Municipal Efficiency Wp.Doc

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DEPARTAMENTO DE GESTIÓ N DE EMPRESAS

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On the efficiency of the delivery of municipal services

Francisco J. Arcelus Pablo Arocena Fermín Cabases Pedro Pascual

DT 92/07

Campus de Arrosadí a, 31006 Pamplona, Spain Tel/Phone: (+34)948.169.400 Fax: (+34)948.169.404 E-mail: [email protected]

1 On the efficiency of the delivery of municipal services

Francisco J. Arcelus Emeritus Professor, University of New Brunswick, Canada Departamento de Gestión de Empresas Universidad Pública de Navarra, Campus de Arrosadía 31006 Pamplona, Navarra, Spain Phone: 34 948 169413; Fax; 34 94 8169404 E-mail: [email protected]

Pablo Arocena Departamento de Gestión de Empresas Universidad Pública de Navarra Campus de Arrosadía 31006 Pamplona, Navarra, Spain Phone: 34 948 169684; Fax; 34 94 8169404 E-mail: [email protected]

Fermín Cabasés Departamento de Economía Universidad Pública de Navarra, Campus de Arrosadía 31006 Pamplona, Navarra, Spain Phone: 34 948 168479; Fax; 34 94 169721. E-mail: [email protected]

Pedro Pascual Departamento de Economía Universidad Pública de Navarra, Campus de Arrosadía 31006 Pamplona, Navarra, Spain Phone: 34 948 169361; Fax; 34 94 169721. E-mail: [email protected]

Abstract

This paper examines the main determinants of the efficiency of the local governments’ delivery of services, with special emphasis on the efficiency contribution resulting from the amalgamation of municipal services. The analysis centers upon a three-step procedure, using stochastic frontier regression analysis, whereby the first step identifies the variables that delimit the level of individual efficiency for each locality; the second step determines the factors that contribute to the level of inefficiency remaining in the system; and the third proceeds to estimate the parameters of the two models simultaneously. The results, based upon data from the municipalities of the autonomous community of Navarre, Spain, highlight the strong and positive impact upon the operating costs of the municipalities of the size of the population base, of the incidence of senior citizens in each community, of the level of housing stock and of available land in the public domain. The evidence also illustrates the substantial and positive, influence on the efficiency in the provision of municipal services in a given community of several socioeconomic factors. Included here are the density and size of its population, its level amalgamation of services, the saliency of taxes, as compared to transfers, in its operating budget and the magnitude of its accumulated past investment policies in infrastructures.

Keywords:municipal services, amalgamation of services, efficiency, stochastic frontier analysis

2 1. Introduction

This paper examines the main determinants of the efficiency of the local governments’ delivery of services, with special emphasis on the efficiency contribution resulting from the amalgamation of municipal services. The theoretical underpinnings of the present study rest on the well-know decentralization theorem of fiscal federalism (e.g. Oates, 1972) that establishes the higher efficiency of decentralized public provision over the centralized case, which is not so sensitive to the diversity of expenditure needs among territories. In fact, the first advantage often cited in favour of fiscal decentralization is economic efficiency, as the literature amply attests (e,g, Bukeley and Watson, 2007; Ezcurra and Pascual, 2007). From a normative point of view, the diversity of preferences among local jurisdictions is probably the best-known reason to advocate a decentralized structure of government. According to this theorem, “in the absence of cost- savings from the centralized provision of a good and of inter-jurisdictional externalities, the level of welfare will always be at least as high (and typically higher) if Pareto-efficient levels of consumption are provided in each jurisdiction than if any single uniform level of consumption is maintained across all jurisdictions” (Oates, 1972, p. 54). However, note that, for this prescription to hold, it is necessary to assume that the central government is not able to differentiate its provision among localities. Oates (1999) justifies such an assumption by means of the supposed better knowledge of state and local governments about the preferences and economic conditions of their constituency. The basic argument is that, even though governments at all jurisdictional levels seek to maximize the social welfare of their own citizenry, local governments can adjust better to the provision of services demanded by their voters. The reasons for this proposition is that, being at the closest level to their constituents, municipalities tend to be better able to overcome problems related to information asymmetry and to political restrictions from competing lower-level jurisdictions suffered by more centralized levels of government. For these reasons, government officials are more likely to allocate resources efficiently and do their best to provide optimal levels of economic development and public services when they are closer to the electorate. Further, when local jurisdictions have to fund the services they provide , they are more likely to do so at a cost-efficient level where the marginal benefits equals the marginal costs if services are decentralized rather than centralized (e.g. Tanzi, 1996) The empirical evidence presented in this paper focuses on the municipalities of the autonomous community of Navarre, Spain. Navarre represents an ideal geographical laboratory to study the efficiency of amalgamating the provision of local services across different municipalities, for three important reasons. First, there is a relatively sizable amalgamation in

3 their provision among different localities. Such occurrence is due to the wide population spread, the absence of administrative units of higher degree of aggregation, such as counties, the encouragement and incentives offered by the government of Navarre and the obvious scale returns inherent in the investments needed to provide these services. For these purposes, our data panel consolidates into a cost dependent variable all revenues and expenditures to provide these services, be they incurred by the municipalities themselves or by other entities at various levels of dissagregation. The second half of Table 1 shows how widespread this amalgamation process is, especially in water and sewage distribution and treatment, social services and particular administrative services. A key hypothesis of the present study is that such an amalgamation process leads to a more efficient management and distribution of the said services. Second, Navarre presents one of the most atomised local structure of the Spanish autonomous communities, both in terms of the number and of the population size of the municipalities within its midst (Cabasés et al, 2007). In 2004, as Table 1 indicates, there were 272 towns in Navarre, with an average population of 2,150, versus an average of 8,102 in Spain. Further, 70% (60.81% in Spain) of them had fewer than 1,000 residents that comprise only 9% (3.99 %) of the entire population. In contrast, the eight (622) cities with over 10,000 people accounted for approximately 53% (75%) of the total number of inhabitants. Such level of atomization reinforces the likelihood of towns amalgamating their services in different spatial patterns, creating “overlapping jurisdictions”, an important component of Buchanan’s (1965) theory of clubs. Third, Navarre enjoys considerable fiscal autonomy, atypical of the average Spanish autonomous community. It has full responsibility for collecting taxes that are a posteriori transferred in part to the central and to the local governments and receives a greater share of capital transfers.

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The paper proceeds along the following lines. First, we present a brief summary of the extant theoretical and empirical literature on the efficiency of local municipal services, followed by a description of the data and of the variables used in the development of the model. Then, we specify the model and describe the statistical methodology used for its estimation. An analysis of the empirical results and some concluding comments complete the paper.

