Do municipal mergers internalise spatial spillover effects? empirical evidence from Japanese municipalities

This study investigates whether municipal mergers could internalise spatial spillover effects by comparing mergers before and after they occur, focusing on local public library services in Japan. A spatial spillover effect occurs when the benefit of a local public service spreads across its own administrative district and into neighbouring ones. A free-rider problem among municipalities might arise when a municipality decides how much to supply internally under a decentralisation system, recognising the existence of spatial spillover effects. Under such circumstances, spatial spillover effects might be internalised through municipal mergers. In Japan, large-scale municipal mergers took place in FY2004 and FY2005 and the number of municipalities decreased from 3,232 to 1,820. By applying cross-sectional spatial econometrics models, we find spatial spillover effects in public library services both before and after the mergers, but the impact becomes smaller. The results imply that municipal mergers could partially internalise spatial spillover effects among municipalities. Additionally, we showed that municipal mergers increase the supply of library services. As a result, due to the merger of municipalities, the undersupply of local public goods with spatial spillover effect may be decreased, which could help achieve the socially optimal supply.


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Do municipal mergers internalise spatial spillover effects?… respectively). The concentration of municipal mergers within this period was due to better financial support measures in the Special Municipal Mergers Law, whereby financial support could be provided only if the merger occurred before 31 March 2006. Several studies have investigated the effects of municipal mergers on financial or economic outcomes. 6 Researchers have studied the effect of municipal mergers on public expenditures using data from Israel, Sweden, Japan, and Germany (e.g. Miyazaki 2006Miyazaki , 2018bReingewertz 2012;Hirota and Yunoue 2013;Hanes 2015;Blesse and Baskaran 2016). These studies indicate possible decreases in expenditures due to municipal mergers.On the other hand, some studies have found that expenditures increase after municipalities merge (e.g. Moisio and Uusitalo 2013). Harjunen et al. (2021) showed that mergers had practically no effect on total expenditure within mergers, indicating that the benefits and costs of merging are distributed unevenly within the mergers. 7 In these studies, the results are mixed, and there is no clear conclusion on the impact of mergers on municipal outcomes.
A few studies have examined the impact of municipal mergers on the supply of individual public goods. Harjunen et al. (2021) hint at health and education provision due to the reallocation of local jobs from peripheral parts to the centre, within the merged municipalities. Furthermore, Sandsør et al. (2021) suggested that municipal mergers may improve the quality of schools.
In addition, a large number of studies in Sweden, the USA, Spain, and Japan have investigated the free-riding behaviour among municipalities before and after mergers (e.g. Hinnerich 2009;Jordahl and Liang 2010;Hansen 2014Hansen , 2019Saarimaa and Tukiainen 2015;Nakazawa 2016;Hirota and Yunoue 2017;Fritz and Feld 2020). The results showed that smaller municipalities tended to issue municipal bonds and free ride on merged municipalities. 8 Thus, existing research into free-riding behaviour among merged municipalities before and after mergers has found a decreasing effect of expenditure post-merger among merged municipalities. However, these studies did not analyse municipalities undergoing mergers free-riding on their counterparts, on means other than fiscal resources. Therefore, we examine whether free-riding behaviour among municipalities is accelerated or attenuated by the merger process itself.
So, what is the relationship between municipal mergers and free-riding behaviour among municipalities? Solé-Ollé (2006) indicated the potential for the undersupply 6 Similar studies have analysed the issue from the perspective of inter-municipal cooperation (IMC) rather than municipal mergers. In these studies, the results are mixed, and show all three results: Cooperation allows small municipalities with a suboptimal size to save costs (Bel et al. 2014), IMC partly improves efficiency (Banaszewska et al. 2022), and it does not improve efficiency (Luca and Modrego, 2021). Then, Jannin and Sotura (2019) showed the possibility that increased fiscal integration in the provision of public goods might substantially improve welfare, by simulating the effect of a reform through redefining jurisdictions' administrative boundaries. 7 In addition, there is a pioneering study by Egger et al. (2022) using nightlight data showing that mergers had net positive effects on local activity in the merged municipality. However, municipalities absorbing their merger partners and hosting the new administrative centre, experience a significant increase in local activity, while the municipalities that are being absorbed and are losing their administrative centres, experience a decrease in such activity. 