Road safety efficiency on interurban roads in Spain

Original Research Article Evaluation Review 2024, Vol. 48(5) 771–796 © The Author(s) 2023 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0193841X231207443 journals.sagepub.com/home/erx Road Safety Efficiency on Interurban Roads in Spain ´ Angel Tejada 1 , Mar´ ıa Pilar S´ anchez 1 , and Francisco Escribano 1 Abstract The slowdown in economic development caused by traffic accidents in Spain, together with the disparity in the risk of death or injury due to trafficaccidentsin its provinces, makes it necessary to evaluate their road safety performance. Therefore, the objectives of the present research are, on the one hand, to find out the level of road safety efficiency of Spanish provinces in the period 2014– 2018. On the other hand, it is also aimed to determine to what extent the annual efficiency change is originated by pure changes in efficiency or by technological changes. To achieve both objectives, the nonparametric technique of Data Envelopment Analysis and the Malmquist Index have been used based on the consideration of the Safety Performance Indicators (SPI) as the inputs of the process. The research findings show changes in the level of road safety efficiency in each of the years of the study period. Thus, it is possible to identify a geographical delimitation of the causes that generate changes in efficiency in recent years. A contraction in efficiency and technological progress is identified in part of the Spanish provinces in the north, northeast, and south of Spain. Keywords data envelopment analysis, Malmquist index, interurban roads, road safety, Spain 1 Faculty of Economic and Business Sciences, University of Castilla-La Mancha, Albacete, Spain Corresponding Author: ´ Angel Tejada, Faculty of Economic and Business Sciences, University of Castilla-La Mancha, Plaza de la Universidad, 1, Albacete 02071, Spain. Email: [email protected] JEL I15, G38, M49 Introduction Road accidents are a global public health problem with significant social and economic consequences. Chen et al. (2019) determined that failing to eradicate road accidents will result in global economic losses of $1.8 trillion between 2015 and 2030. Moreover, the distribution of economic losses from road accidents is uneven for high-income and low-income countries, in addition to the fact that in the latter, the economic assessment is conditioned by data source limitations (Bougna et al., 2022). Over the last two decades, this obstacle to economic growth caused by road accidents has led governments to devote resources to reducing road accidents. The activities defined in the Global Plan for the Decade of Action for Road Safety 2011–2020 (United Nations Road Safety Collaboration, 2011) have provided nations with tools and knowledge to achieve goals 3.6 and 11.2 of the Sustainable Development Goals of the 2030 Agenda (United Nations, 2015) and the objectives of the Global Plan for the Decade of Action for Road Safety 2021–2030 (World Health Organization, 2020). Spain’s commitment over the last two decades to bring its road safety resources in line with the guidelines established worldwide has enabled it to reduce road deaths by 45% between 2010 and 2020 (ETSC, 2021). Beyond the effect of the reduction in traffic due to mobility restrictions by Covid-19, we can affirm that the risk of death or injury (both serious and minor) on Spanish interurban roads has been reduced by measures such as the implementation of the driving license points in 2006 (Albalate et al., 2013; Castillo-Manzano et al., 2010;Novoa et al., 2010;S´ anchez et al., 2018), the increase in the proportion of high-capacity roads (Albalate & Bel, 2012; S´ anchez et al., 2018,2020), and the improvement of road infrastructure through increased investment in replacement and construction (Albalate et al., 2013;S´ anchez et al., 2018,2020). Although the implementation of legislative measures aimed at improving road safety is mandatory for all Spanish provinces, there is some heterogeneity in the risk of death or injury in each province (S´ anchez et al., 2018,2020). This heterogeneity may indicate the different performances of the resources available to reduce road accidents. Therefore, it is necessary to assess the road safety efficiency of provinces and use those with better performance as a reference to define road safety planning for provinces with lower performance (Nikolaou & Dimitriou, 2018). The need to evaluate road safety efficiency is justified by the findings of the scientific literature. Using the nonparametric Data Envelopment Analysis 772 Evaluation Review 48(5) (DEA) technique, scientific studies have attempted to define how different territories perform in road safety. DEA is a nonparametric technique designed to measure the relative efficiency of decision-making units (DMUs) that use multiple inputs to produce one or more outputs. Its wide use in scientific research lies in the few assumptions required, making it attractive for situations in which the relationship between inputs and outputs is complex (Cooper et al., 2011). The