2. Literature review

In this section, we examine the literature on the primary difficulties in identifying and measuring the efficiency of municipal services and present the major methodological approaches used in its

4 measurement. Worthington and Dollery (2000) present an empirical survey of the literature on the subject. An update of the survey appears in Table 2. Both surveys classify the extant studies according to five criteria: the type of sample, the methodology, the variables used in the model, be them inputs, outputs or explanatory variables, the analytical techniques and the main findings. Our analysis of the literature follows this five-criterion approach.

[PLEASE INSERT TABLE 2 ABOUT HERE]

2.1 Samples

The nature of the samples used, both cross-sectional and panel in nature, their size and their geographical coverage, at various levels of disagregation, attests to the importance and popularity enjoyed by the study of municipal services throughout the world. There are recent studies from Australia (e.g. Woodbury and Dollery, 2004; Worthington, 2000) to Japan (e.g. Tanaka, 2006), from Portugal (e.g. Afonso and Fernandes, 2005b, 2006), to Norway (e.g. Borge et al, 2007; Revelli and Tovmo, 2007) and Finland (Loikkanen and Susilouto, 2005), from the U.S. (e.g. Moore et al, 2005) to Brasil (e.g. Sousa and Stosic, 2005) and to Greece (e.g. Athanassopoulos and Triantis, 1998). This paper seeks to bring forth this type of analysis to the special situation of Navarre.

2.2 Methodology/Analytical techniques

Past studies on the efficiency of local services follow closely the more general productive efficiency literature in estimating an efficiency frontier as the benchmark or criterion to evaluate which deviations from the frontier form evidence of inefficiency. Fried et al. (1993), Lovell (2000) and Coelli et al (2005) review this theoretical framework. Worthington and Dollery (2000) groups the methodologies utilized in estimating the efficiency frontiers in the municipal services field into four general approaches. One includes the Deterministic Frontier Analysis (DFA), an econometric technique that assumes all deviations from the frontier to explain inefficiency. A second deals with the Stochastic Frontier Analysis (SFA), which delimits the extent to which deviations from the frontier are attributable to randomness or to inefficiency. A third consists of Data Envelopment Analysis (DEA), a non-parametric linear programming technique that establishes a deterministic frontier from which all deviations are inefficient. Finally, there is the Free Disposal Hull (FDH), another non-parametric technique which looser restrictions on the production technology than DEA. Coelli et al (2005) discusses the main advantages and disadvantages of these approaches. This paper employs the SFA formulation, because it eases the process of isolating the fluctuations due to the inefficiency in the distribution

5 of the services from those attributable to statistical noise.

2.3 Variables

As shown in Table 2, the variables used by the literature on the subject are of two types. One refers to the inputs and outputs that characterize the production process. The other consists of explanatory variables, be they managerial or socioeconomic in nature, that affect directly the inefficiency of such process, without influencing the transformation process itself. This implies the need to capture the simultaneous effects of the inputs and of the explanatory variables upon the outputs. For these purposes, the literature includes two types of formulations. One considers in one estimating equation, the simultaneous effect of the uncontrollable explanatory variables and of the inputs on the outputs. The other follows a two-step methodology that obtains first the efficiency frontier based on only the controllable factors and then regresses the efficiency levels so obtained against the uncontrollable inputs. Lovell (1993) and Coelli et al (2005) discuss the methodological advantages and disadvantages of both methodologies and Worthington and Dollery (2002) do not find substantial differences in the efficiency scores of NSW local governments, using either approach. To overcome these methodological problems, this paper uses a third approach, namely the formulation of Battese and Coelli (1995) that estimate the efficiency and inefficiency effects simultaneously but in two separate equations. Another issue of importance relates to the difficulties inherent in the measurement of the efficiency at the local municipal level, arising from different sources (e.g. Balaguer et al, 2004; Worthington and Dollery, 2000). One refers to the wide variety of users of this municipal information. It includes producers/providers and consumers of such information and public policy managers. This heterogeneity of users often results in different types of analysis and interpretation of the said information. Also, the absence of the price mechanism, as the purveyor of service quality, difficult substantially the search for efficiency indicators. A related problem lies in the complexity of quantifying municipal services into homogeneous units. Such problem often compounded by providers bestowing their services across various municipalities, thereby affecting each local unit upon the efficiency of others. Finally, all these problems multiply the hurdles public accounting systems must overcome in valuating the worth of the production and delivery of these public services. As a result, we follow the lead of some of the papers listed in Table 2 and of other studies on municipal efficiency (e.g. Vanden Eeckaut, et al, 1993) and employ output proxies to get a measure of the value and magnitude of the municipal services provided.

2.4 Main findings

6 In Spain, studies on the efficiency of local services are far and between and primarily devoted to specific services. Examples of this kind are Bosch et al (2000) on refuse collection, García-Sánchez (2006) on municipal water and Prado-Lorenzo and García-Sánchez (2007) on street lighting. This relative neglect of this topic is mostly due to budgetary considerations and/or the scarcity of the appropriate survey or related statistical information concerning the local public sector. Some exceptions to this state of affairs include Giménez and Prior (2003), Balaguer (2004) and Balaguer et al (2007). The first evaluates the efficiency of the Catalonian local governments of more than 2,000 inhabitants and determines the extra cost a given unit from its optimal level. The second presents evidence of the inefficiency of the services provided by the municipalities of the province of Valencia. It also ranks the municipalities in terms of the amount of inputs used in the production of a unit of output. The evidence presented shows the wide margin local officials enjoy in optimizing resource utilization. However, it also illustrates that part of this efficiency is also due to such exogenous factors as the size of the municipality, its per capita fiscal burden, capital transfers and the level of the local economic base. Further, municipalities with higher transferred funds are the most inefficient in their resource utilization. De Borger et al (1994) and De Borger and Kerstens (1996a, 1996b) obtain similar results for Belgian municipalities, thereby giving rise to the hypothesis of a negative relationship between the efficiency of resource utilization and the municipality’s potential to manage these resources efficiently. In addition, with data from the Survey on Local Infrastructures and Equipment of the Ministry of Public Administration (1985) and directly from the municipalities of the province of León, Prieto and Zofío (2001) use a DEA formulation to assess the efficiency of public provision of local infrastructures and equipment. Later on, Prieto and Zofío (2003) extend this analysis to the municipalities of the province of Salamanca for the 1998-2002 period, across three dimensions: the funding shortage to provide services, the capital transfers for their financing and the estimated outlays needed to correct the budget deficit. In addition, Balaguer et al (2004) relate efficiency to the decentralization of local municipalities by testing the hypothesis of a positive relationship between population size and the degree of decentralization. Their results are not conclusive, since all municipalities provide many services by themselves or jointly with other local communities, a practice also common in Navarre (e.g. Cabasés et al, 2002).

3. Methodology and Data

This section introduces the SFA formulation, describes the sources and the nature of the variables

7 used and presents the estimation equations.

