1 Introduction
The French government is currently planning to set a target limiting the increase of current sub-national expenditure to the forecast inflation rate minus 0.5 percentage points. This measure may affect around 500 French sub-national jurisdictions (regions, départements, municipalities, and their intermunicipal groups), whose expenditure amounted to some 40 million euros in 2021. “Agreements to return to the trajectory” could be signed between the prefect (i.e., the representative of the State at the département level) and non-compliant local jurisdictions to ensure financial recovery. With this measure, the French government would put increasing pressure on sub-national jurisdictions to improve efficiency in the provision of public goods and services. However, no tool currently exists in France to measure the cost and, even less, the efficiency of local public expenditure. After the “yellow vests” crisis in 2018–2019, which expressed the profound disillusionment of a cross section of taxpayers, a report written for the French government in early 2019 put forward the idea of sending a fictitious and personalized “bill” to every citizen detailing the cost of the public services and amenities from which they benefit, so that “everyone becomes aware of the way their taxes are used”. However, the conclusions of the report remained in the drawers of the ministry concerned. Today, the proposed “Agreements to return to the trajectory” once again place the efficiency of local public expenditure under the spotlight, which needs to be measured and explained given the large heterogeneity of profiles of sub-national jurisdictions in France and their unequal distribution over the territory.
In this paper, we define as efficient those municipalities that are able to minimize the use of their resources (or inputs) in order to provide a given set of services (or outputs). We exploit a cross-sectional database of the 2955 French municipalities with more than 3500 inhabitants in 2018, and we determine whether municipalities that are located closer to highly equipped centers (that is, groups of neighboring municipalities that host high-rank functions) present higher performance. In this sense, municipalities that belong to the less-equipped centers can ’borrow functions’ from their high-rank neighbors, which can be translated into fewer expenditures for their localities and increase municipal efficiency.
We thus draw on the growing city network theory (Capello
1996,
2000) and consider externalities as the benefits derived from the agglomeration effects of bigger, more diverse cities that spill over to their closest neighbors (Fingleton
2003; McCann and Acs
2011).
1 Cities that interact with each other may benefit from horizontal functional relationships, which may, in turn, create synergies and complementarities between them. These interactions may come in the form of agglomeration externalities and network externalities. The concept of network externalities was proposed by Capello (
1996,
2000) to understand the benefits associated with intercity interactions, where connections between cities go beyond physical distance, e.g., they may be channeled by transport costs and times, information networks, etc. The distinction between agglomeration and network externalities lies in the fact that the former attenuates with geographical distance (van Meeteren et al.
2016). In this paper, we specifically focus on the efficiency spillovers coming from agglomeration: we consider that agglomeration effects might not be limited to the boundaries of a city but can spill over to surrounding ones (Camagni et al.
2016) leading to an extended spatial extent of agglomeration externalities. Hence, through these externalities, the efficiency advantages stemming from the agglomeration effects of larger cities can also be shared by other neighboring small and medium-sized ones. The concept that helps to explain the mechanisms of this interaction is known in the literature as ’borrowed size’ (Alonso
1973). The intuition behind this concept lies in the fact that smaller cities can ’borrow’ some of the agglomeration benefits of their neighbors while avoiding agglomeration costs (Camagni et al.
2016; Burger et al.
2015). In the words of Alonso (
1973, p. 200), “
people can use the shopping and entertainment facilities of other cities to complement their own, businessmen can share such facilities as warehousing and business services, and labor markets enjoy a wider and more flexible range of demand and supply”. Thus, given these interdependencies, smaller cities can ’borrow size’ and host functions they could not have hosted otherwise (Burger et al.
2015).