efficiency of each DMU is defined as the ratio of the sum of its weighted outputs to that of its weighted inputs. Based on the concept of the production frontier, continuity and convexity requirements are necessary. However, without any assumption about its functional form, DEA identifies which DMUs have the highest relative efficiency in the given circumstances to construct the frontier (those with a given level of inputs achieve the maximum output or those that achieve a given level of output with the minimum level of inputs). From a benchmarking perspective, the remaining DMUs are considered inefficient with respect to the former, and their inefficiency is measured as a function of the distance to the frontier (Shen et al., 2013,2015)(Appendix 1). By reviewing the scientific literature, we identified three lines of research linked to road safety efficiency. First, at the macro-regional level, road safety efficiency in Iran was evaluated through a single study (Behnood, 2018). Five pillars of road safety development were defined, and a criterion explaining the success of each pillar was introduced using the DEA technique. However, most research at the macro-regional level has focused on measuring the level of road safety efficiency achieved by the countries of the European Union (EU) over the last 20 years. This is in the interest of indicating the path to be taken by possible European road safety policy changes. Among the authors who have used the DEA technique from this perspective, Hermans et al. (2008,2009) defined DEA as a useful tool to study efficiency in European Union countries; Nikolaou and Dimitriou (2018) focused their analysis on determining the correlation between socioeconomic levels and road safety; and Shen et al. (2011,2012,2013,2015) used DEA as a performance measurement technique to provide an overview of a country’s road safety conditions. Second, at the country level, the use of provincial or municipal data makes it possible to determine the efficiency level in individual countries. Anti´ c et al. (2020) estimated efficiency in Montenegro using DEA analysis. For this purpose, the study examined the road safety information from 21 municipalities. Contextualizing those results with similar research in Serbia, Amelian et al. (2017) conducted a study on road efficiency in the provinces of Iran, using the DEA model and Anderson–Peterson method to determine strong efficiency; Behnood et al. (2014,2017) used DEA to determine a relative inefficiency index for each of the thirty provinces of Iran of study and in each year of the analysis period; Seyedalizadeh Ganji and Rassafi(2018) employ Tejada et al. 773 DEA to evaluate the productivity of Iranian regional safety programs in reducing the number of road fatalities. In addition, these authors provide the Malmquist Productivity Index (MPI) to analyze the efficiency and impact of technological changes (Seyedalizadeh Ganji & Rassafi, 2019); Omrani et al. (2020) conclude that the traditional DEA model has several disadvantages (such as lack of flexibility in weighting input and output variables and inability to consider the judgments of decision makers). Therefore, they combined these models with the group best-word method (BWM) to estimate road safety efficiency in Iranian provinces. Bastos et al., 2015a,2015b added mortality and fatality rates to the DEA model to determine the efficiency of measures in 27 Brazilian states. Egilmez and McAvoy (2013) measure, through a DEAbased MPI model, the relative efficiency and productivity of 50 U.S. states in the period 2002–2008 in the period 2002–2008 to reduce the number of fatal accidents on U.S. roads. Kang and Wu (2021) used the joint method of DEA and the Malmquist productivity index to measure the road safety development of China’s provinces from 2007 to 2016. Zhu et al. (2021) attempted to address the limitations identified by other authors by building a model that integrates the cross-efficiency method, regret theory, and Weighted Aggregated Sum Product Assessment (WASPAS). Chan et al. (2020) employed the DEA technique to determine practices that could be improved in South Korea in terms of road safety. Alper et al. (2015) estimated the relative efficiency of 197 local municipalities in terms of road safety using DEA and concluded that the most significant environmental variable in accident prevention is the population size of the local authority. Third, at the local level, although it is a less studied area, Fancello et al. (2013) analyzed the road safety performance of a group of municipalities and a set of urban roads in Villacidro (Italy). These authors considered that measuring and comparing the performance of different urban areas using the DEA technique was fundamental for understanding road safety performance. They characterized this technique as the most suitable decision support tool because it allows for a more careful definition of priority road safety actions (2020). This research aimed to evaluate road safety efficiency on interurban roads in Spanish provinces during 2014–2018, establishing how it evolved over these periods. This research contributes to the scientific literature specializing in efficiency and is considered novel regarding its subject matter, and the population studied. This is the first study to present results on road safety efficiency for interurban roads in Spain. For this purpose, in this document, we include the data and methodologies used in Material and Methods. In Results and Conclusions, we present the main results and conclusions achieved, and in Section 5, we include the bibliographical references used in the research. 