3.1 The Stochastic frontier model

To determine if the municipalities of Navarre are cost efficient, the SFA formulation of Battese and Coelli (1995) for panel data forms the basis for the methodology used in this paper. A municipality is overall cost-inefficient if it operates at a cost level superior to the cost frontier. SFA allows the researcher to discriminate between the random or stochastic sources of the inefficiency inherent in the municipalities and the true or systematic source of such inefficiency. The SFA formulation contains two models: the operating-cost model and the technical inefficiency model. Their corresponding functional forms are as follows:

Cmt = exp{xmt b + emt }

emt = umt + umt

umt = zmtd + wmt TE = exp - u mt { mt } (1)

In (1), Cmt represents the operating costs of the m-th municipality in year t; •, the vector of parameter coefficients to be estimated; xmt, the values of the set of independent variables, to be identified in the next subsection; emt, the residual differences between the actual costs, Cmt, and exp{x b} the cost frontier, represented by mt . In turn, eit comprises of two types of errors. One, umt, specified by the third equality in (1), denotes the stochastic error associated with the technical

2 inefficiency of production and corresponds to a non-negative truncation of the N(zmt•, • ) normal distribution. The other is the stochastic error component, vmt, assumed to be an i.i.d. random

2 error, N(0,•v ) and independent of the umt´s. In addition, zmt denotes the values of the set of explanatory variables, identified in the next subsection; •, the vector of inefficiency parameter

2 coefficients to be estimated; and wmt is a random error, defined by N(0,• ) and bounded from below at – zmt•. Finally, the parameters, •, of the cost-frontier model and those, •, of its technical efficiency counterpart are estimated simultaneously through maximum likelihood, using FRONTIER 4.1 (Coelli. 1996). Then, the estimation of the technical production inefficiencies, denoted by TEmt, follows the last equality of (1).

3.2 Sources and description of the variables

The definition of variables of the SFA model in (1), as well as the data sources and some descriptive statistics appear in Table 3. Various offices within the government of Navarre

8 (www.navarra.es) were the source of this information. The Department of Local Administration provided the accounting data to compute C, INVEST and Tax Pressure, as well as AREA, one of the variables used by Navarre to allocate the funds from the Fund for the sharing of local taxes in Navarre (Fondo de Participación en Tributos de la Communidad Foral (www.todalaley.com/mostrarLeyI1477p3tn.htm). In addition, the Service for the Ordination of the Territory of the Government of Navarre supplied DIG, a variable used by the Department of Local Administration to classify municipalities in Navarre’s 2002 ¨Special Plan for Local Infrastructures”. Finally, Navarre’s Statistical Institute (http://www.cfnavarra.es/estadistica/) provided the information to compute the remaining variables. The resulting panel data set covers the 1995-2002 period. The number on municipalities included in the data set is 263 out of the 272 existing in Navarre. The exclusion of nine was due to lack of data for some of the explanators of the model. Further, earlier data, before 1995, are not available at the desired disaggregated level, because of the lack of reporting homogeneity in the underlying information. The model estimation proceeds only for 1998 and 2001. The other years are needed for the computation of DIG and INVEST, which require the use of data from the 1995-1998 (1999-2002) sub period to obtain the desired 1998 (2001) values. We now turn to the description of the nature of these variables.

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The dependent variable, Cmt, measures the operating costs, in euros, of municipality m in year t, discounted by the corresponding CPIs for Navarre. Next, we have the outputs, which are proxies for the good and services provided by the municipalities and hypothesized to account for fluctuations in Cmt. The first four, AREA, POP, P65 and HOUSE, deal with explanators of the potential size, in terms of land or people, of the municipal services demanded. AREA measures, in thousands of square meters, the part of the municipality in the public domain. The local government is responsible for the supply of services to this physical space, such as lighting, maintenance, security and the like, thereby providing support to the residential, business and recreational needs of the local community. HOUSE includes the number of dwellings units in the community, an excellent proxy for the potential demand for the urban services listed in Table 1b. The two others deal with the population, measuring either the total, POP or the incidence, P65, of senior citizens. The latter is included because of their relatively large presence within the urban population of most municipalities and the very special set of municipal services required. As indicated in Table 3, whereas senior citizens represent anywhere between 4% and 54% of the inhabitants of a given community, they embody an average of 24% of the entire population, with a very small standard deviation of 8%.

9 Another of output is DIG, a measure of the quality of the local infrastructure, used by Navarre as one of the determinants for capital transfers to the municipalities. It is computed as a linear combination of a series of indicators pertaining to the status of the local infrastructures and endowments and of the services related to them. Its value ranges from zero to 10, with the larger values corresponding to those in the worse state. Table 4a outlines the potential infrastructures, candidates for inclusion in its computation and the weights assigned to each. The addition of DIG into the model reflects the hypothesis that the quality of local infrastructures influences upon the operating costs of the various municipalities, through fluctuations in the costs of maintaining and servicing them. Finally, the model includes the trend variable, t, a binary variable, designed to test the hypothesis of a possible change in operating costs not attributable to the fluctuation in the other outputs of the model.

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The last set of variables in Table 3 includes the explanatory indicators, hypothesized to account for the inefficiencies in the cost function. These variables reflect our hypothesis that the degree of inefficiency is affected by the degree of amalgamation of the services provided (Amalgamation index), the manner of financing the delivery of these services (Tax Pressure), the accumulated level of past investment (INVEST), the degree of population dispersion across each community (Density) and the relative size of the municipalities (P3000). The Amalgamation Index measures the percentage of local costs attributable to the amalgamated activities. Its purpose is to test the hypothesis that there is a positive relationship between the joint provision of services and the efficiency of the services provided. These appear listed in Table 1b. The descriptive statistics of Table 3 indicate that the average value of the Index is 0.11, but with a very low standard deviation. This indicates a rather consistent pattern of usage of the amalgamation process across the municipalities of Navarre. Tax Pressure hypothesizes that there exists two sources of financing service delivery, namely taxes and other financing forms and that the higher the incidence of the former, the more autonomy the municipality enjoys in decision- making and hence, the higher is its efficiency. INVEST considers the proposition that communities with higher accumulated past investments in infrastructures are expected to have more modern endowments, thereby be more efficient in their service delivery function. For reasons of data scarcity stated earlier, four-year cycles comprise the accumulation process, as shown in the definition of INVEST in Table 3. The fourth explanatory variable, Density, consists of the ratio of the number of dwelling units to the size of the municipality in the public domain. The hypothesis is that the higher the concentration of houses in the municipality, the more

10 efficient the provision of services becomes. Finally, the last indicator is P3000, a binary variable intended to take into consideration the impact of the size of the population on efficiency. In Navarre, municipalities with more than 3,000 inhabitants have a public comptroller and must carry a more general and sophisticated accounting system, in lieu of the simplified system required of smaller local units. The hypothesis is that the a higher degree of local supervision and better management practices render the larger communities more efficient in the provision of services.