2
In this framework, Camagni et al. (
2016) claim that it is necessary to distinguish the effects of population from the effects of functions, conflated in the concept of ’borrowed size’. On the one hand, ’borrowed size’ may refer to the potential advantages to the population derived from a pooled and diversified labor supply, a larger market of final goods, and population spillovers from large cities. The effect of ’borrowed size’ is expected to be bigger for larger cities which are more capable of exploiting large markets for their firms. On the other hand, ’borrowed function’ comes with the accessibility of high-level functions yielding advantages that come from wider labor demand, more accessibility of services, and spatial spillovers of functions from larger cities. In this case, the effect is expected to be more beneficial for small cities, which have lower endowment of high-rank functions but can ’borrow’ them from stronger neighboring cities.
Consequently, if particular functions can be ’borrowed’ from other cities in the same regional context, then there is not necessarily a relationship between the size of a city and the function it fulfills (Meijers
2007). Therefore, the efficiency benefits derived from agglomeration do not necessarily have to be linked to urban size, but rather to the availability of higher-order functions and the physical proximity to the places that account for them (so as to benefit from spillovers). The importance of paying close attention to urban efficiency and potential spillovers is straightforward for policy-making: if such externalities are found, national or local authorities may enhance regional performance by concentrating their public resources in cities with a higher endowment of high-rank functions and exploit agglomeration economies that can spill over to their neighbors. As a result, this increase in efficiency may translate into higher growth with less use of resources, creating savings on the public budget. It is here where local governments play a key role as the main suppliers of goods and services in many developed economies, where the effective use of their resources can drive regional performance in the aforementioned way.
Unlike other economies, European countries follow a different pattern of urbanization with more than half of the population living in small and medium-sized municipalities which in many cases grow faster than large cities and show slow rates of urban growth (Meijers et al.
2016). These cities are also located in close proximity and well-connected through infrastructure, thus having the potential for further integration (Boussauw et al.
2018). In this context, it is valid to think that efficiency spillovers could arise from an effect of ’borrowed functions’: If citizens are using public services provided by their neighbors, this entails less expenditure for their corresponding municipalities which can translate into more efficiency. Moreover, taking into consideration that these externalities attenuate with distance (van Meeteren et al.
2016; Burger and Meijers
2016), we can expect stronger efficiency gains for municipalities located closer to those where high-rank functions are concentrated. To capture the level of metropolitan functions, we follow an approach similar to that of Burger et al. (
2015), which uses the level of amenities estimated in a country amenity index. Meijers et al. (
2016) also follow a similar strategy by accounting for the domains of international, science, firms, culture, and sports institutions. In this paper, we leverage the novel work of Hilal et al. (
2020) who classify French municipalities according to four levels of equipment (infrastructure and facilities) and service centers, with the highest one being the best-endowed. These centers are local, intermediate, structuring, and major equipment centers.
3 Following the intuition mentioned above, given the indivisibilities and synergies that give rise to agglomeration economies in more diverse municipalities, we can expect that major equipment centers show higher levels of efficiency and hence, through agglomeration externalities, this efficiency spills over to closer municipalities.
Clearly, this approach potentially affects the efficiency of any (public) production sector, which requires that we observe efficiency in an “overall” or “global” manner. In this sense, we can thus interpret municipal (urban) efficiency as how local governments use their resources (or expenditures) to provide a given set of services and infrastructures. In this context, there is a second strand of literature that relies on production theory to address municipal spending efficiency through the estimation of a single efficiency value that represents the evaluation of different services provided by the same municipality (Giménez and Prior
2007) as well as a general view of how local governments are managing and adapting to their multiple tasks (Kalb et al.
2012).
The methodologies commonly used to estimate efficiency can be differentiated depending on the methodology: parametric and non-parametric. Most studies analyzing efficiency from a global perspective make use of non-parametric techniques (Narbón-Perpiñá et al.
2018a), mainly Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH).
4 Their main advantages over parametric methods are that they do not require an assumption of the functional form of the production function, and they can take multiple inputs and outputs to estimate the efficiency score based on optimization methods, which provides more simplicity and versatility (Balaguer-Coll and Prior
2009). The main difference between DEA and FDH lies in the technology assumption: DEA assumes a convex technology, and conversely, FDH assumes a non-convex one. The non-convexity assumption of FDH makes it particularly stringent with regard to inefficiency measurements and particularly suited for detecting the most obvious cases of inefficiency (Balaguer-Coll et al.
