Measuring Potential Gains from Mergers Of Italian Courts through Non-Parametric Model Massimo Finocchiaro Castro∗ Department of Law and Economics, Mediterranean University of Reggio Calabria, Via dei Bianchi, 2 - 89125 Reggio Calabria, [email protected], tel. +39 0965 499360, fax +39 0965 499347. Calogero Guccio Department of Economics and Business, University of Catania, Corso Italia, 55 – 95121 Catania, [email protected] , tel. +39 095 7537744, fax +39 095 7537710. Abstract Italian judicial reform is entering a new phase through the Italian Government’s proposal (Decree n. 155/2012) of new jurisdiction design of first instance court through merger of some courts and the abolition of 220 local courthouses. Two aspects of merger analysis are the operational cost savings and the potential production efficiency gains. This paper concentrates on the second aspect and uses a non-parametric methodology to assess the potential effect of these mergers and whether the mergers are efficiency enhancing. However, it has to be noted that the reform under consideration suggests a merging procedure that should produce a reallocation of input in an efficient way and not an aggregation of first instance courts keeping constant the total amount of human resources. The available data, unfortunately, do not let us investigate the effects of a potential reallocation of input as suggested by the reform. We compare the actual efficiency levels of observed Italian courts, at the first instance level for the year 2011, with the merger of proposed aggregated courts. Moreover, we make use of the bootstrapping methodology to account for measurement errors. The preliminary results show small efficiency gains from the proposed mergers. JEL codes: D24, K41, K49 Keywords: first instance courts efficiency; non-parametric methods. ∗ Corresponding author. 1. Introduction In most of the countries in the world the role of an efficient judiciary in the achievement of economic and social growth has been widely acknowledged. An efficient judicial system is certain, works out cases in a reasonable time frame and it is accessible to the public (Dakolias, 2014). Recently, CEPEJ (2013) has highlighted the overall low performance of the Italian judicial system despite the several reforms of civil sector aiming to achieve a quicker, less costly and more efficient judicial services1. However, the proposed goal is still far from being reached. The general Attorney of court of cassation, in his 2013 report on the judicial system, describes the necessary goals to be achieved in order to improve the efficiency of Italian system (Ministero della Giustizia, 2013). In particular, the main goals are the rational distribution of judicial districts in Italy; the reform of the stiff and bureaucratic rules regulating the use of financial resources; the introduction of tools able to filter the relevance and importance of litigations before reaching the court or to solve the cases before reaching the court (the attempt at conciliation is mandatory for several kinds of cases). Regardless of the importance of an efficient judiciary, the number of empirical works investigating the performance of the Italian judicial system is still surprisingly low (Marselli and Vannini, 2004; Coviello et al., 2009; Finocchiaro Castro and Guccio, 2012). The lack of research may be due to the difficulty in gaining data for the resources used to supply civil judicial services at the court level in Italy. However, this is a common problem to several civil justice systems (Dakolias, 2014; CEPEJ, 2013). Italian judicial reform is entering a new phase through the Italian Government’s proposal (Decree n. 155/2012) of new jurisdiction design of first instance courts through merger of 31 courts and the abolition of 220 local courthouses. Two aspects of merger analysis are the operational cost savings and the potential production efficiency gains. This paper concentrates on the second aspect and uses a nonparametric methodology to assess the potential effect of these mergers and whether the mergers are efficiency enhancing. For this purpose, we run our efficiency analysis on 160 Italian first instance courts for the year 2011. In details, our analysis refers to 1 In 2010, a tax on incoming cases has been established leading to a clearance rate of over 100%. In other words, in Italy there were more settled cases than new cases for the year (CEPEJ, 2013). the activity of first instance courts (Tribunali ordinari) falling into the areas over which the judicial counties (Circondario di Tribunale Ordinario) have the competence. We empirically analyse potential gains from mergers in first instance courts using the non-parametric Data Envelopment Analysis (DEA) with bias corrections by means of bootstrapping. We apply a methodology developed by Bogetoft and Wang (2005) to investigate whether these proposed mergers in the Italian first instance courts promise potential efficiency enhancement. Bogetoft and Wang’s (2005) methodology is a non-parametric measurement of the potential gains from mergers, and we use it to compare two different comparative static equilibria: the existing organisational structure of first instance courts and the new jurisdiction design, in which the technical efficiency with which observed inputs are transformed to outputs is evaluated relative to the existing structure. Moreover, despite the increased use of non-parametric frontier to measure the efficiency of judicial systems, there are few studies that make use of the bootstrapping methodology to account for measurement errors in its estimates (Finocchiaro Castro and Guccio, 2012). In fact, the bootstrapping makes possible to run sensitivity analyses on efficiency scores and scaling indicators (Simar and Wilson, 1998 and 2000). Hence, the model that is applied in determining the DEA production frontier in this paper is the one outlined by Simar and Wilson, (1998, 2000). This enables us, to overcome some traditional DEA limitations and to provide a robustness check of our findings. More in particular, we employ a consistent bootstrap estimation procedure (Simar and Wilson, 1998), to obtain the sampling distribution of the efficiency scores and derive bias corrected scores. Our first results report the high levels of inefficiency reached by the first instance courts in Italy. Whereas inefficiency seems to be higher in the South of Italy than in the rest of the country, the huge civil caseload appears as a factor able to explain the inefficiency levels of first instance courts. Finally, the preliminary findings show considerable efficiency gains from the proposed mergers. The analysis develops as it follows: in Section 2 a description of the reform of first instance courts jurisdiction design in Italy is offered. Section 3 briefly reviews the literature, whereas Section 4 describes the methodology and the data used. Section 5 provides technical efficiency estimates and Section 6 offers some concluding remarks. 