A Scenario for the New Official French Urban Areas Zoning

A scenario for the new official French urban areas zoning

Marie-Pierre de Bellefon

Paper prepared for the 16th Conference of IAOS OECD Headquarters, Paris, France, 19-21 September 2018

Session 3F, Thursday, 20/09, 10h30: Urbanisation and sustainable city

Marie-Pierre de Bellefon [email protected] INSEE - French National Institute for Statistics and Economic Research

A scenario for the new official French urban areas zoning

Prepared for the 16th Conference of the International Association of Official Statisticians (IAOS) OECD Headquarters, Paris, France, 19-21 September 2018

This Working Paper should not be reported as representing the views of INSEE. The views expressed are those of the author(s).

ABSTRACT

How to harmonize the definition of French urban areas with international standards, while still precisely describing France’s unique territorial characteristics? Answering this question is the purpose of this article, which proposes a scenario for a new French urban areas zoning. Our methodology extends OECD’s Functional Urban Areas definition to analyse thoroughly the French urban system. It distinguishes two categories of Urban Areas and allows to detect secondary centres and analyse their interaction with main centres.

Keywords: urban area definition, French zoning, functional areas, monocentric model, degree of urbanisation.

1. INTRODUCTION

As defined by the French National Institute for Statistics and Economic Research (INSEE), statistical territorial zoning aim to go beyond the logic of administrative zoning, in order to have zoning adapted to economic and social issues. The economist Gilles Duranton (Duranton, 2015) highlights four arguments justifying the interest of statistical zoning. Historically, when cities expanded, they used to integrate neighbouring municipalities. In many countries, this process has stopped, mainly because of administrative, fiscal or political reasons. Cities’ administrative borders thus now delineate only the historical urban core and are not representative of the whole urban extension. In response to this finding, INSEE defined, as early as 1954, statistical Urban Units. Urban Unit’s definition has not changed since 1962: it is based on building’s continuity (no more than 200 meters between buildings), and adds a total population criteria (more than 2000 inhabitants). This morphological definition, although useful to determine cities physical extension, soon appeared insufficient to analyse the intertwining of rural housing and the urban way of life that increased with the parallel development of automobiles and the single-family homes (Le Jeannic, 1988). Indeed, the second argument in favour of statistical zoning, is the need of a territorial breakdown adapted to the study of the interacting network that commuters, companies and individuals form around cities. This network is associated with all kinds of economic ties between neighbouring municipalities. Since administrative units such as municipalities most often do not constitute autonomous functional units, an economic shock or a public policy targeting a given municipality can have diffuse spillover effects on neighbouring municipalities. Considering how difficult it is to precisely anticipate and evaluate these spillovers effects, it is easier and more effective that the public policy directly targets a coherent economic unit. Lastly, confining a city's analysis to economic and social parameters measured within its administrative boundary can present it in an unfavourable light and have a negative influence on investors' decisions. Parr, 2007 gives the example of former industrial cities like Nottingham, whose performances in term of unemployment rate, education level and public health clearly improve when considering the whole urban area instead of the administrative city. Taking all these considerations into account, Insee proposed in 1962 a functional definition of cities, complementary to that of Urban Units. This definition evolved until the actual version, published in 2010 and entitled “Zoning into Urban Areas”. This zoning aims at delineating the city’s influence area. Urban cores are defined as Urban Units with more than 1500 workers, and their periphery consists in all municipalities sending more than 40% of their workers to the core or to a municipality already aggregated to a core.

In line with recent developments in the literature on the definition of urban areas (Dijkstra, 2018; Henderson, 2018; Veneri, 2018), Insee has initiated a complete redesign of its urban area zoning. This article presents and justifies a new zoning methodology, which aims at addressing the multiple challenges faced by a National Statistical Institute when trying to define statistical urban areas.

The first of these challenges is to define what is to be measured under the term of “city’s area of influence”, and which variables are best suited to this objective. Choices must be made such as whether a urban core is predetermined – and, if so, thanks to which criteria - or whether it is endogeneoulsy determined by commuting patterns. The advantages and drawbacks of using commuting data as a measure of city’s influence on its environment also have to be assessed. Lastly, this reflection must take into account the

positioning of Urban Areas in relation to other Insee study zoning. Urban economics theory helps us to answer these questions.

