A probabilistic model of residential urban ...

A probabilistic model of residential urban development along the French Atlantic coast between 1968 and 2008 Iwan Le Berrea, Adeline Maulpoix a, Marius Thériaultb, Françoise Gourmelona a

LETG-Brest GEOMER, IUEM-Université de Bretagne Occidentale, Technopole Brest-Iroise, rue Dumont d’Urville, 29280 Plouzané, France b

Université Laval, Ecole supérieure d'aménagement du territoire et de développement régional, Pavillon Félix-Antoine-Savard, 2325, rue des bibliothèques, Québec, Québec, Canada

Keywords: coastal town, land cover and land use changes, residential development, land registry, suburbanization, probabilistic model Highlights:    

Cross-sectional models summarize the evolution of housing built up probability over 40 years around Brest (France). Proximity to the coast is found to have a significant appeal over the study period. The slower development rate of the coastal strip after 1999 is a likely effect of enhanced planning regulations. The proportion of smaller plots has significantly increased on the coast while larger plots are preferred inland.

Graphical Abstract: Figure 4 (or 2) Abstract: In most developed countries, the acceleration of coastal urbanization during the second half of the twentieth century has gradually resulted in a concentration of residential housing and associated infrastructure and facilities along a narrow coastal strip, along with various environmental, functional and social impacts. This has led certain countries, such as France, to adopt protection legislation with respect to their coastlines. However, while numerous studies describe and analyse the consequences of urbanization on the coastal environment, few of them examine the influence of the coast on urbanization. This paper focuses on the residential development process, considering the coastline as both a pull factor on account of its amenities, and as a constraint due to the legislation put in place to protect it. Our study aims to build a database describing the factors that influence the probability of housing development on vacant land and to analyse the spatiotemporal evolution through a logistic regression modelling approach. While controlling the factors usually mentioned in the scientific literature on urban sprawl and suburbanization, this method is also able to isolate the effects of coastal attractiveness, taking laws and bylaws regulating urbanization in such areas into consideration. It shows in particular that, since the early 2000s, the gradual implementation of a land planning framework specific to the coastal zone has led to improved regulation of housing development in the study area. Throughout the country, the French Coastal Law limited available land for housing development, particularly in coastal areas, by enforcing building restrictions in accordance with conservation principles. The paper concludes with potential improvements to our models, e.g. the integration of local economic factors, such as land costs or changes in taxation, all of which influence housing choices and could potentially regulate suburbanization.

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1. Introduction Throughout history, human settlements have grown and developed in coastal areas for practical reasons that are mainly related to their natural resources and strategic location (Hudson, 1996). In most developed countries, it was only in the eighteenth century that coastal areas became associated with notions of lifestyle and leisure (Mullins, 1991), gradually leading to a concentration of urbanization and associated infrastructure and facilities along a narrow coastal strip. Outside of port towns and coastal villages, other specific forms of urbanization related to the development of tourism thus emerged, including mansions and seaside resorts from different periods. These were followed by more mundane forms related to the proliferation of residential housing, either individual or within a planned framework, such as housing estates. Indeed, with the increasing mobility of households, holiday and retirement resorts have emerged in the same way: as settlements resulting from suburbanization and motivated by expectations of a better quality of life than in town centres, all of which amplify pull factors. Population concentration linked to the attraction of the coast is observed at continental, national and regional scales (Small and Nicholls, 2003), whereas at the local level, it is mostly observed in places that were not previously used for other urban activities, such as ports and sea-related industries. The effects of this coastal population concentration and related developments are well known (Ewing, 1994; Couch et al., 2007), including competition for land, and lead to social exclusion and increased exposure to erosion and flooding risks (Hunt and Watkiss, 2011; Cooper and Lemckert, 2012). This has led some countries (e.g. Spain, Australia or various US states) to adopt legislation with respect to their coastlines (Orsi, 1996; Gurran et al., 2007; Negro et al., 2014) in an attempt to preserve natural areas for the sake of sustainable development and integrated coastal zone management (ICZM) (Cendrero, 1989; Ballinger et al., 1994; Cicin-Sain and Knecht, 1998). However, while numerous studies describe and analyse the consequences of urbanization on the coastal environment (Burak et al., 2004; Romano and Zullo, 2014), few of them examine the opposite effect, i.e. the influence of the coast on urbanization. Nevertheless, understanding the coastal effect is instrumental to the enhancement of geographical analysis and forecasts (e.g. land use simulation) for urban and regional planning that seeks to balance the development and conservation of scarce and fragile coastal environments. This paper focuses on the residential development process, considering the coastline as both a pull factor on account of its amenities, and as a constraint due to the legislation implemented to protect it. Our study is thus based on two questions. Among local pull factors that influence the probability of residential development on vacant land: (1) is it possible to isolate a coastal effect related to its appeal taking into account specific measures adopted to regulate urbanization in such areas? and (2) have these factors changed over recent decades and how are they related to plot size and land availability? Historical land use data at the plot level was used to develop a case study in a French context for Pays de Brest in Brittany. Based on a short literature review of the main determinants and the modelling of housing development, section 2 presents our approach to addressing the research questions. Section 3 describes the context, study site and available data. Section 4 presents the methodology. Sections 5 and 6 show and discuss the results respectively, leading to the conclusion in section 7.

