than in the Paris metropolitan area.(4) The breakdown central city/suburbs/exurbs represents a sizeable and growing share of within-UAs segregation.These high levels of segregation are increasingly due to affluent households, which move to exurban areas in the specific municipalities where they are clustered.A regression analysis conducted at the UA level confirms most of these results.Overall, by combining results (2) and (4), we show that the macro-components of segregation have changed significantly over 15 years (strong decrease in between-UA segregation and strong increase in central city/suburb/exurb breakdown): French geography is changing on a relatively macro-scale.
The paper is structured as follows.The next section presents the theoretical framework and motivations.The third section presents the data and the methodology.The fourth section presents the main descriptive statistics.The fifth section gives the results.The sixth section concludes.

An integrated and comprehensive approach
Our objective is to propose a geographically comprehensive framework of analysis for segregation which leads to two important discrepancies with the existing literature.
Income segregation in France: a geographical decomposition across and within urban areas 443 First, most studies on segregation limit the scope of their analysis to the largest metropolitan areas only.Small or medium-sized UAs are often not considered.Segregation in large areas on the one hand and in medium, small-sized UAs or rural areas on the other are not disconnected but linked by households' mobility.Each year, about 3% of French households move to another UA (long-distance relocation).Over a 15-year period, this means that almost 40% of households have moved to another UA (CGET, 2018).Mobility is therefore a nationwide phenomenon.
An investigation confined to a particular metropolitan area would thus lead to a distorted view of segregation dynamics in our opinion.When top incomes leave their home metropolitan area (often an affluent neighbourhood), this move may lead to lower segregation in the home area.However, if they relocate to an affluent neighbourhood in another UA, this contributes to an increase in segregation there.Segregation has thus shifted from one UA to another, but has not decreased at the national level.
The patterns of residential segregation between Paris and other surrounding areas can therefore only be understood with a more generalnationalframework.Second, the geographical scale for measuring segregation is usually very fine (census tract or block).Other more macro-scales are not simultaneously considered.But it is possible to identify new segregation issues within areas by considering intermediate geographical levels: the city/suburb/exurb distinction is especially relevant (Quillian & Lagrange, 2016).To understand this, take a simple example with two types of households (low and high incomes) and two types of neighbourhoods: affluent (majority of high-income households) and poor (majority of low-income households).Suppose first that neighbourhoods are randomly distributed in the UA (i.e., the shares of affluent or poor neighbourhoods in the city and in the suburbs are the same).Now compare this with another situation where all the affluent neighbourhoods are in the suburbs, and the poor neighbourhoods in the city (the total number of poor and affluent neighbourhoods remains the same).The overall segregation level in the UA is the same in both situations.However, the two situations are very different in terms of income inequities.In the second situation, the rich have moved massively to the suburbs where they have created large wealth clusters.One could therefore say that the second situation is more segregated than the first one, and this can only be captured with an intermediate measure of segregation at the city/ suburb (and exurb) levels.
Generally, we advocate adopting a macro-scale approach to segregation in France (considering some intermediate within-UA scales and the macro between-UA scale).Measuring segregation at one scale only (neighbourhood) limits our understanding of the segregation processes at stake and their social and economic consequences.

