# Is compulsory inter-municipal cooperation an efficiency booster?

Federica Galli, Juan Piedra-Peña, Marie-Laure Breuillé, Julie Le Gallo

► To cite this version:

Federica Galli, Juan Piedra-Peña, Marie-Laure Breuillé, Julie Le Gallo. Is compulsory inter-municipal cooperation an efficiency booster?. Regional Science and Urban Economics, 2026, 117, pp.104185. 10.1016/j.regsciurbeco.2025.104185. hal-05455600

HAL Id: hal-05455600

https://institut-agro-dijon.hal.science/hal-05455600v1

Submitted on 13 Jan 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
<figure><img src="image_2.png" /></figure>

# Is compulsory inter-municipal cooperation an efficiency booster?

Federica Galli<sup>a ID,*</sup>, Juan A. Piedra-Peña<sup>b</sup>, Marie-Laure Breuillé<sup>c</sup>, Julie Le Gallo<sup>c</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

**JEL classification:**

C23

H21

H70

**Keywords:**

Municipal efficiency

Inter-municipal cooperation

Policy evaluation

Spatial spillovers

## ABSTRACT

This paper evaluates the impact of inter-municipal cooperation on municipal efficiency in France. We exploit the "Réforme des Collectivités Territoriales" (RCT) law, approved in 2010, which forced municipalities to join an inter-municipal group (EIMC) by 2014. Focusing on Île-de-France from 2002 to 2019, we first compute municipal efficiency scores, accounting for intra- and inter-EIMC spillover effects. We then causally assess the impact of EIMC integration on municipal efficiency. We find that the RCT law increased municipal efficiency by 1.1% to 1.9%, with a stronger effect for early adopters and with increasing length of exposure.

## 1. Introduction

Many countries in the OECD, such as the UK, the USA, Italy, and France have promoted inter-municipal cooperation (IMC) to improve the management of public services and ensure a more efficient allocation of resources across territories (Breuillé et al., 2018; Breuillé and Duran-Vigneron, 2023). IMC is expected to enhance efficiency by generating economies of scale and internalizing cross-municipal externalities. Among the relevant ex-ante determinants of municipalities favouring IMC, we find municipal size (Brasington, 2003; Carr et al., 2007), sociodemographic and geographical characteristics (Feiock, 2007; LeRoux and Carr, 2007; Morgan and Hirlinger, 1991), fiscal revenues (Di Porto et al., 2013) and spatial features such as neighbours' decision to cooperate (Di Porto et al., 2016). There is also empirical evidence of municipalities unwilling to collaborate, delaying, or even blocking the unification process (Tricaud, 2025). Indeed, IMC can be costly for municipalities due to loss of autonomy over local policies and reduced ability to protect local interests (Tricaud, 2025; Bolton and Roland, 1997; Alesina and Spolaore, 1997). However, this may seem paradoxical if IMC indeed promotes efficiency, especially when it is understood as the capacity to use municipal resources (e.g., expenditures and labour) to maximize municipal output (e.g., income or fiscal capacity).

Empirical evidence on the impact of IMC in promoting municipal efficiency is mixed, inconclusive, and it mainly considers efficiency in terms of cost, i.e., in decreasing local public spending (see Bel and Warner, 2015 and Bel and Sebó, 2021 for a review). While Reingewertz

(2012), Blesse and Baskaran (2016), Cobban (2019), Ferraresi et al. (2018), Dijkgraaf and Gradus (2013) and Bel and Mur (2009) find that IMC leads to a reduction of costs in Spain, Germany, Ontario, the Netherlands, Italy and Israel, respectively, Allers and de Greef (2018) find a positive impact on spending for small and large municipalities in the Netherlands and no effect on medium-sized ones. Moreover, Frère et al. (2014) and Blom-Hansen et al. (2016) do not recover any significant effect of IMC on local public spending for Denmark and France. Additional recent results from Vidoli et al. (2023), considering cost efficiency in terms of social services provided to Italian local communities, indicate that the effects of IMC are heterogeneous depending on the type and degree of implementation of the municipal union itself. For the French case, empirical works have mainly focused on the impact of IMC on total spending and tax competition (Bel and Warner, 2015; Blom-Hansen et al., 2016; Breuillé et al., 2018).

To date, there is still little evidence of the causal effect of such integration patterns on municipal efficiency, measured through a production function approach in which efficiency is considered as the ability to maximize municipal output. To the best of our knowledge, the only paper analysing the impact of IMC on the efficiency of local governments following such an approach is Luca and Modrego (2020). Concentrating on Italian municipal unions, the authors define efficiency as the ability of municipalities to provide local public services based on municipal expenditures. However, they do not find any significant effects.

<footnote><sup>a</sup> Department of Statistical Sciences "Paolo Fortunati", University of Bologna, Italy</footnote>

<footnote><sup>b</sup> Department of Applied Economics, REGIOlab, University of Oviedo, Spain</footnote>

<footnote><sup>c</sup> CESAEER UMR1041, INRAE, Institut Agro, Université Bourgogne Franche-Comté, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: federica.galli14@unibo.it (F. Galli).</footnote>
To address the causal impact of IMC on efficiency, our identification strategy proceeds by exploiting the “Réforme des Collectivités Territoriales” law (hereafter RCT law), which was approved in France in 2010. This reform aimed to achieve a near-global coverage of the French territory by eliminating enclaves and territorial discontinuities and establishing inter-municipal groups (hereafter “EIMC”), except in Paris and three “départements” of the inner suburbs (Hauts-de-Seine, Seine-Saint-Denis and Val-de-Marne). As mentioned by Decree N.2008-1078, the main objective of the RCT law is to “*simplify the structures of local authorities, clarify the distribution of their competencies, and allow a better allocation of their financial resources*” since “*the number and entanglement of competences is a source of inefficiency and additional expenditure*” (Nicolas Sarkozy’s speech in Toulon, Le Monde, September 25, 2008). Tricaud (2025) is the only paper that analysed the impact of inter-municipal cooperation on French municipalities after the adoption of the RCT law, focusing on housing supply, housing prices, firm creation, wages, local public services, public transport, and fiscal revenues as response variables, while efficiency, as defined above, is not considered.

In this paper, efficiency is defined in line with Luca and Modrego (2020), adopting a production function-based approach. This framework is especially relevant for two reasons. First, cooperation may not immediately translate into lower spending, especially in the initial phases of implementation. Extensive cooperative structures can entail higher agency and information costs, while local authorities may refrain from reducing expenditures, either due to self-interest or because they prioritize enhancing service quality to meet citizens' needs rather than pursuing cost savings (Buettner and Holm-Hadulla, 2013). For the case of France, Breuillé et al. (2018) showed that joining an EIMC leads to an increase in cumulative tax rates (measured as the sum of municipal and inter-municipal tax rates applied to the same tax base). This finding contradicts the central political argument that IMC would result in tax reductions due to expected economies of scale. Instead, an upward harmonization of public goods provision quality is frequently observed. Second, a significant portion of public expenditures is allocated to developing local infrastructure and stimulating local economies (as shown in Figure A1 in the Appendix, about 60% of the total budget in Île-de-France is devoted to economic development). In this regard, public expenditures act as a transmission mechanism that removes important ‘bottlenecks’, facilitating job creation and stimulating economic growth, which in turn increases taxes paid and income generated (Kopczewska, 2016). In this case, improving municipal performance rather comes by increasing local output with the available resources, and efficiency measures how effectively municipalities transform given levels of inputs into observable economic-development outcomes.

Therefore, we evaluate, over the period 2002–2019, whether resisting municipalities that did not voluntarily merge with other municipalities before 2010, experienced an efficiency gain by joining an EIMC between 2010 and 2014, under the constraint of the RCT law. We concentrate on Île-de-France region, the French capital region, as it had the lowest percentage of municipalities belonging to an EIMC before the RCT law, with 69% against 93% at the national level. Focusing on Île-de-France also allows for mitigating unobserved heterogeneity due to confounders related to municipalities belonging to different regions of France. Municipal efficiency is obtained by estimating a spatial stochastic frontier model using income and fiscal capacity as outputs, and municipal expenditure and employment as inputs. The rationale is that we interpret economic-development services, such as spatial planning, business park management, transport links, broadband provision, and tourism promotion, as the main output bundle transferred to EIMCs after 2010.<fnref n="1" /> These services aim to enhance local factor productivity and attract higher-income households and firms.

Accordingly, median taxable income and potential fiscal capacity, defined as the local revenues that would be collected under average tax rates, are treated as observable, municipality-level proxies of this latent government output. Fiscal capacity serves as a proxy for public income, reflecting the potential tax revenues that a municipality could raise under average national tax rates and thus capturing the public sector's ability to generate resources. In contrast, median income reflects the private sector's response to local public services, capturing productivity and attractiveness effects.

The first stage of the analysis consists of estimating municipal-level efficiency scores based on the production function approach. Since IMC can lead to fiscal interactions occurring through spillovers of local public goods, tax competition, or yardstick competition (Brueckner, 2003), we extend the production function by considering spatial dependence in the input variables, i.e. public expenditures and labour force. Indeed, Breuillé and Le Gallo (2017), in the case of France, find that municipalities tend to emulate their inter-municipal neighbours when making decisions on current budget items like expenditures and wages. However, strategic interactions may occur not only within, but also between EIMCs. Municipalities within the same group may interact differently with each other compared to nearby municipalities outside the group. For example, Agrawal et al. (2025) show that municipal tax rates in France exhibit strategic complementarity between EIMCs, but tax interdependence within the same EIMC is less intense. Therefore, municipalities are more concerned about the fiscal behaviour of non-group members than members within their own group.<fnref n="2" /> Therefore, to estimate municipal efficiency, we consider a spatial stochastic frontier model that allows capturing these spatial spillovers in inputs. In addition, to address potential heterogeneous interdependencies between and within EIMCs, we define two spatial weight matrices to distinguish between intra- and inter-EIMC spillovers, as in Agrawal et al. (2025).