2. The reform of first instance courts jurisdiction design in Italy Several attempts at reforming judicial system in order to achieve efficiency gains have been put forward in Italy in the last decades. However, the goal seems still far to be reached. The most recent reform of judicial system focused on the positive effects obtainable by designing new jurisdiction for first instance courts and local courthouses. The Italian Government has issued two decrees (n.155/2012 and n.156/2012) to put into practice the legislative decree n.148/2012. The decree n.155/2012 refers to the design of new jurisdiction for first instance courts and local courthouses, whereas the decree n.156/2012 deals with the reform of justice of the peace offices (that will not be considered in our analysis). The main goals of the reform were the reduction of first instance courts, their optimal distribution in order to cut public expenditure and achieve efficiency gains, the optimal allocation of available resources with respect to workloads. The reform posed two constraints to the optimal redistribution of first instance courts: there should remain one first instance court in each provincial capital and at least three first instance courts and relative public prosecutor’s offices in each judicial district according to the provincial capital existing on June 2011. On this basis, 107 out of the 1662 first instance courts are sited in the provincial capitals. Thus, the merging procedure suggested by the decree n.155/2012 has been applied on the remaining 59 first instance courts only. It has to be noted that the above-mentioned constraints were not in force for the 220 local courthouses that have been all included in the merging procedure. The methodology applied to choose among the 59 first instance courts those to be merged was the following. First, the 107 first instance courts sited in the provincial capitals have been used as benchmark. However, five of them have been excluded from this analysis because they are located in metropolitan areas (Rome, Milan, Naples, Turin, Palermo), leaving 102 first instance courts as benchmarks. To do so, it have been computed the statistic averages of four indexes: office workload, population served, judges productivity, and dimension of the offices (number of judges) and they have been sequentially applied to select the first instance courts, among the 59 already chosen, below the benchmarks. The application of this methodology has shown that merging has been 2 However the court of Giugliano, established in 1999, has not been in service yet. necessary for the smallest offices among the least productive. The outcome of the reform should be the creation of new offices to be placed in the most productive class according to the different dimensions. The methodology to be applied to local courthouses closely resembles that used for first instance courts. According to the above-mentioned methodology, the first version of the Decree n.155/2012 required the suppression of 37 first instance courts and all the local courthouses. However, the changes due to the Decree n.155/2012 with respect to the first version of the reform of the distribution and the consistency of courts in the Italian territory are given by the maintaining the six courts previously to be suppressed sited in areas characterised by high levels of criminality - e.g. Sicily (Caltagirone and Sciacca), Calabria (Castrovillari, Lamezia Terme and Paola) and Lazio (Cassino). Moreover, the Costitutional Court has stopped the suppression of Urbino's first instance court (decision n.237/2013) because the city of Urbino, like Pesaro, is provincial capital of the province of Pesaro and Urbino. Hence the number of suppressed courts has been decreased from 37 to 303, whereas all the 220 local courthouses are still to be abolished. The reform is in effect since September 2013. Table 1 shows the outcome of merging procedure listing the Judicial District, the merged courts and the resulting courts. The procedure has involved 17 JudiciaDistricts out of the 27 existing before the reform. Most of the mergers have been done within the same District, with the only exception being the first instance court of Lago Negro that has involved both Judicial Districts of Potenza and Salerno, whereas the District with the highest number of mergers has been the one of Turin. Also Table 1 reports that, in most of the cases, the merging procedure involved two first instance courts, whereas in few cases the first instance courts merged have been three. Overall, the reform that has been conducted on 55 first instance courts has lead to the suppression of 30 'old' first instance courts and to the creation of 25 'new' ones. Thus, it has affected a large part of the courts with significant potential effect on the Italian judicial system. 3 The final suppressed courts are: Alba, Aqui Terme, Ariano Irpino, Avezzano, Bassano del Grappa, Camerino, Casale Monferrato, Chiavari, Crema, Lanciano, Lucera, Melfi, Mistretta, Modica, Mondovì, Montepulciano, Nicosia, Orvieto, Pinerolo, Rossano, Sala Consilina, Saluzzo, Sanremo, Sant'Angelo dei Lombardi, Sulmona, Tolmezzo, Tortona, Vasto, Vigevano and Voghera Table 1 – Proposed mergers of Italian courts by Judicial District Judicial District Ancona Bari Brescia Caltanissetta Catania Catanzaro Firenze Genova Genova L’Aquila L’Aquila Messina Milano Napoli Napoli Perugia Potenza Salerno and Potenza Torino Torino Torino Torino Torino Trieste Venezia First instance courts merged Camerino, Macerata Foggia, Lucera Crema, Cremona Enna, Nicosia Modica, Ragusa Castrovillari, Rossano Montepulciano, Siena Chiavari, Genova Sanremo, Imperia Avezzano, L’Aquila, Sulmona Chieti, Lanciano, Vasto Mistretta, Patti Pavia, Vigevano, Voghera Ariano Irpino, Benevento Sant'Angelo dei Lombardi, Avellino Orvieto, Terni Melfi, Potenza Lagonegro, Sala Consilina Alba, Asti Acqui Terme, Alessandria, Tortona Casale Monferrato, Vercelli Cuneo, Modovì, Saluzzo Pinerolo, Torino Udine, Tolmezzo Bassano del Grappa, Vicenza New courts Macerata Foggia Cremona Enna Ragusa Castrovillari Siena Genova Imperia L’Aquila Chieti Patti Pavia Benevento Avellino Terni Potenza Lagonegro Asti Alessandria Vercelli Cuneo Torino Udine Vicenza Source: our computation on data provided by Ministero della Giustizia 3. Literature review In the last decade the estimation of judicial system efficiency has been the subject of many studies related to the evaluation of public sector performances. The beneficial effects of an efficient judicial system of economic growth and competition are well established in the literature (Mauro, 1995; Levine, 1998, Messick, 1999; Feld and Voigt, 2003). At the same time, the public-good nature of the judicial system poses some problems in optimally allocating the available resources to secure the access to all citizens and to provide the judicial service efficiently. On this matter, the CEPEJ (European Commission for the Efficiency of Justice) has recently undertaken an analysis of the functioning of the justice system in all European states to propose concrete solutions to improve fairness, quality and efficiency of