Segregation across
UAs and the regional convergence literature Interestingly, such a comprehensive approach implies the integration of different theoretical strands into a single analytical framework.First, the analysis of segregation between UAs (i.e., the macro-scale), while largely new to the literature on segregation, can nevertheless be related to the research on regional divergence.Regional divergence measures the extent to which people with different incomes tend to live in different places and might be assessed by the dispersion of incomes across regions or metropolitan areas.Segregation across metros is strongly related to divergence (Manduca, 2019).A rise in macrosegregation directly contributes to regional divergence.
Our results can thus be linked to the vast European literature on regional divergence.It is empirically established that income inequality has been growing over the past decades in the EU (Iammarino et al., 2018).There are important theoretical debates about why the convergence process, although predicted by neoclassical economic theory (Barro & Sala-i-Martin, 1992), has been interrupted: some stress the importance of agglomeration economies (Glaeser, 2011), or barriers to labour mobility (Diamond, 2016).
Another literature discusses the consequences of this growing regional inequality.A thread of research emphasises the role of inequality in causing major societal tensions at the national level (Ballas et al., 2017;MacKinnon, 2017).Other strands focus on the social and economic individual consequences of regional disparities.Intergenerational income mobility varies greatly geographically and is significantly lower in disadvantaged metro areas (Chetty et al., 2014).Some studies insist on the role of informal skills in generating barriers to labour mobility.People from poor regions have a lower level of informal knowledge (social, cultural, networking capacities, etc.; Deming, 2015) which restricts their upward mobility and contributes to locking these regions in a poverty trap.Other studies emphasise the persistent impact of inequalities at a macro-level on access to education (Iammarino et al., 2018) or the prevalence of illhealth and social problems (Wilkinson & Pickett, 2015).
In Europe, these regional disparities have been the basis for European regional policy since the late 1980s.The EU Cohesion Policy targets cities and regions to support, among other things, job creation, competitiveness and economic growth.One of the objectives of the Cohesion Policy is to compensate the less developed regions and promote convergence.Empirical analysis of the effects of this policy on convergence leads to mixed evidence (Bachtrögler et al., 2020).While the overall impact on regional growth seems positive, a large part of the effect is concentrated in Germany rather than in the poorest regions of Southern Europe (Crescenzi & Giua, 2020).

Segregation in large versus small cities
Our study therefore builds on this literature on disparities across metros, but our analytical framework also makes it possible to put these macro-disparities into perspective with other stratification processes which operate at much smaller spatial scales (i.e., within metros).Our model incorporates an analysis of segregation within UAs, considering both Paris and other French large cities, but also medium-sized and small urban, as well as rural areas.Several articles on US data have provided evidence of forms of segregation beyond large metropolitan areas, in rural or small-town America (Lichter et al., 2016).More generally, the size of the UA is one of the key drivers in the ecological model applied to segregation (Wilkes & Iceland, 2004).Larger metropolitan areas, which are often also those with more functional diversity, show higher segregation levels (Timberlake & Iceland, 2007).Large metropolitan areas also have higher minority representation and income inequalities which are associated with more segregation (Reardon & Bischoff, 2011).
Compared with the United States, the French urban landscape has its own specific features.The Paris metropolitan area and other large metros (Lyon, Marseille) concentrate a disproportionate share of the country's wealth (INSEE, 2014).Social problems and income inequalities are also more prevalent than in the rest of the country.As a result, most studies on segregation in France have focused on large metropolitan areas only (Quillian & Lagrange, 2016).Poverty in Paris and other large French metros is also less concentrated in the city centre than in comparable American cities, as low incomes are much more suburbanised.Inner Paris is a historical centre with many public facilities which explains the concentration of high incomes.Meanwhile, various studies have highlighted the relocation to exurban areas of many middleincome and wealthy households over the last 30 years (Charlot et al., 2009).This results in a structure with: (1) a rich centre, (2) suburbs with poor areas and (3) mixed urban fringes with pools of wealth, justifying the centre/suburb/exurb breakdown for segregation in large metros.
The urban pattern for small and medium-sized areas is quite different (Floch, 2017).On average, medium-sized cities have a lower average income and diversity of activities (over-representation of the industrial and administrative sectors) than Paris.While income inequality is lower (with relatively few high-income households), mediumsized cities are becoming more precarious (increase in terms of poverty and unemployment rates) and more geographically stratified (Courtioux & Maury, 2020): due to affordable land costs and modest commuting costs to the central city, middle-income households have moved to the suburban/exurban areas (Goffette-Nagot & Schaeffer, 2011).Low-income households live in the city centre with low access to public facilities and other amenities (CGET, 2018).Part of the segregation in medium-sized cities looks therefore to be based on the gaps between the central city and the suburbs/exurb.

