Keywords: hospitals, justice courts, small cities, shrinkage, disappearance, New Public Management

In many countries, the objective of reducing public spending combined with the introduction of New Public Management reforms have led to changes in the territorial organization of public services and to a withdrawal of public facilities in many places. Our hypothesis is that in France, this territorial process has not occurred in the same way in all cities. We assume that while medium-sized cities are seeing a reduction in some public service facilities, their disappearance usually occurs in small cities. Larger metropolitan areas have not been affected by such territorial retrenchment of public services facilities. These differences could lead to increased territorial inequalities at the level of urban systems and to a marginalization of some small cities. This paper examines these processes through a quantitative analysis of changes in the location of justice courts and hospital beds from 2000 to 2016, within French Functional Urban Areas.

It shows that the decrease in the number of justice and hospital facilities was significant and has affected small cities.

Introduction

In Europe, small cities constitute an essential level of the urban hierarchy. Indeed, [START_REF] Gourdon | Des petites villes davantage touchées par la décroissance ? Comparaison des trajectoires démographiques à l'échelle européenne (1961-2011)[END_REF] have identified 2,862 small urban areas (10,000 to 50,000 inhabitants), which represent 72% of European urban areas. According to Atkinson (2019), small cities (5,000 to 50,000 inhabitants) represent 56% of Europe's urban population. Even though small cities usually tend to grow faster than large metropolises in the short term, the risk of small-city marginalization within the broader context of Western development (whereby larger cities and metropolitan regions seem to polarise demographic and economic growth) has been highlighted by several scholars [START_REF] Bailleul | Les petites villes européennes comme enjeu d'équité territoriale[END_REF], Baron et al., 2010[START_REF] Batunova | Urban shrinkage: an unspoken challenge of spatial planning in Russian small and medium-sized cities[END_REF][START_REF] Filion | Growth and decline in the Canadian urban system: the impact of emerging economic, policy and demographic trends[END_REF][START_REF] Gourdon | Des petites villes davantage touchées par la décroissance ? Comparaison des trajectoires démographiques à l'échelle européenne (1961-2011)[END_REF]. However, [START_REF] Wolff | Urban growth and decline: Europe's shrinking cities in a comparative perspective 1990-2010[END_REF] have shown that the relationship between smaller cities and urban shrinkage is irregular, and depends on the regions in which the cities are located. In Southern and Western Europe, they observed that shrinkage hits smaller cities strongly [START_REF] Wolff | Urban growth and decline: Europe's shrinking cities in a comparative perspective 1990-2010[END_REF]. In France also, several studies show a trend towards recent demographic decline in a large share of small cities [START_REF] Wolff | Shrinking Cities, villes en décroissance: une mesure du phénomène en France[END_REF][START_REF] Cauchi-Duval | La décroissance urbaine en France : les effets cumulatifs du déclin[END_REF] while [START_REF] Paulus | Coévolution dans le système des villes, croissance et spécialisation des aires urbaines françaises de 1950 à 1995[END_REF] and [START_REF] Pumain | Quel rôle pour les villes petites et moyennes des régions périphériques ?[END_REF] showed a tendency to stagnation or decline since 1975 in small and medium-sized cities that are distant from France's main growth axes (the coasts and large valleys).

If small cities can be considered as an important level of the urban hierarchy in Europe, because of their number and their population share, they also constitute essential centres of resources and services. In various countries such as France, Italy or New Zealand, the equality between places and citizens regarding access to health care, judiciary services, or education guided the spatial distribution of public services during the 20 th century [START_REF] Laborie | Les petites villes face aux fermetures des services publics[END_REF][START_REF] Barnett | Equity, access and resource allocation: Planning hospital services in New Zealand[END_REF]Perruca et al., 2018). This often resulted in the use of networks of small and medium-sized cities to achieve a distribution of public services favouring equity. Since the 1960s, public management reforms have been conducted in numerous countries of Europe, America and Australasia [START_REF] Pollitt | Public management reform: a comparative analysis: new public management, governance, and the neo-Weberian state[END_REF]. These reforms participate in redefining the structures and administration of states. They can influence the geographic distribution of public services and the principles that guide their location. In particular, political science scholars have pointed to the diffusion of the New Public Management (NPM) doctrine in reforms. This has led to new injunctions like increasing performance, reducing public expenses, or the introduction of market-type mechanisms in the public sector [START_REF] Pollitt | Public management reform: a comparative analysis: new public management, governance, and the neo-Weberian state[END_REF][START_REF] Bezes | Réinventer l'État : les réformes de l'administration française (1962-2008[END_REF]. In several countries, such reforms have led to closures of public service facilities or infrastructure, specifically where their maintenance was the most expensive because of lower activity levels.

Are smaller cities particularly affected by these new views on the public sector? In other words, have NPM-inspired reforms reinforced spatial inequalities, and participated in the decline of small cities? By examining the territorial restructuring of public services across mainland France's urban system, this paper aims at connecting two strands of research that are rarely combined: the research into urban shrinkage and the decline of small cities on the one hand, and studies about the effects of NPM-inspired reforms on the other hand. Our goal is to understand the territorial outcomes of reforms, and their effects on spatial inequalities, with a focus on the French urban system.

We have chosen to address this issue of public service shrinkage in small cities from the specific angle of physical facilities: i.e., the disappearance or reduction in numbers of infrastructures, and we question their effects on the inequalities of access among cities. We have selected two sets of physical facilities, namely justice courts and hospital beds. Both imply face to face contact. As sovereign and welfare services, both need to be easily accessible to populations.

Our specific contribution lies in the proposition of defining shrinkage as a decrease of facilities provided in cities, in two ways: we distinguish between shrinkage leading to the complete disappearance of a facility, and shrinkage leading to a reduction in the number of facilities [START_REF] Baudet-Michel | La rétraction des services et commerces dans les villes petites et moyennes : modalités et logiques à l'échelle interurbaine[END_REF]. The use of these two indicators clearly shows two processes which do not target the same type of cities. Disappearance occurs more in small cities and reduction in medium-sized or large cities. Our aim is to measure the shrinkage processes of public services in the last decades, and to underline the fact that this creates inequalities among citizens, according to their residential location. As a result, the shrinkage process of public services weakens small cities, often already fragile, and dilutes territorial cohesion.

We start by introducing the dual framework that has inspired this work, namely work on NPM policies and work on urban systems with a special attention to the decline of small cities. We pursue presenting the methodology and databases used. We describe subsequently the shrinkage of justice and hospital facilities in the French urban system through two types of measures: i) shrinkage of public facilities by reduction, which may also lead to ii) shrinkage of public facilities by disappearance. We then test these hypotheses using data indicating justice services provided by courts and short-stay hospital beds (medicine, surgery, and obstetrics (MSO) beds) and the relationship to shrinkage by city size. We show the convergence between shrinkage of court and hospital facilities, both of which operate to the detriment of small cities. Finally, we discuss our results in the light of New Public Management reforms and decline processes of small cities.

The theoretical framework: public management reforms and the weakening of small cities

The proliferation of public sector reforms in different countries since the 1970s has been closely related to economic difficulties and the spreading belief that "Western welfare states had become unaffordable, ineffective and overly constraining on employers and citizens alike" (Pollitt & Bouckaert, 2011, p.6). The term "public management reform" refers to a particular type of public policy, aimed at transforming the public sector [START_REF] Bezes | Réinventer l'État : les réformes de l'administration française (1962-2008[END_REF]. Although the content of reforms has varied from country to country, similarities can be noted. The doctrine of New Public Management (NPM) has, in particular, widely influenced the contents of reforms adopted in Europe, Australasia and North America [START_REF] Pollitt | Public management reform: a comparative analysis: new public management, governance, and the neo-Weberian state[END_REF].

An international approach to the New Public Management doctrine and its territorial impacts

The NPM is a "general theory or doctrine that the public sector can be improved by the importation of business concepts, techniques, and values" (Pollitt & Bouckaert, 2011, p.10).