justice in Europe. Focusing on the Italian situation, the 2013 CEPEJ report, on the one hand, shows that the human resources allocated to justice in Italy are close to those allocated by more efficient European countries (11 judges each 100,000 citizens in Italy, 10.7 in France and 10.2 in Spain). On the other hand, Italy appears at the end of the ranking for the length of civil judicial procedures (493 days in Italy, 270 in France and 260 in Spain), whereas Italy ranks first when we look at the numbers of lis pendens (more than 3.8 millions). The World Bank (2009) annually draws up the report Doing Business ranking countries also according to efficiency of judicial system measured as the length of civil judicial procedures. The 2009 report ranks Italy 156th out of 181 countries right below Angola, Gabon, Guinea and Sao Tome and above Gibuti, Liberia, Sri Lanka and Trinidad, whereas the last European country (Spain) ranks 54th. Considering the available resources, the weight of public spending for justice on the Italian balance changed from 1.22% in 2006 to 1% in 2009, corresponding to 7.56 billions. Thus, the Italian commission for the public spending review, in its final report, investigated the efficiency of the Italian justice system (Ministero dell’Economia, 2007a and 2007b). The main sources of inefficiency were found to be the presence of economies of scale, the delay in adopting new information and communication technologies to conduct the proceedings faster and how legal fees are determined especially for civil proceedings. On the same line of research, Antonelli and Marchesi (1999) point out that the dimension of the geographical areas of 72% of Italian judicial districts is sub-optimal (less than 20 judges) leaving room for relevant economies of scale. The authors suggest that the optimal dimension of judicial districts can be reached by putting small courts together according to some parameters derived from data analysis and supported by experts in public sector management. Moreover, higher efficiency can also be reached exploiting economies of specialisation and adopting better organisational schemes to increase the productivity of judges4. Surprisingly, few works have investigated the efficiency and the factors causing dysfunction of judicial systems from all over the world, mainly due to the lack or incompleteness of available data. However, the analysis of efficiency of judicial system poses other difficulties besides data availability. First, the courts can be seen as production units producing not just a single service but also a mix of different services (Marselli and Vannini, 2004). Second, the activity of the courts is 4 This solution cannot be applied to small court where the same judge often deals with both civil and criminal cases. characterised by low substitution rate between inputs such as judges, clerks and different kinds of courts (Marchesi, 2003). Finally, the public decision-maker can only vary the area under the control of a specific judicial district tailoring the caseload on the quality and quantity of the demand of justice originated by the territory (Antonelli and Marchesi, 1999). Given the above-mentioned difficulties, the technical efficiency of judiciary has been investigated mostly applying the DEA non-parametric technique5 that overcomes all the problematic assumptions required by a parametric production function based on parametric techniques. Lewin et al. (1982) study the efficiency of judicial districts of North Caroline, whereas Kittelsen and Føresund (1992) investigate the Norwegian courts of first instance. Tulkens (1993) looks at the system of judges of peace in Belgium and Pedraja-Chaparro and Salinas-Jiménez (1996) analyse the efficiency levels of administrative courts in Spain. More recently, Marselli and Vannini (2004) have investigated the efficiency Italian JDs looking at both civil and criminal cases. The authors find high levels of inefficiency mainly due to an excessive caseload that the caseload accumulated through years cannot be resolved by increasing the efficiency and, that some judicial districts are affected by strong variable returns to scale. Schneider (2005) focuses on the performance of German labour courts of appeal and shows that employing judges with Ph.D. increases the productivity although the Federal Labour Court more often overrules their decisions. The author also finds that courts employing judges with higher ex-ante promotion probabilities are less productive and write decision that are less often confirmed. Gorman and Ruggiero (2009) apply the DEA to the analysis of the impact of environmental variables on the efficiency of prosecutor offices in the United States, showing that prosecutor offices are more efficient in socio-economically disadvantaged counties. Finally, Finocchiaro Castro and Guccio (2012) employ the two-stage approach to investigate technical efficiency in Italian judicial districts by focusing on civil cases in 2006. The authors report that technical efficiency is explained by demand factors and that opportunistic behaviour from both claimants and lawyers negatively affects technical efficiency in Italian judicial districts. Other papers, not based on DEA technique, focus the attention on the role of 5 An exception is offered by Rosales-López (2008). The author investigates the performance of first instance courts in Spain and determines whether achieving low reversal rates and a high level of output are incompatible goals in the judiciary system applying parametric techniques. different factors in explaining the efficiency of the Italian judicial system. For instance, Coviello et al. (2009) show that the average efficiency depends on organisational features of judges’ activity. In details, a higher efficiency may be achieved if judges work on cases sequentially instead of starting a new case in parallel with others. Di Vita (2010) reports significant level of correlation between the average length of civil proceedings and the indicator of complexity of legal system. The author concludes that a relevant portion of resources seems to be dedicated to enforce the huge number of Italian laws leading to low efficiency of the judicial system. Finally some works (Sobbrio et al., 2009; Carmigniani and Giacomelli, 2010; Buonanno and Galizzi, 2010) raise the attention on the application of the supplierinduced-demand hypothesis to the analysis of determinants of judicial system. Their main common result is that the rising quantity of lawyers causes an increase in the number of unnecessary civil trials (due to asymmetric information, imperfect agency relation between lawyer and client, tougher competition and uniform minimum fees for service) lowering the efficiency of the judicial system. 