Consequences of macro-scale segregation
Several studies have investigated the consequences of macro-scale segregation, notably the disparities between the city centre, the suburbs, and fringe areas, and why these should complement conventional measures based on micro-spatial units (e.g., census tracts).Macro-segregation is linked to the 'political economy of places', that is, a theory on the role of places (cities, suburbs) as political actors that compete with each other to attract economic actors and wealthy taxpayers (Lichter et al., 2015).This theory is linked to the literature on local public finance rooted in Tiebout's 'sorting across jurisdictions' model.A common form of segregation arises from wealthy people moving to suburban/exurban jurisdictions to obtain the desired level of public services (Tiebout sorting).In France, there are several large jurisdictions within UAs (groupings of municipalities) whose political powers are becoming increasingly important compared with the municipal authorities for health services, education or public transit systems (Charmes, 2019).Macro-segregation could arise from high-income households sorting across large jurisdictions and voting for high-quality public services (high investment in healthcare or education).In contrast, this implies that some poor areas face limited access to public services.In several metropolitan areas, poor suburbs are affected by low-quality public transit which limits their access to jobs and other services.In medium or small-sized UAs, the concentration of poverty in the city centre has led to a lack of public investment, notably underfunded schools with many low-achieving students and high dropout rates (Goux et al., 2017).On the whole, a large body of French literature has developed on the decay of city centres in medium-sized UAs, and the resulting adverse peer effects (France Stratégie, 2020).

Data
We use an exhaustive administrative data source: FILO-COM (dwelling files per municipality, CGDD/SDES/ DGFiP) based on tax files.It provides nearly complete information on individual household characteristics between 1999 and 2015 (income, composition, location and characteristics of the dwelling). 1The database is enriched every two years by a new cross-section.Data are therefore available for all, odd-numbered years from 1999 to 2015.We only study here the start and end years of the sample, so 1999 and 2015, since we do not expect significant variations between these two years for slowly changing patterns such as segregation.We will not use household income directly, but rather income per consumption unit in order to take household size into account. 2 Information about the location of households is central to our study.Compared with other European countries, the administrative division in France has a high level of complexity: above the municipalities, there are groupings of municipalities, departments and regions.Not all these divisions are relevant for our analysis because they do not necessarily reflect the spatial dynamics of mobility, nor employment areas.We therefore work with three geographical levels: urban areas (UAs), municipalities and our basic territorial unit: land register units (LRUs).A UA consists of a central city, its suburbs, that is, municipalities with a continuously constructed area (no more than 200 metres between two buildings), and a exurban area, that is, a group of municipalities where at least 40% of people Income segregation in France: a geographical decomposition across and within urban areas work in the related central city or suburbs.We will use this decomposition central city/suburb/exurban area in our analysis of within-UAs segregation.A municipality outside any UA is considered rural.
In 2015, France has a total of 762 UAs, 42 of which have more than 200,000 inhabitants.It is therefore not possible to show the evolution of segregation for each UA.Thus, we will sometimes have to group UAs according to their size.
Figure 1 presents the different UAs in France.Each UA is itself broken down into an urban unit (which includes the central city and its suburbs) and the exurban area.The white area on the map corresponds to rural areas.
France comprises more than 36,000 municipalities.Most of them (around 95%) have fewer than 5000 inhabitants and only 2.5% of them have more than 10,000 inhabitants.As explained above, municipalities may be grouped according to their 'urban type' : rural/ exurban/suburban/central.Finally, an LRU is an administrative submunicipal division designed to ease the process of collecting local taxes. 3The boundaries of an LRU are constituted of natural or artificial limits (roads, railways, rivers, etc.).On average, an LRU consists of about 300 inhabitants (approximately 130 consumptions units per LRU) and is used here as the basic unit for calculating segregation.This number varies according to urban density: it ranges from about 1200 individuals in Paris (where it represents a block) to about 200 individuals (possibly several villages) in rural areas.The LRUs therefore cover larger geographical areas in sparsely populated areas. 4The small size of certain LRUs (compared with, for example, a US census tract) implies an upward bias in the estimation of segregation which we treat with modifiable areal unit problem correction techniques (Carrington & Troske, 1997).