8 However, Goto et al. (2021) have found that municipalities decreased the amount of borrowing before their mergers. 1 3 of a service when positive spatial spillover effect occurs. A possible solution is to internalise the positive spatial spillover effect and thus to remove or decrease the undersupply by changing jurisdictions through municipal mergers. 9 Hirota and Yunoue (2013) and Miyazaki (2006) suggested that expenditure might temporarily increase in the initial stages of a merger, which could indicate a temporary increase in costs to alleviate undersupply. Miyazaki (2006) showed an increase in construction costs. This could be due to previous spatial spillover effects and the undersupply of public facilities before the municipal merger, which decreased following the merger, causing construction costs to rise to mitigate the undersupply. However, these studies did not clarify whether there was a change in the free-riding behaviour between municipalities after municipal mergers.
Since the free-riding behaviour may differ depending on the type of public good, it is necessary to specify it. This study focuses on public library services, 10 which are supplied mainly by a municipality and made accessible to residents of other municipalities. 11 Because commuters and residents in the neighbourhood are able to use the service, it is possible that the public library service is facing crowding spillover, as pointed out by Solé-Ollé (2006). Figure 1 shows the number of municipal mergers and the changes in the rate of increase in public libraries in Japan between 1999 and 2011. The figure shows that several new public libraries were built in 2004 and 2005, when many municipal mergers took place. If there were no spatial spillover effects in library services, and municipal mergers occurred in pursuit of economies of scale, then the number of public libraries would likely have fallen. However, the number of public libraries has increased. This could be attributed to municipal mergers internalising (or lessening) spatial spillover effects and an increase in the supply of library services that were previously undersupplied. Table 1 shows the changes in the number of municipalities and the number of registered users by region. When externalities are internalised by municipal mergers, the supply of library services, which had previously been undersupplied, could increase to socially optimal quantities. For example, in Hokkaido, few municipal mergers occurred between 1999 and 2005, and the number of library registrants did not increase substantially. However, in Kyushu, many municipal mergers occurred, and the number of library registrants increased substantially. When municipal mergers were more frequent, externalities were internalised, and it is possible that the number of registered users increased.
This study focuses on the Kyushu region, which is geographically independent (i.e. independent from the Japanese mainland), and shows trends similar to the 1 3 Do municipal mergers internalise spatial spillover effects?… Japanese national average in terms of municipal mergers in these periods (excluding Okinawa, which is also geographically independent). 12 Our contributions are as follows. First, this study evaluates the effect of municipal mergers from the internalisation of externalities using data before and after mergers. The question of whether the internalisation of externalities can be achieved through municipal mergers is an important perspective when considering the optimal supply of public goods in decentralisation. Thus, this study first examines whether freeriding behaviour in public library services existed among neighbouring municipalities prior to many municipal mergers, using spatial regression. To examine whether there were subsequent changes in free-riding behaviour, we should use data after 2005, when many municipal mergers occurred. By comparing the changes in the behaviour of municipalities in these two periods, we investigate the consequences of municipal mergers on spatial spillover effects.
Second, we evaluate the effect of municipal mergers on an increase in the supply of library services, which were possibly previously undersupplied. It is important to check whether the supply of public goods increased when municipal mergers eliminated (reduced) free-riding behaviour among municipalities. Thus, we examine whether municipal mergers lead to an increase in the supply of library services, which were possibly previously undersupplied in the same two periods using differences in differences (DID).
The rest of the paper proceeds as follows. Section 2 provides the methodology and model specification. Section 3 presents the data sources and features. Section 4 discusses the results of the spatial regression analysis. Section 5 discusses the results of the DID analysis and robustness check, and Sect. 6 presents the conclusion.