2013).
5
However, these methods present a limitation in relation to their sensitivity to outliers and extreme values, given that they envelop all decision-making units (DMUs) in order to estimate the efficiency frontier.
6 To deal with the presence of outliers, Cazals et al. (
2002) suggest the use of partial frontiers, which do not envelop all the data but only a subset and are more robust to extreme observations and outliers. More precisely, they introduce the so-called order-
m approach, which offers two main advantages over DEA and FDH: (1) estimations are robust, even in reduced samples, which helps to overcome the
curse of dimensionality (Daraio and Simar
2005); and (2) they mitigate the impact of extreme observations and outliers.
Our paper’s contribution to advancing research into these issues can be identified in three key areas.
Firstly, we aim to fill the gap in the literature and address municipal spending efficiency for French municipalities. Contrary to the wide range of studies that focus on the analysis of local government spending efficiency and its determinants for different European countries (see Narbón-Perpiñá et al. (
2018a) and Narbón-Perpiñá and De Witte (
2018b) for a review), the literature addressing these issues in the French case is scarce. To our knowledge, there is only one published paper that studies the determinants of the efficiency of French local government through a two-stage approach (Seifert and Nieswand
2014). More recently, Ayouba et al. (
2023) also dealt with this question using a conditional efficiency measurement approach. However, both of these papers consider the case of French
départements, a middle-tier local government, while French municipalities, the lowest tier, have not as yet been the focus of attention.
Secondly, while the literature focuses on the impact of agglomeration externalities on productivity or another related outcome, we focus on spending efficiency, thus providing a link between local public economics and urban economics.
Thirdly, from a methodological viewpoint, we provide empirical support to our environmental variables by means of a separability test. Local governments operate under heterogeneous contexts in terms of social, demographic, economic, political, and geographic characteristics, which creates the necessity to account for the effect of contextual (or environmental) variables and their impact on spending efficiency. Different ways to address this issue have been proposed in the literature. Within the non-parametric field, the most common approach is to carry out a two-stage analysis. In this approach, the first stage calculates the efficiency scores, which are regressed with a set of contextual variables in the second stage using Ordinary Least Squares (OLS), Tobit, or bootstrapped truncated models (e.g., Balaguer-Coll et al.
2007; Benito et al.
2010; Bosch et al.
2012; lo Storto
2016; Pérez-López et al.
2015). A number of other studies have applied alternative approaches such as meta-frontier (Balaguer-Coll et al.
2013), quantile regressions, (Narbón-Perpiñá et al.
2020) or conditional efficiency models (Cordero et al.
2017,
2020). Furthermore, the contextual variables included in the second stage are usually assumed to only influence the distribution of efficiency but not the production process itself. This assumption is commonly known as the separability condition (see Simar and Wilson
2007). However, the lack of proper empirical testing for this assumption has led studies to rely on alternative approaches or economic theory to assume this condition
a priori. We contribute to the literature by applying recent separability tests introduced by Daraio et al. (
2018) and Simar and Wilson (
2020) to empirically support the introduction of contextual variables that comply with this assumption.
Our findings show that major equipment centers are in fact outperforming other municipalities, while externalities appear in the form of higher efficiency for those local centers that are located closer to major ones. Our results are consistent with the theory that less-endowed municipalities are ’borrowing functions’ from stronger neighbors that allow them to host functions that they would not have been able to host in isolation. By ’borrowing’ these functions, local governments are able to save on expenditure and increase their efficiency. However, this effect decays quickly with distance.
The remainder of this paper is organized as follows: Sect.
2 introduces the institutional context of French municipalities and equipment centers. Section
3 describes our two-stage strategy and Sect.
4 presents the data. The results and main conclusions are presented in Sect.
5 and Sect.
6, respectively.