Methodology
There are many segregation indices, the characteristics of which may strongly differ.First, we rely on rank-order income segregation indices.Income is a continuous variable that may be broken down into ordered groups and we wish to build an income segregation index that integrates the ordered nature of these groups.Second, we study segregation at several geographical levels simultaneously, so we must take the decomposability properties of the index into account.
Let N be the total number of households in France (or in a given area).This population is divided into K units (i.e., K LRUs) with N k being the number of households in unit k (k = 1, . . ., K ).Let p denote the income percentile rank.We dichotomise the income distribution and calculate the segregation between households with income rank less than p, and households with income rank greater than p. h p is the entropy level: For a given geographical area, we compute the mutual information index at rank-level p, M p : where p k is the proportion of households with income rank less than p in unit k.M p summarises the evenness of distribution of the two groups (those below and above p).
The M p index is zero in the absence of segregation, if the size of the two groups is p and 1 − p everywhere.By contrast, the index will have its maximum value if segregation is total, that is, if all the municipalities only accommodate one group.This M p index is strongly decomposable.It is possible to break down segregation observed in a geographical area into different groups.
For instance, we may decompose national segregation into two components: the between-UAs component (i.e., segregation due to differences in income distribution across UAs) and the within-UAs component (i.e., segregation due to income differences across LRUs within each UA).We do the same according to the 'urban type' of municipalities and distinguish the amount of within-UAs segregation due to differences between central, suburban and exurban municipalities.This gives a breakdown into three components: (1) segregation between UAs (the macro-level); (2) between 'urban types' in the same UA (the intermediate level); and (3) between LRUs in the same UA among municipalities of the same UT (the smallest level).
The M p index is computed for different values of p. M 10% and M 20% measure the segregation of the poor (poverty indices): the extent to which low-income (below the first quintile) or very low-income (below the first decile) households are evenly distributed.M 80% and M 90% measure the segregation of high-income householdsaffluence indices.M 50% measures the extent to which the poorest 50% live separated from the richest 50%.
In addition to the mutual information indices, we calculate the rank-order information theory index H R which summarises the different mutual information indices in a single index over the entire spectrum of the p percentiles (i.e., poverty and affluence indices together).All results report the bias-corrected measure of segregation.