3.3 The estimation equations

The empirical vehicle to obtain efficiency estimates consists of a translog stochastic frontier regression, described as follows (e.g. Coelli, et al, 2005, eq. 11.13):

5 5 é j j 2 j k j ù 2 Cm ,t = a 0 + å êb j xm,t + b jj (xm,t ) +.5 å b j , k xm,t xm,t + r jt xm,t ú + l1t + l2t + vm, t + um,t j= 1 ë k = j +1 û 5 e um,t = d 0 + å d e zm,t + wmt e= 1

(2)

x j where the subscript m represents the m-th municipality, the m,t ´s denote the log of the j-th

z e output at time t and m,t ´s, the e-th explanatory variables at time t, both listed in Table 3. The remaining variables and parameters of (2) are those in (1).

4. Empirical results

This section deals with the estimation and interpretation of the parameters related to the SFA functions in (2). We start with a discussion of the nature of these estimates. Then, we proceed with a comparative analysis of average efficiencies across two dimensions, namely time and the size of the municipalities. The section ends with the testing of several alternatives to the assumptions made in the development of the model.

4.1 Parameter estimation

The simultaneous maximum likelihood parameter estimates of both the operating cost and the technical-inefficiency effects models appear in Table 5. Our first observation centers on the statistics related to the very high explanatory power of the models in question, which clearly

11 attests to their appropriateness. One is the adjusted R2 value of 0.95, from the first model. It represents the measure of goodness-of-fit of the OLS estimates, used as the starting values to obtain the ultimate MLEs. The other is the g parameter that lies between zero and one. If g = 0 then all deviations from the frontier are due to noise, while g = 1 means all deviations are due to technical inefficiency. Its value of •=0.867 in the table, which suggests the high proportion of variability that can be attributed to operating-cost inefficiency.

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Next, consider the parameters of the operating cost equation. Note that normalizing its variables at their mean points implies that the cost elasticity with respect to each individual variable, evaluated at its mean, corresponds to its first-order coefficient of the translog function.

The first five first-order coefficients, •1 to •5 are of the expected sign, positive, and all but •5 are statistically significant at least at the 10% level. That •1 and •3 are positive is not surprising, since it is reasonable to expect that, other things being equal, the larger the municipality, in terms of the number of its inhabitants or of its geographical area, the higher the demand for municipal services and hence the larger the operating expenditures to provide such services. Similarly, the larger the value of P65 is, the higher the need for such municipal services, such as special social services and recreation, directed to the third-age population. Likewise, with respect to HOUSE, the larger the housing stock, the higher the need for additional urbanization services in the community, such as those listed in Table 1, with the corresponding rise in operating cost outlays.

Further, with respect to the service quality coefficient, •5, recall that the variable DIG, measures the deficit in the quality of delivering primarily four types of services, dealing with water treatment, electricity, solid waste and road paving. Note also that the quality of such services is rather homogeneous, throughout the autonomous community of Navarre, regardless of the size of the particular municipality (e.g. Cabasés, et al, 2002). This leads to minute fluctuations in the value of the output DIG, as the relevant descriptive statistics on Table 3 clearly attest. Hence, a testable interpretation of the lack of statistical significance of •5 is that such variable may no longer be appropriate to account for fluctuations in operating costs, now largely attributed to other factors not measured by this quality index. In addition, the coefficient of t, •6, is positive but statistically insignificant. This suggests that the operating costs have experienced a rather inconsequential increase, during the period under consideration.

The estimates of the inefficiency coefficients, •0 to •6, are all highly statistically significant, at least at the 5% level. The only exception is •6, corresponding to the time trend, which exhibits a non-significant negative sign. The latter result suggests a negligible efficiency

12 increase in the provision of municipal services throughout the period under study. The coefficient of the amalgamation index, •1, is negative and highly significant, which strengthens one of the basic hypotheses of the present study and leads to the conclusion that adroit coordination of efforts among several municipalities in the provision of municipal services represents the embodiment of an exceedingly efficient public policy strategy. Further, the positive and highly significant •2 suggests that the smaller municipalities are operating at a more inefficient level that the larger urban units. A testable explanation for this phenomenon is the lack of administrative services, including the lack of the public comptroller, that characterize communities below the

3,000-population level in Navarre. In addition, the tax pressure coefficient, •3, is negative and statistically significant at the 5% level of significance. This result corroborates the well-known hypothesis of a positive relationship between governmental efficiency and the incidence of taxes in the public disbursements base, as tax-paying voting citizens are more involved in the management of those funds (e.g. Brennan and Buchanan, 1980; Becker and Mulligan, 2003).

Another coefficient, negative in sign and statistically significant at the 5% significance level, is •4, associated with the Density variable. This finding substantiates the proposition that the higher the density of the population living in a geographical area, the more efficient the delivery of services to that particular community. The relevance of such evidence to an autonomous community like Navarre reflects the high proportion of towns located in mountainous areas, with great tradition of living in isolated homesteads. This result also conforms to the proposition that agglomeration is a scale economies process Finally, that the variable INVEST yields also a negative and highly statistically significant coefficient, •5, also follows expectations. More active past investment policies in the infrastructure of a given community tend to render better quality stock, thereby leading towards a more efficient service delivery policy.

4.2 Efficiency/Inefficiency estimates

This subsection presents some average operating-cost efficiency/inefficiency estimates based upon the results of Table 6. The objective is to provide a preliminary assessment of the effect the size of a municipality has on the efficiency/inefficiency of the average municipality over time. Table 6a provides the needed results. Observe that, for consistency with the SFA evidence of Table 5, the definition of size preserves the small/large-municipality dichotomy represented by the P3000 explanatory variable. Thus, small (large) municipalities correspond to those with a population under (of at least) 3000 inhabitants.

