Regional governments in the rural space: the effectiveness of dual-tier regional councils

ABSTRACT The fiscal decentralization literature explores the efficient structure of local governments. However, little consideration has been given to the efficient structure of rural local governments. In this study we show that a dual-tier local government structure in rural areas is more efficient than the prevalent unitary structure. Specifically, we demonstrate that a regional council that incorporates many small villages is more efficient than when each village operates as an independent local government. We present a theoretical model and provide a simulation of the model using Israeli municipal data, which combines both unitary and dual-tier structures. The simulation uses the unitary small towns as the training set and the villages within regional councils as the test set. It thus calculates the cost structure of villages within regional councils based on the data of unitary small towns. The results indicate that most villages that are part of a regional council operate more efficiently than their simulated independent unitary counterparts. Based on the findings, we suggest an alternative lower level local government structure for rural communities that adds a mezzanine dual-tier structure.


INTRODUCTION
Federal and unitary countries are usually divided into several government tiers, including central (country, state), regional (region, county, department, district) and local (municipalities, cities, towns, villages) levels. 1 Fiscal decentralization theory states that public services should be decentralized to the lowest tier mainly due to variance in tastes and information availability (Oates, 1972;Olson, 1969). On the one hand, centralization internalizes spillovers, takes advantage of economies of scale and promotes fairness for all citizens. On the other hand, decentralization allows for the tailored provision of public goods and services. Most studies on fiscal decentralization focus on the division of responsibilities and budgets between the central or federal government and local governments. They tend to debate the scope and magnitude of the delegation of responsibilities and fiscal power (Besley & Coate, 2003;Brennan & Buchanan, 1980;Tiebout, 1961). Some studies even caution about the shortcomings of decentralization, indicating that it might not be the optimal solution in every case (Bardhan, 2002;Prud'homme, 1995;Tan, 2019).
Nevertheless, this voluminous literature overlooks decentralization in the rural sector, which may make it difficult for small communities to benefit from economies of scale. We claim that decentralization to the lowest subnational tier may not be the optimal structure when it comes to the rural sector. Indeed, decentralization to a regional mezzanine level may be a better approach. The rationale is that the mezzanine level benefits from economies of scale and internalizes spillovers that occur in small villages. Our claims build on Bardhan (2002) who focuses on the devolution of political decision-making power in developing countries, and Allain-Dupré et al. (2020) who focus on asymmetric decentralization challenges in urban regions.
This study analyses and compares single and dual-tier government structures in rural areas. We explore this issue using the example of Israel. The country has a unique model of lower tier, asymmetric decentralization in which cities and towns operate as unitary municipalities, whereas the rural sector uses regional councils. We show that adding a mezzanine tier in rural areas is more cost efficient than a single-tier local government structure. We also identify the conditions under which that cost efficiency holds true. Thus, the main contribution of this article is in showing that the dual-tier government structure in rural areas performs better than a unitary system, and identifying the boundary conditions of that efficiency.
The rest of the paper is organized as follows. Section 2 reviews the literature and the theoretical background of local government structures. Section 3 describes the institutional background of the asymmetric local government structure in Israel. Section 4 develops the economic model and explores the efficiency frontier of the dualtier regional council structure. Section 5 presents the empirical simulation testing our model and the resulting efficiency ratios. Section 6 compares the level of services. Section 7 discusses the results and their policy implications, and concludes.

LITERATURE REVIEW
2.1. Local and regional government structure and fiscal federalism theory Most central governments throughout the world decentralize budgets and responsibilities through one or more tiers of subnational governments. Although most of the population, especially in developed countries, lives in urban cities, the number of rural villages outnumbers the number of cities and towns, and also covers a wider area (Pateman, 2011). The control and supervision of so many villages raise the question of the most efficient subnational government structure for these villages that do not benefit from economies of scale (Bel & Warner, 2015).
Several studies have explored various options in this regard. Tiebout (1956) shows how competition between municipalities at the horizontal level results in a better provision of public services under certain assumptions. In his fiscal federalism theory Oates (1972Oates ( , 1999Oates ( , 2005 looks at the division of a country into multiple tiers and subnational governments. According to this theory, decentralization enables communities to express different preferences for public services. Given that lower levels of government are closer to the people they serve, they have more information about what the public wants and needs. Therefore, the central government should control the distribution of wealth and take steps to stabilize the economy, and the lower government tiers should adjust the allocation of resources (Musgrave, 1959). The Tiebout model is based on the assumption that citizens are fully mobile, have full knowledge, and will relocate to communities that best satisfy their requirements. Later research relaxed this assumption, stating that residents are unlikely to move (Boadway & Tremblay, 2012). More recent studies warn of the pitfalls of 'pure' decentralization (Prud'homme, 1995) or that decentralization may not be the optimal solution in every case (Bardhan, 2002;Tan, 2019). The classic model, however, does not distinguish between variations at the horizontal level, meaning between the local governments of cities and small towns or villages, or between counties and districts as regional entities and sparsely populated rural regions.
Countries around the world are witnessing a 'rise to the meso' (Keating, 2014, p. 104), or city-county consolidation (Deng et al., 2021;Martin & Schiff, 2011). This trend maintains that cities and regions are on the rise, while intermediate tiers such as provinces are under threat (Torre & Bourdin, 2022). While cities can cope with this trend, rural villages are becoming more distant from the regional layer. Therefore, they need a tier of government that is closer to them (Torre & Bourdin, 2022). Deng et al. (2021) report that the expansion of cities at the expense of rural areas has resulted in a significant loss of economic activities in nearby rural areas, but has had an insignificant effect at the prefecture level, indicating a backwash effect. In order for developed countries to stem the move from rural areas to cities, the level of services in rural areas needs to be at an acceptable level ( Barcus, 2004;Sørensen, 2014).