2. Determinants of residential development The apparent lack of spatial organization caused by the spread of housing developments can sometimes give the impression that this process is largely spontaneous, guided only by the supply of land and the demand for housing, reflecting the view put forward by Vallega (2001) arguing that urban planning does not apply to suburban areas. However, the literature on land use and land cover changes 2

(Agarwal et al., 2002; Lambin and Geist, 2006; Torrens, 2008; Mas et al., 2014), on spatio-temporal changes in property values (Grether and Mieszkowski, 1974; Can, 1992; Irwin and Wrenn, 2014) and on residential development (Carrion-Flores and Irwin, 2004), shows that the development process involves a combination of factors, partly theorized, and that it can be modelled. 2.1. The main local influencing factors of residential development

Urbanization is based on the interaction between households and amenities that promotes proximity and accessibility concepts as central tenets of the housing development process. Workplace distribution is one of the major factors: jobs are often concentrated in nodes, including city centres, and, more recently, within sub-centres, business parks and industrial zones, which results in a polycentric organization (Anderson and Bogart, 2001). Besides employment, facilities (commercial, educational, leisure or health) are other attractive/necessary elements for households (Des Rosiers et al., 1996). In accordance with bid rent theory (Alonso, 1964), access to these central places can be calculated to verify their polarizing role (Hansen, 1959; Dubin and Sung, 1987). This depends on the configuration and connectivity of transport networks, and, more generally, urban form. Their inclusion in the modelling process is thus based on the computation of accessibility (Geurs and van Wee, 2004; Thériault et al., 2005; Kwan and Weber, 2008). Access to amenities acts as a pull factor towards urban centres. However, scarcity of available land increases competition among potential users and generates a premium (location rent) that internalizes land cost, leading to a push factor towards the periphery for households (and businesses) that cannot or do not wish to pay for centrality. These regional economic factors yield urban sprawl (Harvey and Clark, 1965), which has significant implications for traffic, infrastructure and transportation costs. At the local level, influencing factors include the attributes of available plots (specifically plot size, slope, exposure and view) and either positive or negative associated local externalities. Additionally, proximity to amenities such as transport infrastructure (e.g. highways and airports), facilities and industrial activities can generate noise and pollution (including risk exposure) that exert a push effect on housing development (Hunt and Watkiss, 2011). In contrast, households make their housing choices based on the appeal of landscapes and environmental amenities, and, more generally, the quality of the environment (Benson et al., 1998; Luttik, 2000; Kestens et al., 2004). These choices can be decisive to the extent that they give rise to genuine organization or even spatial segregation, as can be seen along many stretches of coastline (Vallega, 2001). Additionally, urban planning tools and bylaws are usually determined to control the unwanted knock-on effects of housing development. Indeed, in countries where urban planning legislation is implemented, it can be very powerful in the regulation of evolving urban forms, either by promoting certain types of facilities and development, or by being restrictive when it comes to environmental protection (Carrion-Flores and Irwin, 2004; Munroe et al., 2005; Onsted and Chowdhury, 2014). 2.2. How these factors can be integrated into a housing development model

In the housing development literature, modelling can pursue two complementary goals: -