Our second challenge is to reconcile two requirements. One of the main objectives of Insee’s redesign of Urban Areas is to make them coherent with Eurostat-OECD’s Functional Areas, whose use is spreading internationally. Yet Functional Areas are defined for the purpose of making some international comparisons; they do not describe the French urban system with the level of accuracy expected by French users. We therefore propose some extensions of the international method that allow a more thorough description of the national territory: two categories of Urban Areas are distinguished, and secondary centres are identified, while the method remains simple enough to be quickly understood by the zoning’s users.

Lastly, one important issue of study zoning published by National Statistical Institutes is their comparability over time. Our methodology thus allows to proceed to some backward projection, and therefore to study the evolution of the French periurbanization, the intra-urban coherence, and the validity of some of the major predictions of regional and urban economics theory.

Although the outlines of the methodology are based on principles published by Eurostat and the OECD, the efforts to harmonize precise description of the national territory and international comparability contribute to the literature about the definition of urban areas. The identification of secondary centers also gives a novel insight into the relations between systems of cities. Our hope is that this methodology can be useful to other National Statistical Institute facing the same challenges.

The remainder of this paper is organized as follows. Section 2 situates the current French Urban Areas zoning among an international comparison of zoning practices. Section 3 provides some theoretical background for the new scenario and the concrete methodological consequences. Section 4 presents the first results. Lastly, section 5 concludes.

2. FRENCH AND INTERNATIONAL CONTEXT 2.1 THE FRENCH URBANIZATION CONTEXT

In order to propose a zoning methodology adapted to the French specificities, it is important to begin with an analysis of the French urbanization context.

During the last quarter of the 20th century, populations have increasingly gathered around large urban centres (Roux, 2008). Charmes, 2015 describes this sub-urbanisation movement, not as an urban sprawl, but as a “fragmentation of the city”. Indeed, peri-urban population work in a big metropolis, but distinguishes itself from suburban population by the fact that it crosses green spaces before arriving at its pavilion complex. This phenomenon of “leap frog development” is much more marked in France than in the United States or in Great Britain. It is accomplished in two steps: first the central city’s growth increase the demand for housing in outlying villages. This demand is welcomed by local mayors, which see it as a way to revitalize their municipality. Then, when newcomers become a majority, the desire to preserve the living environment dominates and the municipality blocks the extension of its urban spaces. Other municipalities, further from the central city, then engage in the early stages of peri-urbanization. Opinions differ as to the continuation of this phenomenon. Some argue that commuting costs could restrict the peri-urbanization; others argue that

secondary centres emerge, which become relays for the peri-urban extension. According to Charmes, secondary centres are only growth drivers for the major pole, and links between them remain an exception. Veltz, 2010 speaks of a “rurban nebula” which attracts only activities which have been rejected outside of the heart of the urban agglomeration because of their high land consumption or their low added value. These areas maintain a strong dependence on the main pole. One of the objectives of the zoning into Urban Areas is to help researchers to analyse the French Urbanization phenomenon, and to have access to concrete elements to help them to validate or to reject some of the above cited hypothesis. The analysis of secondary centres, their relations with the main centre and their own attractiveness seems to be a promising area of work to analyse the French phenomenon of urbanisation.

2.2 THE ZONING INTO URBAN AREAS: ITS USES AND LIMITS

As mentioned in the introduction, Insee produces a morphological zoning, Urban Units, which aims at distinguishing urban municipalities. In order to be considered as urban, a municipality must have more than half its population in a continuous built-up area which entails more than 2000 inhabitants. The methodology hasn’t changed since 1962. The actual zoning is based on legal populations from the census 2007, and localized population from a 2010 fiscal database. 2293 urban units represent 19% of the territory and host 77,5% of the population. Although it is supposed to be used only for statistical purposes, this zoning serves in practice as a decision aid tool that has an impact over municipalities’ endowment. It is therefore lined with political issues. One of the critics addressed to this zoning, is that it would lead to an overestimation of the urban territory and population. Indeed, a small urban spot is enough for the commune to be considered as entirely urban, regardless of its morphology. The second critic is that it is a binary zoning, which does not define different urbanization degrees. Parr, 2007, underlines that this kind of zoning is an interesting perspective for addressing land use issues, but often fails in representing on an adequate scale the labor market, the real estate market and the system of procurement services.