4. Methods and data 4.1. Methodological framework Effective government service provision, such as judicial service, benefits from the support of rigorous measurement techniques. In this study, we focus on technical efficiency of Italian first instance courts (our Decision Making Units - DMUs), whose measurement requires the comparison between the actual performance of each DMU and the optimal performance of DMUs located on the relevant frontier (the best practice frontier). This approach is based on the efficiency measures proposed by Koopmans (1951) and Debreu (1951) and empirically applied by Farrell (1957). Two main analytical approaches are available to estimate efficiency frontiers: parametric and non-parametric.6 In details, we apply the non-parametric frontier method developed by Charnes et al. (1978) that generalized Farrell’s single input/output measure into a multipleinput/multiple-output technique. The aim of this approach is to measure productive efficiency through the estimation of a frontier envelopment surface for all DMUs by 6 For a more extensive discussion, see Cooper et al. (2007) and Fried et al. (2008). using linear programming techniques. By constructing envelopment unitary isoquants corresponding to comparable DMUs across different situations, DEA identifies as productive benchmarks those DMUs that exhibit the lowest technical coefficients, i.e. the lowest amount of inputs to produce one unit of output. In doing so, DEA allows for the identification of best practices and for the comparison of each DMU with the best possible performance among the peers, rather than just with the average. Once the reference frontiers have been defined, it is possible to assess the potential efficiency improvements available to inefficient DMUs if they were producing according to the best practice of their benchmark peers. From an equivalent perspective, these estimates identify the necessary changes that each DMU needs to undertake in order to reach the efficiency level of the most successful DMU. Following the literature reviewed in the previous section we employ an outputoriented approach7 In order to facilitate the interpretation of the results in the next sections, it is useful to recall that in the output-oriented DEA model, considering n DMUs to be evaluated, an efficiency score θi is calculated for each DMU by solving the following program, for i=1,…., n, in the case of constant returns to scale (CRS): where xi and yi are, respectively, the input and output of i-th DMU; X is the matrix of inputs and Y is the matrix of outputs of the sample; λ is a n×1 vector of weights which allows to obtain a convex combination between inputs and outputs. Solving (1), DMUs with an efficiency score equal to one are located on the frontier and therefore their outputs cannot be further expanded without a corresponding increase in inputs8. Banker et al. (1984) modified the model (1) to account for variable returns to 7 From an output-oriented perspective efficiency is defined as the ratio of a DMU’s observed output to the maximum output, which could be achieved given its input levels (Farrell, 1957). 8 We assume an output-oriented model to maximize the outputs that could be produced given the inputs. Moreover, we assume a Shephard (1970) output-oriented distance function and, consequently, scale (VRS) by adding the convexity constraint: eλ=1, where e is a row vector with all elements unity, which allows to distinguish between Technical Efficiency (TE) and Scale Efficiency (SE). This change is crucial for our merge analysis given that VRS means that there are likely to be disadvantages of being either too small or too large. Based on the estimated DEA frontier, it is possible to analyse hypothetical cases of horizontal integration between first instance courts. In fact, Bogetoft and Wang (2005) propose a simple direct pooling of the inputs and outputs set used by individual first instance courts to be merged. For the analysis of hypothetical cases of horizontal integration, Bogetoft and Wang (2005) use the technology set (1) estimated before any merger as the reference set. Then, the authors decompose efficiency gains from DMU mergers into technical efficiency gains, synergies from joint operation, and size gains. Doing so we can measure both the overall potential gains from mergers and the separate role of the three effects on Italian Government’s proposal (Decree n. 155/2012) of new jurisdiction design of first instance court. As mentioned above, the deterministic nature of non-parametric methods has caused the traditional literature to describe them as non-statistical methods. Moreover, DEA estimators have received some criticisms because they rely on extreme points and may be very sensitive to data selection, aggregation, model specification, and data errors. However, a series of recent developments made it possible to determine statistical properties of non-parametric frontier estimators in a statistical model (Simar and Wilson, 2008). Nowadays, statistical inference based on non-parametric frontier approaches in measuring the economic efficiency is available basically by using asymptotic sampling distributions or by using bootstrap (Simar and Wilson, 2008). To account for DEA traditional limitations, which do not allow for any statistical inference and measurement error, Simar and Wilson (1998, 2000) introduced a bootstrapping methodology to determine the statistical properties of DEA estimators. The idea underlying the bootstrap procedure is to approximate the sampling distributions of efficiency scores by simulating their Data Generating Process - DGP (Simar and Wilson, 2008) 9. efficiency scores assume values between zero and one that is the reciprocal of Farrell (1957) distance function. 9 Some major issues remain regarding the use of asymptotic results and bootstrap: first, the high sensitivity of non-parametric approaches to extreme value and outliers and, second, the way to allow stochastic noises in non-parametric frontiers. Alternative approaches provide robust measures of efficiency at extreme data points based on partial frontiers and the resulting partial efficiency scores. A The model that is applied in determining the DEA production frontier in this paper is the one outlined by Simar and Wilson (1998, 2000) that enables us to overcome some traditional DEA limitations and to provide a robustness check of our findings. In particular, we employ a consistent bootstrap estimation procedure (Simar and Wilson, 1998) to obtain the sampling distribution of the efficiency scores and derive bias corrected scores. 