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To shed light on and/or assess its effects on the evolution of urban forms (Dietzel et al., 2005), the social structure of towns and neighbourhoods (e.g. segregation, spatial mismatch, gentrification) (Kestens et al., 2005), the consumption of agricultural land (Levia and Page, 2000), the cost of land (Abelairas-Etxebarria and Astorkiza, 2012), or the environment (Vimal et al., 2012). To assess the influence of different factors on residential development: the setting up of new services or infrastructure (Dubé et al., 2013), the implementation of regulations and urban

planning tools (Newburn and Berck, 2006), the factors behind urban sprawl (Carrion-Flores and Irwin, 2004), the proximity to open spaces, landscapes, and environmental amenities. For this article, the purpose of modelling is to analyse the marginal contribution of specific and location attributes of available land leading to residential development, and to study their evolution in both space and time. Consequently, our approach is mostly empirical and statistical, while the retained factors are identified through previous research and constrained by data availability. Regression models are highly relevant (Kirk et al., 2011; Kolb et al., 2013; Wang et al., 2013) for such purposes because they enable the testing of each variable’s specific contribution to the variation of the modelled phenomenon, while controlling for inter-variable interactions. However, to secure relevant results, due care should be taken to avoid pitfalls, such as multicollinearity, heteroskedasticity, autocorrelation and misspecification. 2.3. Does the coast have any specific effects on residential dynamics?

The attractiveness of the sea shore for population, and consequently, for housing development, has been well described at various scales and for several countries (Small and Nicholls, 2003; Parcerisas et al., 2012; Lin et al., 2013; Romano and Zullo, 2014). However, most local studies place emphasis on the impact that urbanization has on the coast (land consumption, landscape degradation, pollution, intensive use, seasonal disequilibrium) and often neglect its effects on urbanization. Even so, the latter effect is multi-faceted: a high degree of attractiveness, which is well known to real estate agents and solicitors, a sea view and direct access to the shore being highly appreciated by residents of coastal areas (Robert, 2004, Jim and Chen, 2009). Several countries have enacted laws and bylaws to mitigate or counter the effects of this attractiveness (Gurran et al., 2007; Negro et al., 2014). Moreover, in light of the foreseen climate change-related sea level rise, increased exposure of real estate properties to associated risks are widely covered in the literature (Cooper and Lemckert, 2012; Paula et al., 2013; Masselink, 2014). Given these considerations, we argue that a detailed modelling of land use changes at the plot level is necessary to unveil relationships specific to coastal zones. On the one hand, land registry plots are a repository of entities that correspond to the elementary division of the territory (Manson et al., 2009). On the other hand, it is at the plot scale that households materialize their housing projects, incorporating their own criteria, notably in terms of investment capacity, workplace accessibility, services (schools, shops, etc.) and amenities (Bell and Irwin, 2002). Finally, the land registry plot is the basic level at which land use legislation applies, whether related to urban planning (Pumain, 2004), the economy, or the environment (Vimal et al., 2012). Consequently, as the elementary division of the territory, land registry plots not only allow us to connect individual land use decisions with the urban forms they help produce (Irwin et al., 2009), but also to understand the basic processes behind observed changes in urbanization. This leads to the development of a probabilistic statistical model at the plot level using available attributes to assess or control for the effects of the main determinants mentioned above. While this approach is constrained by data availability and subject to several model specifications, it appears to be appropriate for gaining a more in-depth understanding of the design and regulation of coastal development in France.

3. Context and study site Located in north-western France, the study site consists of peninsulas at the point where the Atlantic and the North Sea meet (Figure 1).

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3.1. The French case

The population of coastal towns in metropolitan France has increased by 25% over the past 40 years. Currently, 10% of the population reside in 4% of the national territory. Up until the 1980s, in the absence of restrictive legislation, urbanization took a “spontaneous” form (Pumain, 2004; Zaninetti, 2006). The French Coastal Law of January 3, 1986, (la loi Littoral), introduced the first regulatory measures for the protection of the coastline (Table 1). In coastal municipalities, this law restricts urbanization based on several principles: in particular, outside of urban perimeters, a 100-metre setback zone was established in which construction is forbidden. In principle, any extension of the urban perimeter must be continuous to the previous housing agglomeration (within 200 metres) served by commercial or public services. On the one hand, the aim is to protect natural and agricultural activities, with such bands acting as green belts or ecological corridors between denser urban zones and thus enhance environmental conservation; on the other hand, this provides a buffer zone that protects urban areas from coastal risks. Insert Table 1 here However, the Costal Law was deliberately vague, which meant that it could be adapted to a high diversity of coastal areas and left a large discretionary margin to local managers and elected representatives. It was only in the early 2000s that a profound change in the institutional framework introduced greater consistency and efficiency in controlling urban sprawl. This was based on encouraging inter-municipal cooperation associated with the obligation to implement urban planning documents at two levels: the Local Urban Development Plan (Plan local d’urbanisme, PLU) at the municipal level, and the Territorial Coherence Programme (Schéma de cohérence territoriale, SCOT) at the inter-municipal level (Deboudt et al., 2008). This attempt to create coherence has facilitated the integration of sectoral policies on transport, housing, urban planning, and economic and commercial development. Moreover, it must comply with the principles of the Coastal Law where urbanization is concerned. 3.2. The study site