Asymmetric decentralization
Central governments usually prefer to see symmetric structures in which each subnational government has similar responsibilities and powers. However, as municipalities vary considerably in their characteristics such as size and geography, asymmetric structures should be considered. Asymmetric decentralization enables more options and flexibility in the subnational local governments' structure. Asymmetric federalism occurs when 'governments at the same level of geographical responsibility have different regulatory and fiscal powers' (Congleton, 2015, p. 126). Asymmetric federalism may be grouped into several categories, including political, structural, fiscal, and territorial (Allain-Dupré et al., 2020;Tan, 2019;Tan & Avshalom-Uster, 2021). Allain-Dupré et al. (2020) note that current trends apply mostly in urban areas. They indicate the benefits and challenges of asymmetric decentralization. The benefits include the ability to resolve capacity issues by aggregating services at higher levels of government in some locations, and decentralizing those services in others. Examples include enabling the step-wise implementation of policy, and accommodating heterogeneous preferences among local governments using 'menu federalism.' The challenges include the lack of transparency and clarity for residents and coordination costs. Similarly, Grazzini et al. (2020) research the asymmetric decentralization requests of three Italian regions for more power. They investigate whether asymmetric decentralization in which the wealthiest regions ask for more autonomy is adequate.
Structural asymmetry occurs when different local governments in similar vertical positions have different structures. We distinguish between asymmetry at the higher levels versus asymmetry at the lower levels. On the one hand, we observe city-county consolidations at the higher levels (Martin & Schiff, 2011), where very large cities are given the powers and responsibilities of both a region and a municipality. On the other hand, asymmetry at the lower levels occurs when small villages at the lowest tier form a mezzanine regional tier through inter-municipal cooperation that offers economies of scale as the major benefit and internalizes spillovers.
The literature dealing with the delegation of responsibilities for the regional level has generally looked at the subnational level (e.g., Foreman-Peck & Zhou, 2020). The research on the lower regional tiers is, however, limited. Hämäläinen and Moisio (2015) compare one and two tiers of a local government experiment in Finland, where around 60% of public services, including healthcare, secondary education and social services, were taken away from the municipalities and given to a new intermediate tier of government. As a result, the cost of providing these services declined by about 3.5%. However, other factors contributed to the decline, casting doubts on the magnitude of the cost savings. Asking 'is local always better? ' Steiner et al. (2018) discuss local tier services and collaboration between subnational tiers. They conclude that in some cases, local is better, as local authorities are closer to their citizens. However, local is not always better, as in the case of dealing with complex challenges and spillovers. To promote economies of scale, central governments encourage or enforce supra-municipal cooperation. For example, the French government has suggested that municipalities should cooperate. However, Frère et al. (2014) report that in the wake of this suggestion, the level of municipal spending did not change. In contrast, the Italian government decreed that towns whose population is smaller than 5000 residents should cooperate with other towns (Bolgherini et al., 2018). In the wake of this mandate Ferraresi et al. (2018) note that municipal cooperation reduces per resident expenses by around 5% without reducing the level of services. However, Luca and Modrego (2021) indicate that the change had no significant effect. Finally, in their meta-analysis of inter-municipal cooperation studies Bel and Sebő (2021) provide support for the contention that the cooperation of small towns and the delegation of services to a higher tier of government offer cost advantages. Most of their data, however, relate to solid waste management.
Studies of cities and towns indicate that they exhibit economies of scale, with at least a 'U'-shaped relationship between per resident expenses and the number of residents (Andrews & Boyne, 2009;Bikker & van der Linde, 2016;Hortas-Rico & Rios, 2020). In contrast, small villages cannot leverage the benefits of economies of scale (Boadway & Shah, 2007;Slack, 2004), which explains why per capita expenses in rural areas are higher than in urban areas, despite the quality of services being poorer (Warner, 2006). Therefore, the village council should provide public goods that have local merit, while the higher tier of government should provide public goods that benefit from economies of scale (Dur & Staal, 2008;Oates, 1972;Warner, 2006). Hefetz et al. (2012) show that per capita expenses in rural areas are similar to those in the metro core, while similar expenses are lower in suburbs. Given that the quality of service in rural areas is poorer than in suburbs and metro areas, we conclude that the cost of services in rural areas is higher.
Most studies discuss asymmetry at the top tiers. They assume that the benefits of decentralizing responsibilities between states, regions, and cities holds for smaller towns as well (Carr & Feiock, 2016;Martin & Schiff, 2011). Yet, there is a gap in the literature between the more researched asymmetry at the top tiers and the limited research in less populated rural regions. Furthermore, these studies provide only general guidelines on the division of responsibilities in a decentralized structure. They do not address the question of how to split responsibilities in an asymmetric structure that will improve the efficiency of providing public goods.