DESCRIPTIVE STATISTICS
We work with exhaustive data for almost 27 million French households between 1999 and 2015.The average income per household (in real terms, euros 2005) was €24,389 in 1999 and €34,026 in 2015.The income per consumption unit (CU) increased by 44.65% (from €14,655 in 1999 to €21,199 in 2015).In 2015, the top 10% had an income per CU above €46,578, while for the bottom 10% the income was below €7025.The 10%/90% ratio was therefore 6.63, a much lower measure than in the United States (12.6 in 2018 according to Horowitz et al., 2020).
We present demographic and income trends according to the size of UAs (Table 1).First, it should be noted that, in 2015, a significant proportion of the French population lived in large UAs: 19.06% in Paris and 24.12% in other large UAs (Lyon, Marseille-Aix, Lille, Toulouse, Nice and Bordeaux).Around 40% of the French population lives in UAs of more than 200,000 inhabitants.Finally, rural areas represent almost 15% of the French population.
As expected, high-income households (top 10%) are relatively over-represented in the Paris UA (almost 16% in 2015) and the proportion of low-income households (bottom 10%) is rather low in Paris.Indeed, the Paris UA is still characterised by high income inequality, but the share of high incomes in Paris decreased between 1999 and 2015 because of their migration to smaller UAs (CGET, 2018).On the contrary, the share of lowincome households is increasing in Paris, while falling sharply in rural areas.
The share of high-income households decreases continuously as the size of the UA decreases.It is close to 10% in large UAs (excluding Paris), but only 7% in small UAs and less than 6% in rural areas.In contrast, the proportion of low-income households is not a monotonic function of the size of the UA.They are relatively over-represented in large or medium-sized UAs (excluding Paris), but less present rural areas.Note that, outside Paris and rural areas, the share of high and low incomes is relatively stable between 1999 and 2015, but this masks profound changes within UAs.Overall, in terms of general population dynamics, in mid-sized UAs central Income segregation in France: a geographical decomposition across and within urban areas cities are losing population (only 33% city centres are growing in population share; CGET, 2018), while exurban areas are gaining population in relative terms (70%) and suburban areas are stable (50%).In terms of income, we observe a sharp fall in the share of low incomes in exurban areas as opposed to central cities and suburbs.Middleincome households are historically over-represented in exurban areas.This is in line with an important literature on the 'peri-urbanisation' of the middle classes in France, who live in the exurban areas (Charmes, 2009).But further results show that this pattern also extends to top incomes.The overall increase in the share of high incomes in exurban areas observed in Table 1 is actually largely due to residential mobility (see also Table A1 in Appendix A in the supplemental data online).Indeed, if we focus on top incomes who moved between 1999 and 2015, we find that they are disproportionally living in exurban areas in 2015, compared with households who have not moved.The increase in income observed in exurban areas therefore seems to be linked to the inflow of mobile high-income households, rather than to a noticeable income growth of the people living there.