Strengthening performance is at the heart of this doctrine: results measurement and increasing yields have become central to public action [START_REF] Pollitt | Public management reform: a comparative analysis: new public management, governance, and the neo-Weberian state[END_REF][START_REF] Bezes | Réinventer l'État : les réformes de l'administration française (1962-2008[END_REF]. NPM spread widely among Western states from the 1970s onwards, as part of neoliberalism views on the necessary reform of welfare states and public services. Sometimes associated with radical political discourses about the dismantling of the welfare state [START_REF] Pierson | Dismantling the Welfare State ?: Reagan, Thatcher and the Politics of Retrenchment[END_REF], NPM forms a composite doctrine, which has been considered as strongly tied to neoliberalism (Le Galès & Vezinat, 2014). In the United Kingdom, the United States, New Zealand or Australia, where such reforms were first adopted when "New Right" parties came to power (ibid.), public management reforms have been interpreted by scholars as tools for welfare state retrenchment [START_REF] Artioli | When Administrative Reforms Produce Territorial Differentiation. How Market-oriented Policies Transform Military Brownfield Reconversion in France (1989-2012)[END_REF] and the reduction of the functions carried out by public authorities within society [START_REF] Jessop | The transition to post-Fordism and the Schumpeterian workfare state[END_REF][START_REF] Starke | The Politics of Welfare State Retrenchment: A Literature Review[END_REF]. Indeed, the role of government changed progressively, towards coordinating and making private management possible, and no longer directly providing services. For these reasons, NPM has been associated with the application of neoliberal ideology, in which the role of the state is to guarantee favorable conditions for the market and entrepreneurship [START_REF] Morange | Ville, néolibéralisation et justice[END_REF]. [START_REF] Jessop | The transition to post-Fordism and the Schumpeterian workfare state[END_REF] formulated a critique of this new form of state. According to him, the post-Fordist era is characterized by a transformation of the welfare-state into a "Schumpetarian workfare state", meaning a state which aims at "strengthening the structural competitiveness of the national economy by intervening on the supply side, assisted by lessening the financial burden of welfare and subordinating social policy to the need of the labor market" (Barnett 1999, p.260). This neo-liberalization is coupled with a transfer of the powers of the central state to other entities (local, supranational, or private): the author describes this process as a "hollowing out of the state" (ibid.; [START_REF] Jessop | The transition to post-Fordism and the Schumpeterian workfare state[END_REF].

According to C. [START_REF] Pollitt | Public management reform: a comparative analysis: new public management, governance, and the neo-Weberian state[END_REF], NPM was variously appropriated among countries. The resistance to NPM depended on each state's specific "politico-administrative regime" (ibid. p. 73). For instance, justice reforms conducted in the United Kingdom [START_REF] Haravon | Dix années de réforme de la procédure civile anglaise : révolte ou révolution ?[END_REF]), Italy, Belgium, Germany (Schemtz, 2006) were inspired by NPM, but they were adapted to each national context [START_REF] Vigour | Politiques et magistrats face aux réformes de la justice en Belgique, France et Italie[END_REF][START_REF] Brunin | Les chiffres de la justice française à l'aune des critères européens d'efficacité[END_REF]. Two opposing groups of countries have been distinguished by the [START_REF] Pollitt | Public management reform: a comparative analysis: new public management, governance, and the neo-Weberian state[END_REF]. The first are the "NPM marketisers" (p. 117), including Australia, New Zealand, the UK and the USA, conducted substantial reforms, introduced competition, and business-like methods into the public sector. They have given a large role to the private sector in the restructuring of public sector. In the UK, under Mrs Thatcher's governments, market-type mechanisms were introduced in health care, community care and education. After 1997, the New Labour governments of Tony Blair pursued NPM thinking, and major public services such as education, health care, welfare state services were repeatedly reorganized and their performance measured. After 2010, a Conservative-Liberal Democrat Coalition led by David Cameron pursued major cuts in public expenditure in justice, defense, and local government services. The second group of "continental European modernizers", includes countries such as Finland, France, Sweden, the Netherlands, Italy, and at the federal level Belgium and Germany. In this group, the state remains "irreplaceable and integrative in society, with an operative value system that cannot be reduced to the discourses of efficiency, competitiveness" (ibid. p. 73). However, in these countries, governments tried to "modernize traditional bureaucracy by making it more professional, efficient and citizen friendly" (p.73). They "rationalized" and modernized their public services using NPM management tools such as performance-based pay for civil servants, performance indicators, and evaluation of public services. Each country developed its own reform mix, "sometimes selecting from and transforming NPM tools as they do so" (ibid., p.73).

The territorial and social consequences of the implementation of reforms have been the subject of several case studies. In New Zealand, [START_REF] Barnett | Hollowing out the state? Some observations on the restructuring of hospital services in New Zealand[END_REF] studied the health-sector restructuring of the 1990s. He showed that "the cost-saving approach underlying the government strategy resulted in closing or downsizing services, particularly peripheral rural hospitals" (Barnett, 1999, p. 265), and in southern regions. In Italy, the health system reform has also affected some regions more than others: it too targeted regions where deficits were the most important, by imposing important reorganization or closures of hospital services [START_REF] Perucca | Spatial inequality in access to healthcare: evidence from an Italian Alpine region[END_REF].

According to De [START_REF] De Belvis | The financial crisis in Italy: Implications for the healthcare sector[END_REF], this targeted restructuring may have contributed to reinforcing inequalities regarding health and access to care at the national level, sharpening existing inequalities. For example, Sicily is one the most indebted regions, and was strongly targeted by the reform, while the health situation of its inhabitants is one of the worst in the country [START_REF] Franzini | Determinants of health disparities between Italian regions[END_REF]). Campania's situation is similar [START_REF] De Belvis | The financial crisis in Italy: Implications for the healthcare sector[END_REF].

In targeting specific geographical areas, reforms may worsen the difficulties faced by some regions, and reinforce territorial and social imbalances. Such a method for restructuring enhances inequalities and carries negative effects for residents' well-being. Indeed, in New Zealand, Brabyn and Beere (2006) studied the impacts of health reform on access to Emergency Departments (ED) in hospitals between 1991 and 2001. During this period, ED closures occurred primarily in rural areas and places further than 55km by road from a built-up metropolitan area. Increased distance negatively impacted health service frequentation and the Maori population was especially disadvantaged, enhancing social inequalities in health access. According to the same authors, "the belief [this] did improve efficiency is far from straightforward" (ibid., p. 228). In Italy, the reforms of the health system, which led to hospital closures, also impacted visits to hospitals, in particular in some regions like the Italian Alps [START_REF] De Belvis | The financial crisis in Italy: Implications for the healthcare sector[END_REF][START_REF] Perucca | Spatial inequality in access to healthcare: evidence from an Italian Alpine region[END_REF]. In the Province of Manitoba in Canada, the reforms conducted in the 1990s led to an important reduction in bed numbers, and a drop in visitor rates was consequently recorded [START_REF] Carriere | Across time and space: variations in hospital use during Canadian health reform[END_REF]. This same phenomenon has been observed in the neighboring Province of Saskatchewan (Canada) by [START_REF] Liu | Impact of rural hospital closures in Saskatchewan, Canada[END_REF], who studied the effects of hospital closures following the public hospital reform of 1992. While hospital closures are often presented as a way to increase the quality of infrastructure for the well-being of patients, the fall in visits observed in several cases suggests that closures could, in the first place, cause public health issues [START_REF] Perucca | Spatial inequality in access to healthcare: evidence from an Italian Alpine region[END_REF]. Another possible impact of public services closure is the deterioration of a local economy. These effects are frequently mentioned in work about public service closures, but there are only a very small number of studies that focus on this specific topic [START_REF] Slee | School Closures as a Driver of Rural Decline in Scotland: A Problem in Pursuit of Some Evidence?[END_REF][START_REF] Holmes | The Effect of Rural Hospital Closures on Community Economic Health[END_REF].