INSTITUTIONAL BACKGROUND
As a unitary, highly centralized state, the local government structure in Israel is asymmetric at the lower tiers, which includes cities and towns in a unitary structure, and regional councils in a dual-tier structure. A regional council acts as the local government for a large number of small rural villages. It is composed of two tiers: villages in the lower tier, administered by a village council, and regional councils in the second (mezzanine) tier, which, through pooled resources, provide public services.
The status of a city is awarded to a town with a population of over 20,000. A village within a regional council may be awarded the status of town if it has more than 10,000 residents. There are, however, many exceptions through the discretion of the Minister of the Interior. In 2020, there were 77 cities, 124 towns, two industrial councils and 1013 villages clustered within 54 regional councils in Israel. The number of villages in a regional council ranged from three to 64. The average population size of a local authority in Israel was 36,147, larger than in most European countries, which is due to the structure of Israel's regional councils. However, when all small villages are counted separately, the average size of a local government drops considerably to 7593 people. Therefore, the Israeli central government regulates only 257 local governments instead of 1214 (Razin, 2004 with figures updated to 2020). Internal migration within Israel is limited. According to data from the last five years from the Israel Central Bureau of Statistics (ICBS), the average yearly relocation between local governments is 0.64%.
The Israeli Local Municipalities Act (Regional Councils)-1958 defines the powers of regional councils. These powers are equivalent to those of towns and cities, with the exception that regional councils may delegate some of their powers to village councils (Hananel & Fishman, 2017;Rasis & Applebaum, 2009). The regional councils' jurisdiction covers 85% of the land of Israel but only 10% of the population lives there. 2 The political structure of regional councils differs from that of single-tier authorities, mainly in the election of council members. The mayor is elected directly through two-round, majoritarian elections. In contrast, council members are elected by political parties in proportional elections. However, the electoral base of council members varies. In regional councils, each village forms a constituency, whereas in cities, the entire city is one constituency. The result is that in regional councils council members represent their village in what is called 'geographically dispersed interests' (Alesina & Perotti, 1995). In contrast, in single-tier authorities, each council member is a member of a party and is expected to adhere to the party's decisions and position as part of the ruling majority or the opposition. They do not represent any geographical interests.
Several researchers have examined the rationale behind the dual-tier structure in Israel, the political background for creating their large jurisdictional areas, and the changes in the rural space over time (Applebaum & Newman, 1997;Ben-Bassat & Dahan, 2009;Delgo, 2006;Feinerman et al., 2011;Hananel & Fishman, 2017;Razin, 2012;Sofer & Applebaum, 2006. However, they have not investigated whether or not the dual-tier structure is efficient. Delgo (2006) and Feinerman et al. (2011) report that the cost of providing local and regional public goods is increasing and that the average per resident cost function is convex ('U'-shaped). They also discuss the utility of farmer and non-farmer residents in rural areas, based on the assumption that all the land area is available for agricultural production, and is equally divided among the farmers. The non-farmer residents use the same local and regional public goods, obtain the same utility from using them, and share their costs. We build on Feinerman et al.'s (2011) model to compare the efficiency frontier of the dual-tier structure with the single-tier unitary structure.
Governments are looking for a better structure for providing public services at the local level. The tools currently in their toolbox are mergers between municipalities and inter-municipal cooperation. There have been a few cases where an independent town merged into a regional council, becoming another village, which resulted in cost savings (Reingewertz, 2012;Zeedan, 2017). These findings indicate the efficiency of the dual-tier structure. However, these studies investigated the marginal benefits of adding a village to an existing regional council. Regional councils are charged with the development of their entire jurisdiction. They promote regional development, which should be done in coordination with neighbouring towns (Ward & Brown, 2009).
The Israeli asymmetric structure allows us to model the small towns' financial structure as the training set, which then serves as the basis for simulating the villages' financial performance as if they were an independent unitary local government.