After having retrieved municipal time-varying efficiency score from stochastic frontier estimation, in the second stage of the analysis, we conduct a causal analysis using a difference-in-differences model for multiple groups and time periods (Callaway and Sant'Anna, 2021). In particular, we compare municipalities that still had not joined an inter-municipal group in 2010 and thus, that were forced by the RCT law to enter an EIMC by 2014 with municipalities that were already part of an inter-municipal group before 2010 since they voluntarily joined it. Thus, the treatment groups consist of municipalities that were not yet integrated in 2010 but joined an EIMC between 2010 and 2014. On the other hand, the control group in a given year consists of municipalities that were already members of an EIMC before 2010

<footnote n="1">¹ More precisely, joining an EIMC entails the mandatory transfer of seven core competences. Among them are:(i) spatial planning, including community-level land-use planning, the preparation of “schémas de cohérence territoriale (SCoT)”, and inter-municipal local urban plans (“PLUI”, unless municipalities oppose the transfer); (ii) economic development, covering the creation and management of business and industrial parks, local commercial policy and support to commercial activities of community interest, as well as tourism promotion, including the mandatory creation of inter-municipal tourism offices (with an exception for municipalities classified as “tourist resorts”, which may retain this competence; tourism events remain a shared competence).</footnote>

<footnote n="2">² As discussed in Ward and John (2013), this behaviour may be the result of a “pure learning” process in which municipalities tend to mimic the good practices of high-performing (neighbouring) jurisdictions to mitigate the high costs associated with the provision of public services resulting from the implementation of unsuccessful initiatives. It may also come as the result of a “competitive learning” process, where local authorities compete to attract mobile tax-payers and investors by implementing best practices from high-performing neighbours. Another reason may be driven by electoral purposes. To be reelected, the incumbent party may copy successful practices of their neighbouring locality to improve public services and working conditions. Citizen voters lack comprehensive knowledge about the fiscal performance of their incumbent politicians, leading them to bridge this information gap by comparing their performance with that of neighbouring municipalities.</footnote>
(never-treated) plus those that had not yet joined an inter-municipal
group by that year (not-yet-treated). However, we also consider the
possibility of defining the control group only based on never-treated
or not-yet-treated municipalities. This definition of treatment and com-
parison groups follows the same conceptual logic as in Tricaud (2025),
who also exploits the 2010 RCT law as an exogenous shock to inter-
municipal cooperation. The definitions of the treatment and control
groups are the same, except that she further distinguishes within the
control group between municipalities that had joined by 1999 and
those that integrated between 2000 and 2010, without this distinc-
tion implying any notable difference in terms of outcomes. The main
differences between the two studies concern the geographical scope,
as we focus on the Île-de-France region, and the empirical design,
as we implement a staggered Difference-in-Differences approach à la
Callaway and Sant'Anna (2021) to account for the gradual integration
of municipalities between 2010 and 2014. Moreover, while Tricaud
(2025) analyses fiscal and tax-related outcomes, we examine productive
efficiency, providing a complementary perspective on the effects of
compulsory inter-municipal cooperation.

Our main identification assumption is the parallel trend assumption. The first potential issue with this assumption concerns self-selection into treatment. Indeed, municipalities in the control group voluntarily chose to join an EIMC before 2010 while treated municipalities decided to remain isolated. To assess the validity of the pre-treatment parallel trend assumption, we control for several municipal characteristics, including population density and typology (i.e., rural, central, urban, etc.). Our results indicate that we cannot reject the pre-treatment parallel trend assumption, both unconditionally and when conditioning on selected pre-treatment variables. Another possible issue concerns the effect of the reform on the control group since these municipalities can be affected by changes in their EIMC composition due to the entrance of treated municipalities. To address this, we perform a robustness check considering only not-yet-treated units as the control group in order to control for possible confounders related to impacts on municipalities already belonging to an EIMC. Finally, intra-EIMC heterogeneity may also influence selection into treatment, as municipalities that differ significantly within their EIMC group may be more reluctant to join the EIMC and may delay their entry. To account for this, we conduct a robustness check by incorporating several indices that capture intra-EIMC heterogeneity across various dimensions, such as population size, density, and political composition.

In sum, this paper contributes to the literature on the effects of IMC
in several directions. First, it is among the few studies that evaluate
efficiency from the production side, viewing local governments as
producers of economic development services. Second, it incorporates
spatial dynamics into the measurement of efficiency by employing
a spatial stochastic frontier model augmented with both inter- and
intra-EIMC spillover effects. Third, it exploits a dynamic staggered
difference-in-differences design that distinguishes between mandatory
and voluntary cooperation, providing a credible causal identification
strategy that allows us to estimate how the impact of IMC evolves
over time. Our findings indicate that the RCT law positively affected
municipalities in Île-de-France region with an impact between 1.1%
and 1.9% which is increasing over time. Moreover, considering income
as the outcome variable, early adopters were more affected than others.
Our findings are robust to different model specifications (i.e., spatial
weight matrices, outcome variables, conditioning variables, and control
groups) and estimation procedures.

The rest of the paper is organized as follows. Section 2 discusses the
institutional setting, Section 3 introduces the data and variables used
for the analysis, Section 4 presents the econometric approach, Section 5
analyses the results, and Section 6 concludes.

## 2. Institutional setting

The territorial organization in France is structured around three
constitutional tiers of jurisdictions, i.e., the “régions”, the “départe-
ments” and at the bottom-most tier, the municipalities (called “comm-
munes”) that are 34,945 in metropolitan France and overseas depart-
ments and regions in 2022. Since the 1990s, an additional tier (without
constitutional recognition even though it is operational) composed
of Establishments for Inter-Municipal Cooperation (EIMC) has been
strongly strengthened, following the law of February 6th, 1992, which
created the new status of “communautés de communes”, and the
financial incentives of the Chevènement law (1999).

Inter-municipal cooperation has been thought of as a response
to the French territorial fragmentation and designed to improve the
effectiveness of public expenditure through scale economies generated
by the transfer of some competencies to a higher tier. Optional until
2010, IMC became mandatory with the law “Réforme des Collectivités
Territoriales” (RCT law) of December 16th, 2010, which required each
municipality to belong to an EIMC by the beginning of 2014, with
the exception of municipalities within the territory of Paris and its
little crown (composed of the “départements” of Hauts-de-Seine, Seine-
Saint-Denis and Val-de-Marne). In addition, the RCT law fostered the
rationalization of IMC by giving the representatives of the State in
the departments (“préfets”) more powers to merge EIMCs in order
to achieve a minimum threshold of 5000 inhabitants or to collapse
structures without tax powers (i.e., syndicates).

We focus in this paper on EIMCs with tax power, which can take five
different legal statuses: (i) “communauté de communes” (CC) which are
the smallest EIMCs, (ii) “communauté d’agglomération” (CA) with at
least 50,000 inhabitants and a central municipality of at least 15,000
inhabitants, (iii) “communauté urbaine” (CU) with at least 250,000
inhabitants, (iv) “ métropole” (METRO) with more than 400,000 in-
habitants in an urban area as defined by the French national institute
of statistics (INSEE) of more than 650,000 inhabitants, or a group of
existing EIMCs belonging to an employment zone of more than 400,000
inhabitants as defined by INSEE and (v) “syndicat d’agglomération
nouvelle” (SAN) that were created in the ’70s and progressively trans-
formed into “communautés d’agglomération” until their abolition by
January 1st, 2017 by the NOTRE law.

Depending on their legal status, EIMCs exert different sets of com-
pulsory competencies, which increase with their size, e.g. “commu-
nautés de communes” have seven compulsory powers, whereas
“ métropoles” have 40 compulsory competencies. EIMC is much more
than an accounting reconfiguration, as EIMCs exert transferred com-
petencies and finance them through their own budget, in place of all
the member municipalities. As a result, municipalities refocus their
efforts on the competencies that remain under their direct control. In
terms of governance, EIMCs are administered by a council composed
of delegates from member municipalities. Since 2014, inter-municipal
councillors have been elected at the same time as municipal councillors,
instead of being appointed by the municipal councils, as was previously
the case.

The Île-de-France region is specific in several respects. First, IMC
took more time to anchor itself in the landscape. In 2009, 93.1% of
French municipalities belonged to an EIMC, while, when focusing on
Île-de-France, this figure decreases dramatically to 69.6%. Fig. 1 shows
the evolution of the proportion of municipalities that have joined an
EIMC in Île-de-France. In addition, a large central part of the region,
whose frontiers are now those of the Métropole du Grand Paris<fnref n="3" /> created

<footnote n="3">³ As pointed out by numerous authors like Desjardins (2016), the Métropole du Grand Paris was an empty shell in its early days. Senate Information Report No. 444 of 2021 highlighted that the MGP had limited competencies, lacked political power, and had an overly modest metropolitan budget of only €206 million for 2019, including €42 million for operating expenses.</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** EIMC formation over time in Île-de-France region.
*Source:* The authors.</figcaption></figure>

by the MAPTAM law (loi de Modernization de l'Action Publique Territoriale et d'Affirmation des Métropoles) in 2014 and operating since 2016, has a derogative legal status. Finally, the Île-de-France region concentrates the most important part of wealth, economic activity, and population.

Fig. 2 presents Île-de-France's territorial division in 2010 and 2015. Specifically, the map on the left-hand side of Fig. 2 shows which municipalities did not belong to an inter-municipal group before the RCT law, while the map on the right-hand side of Fig. 2 shows the complete territorial organization of EIMCs in Île-de-France after the completion scheme required by the RCT law as well as the formation of the Metropole du Grand Paris. Moreover, Figure A2 in the Appendix shows the connectivity map (i.e. the links between each pair of municipalities belonging to the same EIMC) of municipalities belonging to an EIMC differentiating for the years 2010 and 2015 (pre- and post-RCT law). This figure clearly highlights how the number of connections has increased greatly after the adoption of the RCT law.

## 3. Data

We build and exploit a panel dataset comprising all municipalities within Île-de-France during the period 2002–2019. In the first stage of our analysis, we use both the collection of inputs and outputs to estimate the local production function as well as the various municipal contextual variables that can potentially affect the distribution of efficiency.

The selection of the input variables is straightforward, as we define municipal efficiency as the optimal use of municipal and EIMC resources (expenditures and labour) to maximize municipal production; hence, we use municipal expenditures disaggregated in operating (Op-exp), personnel (Persexp), and investment (Invexp) expenditures each adjusted to include the corresponding portion of EIMC expenditures weighted by the municipality's proportion of the total EIMC population. Therefore, expenditures managed jointly through IMC are proportionally distributed across member municipalities, thereby aligning the measurement of inputs with the actual governance and production structure. By adopting this approach, we ensure that the efficiency frontier reflects the total resources effectively mobilized for local service provision, regardless of whether they are administered directly by the municipality or through the EIMC. In addition, we include employment measured as the total number of jobs at the municipal level (Empl).