4.2. Data In Italy, the administration of justice is articulate into judicial districts (Distretto di Corte di Appello) and judicial counties (Circondario di Tribunale Ordinario). The 29 Judicial districts are usually located in the main town of the region, although the most populated regions have two, whereas the judicial counties are 16510 and are distributed in the territory. In the judicial counties, courts of first instance are organised according to their field of specialization and may sub-divided into different benches. However, for statistical purpose, the data on resources (mainly judges and administrative staff) of judicial counties are collected at aggregate level only, whereas data on judicial counties activities are disaggregate in civil and penal services. This poses a severe problem to the measurement of the efficiency in judicial sector. Only in some cases, it is possible to obtain estimates able to disaggregate the data on the resources adopted to provide civil and penal services. For instance Carmignani and Giacomelli (2009) estimate the number of judges and administrative staff at district level employing data achieved by the self-governing body of ordinary judges (Consiglio Superiore della Magistratura). However, such computation poses sever difficulties and large likelihood of systematic bias. Our analysis refers to the activity of 165 first instance courts (Circondario di Tribunale Ordinario) in Italy for the year 2011The dataset employed in our empirical analysis has been obtained from Italian Department of Justice (Ministero della Giustizia - Direzione Generale di Statistica). Our model specifications have been limited by data availability, e.g., the dataset does not include cost and input factor prices. Thus we examine only the first instance detailed survey of these approaches can be found in Simar and Wilson (2008). See also Wilson (2012) for a discussion on these approaches and for a proposed extension of order-m estimator obtained by Cazals et al. (2002). 10 However the court of Giugliano, established in 1999, has not been in service yet. courts’ technical efficiency. Table 2 reports all the variables employed in efficiency analysis as well as their descriptive statistics. Specifically, our analysis includes the number of judges (JUDGES) administrative staff (ADM_STAFF), size of the caseload - both civil (C_LOAD_CIVIL) and criminal (C_LOAD_CRIMINAL) cases as inputs and . In our computation the caseload is the sum of the number of filed cases during the year and the number of pending cases at the beginning of that year. Regarding the output we employ the number of civil and criminal cases finished during a specific period (RES_CIVIL_CASES; RES_CRIMINAL_CASES) without distinguishing between cases resolved through the full legal process and other resolved cases. Table 2 – Summary statistics of the variables used in the DEA models for the Italian courts of first instance – year 2011 Variables Obs Mean Std. Dev. Min Max JUDGES 165 30.68 48.81 6.00 379.00 ADM_STAFF 165 99.36 136.96 18.00 1198.00 C_LOAD_CIVIL 165 37138.56 53577.68 2853.00 409190.00 C_LOAD_CRIMINAL 165 15373.67 18062.76 793.00 136979.00 RES_CIVIL_CASES 165 16387.03 24706.64 1235.00 199304.00 RES_CRIMINAL_CASES 165 7659.07 9452.46 427.00 65268.00 Source: our computation on data provided by Ministero della Giustizia - Direzione Generale di Statistica From the analysis of the data it appears that the first instance courts differ considerably in terms of personnel - ranging from 6 to 379 judges and from 18 to 1,198 members of administrative staff – of both civil and criminal caseload and, in the number of resolved cases. Table 3 shows the inputs and the outputs employed in the four different models we have estimated. Table 3 – The estimated models Variable Mod_1 Mod_2 JUDGES ♦ ♦ ADM_STAFF ♦ ♦ inputs C_LOAD_CIVIL ♦ C_LOAD_CRIMINAL ♦ outputs RES_CIVIL_CASES ♦ ♦ RES_CRIMINAL_CASES ♦ ♦ Source: our elaboration 5. Results and Discussion In this Section, we first calculate average efficiency estimates for the unmerged courts and analyse the inefficiency as well as the impact of model specification and bootstrap bias correction. Second, we present merger gains under constant and variable returns to scale. 5.1 Benchmark analysis Here we report the technical efficiency scores achieved by the different production function specifications as shown in Table 3. We choose the output orientation so that output efficiency is measured for a given level of input and use a Shephard (1970) output-oriented distance function. Consequently, efficiency scores assume values between zero and one, which is the reciprocal of Farrell (1957) distance function. The output orientation is justified by very large back log of cases of the Italian courts that calls for higher case resolution rates, given the existing staff levels. We now evaluate the best possible input-output specifications. The first inputoutput specification with judges (JUDGES) and administrative staff (ADM_STAFF) as a inputs and the number of civil and criminal cases finished during a specific period (RES_CIVIL_CASES; RES_CRIMINAL_CASES) is the most common because the variables incorporate the main function of the courts. In comparison to the second input-output specification including both civil (C_LOAD_CIVIL) and criminal (C_LOAD_CRIMINAL) cases it takes into accounts the different condition of the demand of justice in which courts operate. Thus, the focus of this model on the demand side is justified in an economic perspective. More in general the literature investigating the efficiency of justice services, reviewed in section 2, has mainly adopted the one-stage-production model. Under this approach, it is assumed that the justice institution disposes of a set of resources (e.g. judges, support staff equipment, expenditure, etc.) used exclusively to provide judicial services (basically the resolution of disputes) to the litigants. In such context, each DMU controls both the outputs, which are mainly related to the level of services provided to the litigants, and the inputs, which are related to the level of resources used for that purpose. Excluding those variables connected to the operating environment, the efficiency analysis is, thus, confined to managerial aspects. However, there are cases in which it might be important to consider non-discretionary variables in order to take into account the differences among justice institutions in the operating environment.11 In what follows, we employ the one-stage approach considering both discretionary and non-discretionary inputs, since it allows for the potential identification of the effects of operating environment in the production system12. Moreover, for comparison purpose, we also use the subsample of first instance courts excluding the courts located in some metropolitan areas (Rome, Milan, Napoli)13. Table 4 reports the benchmark analysis of the whole sample of 165 first instance Italian courts in order to indicate the relative performance of each of the different courts. Table 4 - The descriptive statistics of the models outcome Sample Obs. CRS Average St. dev. VRS Min Max Average St. dev. Min Max Model 1 All sample 165 0.6332 0.1676 0.2324 1.0000 0.7124 0.1807 0.2332 1.0000 North 64 0.6978 0.1490 0.4294 1.0000 0.7725 0.1436 0.4786 1.0000 Centre 38 0.6713 0.1380 0.3739 1.0000 0.7782 0.1327 0.5348 1.0000 South 63 0.5445 0.1648 0.2324 1.0000 0.6115 0.1953 0.2332 1.0000 Model 2 11 More in general, the one-stage-production model might directly include uncontrollable variables in its linear functions, along with traditional inputs and outputs use of the capability of DEA to accommodate multiple variables (Banker and Morey, 1986). From this approach, the DMU can decide on some controllable factors internal to production activities, while the impact of the uncontrollable factors is out of the control of the DMU. Conversely, studies that have constructed models using controllable factors only, implicitly assume that all the inefficiencies of DMUs are caused by bad management and could underestimate the evaluation of those DMUs. To take into account the impact of the uncontrollable factors in one-stage framework, Lewin et al., (1982) and Schneider (2005) have used the courts' caseload as a non-discretionary input. A different point of view is provided by the socalled two-stage approach, which starts with a standard DEA model based on traditional inputs and outputs in the first stage, and regresses11 the efficiency scores of the first stage against a set of selected uncontrollable variables in the second stage (Finocchiaro Castro and Guccio, 2012). 