THEORETICAL MODEL
Our model is based on that of Feinerman et al. (2011) with regard to the optimal provision of local and regional public goods in two-tier rural areas. Given that the share of farmers out of all residents in rural areas is declining (Applebaum Sofer & Applebaum, 2006), we modified the utility function Feinerman et al. (2011) developed to treat residents of rural villages that are part of a regional council, both farmers and non-farmers, equally.
We developed the model in two stages. In the first stage we looked at maximizing the utility of the residents. Using the results of the first stage, we then compared two subnational government structures: unitary and dual-tier.
Doing so allowed us to identify the conditions under which one structure is more economically efficient than the other.

The first stage of the model's development
The utility of residents in the dual-tier subnational government structure in rural areas is composed of their utility from consuming private goods, as expressed in their income before local taxes, and public goods, both regional and local, minus the cost of providing these public goods. Naturally, the benefits of consuming private goods increase with people's available income, and the benefits of consuming public goods increase with their availability. The cost of providing regional public goods per resident is convex, indicating that there is an optimal point at which the cost per resident drops to a minimum (Buljan et al., 2021;Feinerman et al., 2011;Hochman et al., 1995;Southwick, 2012).
We investigated two structures of subnational government in the rural space: a unitary system, where each village has responsibilities and standing similar to those of a nearby town, and a dual-tier structure with a mezzanine tier that provides regional public goods to the villages in the lower tier. A regional council incorporates V villages dispersed over a relatively large geographical area, with a mean distance D between its villages. The division of responsibility for providing local and regional public goods is at the discretion of the regional council. The local village provides local communal public services, and the regional council provides public services that benefit from economies of scale or that are too complex for the local village to provide (Delgo, 2006;Hananel & Fishman, 2017).
Our model explores the conditions under which the utility and benefits for residents are maximized. It demonstrates that the per resident cost of providing regional public goods is a second-order quadratic function of the number of residents and that the marginal benefits equal the marginal cost (Samuelson's condition). Given that regional councils should benefit from economies of scale, we assume that the cost of providing regional public goods increases with the number of villages, but is proportionally less than if the village provided these services itself. The model shows that the optimal condition for maximizing residents' benefits is inversely proportional to the number of villages times the number of residents (see Appendix A in the supplemental data online for the formal presentation; and Figure 2 for a graphical presentation of the optimal frontier).

The second stage of the model's development
Using the results of the first stage, we developed a model of the per resident cost of providing regional public goods under optimal conditions. We considered two alternative formats of subnational governments in rural areas: unitary and dual-tier. In the unitary subnational government structure, each village is an independent local government. In such a case, each village provides its residents with local Regional governments in the rural space: the effectiveness of dual-tier regional councils and regional public goods. The model indicates the cost of providing public goods per resident. In the dual-tier structure, we assumed that all villages that are part of the dualtier regional entity have the same number of residents and the same socio-economic standing, as reflected by the socio-economic index, and are identical in all other characteristics.
We then calculated the efficiency ratio (η)the per resident cost of providing comparable public goods in the unitary system divided by the per resident cost of providing public goods in the dual-tier system, under the assumption that the public goods are comparable. When η > 1, the dual-tier structure is more efficient than the unitary structure. However, if η < 1, the regional council structure is less efficient.
The first stage showed that the per resident cost of providing public goods is a quadratic function of the number of residents, when holding the socio-economic status, geographical location, and demographic characteristics constant. Therefore, there are two options when comparing a unitary village to the dual-tier system: no intersection of the cost functions, and an intersection of the two cost functions. Centralizing services that benefit from economies of scale at the mezzanine tier should result in lower per resident expenses than a unitary structure with a small number of residents. On the other hand, the per resident cost of providing services in rural villages is higher than in towns (Hefetz et al., 2012;Slack, 2004;Warner, 2006), indicating that when the population grows beyond a certain point, the benefits of economies of scale by centralizing rural villages decline. Therefore, we expect to see intersecting behaviour ( Figure 1).
When the cost functions intersect, there is an inflection point, denoted by N* in Figure 1, where the unitary structure becomes more cost-efficient than the dual-tier system. We hypothesized that the dual-tier structure is more efficient. Therefore, under certain conditions, especially with a small number of residents (n < N*), we expected η > 1. As the number of residents grows, the economies of scale of the dual-tier diminish, and the unitary structure will be more cost-efficient. 3 At the inflection point, N*, the per resident cost of providing public services in the unitary and dual-tier structures are equal. Equating the two cost functions yields the efficiency frontier of the dual-tier structure and the conditions under which the efficiency diminishes. Formal mathematical modelling, presented in Appendix A in the supplemental data online, shows that the efficiency frontier 4 when η ¼ 1, is when the multiplication of the number of villages in the dual-tier regional council by the number of residents in each village is below a certain threshold value. Small villages suffer because they cannot take advantage of economies of scale. However, larger villages come close to benefitting from economies of scale. Therefore, the benefits that the dual-tier regional council structure provides are significant when they group together many smaller villages, but diminish when there are just a few large villages.
In a dual-tier structure, the larger the village or the more large villages there are, the greater the managerial burden, emphasizing the need for local government. On the other hand, the more small villages in a single prefecture, the greater the managerial burden. At some point, the one dual-tier regional council reaches its limitations and cannot provide adequate services. At that point, the prefecture should be split into two regional councils. The theoretical conclusion that the multiplication of the number of villages by the number of village residents yields the efficiency frontier summarizes both cases. The results indicate the locus at which the efficiency of the dual-tier structure diminishes.