Spatial Regression Model
First, this study adopts methods for spatial econometrics to detect free-riding behaviour in public library services among municipalities in Japan. We focus on the decision-making of municipalities and, therefore, use aggregated data per municipality in the analysis. The analysis uses four approaches. First, we apply an ordinary least squares (OLS) model to examine whether the number of external library users affects the total number of library users. Second, we investigate the potential spillover effect among municipalities regarding public library services by applying a maximum likelihood estimation of the spatial autoregressive model (SAR), taking the number of external library users as an independent variable. Although the number of external library users could have no effect, there could be a correlation with error terms, such as similarities of regional characteristics with other (external) areas. To account for this possibility, we apply a maximum likelihood estimation of the spatial error model (SEM) as the third approach. Finally, we apply a maximum likelihood estimation of the generalised spatial autoregressive model with a correlated error term (SAC), which uses the number of external library users as an independent variable and considers the possibility of correlation with error terms, such as regional similarities.  where Y is an N × 1 vector consisting of one observation of the dependent variable for every unit in the sample (i = 1,…, N). X is an N × K matrix of exogenous explanatory variables. I N is an N × 1 vector of those associated with the constant term parameter α. W is an N × N matrix, which is usually referred to as a spatial weight matrix. β, ρ, and λ are parameters to be estimated, and ε is a random error term. ρ shows the endogenous interaction effects, where the decision of a spatial unit to behave depends on the decisions taken by other spatial units. Wu represents the interaction effects among the disturbance terms of different units. λ shows the correlated effects, where similar unobserved environmental characteristics result in similar behaviour.
When ρ = 0 in the SAC model, we obtain the SEM model. When λ = 0 in the SAC model, we obtain the SAR model, and when both ρ = 0 and λ = 0 in the SAC model, we obtain the OLS model. Thus, these models share a nested relationship, enabling us to select the most explanatory model by examining each with a likelihood-ratio test.
Furthermore, when calculating these models, we must assume the extent of the affected area (W in the previous formulas). When a spatial spillover effect exists and external users (i.e. residents of other areas) use public library services, distance is an important factor. Thus, W is defined as: where d i,j is the distance between the main building of local government offices of municipality i and municipality j . In other words, we consider that the shorter the distance from the main building of local government offices, the stronger the influence, and we apply the weighting accordingly. Additionally, we analysed five ranges of distances to confirm whether the estimation results would differ across distance settings. We used distance bands of 75 km, 100 km, 125, 150, and 200 km. 13 Public libraries are often located near the main building of local government offices. When municipalities are merged, not only does the area of the municipality become larger, but also the location of the main building of local government offices becomes central to the merged municipality. As a result, there are cases where the distance among the main building of local government offices of neighbouring municipalities increases. In the Kyushu region, giving an example, the distance between Saiki City in Oita Prefecture and Hinokage Town in Miyazaki Prefecture is about 60 km. Considering the distance between the municipal offices of these neighbouring municipalities may be far in some cases, we used 75 km, 100 km, 125 km, 150 km, and 200 km as the bands in this paper.
We used the number of registered users as the dependent variable (Y) for several reasons. First, Solé-Ollé (2006) indicated that crowding spillovers might occur in public facilities, such as libraries, where both local and neighbouring (external) residents use the service. Under these circumstances, when any municipality similarly reduces public library services, the municipality might decide to lower the level of its own library service and free ride on the library services of other areas. In this case, the number of local public library users would decrease, and the number of public library users from other areas would increase. Meanwhile, if there were no spatial spillover effect and no free-riding behaviour between municipalities, there would be no effect on the number of local public library users relative to the number of external public library users.
Second, the function of public libraries has changed since the Ministry of Education, Culture, Sports, Science and Technology announced a guideline for public libraries in 2000 (Desirable Standards for the Establishment and Operation of Public Libraries: Report). The guideline stipulated that public libraries should aim to provide multiple functions; public libraries should provide not only book-lending services, but also a lifetime-learning system and a network system constructed with neighbouring public libraries, among other components. In particular, even if users were not residents of a municipality, they should be able to access most neighbouring library services, if they were to register.
Moreover, many municipalities have built multipurpose public facilities, including public libraries, over the years. In terms of new public management, some public libraries cooperate with the private sector to provide many location services, such as theatres, galleries, museums, restaurants, and cafés.
Therefore, we believe that it is difficult to evaluate public library services based on the number of books borrowed or the number of books in stock, which have been used in previous studies. However, in Japan, users must register to use public libraries; thus, the number of registered users provides a useful indicator for evaluating the use of public library services. Moreover, we think that the number of registered users reflects an increase in supply rather than demand. First, one cannot use the library service without library facilities; second, without a large number of books in the library, the probability of finding the book people want to read will be low, and few people will use the library.
Two factors are available as independent variables: variables related to public libraries and variables relating to municipalities. For the public library variables, we have 'total floor area', 'number of employees', 'number of books in stock', 'audiovisual material cost', 'number of public libraries', 'consignment dummy', and 'number of employees × consignment dummy'. In addition, we use 'population' and 'area' as the municipality variables. Section 3 provides detailed definitions of the variables and their sources.
Do municipal mergers internalise spatial spillover effects?…