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13 Table 6a provides the average efficiency estimates, together with estimates of their corresponding standard deviation and coefficient of variation, for each size category and each year. The incidence of the cost inefficiency of a municipality is measured by how much the average estimate exceeds one. Consider, for example, the 1.106 mean efficiency for municipalities of at least 3,000 inhabitants in 2001. Its magnitude implies that the average large municipality in that year spent approximately 10.6% more than what they would have, had it be fully efficient in its operating expenditure patterns. The evidence indicates a slight decrease in inefficiency from 1998 to 2001, going from 1.229 to 1.202, and a more substantial decrease in variability. This results in a much lower coefficient of variation, reflecting a more homogeneous spending pattern in 2001 than in 1998. Further, the higher degree of homogeneity in 2001 is largely due to the cost behaviour of the smaller municipalities, for which the coefficient of variation decreased from 19.3 to 15.6, whereas its larger-municipalities counterparts went in the opposite direction, experiencing a small increase in relative variability from 2.6 to 3.6, during the same period. A problem with the size of the expenditures arises when computing the efficiencies as done for Table 6a. In monetary terms, a 1% increase in inefficiency for a large municipality implies a larger additional expenditure outlay than for a smaller unit. However, the computations in Table 6a do not reflect this relative difference. To correct this oversight, we weighted each inefficiency estimate by the cost saliency of the corresponding municipality, represented by the ratio of each municipality’s operating costs over the sum of operating costs of all the localities. Then, the weighted inefficiency estimates of Table 6b arise from correcting each inefficiency estimate by the importance of its associated cost outlay. These new estimates represent a decrease in the total overall inefficiency from 22.9% (Table 6a) to 13.7% (Table 6b) in 1998 and from 20.2% (Table 6a) to 12.7% (Table 6b) in 2001. Further, the weighting scheme appear to be primary responsible for the decreases, to judge by the relatively stable mean estimates by size. Other interesting observations occur from the comparison of the potential cost savings, if the municipalities were fully operating-cost efficient in the provision of local services. Both size cohorts experienced larger savings over time, with a higher increase attributable to the larger units. Nevertheless, the smaller units contribute to these savings substantially more, on a proportional basis, than their total cost structure would otherwise indicate. Whereas their total cost contribution hovers around the 24% range in both years, versus 76% for the larger municipalities, their potential total cost savings (13.8 vs. 14.7 in 1998; 14.4 vs. 17.3 in 2001) are similar in magnitude, regardless of size. These results have important policy implications, as they point towards the smaller units as the prime candidates for policies designed to correct inefficiencies in the provision of services at

14 the municipal level.

4.3 The generalized likelihood-ratio (LR) tests

This subsection contains a series of generalized likelihood-ratio (LR) tests of the well-known form:

LR = -2 {log[Likelihood(Ho)] - log[Likelihood(H1)]} (3)

In all cases, the alternate hypothesis, H1, considers the translog formulation of (2) as the appropriate formulation for our cost model. The various null hypotheses, H0, seek to determine the appropriateness of other optional formulations, as alternatives either to the preferred functional form of the SRF model or to the distribution of the residual error term or to the distribution of the random variables associated with the existence of technical inefficiency. Observe that each LR test is asymptotically distributed as a •2, with degrees of freedom equal to the difference in the number of parameters estimated for each pair of (H0, H1) hypotheses, described in this subsection. In (3), log[Likelihood(H1)] denotes the logarithm of the maximum likelihood function of the SFA, for the translog formulation. Its value of -100.30 appears in Table

5. Table 7 shows the value of log[Likelihood(H0)], for each null hypothesis tested. It also provides the corresponding LR statistic and the critical •2 values, at a significance level of •=0.05. These values can be obtained from any statistical textbook, except for that associated with the second hypothesis, involving •=0. The appropriate statistic in that case has a mixed •2 and its values appear in Table 1 of Kodde and Palm (1986). We now explain each hypothesis in turn.

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The first hypothesis deals with the functional form of the stochastic frontier. It tests for the adequacy of the Cobb–Douglas formulation (null hypothesis, H0), relative to its less restrictive

Translog counterpart (alternate hypothesis, H1), given the specification of the technical- inefficiency-effects model of (1). The Cobb Douglas formulation corresponds to (2), with only the single-subscript beta parameters and the coefficient of the trend variable, •1, not set to zero.

From Table 7, the value of log[Likelihood(Ho)], the logarithm of the maximum likelihood function for the Cobb-Douglas model of H0, equal -125.46. The number of degrees of freedom amounts to 15, which, together with a significance level of •=0.05, yields •2(15, 0.01)=30.6, way below the LR value of 50.32. The conclusion clearly points towards the rejection of the null hypothesis related to the Cobb–Douglas being an adequate representation for the Municipal Cost model. Confirmation of this result appears in Table 5, where five (•15, •23, •24, •34, •45) of the 21

15 coefficients associated with the non-linearity hypothesis of the operating-cost function in (2) are statistically significant. Hence, the translog cost function appears to be the preferred formulation. Thus, from now on, all results presented here refer solely to the translog formulation. The second null hypothesis in Table 7 refers to the absence of inefficiencies in our overall cost model. The non-rejection of H0 would lead to the conclusion that the appropriate overall cost model corresponds to the traditional cost function with no inefficiency effects and hence where the •e´s and thus the corresponding um,t´s of (2) equal zero. The evidence from Table 7 clearly rejects the null hypothesis at the 5% level of significance. Instead, this test leads to the conclusion that the average response function, in which all municipalities are assumed fully cost efficient in the provision of local services, is not an adequate representation of the data given the assumption of the translog stochastic frontier model. Finally, hypothesis 3 questions the appropriateness of the inefficiency effects model. It considers that the inefficiency effects are not a function of the explanatory variables discussed earlier. The evidence of Table 7 suggests otherwise. The joint effect of these variables on technical inefficiency is statistically significant. Such inference leads to the rejection of the null hypothesis and leads to the conclusion that the explanatory variables of Table 3 should indeed be included in the inefficiency effects model.

5. Some concluding comments

The results of this paper clearly illustrate the substantial and positive influence on the efficiency in the provision of municipal services in a given community of several socioeconomic factors. Included here are the density and size of its population, its level amalgamation of services, the saliency of taxes, as compared to transfers, in its operating budget, and the magnitude of its accumulated past investment policies in infrastructures. The present study also yields some important implications for the improvement of management practices at the municipal level. The first refers to the unquestionable relevance of the topic in question. Its saliency is clear when considering the depth of coverage worldwide, shown in the Literature Review section. There is also great convergence in terms of the nature of the explanators of the cost and of the inefficiencies in the system. There exists a broad consensus in favour of such determinants as the size of each municipality, the financing formula, the need to