RESULTS AND DISCUSSION
Before looking at the breakdown of segregation, we begin by exposing the results for France as a whole.Table 2 presents all the bias-corrected segregation indices in 1999 and 2015.According to the H R synthetic index, segregation increased slightly in France between 1999 and 2015 (from 9.35% to 9.68%).Income segregation is moderate and stable in France compared with the United States (Quillian & Lagrange, 2016).However, this result, covering all income percentiles, conceals much more striking changes when we focus on certain income groups.First, segregation is much higher for high income households.In 2015, the M 80% or M 90% are in the order of 11-13% once normalised, while only 7-9% for the M 10% and M 20% .Affluent households are more geographically separated from the rest of the population than poor households.In other words, the middle-income groups are geographically closer to low-income than to high-income groups.
Second, if we look at the evolution of the indices, it appears that extreme groups have experienced the strongest increase in segregation levels.The M 10% index, has increased much more rapidly than the national H R  (from 7.38% to 9.01%).The increase is also quite noticeable for top 10% households.M 90% rose from 12.95% to 13.41%.Segregation measured by the M 20% and M 80% indexes increased less strongly and M 50% decreased.These results suggest that while the extreme groups (bottom and top 10%) are becoming increasingly geographically isolated, the rest of the population (the remaining 80%) are getting more integrated with each other.Segregation in France is driven by very poor and very rich households.
We now turn to the geographical and urban breakdown of segregation (Table 3).We proceed with a three-component decomposition: (1) between UA (between-UA, macro-scale segregation); ( 2) between UTcentral/suburban/exurbanof each UA (i.e., between-UT, within-UA, intermediate-scale segregation); and (3) the remaining component of segregation (microscale segregation): between-LRUs, within-UA within-UT.The sum of these three components mechanically gives the total level of segregation provided in Table 2 (see also Tables A2 and A3 in Appendix A in the supplemental data online for the results without the Paris area).
The first component simply measures income segregation at the UA level.In 2015, the between-UA level (macro-scale) of segregation was 0.0213, which represented 22.04% of the total segregation obtained in Table 2.The remaining within-UA part of segregation (which we split again in Table 3) is then 77.96%.Segregation is therefore mostly local.Since 1999, the share of macro-segregation has fallen sharply from 30.53% to 22.04%: UAs are getting increasingly similar to each other.But meanwhile, as segregation for France as a whole is rising, it means that segregation within-UAs is increasing, that is, units within UAs are becoming increasingly homogenous: some with more and more affluent households, others with more and more low-income households.This process to greater homogeneity had already been evidenced (Charmes, 2009;Préteceille, 2006), but our study integrates it for the first time into a framework measuring segregation across the whole of France.Furthermore, it is interesting to note that while macro-segregation is declining in France, this is much less pronounced for top 10% group.Between-UA M 90% remained high and almost constant from 1999 and 2015.Some UAs therefore remain clusters of highincome households.One of our results is therefore that macro-scale segregation is a significant component of national segregation.
If we now focus on segregation within UAs in France, we note that this component of segregation has risen sharply since 1999.In particular, income divides between urban types are much more prominent in 2015 than in 1999.The between-UT (within-UA) H R has increased in level and now represents almost 9% of total segregation (against only 5% in 1999).This phenomenon is especially pronounced for the bottom 10%.As shown in Table 1, the relative share of low-income people in exurban areas has fallen since 1999.Overall, a social division is beginning to emerge between urbanised areas (especially central cities) where the bottom 10% are increasingly represented and the outer fringes where they are disappearing.The UT is a key factor to understanding the segregation of low-income households.We do not see such a large increase in the between-UT segregation of better-off households, especially for the top 10%.While there is indeed a movement of affluent households towards exurban areas (Table 1), this corresponds much more to a 'rebalancing' effect, a geographical homogenisation: the top 10% were over-represented in the suburbs or in the central cities in 1999.They are still over-represented, but less so as they start to join middle-class households in exurban areas.This mixing of intermediate and high-income households by UT explains the low level and quasi stability of the between-UT component of M 90% (from 5.86% to 6.88%).
Finally, the last two columns of Table 3 give the residual (micro) component of segregation at the LRU level (within-UA and UT).This residual component is quantitatively important (almost 70% of total H R segregation in 2015), and especially for low-income households, but changes relatively little, so it seems that the most noticeable changes in segregation in France relate to the between-UA and between-UT components.While local residential competition across neighbouring districts still accounts for the bulk of segregation, the important sociological changes concern longer distance mobility.French geography is changing on a relatively macro-scale with UAs that look increasingly similar and UTs more and more dissimilar.
We have proposed a macro/micro-breakdown of income segregation in France.However, the micro part deserves a more in-depth analysis.Segregation within UAs is increasing, according to most indices.But we would like to know which UAs or UTs are the most segregated.Table 4 measures the level of segregation for different UA size ranges: in small, medium-sized, large UAs and in Paris.We also decompose segregation into a between-UT component (across central city/suburbs/ exurbs of each UA in a given size range) and a within-UT component (within UA of a given size range).
Globally, segregation increases monotonically with the size of the UA and is, as expected, higher in Paris than in other UAs.These results are in line with those obtained by Courtioux and Maury (2020) who showed that school segregation increased continuously with the size of the UA.However, in small UAs, levels of segregation are far from being negligible and, interestingly, they rise relatively faster than in Paris or large UAs.For instance, segregation increased by 60% in small UAs against only 31.5% in Paris and 19.3% in UAs with more than 500,000 inhabitants.This higher level of segregation in Paris comes mainly from the middle and upper percentiles of the income distribution.Segregation of high-income households is between three and four times higher in Paris than in UAs of over 500,000 inhabitants (0.0902 in Paris against < 0.0251 in any other range of UAs).High-income households in the Paris UA are overwhelmingly isolated from other households, and such a degree of separatism of the richest is not observed anywhere else in France.
Income segregation in France: a geographical decomposition across and within urban areas 449