In order to describe more thoroughly the intertwining of territories and the influence of cities over their environment, Insee also produces Urban Areas. Centres are Urban Units which entail more than 10 000 jobs (for big urban areas), between 5000 and 10 000 jobs (for medium urban areas) or between 1500 and 5000 jobs (for small urban areas). Peripheries are municipalities where at least 40 % of the resident employed population works in the centre or in a municipality already aggregated to the centre. This iterative algorithm, sometimes called “snowball effect”, is justified by the fact that employment centres that are not located in the principal centre but in its suburb still have to be taken into account in the computation of the city’s influence area (Le Jeannic 1997). This phenomenon of firm’s decentralization is especially important in the United States: according to Glaeser, 2001, less than 10% of US citie’s employment is concentrated within 5 kilometers of their centre. The last category of the zoning: multipolarized municipalities, are those which have more than 40% of their resident population working in urban areas, without reaching this threshold with one urban area in particular. The 2010 version of this zoning is based on data from the national census 2008. 792 areas structure the French territory and 85% of the population lives there. More precisely, 82.6% of the population live in one of the 241 big urban areas ; 3,6% in one of the 131 average urban areas and 4% in one of the small urban areas. See Figure 1. This zoning is used as a territorial breakdown for local studies produced by Insee in partnership with regional administrations, but also for studies produced by other entities such as Urban Agencies. It acts a decision aid tool for local public policies. Lastly, the zoning into Urban Areas serves as a reference zoning for academic studies: either studies about the nature of rural and urban

spaces themselves (Bretagnolle 2015, Mora 2008) or urban economic studies, that need a relevant zoning (Combes 2012, 2013, Cailly 2010).

Although widely used, the zoning into Urban Areas 2010 faces numerous critics. First of them: the iterative aggregation algorithm is difficult to explain and to understand, and its consequences are difficult to analyse, whereas the simpleness of the methodology is one crucial point for an official zoning. A more technical argument about the use of this algorithm is raised by Chalonge, 2012: the expansion of urban areas is not always due to the the expansion of the centre’s direct influence area, but sometimes to that of secondary centers that surround cities, without it being possible to distinguish the two phenomena. The statistical method would therefore be responsible for an overvaluation of the periurbanization. Julien, 2007, adds that only half of the municipalities that became periurban1 between 1990 and 1999 present the characteristics of a sprawl (population growth due to positive net migration and above the national average). Annex A presents some tests of the sensibility of this zoning to the choice of threshold of the iterative algorithm.

Figure 1 : French zoning into urban areas (ZAU 2010) The second main critic of this zoning is the choice of the thresholds that distinguish the different urban areas. There exist indeed great disparities in the economic and demographic characteristics of the three categories of urban areas, and also great disparities between the big urban areas themselves.

1 the periurban space being defined as areas under the influence of large urban areas.

Lastly, the fact that this zoning doesn’t characterize rural areas has led some to call Insee “the rural gravedigger”. In order to take into account both these critics and the recent literature dealing with the question of the definition of cities, Insee has initiated a reflexion, in order to produce a new urban area zoning in 2020. The guidelines for this zoning is that it should be coherent with international standards, while at the same time precisely and accurately describe France’s territorial characteristics, and maintain some consistency with current zoning.

2.3 CURRENT INTERNATIONAL PRACTICE AND LITERATURE

Zoning methods that aim at analysing cities’ influence over their environment differ from each other according to three main elements.

First, an appropriate variable to connect cities to their peripheries has to be chosen. The use of commuting data appears to be a consensus among national statistical institutes, see for example british Travel to Work Areas, american Standard Metropolitan Areas or japanese Urban Employment Areas (Coombes, 2008; OMB, 2002 ; Kanemoto, 2005). Yet, in France, the question about the employment municipality was first introduced in the 1896 census to create a stock object assigning the population to the municipality of work and no longer to that of residence (Commenges, 2017). Then it was used in the 1950s to analyse the imbalance between the location of firms and that of individuals, and to feed the statistical system of traffic engineering. It is only from the 1970s that it began to be used as a variable structuring the territory. Commuting data constitute indeed the only indicator of interdependency between urban and periurban that is known on a simple, objective and exhaustive way. Commenges, 2017 warns about the need to keep in mind that the commuting variable produced by the national census concerns only the active population, whereas, as described by Coombes, 2004, daily journeys are multiple and multi-directional: flows are not only directed towards the place of work, but also towards schools and shops. Using commuting data for delineating urban areas is consequently based on the assumption that the spatial organisation of work is the primary vector for structuring space. Yet this choice is not only due to data availability: considering urban areas as integrated labour markets is also consensual among economists. Indeed, the literature about agglomeration economics consider three mechanisms at play in metropolitan areas. First: sharing of external, indivisible goods that attract consumers and companies (airports for instance) and which also lead to a greater variety of products for the consumer and a greater number of potential employees for companies in case of a positive demand shock. Secondly, matching: the bigger number of workers and companies allow a better match between them. Lastly, cities increase their productivity thanks to a better knowledge diffusion, between workers and between companies. Among these mechanisms, measuring the geographical extent of the gains due to the variety of available products is very difficult (Holmes, 1999), as is the measure of gains due to knowledge sharing (Charlot, 2004). This is why it seems more relevant to focus on the fact that cities benefit from being integrated labor markets (Duranton, 2015), and to define them using commuting data.