12 However, the efficiency estimates basically do not change also in the case in which we employ Banker and Morey, (1986)s’ algorithm since we use an output oriented approach. 13 The district of Naples represents a special case in which all the local courthouses have been unified with the district of Giugliano (not in service yet) that has been renamed as Court of Northern Naples. We included into the analysis Turin and Palermo because of the specific characteristics of the two districts. All sample 165 0.7923 0.1427 0.4721 1.0000 0.8285 0.1455 0.5021 1.0000 North 64 0.8805 0.0934 0.5832 1.0000 0.9182 0.0819 0.6907 1.0000 Centre 38 0.8115 0.0940 0.6407 1.0000 0.8557 0.0988 0.6448 1.0000 South 63 0.6911 0.1452 0.4721 1.0000 0.7210 0.1511 0.5021 1.0000 Source: our elaboration on data provided by Ministero della Giustizia - Direzione Generale di Statistica The results reported in Table 4 support the common perception of the inefficiency as a major problem of the Italian first instance courts and that it varies significantly across the country. In details, the average aggregate technical efficiency score of 63.32%, in the Model 1 with constant returns to scale (CCR), indicates that the DMUs are, on average, largely technically inefficient in the provision of judicial services. The quite large standard deviation as well as the large difference between the minimum and maximum efficiency scores indicates, however, that there are considerable differences in the aggregate technical efficiency of Italian First instance courts. Table 4 also shows the efficiency scores of sub-samples obtained according to years and geographical macro areas in the country. Strong differences among DMUs exist in relation with the geographical macro areas (North, Centre and South). In all models and with different scale assumptions, the result confirms the geographical gap between the Northern and Southern areas. Table 4 includes also estimates for the case of variable returns to scale (VRS), which show results generally overlapping with those under constant returns to scale (CRS). In the lower part of Table 4, we show estimates for the models with uncontrollable inputs, where caseload - both civil (C_LOAD_CIVIL) and criminal (C_LOAD_CRIMINAL) - is considered an input external to managerial control that affects technical efficiency though. As expected, average levels of efficiency of DMUs in our sample increase when we consider such an input, reaching the efficiency scores of 79.23% in the Model 2 with constant returns to scale (CCR). However, observation of the score distribution in subsamples reveals regularities with respect to the previous models. Given the importance of scale efficiency for our analysis, Table 5 shows the distribution of returns to scale of the sample. It can be noted that in Model 1 more than 75% of first instance courts have increasing returns to scale, whereas only 13% of them have decreasing returns to scale. The results change significantly when we consider Model 2, where considering the caseload the 43% of first instance courts show diseconomies of scale, being the productive scale too high. Tables 6 and 7 report no changes when we exclude, from the analysis the first instance courts belonging to the metropolitan areas of Milano, Rome and Naples respectively. Table 5 – Distribution of returns to scale Mod_1 Returns to scale Mod_2 Obs. % Obs. % 124 75.15 61 36.97 EFF_SCALE 19 11.51 33 20.00 DRS 22 13.34 71 43.03 Total 165 100.00 165 100.00% IRS Source: our elaboration on data provided by Ministero della Giustizia - Direzione Generale di Statistica Table 6 - The descriptive statistics of the models outcome for subsample excluding courts in metropolitan area Sample Obs. CRS Average St. dev. VRS Min Max Average St. dev. Min Max Model 1 All sample 162 0.6326 0.1690 0.2324 1.0000 0.7095 0.1792 0.2332 1.0000 North 63 0.6976 0.1502 0.4294 1.0000 0.7726 0.1442 0.4786 1.0000 Centre 37 0.6730 0.1395 0.3739 1.0000 0.7736 0.1301 0.5348 1.0000 South 62 0.5426 0.1654 0.2324 1.0000 0.6073 0.1909 0.2332 1.0000 All sample 162 0.7916 0.1436 0.4721 1.0000 0.8257 0.1448 0.5021 1.0000 North 63 0.8799 0.0940 0.5832 1.0000 0.9169 0.0819 0.6907 1.0000 Centre 37 0.8106 0.0952 0.6407 1.0000 0.8518 0.0971 0.6448 1.0000 South 62 0.6904 0.1463 0.4721 1.0000 0.7173 0.1482 0.5021 1.0000 Model 2 Source: our elaboration on data provided by Ministero della Giustizia - Direzione Generale di Statistica Table 7 – Distribution of returns to scale for subsample excluding courts in metropolitan area Returns to scale Mod_1 Mod_2 Obs. % Obs. % 124 76.54 61 37.65 EFF_SCALE 17 10.49 30 18.52 DRS 21 12.96 71 43.83 Total 165 100.00 165 100.00% IRS Source: our elaboration on data provided by Ministero della Giustizia - Direzione Generale di Statistica These results are relevant especially with respect to the effects of nondiscretionary variables in explaining efficiency variation. Moreover, not taking into account the caseload in the merging procedure may have relevant effects on the efficiency gains to be achieved with the reform. Finally, in order to test the sensitivity of the efficiency estimates relative to the variables used we employ the biased corrected efficiency scores. In fact, the DEA efficiency estimate measures performance relative to an estimation of the true and unobservable production frontiers and provides point estimates of performance. Since estimates on the frontier are based on finite samples, DEA measures, based on these estimates, are subject to sampling variation of the frontier. To address this problem, we implement a bootstrap procedure, with 2,000 bootstrap draws as described by Simar and Wilson (1998), to correct the bias in DEA estimators and obtain their confidence intervals. Table 8 reports the average values of technical efficiency at DMU level, estimated with different models under CRS and VRS assumption. The reported results show that, from the perspective of sensitivity analysis, only the efficiency estimate in Model 1 under CRS assumption are quite robust with respect to sampling variation since there are only small differences due to bootstrapping efficiency estimates. Under VRS assumption the bootstrapped bias correction has relatively strong effects on efficiency estimates. Table 8 – Uncorrected