Data and variables
The main subjects of observation in this study are the effects for 2004 and 2005, when many municipal mergers took place. Here, we took 2001 as the year for the pre-merger analysis and 2008 as the year for the post-merger analysis. Nationally, large-scale mega-mergers began in Japan in 1999 in Sasayama City, and by March 2002, the total number of municipalities had decreased by 14. However, in the Kyushu region, which is the focus of the analysis in this study, there were no municipal mergers until April 2003. Thus, we considered that no effect arose from municipal mergers in 2001. 14 We chose 2008 as the year for the post-merger analysis owing to the possibility that the effects might not materialise immediately after a merger and the implementation of the Greater Independence Settlement Area Concept (GISAC) across Japan in 2009. In particular, the GISAC involved cooperation between core cities with populations of more than 50,000 and their surrounding municipalities. Analysing the effects in the year after this initiative was first implemented would risk the possibility of observing cooperative behaviour as free-riding behaviour; thus, we chose to analyse data from 2008, the year before GISAC was implemented.
Note that it is difficult to use panel data analysis in our spatial models because of the unbalanced panel data from municipal mergers. Normally, we should apply a panel data approach for policy evaluations, as well as in other papers. However, Elhorst (2010) pointed out that unbalanced panel data created in a specific event may become problematic, including their asymptotic properties if the reason for missing data are not random. In particular, Japanese municipal mergers had some propensities; municipalities that suffered from poor fiscal conditions or depopulation chose to merge after the introduction of a special municipal merger law in FY1999, because the merged municipalities were allowed to receive special treatment or financial support from the central government. Moreover, Hirota and Yunoue (2017) revealed that some merged municipalities increased their expenditure or local bond issues just before mergers. In other words, there is no econometric consistency when a spatial panel analysis with unbalanced panel data is applied. Therefore, in this study, we attempt to estimate the fiscal effects by comparing before and after mergers.
Data on Japanese public libraries were obtained from Nihon No Toshokan (Japan's Libraries) and the Ministry of Internal Affairs and Communications Kōkyō Shisetsu Jōkyō Chōsa [Survey of the State of Public Facilities]. We obtained data on the number of registered users, total floor area, number of books in stock, and number of public libraries from Nihon No Toshokan. We obtained the consignment fee data from Kōkyō Shisetsu Jōkyō Chōsa.

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First, as users must register to use a public library, we employed the total number of registered users as 'number of registered users'. We used 'total floor area' as a variable to indicate the size of the library facilities. We used the 'number of employees' as a variable to show the number of employees working at the libraries, calculated as the sum of specialist, emergency, and temporary staff. We used 'number of books in stock' as an indicator of public libraries' capital. We used 'audio-visual material cost' as a measure to expand the library's audio-visual materials. We used 'number of libraries' as a variable to show the number of public libraries within an area. A designated administrator system was established in 2003, which allowed public libraries to outsource or contract administrative management to private firms. 15 To account for the effect of this action, we used the variables 'consignment dummy' and 'number of employees × consignment dummy'. The 'consignment dummy' equals 1 for municipalities that have at least one temporary employee and pay consignment fees, and 0 otherwise. The 'number of employees × consignment dummy' variable was calculated as the 'number of employees' multiplied by the 'consignment dummy'.
Because we used library variables aggregated at the municipal level, we adopted a municipality's 'population' and 'area' to control for the municipality's environment changes. The populations and areas for each municipality were obtained from Chihō Zaisei Tōkei Nenpō (Annual Statistics on Local Public Finance). Tables 2 and 3 summarise the pre-merger statistics for 2001 and post-merger statistics for 2008, respectively.
Because some municipality has no libraries, we have zero data for library variables (i.e. registered users, total floor area, number of employees, number of books in stock, audio-visual material cost, and number of public libraries). In contrast, Kitakyushu City has 17 public libraries, thus showing the difference between municipalities regarding the number of libraries they have, the size of library facilities, the number of library employees, the number of books in stock, and audio-visual material cost. Figures 2 and 3 show the number of registered users by municipality on a map in FY2001 and FY2008. These figures show that many municipalities do not have libraries in FY2001, and municipalities without libraries decreased in FY2008. In particular, while approximately 60% of municipalities in the Kyushu region did not have a public library in 2001, this had decreased to approximately 30% by 2008. Moreover, the total number of public libraries in the Kyushu region increased by approximately 80 during this period.