The second element that distinguishes urban area zoning methods is the definition of a core towards which commuters travel: does this core has to be ex-ante defined? If yes, which criteria are to be used? ONS Travel to Work Areas or Insee and Istat’s Employment Areas use only commuting patterns to define urban areas. These zoning aim at maximizing the number of workers living and working in the same area. More than the influence of a city over its surrounding, these zoning delineate integrated labor markets, they are designed

to study their functioning and cover the entire territory. Both the ONS and Insee proceed to some manual ex-post adjustments of these areas, in order to take into account some local constraints (Coombes, 1982 ; Aliaga, 2015). Duranton’s Metropolitan Areas are also determined endogenously thanks to an algorithm that aggregates municipality A to municipality B if the number of commuters from A to B is above a certain threshold. Duranton argues that this kind of algorithm avoids the introduction of an arbitrary ex-ante criteria to define cores. In the case of Colombia where he applies this algorithm, the algorithm systematically detects the most populated city as the core, and there is no need for ex-post adjustment of anomalies. Still, most of the zoning used by statistical institutes and researcher predefine a core, to which municipalities are aggregated. OECD’s Functional Urban Areas are based on Cities which are defined thanks to a total population and a population density criteria. US OMB’s Metropolitan Areas’ cores are based on contiguous census blocks which have a very high density of population and are surrounded by census blocks with a slightly lower density of population. A criterion of total population is also added. In Japan, Kanemoto and Kurima base their Urban Employment Areas on cores which are defined thanks to population density, total population and the presence of some public, industrial, educational or leisure equipment. Parr, 2007 proposes and compares different interesting city definition with various aggregation criteria. The Consumption City aggregates to a central city based on building continuity, all municipalities for which the consumption made by its inhabitants inside the central city is more than two times higher than the sum of consumptions made by its inhabitants in the central city and in their own municipality. This functional zoning exploits the fact that larger cities offer a larger variety of goods and services, so that commuters will make part of their expenses in the central city where they work. This kind of method is interesting for the study of issues concerning marketing and distribution. Secondly, the Employment City gathers municipalities where more than 50% of jobs are directly or indirectly linked to the city. Examples of jobs indirectly linked to the city are those generated by the commuting (services to individuals, transportation…) This kind of zoning is accurate for the study of public transportation and the local economic development. Lastly, the Workforce City is based on level lines such that the total number of jobs in the central city equals the total number of jobs inside the level line. This zoning reflects the employment demand of the central city towards its periphery. This perspective seems interesting for studying the labour market, but also the real estate market and the infrastructure organization. Parr’s city definitions have the advantage of distinguishing different methods adapted to specific problematics, yet they haven’t been yet implemented on a large scale, mainly because of the difficulty of collecting the necessary data.

Lastly, zoning methods based on commuting patterns differ according to the type of aggregation algorithm they use. This algorithm can be either iterative or hierarchical. The iterative approach consists in aggregating a municipality A to a municipality B if more than a certain threshold of workers living in A commute to B. Once this first iteration has been made, municipality C is aggregated to the city A+B if it sends more than the defined percent of its workers to the aggregated city A+B. Duranton, 2013, justifies the use of this method by the decentralization of jobs outside the central city and the fact that commuting flows are gravitational (the number of commuters decreases with distance). Yet this method is less coherent with the theoretical framework of the monocentric model (see below) which makes it harder to explain and interpret. French Urban Areas or american Metropolitan Areas are based on this algorithm, with a threshold of 40%, respectively 25%. The hierarchical algorithm aggregates a municipality A to a municipality B if more than a certain threshold of workers living in A commute to B. If A exceeds the given threshold with more than one municipality, it aggregates with the one to which it sends the higher percent of commuters. This method is used by OECD-

Eurostat’s functional urban areas, with a 15% threshold, but also for Japanese urban areas with a 10% threshold (Kanemoto, 2015).