and bias corrected estimate Models CRS Bias corrected CRS estimate Mod 1 VRS Bias corrected VRS estimate CRS Mod 2 Bias corrected CRS estimate VRS Bias corrected VRS estimate Obs Mean Std. Dev. Min Max 165 0.6332 0.1676 0.2324 1.0000 165 0.5947 0.1549 0.2192 0.9234 165 0.7124 0.1807 0.2332 1.0000 165 0.6335 0.1475 0.2133 0.9440 165 0.7923 0.1427 0.4721 1.0000 165 0.7342 0.1258 0.4419 0.9636 165 0.8285 0.1455 0.5021 1.0000 165 0.7519 0.1210 0.4720 0.9366 Source: our elaboration on data provided by Ministero della Giustizia - Direzione Generale di Statistica In order to test more thoroughly the efficiency scores before and after the biased correction between the four models we used kernel density estimates of the efficiency scores that rely on the reflection method (Simar and Wilson, 2008). In such a way we are able to avoid the problems of bias and inconsistency at the boundary of support. In Figures 2 and 3, we report the univariate kernel smoothing distribution (Wand and Jones, 1995) and the reflection method to determine densities for the performance estimates, respectively under CRS and VRS assumption. The criterion for bandwidth selection follows the plug-in method proposed by Sheather and Jones (1991). The kernel density functions, reported in Figures 2 and 3, allow us to confirm the abovementioned results. The specification of returns to scale of the reference technology is important to evaluate the merger possibilities because by definition a merged group of courts is a rescaling of the individual resources in the group. To check the importance of economies of scale, we perform the Banker (1996) test for both Models and the results show that we can reject the null hypothesis of CRS at any conventional level of significance14. This result is not surprising since the courts in our sample vary considerably in size, and size can be an important factor in determining the organization and the production of services by courts. However, Bogetoft and Wang (2005) demonstrate that only under CRS reference technology there are the necessary and sufficient conditions to ensure a feasible solution to the DEA linear programme. In fact, under VRS reference technology, these conditions may not hold and it is possible that there will fail to be a feasible solution to the linear programme. This suggests to use the CRS technology as reference point to evaluate the potential efficiency gain of mergers. 3 2 Density 1.5 0 0 .5 1 1 Density 2 2.5 3 Figure 2 – Kernel densities estimates of the CRS and CRS bias corrected scores distribution for the estimated models .2 .4 .6 .8 Model 1 - CRS density estimate 1 .4 .6 .8 Model 2 - density estimates (CRS) 1 Eff scores - CRS density estimate Eff scores - density estimate CRS Bias corrected eff scores - CRS density estimate Bias corr Eff scores - density estimates CRS 1.2 Notes: Plots show respectively the Model 1 and Model 2 kernel estimates under CRS assumption. CRS bias corrected scores estimated with the procedure proposed by Simar and Wilson, (1998). Univariate kernel smoothing distribution (Wand and Jones, 1995), estimated through reflection method. The criterion for bandwidth selection followed the plug-in method proposed by Sheater and Jones (1991). Source: our elaboration on data provided by Ministero della Giustizia - Direzione Generale di Statistica 14 Results are available upon request. 3 2 Density 1.5 0 0 .5 1 1 Density 2 2.5 4 Figure 3 – Kernel densities estimates of the VRS and VRS bias corrected scores distribution for the estimated models 0 .2 .4 .6 .8 Model 1 - VRS density estimate 1 .2 .4 .6 .8 Model 2 - VRS density estimate Eff scores - VRS density estimate Eff. Scores - VRS density estimate Bias corrected eff scores - VRS density estimate Bias-Corrected eff scores - VRS density estimate 1 Notes: Plots show respectively the Model 1 and Model 2 kernel estimates under VRS assumption. VRS bias corrected scores estimated with the procedure proposed by Simar and Wilson, (1998). Univariate kernel smoothing distribution (Wand and Jones, 1995), estimated through reflection method. The criterion for bandwidth selection followed the plug-in method proposed by Sheater and Jones (1991). Source: our elaboration on data provided by Ministero della Giustizia - Direzione Generale di Statistica 5.2 The efficiency gains of the courts mergers In this section, we present our estimates of the potential gains from mergers and our decompositions of the efficiency gains. As above-mentioned, we apply the methodology proposed by Bogetoft and Wang (2005) to estimate the overall potential gain from our sample and to decompose the overall potential gain into constituent components. In particular the authors suggest a decomposition of the overall potential gain merger efficiency into three components: technical efficiency gains; synergies from joint operation; and size gains. The overall potential efficiency gains (EJ) is the simple efficiency evaluation of a hypothetical DMU using the sum of inputs of the pre-merger DMUs to produce the sum of the pre-merger outputs. A merger is assumed to be beneficial for EJ < 1. (e.g. a value of EJ = 0.9 indicates a potential for output increasing of 10% through merging the DMUs). For EJ > 1, a merger is assumed to have a negative impact on efficiency. However the potential overall gains (EJ) from merging still include inefficiencies of the individual DMUs from before merging that cannot be attributed to a merger. To correct the overall potential gains from merging we need to project the individual DMUs into the efficient pre-merger DEA frontier using the efficiency scores of the individual DMUs. The performance measure E*J represents the corrected overall potential gains from merging. As before, a merger is evaluated as being beneficial for E*J < 1. For the previous consideration it is more meaningful to represent the potential gains from merger by the corrected E*J. We turn now to investigate the efficiency gains of the mergers and their decomposition into technical efficiency effects (or learning effects), synergies from joint operation (or scope) effects, and scale effects. We report each of these with respect to the CRS reference technology since we observed that they represent a reference point of the organizational structure and can therefore be regarded as a benchmark in evaluation of efficiency gain of proposed mergers. We start the analysis looking at the efficiency of courts involved in the merging procedure. As described in Section 2, the courts under analysis have been 55 of which 30 have been suppressed and merged into 25 new first instance courts. Table 9 reports the efficiency levels of the models presented in paragraph 5.1 distinguishing merged from not merged courts. It can be noted that, under the CRS assumption, the merged courts have lower average efficiency levels than not merged ones, leading to potential higher efficiency gains. This result holds for both Models. Differently, under VRS assumption, the differences in efficiency levels between the two groups of courts are smaller. In fact, Model 2 