REGIONAL STUDIES
The results are much more startling regarding the segregation of low-income households.We provide evidence of a non-linear profile of M 10% segregation with the size of UAs.In 2015, M 10% segregation is weaker in small UAs, although not negligible compared with the other areasize ranges.Segregation peaks for large UAs between 500,000 and 10,000,000 inhabitants, but is higher in medium-size UAs than in Paris.This result confirms that one should not limit oneself to Paris and a few metropolitan areas when studying segregation in France.The isolation of low incomes is now a more pronounced phenomenon in medium-sized cities than in Paris.This separation of the poorest in medium-to-large UAs has been growing much faster than in Paris and seems to be spreading to small UAs where the M 10% index is growing more rapidly than anywhere else.
The analysis of the breakdown of segregation according to the UT provides additional elements to explain these phenomena.In small UAs, the central/suburban/ exurban division explains a very large fraction of the observed segregation, especially for low incomes.Moreover, the contribution of this component has increased significantly since 1999 (from 45.46% to 61.01% for small UAs) whereas it has remained low and relatively stable in Paris.In small and medium-sized areas, there is a tendency for middle-or high-income households to settle in exurban areas (leaving low-incomes living in the central cities or suburbs), thus reproducing a phenomenon that is already underway in large UAs.
In summary, Table 4 sheds new light on segregation in France: while in Paris the separation is mainly between very high income households and others (low and middle incomes who still live, to some extent, in the same neighbourhoods) and is fundamentally local, in medium and large UAs the separation between very low incomes and others (middle and high income) predominates and reflects a division according to UT.This trend seems to be spreading to smaller UAs.
Overall, by comparing the results in Table 4 with the previous ones, we show that segregation in France is relatively low, with only the levels of segregation in Paris being comparable with those evidenced in the United States (Reardon et al., 2018).In small cities, levels of segregation are almost negligible (see measures of H R for small UAs in Table 4).This is in line with the ecological model approach outlined in the conceptual framework section: the limited functional diversity of small towns explains the low level of segregation.The role of small and medium-sized cities in segregation only becomes significant on a more macro-scale.Indeed, national segregation is partly due to differences between UAs, and especially between UAs of different sizes, or between UTs (Table 3).Macro-segregation is related to the political economy of places with households sorting across jurisdictions or UAs according to the level of public services or other amenities (see again conceptual framework).The residential mobility of householdsparticularly the wealthiesttowards less urbanised or rural areas makes a significant contribution to national segregation.Segregation in France, although low, is undergoing major changes that can only be analysed on a relatively macro-scale, including small and medium-sized cities.
To confirm the role of UA size on segregation levels, we finally conduct a regression analysis.We collect the levels of segregation for all UAs.More specifically, we consider the within-UA levels of segregation in 2015 in each of the 762 UAs and regress it on some of the socio-economic characteristics of the UAs: their size, their composition (population share in the city centre, in the suburban areas, and exurban areas), the share of bottom and top 10% inhabitants, and a list of contextual variables.Income segregation in France: a geographical decomposition across and within urban areas All results are summarised in Table 5.Overall, the results of this analysis confirm those of the previous tables: even with covariates for the socio-demographic or geographical characteristics of UAs, we can still identify a strong impact of UA size on segregation levels.With the synthetic index H R , we show that segregation increases with the size of the UA.While we do not detect a difference between mid-sized UAs (between 20,000 and 100,000 inhabitants) and small ones (less than 20,000 inhabitants, our reference category), the differences are significant for large UAs (over 100,000 inhabitants).Segregation is about 1 point higher in areas with between 100,000 and 200,000 inhabitants, 2 points higher in areas with between 200,000 and 500,000 inhabitants, and almost 3 points higher in areas with more than 500,000 inhabitants (including Paris) compared with small UAs (less than 20,000 inhabitants).As expected, segregation is significantly higher in large UAs and this result is valid even though we control for socio-demographic factors potentially linked to levels of segregation (the share of social housinghigher in large cities, the level of educationalso higheror the unemployment rate).The share of high-income (top 10%) or low-income (bottom 10%) household also contribute significantly and positively to segregation.In contrast, the UT does not seem to affect segregation at the UA level.
Results with M 10% and M 90% also confirm those obtained in Tables 3 and 4. Segregation of low-income households has a reversed 'U'-shape according to the UA size.It peaks for areas with 200,000-500,000 inhabitants (1.5 points above small UAs) and decreases for areas with more than 500,000 inhabitants (about 1.2 points).Again, this result is preserved despite the strong correlation between M 10% and the low-income households share (low incomes are more segregated the higher their share in the UA).With M 90% , we do not detect a significant difference among UAs below 200,000 inhabitants, but segregation increases strongly above this threshold and is about 1.3 higher in UAs above 500,000 inhabitants.Finally, if we study the growth of segregation (DH R ), we show that it is higher in medium-sized areas than in large ones.This confirms our previous conclusion: since 1999, segregation is a phenomenon that is spreading to medium-sized UAs, and even to a lesser extent to small UAs.Only the smallest areas as well as rural areas seem to be partially immune to this process.