METHODS
A more comprehensive approach to comparing the two local government structures would be to model the local government of rural villages, each as an independent, single-tier entity that provides local public services directly. The Israeli system is a good testing ground for comparing single and dual-tier structures, as there is an overlap of similar size and scale of villages and towns. The asymmetric local government structure in Israel allowed us to calculate the costs that both unitary small villages and regional councils incur when providing public services. Using these results, we calculated the dual-tier regional councils' efficiency frontier and identified the conditions under which the dual-tier structure is more efficient than the unitary one.
We then created a simulation in which we used the empirical expense model of small towns as a training set to simulate each village in all regional councils as if it were an independent unitary town. Then, we summed all the simulated expenses to the regional level. We compared the simulated regional expenses to the regional council's actual expenses, calculating the efficiency ratio (η) for each regional council each year.

Data
The data for the analysis came from official publications of the ICBS and the Ministry of the Interior. We used these  Ron Shani et al.
databases to compile financial and demographic data for all local municipalities between 2005 and 2019, and demographic data for all villages that were part of a regional council between 2013 and 2019. 5 We adjusted all the financial data to be in real 2019 new Israeli shekels (NIS, each worth about US$0.28). Comparing public services in municipalities raises questions about the level and quality of these services. To determine whether they could be compared, we used data from the 2019 ICBS Social Survey. 6 Table 1 presents the descriptive statistics of the average village in a regional council. As the table indicates, the characteristics of small towns and regional councils are similar. The major difference is that regional councils govern in a dual-tier structure that includes many villages that are spread over a large geographical area. In contrast, small towns are unitary entities, situated in a small geographical area. The similarity in the control characteristics allowed us to compare these two government structures. The location of a village determines its ability to set its property tax rates. The closer the village to the central zone (the Tel Aviv district), the higher the rates. Likewise, the higher the socio-economic status of a village's residents, the higher the residential tax rates. The ICBS periodically publishes socio-economic and periphery indices. The socio-economic index is a weighted average of 14 variables, including income, education, demographics, standard of living, and employment. The periphery index is a weighted average of two variables: potential accessibility and proximity to the boundary of the Tel Aviv district. Following normalization and clustering, both indices range from 1 (most peripheral or lowest socio-economic status) to 10 (most central or highest socioeconomic status). We used the socio-economic and periphery indices as control variables to capture their influence on the per resident expenses.

Efficiency frontier: an empirical analysis
Using the real per capita total current expenses between 2005 and 2019, we estimated the expenses of unitary small towns with the theoretical model in specification (1): The specification for regional councils is similar to (1) with the addition of the number of villages: To avoid bias, the analysis excluded Arab towns, as most of the residents in the regional councils' villages belonged to the Jewish society. The analysis also excluded regional councils with a majority of Arab residents, mainly due to data limitations. Table 2 shows the results of the analysis.
As expected, both small towns and regional councils exhibit a convex dependency of the per resident expenses versus population: β 1 < 0 and β 2 > 0. The coefficient of the number of villages is 0 < β 3 < 1, implying that adding villages increases the per resident cost, as the theoretical model expected. However, it is < 1, indicating economies of scale.
The theoretical model indicates that the efficiency frontier, which is the locus that differentiates between the conditions where the dual-tier structure is more efficient and where the unitary structure is more efficient, occurs when the multiplication of the number of villages by the population in each village is below a certain threshold, assuming that all villages are similar. The empirical analysis, solving the conditions where specification (1) is equal to (2), indicates that the efficiency frontier occurs when the result of that multiplication is about 60,570. 7 As Figure 2 illustrates, regional councils that are below the line are more efficient than the alternative unitary structure. The opposite is true when they are above the line.
We calculated the confidence interval using a Monte Carlo simulation, where each of the control variables and the regression coefficients from Table 2 varied randomly according to its mean and standard deviation (control variables) or standard error (regression coefficients) using a truncated normal distribution. The theoretical model indicates that the sensitivity of the efficiency frontier, which is reflected in the confidence interval, is inversely proportional to the number of villages. Figure 2 illustrates these results.
The theoretical model and empirical analysis suggest that the dual-tier structure provides cost benefits for small villages. However, these benefits decline when the villages are larger or when the number of villages grows, such that the multiplication, which is the total number of residents, exceeds 60,570. This result is somewhat different from Delgo (2006) and Feinerman et al. (2011) who, using data from 1995 to 1999, indicate that the optimal size of a regional council is about 20,000. At that time, the average number of residents in a regional council was 9645. Their studies concentrate on regional councils only, minimizing per resident expenses. In contrast, our study compares dual-tier to unitary government structures, showing that the efficiency frontier is bounded by 60,570 total residents.