Regarding the output selection, it is common in the empirical literature to measure local production either with Gross Domestic Product (GDP) or Gross Value Added (GVA) (e.g., Polo et al., 2021; Otsuka,

2020). However, one of the limitations we face is the lack of data for these variables at the municipal level in France. Instead, to proxy local output, we use two variables. First, we use the median income of households located in the municipality (Inc), a variable commonly used in the literature, particularly in studies that identify the relationship between public expenditures and productivity improvement (e.g., Kara et al., 2016; Saygılı and Özdemir, 2021). Furthermore, in France, many competencies transferred to EIMCs pertain to services and infrastructure that foster economic development, including business parks, transportation networks, broadband access, and tourism promotion facilities. These services are designed to enhance total factor productivity, which in turn contributes to higher income levels for both households and firms. Thus, median income serves as an appropriate output indicator to capture the impact of these transferred competencies within EIMCs. However, this variable may be capturing both private and public output within the region. Moreover, income originating from municipalities outside the region may also be playing a role, particularly considering Paris's status as the economic centre of France. Thus, to proxy the potential for public revenues raised in the locality, we also use fiscal capacity, defined as the amount of local fiscal revenues collected if the average local tax rates are applied. This measure has the advantage of neutralizing the choices made by the municipality.<fnref n="4" /> This way, we are able to capture the potential tax revenues that a municipality could raise under average tax rates, thus reflecting the capacity of the public sector to generate resources. As a robustness check, we consider alternative dependent variables such as gross or net salaries. The rationale is that an increase in public spending can lead to a boost in the aggregate demand for goods and services, increasing labour productivity and real wage (Blanchard and Perotti, 2002; Galí et al., 2007). In addition, increasing government spending on infrastructure projects, education, and other sectors may foster economic growth, and create jobs directly through public sector employment translating into higher wages as a result of increased demand for labour.<fnref n="5" />

Regarding the contextual determinants of inefficiency, to select our variables, we follow previous literature (for a complete overview, see Narbón-Perpiñá and De Witte, 2018) considering data availability and variables of particular interest for the French context.<fnref n="6" /> First, we use population density (Density) to control for potential economies of scale in the supply of public services (Kalb et al., 2012; Lo Storto, 2016) or potential congestion effects that may increase inefficiency (da Cruz and Marques, 2014; Lampe et al., 2015).

We also introduce a market accessibility index (ACC) to measure the strength of inter-municipal relations. Considering French municipalities located in close proximity and well-connected through infrastructure, they may benefit from horizontal relationships that may create complementarities among them. In other words, smaller municipalities may

<footnote n="4">⁴ In the literature, the direction of the causality of these two variables is not always clear. It may be the case that a change in taxes leads to changes in expenditures or even that they are determined simultaneously. Studies addressing this question in the case of France are scarce. However, there is recent literature that considers the French case – within a sample of selected countries – and finds empirical evidence of a *spend-tax* relationship (Afonso and Rault, 2009; Linhares and Nojosa, 2020).</footnote>

<footnote n="5">⁵ The choice of income and fiscal capacity over wages in our main analysis is driven by data availability reasons since for salaries we just have data in the time period 2009–2019 with about 7% missing observations.</footnote>

<footnote n="6">⁶ We departed from a wide set of socio-economic and demographic variables that could potentially influence municipal efficiency, according to the literature, and followed a step-wise selection dropping those that did not significantly contribute to increasing the quality our the model, i.e. those that did not significantly reduce the Akaike and Bayesian information criteria. Finally, we checked that the remaining variables were not affected by collinearity issues by computing the VIF, that is on average equal to 2.16 with a maximum value of 6.84, which is under the threshold of 10.</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 2. Geography of Île-de-France, years 2010 on the left and 2015 on the right.
Source: The authors.</figcaption></figure>

'borrow' some benefits of agglomeration economies from larger neighbouring municipalities. This phenomenon is known in the literature as 'borrowed size': "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 labour markets enjoy a wider and more flexible range of demand and supply" (Alonso, 1973, p. 200). Thus, in line with Otsuka (2020), we construct the ACC index that allows controlling for these complementarities, calculated as:

$$ACC_{jt} = \sum_{i \neq j} \left( \frac{Pop_{it} / \sum_{i \neq j} Pop_{it}}{d_{ij}} \right) \quad (1)$$

where Popit represents the population of municipality i at time t and dijt is the distance in kilometers between municipalities i and j. The borrowed size of cities is a function of density and distance between neighbouring cities, that is, the larger the neighbouring population and the shorter the distance to large cities, the larger the borrowed size (Camagni et al., 2015).

To proxy for touristic activity, we introduce the touristic accommodation capacity (Touristic) as a variable that is commonly accounted for in the literature and is expected to have either a positive effect on inefficiency given the potential extra municipal cost to non-residents (Seifert and Nieswand, 2014) or a negative effect due to the demanded quality increase in public services on touristic seasons (Kalb et al., 2012). We also account for the share of the elderly population over 65 years old (Pop65). This variable can have a positive effect on inefficiency, as the elderly are less likely to use recreational services (Narbón-Perpiñá et al., 2020). However, they can also be more involved in local organizations that may influence local government decisions, reducing inefficiency (Bosch et al., 2012). We then control for vacant dwellings in the housing stock (Emptyhous) given their potential long-term negative effect on public revenues, due to deterioration of public services, the increase in real estate prices, and impact on general consumption (Garrido-Jiménez et al., 2019) which could eventually have a positive impact on inefficiency. Furthermore, we introduce a set of variables to control the share of the municipality population and expenditures relative to the respective EIMC (PopcomEIMC, OpexpEIMC, PersexpEIMC, and InvexpEIMC). Moreover, we account for the municipal share of labour by sector to control for the level of specialization. We include the workforce level in agriculture (EmplAgric), industry (EmplInd), construction (EmplCons), private services (EmplTTS), and public services (EmplAEH). Finally, we introduce a set of dummies to account for the municipality's respective EIMC (CA, CC, SAN, CU, and METRO) as well as the typology of urban area (centre, rural, and isolated).

Table 1 shows the variables used in the analysis with their description and measurement, as well as some descriptive statistics.

# 4. Methodology

## 4.1. First stage: Spatial stochastic frontier model

To measure efficiency at the municipal level, we estimate a spatial stochastic frontier (SF) production function as shown in Eq. (2). There are several advantages in estimating a parametric SF model instead of using a non-parametric approach (see Asmare and Begashaw (2018) and references therein). First, SF models allow for the use of panel data, which in our case is a fundamental feature of the database. Second, this parametric technique allows distinguishing the random noise from inefficiency, while non-parametric methods are non-stochastic since all deviations from the frontier are attributed to inefficiency. As a consequence, mean technical efficiency scores tend to be larger in magnitude since there is more dispersion in the data (Huang and Wang, 2002). Third, parametric methods are less sensitive to outliers compared to non-parametric techniques and allow more efficient inference (Parman and Featherstone, 2019). Fourth, SF models allow estimating together the production/cost function and an inefficiency model, while in the non-parametric case, two-stage procedures are usually adopted, obtaining biased and less robust estimates (Simar and Wilson, 2007; Wang and Schmidt, 2002). Finally, parametric SF models easily accommodate the inclusion of spatial terms.

In this work, in addition to considering the direct contribution of inputs for each municipality i at time t, we also include input spillovers from neighbouring municipalities j (i ≠ j) differentiating between inter- and intra-EIMC spillover effects.<fnref n="7" /> Thus, we consider an “SLX” specification for the frontier function (Elhorst, 2010), which includes the spatial lag of input variables. The complex spatial specification used to capture inter- and intra-EIMC input spillovers motivates us to keep the model specification as simple as possible using a Cobb-Douglas

<footnote n="7">⁷ We also estimated two benchmark models, one non-spatial model and a spatial model without differentiating between intra- versus inter-EIMC spillovers. However, the LR test as well as the AIC and BIC information criteria provide a greater preference for the spatial model distinguishing between inter- and intra-EIMC spillovers.</footnote>
<caption>**Table 1**
Variables and descriptive statistics.</caption>

*Source:* The authors.

<table><thead><tr><th>Variable</th><th>Description</th><th>Unit</th><th>Min</th><th>Mean</th><th>Max</th><th>SD</th></tr></thead><tbody><tr><td>Inc</td><td>Median income of consumer units</td><td>Euros</td><td>8508.00</td><td>23540.53</td><td>48824.00</td><td>4863.92</td></tr><tr><td>Fisc</td><td>Potential fiscal capacity by inhabitant</td><td>Euros</td><td>158.36</td><td>411.92</td><td>17335.4</td><td>434.91</td></tr><tr><td>Opexp</td><td>Operating expenditures</td><td>Euros</td><td>249.93</td><td>893.97</td><td>12361.65</td><td>504.98</td></tr><tr><td>Persexp</td><td>Personal expenditures</td><td>Euros</td><td>0.05</td><td>387.32</td><td>2328.27</td><td>264.18</td></tr><tr><td>Invexp</td><td>Investment expenditures</td><td>Euros</td><td>0</td><td>456.76</td><td>23503.92</td><td>573.02</td></tr><tr><td>Empl</td><td>Workplace Jobs</td><td>Num. jobs</td><td>2.04</td><td>4363.95</td><td>1842064</td><td>50423.52</td></tr><tr><td>CA</td><td>1 if Communauté d'agglomération</td><td>Dummy</td><td>0</td><td>0.21</td><td>1</td><td>0.41</td></tr><tr><td>CC</td><td>1 if Communauté de communes</td><td>Dummy</td><td>0</td><td>0.51</td><td>1</td><td>0.49</td></tr><tr><td>SAN</td><td>1 if Syndicat d'agglomération nouvelle</td><td>Dummy</td><td>0</td><td>0.01</td><td>1</td><td>0.12</td></tr><tr><td>METRO</td><td>1 if Métropole</td><td>Dummy</td><td>0</td><td>0.02</td><td>1</td><td>0.15</td></tr><tr><td>CU</td><td>1 if Communauté Urbaine</td><td>Dummy</td><td>0</td><td>0.01</td><td>1</td><td>0.11</td></tr><tr><td>ACC</td><td>Strength of the network</td><td>Indicator</td><td>0.12</td><td>0.35</td><td>1.13</td><td>0.20</td></tr><tr><td>Dens</td><td>Population density</td><td>Kilometers<sup>2</sup></td><td>2.31</td><td>39.35</td><td>574.28</td><td>53.63</td></tr><tr><td>Centre</td><td>1 if Centre</td><td>Dummy</td><td>0</td><td>0.06</td><td>1</td><td>0.24</td></tr><tr><td>Rural</td><td>1 if Rural</td><td>Dummy</td><td>0</td><td>0.50</td><td>1</td><td>0.50</td></tr><tr><td>Isolated</td><td>1 if Isolated</td><td>Dummy</td><td>0</td><td>0.03</td><td>1</td><td>0.18</td></tr><tr><td>Touristic</td><td>Tourist accommodation capacity</td><td>Num. beds</td><td>0</td><td>949.05</td><td>806301.5</td><td>17910.75</td></tr><tr><td>Pop65</td><td>Population over 65</td><td>Share</td><td>1.47</td><td>13.23</td><td>52.87</td><td>4.45</td></tr><tr><td>PopcomEIMC</td><td>Municipal population over EIMC population</td><td>Share</td><td>0</td><td>7.02</td><td>92.29</td><td>11.47</td></tr><tr><td>Emptyhous</td><td>Vacant dwellings in the housing stock</td><td>Share</td><td>0</td><td>5.78</td><td>60.49</td><td>3.01</td></tr><tr><td>OpexpEIMC</td><td>EIMC operating exp. on total* operating exp.</td><td>Share</td><td>0</td><td>0.19</td><td>4.21</td><td>0.25</td></tr><tr><td>PersexpEIMC</td><td>EIMC personal exp. on total* personal exp.</td><td>Share</td><td>0</td><td>0.11</td><td>2.88</td><td>0.20</td></tr><tr><td>InvexpEIMC</td><td>EIMC investment exp. on total* investment exp.</td><td>Share</td><td>0</td><td>0.24</td><td>23.90</td><td>0.61</td></tr><tr><td>EmplAgric</td><td>Share of workplace jobs in agriculture</td><td>Share</td><td>0</td><td>6.98</td><td>100</td><td>14.11</td></tr><tr><td>EmplInd</td><td>Share of workplace jobs in industry</td><td>Share</td><td>0</td><td>10.73</td><td>100</td><td>12.40</td></tr><tr><td>EmplCons</td><td>Share of workplace jobs in construction</td><td>Share</td><td>0</td><td>10.95</td><td>100</td><td>11.44</td></tr><tr><td>EmplTTS</td><td>Share of workplace jobs in trade, transport, and services</td><td>Share</td><td>0</td><td>43.33</td><td>100</td><td>18.96</td></tr><tr><td>EmplAEH</td><td>Share of workplace jobs in public administration, education, health and social work</td><td>Share</td><td>0</td><td>29.07</td><td>100</td><td>17.36</td></tr></tbody></table>