Located at the western tip of France, the city of Brest has a population of 140,000 (Figure 1). It constitutes the centre of an urban region known as Pays de Brest, or the Brest region, which has nearly 400,000 inhabitants (INSEE figures) and contains 89 towns and villages. Covering an area of 170,000 ha, 95,000 ha of which are given over to agriculture, Pays de Brest includes a large number of landscape and recreation amenities, notably related to its 370-km coastline. Despite its peripheral location, it is subject to dynamics similar to those found on the rest of the French Atlantic coast. On average, the rate of land development is higher than in the rest of France (13.8% versus 9% in 2006)1 and its growth rate was also higher in the period 1985-2004 (+78% versus +43%). Insert Figure 1 here In Brest, as in other French towns and cities, high population and economic growth, accompanied by a massive rural exodus, resulted in a rapid increase in the urban population between 1950 and 1975 (roughly 2% per year). Subsequently, and although the natural balances remained positive, the population of the city of Brest steadily declined until 2008, with 90% of this migration loss to the gain of the rest of Pays de Brest. Consistent with the trend observed in most French towns and cities, urban growth in the Brest region has since taken on a “fragmented” form. However, at the same time, Brest has not lost its economic influence, since it accounts for more than half of the jobs in the region. These developments are representative of the suburbanization phenomenon, which can be interpreted as an 1

See the INSEE report on land use changes in the Finistère region: http://www.insee.fr/fr/themes/document.asp?ref_id=15689&page=dossiers/dossier_octant/dossier_52/T2_sol.htm#t1

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extension of the accessible area through the development of road infrastructure, the strong preference of households for individual housing, and the requirement for environmental amenities (Zaninetti, 2006). The central role of Brest in the region is also visible in various metropolitan-level commercial, medical, educational and cultural services and amenities used by a population that far exceeds the city limits.

4. Methodology Based on data availability, the analysis of residential development was carried out from 1968 to 2008 using French census dates (1968, 1975, 1982, 1990, 1999 and 2008) as breakpoints to define five inter-census periods, thus allowing for the measurement of changes in the factors determining the probability of available plots of land being used for housing during each successive period. The objective of this research is to test three hypotheses: 1) proximity to the shore matters and increases the probability of a suitable plot being developed for housing; 2) the plots more likely to be developed close to the shore are smaller to counterbalance the scarcity of such land; 3) the shore proximity effect declines during the study period following the gradual implementation of the Coastal Law. Statistical models are used to test the hypotheses while controlling for other covariates that influence the probability, to the extent that data is available. The analysis procedure is based on land registry plots of land and comprises four steps: 1) assessment of the development status of each plot (already built on, available) at the beginning of each period; 2) measurement of the physical, neighbourhood, accessibility, environmental and statutory attributes (influence variables) for available plots at the beginning of each period; 3) filtering of the available plots based on restricted land use zoning, risk mitigation and environmental conservation restrictions in force during the period to select suitable plots for residential development at the beginning of the period; 4) for suitable plots only, cross-sectional binary logistic regression modelling of housing development at the end of each period (dependent variable) considering the marginal effect of influencing variables (independent). Given the length of the study period, some of the independent variables are time-varying covariates (e.g. distance to the nearest developed housing area, distance to schools). The functional form of their relationship with housing development may change over time, partly because they are constrained by former stages of urban development, but also because the bylaws and behaviour of households may evolve. 4.1. The land registry and the status of each plot