Empirical analysis: a simulation
What would be the per resident cost of providing public services if all the villages in a regional council were each a unitary town? To explore this question, we developed a simulation in which we used the data of unitary small towns as a training set to construct the per resident expense model shown in specification (1). We then used the model with the data from each village that was part of a regional council prefecture and totalled all the expenses for all villages in that region. We defined the efficiency ratio (η) as the ratio of the simulated expenses over the actual regional council expenses for each regional council between 2013 and 2019.

Expense model of small towns and regional councils
The Ministry of the Interior requires all local authorities to report their audited financial statements in the same format. These statements are comprised of six major categories: revenues, general and administration expenses, local public services, public services that the local authorities provide on behalf of the state such as education and social services, plants, and incidental activities. Appendix B in the supplemental data online provides details for each category. Using the audited financial statements, we calculated the training model for each major category's total and per capita expenses for small towns with a population of up to 15,000. Using this method, we obtained the coefficients of specification (1) for every year between 2013 and 2019. 8 Table 3 presents the regression results of the natural log of the per capita expenses for the total and the major categories between 2013 and 2019 (pooled with year fixed effects). Similar cross-section tables for each year are available from the authors on request.

Ex-ante prediction: accuracy of prediction
We used the audited data from the small towns as the training set to develop a model for small towns' per capita current expenses (ln). We then used the model to predict the expenses of small villages that were in a dual-tier regional council structure as if they were in a unitary structure. To verify the accuracy of the prediction and calculate its error, we reduced the training set so it included only Note: The dependency ratio is the number of dependent residents (ages 0-19 and 65+) relative to the total working-age residents (ages 20-64) × 1000. The ratio of students is the number of students (kindergarten to high school) divided by the total population. Small towns include those with a population of fewer than 15,000 residents. We dropped the regional councils that were predominately Arab because their formal information, which indicates high per resident expenses, is not accurate. We also dropped one regional Jewish council, Tamar, due to its very high income and population of only about 1500 residents, making it an outlier. A t-test of all variables showed that we cannot reject the null hypothesis that the means of the socio-economic index, periphery index and dependency ratio are equal. However, we can reject it for the means of the ratio of students, indicating that they are significantly different. Table 2. Total regular expenses for small towns and regional councils between 2005 and 2019.

Regional councils
Population (000)  were 51 small towns whose populations were < 15,000. That number dropped to 43 in 2019. There were 49 regional councils during this period. We used the regression results to validate the convex behaviour of both regional councils and small towns and to calculate the efficiency frontier shown in Figure 2. The formal presentation is equation (A12) in the supplemental data online. Robust standard errors are shown in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.
small towns whose population was fewer than 15,000 and more than 2000, 3000 or 4000. We then used the data from very small towns with fewer than 2000 people as the test set. Each of the reduced training sets resulted in a different model, which we then used to predict the current expenses of all small towns. The ex-ante prediction in these models was for towns whose population was fewer than 2000. We chose this threshold because most of the villages that are in regional councils have fewer than 2000 residents. Table 4 shows the distribution of the population in the villages and small towns. We calculated the mean squared prediction error (MSPE) as the mean square error (MSE) of the out-ofsample prediction (towns with a population smaller than 2000the test set). Table 5 presents the descriptive statistics for the actual and predicted per capita current expenses (ln) and the MSPE for 2013-19. As the results indicate, when we reduced the training set to exclude Figure 2. Efficiency frontier of the dual-tier regional structure versus unitary town structure. Table 3. Regression results of the natural log of the expenses of the major categories in small towns with a population of fewer than 15,000, pooled from 2013 to 2019.
(1) small towns with a population up to 2000, the MSE changed a little, the MSPE grew, and the correlation between the actual and predicted expenses declined a bit. Given these results, it is safe to assume that the full training set can be used to predict the expenses of the rural village.