CONCLUSIONS
In this paper, we present the first comprehensive analysis of income segregation in France all over the country.Segregation is broken down by urban area (UA), size and First group of covariates is for the UA size (< 20,000 is the reference).% suburban and % centre are the shares of UA inhabitants (inh.)living in the suburbs or centre (% exurban is the reference).% bottom and top 10% are the share of inhabitants in the bottom or top 10% group in the UA.Sociodemographic attributes of the UA are included in contextual effects.Each cell delivers parameter estimates shown in parentheses.**5% significant, *10% significant.
urban type (UT) (central, suburban, exurban).Extending the analysis to the whole of France, and not only to the largest UAs, allows new stylised facts to be highlighted.First, a significant, albeit decreasing share of the segregation in France is due to differences between UAs and not within them.This macro-component of segregation has important consequences from a policy perspective.Local integration policies led by metropolitan authorities are likely to fail, as they could reinforce the gaps across UAs because of selective residential mobility, while attempting to reduce segregation within UAs.This observation advocates larger scale (national, or Europeanbuilding on EU Cohesion Policy) policies for the revitalisation of small towns or rural areas.Several studies insist on the broad range of motivations to migrate to low density areas (school vitality, Lehtonen, 2021; service amenities, Elshof et al., 2017;or employment, Champion, 2002) some of them could be the target of investment policies.Second, a significant share of the segregation (especially low-income) is observed in small and medium-sized UAs, and not only in the very large areas usually studied (Paris, Lyon or Marseille).This calls for a change in the political and academic scale of segregation analysis.Finally, exurban areas have undergone profound changes in the last 20 years and they increasingly contribute to the segregation of affluent households.However, these municipalities at the outer fringes of urban units have often been forgotten in the main policy schemes to promote social mixing in France, and in national public housing policies in particular.It now seems necessary to reconsider these exurban areas as major concerns in terms of residential segregation.

DISCLOSURE STATEMENT
No potential conflict of interest was reported by the authors.

NOTES
1.The income refers to gross income reported to the tax authorities before taxes and transfers.Censoring on top incomes is limited as tax statements are comprehensive.Some income may be generated abroad, however, but since we aggregate income into classes, this will not affect much high incomes that already belong the top 10% even without income not reported in France.2. We use the EUROSTAT scale to calculate the number of consumption units: 1 unit for the first adult in the household, an additional 0.5 points for each person over 14 years, and an additional 0.3 points for each person aged 14 years or less.3.There are more than 300,000 LRUs in France.4.Even in small LRUs we have 100% coverage rate with exhaustive individual data (only the exact X-Y geolocation is not available).

Figure 1 .
Figure 1.Urban areas in France with a breakdown between urban units (central city and suburbs) and exurban areas.
Note: A total of 19.06% of French households live in the Paris UA in 2015; 6.74% of them have an income lower than the national first decile in 2015.inh., Inhabitants.

Table 2 .
Income segregation: whole of France.

Table 5 .
Regression analysis of the urban area (UA) size and composition on segregation.: We run regressions with four different endogenous variables (H R , M l0% and M 90% in 2015, and ΔH R the growth of H R between 1999 and 2015) at the UA level. Note