In France, the land registry uses two tools: a computerized cadastral map called the PCI (Plan Cadastral Informatisé) which provides a geographical representation of land using sets of objects; and tabular documentation (land registry matrix) in the form of the MAJIC database. Both the PCI and MAJIC supply land use information: PCI provides polygons for each plot of land with identifiers, buildings, and topographic features such as cemeteries and railway lines, and MAJIC comprises several tables on land ownership (owner, tax exemption, etc.), and land status (built on and vacant land). This study is based on anonymous data sets (PCI and MAJIC) which are linked by a single identifier and do not contain land or building value (confidential data). A Temporal Geographical Information System (TGIS; Frank et al., 1995) was required to manage changes in plot attributes between 1968 and 2008, to relate the plots with land features (shoreline, slope, etc.), amenities (schools, urban centres, etc.), land use, regulations, limitations and restrictions. Figure 2 presents an overview of the data sources, features, attributes and data processing involved in the preparation of the data sets required for the regression analyses. Various procedures concerning

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spatial analysis, travel simulation on road networks, buffering and filtering were needed to compute the attributes and update each plot at the beginning of each period. Insert Figure 2 here Furthermore, faced with certain idiosyncrasies of the land registry requiring very small plots to be regrouped prior to construction, we decided to merge adjacent plots to reproduce the importance of landholdings that were built on in 2008. This is the consequence of excessive land division in some areas, and extreme care was taken in the adjustment procedure to avoid any adverse impact on the analyses. Otherwise, empty plots were kept as reported in the land registry.

4.2. Local context of each plot (independent variables)

In this study, the independent variables are related to the physical attributes of the plots, as well as to neighbourhood and accessibility attributes. We focus on the distance to the shore, while other variables have been used to control for known effects on the probability of development of a plot of land, when feasible. Independent control variables are: accessibility to urban centres (Brest, secondand third-order urban service centre, travel time by car), proximity to main roads, to primary or secondary schools and to existing settlements, technical constraints (sloping), and plot size (which is used in combination with distance to the shore). Unfortunately, some variables known to have a significant effect on housing development (e.g. land prices, landscape views) were unavailable and ways to mitigate their absence are discussed in section 4.4. Considering the substantial number of plots to be characterized, TGIS data accuracy and associated computation burden, distances and travel times were computed using the geometric centre of each plot and a point-in-polygon approach to relate it to incremental buffers or travel time zones from or around amenities (e.g. urban service centre, school). Thus, we obtained ordered categorical variables associated with buffers and zones bounded to thresholds. Each category was coded with dummies. An alternative would involve continuous interval variables, but this option was discarded because continuous estimates would generate illusory accuracy. Moreover, continuous variables imply choosing among shapes of distance-decay functions (e.g. linear, polynomial, Fourier), assuming monotonous relationships and, in our case, that the same shape was maintained during the entire study period. Except for some known relationships, this approach may be problematic. Thus, we decided to explore the similitude of shapes using ordered categorical variables, which incidentally lowered the risk of generating common spatial structures among travel simulations (and multicollinearity). However, for each variable, the choice of thresholds and reference categories is of prime importance. The number of categories and thresholds have been set considering: accuracy of distance (or slope) estimates (e.g. map resolution, feature identification), precision requirements for this research (width of intervals) and the counting of plots and development events that should be secured for each category at each time period to compute valid odd ratios. When necessary, adjacent categories were merged to obtain appropriate counts and/or to lower excessive relationships among independent variables (chi-square tests). Minimum counts and development event requirements are crucial for the choice of reference categories (it is generally the first or the last categories that are used as analysis references) which are decisive for the stability of parameter estimates and odds ratios of other categories, as well as for the appropriate estimation of the regression intercept (Hosmer and Lemeshow, 2000). This was checked independently for each cross-sectional model, but considering attrition from one period to the next, counts and development events slightly decrease over time.