Even though the local impacts of closures have been less studied, the results from existing examples suggest that closures may have negative effects for local residents.

The specificities of New Public Management reforms in France: modernizing the state and reducing public spending through the closure of various public service facilities

In France, although neoliberal ideas were adopted by the elite and the Ministry of Finance in the 1980s [START_REF] Pollitt | Public management reform: a comparative analysis: new public management, governance, and the neo-Weberian state[END_REF], the idea of administrative failure did not emerged in the public debate before the 1990s. From then on, there was a spreading belief that NPM could provide the tools to modernize French administrations, resize the central State (l'Etat), modify its competences and improve its efficiency [START_REF] Pollitt | Public management reform: a comparative analysis: new public management, governance, and the neo-Weberian state[END_REF]. According to [START_REF] Bezes | Réinventer l'État : les réformes de l'administration française (1962-2008[END_REF], the 1990s marked a turn in France towards the adoption of NPM principles. 1 In 1995, a circular by Alain Juppé (President Jacques Chirac's Prime Minister) entitled "Reforming the State and public services" initiated these changes, introducing public service contracting. The failure to reduce France's public deficits was also an important factor, which lead to the implementation of an organic law on public finances in 2001 (Loi Organique relative aux Lois de Finances), which organizes performance-based budgeting and systematic public policy evaluation. Under the right wing governments of Presidents Chirac (2002Chirac ( -2007) ) and Nicolas Sarkozy (2007Sarkozy ( -2012)), NPM ideas gained ground. In 2007, the General Review of Public Policies (Révision Générale des Politiques Publiques, RGPP) adopted the principles of the NPM, aimed at rationalizing public expenditure. The RGPP was organized in two phases (2007 and 2010). Several reforms followed from the RGPP, such as the Reform of the Territorial Administration of the central State (Réforme de l'Administration Territoriale de l'État, REATE). The reforms reorganized and compressed the devolved services of the central State that operate at the local level. The sectoral and spatial restructuring of France's tax centers, employment agencies, judicial services, military compounds, police stations and hospital services has also been influenced by the principles of NPM (De [START_REF] Legge | Mission d'information sur les conséquences de la révision générale des politiques publiques pour les collectivités territoriales et les services publics locaux[END_REF]. In France, reforms operated through the evaluation and reorganization of public services and administrations, rather than privatization. As such, France belongs to the category of the "continental modernizers" identified by [START_REF] Pollitt | Public management reform: a comparative analysis: new public management, governance, and the neo-Weberian state[END_REF]. These reorganizations, added to the non-replacement of one in two retiring civil servants, and had very serious consequences for public services and their geographic distribution in the country.

1

The model of the strategic state, which inspired French reforms in the 1990s, illustrates this synthesis between the French administrative tradition and elements from the NPM. This model calls for refocusing the role of central government on steering policy and on strategic functions, by delegating "administrative" tasks to devolved units, local authorities or through outsourcing (privatization or contracting) [START_REF] Bezes | Réinventer l'État : les réformes de l'administration française (1962-2008[END_REF].

In France, two reforms conducted on NPM lines led to a reduction in the number of justice courts. The network of various courts (Figure 1a) has always been dense in France: the 164 Regional high courts (for major civil and criminal matters), 134 Commercial courts (for business disputes) and 210 Labor courts (for employer/employees disputes). These have historically been located in medium or large cities, where prefectures are located (i.e., offices representing the central State located in the main city of each département). 2 The 307 District courts (civil and criminal matters) are located in smaller cities, usually in so-called subprefecture cities: 34 this geographical settlement mirrors the dense presence of France's central State in small cities throughout the country. With the diffusion of NPM, the widespread settlement of justice court services was seen as oversized, inefficient and archaic. In the 1990s, the Ministry of Justice was put under pressure by the Ministry of Finance to close sites. In 2001, an initial reform leading to the closure of some Commercial courts was undertaken. In 2008, a second reform focused on District and Regional high courts. These reforms followed NPM recommendations by using quantitative measures to identify which courts to maintain, transform or close: thresholds of activity and magistrate numbers were used as efficiency measures to identify sites to close. 5 The territorial impacts of these reforms were not taken into account, that latter not being "intended as a tool for regional planning" according to President Sarkozy's Prime Minister from 2007 to 2012, François Fillon (Artioli, 2017, p. 98). Considerations of regional development planning were limited to the desire to keep at least one Regional court open per département. This paper examines how these reforms have changed the location of courts in the past 16 years. Compared to the District courts, Regional high courts deal with more complex or more important cases (involving litigation exceeding €10,000).

4

These figures correspond to the number of courts in 2016.

5

The minimum activity standard adopted was "1,500 civil cases and 2,500 prosecutable criminal cases per year for District courts, 615 cases per year for Regional courts and 300 for Labor courts. In addition, District courts with fewer than ten judges and Regional courts with no full-time judge were also considered unsustainable" [START_REF] Ficet | Trajectoires de réforme de la carte judiciaire et managérialisation de l'État. Analyse comparée des politiques de territorialisation de la Justice en France et en Belgique[END_REF].

The reorganization of hospitalization along NPM lines in France has led to a reduction in hospital bed numbers. As with court services, France's provision of hospital care has been marked by a hierarchical conception of its national territory. According to [START_REF] Kervasdoué | col. Que sais-je ?[END_REF], there are 33 regional hospitals, located in large cities, each with a medical school. 6 In these hospitals, complex care (for burns, transplants, etc.) can be provided, in addition to the whole range of more common health care treatments. The next level of the hierarchy comprises 627 hospital centers, with operating theatres for surgery [START_REF] Kervasdoué | col. Que sais-je ?[END_REF]. These are located in large and medium-sized cities, often with more than 50,000 inhabitants, but sometimes with only as little as 20,000 persons, in sparsely populated areas, such as mountainous regions.

Since the 1990s and the circular Juppé of 1995, successive reforms have affected the health sector. These reforms have all been shaped by NPM. In 1990, under a center-left government, hospitals were encouraged to develop a project-based approach to management, while also being subject to contracting. In 1996, the government decided that annual health expenses would be controlled under the National Objective of Health Insurance Expenditure (Objectif National des Dépenses d'Assurance Maladie) fixed in a yearly financial law. Reducing expenditure became a priority from the 2000s onwards [START_REF] Lerouvillois | Les hôpitaux sous contraintes : des restructurations aux recompositions de l'offre, l'exemple de la Basse-Normandie[END_REF][START_REF] Granger | L'hôpital en sursis. Idées reçues sur le système hospitalier[END_REF]. In 2007, at the time of the RGPP, health spending accounted for 9% of GDP, with hospitals representing 44% of this. For the Sarkozy/Fillion government, the public health which determine hospitals' financial resources through General Operating Grants (Dotation Globale de Fonctionnement), bed capacities, and the reorganization of work between public hospitals and private clinics (in which care is also partly funded by the public health insurance system). All these reforms were inspired by NPM tools and ideas and included: quantifying and pricing activities, reporting, budget control, and creating Agencies. Two main consequences ensued: firstly, there were mergers, consolidations, and transformations; 7 secondly, bed numbers were cut and small establishments closed. As with the court reforms, activity thresholds were set in order to identify possible targets for closure in hospitals or clinics [START_REF] Vallancien | L'évaluation de la sécurité, de la qualité et de la continuité des soins chirurgicaux dans les petits hôpitaux publics en France[END_REF]: for example, the Decree of 9 October 1998 specified that obstetric care could only take place in maternity wards with more than 300 deliveries a year [START_REF] Baillot | Les maternités : un temps d'accès stable malgré les fermetures[END_REF].