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Do municipal mergers internalise spatial spillover effects?… Table 4 reports the results of the analysis using the 2001 data with a distance band of 100 km 16 . 17 We selected the most explanatory model by examining each with a likelihood-ratio test. When comparing with SAC and SEM using the likelihoodratio test, the hypothesis that ρ = 0 is rejected. Similarly, by comparing with SAC and SAR using the likelihood-ratio test, the hypothesis that λ = 0 is rejected. Finally, by comparing with SAC and OLS using the likelihood-ratio test, the hypothesis that both ρ = 0 and λ = 0 is rejected. The results of the model selection show that the SAC model is the most appropriate.

Spatial regression before municipal mergers
The estimation results for the SAC model in Table 4 show statistically significant positive values for several variables related to library facilities: 'number of books in stock', 'audio-visual material cost', and 'number of employees × consignment dummy'. Meanwhile, the 'total floor area', 'number of employees', and 'consignment dummy' have statistically insignificant and the 'number of public libraries' have statistically significant negative results. This means that not only the expansion of facilities, such as the number of libraries and the total floor space, but also the quality of the contents of the libraries (number of books, audio-visual materials, etc.) is more important for increasing the number of users.
The municipal population has statistically significant positive results, showing a higher number of registered users for a larger population. In addition, we note statistically insignificant results for municipality areas.
The endogenous interaction effect (ρ) of the number of external public library users shows statistically significant negative results, while the correlated effect (λ) from external areas shows statistically significant positive results. The endogenous interaction effects indicate the possibility of spatial spillover effects in public library services; that is, if a local area improves its library services, then the number of registered users increases due to an influx of external users. However, at the same time in another area, this leads to a reduction in the number of registered users because the number of external users drops. In other words, these results suggest free riding in public library services in external areas. The correlated effects show that significantly positive results for the correlated effect (λ) could be because education and income levels might be similar within an area and its neighbouring areas, and thus, these regions might share similar book-reading and library-using habits. 16 Considering a possible influence on the spatial lag value of the explanatory variables (i.e., WX), we estimated even the Spatial Durbin Model (SDM) in 2001 and 2008. We checked the hypothesis that coefficients on the spatial lag value of the explanatory variables equal to zero (i.e., WX = 0) by using the Wald test and failed to reject this hypothesis. Therefore, we concluded that SAR is the more explanatory model when compared with SDM in both periods. 17 The results are similar for other distance bands (75 km, 125 km,150 km and 200 km); kindly check Appendix 2 for other results. Table 5 reports the results of the analysis using the 2008 data with a distance band of 100 km. 18 As in Sect. 4.1, we select the most explanatory model by examining each with a likelihood-ratio test. When comparing with SAC and SEM using the likelihood-ratio test, the hypothesis that ρ = 0 is rejected. Similarly, by comparing with SAC and SAR using the likelihood-ratio test, the hypothesis that λ = 0 is rejected. Finally, by comparing with SAC and OLS using the likelihood-ratio test, the hypothesis that both ρ = 0 and λ = 0 is rejected. The model selection indicates that the SAC model is the best, as with the 2001 data.  Do municipal mergers internalise spatial spillover effects?… Do municipal mergers internalise spatial spillover effects?…

Spatial regression after municipal mergers
The estimation results for the SAC model in Table 5 show statistically significant positive values for several variables related to library facilities, that is, the number of books in the stock and the Consignment dummy. Meanwhile, the 'total floor area', 'number of employees' and 'audio-visual material cost' have statistically insignificant and the 'number of public libraries' have statistically significant negative results. This means that not only the expansion of facilities, such as the number of libraries and the total floor space, but also the quality of the contents of the libraries (number of books, etc.) is more important for increasing the number of users. Furthermore, both the endogenous interaction effect (ρ) of the external registrants and the correlated effect from external areas (λ) have the same signs as in the 2001 estimation results.