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However, they never fall below 940 plots and 20 development events per reference category; most of the time, the statistics are far greater than these minima (several thousand plots and events). Distance to the shore was estimated with inland buffers to set categories: 100 metres and less, 101200 metres, 201-300 metres, 301-400 metres, 401-500 metres, 501-750 metres, 751-1,000 metres, and more than 1,000 metres. The first 100-metre limit is needed to test for the potential impact of the Coastal Law. It is repeated up to 500 metres to analyse the scale of its effect. Exploratory analyses shed light on the 400- and 1,000-metre thresholds above which the impact of the shore fades and vanishes respectively. The reference was the last category (more than 1,000 metres; no coastal impact). A second, independent variable (plot size) was of special interest for this research because it defined the area available (and necessary) to build a house, and, ceteris paribus, conditioned the total land price. This variable was taken from the land registry and divided into categories (100 m² and less, 101200 m², 201-300 m², 301-400 m², 401-500 m², 501-750 m², 751-1,000 m², 1,001-1,500 m², 1,5012,000 m², 2,001-3,000 m², and more than 3,000 m²). The reference was the last category. It was also used to establish an interaction with proximity to the shore for land located less than 300 metres from the shoreline to test for the second hypothesis. Widening intervals rely on the fact that the marginal utility of extra square metres of land is lower for larger plots. Looking at smaller plots is necessary because they potentially entail or constrain development, and can also offer a trade-off at higher costs. The average slope of land on the plot needed to be controlled because construction costs increase when the terrain is hilly, leading to a higher likelihood of flat land being developed. A digital elevation model (BD Alti®) from the National Institute of Geographic and Forestry Information (Institut national de l’information géographique et forestière, IGN), with a grid cell resolution at 25 metres, was used to calculate the slope at the centre of each plot and to estimate the average slope of larger plots. This variable was divided into four categories: 5° and less, 5.1-10°, 10.1-15°, and more than 15° (the reference category). Other physical factors to be controlled for were related to the immediate neighbourhood of available plots and accessibility to schools and urban amenities. Neighbourhood was characterized by two categorical variables: Euclidean distance to the nearest main road (reference more than 300 metres) and Euclidean distance to the nearest housing area at the beginning of the period (reference more than 400 metres). The distance to the nearest main road (located using BD Topo® 3D from the IGN) was divided into classes of 50 metres. This needed to be included in the model because a certain level of road network access is a prerequisite for development, as proximity helps to lower infrastructure costs. Conversely, close proximity to roads can also generate negative externalities. The effect of proximity to the nearest housing area was likely to increase over time due to more stringent land planning policies in later periods, meaning that time-varying covariates needed to be computed for each period to take into account previous housing developments. Accessibility to schools and urban amenities involved simulating trips on the road network. Monitoring these elements is crucial for taking into consideration bid-rent theory and Central Place Theory (CPT). In France, the existence of school districts does not necessarily influence choice of school which gives parents a certain amount of freedom when making their decision. However, most parents do choose the closest school. Access to schools was simulated on foot (shortest walking distance algorithm), and access to urban centres (and the job market) was based on travel time by car. The road network was topologic, with impedance and directions. The road links were selected from the appropriate layers of BD Topo®; impedance was set using free flow maximum speeds with turn penalties, and simulations were carried out in ArcGIS with Network Analyst (Thériault et al., 1999). 8

Except for local improvements in road capacity, the network remains relatively stable throughout the study period, but the lack of data to trace back its evolution impedes the study of previous states. However, its evolution is marginal and would not substantively change the assignment of plots to categories. For each period, schools were identified from the French Ministry of Education data sets, and independent simulations were carried out for each period taking into account school closures and openings (leading to a time-varying covariate). Finally, in order to take into consideration the decreasing effect of the urban hierarchy on housing demand (as a positive externality), travel time by car to urban centres was computed for three levels of urban centres in accordance with the SCOT of Pays de Brest2. Brest is at the top of the urban network (first level); Landerneau and Lesneven are second-order centres; and, Crozon, Daoulas, Ploudalmezeau, Lannilis, Plouguerneau, Plabennec and Saint-Renan are third-order local activity centres. These four access variables were divided into categories with references as shown in Table 6. 4.3. Filtering of the available plots (dependent variable) Available plots of land (unbuilt) were then selected and filtered using the criteria in Table 2 to define suitable plots for residential development at the beginning of the period. Available plots comprise agricultural and undeveloped areas. Actual land use zoning was unavailable (and/or non-existent) for the majority of the study period and was not included in the analysis. Filters were used to remove plots that could not be developed from the models. Globally, the filters relate to three categories: 1) incompatible or restricted land use (e.g. cemetery, airport, military tenure, agricultural use); 2) risk mitigation zones; 3) environmental protection or conservation zones. Suitable plots where the filter applied during a specific period (a permanent restriction or one which came into effect before the end of the period) were excluded from the cross-sectional regression model, with the exception of the construction date which was used to exclude built-up plots (unavailable) at the beginning of each period. For each period, the dependent variable is binary: 1 if the plot was built on during the period and 0 otherwise. Insert Table 2 here Table 3 presents a summary of the plots, filtered plots, suitable plots and houses built for each census period between 1968 and 2008. The land registry comprises 415,436 plots, 50,869 of which were already built up in 1968, compared with 109,231 in 1999. Depending on the period, the filters removed between 36,248 and 49,526 empty plots from the analysis, leading to a decreasing number of suitable plots between 1968 (328,319) and 1999 (256,679). The consumption rates of suitable plots for new housing projects changed over time (between 3.1% and 5.8% per period), leaving more than 240,000 plots suitable for development in 2008 (no shortage). Similarly, the stock of suitable plots in close proximity to the shoreline (less than 300 metres) slowly diminished between 1968 (44,668) and 1999 (29,951), while the share of this zone accounted for 10.6% to 14.7% of the new housing market development in Pays de Brest. Insert Table 3 here 4.4. Cross-sectional logistic regression models and testing for changes over time