16 amalgamate services and some socio-economic and geographical perspectives. Others, institutional and political in nature were disregarded for lack of the needed information. Further, the wide availabily of research coverage on the subject allows for cross evaluation of operating- cost policies of service delivery across local units of equivalent sizes throughout the world, designed to improve the quality of municipal services. Examples of such analysis include the comparisons, carried out by Quebec municipal affairs department, between Philadelphia and Montreal and Indianapolis and Quebec City, both pairs of cities of equivalent size (e.g. Eggers and Goldsmith, 2003). The second important implication is the importance of the amalgamation of services in correcting the inefficiencies in the service delivery system. As the needed information becomes available, additional important analysis on the design and managing of the system may be undertaken. Open questions of interest include determining the type of amalgamation that produces the best cost-benefit results, the optimum level of amalgamation for a given service or the design of alternate forms of grouping services as a way of enhancing intermunicipal cooperation. With respect to the effect of the tax pressure on efficiency, the evidence indicates that taxes are more efficient than transfers are in financing the operating budget of the municipalities. This result is not uncommon in the literature presented earlier. It also conforms to the proposition that the higher the incidence of taxes over transfers results in higher financial autonomy on the part of the local governments, while tightening the control of the tax-paying citizens over the decision- making powers of the local authorities. However, note that the value of the tax pressure variable depends not only on the tax rate. It is also a function of the taxable income of the tax-paying citizens. This implies that the impact of the tax pressure variable may be due to the wealth of the citizens as well as to the fiscal policies of the local authorities. In the case of Navarre, a testable proposition is that wealth may be primarily responsible for the efficiency effect, in view of the great degree of homogeneity existing in the tax structure. As for INVEST, it is not surprising that well developed investment policies improves efficiency. After all, newer assets are likely to prove more effective in the process of service delivery. Another open question of interest is to rank the contribution of the assorted types of investment in terms of their ability to increase efficiency and to assess the optimal level of investment and maintenance that maximizes efficiency yields. This is a particularly important issue for further investigation, because the literature on the productivity of public and private investments (e.g. Gramlich, 1994). Yet another open question contrasts the high explanatory power of INVEST with the statistically insignificant role of DIG. This unexplained puzzle brings

17 forth alternate solutions to the dichotomy: either the lag needed to ascertain important efficiencies effects of past investments exceeds the four-year horizon utilized in the current study or DIG’s role as a quality benchmark is nearing the end. As stated earlier, the latter interpretation appears more likely to be the case, given the low variability of the explanatory in question and the possible saliency of other types of investment not adequately incorporated into the index. The congestion of the infrastructures may also play a part, suggesting a possible connection between the size of the investment in infrastructures, its level of utilization and the efficiency in the delivery of the services provided (e.g. Boarnet, 2001). Finally, the evidence highlights the inefficiency problems embedded within the small municipalities. Although representing not more than 24% of the total operating costs of Navarre’s municipalities, the high cost savings of correcting their levels of inefficiency approach the magnitudes from the bigger local units. There are broadly accepted reasons for this state of affairs, such as economies of scale, the particular characteristics of specific public services and the special circumstances, usually geographical in nature, of certain towns. However, a variety of management practices used by larger municipalities might contribute to solving these problems. Included here are the availability of public comptrollers for towns with a population under 3,000 and the implementation of more sophisticated accounting systems. Another management tool of interest could be the standardization of the cost analysis system or any similar effort intended to enhance the quality of information of the input/output system, through the harmonization of management tools and of performance indicators (e.g. Giménez, 2007) throughout the entire municipal network. The study of these and other issues justifies additional research.

Acknowledgements: We thankfully acknowledge the financial support for the completion of this research from the Natural Sciences and Engineering Research Council of Canada and from Spain’s Ministry of Education and Science, project SEJ2007-67737-C03-02/ECON and the project SEJ2005-08738-C02-02/ECON, Office of Research, National Program of Social and Economic Studies. We are also grateful to Navarre’s Department of Local Administration and to the Service for the Ordination of the Territory, for their contribution to the data collection effort

References

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22 Table 1: Municipalities of Navarre by population size and the incidence of amalgamation.

1a: POPULATION BY SIZE AND STRATA

Population strata Population size Municipalities Number Percentage Number Percentage > 10,000 310,868 53% 8 3% 5,000-10,000 63,379 11% 9 3% 3,000-5,000 113,167 19% 37 14% 1,000-3,000 94,309 16% 51 19% < 1,000 55,474 9% 188 69% TOTAL 584,674 272 Average 2,150

1b: INCIDENCE OF AMALGAMATION

Type of services % of population % of municipalities Water distribution 79% 69% Water treatment 74% 60% Urban solid waste 96% 96% Social Services 35% 75% Sports services 18% 17% Transportation 54% 17% Rural development 12% 28% Administrative services 1% 7% Urban counselling 12% 28%

Source: Prepared by the authors from more aggregated data provided by Navarre’s Department of Local Administration

23 Table 2: Summary of the extant literature

AUTHOR(S) SAMPLE METHODOLOG INDICATORS DE INPUTS, OUTPUTS AND EXPLANATORY VARIABLES MAIN FINDINGS Y/ ANALYTICAL TECHNIQUE Athanassopoulos 172 Greek Parametric SFA Inputs: Operating costs (Expenditures on services, salaries, maintenance, materials) DEA proved to be more sensitive to and Triantis municipaliti (Cobb-Douglas) Outputs: Actual households, Built up area, Average HOUSE size, Heavy industrial use outlier observations. (1998) es (1986) area, Average size of industrial site. Dummy for tourist area The main drivers of the cost efficiency with Non-Parametric Explanatory variables: performance are the population, the population DEA For Fuzzy K-means clustering analysis: Measure of technical efficiency, Service size, the degree of industrial activity, over 2.000 expenditures, Income of extraordinary governmental grants, Infrastructure and whether the unit was involved inhabitants Fuzzy K-means investments, Dummy for Political party in charge of the local municipality, Density with tourism . clustering (households per m2), Fees and charges index (fiscal effort) Municipalities that spent more on analysis For Tobit Analysis: % of costs on service expenditure, % income from fees and charges, services, more dependent on the % income from extraordinary governmental grants, Infrastructure investments, central government for extraordinary Tobit regression Political party in charge of the local municipality, Density of local municipality, Fees revenues, higher household density, and charges index . and intended to collect more in terms of fees and charges, had lower cost efficiency. Municipalities that had succeeded in collecting a higher proportion of fees and charges had higher cost efficiency. Worthington 177 New DEA, SFA cost Inputs: Number of full time workers (equivalent time), Expenditures in largely and There is no superior theoretical (2000) South Wales frontiers inventory materials (excluding depreciation), Financial expenditures, Prices, Average approach of efficiency. local (Translog) municipal salary, Physical expenditures divided by current assets, Average interest rate DEA and stochastic frontiers should governments paid on borrowed funds. be thought of as complementary tools , 1993 Second-stage Outputs: Population, Number of properties receiving potable water, domestic waste in the analysis of local public sector Tobit regression collection and sewerage, Length (Km) of urban sealed roads and rural unsealed roads. efficiency. Explanatory variables: Grants dependence ratio (percentage of total revenue), Debt service Advantages of DEA in identifying ratio (net debt service cost divided by operating revenue), Level of current assets, benchmark local governments. Number of staff per 1000 population, Average rate per residential assessment (excluding water and sewerage rates). Afonso and 278 DEA Inputs: Municipal per capita expenditure Analysis performed by clustering Fernandes Portuguese Output: Local Government Output indicator (LGOI) , % Local inhabitants > 65 years old, municipalities into five regions. (2005a) municipal Second-stage % School buildings per corresponding school age inhabitants, % enrolled students per Significantly different level of governments Tobit regression corresponding school age inhabitants, % library users / total population, Water supply inefficiency between clusters (located in only for non- (1000m3), Solid waste collection (Tons), Number of licences of building construction, The most relevant non-discretionary mainland) discretionary Length of roads maintained by municipalities per resident population factors seem to be: high educational 2001. factors. Explanatory variables: Purchasing power, Population with secondary education, level, municipal per capita purchasing Population with tertiary education, Inverse of distance of capital of district, Population power and geographical distance. density, Population growth