Notes: * Total expenditure is defined as the sum of EIMC and municipal expenditures of all municipalities in the EIMC.

All variables, except the dummy variables and ACC are included in a logarithmic form.

functional form.

$$Y_{it} = \beta_0 + Opexp_{it}\beta_1 + Invexp_{it}\beta_2 + Persexp_{it}\beta_3 + Empl_{it}\beta_4 + Empl_{it}^2\beta_5 \\ + \sum_{j=1}^{N} w_{intra,ijt} Opexp_{jt}\theta_1 + \sum_{j=1}^{N} w_{inter,ijt} Opexp_{jt}\theta_2 + \sum_{j=1}^{N} w_{intra,ijt} Invexp_{jt}\theta_3 \\ + \sum_{j=1}^{N} w_{inter,ijt} Invexp_{jt}\theta_4 + \sum_{j=1}^{N} w_{intra,ijt} Persexp_{jt}\theta_5 + \sum_{j=1}^{N} w_{inter,ijt} Persexp_{jt}\theta_6 \\ + \sum_{j=1}^{N} w_{intra,ijt} Empl_{jt}\theta_7 + \sum_{j=1}^{N} w_{inter,ijt} Empl_{jt}\theta_8 + t\beta_6 - u_{it} + v_{it} \quad (2)$$

As described before, the dependent variable $Y_{it}$ alternatively represents the median income level of consumer units in municipality $i$ at time $t$ (Inc) or municipal potential fiscal capacity by inhabitant (Fisc). Opexp, Invexp, Persexp, are the disaggregated expenditures, and Empl is employment at the municipal level, with associated parameters $\beta$. Moreover, to control possible non-linearities related to workplace jobs, we also include the square of Empl, in addition to Empl. Finally, to take into account temporal changes in the frontier, we also include the time trend.

To capture spillover effects between neighbouring municipalities $j$ ($i \neq j$) in terms of inputs, we include in the model specification spatially lagged input variables differentiating between spillovers occurring inside the inter-municipal group (intra-EIMC spillover) and spillover effects generated between neighbouring municipalities that do not belong to the same EIMC (inter-EIMC spillovers). The spatial weight matrix used to identify intra-EIMC input spillovers ($w_{intra}$) considers as neighbours all municipalities belonging to the inter-municipal group at time $t$ by assigning a weight equal to 1 for all municipalities in the same EIMC and zero otherwise. As a robustness check, we also consider alternative intra-EIMC spatial weight matrices following an inverse distance criteria or a binary contiguity criteria. The spatial weight

matrix used to capture spillover effects between municipalities that do not belong to the same EIMC ($w_{inter}$) is defined as an inverse distance spatial weight matrix truncated at 50 km, considering only pairs of municipalities belonging to different EIMCs. The distance threshold has been defined based on the geographical features of Île-de-France (the average distance between the centroids of municipalities is 25.05 km and the maximum is 136.62 km) considering that spillover effects tend to decay at larger distances (Griliches, 1992). As a robustness check, we consider different truncation points at a 40 and 60 kilometer radius. Both spatial weight matrices are row-standardized and time-varying since the EIMC structure changes during time as highlighted in Fig. 1. Intra-EIMC input spillovers are captured by $\theta_1, \theta_3, \theta_5$ and $\theta_7$ respectively for operating, investment, personal expenditures, and employment, while $\theta_2, \theta_4, \theta_6$ and $\theta_8$ measure inter-EIMC spillovers related to the same set of inputs.

According to the classical specification of SF models (Aigner et al., 1977), the error term is split into two independent components, $u_{it}$ and $v_{it}$. While $v_{it}$ is the random error term and follows a normal distribution with zero mean and variance $\sigma_u^2$, $u_{it}$ represents the inefficiency error component and captures the decrease in the level of output due to technical or economic inefficiency. Following Battese and Coelli (1995), the inefficiency error term is modelled as a half-normal distribution with mean $\mu_{it}$ and variance $\sigma_u^2$ since inefficiency can take only positive or at least zero values. The mean of this error term is then modelled as a function of some exogenous inefficiency determinants, capturing the main characteristics of the municipalities and the EIMC to which they belong, as described in the previous section.

The parameter estimates are simultaneously obtained by numerically maximizing the associated log-likelihood function using the Newton-Raphson method. The estimated variance-covariance matrix is calculated as the inverse of the negative Hessian matrix of second-order partial derivatives. Starting from the parameter estimates of the spatial SF model, the technical efficiency score of municipality $i$ in
year *t* can be defined as $TE_{it} = E(\exp(-u_{it})|\epsilon_{it})$ (Battese and Coelli, 1988). In practice, the expectation $E(\exp(-u_{it})|\epsilon_{it})$ can be calculated by substituting the parameter estimates into the following equation,

$$TE_{it} = \exp \left[ -\mu_{it} (1 - \lambda) + \epsilon_{it} \lambda + \frac{1}{2} \left( \sigma \sqrt{(1 - \lambda) \lambda} \right)^2 \right] \cdot \left\{ \frac{\Phi \left( \frac{\mu_{it}(1-\lambda)-\epsilon_{it}\lambda}{\sigma\sqrt{(1-\lambda)\lambda}} \right)}{\Phi \left( \frac{\mu_{it}(1-\lambda)-\epsilon_{it}\lambda}{\sigma\sqrt{(1-\lambda)\lambda}} \right)} \right\} \quad (3)$$

where $\lambda = \frac{\sigma_u^2}{\sigma_u^2 + \sigma_v^2}$, $\sigma^2 = \sigma_u^2 + \sigma_v^2$, $\Phi$ represents the cumulative distribution function of the standard normal random variable, and $\epsilon_{it} = v_{it} - u_{it}$ and $\mu_{it}$ are respectively obtained from Eq. (2) and the inefficiency model.

## 4.2. Second stage: Difference in difference analysis

Based on the efficiency scores obtained in the first stage, in the second stage of the analysis, we adopt a difference in difference design to evaluate the impact of having joined an inter-municipal group from 2010 onward to comply with the RCT law on the efficiency level of municipalities in Île-de-France. Overall, we have a balanced panel of 1238 municipalities observed between 2002 and 2019, composed of 892 non-treated municipalities, 66 treated in the year 2010, 48 in the year 2011, 59 in 2012, 112 in 2013, and 61 in 2014. The remaining 42 municipalities are those that joined the Métropole du Grand Paris in 2016 and thus were not affected by the RCT law. In the analysis, to compute the efficiency scores, we estimate a spatial SF model that considers all municipalities in Île-de-France in order to consider the role of spillovers originating from everywhere in the region and, in particular, from the Métropole du Grand Paris. However, these municipalities are not considered in the second stage of the analysis.

Typically, dynamic treatment effects are estimated by specifying an event study regression with unit and time-fixed effects. However, standard DiD regression estimates with staggered treatment timing often do not provide valid estimates of causal effects, as standard event studies use early-treated units as controls for later-treated units introducing a bias due to a “bad comparisons” problem (Baker et al., 2022). Therefore, we adopt the alternative Callaway and Sant'Anna (2021) estimator that ensures that units receiving treatment in a certain year are not compared to those that received it previously. In particular, the average treatment effect on the treated for group *g* at time *t* is given by

$$ATT(g, t) = E(Y_t(g) - Y_t(0)|G_g = 1), \quad (4)$$

where $G_g$ is an indicator function that equals 1 if a unit belongs to group *g*, meaning it was first treated in period *g*. Thus, $ATT(g, t)$ is defined as the expected difference between the outcome variable *Y* of units in group *g* at time *t* and the potential outcome if they had not been treated. In our setting, groups *g* are defined by municipalities that joined an inter-municipal group in a specific year (2010, 2011, 2012, 2013 and 2014), while time *t* corresponds to the years before and after the treatment. The outcome variable is given by the time-varying efficiency scores computed in step one. Despite the RCT being approved at the end of 2010, we include municipalities that joined an EIMC in 2010 as a treated group due to possible anticipation effects. Indeed, recommendations about the need to simplify French territorial organization to increase its efficiency through agglomerations of municipalities started in 2007 with the assignment of the Attali commission and reinforced over time until the formal approval of the RCT law.

As in standard difference-in-difference settings, since we cannot observe the potential untreated outcome for treated units, a control group of never-treated municipalities is used to proxy what would have occurred if a treated municipality had not been exposed to the treatment. In this setup, the control group is defined by both municipalities

<caption>**Table 2**
Spatial SFA estimates.</caption>

Source: The authors.