Discussion
Sections 4.1 and 4.2 show the results of the analysis using the pre-merger period (2001) and the post-merger period (2008). Both the endogenous interaction effect   Table 6). Furthermore, because the λ value is in the range of 0.942 to 0.776 for 2001 and 0.807 to 0.472 for 2008, it shows a small decrease (see Table 6), but not to the extent of the endogenous interaction effect (ρ). Accordingly, the fact that ρ reduced in absolute terms suggests that the scale of post-merger free riding is less than before the municipal mergers. 19 This means that municipal mergers could partially internalise the spatial spillover effect. Furthermore, the consignment dummy is statistically insignificant for 2001; on the other hand, a statistically significant positive value for 2008. It may be possible that the effects of consignment were higher in 2008 due to the introduction of a designated administrator system, making it easier for public facilities to begin private consignment, resulting in private firms handling more consignment-related work.

Difference in differences
In this section, we explore whether the merging municipalities experience improved public good provision for library services when compared to other municipalities. We clarify this question using a DID analysis with data over two periods from FY2001 (before mergers) and FY2008 (after mergers). However, due to the change in the form of municipalities through municipal mergers, the number of municipalities differs between the two periods, making it difficult to use actual values for DID analysis. Therefore, to adjust the balance between the different datasets in these two periods, we recalculate the pre-merger values of the municipalities based on their post-merger forms. Specifically, we created 2001 municipal data according to the composition of the municipalities in 2008. In other words, in the municipalities that merged by 2008, the 2001 data set was created by summing the data of municipalities that were in the same municipality in 2008. Our estimation model is where Y is an N × 1 vector consisting of one observation of the dependent variable for every unit in the sample (i = 1,…, N). X is an N × K matrix of exogenous explanatory variables. I N is an N × 1 vector of those associated with the constant term parameter α. Here, the individual effect is , and t is the year effect. We use dependent variables (Y) and explanatory variables (X), which are the same as in Sect. 4. In other words, we use the number of registered users as a dependent variable (Y) and 'total floor area', 'number of employees', 'number of books in stock', 'audio-visual material cost', 'number of public libraries', 'consignment dummy', and 'number of employees × consignment dummy',' population' and 'area' as explanatory variables (X) in this model. In particular, we use 'Treatment' as an explanatory variable in this section, which is defined as a dummy variable, with 1 for merging municipalities' experience (treatment group) and 0 for all other municipalities (control group). By controlling for individual effects (µ) and time effects (t) in the estimation, we can evaluate 'Treatment' as a DID estimator. In other words, 'Treatment' indicates the effect that municipal mergers have on the level of library services. Table 7 reports the results of the DID analysis. 20 The variable of 'Treatment' has statistically significant positive results, showing an increasing number of registered users by municipal merger. Our estimation results may show municipal mergers increase the supply of library services, which were previously undersupplied.

Robustness check
According to the Kyushu area library data used in this study, about 60% of municipalities had no libraries in 2001, and 30% of municipalities had no libraries in 2008. 20 To check the parallel trend assumption, we conducted a pseudo-estimation using data from 2000 and 2001. See Appendix 1 for the results of this pseudo estimation.
It is conceivable that many municipalities did not have libraries, which may have biased the estimation. The dependent variable in our model is censored at zero because there are many municipalities where no public library exists. When municipalities maximise their regional benefits of library services, there are two types of municipalities. One type of them choose to supply a positive amount of library services as their optimal levels. The other type of them choose to supply zero service. Under such a situation, we should be concerned about the bias in our estimation due to the censoring problem because the dependent variable takes non-negative values. In order to consider the censoring problem, we apply Tobit model to ensure robustness. 21 In our estimation, the share of municipalities with no libraries is comparable to a similar share to other papers. Therefore, we use the spatial Tobit model 22 to check whether our analysis is robust. Table 8 Table 8). Our estimation results are robust because the trend is similar to that of Sect. 4 for the value of ρ estimated using the spatial Tobit model.