does not report any significant difference between merged and not merged courts. Table 9 - The descriptive statistics of the models outcome Sample Obs. CRS VRS Average St. dev. Min Max Average St. dev. Min Max Model 1 All sample 165 0.6332 0.1676 0.2324 1.0000 0.7124 0.1807 0.2332 1.0000 Not merged 110 0.6562 0.1686 0.2324 1.0000 0.7078 0.1812 0.2332 1.0000 Merged 55 0.5872 0.1571 0.2773 1.0000 0.7215 0.1809 0.3498 1.0000 Model 2 All sample 165 0.7923 0.1427 0.4721 1.0000 0.8285 0.1455 0.5021 1.0000 Not merged 110 0.7964 0.1392 0.4973 1.0000 0.8285 0.1411 0.5021 1.0000 Merged 55 0.7840 0.1505 0.4721 1.0000 0.8286 0.1552 0.5035 1.0000 Source: our elaboration on data provided by Ministero della Giustizia - Direzione Generale di Statistica In this preliminary assessment we calculate the overall potential merger effects for CRS absent non-discretionary input (Model 1). In Table 10 we report the merger efficiency gains derived from our sample. The potential gain from each merger is indicated by the difference between unity and the relevant number in each column. Table 10 - Efficiency scores and decomposition for proposed court mergers (CRS), by Judicial District New courts First instance courts merged Overall potential Eff. Gain Individual technical efficiency gain Learning effects Scope effect Size effect Macerata Camerino, Macerata 0.7458 1.0000 0.7458 1.0000 1.0000 Foggia Foggia, Lucera 0.7708 0.9975 0.7727 0.9975 1.0000 Cremona Crema, Cremona 0.6783 0.9577 0.7083 0.9577 1.0000 Enna Enna, Nicosia 0.3836 0.9965 0.3850 0.9965 1.0000 Ragusa Modica, Ragusa 0.5204 1.0000 0.5204 1.0000 1.0000 Castrovillari Castrovillari, Rossano 0.4075 0.9817 0.4151 0.9817 1.0000 Siena Montepulciano, Siena 0.5304 1.0000 0.5304 1.0000 1.0000 Genova Chiavari, Genova 0.4517 0.9891 0.4567 0.9891 1.0000 Imperia Sanremo, Imperia 0.6134 0.9619 0.6377 0.9619 1.0000 L’Aquila Avezzano, L’Aquila, Sulmona 0.5704 1.0000 0.5704 1.0000 1.0000 Chieti Chieti, Lanciano, Vasto 0.7070 1.0000 0.7070 1.0000 1.0000 Patti Mistretta, Patti 0.5677 0.8977 0.6324 0.8977 1.0000 Pavia Pavia, Vigevano, Voghera 0.5774 0.9663 0.5976 0.9663 1.0000 Benevento Ariano Irpino, Benevento 0.8011 0.8939 0.8962 0.8939 1.0000 Avellino 0.6495 0.9960 0.6521 0.9960 1.0000 Terni Sant'Angelo dei Lombardi, Avellino Orvieto, Terni 0.5580 1.0000 0.5580 1.0000 1.0000 Potenza Melfi, Potenza 0.4380 1.0000 0.4380 1.0000 1.0000 Lagonegro Lagonegro, Sala Consilina 0.4477 0.9586 0.4670 0.9586 1.0000 Asti Alba, Asti 0.6551 0.9666 0.6777 0.9666 1.0000 Alessandria 0.5662 0.9239 0.6128 0.9239 1.0000 Cuneo Acqui Terme, Alessandria, Tortona Cuneo, Modovì, Saluzzo 0.4759 0.9483 0.5018 0.9483 1.0000 Torino Pinerolo, Torino 0.6317 1.0000 0.6317 1.0000 1.0000 Vercelli Casale Monferrato, Vercelli 0.7067 1.0000 0.7067 1.0000 1.0000 Udine Udine, Tolmezzo 0.6425 0.9987 0.6433 0.9987 1.0000 Vicenza Bassano del Grappa, Vicenza 0.7496 1.0000 0.7496 1.0000 1.0000 Mean efficiency 0.5939 0.9774 0.6086 0.9774 1.0000 0.0226 0.0000 Average efficiency gain 0.4061 0.0226 0.3914 Source: our elaboration on data provided by Ministero della Giustizia - Direzione Generale di Statistica The first column reports the potential overall gains (EJ), whereas the second column reports the corrected overall potential gains from merging (E*J). In all cases, a merger between the courts would be beneficial when looking at the potential overall gains EJ. However, since those results still include the individual inefficiencies within courts before merging, we must consider the projections of the individual courts and calculate the corrected potential gains E*J. The merger gains drop down dramatically after correcting for individual inefficiencies. On average, we find low potential merger gains of 2.26%. In Table 10 after calculating overall gains from merging, we provide the decomposition into the technical efficiency effects (or learning effects), synergies from joint operation (or scope) effects, and scale effects. On average, around 39% of the overall merger gains EJ could be realized by improving efficiency within the individual courts. Thus, significant potentials for efficiency increase arising from a better management in the individual production plans of the different courts. Such efficiency improvement potentials are usually not attributable to a merger since efficiency could be improved by, for example, sharing best practices between individual courts. On average, less than 3% of the efficiency could be gained by reallocating the inputs in the integrated courts. The scope (or synergy) effect thus inhibits the weak potential for efficiency increases. We can further only find weak scale effects for all merger cases. Considering the median, there are already no efficiency gains from an increase in courts size. However, some limitations of our results have to be noted. First, the reform under consideration suggests a merging procedure that should produce a reallocation of input in an efficient way and not an aggregation of first instance courts keeping constant the total amount of human resources. The available data, unfortunately, do not let us investigate the effects of a potential reallocation of input as suggested by the reform. Second, when checking the efficiency gains from merging procedure we do not consider all the remaining estimated models described in paragraph 5.1 and we also do not study the effects of caseload on efficiency gains. Finally, we do not account for potential bias of efficiency scores and we do not perform estimation with bootstrapping procedure when considering the effects of merging. 6. Conclusions In this paper, by using DEA technique and focusing on the performance of 165 Italian first instance courts in the year 2011, we found evidence that there is considerable scope for efficiency improves in judicial services. The empirical analysis reports higher level of inefficiency across the country. To the best of our knowledge, this is the first paper to use non-parametric techniques, proposed by Bogetoft and Wang (2005), to analyse Italian first instance court mergers. Our research provides a preliminary investigation of the influence of some obstacles, geographical location and the civil caseload, on measured efficiency. In details, while the level of inefficiency appears to be higher in the South of Italy rather than in the Centre or in the North of Italy, the level of civil caseload strongly affects the performance of first instance courts, especially in those areas where the demand for civil judicial services is higher. Hence, given the relevant impact on efficiency of the context in which the DMUs operate, policy-makers should focus the attention of the re-shaping of the territorial distribution of first instance courts. The importance of such aspect is also confirmed by a new reform of first instance courts that, among other interventions, calls for the merging of most of the existing courts in order to gain more efficiency. Our preliminary results show considerable efficiency gains from the proposed mergers. 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