<table><thead><tr><th rowspan="2"></th><th colspan="2">Income</th><th colspan="2">Fiscal capacity</th></tr><tr><th>Coeff.</th><th>SD</th><th>Coeff.</th><th>SD</th></tr></thead><tbody><tr><td colspan="5"><strong>Frontier Function</strong></td></tr><tr><td>Opexp</td><td>0.001</td><td>0.003</td><td>0.366</td><td>***</td></tr><tr><td>Persexp</td><td>-0.002</td><td>0.002</td><td>-0.013</td><td>**</td></tr><tr><td>Invexp</td><td>0.003</td><td>**</td><td>0.027</td><td>***</td></tr><tr><td>Empl</td><td>0.024</td><td>***</td><td>0.003</td><td>0.019</td></tr><tr><td>Empl<sup>2</sup></td><td>-0.003</td><td>***</td><td>0.001</td><td>-0.006</td></tr><tr><td>Inter_opexp</td><td>-0.685</td><td>***</td><td>0.042</td><td>-0.977</td></tr><tr><td>Intra_opexp</td><td>-0.115</td><td>***</td><td>0.006</td><td>-0.292</td></tr><tr><td>Inter_persexp</td><td>1.673</td><td>***</td><td>0.034</td><td>2.237</td></tr><tr><td>Intra_persexp</td><td>0.073</td><td>***</td><td>0.007</td><td>0.197</td></tr><tr><td>Inter_invexp</td><td>0.180</td><td>***</td><td>0.010</td><td>0.297</td></tr><tr><td>Intra_invexp</td><td>0.005</td><td>***</td><td>0.004</td><td>0.107</td></tr><tr><td>Inter Empl</td><td>-0.202</td><td>***</td><td>0.007</td><td>-0.331</td></tr><tr><td>Intra Empl</td><td>0.042</td><td>***</td><td>0.002</td><td>0.027</td></tr><tr><td>Time</td><td>-0.011</td><td>***</td><td>0.001</td><td>-0.011</td></tr><tr><td>Cons</td><td>5.392</td><td>***</td><td>0.179</td><td>-2.117</td></tr><tr><td colspan="5"><strong>Inefficiency Model</strong></td></tr><tr><td>CA</td><td>-0.258</td><td>***</td><td>0.025</td><td>-0.119</td></tr><tr><td>CC</td><td>-0.521</td><td>***</td><td>0.034</td><td>-0.138</td></tr><tr><td>METRO</td><td>-0.068</td><td>***</td><td>0.021</td><td>-0.078</td></tr><tr><td>CU</td><td>-0.154</td><td>***</td><td>0.043</td><td>-0.215</td></tr><tr><td>SAN</td><td>-0.509</td><td>***</td><td>0.041</td><td>-0.268</td></tr><tr><td>ACC</td><td>-0.044</td><td>**</td><td>0.021</td><td>-0.029</td></tr><tr><td>Dens</td><td>0.396</td><td>***</td><td>0.012</td><td>0.279</td></tr><tr><td>Centre</td><td>-0.046</td><td>**</td><td>0.022</td><td>0.079</td></tr><tr><td>Rural</td><td>-0.402</td><td>***</td><td>0.027</td><td>-0.042</td></tr><tr><td>Isolated</td><td>-0.262</td><td>***</td><td>0.036</td><td>0.079</td></tr><tr><td>Touristic</td><td>-0.096</td><td>***</td><td>0.005</td><td>-0.018</td></tr><tr><td>Pop65</td><td>-0.426</td><td>***</td><td>0.018</td><td>-0.282</td></tr><tr><td>PopcomEIMC</td><td>0.104</td><td>***</td><td>0.008</td><td>0.075</td></tr><tr><td>Emptyhous</td><td>0.099</td><td>***</td><td>0.014</td><td>-0.011</td></tr><tr><td>OpexpEIMC</td><td>0.037</td><td>***</td><td>0.063</td><td>-0.176</td></tr><tr><td>PersexpEIMC</td><td>0.149</td><td>**</td><td>0.069</td><td>0.074</td></tr><tr><td>InvexpEIMC</td><td>0.011</td><td>***</td><td>0.022</td><td>0.116</td></tr><tr><td>EmplAgric</td><td>-0.079</td><td>***</td><td>0.011</td><td>0.006</td></tr><tr><td>EmplInd</td><td>0.021</td><td>***</td><td>0.007</td><td>0.014</td></tr><tr><td>EmplCons</td><td>0.114</td><td>***</td><td>0.010</td><td>0.032</td></tr><tr><td>EmplITTS</td><td>-0.120</td><td>***</td><td>0.012</td><td>-0.005</td></tr><tr><td>EmplAEH</td><td>0.011</td><td>***</td><td>0.106</td><td>0.083</td></tr><tr><td>Cons</td><td>0.148</td><td>***</td><td>0.107</td><td>0.216</td></tr><tr><td colspan="5"><strong>Test</strong></td></tr><tr><td>θ<sub>1</sub> = θ<sub>3</sub></td><td>175.55</td><td>***</td><td>61.68</td><td>***</td></tr><tr><td>θ<sub>3</sub> = θ<sub>4</sub></td><td>2047.07</td><td>***</td><td>788.70</td><td>***</td></tr><tr><td>θ<sub>5</sub> = θ<sub>6</sub></td><td>243.73</td><td>***</td><td>70.33</td><td>***</td></tr><tr><td>θ<sub>7</sub> = θ<sub>8</sub></td><td>1040.01</td><td>***</td><td>568.41</td><td>***</td></tr></tbody></table>

that did not receive the treatment (i.e. municipalities that had already joined an EIMC before the RCT law adoption) and the not-yet-treated units. For example, ATT(2013, 2018) refers to the average treatment effect of having joined an EIMC in the year 2013 on the municipal efficiency observed in 2018. The control group is defined by all never-treated units plus all municipalities affected by the RCT law that were treated after 2013 (i.e. in 2014).<fnref n="8" />

The comparison between treated units and the control group is based on the standard difference-in-difference parallel trend assumption stating that treatment and control units would have followed parallel outcome trends in the absence of treatment. The credibility of this assumption may be partially assessed by testing if parallel trends

<footnote>\*\*\*: p-value ≤ 0.01; \*\*: p-value ≤ 0.05; \*: p-value ≤ 0.10.</footnote>

<footnote n="8">⁸ In the second stage, to concentrate on EIMC formation, we did not consider the Métropole du Grand Paris as a treated group since it was established separately in 2015 after the complete formation of the EIMCs required by the RCT law. Therefore, municipalities belonging to it are excluded from the second stage of the analysis.</footnote>
<figure><img src="image_6.png" /><figcaption>Fig. 3. Technical efficiency scores over time.</figcaption></figure>

Source: The authors.

hold before treatment (pre-treatment test). Besides assuming parallel trends unconditionally, we also perform the analysis controlling for different pre-treatment covariates (i.e. assuming that the parallel trend assumption holds after conditioning on some observable characteristics). In particular, we separately consider population density and municipal typology (rural, centre, isolated, suburb) as conditioning variables due to possible multicollinearity issues.

Finally, the Callaway and Sant'Anna (2021) method allows $ATT(g,t)$ to be aggregated in various ways. This feature is particularly meaningful in our case study since it enables us to compute the average treatment effect by group, by calendar time and for different lengths of exposure to the treatment in order to respectively verify if the impact of the RCT law changes between early and later adopters, from year to year and in duration. The difference between groups, years and lengths of exposure based on the different $ATT(g,t)$ aggregation schemes can be straightforwardly tested using standard t-tests since inference is based on simultaneous confidence bands (which can be estimated with a multiplier bootstrap procedure) that are robust against multiple-testing problems.

# 5. Results

## 5.1. Spatial SFA

Table 2 shows the estimates of the spatial stochastic frontier model defined in Eq. (2) alternatively using income and fiscal capacity as dependent variables.

The first block of variables of Table 2 refers to the frontier function and shows the impact of the various input variables on the level of outcome as well as the effect of intra- and inter-EIMC spillover effects. While operating expenditure and personal expenditure do not have a significant impact on income, the effect of investments and employment is positive and significant on both the level of income and taxes. However, the impact of workplace jobs tends to decrease as employment increases due to possible saturation effects.

Concentrating on intra- and inter-EIMC input spillover effects, the tests in the third panel of Table 3 indicate that we always reject the null hypothesis of equality of inter- and intra-EIMC spillovers, highlighting the importance of differentiating between spillover effects originating from inside and outside inter-municipal groups. In particular, we find evidence of competition effects for operating expenditures since having peers with high levels of spending in this category negatively affects neighbouring municipalities in Île-de-France, with a greater negative impact for inter-EIMC spillovers. On the other hand, spillover effects from personal and investment expenditures are positive, with a greater magnitude for inter-EIMC spatial effects. Interestingly, while spillovers from workplace jobs are positive and significant for municipalities

located in the same EIMC, they turn out to be negative for neighbouring municipalities located in different EIMCs likely due to possible competition effects between peers in terms of available job positions.

The estimates in the inefficiency model section indicate how each inefficiency determinant contributes to the level of inefficiency of municipalities. In particular, we find that most inefficiency determinants contribute to decreasing the level of inefficiency of municipalities (ACC, Touristic, Pop65) while population density and the share of the municipal population over the EIMC population tend to increase municipal inefficiency. Moreover, municipalities belonging to inter-municipal groups perform better than isolated municipalities in terms of efficiency, regardless of the legal status of the EIMC. However, municipalities belonging to Paris Métropole are those reaching lower efficiency levels compared to other grouped municipalities. The explanation is likely because municipalities that do not belong to an EIMC (e.g., municipalities of Métropole du Grand Paris), have ceteris paribus larger expenditures since they exert all competencies given that they do not transfer them to the EIMC. Considering the degree of urbanization, rural municipalities are those that reach higher levels of efficiency. Between employment variables, a higher share of jobs in trade, transport, and services positively affect municipal efficiency, while employment related to industry and construction is negatively linked to efficiency. Finally, only the share of EIMC personal expenditures significantly affects municipal inefficiency for both dependent variables, with a positive sign.

Fig. 3 shows the temporal evolution of the technical efficiency scores retrieved from the estimates of the stochastic frontier model in Table 2. In particular, the average technical efficiency scores have very similar trends over time despite being smoother for fiscal capacity and more irregular for income. However, in general, we observe a strong increase in municipal efficiency after the RCT law came into force in 2010 and in particular after the EIMC completion in 2014. This insight may depend on the ability of municipalities to transfer some competencies to the EIMC which may reduce their level of expenditures.