Several approaches could be used to model detailed changes in land use, from hedonic to agent-based simulation principles, including several types of probabilistic models based on longitudinal data (Irwin and Wren, 2014). Regression modelling provides several ways to test for simultaneous effects of several local factors on the change process at plot level and to estimate marginal probabilities (or coefficients). In this case, because of delays in the enforcement of the Coastal Law and its local 2

See the SCoT du Pays de Brest website: http://www.pays-de-brest.fr/scot.php

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peculiarities, it was not feasible to follow a treatment or quasi-experiment approach and specify a difference-in-differences model (Meyer, 1995). Moreover, this would assume that enforcement of the law is exogenous to agents, which is not necessarily the case for policy making at the municipal level. Another option would have been to rely on an event-history or hazards model (Allison, 1984; Hosmer and Lemeshow, 1999; Box-Steffensmeier and Jones, 2004) simultaneously estimating the probability of land use change and the time elapsed after the law was enforced (e.g. using the Cox proportional hazards model). However, in order to specify such a model, several time-varying covariates are needed to control for global and local level evolution of land price and socio-demographics. This could lead to cumbersome specifications, and price data is not available at this scale. A third option would be to combine the five census periods and specify a panel-based, fixed-effects logit model (Hsiao, 2003; Frees, 2004). However, considering the duration of the study period (40 years), special care should be taken when combining evolution data in a single model because factors leading to land use change can evolve over time (e.g. the post-war reconstruction of Brest in the 1960s and 1970s versus the urban sprawl that took place afterwards). It is unlikely that omitted variables have time-invariant effects. Moreover, the dependent variable is single-spell, leading to endogenous attrition of cases in panels. Finally, we retained a simple approach based on five logistic cross-sectional models (Hosmer and Lemeshow, 2000) to identify significant physical and access factors related to land use change and to test for differences among coefficients of independent successive models using a generalized Hausman test (Hausman and McFadden, 1984) based on a seemingly unrelated estimation approach (Wessie, 1999). This choice has some limitations and pitfalls that will be discussed in the following sections, but it does provide a simple approach to testing for the plausibility of effects. Moreover, the use of census-based periods provides linkage with municipal-level census data (for 89 towns and villages) to further discuss relationships with the socio-economic context at the beginning and end of each period, and eventually consider the price of land, which is known only at the municipal level and for the last ten years. The aim of these five cross-sectional models is to test the significance of various modalities (categories) of the independent variables by increasing the probability of development of a suitable plot during a period. This makes it possible to measure the coefficient of influence (odds ratios leading to marginal probabilities). More formally: (Equation 1) (Equation 2) Where is the logit of the logistic regression model for the p time period; is the intercept of that period; is a dummy variable for the distance to the shore category i; is the coefficient for distance class i at time p; is a dummy variable for plot size category j; is the coefficient for size j at time p; is a dummy variable for any (potentially time-covariate) environmental variable category k at time p; is associated coefficient; is a dummy variable for any (potentially timecovariate) accessibility variable category m at time p; is associate coefficient; and, I, J, K and M are the total number of categories in each type of independent variable. Finally, regression model for time period p, and odds ratios set to one ( ).