24 Moore, Nolan 11 services of Two-stage Inputs: number of FTE staff and budget for building management, emergency medical Phoenix rated as the city with the best and Segal 46 of the efficiency services, fire, fleet management, parks an recreation, solid waste, street maintenance service record and Oakland, as the (2005) largest cities analysis and water provision; number of library branches; library operating expenditures per worst. in US (1993- capita; number of librarians; number of other library staff; book holdings; number of The employment of professional city 1998) DEA sworn police officers; number of police support staff; number of FTE Transit staff; managers or administrators rather number of transit vehicles in peak services; transit fuel than strong elected majors greatly Tobit regression Outputs: square feet of city building space available; reported response time for medical improved the efficiency of municipal services; number of civilian fire deaths; total fire losses; number of vehicles in fleet services. management; number of library registrations; total number of library visits; library More compact development does not collection turnover ratio; area of park space in use; city crime index; number citizens appear to lead to greater efficiency. served –solid waste; number of streets served-street maintenance; annual transit vehicle Suburban development is not miles and annual revenue transit miles; number of citizens served and volume of water necessarily inefficient. produced in water provision The efficiency case for regionalizing Explanatory variables: average precipitation; average snowfall; average temperature; government services may be weaker population 1990-1996 change; % of state and local government employees working for than commonly thought. local government state-wide; strong major vs. city manager/administrator; state litigiousness index; maximum and minimum temperatures; 1990, 1994, 1995 and 1996 population; size of city in 1990; state and local tax collected per $100 personal income; state and local tax revenue per capita Afonso and 51 DEA Inputs: Composite indicator of municipal performance (linear combination) (TMOI), Wide dispersion in performance Fernández Portuguese Resident population, Centrality index, Education, Social services, Sanitation and (2006) municipaliti Descriptive environment More spending does not translate in es in the analysis Output: Municipal per capita expenditure. better local living standards Lisbon and Vale do Tejo regions (2001) Tanaka (2006) 317 DEA/Translog Inputs: Quality of services: Social assistance expenditure per household, Ratio of the Increased use of information municipal waiting toddler for nursery school, Teacher-student ratio of compulsory education, The technology results in greater cost governments Maximum length of paved main roads per area, Ratio of the treatment of human waste, Nº of fire efficiency. of Kinki area Likelihood buildings/ total population. in Japan Method Output: Total cost The Local Allocation Grant does not (2001). (FRONTIER Explanatory variables: Staff engaged in information technology operations (ratio), Stock of promote cost inefficient behaviour , Version 4.1) information technology, Expenditure related to information technology divided by the but governments that have large debts total non-personnel cost. Local Allocation Grant divided by the general account budget. are cost inefficient.

25 Geys (2006) 304 Flemish Translog and Inputs: Number of subsistence grants beneficiaries, Students enlisted in local primary Spatial pattern in Flemish local municipal Cobb-Douglas schools, Surface area of public recreational facilities, and Total length of municipal government’s efficiency ratings. governments functions) roads. (2000) Output: Total current expenditures The spatial pattern is only weakly DEA and FDH Explanatory variables: related to the political situation in the For spatial effects: Spatial weights matrix of neighbouring. Flemish municipalities. OLS Maximum Control variables: Municipal per capita income level, Share of homeowners, Population Likelihood density, Number of “pre-1977” communities (amalgamation), Lagged level of long term local public debt (share of total revenues), Lagged level of fiscal surplus (share of total revenues), Level of grants awarded by higher level governments (share of total revenues) Political variables: Government fragmentation (Index of number of parties in coalition), Ideological fragmentation (standard deviation of the ideological positions), Ideological position (average ideological position) Balaguer et al 414 local DEA, FDH Inputs: Total Population, Number of lighting points, Waste (tons), Street infrastructure It is possible to carry out the second (2007) governments surface area (square metres), Registered surface area of public parks, Quality indicator stage without having to abandon the of Comunitat Non parametric Outputs: Budgetary costs: Wages and salaries, Expenditure on goods and services, Current non-parametric field. Valenciana Kernel transfers, Capital transfers, Capital expenditure. Persistent growth in overall cost (Spain) regression Explanatory variables: Tax revenue per capita, Current grants received per capita, efficiency with the size of Patrimonial revenues per capita, Financial liabilities per capita, Financial vulnerability municipalities Non parametric (total expenditure/total revenue), Governing party power (Votes obtained by governing Self–generated revenues, grants, bivariate party/population). deficit and governing party votes have density negative impact on efficiency. estimation Is necessary to split short-run from long-run inefficiencies Borge et al 362-384 Baseline measure Outputs: Aggregate Output measure based on 17 indicators of production for six service High fiscal capacity is associated with (2007) Norwegian of global sectors (D-output): Care for the elderly, Primary and lower secondary education, Day low efficiency. local efficiency: care, Welfare benefits, Child custody, Primary health care. The Herfindahl-index has the most governments Ratio between Explanatory variables: Herfindahl-index as indicator of political strength, Classification of consistent impact and indicates that a (2001-2005) aggregate output political regimes 4-way., Political ideology (share of socialist in the local council), Level strong political leadership contributes and local of budgetary procedure (Dummy for Centralized vs. Decentralized),Fiscal capacity to higher efficiency. government (taxes and block grants adjusted for spending needs and payroll tax, Democratic High democratic participation revenue. participation (% votes of the number of eligible voters in the previous election). contributes to high efficiency. Pooled OLS Centralized top down budgetary regressions procedure contributes to low Random effects efficiency.