Technological transformations also drove developments in ambulatory care [START_REF] Côté | Le virage ambulatoire : vers l'humanisation des soins ? Le virage ambulatoire : défis et enjeux[END_REF]: cuts in full-time hospital beds (for stays of more than 24 hours), and an increase in the number of alternative hospitalization places (day or night stays, ambulatory or in-home surgery and anesthetics). These have all constituted two highly visible aspects of changes in techniques.

The arguments about the efficiency of the courts and hospitals which emerged in the late 1990s, the reform of the judicial system in 2007 and the reforms in hospital management launched in the 2000s have all followed on from the gradual adoption of NPM by both European and national authorities. According to Taulelle (2012a) and De [START_REF] Legge | Mission d'information sur les conséquences de la révision générale des politiques publiques pour les collectivités territoriales et les services publics locaux[END_REF], the reforms did not take into consideration the question of the territorial impact of closing public services considered (specifically on employment and induced services): nor was equal accessibility for 7 Mergers led to the creation of a single legal entity; the cooperations have maintained all establishments concerned but have led to contractualised exchanges (e.g., personnel or services); while transformations modified the orientation of care (e.g., units switching from short-term hospital functions to long-stay care functions, generally reserved for dependent elderly persons).

inhabitants to services accounted for. Our hypothesis is that the use of activity threshold levels lead to more closures in small and medium size cities. This was in line with the dynamics of change in France's urban system that was already disadvantages for small cities.

Urban dynamics since the end of the 20 th century: growing metropolitan areas, urban shrinkage and the weakening of small cities

In the 1990s, as the tendency to urban concentration arose [START_REF] Hall | The polycentric metropolis: learning from Mega-cities Regions in Europe[END_REF][START_REF] Scott | A World in Emergence: Cities and Regions in the 21st Century[END_REF][START_REF] Taylor | Extraordinary Cities[END_REF], the decline of sub-groups of small and medium-sized cities was pointed out in urban shrinkage studies (Turok & Mykhnenko, 2007;Fol & Cunnimgham, 2010). For his part [START_REF] Filion | Growth and decline in the Canadian urban system: the impact of emerging economic, policy and demographic trends[END_REF], referring to current economic transformations in the Canadian urban system, presented a dualization scenario, with shrinking small urban areas on the one hand, and growing heartland cities on the other hand. Nel et al. (2019) signaled the "reality of long-term population decline, ageing and the loss of youth from rural and small-town New Zealand for decades" (p. 168). [START_REF] Cottineau | Un système intermédiaire, les trajectoires des villes russes entre dynamiques générales et histoires spécifiques[END_REF], [START_REF] Batunova | Urban shrinkage: an unspoken challenge of spatial planning in Russian small and medium-sized cities[END_REF] underlined a shrinking process in Russia, especially in small cities. In Japan [START_REF] Buhnik | Géographie de la décroissance démographique et évolution des mobilités quotidiennes dans la conurbantion Osaka-Kyoto-Kobe[END_REF], Germany [START_REF] Chatel | Une mesure du déclin démographique des villes allemandes de 1820 à 2010[END_REF][START_REF] Roth | Les "villes rétrécissantes" en Allemagne[END_REF], and in East European countries [START_REF] Haase | Shrinking Cities in Post-Socialist Europe: What Can We Learn From Their Analysis for Theory Building Today?[END_REF], ongoing urban shrinkage processes have been described. These processes are not systematically specific to small cities, but rather concern old industrial regions and rural environments. In 2019, Gourdon et al. focused on the demographic dynamic of 3,953 European cities between 1961 and 2011 and identified 4 demographic trajectories, including stagnation, decrease, growth and slow down after 1990. Although they did not find a statistical relationship between demographic trajectories and city size, they underline the fact that very small cities (under 25,000 inhabitants, and so 1,685 urban areas in the sample studied) are frequently found in the growth and slow down categories, while small cities make up 48% of the stagnation and decrease categories. They also put forward the fact that 40% of the small cities faced decline from 1981 onwards. At the European level, Baron et al. (2010) documented the shrinking processes occurring in Europe, and stated the weakening of some small cities located in old industrial regions or peripheral areas. Factors, among others, listed to explain demographic decline have included: trends in outward migration and loss of attractiveness [START_REF] Miot | Face à la décroissance urbaine, l'attractivité résidentielle ? Le cas des villes de tradition industrielle de Mulhouse, Roubaix et Saint-Etienne[END_REF]; dependency on industrial activities [START_REF] Kresl | Smaller Cities in a World of Competitiveness[END_REF]; remoteness from new information economic cycle hubs or high speed transportation infrastructure [START_REF] Bretagnolle | Villes et réseaux de transport : des interactions dans la longue durée[END_REF]; or a combination of all of these processes [START_REF] Roth | Les "villes rétrécissantes" en Allemagne[END_REF][START_REF] Friedrichs | A theory of urban decline: Economy, Demography and Political Elites[END_REF]. Some studies have also looked at the withdrawal of services: in the Canadian context, "there has been a dramatic retrenchment of both public and private sector services in the past two decades" (Halserth & Ryser, 2006, p. 70), particularly in small cities. According to the same authors, this was particularly the case for police, educational services and hospital care. In New Zealand, Nel et al. ( 2019), Brabyn & Beere (2006) have both pointed to population loss and the withdrawal of public services in small cities. In Germany, [START_REF] Reichert-Schick | Les services à la population dans les régions rurales périphériques de l'Allemagne : les exemples de la Poméranie occidentale et de l'Eifel occidentale[END_REF] documented the withdrawal of postal, educational and health services, as well as grocery shops and restaurants in peripheral regions.

In France, over the past 30 years, analysis of population variations in French cities have highlighted two simultaneous redistribution processes: growth of large urban areas [START_REF] Veltz | Métropoles, périphéries et économie mondiale : une économie d'archipel[END_REF] and urban decline [START_REF] Wolff | Shrinking Cities, villes en décroissance: une mesure du phénomène en France[END_REF][START_REF] Cauchi-Duval | La décroissance urbaine en France : les effets cumulatifs du déclin[END_REF]. The former has resulted in a concentration of individuals, human activities, services and the main government functions at the top of the urban hierarchy. The latter process has manifested itself in the continued decline of some cities in the French urban system, due to declining populations, employment, activities and often services too. For [START_REF] Pumain | Quel rôle pour les villes petites et moyennes des régions périphériques ?[END_REF], the trend to greater hierarchies (i.e., the increasing inequality in the size of cities in favor of metropolitan centers and large cities) is a phenomenon that weighs on the development sustainability of small cities: given globalization, metropolitan areas consolidate their positions while small and medium-sized cities are more on paths to stagnation or demographic decline. Indeed, in recent times, Paulus noted that one third of French urban areas with less than 10,000 inhabitants were in decline, and one-fifth in stagnation. 8 The concentration of populations in small cities fell from 10% of all urban inhabitants in mainland France to 8.5%, between 1968 and 2011 [START_REF] Paulus | Croissance et déclin dans le système des villes françaises, La population des aires urbaines entre 1968 et 2011[END_REF]. He also noted, however, that 18% of small cities had grown faster than the average, especially those with less than 5,000 inhabitants. Studying the decrease in France's 771 functional urban areas, Cauchi-Duval et al. (2017) showed that 283 cities have been decreasing since 1990, among which two thirds are small cities.