3. THEORY

As underlined by Parr, 2007, to each zoning methodology corresponds a specific issue that the zoning helps answering. France produces Urban Units which analyse the location of population, and Employment Areas which delineate integrated job markets. For the new scenario of French zoning into Urban Areas, our goal is to measure the extent of the city’s influence on its territory. Urban economics theory gives us some insight into the signification of some key economic and demographic variables, and how we could use them for defining Urban Areas.

3.1 THE MONOCENTRIC MODEL

Since the pioneering studies of Von Thünen, 1930, the economic literature considers that prices of land and houses are an accurate variable for summarizing the economic impact of cities. Prices in a location are considered to be determined by its accessibility. Yet accessibility differences between locations are affected by the choices of localization of firms and workers, which are themselves correlated with land and housing prices. These multiple feedback effects add to the complexity of the analysis of the spatial equilibrium which determines land and housing prices. The major theoretical model used by economists to tackle this question is the monocentric model first developed by Alonso, 1964, Mills, 1967 and Muth, 1969. Accessibility is considered only in terms of access to a job. All jobs are located in the central business district (CBD) and all inhabitants commute daily to the CBD. Workers and consumers choose their location at distance x from the CBD. Working at the CBD provide the individual with a wage w. Commuting to the CBD from residence at distance x from it implies a commuting cost τx. Income is used to pay commutes, housing consumption and purchasing goods. Consumer maximize their utility U(z,h) where h is housing consumption and z the composite good consumption, under the budget constraint : w-τx = R(x)h + z R(x) is the housing price. At the spatial equilibrium, no worker wants to change location, the utility is the same at any point of the city. Thanks to these approximations, the monocentric model allows to predict some very general phenomenon: When moving further from the CBD, (i) housing and land prices decrease, (ii) the size of dwellings increases, (iii) the density of construction and the density of population decrease. More quantitatively, the model predicts that the increase in commuting costs as one one moves further away from the CBD is exactly compensated by a decrease in housing prices and an increase in housing consumption. This model also allows to quantify the impact of demographic variables on the city’s extent. Indeed, it considers that land can also be used as an input to an activity that does not require commuting to the CBD, agriculture for instance. Landlords allocate land to the highest bidders: 휓(푥, 푢̅) is the highest price people are ready to pay for housing. See figure 2, from Combes 2016.

Figure 2 : equilibrium land price

The model predicts that the city fringe xf decreases with τ’(x) the commuting cost per unit of distance ; it increases with the share of housing in consumers' preferences and it increases with the wage at the CBD. One last interesting prediction is that the total population of the city increases with the land-rend differential between the CBD and the city fringe, and decreases with commuting costs: 휓(0,푢̅)−푅 푁 = 푎 휏

The monocentric model has been developed to include various modifications of the simplifying assumptions. De Bartolome, 2003 or Baum-Snow, 2007 prove that differences in local amenities and heterogeneity of access to the transport network can disrupt the monotonic decrease of housing prices with distance from the city center. See figure 3, from Combes 2016.

Figure 3 : influence of amenities on city shape

Fujita, 1980 allow firms to choose their localization in the whole urban area in order to optimize their budget constraint. In their model, the real estate gradient still decreases with distance from the CBD, but there can exist local pics at some distance from the center, correlated with the distance to these secondary centers.

3.2 CONCRETE CONSEQUENCES FOR THE ZONING INTO URBAN AREAS

It appears from the economic literature, that the shape of the city is not only determined by distance to an employment center : distance to amenities matters as well, and the nature of amenities is very diverse and difficult to assess. We don’t have access to detailed land and housing prices, yet population density is a key parameter, easy to measure and maximum at the locations which are the most attractive for residents. Total population reflects the local economic configuration and allows to distinguish between different categories of cities. A combination of population density and total population would therefore allow to delineate cores, considered as areas which attract residents. Contrary to the actual Urban Area definition, this definition doesn’t take into account the number of jobs of the core. Indeed, we have seen in 3.1 that residents can choose to live in a place with valuable amenities, independently from the amount of jobs located directly in this place. Of course, the combination of amenities and a good transportation connexion to the central business district increases the attractiveness of places for workers, yet this definition allows to take into account a place’s attractiveness for both workers and non-workers.