26 Giménez and 258 Non-parametric Outputs: Results suggest the need to separate Prior (2007) Municipaliti cost frontier FOR THE SHORT TERM: short-term from long-term cost

es with more decomposed into Variable costs: Materials consumption and service acquisition (VC1) and Current inefficiencies. than 2000 long and short- transfers to decentralised organisations (VC2). The majority of cost excess inhabitants term efficiency. Fixed costs: Total labour cost (FC) (inefficiency) can only be tackled in the region FOR THE LONG TERM: Total cost (TC) from the long-term perspective.

of Catalonia. Second-stage Inputs: Urban area (ha), Total population, No Cars, No Buildings, Ordinary refuse (tons) To sort out the cost inefficiency found, Tobit regression Explanatory variables: Index of per capita income level ((low medium, high), Index of actions would need to influence the industrial activity, Index of importance of commerce, Index of importance of tourism, size of municipalities. 2 Total population, Density (inhabitants per km ), No Children ender 14 years, No Big municipalities, with low or Inhabitants over 65 years, Total members of local police force, Existence of public medium income per capita, having library (dummy). commercial and tourism activities and not especially oriented towards the promotion of cultural activities beyond their respective compulsory services, are cost efficient. Lorenzo and 113 Spanish Two-stage Inputs: staff, power consumed, number of lamps, total costs There is a significant relationship Sánchez (2007) municipaliti efficiency Outputs: number of m2 lighted, number of lighting hours; number of hours in which the between efficiency and the inputs, but es with over analysis lamps remained unrepaired only sometimes with the outputs 50,000 Explanatory variables: municipal area, population density, annual hours of daylight, Not a significant link between inhabitants, DEA offences against public order efficiency and type of management, plus all whether private or public or the provincial Truncated explanatory characteristics capitals regression

27 Table 3: Variables of the model and their definitions

Variable Name Variable Definition Data Source Min Max Mean Median st.d. Input C Total operating costs incurred by Department of Local 6,038 92,297,573 868,890 134,706 5,338,688 each municipality in the Administration provision of services

Outputs AREA Part of the municipality in the Department of Local 2,726 4,316,120 105,771 44,485 271,453 public domain Administration POP Total population of each Navarre’s Statistical 21 186,245 2061 377 11,315 municipality Institute P65 Percentage of the total population Navarre’s Statistical 0.04 0.54 0.24 0.23 0.08 over 65 years of age Institute HOUSE Number of dwelling units Navarre’s Statistical 11 84,620 918 209 4,863 Institute DIG An index that measures the scarcity Service for the Ordination 0.06 3.54 1.43 1.37 0.69 in the provision of municipal of the Territory services t Time trend

Explanatory variables P3000 =1, for municipalities with a Navarre’s Statistical population under 3,000 Institute inhabitants; 0, otherwise Amalgamation Percentage of the total costs in Navarre’s Statistical 0 0.23 0.11 0.10 0.04 index amalgamated services Institute Tax Pressure Percentage of inflows attributable Department of Local 0.05 0.91 0.46 0.47 0.13 to taxes Administration INVEST Average investment in the last four Department of Local 0.00 11.05 1.23 0.94 1.13 years/average operating costs of Administration the last four years

28 Density = HOUSE/AREA Navarre’s Statistical 0.11 4.11 0.61 0.50 0.40 Institute

29 Table 4: Composition of DIG (1)

Service or Endowment Weight of the Service or Endowment

Water Distribution networks 11% Volume and quality of water 11% Local networks of water supply and 11% treatment Residual treatment 11% Collection and treatment of solid waste 11% Electrification 11% Street lighting 11% Paving 11% Administrative Buildings 11%

(1) Drawn up by authors from DIG`s Regulatory Act of 17/05 (www.lexnavarra.es/detalle.asp?r=28056)

30 Table 5: Maximum-likelihood parameter estimates of the stochastic cost frontier model.

Variable Parameter Estimate Variable Parameter Estimate Cost model

Constant •0 -.303** ln POP*ln AREA b13 .125 (.122) (.121)

ln POP b1 .887*** ln POP*ln HOUSE b14 .236 (.078) (.269)

ln P65 b2 .149** ln POP*ln DIG b15 -.167* (.059) (.093)

ln AREA b3 .067** ln POP* t r1 -.125 (.029) (.111)

ln HOUSE b4 .141* ln P65*ln AREA b23 -.260*** (.079) (.088)

ln DIG b5 .003 ln P65*ln HOUSE b24 .335** (.028) (.170)

t •1 .105 ln P65*ln DIG b25 .038 (.093) (.068) 2 (ln POP) b11 -.258 ln P65* t r2 -.096 (.290) (.089) 2 (ln P65) b22 .123 ln AREA*ln HOUSE b34 -.224* (.172) (.127) 2 (ln AREA) b33 .082 ln AREA*ln DIG b35 -.026 (.053) (.052) 2 (ln HOUSE) b44 -.096 ln AREA *t r3 .066 (.306) (.057) 2 (ln DIG) b55 .022 ln HOUSE *ln DIG b45 .214** (.045) (.101) 2 t •11 .057 ln HOUSE * t r4 .068 (.989) (.117)

ln POP*lnP65 b12 -.138 ln DIG * t r5 .031 (.174) (.046) Inefficiency model

Constant d0 -1.552** Density d4 -3.642** (.766) (1.858)

Amalgamation Index d1 -3.485*** Investment d5 -.353*** (1.077) (.019)

P3000 d2 2.065*** t d6 -.165 (.698) (.168)

Tax pressure d3 -2.433** (.972) Assorted statistics

Variance s 2 = s 2 +s 2 .428*** Gamma g = s 2 / s 2 .867*** parameter u v (.093) u (.0385) Adjusted R2 from OLS 0.95 Number of years 2

Number of observations 526 Log-likelihood (H0) -100.3

31 Notes: Standard errors are in brackets. ***Significant at the 1% level; **Significant at the 5% level; *Significant at the 1% level.

32 Table 6: Weighted and non-weighted mean inefficiency estimates.

6a: Non-weighted mean inefficiency estimators

1998 2001 mean s.d. c.v. mean s.d. c.v. Large municipalities 1.107 0.029 2.6 1.106 0.040 3.6 (³ 3,000) Small municipalities 1.246 0.240 19.3 1.215 0.190 15.6 (<3,000)

Total 1.229 0.230 18.7 1.202 0.182 15.1

6b: Weighted mean efficiency estimators

weighted Total costs Potential cost weighted Total Potential mean savings mean costs cost (€ millions) savings (€ millions) Large municipalities 1.093 157.6 (76%) 14.7 1.091 190 17.3 (³ 3,000) (76.1%) Small municipalities 1.277 49.7 (24%) 13.8 1.241 29.7 14.4 (<3,000) (23.9%)

Total 1.137 207.3 28.5 1.127 249.7 31.7

33 Table 7: Test of hypotheses

2 Hypothesis No. Null hypothesis, H0 Log(Likelihood) X value (5%) LR-Test statistic

1 H0: •ii = •ij =0 (Cobb Douglas specification) -125.46 32.67 50.32*

2 H0 : •=d0 = … d6 = 0 (implies no inefficiency) -120.0 14.85 39.4*

3 H0 : d1 =… d6 = 0 (joint effects of explanatory -106.7 12.59 12.8* variables is not significant)

* Significant at the 1% level.