In France, the legacy of a fine administrative mesh and an egalitarian principle for access to public services for a long time favoured a grid of small cities whose public service activities often provided the basis of development [START_REF] Jennequin | Politiques publiques et développement territorial en France : quid des activités tertiaires ?[END_REF]. More recently, however, both the growth of metropolitan urban areas and the challenging of egalitarian planning policies through the implementation of NPM have weakened small cities [START_REF] Berroir | Villes moyennes et dévitalization des centres : les politiques publiques face aux enjeux d'égalité territoriale[END_REF]. From the 2000s, small cities have been put aside the political agenda: they have suffered the closure of public services, even though many of them had already been facing deindustrialization. In France, [START_REF] Courcelle | Services publics et territoires : adaptations, innovations et réactions[END_REF], [START_REF] Cahu | De la réforme de la carte judiciaire ou l'instrumentalisation de critères objectifs au service d'un nouveau rapport scalaire de pouvoir[END_REF], and De [START_REF] Legge | Mission d'information sur les conséquences de la révision générale des politiques publiques pour les collectivités territoriales et les services publics locaux[END_REF] found that rural places and cities were indeed affected by the withdrawal of public services. The use of a threshold to decide the closure of facilities in the territorial reorganization of public services (for example the closure of obstetric hospital unit with less than 300 childbirths per year) has mechanically paved the way for closure of small city facilities. [START_REF] Barczak | Quelle évolution de la présence des services publics en France[END_REF] have worked on the evolution of public services at the level of all communes, France's basic municipal unit. 9 By looking at many facilities, they concluded that "the withdrawal, expressed by a reduction in the number 8 According to a communication by Paulus made at the Labex seminar on Degrowth, 28 May 2015. 9 These are about 36,000 communes throughout the country. of municipalities equipped, has been widespread: it affects all French regions and weakens rural communes and small cities especially" (p.31). 10 In this process, some small or medium-sized cities have even been called "martyr" cities where several facilities were closed simultaneously: for example, Joigny (Yonne) has suffered the closure of its two justice courts, its military base, as well as its surgery and obstetric facilities. Montluçon (Allier) has combined the closure of the obstetric hospital and its administrative court.

Therefore, drawing on both strands of public service reform and small city decline, our hypothesis is that the shrinkage of public services does not affect the urban system in a homothetic way, but rather affects small cities especially. We will test this hypothesis in mainland France, looking at two categories of public facilities: hospital beds as indicative of welfare facilities and justice courts, as a sovereign service. Doing so, we will not try to draw a causal relationship between small cities demographic shrinkage and public service withdrawal for two reasons: first, most authors emphasize the multi-factorial aspects of shrinkage, and second our methodological approach does not provide insight into the inter-related causes.

Methods and data: hospital beds and justice courts in functional urban areas

To address these questions, we built two specific databases respectively for justice courts and hospital beds. A third database was used which reconstituted the demographics of urban areas from 1975 to 2010.

10

For the majority of the public services observed over the period 1980-2013, closures were greater than the number of openings at the communal/municipal level: 24% of the municipalities lost their primary and nursery school; 36% of the municipalities lost their post office; 31% of the communes their tax collection office; 28% their rail station; 48% their maternity unit and 4% their hospitals. The RGPP has amplified these trends, and the authors have shown that the impact has been particularly strong for post offices, tax offices and gendarmeries (rural police offices).

Cities as functional urban areas

We chose functional Urban areas as the level to observe the evolution of the population in the French urban system. 11 Using this functional delimitation of cities, rather than a morphological or administrative definition, we take into account the attraction that a city exerts on its surrounding space, notably through the location of higher functions, such as hospital care or the exercise of justice. Only mainland France has been studied here, as overseas departments and regions face specific sets of issues, including a relatively small number of equipped cities. This makes analyzing them simultaneously with the rest of France complex. 771 urban areas were identified for mainland France in 2010 by the French National Institute of Statistics and

Economic Studies (INSEE).

Data on justice courts

To document the evolution of the distribution of the courts across cities, we adopted the nomenclature used in the Permanent Database of Facilities and Equipment of INSEE (Base Permanente des Equipements). Five types of courts are identified at the municipal level and are considered as different types of facilities: Regional courts, District courts, Courts of appeal, Commercial courts and Labor courts. We consider these courts as five types of justice facilities, and use the term "court" for convenience to discuss the presence of the judicial institutions in a city. To document the evolution of their presence since the 2000s, we created intermediate databases at the municipal level for eight years: 2000, 2002, 2004, 2007, 2009, 2011, 2014 and 2016. For the 2000s until 2011, we collected the data found on <Data.gouv.fr> and in the <Justice.gouv.fr> website directories, which we have completed or verified, based on a history 11 Urban area: An urban area is a group of contiguous municipalities, encompassing an urban core providing at least 1,500 jobs (the urban unit), surrounded by peripheries, among which at least 40 % of the employed resident population works in the urban core (https://www.insee.fr/en/metadonnees/definition/c2070; le 12.9.2019). each year, providing data on the main hospital disciplines : medicine, surgery and obstetrics (MSO). Beds for MSO are in principle reserved for full-time care (more than 24 hours), and for acute conditions. The SAE is produced following an annual, exhaustive and mandatory survey of public and private health establishments located in France, conducted by the Ministry of Health's statistical unit. It contains information on the structures, capabilities, facilities and equipment, personnel and activities of these institutions. We have reconstructed a longitudinal table from 2000 to 2016, to allow for the location of these beds in hospitals. 12 Information on health facilities was subsequently aggregated for urban areas. 13 We choose hospital beds rather than hospital establishments, since some establishments lost their MSO beds but were maintained as retirement homes or rehabilitative care structures.

Methods: measures and statistical correlations

We built up two measures in order to identify two shrinkage processes. If the number of courts or the MSO beds decreases in a city, while facilities remain, we refer to public facilities shrinkage by reduction. By contrast, if a city loses all of one of these facilities, we use the term public facilities shrinkage by disappearance. We have disassociated these two forms believing 12

In our paper, we often use the term hospital in order to talk about both public hospitals and private clinics. Both of them offer a public service, since the public social security system covers hospitalization costs, whether in public hospitals or private clinics.

13

Analyses were also conducted at the level of urban units: the results agree with those obtained for urban areas, and it was decided to favour urban areas as the level of analysis, as these geographical entities are more relevant in the light of the research subject here. Beds for health care in rural communities are excluded from our analysis, as they only concern very small numbers (e.g., 1,500 beds or 0.7% of all beds in 2016).

that they are different situations symbolically. In extreme circumstances, courts or MSO hospital beds for short stays may disappear: a city then loses a symbolic function and power of attraction on its surroundings. In the case of reductions, the function is maintained and the city continues to play a central role in matters of justice or hospital care.

Two samples of cities have been considered for analysis: the first relates to the 380 urban areas which had at least one court between 2000 and 2016, and the second to the 539 urban areas that had at least one bed for MSO care in the same period. We test for the existence of statistical relationships the shrinkage of court facilities on the one hand, and of hospital beds on the other hand, and certain characteristics of these cities (in mainland France) using Chi-square tests. For this, we establish three categories of shrinkage: i) the loss of the service in question, ii) the reduction in the number of courts or beds, and iii) the maintenance or increase of courts or beds.

To test the hypothesis of public facilities shrinkage affecting small cities, the two samples of cities were broken down into three discrete population class sizes. The use of only demographic criteria to identify categories of small cities has been much discussed [START_REF] Taulelle | La France des villes petites et moyennes[END_REF][START_REF] Gourdon | Des petites villes davantage touchées par la décroissance ? Comparaison des trajectoires démographiques à l'échelle européenne (1961-2011)[END_REF]. In this case, the two city samples differ, because they are adjusted to the distribution of each facility: 380 cities with court facilities for at least one year during the period, compared to 539 cities with MSO beds. The distribution of the courts in the city system allowed us to retain an upper threshold of 20,000 inhabitants for small cities, and 100,000 inhabitants for medium-sized cities. These thresholds are frequently mentioned in the literature on small cities [START_REF] Edouard | La petite ville : contexte scientifique et enjeux de développement/aménagement[END_REF] or medium-sized cities [START_REF] Santamaria | La notion de "ville moyenne" en France, en Espagne et au Royaume-Uni[END_REF]. Other authors, however, have emphasized the simplistic nature of this size indicator and recall the limits of these small and medium categories [START_REF] Edouard | La petite ville dans la recherche géographique en France : de la simple monographie au territoire témoin[END_REF]Mainet, 2011;[START_REF] Laborie | Les petites villes face aux fermetures des services publics[END_REF][START_REF] Santamaria | Les villes moyennes françaises et leur rôle en matière d'aménagement du territoire : vers de nouvelles perspectives ?[END_REF]. The geographical distribution of hospitals led us to use different class limits: we use the upper limit of 50,000 for small cities, and the lower limit of 200,000 inhabitants for large cities.