Secondly, we’ve seen that commuting costs have an impact over land prices, which impact the location of both workers and non-workers and thus which impact directly the city fringe. Moreover, commuters might make one part of their expenses in the core, which has an impact over the economy of their residence municipality. We therefore propose to keep on with the idea of using the share of residents which commute to the core to determine municipalities which are under the influence of the core. In order to avoid spillover effects difficult to measure and to interpret, the commuting has to be to the core itself (hierarchical algorithm). With this kind of algorithm, we know exactly to which city the flow is directed, and which municipalities are only crossed by this flow. On the contrary, with an iterative algorithm, a municipality can send a high percent of commuters not to the center, but to the neighboring municipality which has already been aggregated to the center. Yet the economic impact of this flow of commuters on this particular neighboring municipality will be difficult to asses because it will be impossible to know wether the commuting flow is directed towards it or towards the center. In the pursuit of previous reflections, it seems also important for analysing the interweaving of cities, to allow the possibility of a nested zoning. That is, the possibility to identify secondary centers inside the area of influence of primary centers, and to delineate the area of influence of these secondary centers. Not only is this a recurrent request from the users of the zoning into urban areas, but it is also coherent with the polycentric extensions of the monocentric model where local pics of attractiveness can exist in the periphery of the main pic. Two cores that exchange a high amount of commuters also have to be considered as part of the same polycentric area, because of all the economic exchanges correlated with these flows.

3.3 EMPIRICAL METHOD

For the reasons explained above, we propose to delineate peripheries with a hierarchical algorithm. In order to tend towards a harmonization with european criteria, we choose a 15% threshold. It is interesting to note, that the extent of peripheries with a 15% threshold and a hierarchical algorithm is quite similar to that obtained with a 40% threshold and an iterative algorithm. See Annex B for a comparison between the Zoning into Urban Areas 2010 and the actual method.

For defining cores, we propose to use Eurostat’s degree of urbanisation (DEGURBA). Its principles are described in figure 4. Raster cells of 1km2 are classified using criteria of population density an contiguous cells are aggregated, ignoring administrative borders. Aggregates of contiguous cells of more than 300 inhabitants/km2, holding more than 5000 inhabitants are named urban clusters. Aggregates of contiguous cells of more than 1500 inhabitants/km2, holding more than 50 000 inhabitants are named urban centers. In order to better describe the low density areas specific to the French territory, Insee has added another level to this classification : aggregates of contiguous cells of more than 25 inhabitants/km2 holding more than 300 inhabitants are named intermediate rural cluster. Municipalities where more than 50% of the population lives in an urban center are considered as densely populated areas ; those where more than 50% of the population lives in an urban cluster are intermediate density area ; for the French case, those where the percent of population outside any cluster (either urban cluster, urban center or intermediate rural cluster) is less or equal than 50% are classified as low density area and municipalities where the percent of population outside any cluster is more than 50% are classified as very low density area.

Figure 4 : the degree of urbanisation - OECD Eurostat Thanks to the use of grid cells, this zoning is based on a precise morphological approach that fits to the location and characteristics of population. The grid is common to all european countries, which allows some easy comparisons. It is often used in France to characterise low dense areas more precisely than with the

urban units zoning. This zoning is the basis for OECD-Eurostat’s cities, which are defined for all OECD countries and used for international comparisons. Cities consist in contiguous densely populated municipalities, see figure 4. One of the guidelines for the new scenario of zoning into Urban Areas is to ensure a certain coherence with OECD’s cities based on densely populated areas. Yet in France there are only 62 OECD-cities, to be compared with 241 large urban areas, 131 average urban areas and 420 small urban areas in the actual French zoning. It is thus necessary to extend the core definition. If we extend cores to intermediate density areas, it results in cores that are too extended to allow an accurate analysis, especially in coastal regions. See figure 5 where the commuting areas with a 15% threshold and an iterative algorithm have been added. Yet in 2017, Dijkstra has presented an “extended version” of the degree of urbanisation classification: it considers clusters of contiguous 1km2 cells that contain more than 1500 inhabitants per km2 (same density as in the urban centers of the DEGURBA), but the total number of inhabitants in the cluster has to be between 5000 and 50000 inhabitants. As will be shown in the following part, this definition seems to be a good compromise for analysing the French case.

Figure 5 : test of cores defined as intermediate population area

A last point raised by zoning users is the question of nomenclatures. Some fear that names coming from the common language could lead to an overinterpretation of the zoning results. That is why, in a first time, we propose to use names that describe the statistical content of the zoning. The method is summarised in figure 6.

Figure 6 : summary of the methodology

4. FIRST RESULTS

Figure 7, 8, 9 and 10 present the results of this new methodology, applied to French data (fiscal population 2010 redressed by the census 2013 for the definition of the cores, and census 2013 for the commuting data).