Fig. 4 shows the technical efficiency score map for income as the dependent variable differentiating between the first and last year of the analysis. The main insight concerns the strong increase in efficiency experienced by municipalities located on the borders of Île-de-France while municipalities located in the centre of the region and in particular around Paris did not exhibit such a notable increase in efficiency over time. Indeed, municipalities that joined the Métropole du Grand Paris outsourced very few competencies until its creation and this may have slowed down their efficiency gain. However, a specific analysis would be required to investigate the specific efficiency patterns related to the formation of the Métropole du Grand Paris, which is outside the scope of the current paper. Considering fiscal capacity instead of income leads to very similar results in terms of spatial distribution of the TE scores as shown in Figure A3 in the Appendix.
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Technical efficiency scores map, years 2002 and 2019. Notes: TE scores from the model with Income as dependent variable.
Source: The authors.</figcaption></figure>

<table><caption>**Table 3**
ATT by group.
Source: The authors.</caption><thead><tr><th rowspan="2">Conditioning var.</th><th colspan="3">Income</th><th colspan="3">Fiscal capacity</th></tr><tr><th>No</th><th>Density</th><th>Typology</th><th>No</th><th>Density</th><th>Typology</th></tr></thead><tbody><tr><td><em>Average effect</em></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ATT</td><td>0.017***<br>(0.002)</td><td>0.019***<br>(0.002)</td><td>0.018***<br>(0.002)</td><td>0.014***<br>(0.004)</td><td>0.012***<br>(0.004)</td><td>0.011***<br>(0.004)</td></tr><tr><td><em>Effect by group</em></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>g2010</td><td>0.022***<br>(0.005)</td><td>0.023***<br>(0.005)</td><td>0.023***<br>(0.005)</td><td>0.005<br>(0.008)</td><td>0.004<br>(0.007)</td><td>0.004<br>(0.008)</td></tr><tr><td>g2011</td><td>0.015***<br>(0.003)</td><td>0.018***<br>(0.003)</td><td>0.017***<br>(0.003)</td><td>0.018*<br>(0.010)</td><td>0.014<br>(0.010)</td><td>0.014<br>(0.011)</td></tr><tr><td>g2012</td><td>0.023***<br>(0.003)</td><td>0.026***<br>(0.003)</td><td>0.025***<br>(0.003)</td><td>0.032***<br>(0.008)</td><td>0.029***<br>(0.008)</td><td>0.027***<br>(0.008)</td></tr><tr><td>g2013</td><td>0.014***<br>(0.003)</td><td>0.018***<br>(0.003)</td><td>0.016***<br>(0.003)</td><td>0.008<br>(0.006)</td><td>0.005<br>(0.006)</td><td>0.006<br>(0.006)</td></tr><tr><td>g2014</td><td>0.007*<br>(0.004)</td><td>0.008*<br>(0.004)</td><td>0.004<br>(0.004)</td><td>0.014*<br>(0.008)</td><td>0.014*<br>(0.008)</td><td>0.014*<br>(0.008)</td></tr><tr><td><em>Pre-trend test</em></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>χ<sup>2</sup> stat.</td><td>6.53</td><td>9.98</td><td>11.70</td><td>7.56</td><td>7.17</td><td>8.03</td></tr></tbody></table>

Notes: No: unconditional model; Density: population density; Typology: rural, centre, isolated, suburb.

\*\*\* : p-value ≤ 0.01; \*\* : p-value ≤ 0.05; \* : p-value ≤ 0.10.

Robust and asymptotic standard errors in parenthesis.

## 5.2. DiD

Table 3 shows the average treatment effect and the average effect by group for the two sets of TE scores computed in stage one and considering various combinations of conditioning variables. In particular, we consider both the unconditional model (column No) and the conditional one with population density (column Density) or typology of the municipality (column Typology) as covariates. The pre-treatment parallel trend test in the last row of Table 3 indicates that the null hypothesis of parallel trends before treatment both for unconditional and for different conditional models can never be rejected.

The results of the DiD analysis are quite robust across the two typologies of TE scores and the different model specifications. Overall, we find that the average effect of having joined an inter-municipal group after the implementation of the RCT law is positive with both dependent variables. In particular, the ATT is between 1.7% and 1.9% with income as the outcome and between 1.1% and 1.4% with fiscal capacity. Although the impact appears small given that TE scores are bounded between 0 and 1 (an effect of 1%–2% translates into an absolute increase of 0.01 to 0.02), it is statistically significant. Economically, this means that municipalities joining an EIMC group tend to become more efficient, achieving higher output levels with the same resources. This finding aligns with previous studies. For instance,

Luca and Modrego (2020), using Italian data, report effects between 3 and 6.7 percentage points on the technical efficiency of municipal services, although their estimates are not statistically significant.

Some differences apply when disaggregating the effect by group. Considering income, the average treatment effect tends to be higher for groups of municipalities that joined an EIMC in the first years after the proclamation of the law and then it decreased for later adopters, mostly for the year 2014. The paired tests in Table A1 in the Appendix confirm that the ATT for group 2014 is statistically different from that of all other groups. Therefore, municipalities that joined an inter-municipal group in the last available year experienced a reduced increase in efficiency compared to advanced adopters since, under the constraint, they may have decided to transfer fewer competencies at the inter-municipal level. Results for fiscal capacity show a positive and significant impact only for the 2011, 2012 and 2014 groups. In sum, although the effect of IMC appears small in absolute terms, our results suggest that it tends to accumulate over time, potentially leading to substantial improvements in overall efficiency in the long run.

Fig. 5 shows the average treatment effect by year for the two types of TE scores considering the unconditional DiD model. Overall, the ATT seems to increase from 2010 to 2015 and then it tends to decrease slightly after 2015 considering income. For fiscal capacity, we cannot detect a clear trend due to larger confidence bands for yearly impacts.
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** ATT by year.
Notes: Unconditional model
Source: The authors.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** ATT by length of exposure.
Notes: Unconditional model
Source: The authors.</figcaption></figure>

The paired tests in Table A1 in the Appendix indicate that the ATT with income as the dependent variable is statistically different mainly between pairs of years after 2014. While the efficiency scores show a notable increase after 2015 (Fig. 3), here we find that the causal effect of integration is higher between 2010 and 2015. This may depend on the fact that it took some time to make an EIMC operational transferring competencies from the municipalities to the inter-municipal group. Moreover, the NOTRE law voted in 2015 strengthened the authority of EIMCs by transferring a new set of competencies such as water service. Finally, also the creation of the Métropole du Grand Paris in 2015 may have had a positive impact on the efficiency level of all municipalities in the region.

Fig. 6 shows the average treatment effect by length of exposure for the two types of TE scores considering the unconditional DiD specification. The results indicate that, for both model specifications, the ATT tends to increase with the length of exposure up to the period 7. However, with income, we still have increasing values in periods 8 and 9 reaching values up to 4% with nine years of exposure to the treatment, while with taxes the ATT tends to decrease in the last two periods. Moreover, the non-significant ATT for pre-treatment adoption periods further confirms the validity of the parallel trend assumption. The paired tests in Table A1 in the Appendix, referring to the model with income as output, indicate that, as expected, all pre-treatment periods are statistically different from post-treatment ones. Moreover, we find that the ATT results are statistically different across different lengths of exposure starting from 7 years of exposure to the treatment, confirming the insights on the increasing effect of the treatment with time detected in the left panel of Fig. 6.

Given the scarce literature that exploits a similar research question for French municipalities, a comparative analysis is difficult. However, our results are in line with Tricaud (2025), who finds that municipalities that were forced to integrate after the reform experienced a loss

in public services, which might explain why municipalities that joined an EIMC in the early stages benefit from a higher positive impact in their TE. This effect might also be driven by experience acquired over the years. Cooperation can lead to interactive learning among local governments (Hefetz et al., 2012), which may lead to a decrease in transaction costs over time due to the learning process (Máñez et al., 2016). However, Tricaud (2025) also finds that municipalities forced to join an EIMC benefited from higher access to public transport and increased fiscal revenues, which could explain part of the positive effect we find, especially the increase in average efficiency after 2015.

Other potential determinants of the decreasing impact of IMC on efficiency might come from higher transaction costs to governance arrangements that municipalities forced to cooperate must face, such as information and coordination, negotiation and division, bargaining, etc. (Bel and Sebő, 2021). Pérez-López et al. (2015) also argue that the potential reduction in municipal performance of local governments implementing IMC may come from the loss of economies of scope of municipalities regarding the services not included in the cooperation. They also find evidence that IMC is a suitable form of public service delivery for periods of crisis (after the Great Recession of 2008), given that it enables local governments to adjust their resource use before reducing expenditures. Thus, municipalities that joined an EIMC after the reform – which took place in the early years after the crisis – could have coped better with their effects.

An additional interesting aspect is comparing the effect of mandatory IMC, as imposed by the RCT law, and voluntary IMC, as adopted by municipalities that joined an inter-municipal group before 2010. To compare the impact of voluntary IMC with mandatory IMC, in addition to the 2010–2014 groups, which represent mandatory IMC, we incorporated the 2003–2009 treatment groups into our second-stage analysis to account for municipalities that voluntarily joined an inter-municipal group before the RCT law was enacted. In this case, the
<caption>**Table 4**
Impact of voluntary and mandatory IMC: ATT by group.</caption>

*Source:* The authors.