Results: Public facilities shrinkage: reduction and disappearance

We observe a decrease in the number of courts and hospital beds in mainland France during the period 2000-2016. In this section, we contextualize the results specific to each public service in order to highlight current trends.

Decreasing numbers in MSO beds and courts

Between 2000 and 2016, the number of courts fell from 1,158 to 829 in mainland France: i.e., by 28% (329 closures). This decrease varied according to the types of courts considered (Figure 2a): the number of Commercial courts fell by 38%, District courts by 36%, Regional courts by 8%, and Labor courts by 23%.

Over the same period, the number of medical, surgery and obstetrics beds also fell a lot in the cities of mainland France (Figure 2b): down from 239,059 to 203,011 (i.e., a cut of 36,048 or -5%). The decline was particularly strong for surgical beds (down by -32,393), while the number of beds in obstetrics only decreased slightly (-5,710). By contrast, the number of medical beds increased a little (up by 3,018).

Cities, justice court and MSO hospital bed shrinkage: disappearance or reduction

How have the decrease in the number of courts and hospital beds affected cities? Have these cuts led to falls in the number of cities hosting these facilities?

Shrinkage by disappearance is predominant for justice courts. The reduction in the number of courts has indeed resulted in a decrease in the number of urban areas with court facilities: 160 cities lost a court (i.e., 42% of cities in the sample that had at least one facility between 2000 and 2016). In the case of hospital beds, 59 urban areas in the sample 14 experienced the complete disappearance in their provision of MSO beds (i.e., 11% of the cities surveyed and totaling 2,022 beds in 2000) (Map 3b). 15 The disappearance of MSO beds was rather widespread.

Hospital withdrawal was reported in the literature for the 1990s [START_REF] Lerouvillois | Les hôpitaux sous contraintes : des restructurations aux recompositions de l'offre, l'exemple de la Basse-Normandie[END_REF][START_REF] Jousseaume | Diffusion et recompositions de l'offre médicale : l'exemple des Pays de la Loire (1967-2000[END_REF][START_REF] Vigneron | 10 ans de recomposition hospitalière[END_REF]. It continued in 2000-2016.

14 There were 56 cases, when only taking into account urban areas experiencing openings of beds after 2000 and closures before 2016.

15

In the case of hospital beds, at least half a million residents of these 59 cities, and probably more including people living in neighboring, unequipped urban areas and rural areas, found themselves far from hospital services.

Figure 3a. Typology of shrinking justice courts Figure 3b. Disappearance of MSO bed: Shrinkage by disappearance

Shrinkage by reduction has been most common in the case of hospital beds (75% cities). Out of 380 cities with a justice court in 2000, 83 cities (22%) saw a decrease in the number of courts while maintaining this public facility (Figure 3a). 128 cities (34%) maintained all their courts and 9 cities gained one. 16 Out of 539 cities with hospital facilities in the period, the vast majority, 402 urban areas (75% of the sample) have been affected by falling bed numbers (the loss of at least one bed) (Figures 3b,3c). 78 urban areas (14%) have been spared by the shrinkage or have even experienced an increase in their number of MSO beds. For all urban areas of the sample, the average fall in numbers was -25%, and more than half of them showed a loss of MSO beds greater than -18%. 17 A strong fall can also be observed relative to populations living in cities: 18 Supply fell from an average of 62 beds per 10,000 inhabitants in 2000 to 48 in 2016 (or -23%). In half of the cities, the density of beds fell from less than 54 to less than 44 beds per 10,000 inhabitants, between these dates.

Gains have affected few cities: altogether 11 urban units (9 new urban areas) obtained a court during the period. These have mostly been Commercial courts, in places where Regional courts had previously dealt with commercial mattersespecially in eastern France. The cities include: Mulhouse, Metz, Colmar, Annecy, Guéret, Mende, Strasbourg and Saverne. Montbard and Pertuis obtained a District court each, and Avesnes-sur-Helpe a Labor court. 17 By contrast, in 2000, cities with facilities provided an average of 457 beds. This figure had dropped to 423 by 2016. The fall in the median number of beds also reflects this decline: half of cities with facilities had less than 118 beds in 2000, and this figure fell to 105 by 2016. The tails of the distribution were not spared: the mostequipped urban area (Paris) lost 11,160 beds, while the least-equipped lost one bed.

18

The calculations presented for 2016 are carried out for functional urban areas equipped with MSO beds, excluding the Noyal-Pontivy functional urban area, which had an exceptional evolution that would artificially affect our conclusions. Noyal-Pontivy experienced an unusual rise in the number of beds per inhabitant because a new health facility opened in 2012, following the merger of establishments in Pontivy and Plémet-Loudéac.

Figure 3c. Evolution rates in MSO bed numbers: Shrinkage by reduction

The shrinkage of justice courts and MSO hospital bed shrinkage: the case of small cities

How has the shrinkage of courts and hospital beds occurred in the urban system? Our hypothesis is that NPM policies in justice and health services have targeted small cities and spared large ones. Chi-square tests do show a relationship between public facilities shrinkage and city size.

The indicator on disappearance validates the hypothesis that shrinkage has been disproportional in small cities, but the indicator for shrinkage by reductions qualifies this finding.

In the case of courts, the results of the statistical test are significant and indicate a high intensity relationship (a Tschuprow's T coefficient of 0.5) between types of changes in court facilities in cities (disappearance, stability and decrease/increase) and the class sizes. 19 A comparison of the observed distribution of the functional urban areas between these crossed categories with a random distribution reveals that justice court shrinkage occurs in its most extreme formdisappearanceto the detriment of the small cities (Table 2a). By contrast, justice court shrinkage by reduction concerns average-size cities.

For hospital beds, the Chi-square 2 test is also significant (Tschuprow's T coefficient of 0.14) and demonstrates a size effect: small cities are more likely to fall in the "disappearance" category of MSO beds between 2000 and 2016 (Table 2b). 20 Fewer medium-sized cities are affected by disappearances: instead, they are more affected by shrinkage through reduction. In the case of hospital beds, small cities had a special place in the shrinkage process: 90% of the functional urban areas that have seen MSO beds disappear are smaller than 17,000 inhabitants, half of them smaller than 6,200. 21 These results converge with previous studies : Jousseaume 19 This test makes it possible to interpret the relationship between the categories of the variables: 0.25 < is weak; 0.25 << 0.50 is average; 0.50 << 0.75 is strong; and > 0.75 is very strong.

20

Chi-square tests make it possible to measure deviations from a theoretical situation in which there is independence between the size and shrinkage categories. The test compares the observed situation (a distribution of cities into 9 categories) to a situation where the cities would be randomly distributed (across these 9 categories). The difference between the observed and random distribution is indicated in italics for each case in Table 2a andb.

21

Given the sample of 539 cities, the 392 urban areas with less than 50,000 inhabitants are defined as "small", and the 100 urban areas with 50,000 to 200,000 inhabitants as "average". The remaining 47 cities are "big" (Map 1). Other size classes were tested and our analyses provided similar results. (2002) in Pays de la Loire showed that the 1991 hospital reform challenged the existence of hospital services in small cities. They also converge with the 2016 report of France's Small Cities Association (Association des Petites Villes de France) which indicated that they have been particularly affected by the complete closure of hospitals.