Figure 7 : new scenario of zoning into Urban Areas - France

Figure 8 : new scenario of zoning into Urban Areas - Ile de France

Figure 9 : new scenario of zoning into Urban Areas - Center

Figure 10 : new scenario of zoning into Urban Areas - South

In order to illustrate the new methodology, we chose three French regions with very different characteristics. Ile de France is a very dense region, very complex to analyse because of the attractive power of Paris, whose influence dominates the whole region. Yet, contrary to the previous Urban Area zoning method (map in Annex B), the new scenario allows to identify some secondary centers and their area of influence (like Etampes or Rambouillet) which are also under the influence of the main center : Paris. The secondary centers (Medium Populated High Density Areas) which do not have their own area of influence are areas which attract residents, probably because of high amenities and a good connexion to the transportation network, but which are not important employment centers : none of their neighboring municipalities sends more than 15% of commuters to them. This detection of attractive residential areas is one key element for the analysis of cities inter-relations. The other illustration is French central region. This region allows an easier analyse: attractive centers are more distant from one another and the urban structure corresponds more to the classical monocentric analysis. Lastly, the south of France is also a complex region, with a succession of high density areas along the mediterranean coast, and along the Rhone corridor. Yet each core’s area of influence seems clearly identifiable, and corresponds to the local economic situation - according to local experts. Table 1 presents some descriptive statistics, and in Annex B is the comparison with the actual zoning into Urban Areas.

Table 1 : descriptive statistics of the new zoning scenario

5. CONCLUSION

The new scenario of zoning into urban areas is a microfounded method, based on urban economic’s essentials. It is also a simple method, easy to understand and interpret, with only four categories. This method is harmonized with international latest advances and yet describes accurately the French territory. Yet before deciding between this new methodology and a continuation of former urban area zoning methodology, many points still have to be explored. On a statistical point of view, robustness checks testing the sensibility of the results to the choices of thresholds have to be performed. On a more economical point of view, it is important to perform to retropolations that will be very useful to our users. The study of the intra urban coherence of the new cities will also be an important point to analyse. Lastly, we still have to compare the measure of cities extension obtained with this zoning with the one obtained with the previous method.

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7. ANNEX A : ROBUSTNESS CHECKS

In order to test the zoning robustness to a change of the commuters’ threshold in the iterative algorithm, we simulated nine different thresholds. According to results presented in table 2, the higher the threshold, the smaller the extension of the periphery. Figures 11, 12, 13 illustrate this phenomenon.

Number of municipalities per category of the ZAU 2010 Commuters’ threshold 111 112 211 212 221 222 30% 3255 16 539 447 1 541 869 1 475 32,5% - 15 382 - 1 298 - 1 139 35% - 14 008 - 1 067 - 889 37,5% - 12 726 - 853 - 694 40% 3255 11 527 447 673 869 519 42,5% - 10 308 - 551 - 429 45% - 9 022 - 379 - 294 47,5% - 7 814 - 256 - 228 50% 3255 6 545 447 192 869 156 Table 2 : number of municipalities belonging to each category of the ZAU, according to the commuters' threshold 111 Big Urban Areas : centers 112 Big UA : peripheries 211 Medium Urban Areas : centers 212 Medium UA : peripheries 221 Small Urban Areas : centers 222 Small UA : peripheries

Several methods and indices allow to quantify the differences between two maps. The first one is the percent agreement. This statistic is obtained by dividing the number of municipalities belonging to the same category in the two maps, by the total number of municipalities. Although intuitive, this statistic is biased, because it considers maps with few categories, or categories unevenly distributed throughout the territory, as more similar than maps with many categories, well distributed in space. The Kappa statistic adjusts the percent agreement in order to take into account the percent agreement that could be expected, given the total area occupied by each category.

The Kappa statistic is based on a contingence table. This table describes to which extent the distribution of the categories of map C is related to the distribution of categories of map C’. Let 푋 be a finite set of geographical units, of cardinal |푋| = 푛 that can be aggregated to define cities according to different zoning. A zoning 퐶 is a set of {퐶1, … , 퐶퐾} disjoints subsets such that ∪푘 퐶푘 = 푋. Let’s consider that there is the same number of categories : 퐾 in the two zoning. ′ Let 푛푖푗 = |퐶푖 ∩ 퐶푗 | be the number of geographical units that are simultaneously in the two subsets 퐶푖 and 푛 퐶 ′ and 푝 the equivalent brought back to a proportion of the total number of geographical units: 푝 = 푖푗 푗 푖푗 푖푗 푛 퐾 Let 푛푖. = ∑푗=1 푛푖푗 be the total number of geographical units that belong to the subset 퐶푖 and 푝푖. the 푛 equivalent brought back to a proportion of the total number of geographical units: 푝 = 푖. . 푖. 푛