What if all villages had a unitary local government?
Using the model developed with the training set of small towns, we calculated the simulated expenses of all villages that are part of a regional council prefecture as if they were in a unitary structure, according to specification (1). Figure 3 shows a scatter overlay of the actual per resident expenses of small villages (circles), and the simulated villages' per resident expenses ('+' signs). The results indicate that the simulated expenses are almost a natural extension of the actual expenses. Table 4 shows that in most villages there are fewer than 1000 residents, whereas in most small towns there are more than 1000 residents. Thus, a large portion of the prediction is out-of-sample. To verify the robustness of the simulation, we regressed the in-sample villages' simulated expenses and compared the results with the small towns' training set. Table 6 presents the comparison, indicating that the small towns and in-sample villages groups exhibit similar coefficients, and are not statistically different.
We summed the simulated expenses of all villages that were in a regional council prefecture to the regional level to obtain the alternative unitary structure expenses for each major category. The efficiency ratio for the total and each major category is the simulated regional expenses divided by the actual regional council expenses for every regional council and year. As we derived the unitary expenses model from the small towns' training set, both for the total and for every major category, administrative and spillover expenses, if they exist, are embedded within the model. The simulation results are presented in Table 7. All the efficiency ratios are > 1, and the average efficiency ratio, η total , is 1.5, indicating that the dual-tier is more efficient than the unitary structure in rural villages. The simulation results in the table also show that throughout the years and for the total and all the major categories, the dual-tier regional structure is more efficient than the equivalent unitary structure (η > 1). The main contributors to the efficiency of the dual-tier structure are the administrative and management overhead and the local public services. One explanation for the results is that the economies of scale of the dual-tier structure result in lower per resident overhead. In the dual-tier structure there is only one mayor, one controller, one legal advisor, etc. In contrast, in individual villages (V ) there are V mayors (even if they receive smaller salaries), V controllers, etc. Nevertheless, the expenses for providing state services are similar in both structures.
Similarly, the efficiency ratio of each village for each year is its simulated per resident expenses divided by the actual per resident expenses of the regional council of which it is a part. Figure 4 illustrates the distribution of the efficiency ratio of all villages between 2013 and 2019 with a normal distribution overlay. The villages whose efficiency ratio is < 1 are more efficient with regard to the dual-tier structure, as their simulated expenses are less than the current regional council's per capita expenses. Between 2013 and 2019, there were 500 such occurrences out of 6947 observations (about 7%), indicating that the dual-tier structure is more efficient for the vast majority of the villages in rural areas. Thus, the results of our simulation indicate that the average efficiency ratio is > 1, supporting the efficiency of the dual-tier structure over the unitary one. Probing deeper into the results shows that there are regional councils whose efficiency ratio is < 1, meaning that they are less efficient than a unitary structure. Figure 5 presents a scatter plot of the regional councils' efficiency ratios from 2013 to 2019. As the figure illustrates, most of the regional councils are quite efficient. Only a few exhibit inefficiencies. In 2017 there were eight regional councils whose efficiency ratio was < 1, and during 2018 and 2019 the number dropped to five out of 49. Figure 5 also shows that the reason for the inefficiency is the high per capita expenses of these regional councils. Regression analysis of the contributors to the efficiency ratio (Table 8) indicates that the more residents in the regional council, the more central it is, or the smaller number of villages it has, the more the efficiency ratio declines. In line with Figure 5, an increase in the per resident expenses results in a decrease in the efficiency ratio.
Table 8 also indicates that when the per resident expenses are below about 14,300 NIS, the efficiency ratio is > 1.
The theoretical model indicates that the efficiency frontier is where the multiplication of the number of villages by the number of residents in the average village is about 60,570. Using the simulation results, Figure 6 illustrates the location of each regional council based on its number of villages and average village population (showing the means and standard deviations). It also overlays the efficiency frontier from Figure 2. Regional councils whose efficiency ratio is > 1 are shown as an orange circle, and those whose efficiency ratio is < 1 are represented with a triangle. Note that all regional councils lie in the efficiency zone. Indeed, most are in the range of η ≥ 1. Only a few are in the range of η < 1.

COMPARISON OF THE LEVEL OF SERVICES
As noted above, another question that arises is the level of services provided. Perhaps differences in the level or quality of services are reflected in the expenses for these services, leading to bias errors. To deal with this issue, we compared towns and regional councils using success in matriculation examinations as a proxy for education services, and waste recycling percentages as a proxy for sanitation services. We also present results from the 2019 ICBS Social Survey, which compares rural villages and small towns.
Our analysis indicates that the average success in matriculation exams in regional councils is about 3% higher than in small towns. However, when controlling for all other characteristics, the success rate in matriculation exams in regional councils is about the same as in small towns. Recycling rates in small towns are about 4% lower than in regional councils, a result that is significant after controlling for all other control variables.
The ICBS Social Survey shows that overall satisfaction in rural villages is equal to or greater than that of small towns. The only exception is transportation, which has a Note: There are more students in regional councils' villages than in small towns, as expressed in the ratio of students. Table 3 shows that the coefficient of this ratio is positive and significant, which explains why the simulated villages' per capita expenses are above the average per capita expenses of towns.
poorer quality of service in rural places. The results of the Social Survey are in line with a similar study in the European Union, which found that rural residents are more satisfied with life than city residents (Sørensen, 2014). They also accord with the satisfaction levels of Americans who have moved from cities to rural communities (Barcus, 2004). Appendix C in the supplemental data online provides a detailed analysis of the level of services with descriptive statistics and regression results. Our analysis indicates that the quality of public services in regional councils is at the same level, or even slightly higher, than that of small towns.  (1) is the same as column (1) in Table 3, and is presented for ease of comparison. Column (2) presents the in-sample village regression. Column (3) presents the pooled fixed-effect regression of small towns and the in-sample villages with a dummy for Village to test whether the small towns' training set is significantly different than the in-sample test set. The coefficient of the Village dummy variable shows that the per resident expenses in the village group are 0.9% higher than the training set, but it is insignificant, meaning that the two groups are not statistically different. Robust standard errors are shown in parentheses. Dependent variable: Natural log of regular total expensesactual expenses for small towns, simulated expenses for in-sample villages. Fixed effects regression with year fixed effects. ***p < 0.01, **p < 0.05, *p < 0.1. Note: η G&A is the general administrative and management overhead efficiency ratio. η local and η state are the efficiency ratios of the local municipal services and state public services, respectively. Standard deviations are shown in parentheses. All means are significant at less than the 5% level.