Discussion: the Shrinkage of Public Services in Small Cities in Perspective

Our aim is to measure the shrinkage processes that have occurred in public facilities in recent decades; we also wish to underline two types of shrinkage processes that differentiate small cities and other cities. In order to do so, we created two databases tracking the location of justice courts and hospital (as well as private clinic) facilities. We have shown that there has been a decrease in the numbers of MSO beds and justice courts in cities in mainland France. Our results show a predominance in shrinkage by disappearance for justice courts, and by reduction for hospital beds. However, both processes target small cities and have aggravated inequalities in access to public facilities among citizens living in small cities, and for citizens living in large and medium-size cities. How do our results fit in with the current international research on the territorial impact of NPM management tools and dynamics of decline in small cities?

The decrease in court facilities and hospital beds: an outcome of NPM-inspired reforms

In both cases studied here, the decline in the number of facilities is clear, as 28% of courts (329) and 15% of MSO beds (36,048 beds) were closed between 2000 and 2016. For the courts, the break introduced by the 2007 Dati reform was significant. Named after Minister of Justice Rachida Dati, the reform led to a steep fall in the number of courts between 2008 and 2011, with the closure of almost one third of jurisdictions [START_REF] Cahu | De la réforme de la carte judiciaire ou l'instrumentalisation de critères objectifs au service d'un nouveau rapport scalaire de pouvoir[END_REF]. A slight increase, however, then occurred in the number of Regional courts after 2014, when Christine Taubira (Minister of Justice for the new Socialist government), 22 reversed some of the 2008 closures, on the basis of difficulty of access and the fact that service rationalization should not lead to any litigant being more than 45 minutes-drive from a Regional court [START_REF] Cahu | De la réforme de la carte judiciaire ou l'instrumentalisation de critères objectifs au service d'un nouveau rapport scalaire de pouvoir[END_REF]. 23 For MSO beds, the recent decline has continued a trend which began in the 1990s [START_REF] Tonnelier | Les équipements hospitaliers en France[END_REF]. It is both related to technological developments, and to continuity in the NPM-inspired reforms started in the 1990s [START_REF] Baillot | Les maternités : un temps d'accès stable malgré les fermetures[END_REF][START_REF] Belorgey | Une consultocratie hospitalière ? Les consultants, courtiers de la réforme du système de santé[END_REF]. 24 Smaller hospitals could not face competition and saw falls in their number of medical acts and so in their financial resources: this led to closure of MSO beds, or their transformation into retirement homes or rehabilitative care centers [START_REF] Delas | L'hôpital public, un nouvel acteur territorial entre aménagement sanitaire et rivalités stratégiques[END_REF][START_REF] Granger | L'hôpital en sursis. Idées reçues sur le système hospitalier[END_REF]. For both justice courts and MSO beds, the decrease in facilities occurred in parallel to the implementation of the Dati and T2A reforms inspired by some NPM principles: cost cutting of public expenses, means' concentration, and increased competition between providers. The Dati reform and the T2A were implemented by the right wing governments of Chirac and Sarkozy. However, France's application of NPM principles has been more interpreted as being managerial rather than anti-statist, and our results concur with Pollitt and Bouckaert's classification (2011), whereby France belongs to the "continental European modernizers" rather than the "NPM marketizers".

As in other countries, shrinkage and NPM both target small cities

The Chi2 test shows the over-representation of small cities in the sample of cities hit by disappearance or reduction of justice courts or MSO beds. Indeed, the 2007 justice reform led to the closure of courts in 123 small cities, i.e., a third of the sample. Therefore, the justice reform introduced inequality of access between small and large cities. For MSO beds, shrinkage 23 Three Regional courts were thus (re)opened in Saint-Gaudens (Haute-Garonne), Saumur (Maine-et-Loire) and Tulle (Corrèze), as were three separate courtrooms of Regional courts: in Dole (Jura) for the Regional court in Lons-le-Saunier, in Guingamp (Côtes-d'Armor) for the Saint-Brieuc court, and in Marmande (Lot-et-Garonne) for the Agen court.

24

Nearly 790,000 deliveries took place in mainland France in 2010, 5% more than in 2001. In addition, hospitalizations for childbirth lasted 5 to 6 days in 2001, and 5 days in 2010 [START_REF] Baillot | Les maternités : un temps d'accès stable malgré les fermetures[END_REF].

by disappearance hit 55 cities, a tenth of the total sample of MSO cities, but reduction occurred in 194 small cities, one third of the sample. For MSO beds, shrinkage has been predominantly carried out through reduction. In fact, the complete disappearance of MSO beds is not as widely spread, since the necessity of access to hospital care has sometimes been taken into account to maintain some small units [START_REF] Baillot | Les maternités : un temps d'accès stable malgré les fermetures[END_REF]. Bed-number reduction has been one of the various managerial tools used in the health care reforms in order to rationalize hospitalization provision [START_REF] Belorgey | Une consultocratie hospitalière ? Les consultants, courtiers de la réforme du système de santé[END_REF][START_REF] Baillot | Les maternités : un temps d'accès stable malgré les fermetures[END_REF]. While small cities are generally equipped with small establishments, the impact of rationalization policies has occurred at the expense of smaller institutions and cities [START_REF] Granger | L'hôpital en sursis. Idées reçues sur le système hospitalier[END_REF][START_REF] Delas | L'hôpital public, un nouvel acteur territorial entre aménagement sanitaire et rivalités stratégiques[END_REF]. Thus, after having been influenced by a national tradition of intervention and supervision of public services towards equality, NPM inspired policies have turned towards a strategy of "tightening public services" [START_REF] Soumagne | Les services en milieu rural, enjeu d'aménagement du territoire[END_REF][START_REF] Barral | La suppression des tribunaux d'instance : la fin d'une justice accessible à tous[END_REF]. This is completely in line with Halseth and Ryser's observation in Canada (2006), or by Brabyn and Beere (2006) in New Zealand for health services: a shift in health facilities' location from an egalitarian territorial approach towards an efficiency objective. However, in contrast to New Zealand (Brabyn & Beere, 2006), or Canada [START_REF] Halseth | Trends in servcice delivery: Examples from rural and small town Canada, 1998 to 2005[END_REF], where the closure led to the complete withdrawal of hospitals, the majority of cities in France are not facing a complete disappearance of services, but rather a reduction. Reduction in bed numbers rather than complete disappearance may have occurred thanks to local action to maintain structures. Such success in postponing closures was also observed by [START_REF] Artioli | Les politiques du retrait territorial de l'État : Réformes de la carte militaire et gestion des mobilisations locales (1989-2012)[END_REF] for military reforms. Shrinkage by reduction rather than by disappearance may be interpreted as a softer implementation of NPM principles in the continental European states, as opposed to a harder implementation by the Anglo-Saxon marketizers [START_REF] Pollitt | Public management reform: a comparative analysis: new public management, governance, and the neo-Weberian state[END_REF].

These results confirm Laborie 's assertion that "the scope of the contraction of public services now includes small cities, in addition to rural areas; that is to say the centralities of proximity Losing functions or population is not new for small cities, and the literature on urban systems and shrinking cities abounds with examples of small city decline [START_REF] Batunova | Urban shrinkage: an unspoken challenge of spatial planning in Russian small and medium-sized cities[END_REF][START_REF] Cauchi-Duval | La décroissance urbaine en France : les effets cumulatifs du déclin[END_REF][START_REF] Chatel | Une mesure du déclin démographique des villes allemandes de 1820 à 2010[END_REF][START_REF] Paulus | Croissance et déclin dans le système des villes françaises, La population des aires urbaines entre 1968 et 2011[END_REF][START_REF] Pumain | Quel rôle pour les villes petites et moyennes des régions périphériques ?[END_REF]. What is new here, is that some small cities, already weakened by globalization [START_REF] Pumain | Quel rôle pour les villes petites et moyennes des régions périphériques ?[END_REF] or deindustrialization processes [START_REF] Kresl | Smaller Cities in a World of Competitiveness[END_REF]Atkinson, 2019) are now further weakened by state reforms.