<table><thead><tr><th rowspan="2"></th><th colspan="2">(i)</th><th colspan="2">(ii)</th></tr><tr><th>Inc.</th><th>Fisc.</th><th>Inc.</th><th>Fisc.</th></tr></thead><tbody><tr><td>Average effect</td><td></td><td></td><td></td><td></td></tr><tr><td>ATT</td><td>0.016***<br>(0.002)</td><td>0.004<br>(0.003)</td><td>0.012***<br>(0.002)</td><td>-0.002<br>(0.003)</td></tr><tr><td>Effect by group</td><td></td><td></td><td></td><td></td></tr><tr><td>g2003</td><td>0.012***<br>(0.003)</td><td>-0.005<br>(0.005)</td><td>0.008***<br>(0.003)</td><td>-0.007<br>(0.005)</td></tr><tr><td>g2004</td><td>0.022***<br>(0.004)</td><td>0.012*<br>(0.007)</td><td>0.018***<br>(0.004)</td><td>0.012*<br>(0.007)</td></tr><tr><td>g2005</td><td>0.018***<br>(0.005)</td><td>-0.007<br>(0.006)</td><td>0.015***<br>(0.005)</td><td>-0.010*<br>(0.006)</td></tr><tr><td>g2006</td><td>0.017***<br>(0.002)</td><td>0.010<br>(0.007)</td><td>0.013***<br>(0.002)</td><td>0.006<br>(0.007)</td></tr><tr><td>g2007</td><td>0.008<br>(0.011)</td><td>-0.031***<br>(0.008)</td><td>0.004<br>(0.011)</td><td>-0.035***<br>(0.008)</td></tr><tr><td>g2008</td><td>0.025***<br>(0.008)</td><td>0.007<br>(0.014)</td><td>0.022***<br>(0.008)</td><td>0.002<br>(0.014)</td></tr><tr><td>g2009</td><td>-0.010<br>(0.014)</td><td>-0.043***<br>(0.014)</td><td>-0.014<br>(0.014)</td><td>-0.050***<br>(0.014)</td></tr><tr><td>g2010</td><td>0.019***<br>(0.005)</td><td>0.005<br>(0.008)</td><td>-</td><td>-</td></tr><tr><td>g2011</td><td>0.021***<br>(0.003)</td><td>0.020*<br>(0.011)</td><td>-</td><td>-</td></tr><tr><td>g2012</td><td>0.021***<br>(0.003)</td><td>0.035***<br>(0.009)</td><td>-</td><td>-</td></tr><tr><td>g2013</td><td>0.011***<br>(0.003)</td><td>0.010*<br>(0.007)</td><td>-</td><td>-</td></tr><tr><td>g2014</td><td>0.004<br>(0.004)</td><td>0.015*<br>(0.009)</td><td>-</td><td>-</td></tr></tbody></table>

Unconditional model

***:p-value ≤ 0.01; **:p-value ≤ 0.05; *:p-value ≤ 0.10

Robust and asymptotic standard errors in parenthesis.

control group consists of municipalities that joined an EIMC before 2003 and those that have not yet been treated.

The results shown on the left panel (i) of Table 4 indicate that both voluntary and mandatory IMC positively and significantly enhance municipal efficiency in terms of income with similar magnitudes. However, when considering fiscal capacity, we find that while mandatory IMC shows a positive and significant effect (as shown in Table 3), considering both voluntary and mandatory IMC exhibits mixed results. Specifically, before 2010, we find non-significant or negative effects, with 2004 being the only year showing a positive and significant, despite very low, impact.

To further examine the effects of voluntary IMC, we analysed it in isolation by estimating the ATT only for municipalities that joined an EIMC between 2003 and 2009. In this case, the control group comprises municipalities that had joined an EIMC before 2003, those that were mandated to enter an EIMC under the RCT law and not yet treated municipalities. The results, shown in the right panel (ii) of Table 4, are consistent with previous findings indicating that while voluntary IMC for most groups significantly enhances municipal efficiency when measured in terms of income. However, for fiscal capacity, the overall average effect remains non-significant, and for income, its magnitude (0.012) is smaller compared to cases where both voluntary and mandatory IMC (0.016) or only mandatory IMC (0.017) are considered. Therefore, while our findings provide strong evidence of the positive impact of mandatory IMC on municipal efficiency, the effect of voluntary IMC remains ambiguous and warrants further investigation.

### 5.3. Robustness checks

First, as robustness checks, we choose alternative control groups (i.e. only never treated units or only not yet treated units), we perform estimates considering the (de Chaisemartin and D'Haultfoeuille, 2020)

estimator for different groups and time periods instead of Callaway and Sant'Anna (2021), we adopt different outcome variables, and we use alternative spatial weight matrices to capture intra- and inter-EIMC input spillover effects. Table A2 in the Appendix confirms the robustness of our estimates for different control groups (using only not yet treated municipalities or, as an alternative, municipalities that joined an EIMC group before 2010). Figure A4 in the Appendix showing the ATT by event time by employing the (de Chaisemartin and D'Haultfoeuille, 2020) estimator indicates a very similar pattern with respect to the results in the main results section. When we consider wages as an alternative to income and fiscal capacity, we still find a positive and significant causal effect of having joined an EIMC on municipal efficiency. However, as shown in the estimates in Table A3 in the Appendix, the ATT estimates are slightly higher in magnitude compared to our main results. Considering alternative neighbourhood criteria, Table A4 indicates that our results are robust to different choices of the spatial weight matrix.

Second, since some of the variables included in the inefficiency model may be affected by endogeneity issues, we also estimate the model considering one-year-lagged socio-economic contextual variables and removing EIMC-related variables such as PopcomEIMC, OpexpEIMC, PersexpEIMC, and InvexpEIMC. The ATT estimates in Table A5 and A6 in the Appendix are overall in line with our main results in terms of significance, with slightly lower magnitudes, and confirm the robustness of our main results.

Third, an additional key point relates to possible selection into treatment driven by intra-EIMC heterogeneity. Indeed, the more heterogeneous municipalities in the same EIMC are, the higher the political transaction costs of agreeing on common politics (Feiock, 2009; Feiock et al., 2009). Therefore, relevant differences among municipalities in an EIMC may lead them to be more reluctant to join the inter-municipal group, affecting the selection into treatment. To control for this, as a robustness check, we include in the contextual equation some variables capturing intra-EIMC heterogeneity. In particular, we computed the yearly EIMC-level Herfindahl index for population size, population density, unemployment rate in 15–64 year olds, total outstanding debts, potential fiscal capacity by inhabitant, and the EIMC-level Herfindahl index for the number of votes for the right candidate at the presidential election of 2012 (second round). The results shown in Table A7 in the Appendix indicate that, for most of the aspects considered, intra-EIMC heterogeneity significantly influences municipal efficiency. However, the ATT estimates in Table A8 in the Appendix are completely in line with those presented in the main results section, indicating that intra-EIMC heterogeneity is not affecting our main findings.

Another aspect we check for is individual unobserved heterogeneity driven by political factors, which may have a role in the combination of factors of production chosen. To control for this, in stage one, we incorporate EIMC-level fixed effects in the contextual equation. The DiD results, presented in Table A9 in the Appendix, are overall in line with those in the main results section of the paper. The main difference with respect to our findings concerns the fact that the ATT based on fiscal capacity shows a higher magnitude compared to the one measured through income as a dependent variable. However, based on the results of the unconditional DiD model, the magnitude of the average impacts remains in the range 1.3%–1.7%.

## 6. Conclusion

This paper contributes to the scarce literature on the role of IMC on municipal efficiency. For that purpose, we build and exploit a panel dataset of French municipalities from the Île-de-France region for the period 2002–2019, and evaluate the impact of the 2010 “Réforme des Collectivités Territoriales” (RCT) law on municipal performance. This law made it compulsory for all French municipalities to join an inter-municipal cooperation group by 2014. To the best of our knowledge, this is the first paper to tackle this question in the French case. In
doing so, we develop a two-stage approach where in the first stage we calculate municipal efficiency controlling for heterogeneous strategic spatial interactions among municipalities both inside and outside an inter-municipal cooperation group. We also control for various contextual variables that may affect the distribution of inefficiency. In the second stage, we implement a novel staggered DiD model with multiple groups and time periods that allow us to disaggregate the causal effect of each group of municipalities that joined an EIMC in a given year, after the adoption of the RCT law.

Our main results show that, on average, there is a positive effect of joining an EIMC that oscillates around 1.1% and 1.9%. However, the size of this effect is heterogeneous. In particular, we find that municipalities that joined an EIMC right after the law came into force benefited from a higher impact on their performance (especially for the year 2012 considering fiscal capacity); whereas those that joined an inter-municipal group in the final year (2014) experienced lower effects. Moreover, when we decompose the effect by the length of exposure to the treatment, we observe that those municipalities with 7 years of exposure or more present the highest impact on their performance (based on income).

Potential questions to be addressed in future research can be taken from our results. In particular, it would be interesting to focus on the determinants that explain these heterogeneous impacts over time, and whether these effects are the same for other French regions. These questions escape the scope of this study. Here, we focus on the Île-de-France region given that it accounted for the lowest share of municipalities within an EIMC before the reform. Furthermore, we do this to increase the internal validity of our approach by limiting the unobserved heterogeneity of other regions. However, we argue that potential determinants might be related to the experience gained from voluntarily joining an EIMC in the early stages of reform. Other potential explanations may come from the scarce literature that tackles similar questions. In particular, we can mention Tricaud (2025) who shows that municipalities that were forced to join an EIMC – and probably joined one in 2014 – experienced a loss in public services compared to early adopters, but benefited from higher fiscal revenues and access to public transport similar to those of early adopters, which could be explaining part of the lower but still positive impact on their efficiency.

### CRediT authorship contribution statement

**Federica Galli:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Juan A. Piedra-Peña:** Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Marie-Laure Breuillé:** Writing – review & editing, Validation, Supervision, Project administration, Conceptualization. **Julie Le Gallo:** Writing – review & editing, Validation, Supervision, Project administration, Methodology, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

We acknowledge Camille Grivault's very valuable support. We also thank all the participants of the AFSE congress, AISRe (Associazione Italiana di Scienze Regionali) conference, ERSA (European Regional Science Association) conference, meeting in public economics (Spain), AMSE public economics conference (France), and seminar at the University of Oviedo for their comments. Juan Piedra-Peña wishes to

acknowledge the support of the Margarita Salas Scholarship funded by the Ministerio de Universidades and the European Union (Unión Europea-NextGenerationEU)

## Appendix A. Supplementary material

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.regsciurbeco.2025.104185.

### Data availability

The data that has been used is confidential.

### References

Afonso, A., Rault, C., 2009. Spend-and-tax: a panel data investigation for the EU. Econ. Bull. 29, 2542–2548.

Agrawal, D.R., Breuillé, M.-L., Le Gallo, J., 2025. Tax competition with intermunicipal cooperation. Natl. Tax J. 78 (1), 000–000.

Aigner, D., Lovell, C.K., Schmidt, P., 1977. Formulation and estimation of stochastic frontier production function models. J. Econometrics 6 (1), 21–37.

Alesina, A., Spolaore, E., 1997. On the number and size of nations. Q. J. Econ. 112 (4), 1027–1056.

Allers, M.A., de Greef, J.A., 2018. Intermunicipal cooperation, public spending and service levels. Local Gov. Stud. 44 (1), 127–150.

Alonso, W., 1973. Urban zero population growth. Daedalus 102 (4), 191–206.

Asmare, E., Begashaw, A., 2018. Review on parametric and nonparametric methods of efficiency analysis. Biostat. Bioinform. 2 (2), 1–7.

Baker, A., Larcker, D.F., Wang, C.C.Y., 2022. How much should we trust staggered difference-in-differences estimates? J. Financ. Econ. 144 (2), 370–395.

Battese, G.E., Coelli, T.J., 1988. Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data. J. Econ. 38 (3), 387–399.