Conclusion
Most studies on municipal mergers have focused on cost-reduction effects and freeriding behaviour between merged municipalities. Other researchers have investigated spatial spillover effects in the context of free-riding behaviour among local governments. Few studies have focused on the relationship between municipal mergers and spillovers between municipalities. However, even these studies did not clarify whether there was a change in the free-riding behaviour between municipalities after municipal mergers. The contribution of this study is its evaluation of the effect of municipal mergers from the internalisation of externalities using data before and after mergers.
Many municipal mergers took place in Japan from 1999, and particularly in 2004 and 2005. Changes in jurisdictional areas accompanied municipal mergers. This study examines potential free-riding behaviour between neighbouring municipalities in public library services managed and operated mainly by municipalities in the Kyushu region of Japan using data from 2001, before the mergers, and from 2008, after the mergers. By comparing the changes in municipality behaviour during these two periods, this study investigates the effects of municipal mergers on spatial spillover effects. 21 To address the problem, we apply the Tobit model (e.g., Greene 2012, Wooldridge 2018. For example, Greene (2012) applies Tobit analysis to the estimation of the labor force participation rate. The share of non-participation is approximately 60%. Furthermore, Iimi et al. (2015) apply a Spatial Tobit model to address a similar problem. The share of the zero value in the dependent variable is approximately 66% and larger than our paper. Thus, in our estimation, the share of municipalities with no libraries is comparable to a similar share in other papers. See details, Greene (2012) or Wooldridge (2018), etc. 22 For estimation we rely on a STATA command sptobitsac developed by Shehata and Mickaiel (2013).
Free-riding behaviour can emerge between municipalities when the spatial spillover effect occurs. Meanwhile, if there are changes in jurisdictional areas due to municipal mergers, spatial spillover effects could be internalised and free-riding behaviour could disappear or decrease. This study contributes to the literature by highlighting this point. In this study, we have used library services as an example of a local public good with spatial spillover, but we expect it is possible to examine other similar local public goods (e.g. museums and public hospitals) in the same way.
In Japan, several new public libraries were built in 2004 and 2005, when many municipal mergers took place. This could be attributed to municipal mergers internalising (or lessening) spatial spillover effects and an increase in the supply of library services, which were possibly previously undersupplied.
The first contribution of this study is to show that municipal mergers could partially internalise the spatial spillover effect. The results of the analysis showed free-riding behaviour between neighbouring municipalities in the pre-merger period (2001). Similarly, free-riding behaviour between neighbouring municipalities existed in the post-merger period (2008), but on a smaller scale. This suggests that municipal mergers could partially internalise the spatial spillover effect and partially lessen free-riding behaviour.
The second contribution of this study is demonstrating that municipal mergers increased the supply of library services. As a result, due to the merger of municipalities, the undersupply of local public goods with spatial spillover effects may be decreased, which could help achieve a socially optimal supply. This study's third contribution is showing the positive effect of introducing the designated administrator system on public library service levels. The results further suggest that while private consignments resulted in a small increase in library service use in 2001, the introduction of the designated administrator system in 2003 facilitated the implementation of private consignments, potentially resulting in an increase in the number of users.

Appendix 1: Placebo Test
To check the parallel trend assumption, we conducted a placebo test using data from 2000 and 2001. Since there were no municipal mergers in the Kyushu region in 2000 or 2001, it is unlikely that there would be any difference in the number of registered users between the two groups, comparing municipalities that had merged by 2008 versus those that had not, using data from these two periods, if this analysis holds the parallel trend assumption. We used the same framework as described in Sect. 5.1. In this section, we define 'Treatment' as a dummy variable that is set to 1 for the 2001 data of municipalities that merged by 2008 (treated group), and 0 for other municipalities (control group). If 'Treatment' is statically insignificant in this section's analysis, we can evaluate that holding the parallel trend assumption in our DID analysis. Table 9 reports the results of the DID analysis for the placebo test using 2000 and 2001. 'Treatment' is statically insignificant in this analysis. Since this means there is no difference in the pre-merge period between municipalities that merged by 2008 (treated group) and non-merged areas (control group), we conclude holding the parallel trend assumption in our DID analysis in Sect. 5.1. Appendix 2: Appendix Table   Tables 10 and 11