Although [START_REF] Gourdon | Des petites villes davantage touchées par la décroissance ? Comparaison des trajectoires démographiques à l'échelle européenne (1961-2011)[END_REF] underline the fact that decline occurs not only in small cities, and Atkinson (2019), Kresl and Ietri (2017) insist on the fact that small cities are not a homogeneous category, it must be emphasized that for small cities, the provision of public services is an essential part of their attractiveness [START_REF] Boutet | Petites centralités. Entre desserrement urbain et dynamiques macro-régionales[END_REF][START_REF] Bailleul | Les petites villes européennes comme enjeu d'équité territoriale[END_REF]: "the availability of services is a key building block for economic diversification and the consequences of service closures can have significant effects upon community" (Halseth & Ryser, 2006, p. 71). Indeed, the fragility induced by the shrinkage of justice courts or MSO beds may affect the functioning of these cities in three broad ways. To start with, closures mean that inhabitants are increasingly remote from services and face greater inequalities in access: as an example we observed that the share of the population living in a municipality less than 30 minutes drive from a District or Regional court fell by 10%, from 2000 to 2016 [START_REF] Guiraud | Les réformes de la Justice entre 2000 et 2016 : une rétraction des tribunaux au détriment des petites et moyennes villes de France métropolitaine[END_REF]. This concerns 3 million people. Similarly, the share of the population living more than 30 minutes away doubled following the 2008 reform, affecting more than 14.8 million people:

i.e., 7 million more than before the reforms. Secondly, the disappearance of facilities weakens small cities by reducing their local centrality functions. Disappearance weakens their power of attraction in surrounding areas, and local users then have to travel to cities still equipped with facilities. Indeed, "the closure of courts contributed to a feeling of being 'downgraded' in small, sub-prefecture cities which lost certain functions related to their status" [START_REF] Laborie | Les petites villes face aux fermetures des services publics[END_REF].

Thirdly, the disappearance of facilities may have chain effects on the other functions and activities of a city. "Snowball" (Taulelle, 2012b) or "domino" effects (De Legge, 2011) are specifically mentioned in several studies: the closure of a public service may lead to other closures, and thus have negative impacts on "the local economy, employment and the demographic vitality on the territory affected" (De Legge, 2011, p.147). This seems problematic as small cities often have limited economic diversity, so that chain reactions associated with closures are particularly strong. Public service reforms could thus contribute to creating or strengthening the dynamics of urban decline.

In all, by drawing on quantitative measures and statistical tests, we have been able to demonstrate that the shrinkage of courts and hospital beds mainly affects small cities. Using two indicators of shrinkagedisappearance and reductionour study highlights common trends and specificities: as in various Western countries, NPM implementation in France has resulted in the withdrawal of public facilities in small cities. However, for hospital beds, the shrinkage in France also operates through reduction in bed numbers and appears in most cities: falling bed numbers are also due to the extensive transformation of hospital services into ambulatory care. France's new (organizational) maps 25 of both facilities are no longer part of a vision for the egalitarian location of public services throughout the whole national territory, as they were in the 1960s and 1970s, when the Debré reforms of 1958 were implemented. While the need for reorganizing public services is not new [START_REF] Barczak | Quelle évolution de la présence des services publics en France[END_REF], the RGPP has constituted a paradigm shift, by challenging the balancing of territories that had been achieved during the 1960s to the 1980s. The changes in the location of hospital and court services weaken access to public services for some small cities. This compounds the economic difficulties and lack of attractiveness faced by some small cities, and so aggravates inequalities across the country.

2A

  département is an administrative division (nuts3) under the authority of a préfet (representing the central State) and a Conseil Départemental (local authority).

3

 3

  system and hospitals therefore had to cut spending. The Plan Hospital 2007 and 2012 organized the medical information system (Programme Medical Système Information) in order to count and precisely price all medical acts conducted in the hospitals. From 2005 onwards, hospitals were financed mostly through activity pricing (Tarification à l'Activité, called T2A). In 2009, the Hôpital Patient Santé Territoire Law organized the supervision of hospitals by Agencies 6 Exceptions being Orleans and Metz-Thionville.

  of court closures following the 2001 and 2008 reforms and recorded in <Legifrance.gouv.fr> (France's official online legal database). For 2014 and 2016, we have simply drawn on information in INSEE's Permanent Database of Facilities and Equipment. We then aggregated this information for urban areas.

Figure 1a .

 1a Figure 1a. Administrative status and location of justice courts

Figure 2a .

 2a Figure 2a. Change in numbers of courts between 2000 and 2016 in mainland France

22

  Rachida Dati was Minister of Justice when Nicolas Sarkozy was elected President in May 2007 until June 2009. Christiane Taubira became Minister of Justice in May 2012 when François Hollande and the Socialists were elected to the Presidency and in Parliament respectively. She remained Minister until January 2016.

  in which services of elementary urban proximity were gathered" (2008 p. 2). Public facilities shrinkage has occurred in the French urban system, where the French central State had previously been very universally represented at a detailed territorial level, between 1960 and 1980. Recent reforms have therefore challenged de facto the old principle of equal treatment and access to public services as promoted historically in the De Rolland Law of 1938 and Debré reforms of 1958.

Table 1 .

 1 Justice courts, MSO hospital beds and functional urban areas according to size in

	2013
	JUSTICE COURT
	Urban areas (number)	Urban areas (%)
	Small (less than 20,000 in population)	149	39%
	Medium size (from 20,000 to 100,000	142	37%
	inhabitants)
	Large (more than 100,000 in inhabitants )	89	24%
	HOSPITAL
	Urban areas (number)	Urban areas (%)
	Small (less than 50,000 inhabitants)	392	72%
	Medium size (from 50,000 to 200,000	100	19%
	inhabitants)
	Large ( more than 200,000 inhabitants )	47	9%

Table 2a :

 2a Chi-square test results according to urban areas' size and change in courts Justice courts disappeared in 123 small urban areas, This means 59 urban areas more than expected in the category of small urban areas recorded a loss of their court. **16 urban areas more than expected in the category of medium-sized urban areas recorded a decrease in the number of courts . *** 83 urban areas registered a reduction. Sources:BPE, <Data.gouv.fr>, <Justice.gouv.fr>, <LegiFrance.gouv.fr> and INSEE, authors' calculations.

		Disappearance (-100%)	Reduction (-1 justice court)	Other (stable court) or gain of at least 1 justice	Total
	Small (less than 20,000)	123 (59*)	16 (-18)	13 (-42)	152
	Medium (between 20,000 and 100,000)	36 (-23)	47 (16**)	64 (7)	147
	Large (more than 100,000)	1 (-36)	20 (2)	60 (35)	81
	Total	160	83***	137	380
	Key: *Table 2b: Chi-square test results according to functional urban areas' size and change in
	hospital beds
		Disappearance (-100%)	Reduction (] -100%; -10 % ] )	Other (> -10 %)	Total
	Small (less than 50,000)	55 (14*)	194 (-2)	143 (-12)	392
	Medium (between 50,000 and 200,000)	1 (-9)	53**(3)	46 (6)	100
	Large (more than 200 000)	0 (-5)	23 (-1)	24 (5)	47
	Total	56	270 ***	213	539
	Reading : *55 small urban areas lost their MSO beds; 14 urban areas more than expected in
	the small urban areas category
	** 53 average urban areas (3 more than expected) having recorded a falling rate of MSO beds
	between -10% to -100% excluded . *** 270 urban areas fall into the reduction category.
	Sources: DREES & INSEE, exploitation by the authors.

Acknowledgments

We thank the referees and the editor for their constructive comments. We also warmly thank Christophe Queva and Sylvie Fol for all the discussions, attentive reading and informed advices, and Nicholas Sowels for his professional-proof reading. This work was supported by Agence Nationale de la Cohésion des Territoires and by the Banque des Territoires, under the grant "Retail and public services shrinkage in small and medium size cities in France" and by the Labex Dynamite.