퐾 Let 푛.푗 = ∑푖=1 푛푖푗 be the total number of geographical units that belong to the subset 퐶′푗 and 푝.푗 the 푛 equivalent brought back to a proportion of the total number of geographical units: 푝 = .푗 . .푗 푛

Table 3 : contingence table of zoning C and C' Based on the contingence table, many statistics can be calculated. 푃(퐴) : the percent agreement is the sum of the table’s diagonal elements 퐾

푃(퐴) = ∑ 푝푖푖 푖=1 P(E) : the expected percent agreement depends upon the spatial distribution of the zoning categories.

푝푖.∗ 푝.푖 is the probability that two units belong to the same category simply by chance.

퐾

푃(퐸) = ∑ 푝푖. ∗ 푝.푖 푖=1

The Kappa statistic corrects the percent agreement P(A) of what could have been expected simply by chance.

푃(퐴) − 푃(퐸) 휅 = 1 − 푃(퐸)

The thresholds generally used are detailed in table 4.

Figure 11 presents the values of the Kappa statistic when comparing the actual ZAU with simulations where the percent of commuters used to determine the municipalities that belong to a center’s periphery has been changed. Logically, the closer the threshold is to 40%, the closer the index is to 1. Two facts are particularly interesting: first there is a symmetry around the 40% threshold. The zoning obtained with a 30% threshold is as different from the official zoning as the zoning obtained with a 50% threshold. This confirms the intuition we could get from table 2 where the number of municipalities belonging to peripheries decreases monotonously when the threshold increases, and from figures 12 to 13 where the progressive extension of the periphery is visible. This monotonicity is inherent to the iterative nature of the algorithm. Secondly, the kappa statistic shows a relative robustness to a change of the aggregation threshold. Indeed, except from zoning obtained with a 30% and a 50% threshold which show only a “strong agreement” with the official zoning, all the simulations exhibit a kappa higher than 0.8, which attests for a “nearly perfect agreement”.

Yet the Kappa statistic is only one indicator based purely on the distribution of zoning’s categories. It would be interesting to enrich the analysis with a comparison of demographic and economic descriptive statistics associated with the different zoning simulations.

κ Interpretation < 0 Disagreement 0.0 – 0.20 Very weak agreement 0.21 – 0.40 Weak agreement 0.41 – 0.60 Moderate agreement 0.61 – 0.80 Strong agreement 0.81 – 1.00 Nearly perfect agreement

Table 4 : interpretation of Kappa coefficient

Figure 11 : kappa statistic according to the threshold of commuters used in the ZAU aggregation algorithm

Figure 12 : robustness check to a change of commuters' threshold - Ile de France

Figure 13 : robustness check to a change of commuters' threshold - Center

8. ANNEX B : COMPARISON BETWEEN 2010 ZONING AND NEW SCENARIO

Table 5 : intersection between categories of the ZAU 2010 and the new scenario (number of municipalities)

Table 6 : descriptive statistics of the new zoning scenario

Table 7 : descriptive statistics of the ZAU 2010

Some first elements of comparison between the ZAU 2010 and the proposed new scenario can be learned from table 5, 6 and 7. 97% of high populated centers and 74% of medium populated centers of the new scenario were big urban areas in the ZAU 2010. Only 11% of the municipalities belonging to ZAU big urban areas are outside the new scenario. The new scenario thus allows to distinguish two categories inside the former big urban areas, which responds to a critic of the ZAU saying that the category of Big Urban Areas was so large that it hid many disparities between urban areas. Centers of medium urban areas of the ZAU represent 9% of the new scenario’s medium populated centers, but 65% of medium urban areas and 87% of small urban areas of the ZAU are not characterised in the new scenario. The new scenario nevertheless represents 79% of the French population (versus 95% for the ZAU 2010). The new scenario identifies 123 municipalities as secondary centers : medium populated centers belonging to the commuting area of a high populated center. Some of them have a commuting area, other don’t, which meets the explanations of the main part of the article : some areas can be attractive for residents because of many amenities, and still be under the main influence of a bigger center for the commuting patterns.

Figure 14 : cartographic comparison of the ZAU 2010 and the new zoning scenario – Ile de France

Figure 15 : cartographic comparison of the ZAU 2010 and the new zoning scenario - centre

Figure 16 : cartographic comparison of the ZAU 2010 and the new zoning scenario – south