DISCUSSION, POLICY IMPLICATIONS AND CONCLUSIONS
Our results indicate that the dual-tier structure for rural villages is more efficient than a single-tier structure, but has efficiency boundaries. Based on the theory, we demonstrate that taking the public services that benefit from economies of scale from the local village tier and aggregating them into a second, mezzanine tier, while leaving the provision of local services that have local merit at the village level, improves economic efficiency as measured by per resident service expenses.  There are 86 villages whose efficiency ratio is < 1 in 2019.
Regional governments in the rural space: the effectiveness of dual-tier regional councils 1827 The theoretical model, which builds on Feinerman et al. (2011), shows that the dual-tier local government structure in rural places has an efficiency frontier that can be calculated by multiplying the number of villages by the number of residents in each village and is constant.
The empirical analysis suggests that this constant boundary is about 60,000 people, which sets limits to the dual-tier structure. The efficiency frontier implies that dual-tier regional councils reap the most benefits when they are comprised of many small villages. However, these benefits fade when these councils contain only a few larger villages.
The empirical analysis also shows that the average efficiency ratio, which is the ratio of the per resident expenses in a unitary structure to those in a dual-tier structure, is about 1.5, demonstrating the greater efficiency of the latter. Furthermore, breaking down the current expenses into their main categories indicates that it is the reduction in overhead expenses that accounts for most of the efficiency of the dual-tier structure. This finding is unsurprising given that such expenses are common to all villages, so they benefit from economies of scale. In contrast, in the unitary structure, each village must provide its own general and financial management. The dual-tier structure is also more economically efficient in providing local public services and slightly more efficient in providing state public services. Our findings confirm those of Ferraresi et al. (2018). However, we report much larger cost savings than their finding of a 5% drop in costs.
This difference in expenses raises the question of the level and quality of services, as a local government can reduce the cost of its services by reducing their quality. However, our quality of services analysis indicates that regional council residents are, in general, more satisfied with the services they receive than residents in small towns. Moreover, using success in matriculation exams as a proxy for the quality of educational services and recycling ratios as a proxy for sanitation services, we also find that the quality of public services in regional councils is Table 8. Regression of efficiency ratios of regional councils from 2013 to 2019.
(1) Year fixed effects Yes Note: There were 49 regional councils, excluding five outliers. The first column presents the pooled regression for all years, whereas the second column shows the fixed-effect regression with year fixed effects. Robust standard errors are shown in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. Figure 6. Average village population in each regional council versus the number of villages.
at the same level, or even slightly higher, than that of small towns.
Most of the literature on fiscal decentralization discusses centralization versus decentralization at the national or federal levels (Oates, 1972(Oates, , 2005Olson, 1986). Our research sheds light on the issue of centralization within subnational regional governments. Our findings suggest that a dual-tier regional council structure in rural areas has advantages over the unitary structure. Adding a mezzanine tier creates asymmetric federalism at the lowest levels, which is a different approach than asymmetry at the top-level described in the literature (Carr & Feiock, 2016;Martin & Schiff, 2011).
Governments look at the mergers of municipalities and inter-municipal cooperation as a way to reduce costs and benefit from economies of scale and size. However, the former is difficult to execute and the latter is voluntary. Furthermore, their cost savings are minimal (Ferraresi et al., 2018;Hämäläinen & Moisio, 2015;Luca & Modrego, 2021). We offer another tool in the toolboxadding a mezzanine tier that incorporates many small villages up to the efficiency frontier limit. This tool is a kind of compulsory inter-municipal cooperation. The results of our simulation demonstrate that the cost savings of a mezzanine tier are much greater, mainly due to the reduction in overhead and expenses for local services. One final benefit is that a dual-tier regional council structure in rural areas means that the higher levels of government at the national or county level can deal with a smaller number of local governments instead of needing to control and supervise thousands of small villages, making the higher levels of government more efficient as well. Thus, our alternative structure of local government should prove beneficial for all residents, regardless of where they live.