is the logistic

is the odds ratio associated to . Reference categories have

However, as noted above, some important variables (mostly economic) known to have an impact on the probability of a plot being developed (e.g. unit price of land) are not available at this scale and over time. Such omitted variables may be detrimental to the estimation of parameters because they can be 10

correlated with other variables in the model and generate spatial patterns that are incompatible with the independence among observations, which is assumed by the logistic model. Autoregressive approaches provide an efficient way to compensate for the spatial dependence in the models (Anselin, 1988) and avoid bias and/or inefficient estimates. However, they are based on an interaction (or inverse distance) square matrix among cases leading to a strong computation burden with hundreds of thousands of cases. While less efficient than autoregressive approaches, the incorporation of spatial fixed effects helps mitigate the bias linked to spatial clusters in omitted variables (Anselin and Arribas-Bel, 2013). In this study, it makes sense to incorporate municipality-based fixed effects in the models because: 1) local urban development (urbanism) is regulated at this scale (and beyond); 2) building permits are issued and urban zoning decisions are made by municipalities; 3) local services are often managed by municipalities, meaning common amenities; 4) property taxes are collected by municipalities as they fix uniform taxation rates (negative externality); 5) available land prices are published at this scale; and, 6) it is the smallest scale at which French censuses are readily available. Dummy fixed effects were included for 88 municipalities, leaving Brest as the reference. To avoid over-specification, the variables were entered one by one, ordered according to the strength of their known effect (accessibility first, followed by neighbourhood, slope, plot size, distance to the shore, interaction between proximity to the shore and plot size, and lastly, fixed effects of municipalities), making sure that, at each stage, Akaike and Schwartz information criteria were minimized to maximise information without compromising model parsimony. Furthermore, statistical computations were done using both R 3 and Stata4, and outcomes were identical. Table 4 shows the cross-sectional model adjustment indicators for each period. All models were globally significant and the strength of adjustment increased over time (pseudo R-square). Models with fixed effects outclass other specifications, both in terms of pseudo-R2 and information criteria. Insert Table 4 here While tests on the cross-sectional models may be sufficient to verify hypotheses 1 and 2, a longitudinal approach is required for hypothesis 3 (change of parameters and relationships over time). The questions are: 1) do two successive cross-sectional models yield similar or significantly different results for the impact of distance to the sea shore and its interaction with plot sizes? 2) Are there significant differences between successive estimators (e.g. )? However, our successive models are based on partly overlapping datasets; the next one is made of cases remaining after attrition of build up plots at the end of the previous one. They are not independent and this fact impedes the use of standard Wald tests because covariance between estimators should be considered. For longitudinal tests, we thus retained the approach developed by Wessie (1999) based on seemingly unrelated estimation and the cluster-sandwich estimator to generalize the Hausman (1978) and White (1982) tests. In Stata version 13, the suest command was used to combine successive cross-sectional models, followed by a test of equality between coefficients or sets of coefficients under the null hypothesis H0: or H0: , etc. As such, these longitudinal tests permit the comparison of single parameters, sets of parameters for all categories of a variable (its shape coefficients) and, potentially, full model specifications. We used them to compare results of successive cross-sectional models (e.g. 1968-1975 versus 1976-1982).

3 4

The R Project website: http://www.r-project.org/ The Stata software website: http://www.stata.com/

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5. Results This section presents the findings of the study that concern: 1) changes in housing development in Pays de Brest between 1968 and 2008; 2) results of the logistic regression models; 3) characterization of the coastal effect on residential development and its evolution; 4) evolution of this effect during the study period. 5.1. Evolution of housing development in Pays de Brest between 1968 and 2008

During the study period, the residential construction market in Pays de Brest followed a trend that was similar to the rest of France, but with larger differences between highs and lows (Figure 3). Furthermore, the slowdown occurring between 1974 and 1984 in France was delayed in Pays de Brest (from 1981 to 1992) after an all-time peak in 1980. The effect of the recession in the early 1990s was stronger in this region than the national average, but the recovery was similar up to 2008. The attractiveness of coastal municipalities was maintained over the entire period (except in 1973): they received both more new constructions than Brest, and over 50% of new buildings outside Brest. In line with hypothesis 3, a slow decrease in new housing projects at less than 100 metres from the coast was observed, but should be confirmed by models controlling for other influences. Insert Figure 3 here Table 5 presents the evolution of suitable land and yearly development rates during each time period for the study area, the Brest metropolitan area, the city of Brest and two bands or strips along the sea shore (