Battese, G.E., Coelli, T.J., 1995. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empir. Econ. 20 (2), 325–332.

Bel, G., Mur, M., 2009. Intermunicipal cooperation, privatization and waste management costs: Evidence from rural municipalities. Waste Manage. 29 (10), 2772–2778.

Bel, G., Sebó, M., 2021. Does inter-municipal cooperation really reduce delivery costs? An empirical evaluation of the role of scale economies, transaction costs, and governance arrangements. Urban Aff. Rev. 57 (1), 153–188.

Bel, G., Warner, M.E., 2015. Inter-municipal cooperation and costs: Expectations and evidence. Public Adm. 93 (1), 52–67.

Blanchard, O., Perotti, R., 2002. An empirical characterization of the dynamic effects of changes in government spending and taxes on output. Q. J. Econ. 117, 1329–1368.

Blesse, S., Baskaran, T., 2016. Do municipal mergers reduce costs? Evidence from a German federal state. Reg. Sci. Urban Econ. 59, 54–74.

Blom-Hansen, J., Houlberg, K., Serritzlew, S., Treisman, D., 2016. Jurisdiction size and local government policy expenditure: Assessing the effect of municipal amalgamation. Am. Political Sci. Rev. 110 (4), 812–831.

Bolton, P., Roland, G., 1997. The breakup of nations: A political economy analysis. Q. J. Econ. 112 (4), 1057–1090.

Bosch, N., Espasa, M., Mora, T., 2012. Citizen control and the efficiency of local public services. Environ. Plan. C: Gov. Policy 30 (2), 248–266.

Brasington, D., 2003. Size and school district consolidation: Do opposites attract? Economica 70 (280), 673–690.

Breuillé, M.-L., Duran-Vigneron, P., 2023. Intermunicipal Cooperation in France and Related Tax Issues. Tech. rep., National Bureau of Economic Research.

Breuillé, M.-L., Duran-Vigneron, P., Samson, A.-L., 2018. Inter-municipal cooperation and local taxation. J. Urban Econ. 107, 47–64.

Breuillé, M.-L., Le Gallo, J., 2017. Spatial fiscal interactions among French municipalities within inter-municipal groups. Appl. Econ. 49 (46), 4617–4637.

Brueckner, J.K., 2003. Strategic interaction among governments: An overview of empirical studies. Int. Reg. Sci. Rev. 26 (2), 175–188.

Buetner, T., Holm-Hadulla, F., 2013. City size and the demand for local public goods. Reg. Sci. Urban Econ. 43, 16–21.

Callaway, B., Sant'Anna, P.H.C., 2021. Difference-in-Differences with multiple time periods. J. Econometrics 225, 200–230.

Camagni, R., Capello, R., Caragliu, A., 2015. The rise of second-rank cities: what role for agglomeration economies? Eur. Plan. Stud. 23 (6), 1069–1089.

Carr, J.B., Gerber, E.R., Lupher, E.W., 2007. Explaining horizontal and vertical cooperation on public services in michigan: The role of local fiscal capacity. In: Jelier, R., Sands, G. (Eds.), Sustaining Michigan: Metropolitan Policies and Strategies. Michigan State University Press, East Lansing, MI, pp. 207–235.

Cobban, T.W., 2019. Bigger is better: Reducing the cost of local administration by increasing jurisdiction size in Ontario, Canada. Urban Aff. Rev. 55 (2), 462–500.

da Cruz, N.F., Marques, R.C., 2014. Revisiting the determinants of local government performance. 44, (ISSN: 03050483) pp. 91–103.
de Chaisemartin, C., D'Haultfoeuille, X., 2020. Difference-in-differences estimators of intertemporal treatment effects. Working Paper.

Desjardins, X., 2016. Ce grand Paris qui advient. Leçons pour la planification métropolitaine. Inf. Géographique (4), 96-114.

Di Porto, E., Merlin, V.R., Paty, S., 2013. Cooperation among local governments to deliver public services: A structural bivariate response model with fixed effects and endogenous covariate. GATE Groupe D'Analyse et de Théorie Économique Lyon-St Étienne. (Working paper no. WP 1304, 1304).

Di Porto, E., Parenti, A., Paty, S., Abidi, Z., 2016. Local government cooperation at work: A control function approach. J. Econ. Geogr. 17 (2), 435-463.

Dijkstra, E., Gradus, R.H.J.M., 2013. Cost advantage cooperations larger than private waste collectors. Appl. Econ. Lett. 20 (7), 702-705.

Elhorst, J.P., 2010. Spatial panel data models. In: Fischer, M., Getis, A. (Eds.), Handbook of Applied Spatial Analysis. Springer, New York.

Feiock, R.C., 2007. Rational choice and regional governance. J. Urban Aff. 29 (1), 47-63.

Feiock, R.C., 2009. Metropolitan governance and institutional collective action. Urban Aff. Rev. 44 (3), 356-377.

Feiock, R.C., Steinacker, A., Park, H.J., 2009. Institutional collective action and economic development joint ventures. Public Adm. Rev. 69 (2), 256-270.

Ferraresi, M., Migali, G., Rizzo, L., 2018. Does inter-municipal cooperation promote efficiency gains? Evidence from Italian Municipal Unions. J. Reg. Sci. 58, 1017-1044.

Frère, Q., Leprince, M., Paty, S., 2014. The impact of intermunicipal cooperation on local public spending. Urban Stud. 51 (8), 1741-1760.

Galí, J., López-Salido, J.D., Vallés, J., 2007. Understanding the effects of government spending on consumption. J. Eur. Econ. Assoc. 5, 227-270.

Garrido-Jiménez, F.J., Magrinyà, F., del Moral-Ávila, M.C., Delgado-Méndez, L., 2019. Impact of unfinished residential developments on municipal economic forecasts: evidence from medium-sized spanish cities. J. Hous. Built Environ. (ISSN: 15737772) 34 (2), 489-509.

Griliches, Z., 1992. The search for R & D spill-Overs. Scand. J. Econ. 94, 29-47.

Hefetz, A., Warner, M.E., Vigoda-Gadot, E., 2012. Privatization and intermunicipal contracting: The US local government experience 1992-2007. Environ. Plan. C: Gov. Policy 30 (4), 675-692.

Huang, T.H., Wang, M.H., 2002. Comparison of economic efficiency estimation methods: Parametric and non-parametric Techniques. Manch. Sch. 70 (5), 682-709.

Kalb, A., Geys, B., Heinemann, F., 2012. Value for money? German local government efficiency in a comparative perspective. Appl. Econ. 44 (2), 201-218.

Kara, M.A., Taş, S., Ada, S., 2016. The impact of infrastructure expenditure types on regional income in Turkey. Reg. Stud. 50 (9), 1509-1519.

Kopczewska, K., 2016. Efficiency of regional public investment: An NPV-based spatial econometric approach. Spat. Econ. Anal. 11, 413-431.

Lampe, H.W., Hilgers, D., Ihl, C., 2015. Does accrual accounting improve municipalities' efficiency? Evidence from Germany. Appl. Econ. 47 (41), 4349-4363.

LeRoux, K., Carr, J.B., 2007. Explaining local government cooperation on public works evidence from Michigan. Public Work. Manag. Policy 12 (1), 344-358.

Linhares, F., Nojosa, G., 2020. Changes in the tax-spend nexus: Evidence from selected European countries. Econ. Bull. 40, 1-12.

Lo Storto, C., 2016. The trade-off between cost efficiency and public service quality: A non-parametric frontier analysis of Italian major municipalities. Cities 51, 52-63.

Luca, D., Modrego, F., 2020. Stronger together? Assessing the causal effect of inter-municipal cooperation on the efficiency of small Italian municipalities. J. Reg. Sci. 61 (1), 261-293.

Máñez, J., Pérez-López, G., Prior, D., Luis Zafra-Gómez, J., 2016. Understanding the dynamic effect of contracting out on the delivery of local public services. Reg. Stud. 50 (12), 2069-2080.

Morgan, D.R., Hirlinger, M.W., 1991. Intergovernmental service contracts a multivariate explanation. Urban Aff. Rev. 27 (1), 128-144.

Narbón-Perpiñá, I., Arribas, I., Balaguer-Coll, M.T., Tortosa-Ausina, E., 2020. Explaining local governments' cost efficiency: Controllable and uncontrollable factors. Cities 100, 102665.

Narbón-Perpiñá, I., De Witte, K., 2018. Local governments' efficiency: a systematic literature review—part II. Int. Trans. Oper. Res. 25 (4), 1107-1136.

Otsuka, A., 2020. Inter-regional networks and productive efficiency in Japan. Pap. Reg. Sci. 99 (1), 115-133.

Parman, B.J., Featherstone, A.M., 2019. A comparison of parametric and nonparametric estimation methods for cost frontiers and economic measures. J. Appl. Econ. 22 (1), 60-85.

Pérez-López, G., Prior, D., Zafra-Gómez, J.L., 2015. Rethinking new public management delivery forms and efficiency: Long-term effects in Spanish local government. J. Public Adm. Res. Theory 25 (4), 1157-1183.

Polo, C., Ramajo, J., Ricci-Risquete, A., 2021. A stochastic semi-non-parametric analysis of regional efficiency in the European Union. Reg. Sci. Policy Pr. 13 (1), 7-24.

Reingewertz, Y., 2012. Do municipal amalgamations work? Evidence from municipalities in Israel. J. Urban Econ. 72 (2-3), 240-251.

Saygılı, H., Özdemir, K.A., 2021. Regional economic growth in Turkey: the effects of physical, social and financial infrastructure investment. Empir. Econ. 60 (4), 2039-2061.

Seifert, S., Nieswand, M., 2014. What drives intermediate local governments' spending efficiency: The case of French departements. Local Gov. Stud. 40 (5), 766-790.

Simar, L., Wilson, P.W., 2007. Estimation and inference in two-stage, production processes. J. Econometrics 136, 31-64.

Tricaud, C., 2025. Better alone? Evidence on the costs of intermunicipal cooperation. Am. Econ. J.: Appl. Econ. 17 (1), 160-207.

Vidoli, F., Quintiliani, F., Marinuzzi, G., Porcelli, F., Tortorella, W., 2023. Do municipal unions improve cost efficiency for the social function? A quasi-experimental endogenous stochastic frontier approach. J. Reg. Sci. 1-25.

Wang, H.J., Schmidt, P., 2002. One-step and two-step estimation of the effects of exogenous variables on technical efficiency levels. J. Prod. Anal. 18, 129-144.

Ward, H., John, P., 2013. Competitive learning in yardstick competition: Testing Models of policy diffusion with performance data. Political Sci. Res. Methods 1, 3-25.