774 Evaluation Review 48(5) Materials and Methods Analysis of road safety efficiency requires a robust and validated methodology to achieve the objectives of this research. A review of the scientific literature related to road safety efficiency identified DEA as the most widely applied nonparametric technique for evaluating this efficiency (Alper et al., 2015; Bastos et al., 2015b;Hermans et al., 2009;Seyedalizadeh Ganji & Rassafi, 2018,2019;Shen et al., 2012;Zhu et al., 2021). Therefore, the empirical approach of the present study comprises DEA and Malmquist Index (MI). DEA, initially defined by Charnes et al. (1978) and later developed by Banker et al. (1984), evaluates the relative efficiency of DMUs using linear programming. The efficiency measure on which it is based is the ratio of weighted output to weighted input. The use of DEA for road safety evaluation has many advantages. This nonparametric technique not only allows the ranking of DMUs according to their efficiency but also establishes a benchmark analysis (Zhu et al., 2021). This method allows working with multiple inputs and outputs. It does not require any assumptions about the functional form of the boundary (Shen et al., 2013), and the DMUs are compared directly with other units or a combination thereof. Moreover, it has fewer assumptions than other techniques (Bogetoft & Otto, 2011) and greater flexibility and ability to assume inputs and outputs (Ruggiero, 2007). It should be noted that this method has some limitations. It is strongly affected by the presence of atypical observations or measurement errors, and it does not allow the applicability of statistical hypothesis tests, as it is a nonparametric method (no assumption of the functional form) and nonstatistical method (efficiency does not follow a probability distribution), which does not allow statistical inferences and hypothesis testing. Finally, the method allows obtaining relative efficiencies but not absolute efficiencies; thus, it does not allow future projections. Following the advances in safety research achieved in the European Safety Net project (SafetyNet, 2005) on safety performance indicators, the importance of the benchmarking concept for analysis has been incorporated, and different road safety domains and indicators have been identified (AuerbachHafen et al., 2007). The benchmarking concept focuses on a composite road safety index to identify value-based assessments of road safety performance (Al Haji, 2005). In our research, n Spanish provinces, j = 1, …, n, called DMUs, are considered to produce a set of s outputs (y rj ), r = 1, …, s, from a set of m inputs (x ij ), i = 1, …. m. An output orientation is assumed, so the DEA attempts to optimize the output defined from the different inputs considered, considering that the level of inputs controlled by the political authorities in charge of road safety in Spain has a relative margin of change. Tejada et al. 775 Heterogeneity among Spanish provinces in terms of road safety determines the efficiency of scale in relation to the production function. Thus, these are considered to operate under variable returns to scale, which translate into a nonproportional change in output and inputs. This approach is considered more realistic and robust than the assumption of constant returns to scale (Egilmez & McAvoy, 2013). The mathematical formulation of the linear programming problem is (Huguenin, 2012) Max h ¼θj0 Subject to θj0yr0Xn j¼1 λjyrj ≤0r¼1, …,s xi0Xn j¼1 λjxij ≥0i¼1, …,m λj≥0; Xn j¼1 λj¼1j¼1, …,n where λ j are the relative weights with respect to the evaluated unit “0.” DMUs with an efficiency (θ) equal to 1 are efficient, whereas inefficient provinces have an efficiency below 1. The individual efficiencies for each year in this study indicate the higher or lower capacity of the provinces in termsofroadsafetyefficiency. However, comparing the levels of efficiency between the years of the study period provides more disaggregated information to policymakers for planning future road safety policies. Therefore, the MPI defined by Caves et al. (1982) was used in this study. Thus, the effect of a change in efficiency (pure efficiency) can be separated from the change brought about by technological transformation (technological change). Considering that the production function operates under variable returns to scale, we use the MPI definition proposed by F¨ are et al. (1994). The mathematical formulation is as follows: Mxt,yt,xtþ1,ytþ1¼PEC x TC x SEC Each component is defined as follows: PEC ¼Dtþ1 oðxtþ1,ytþ1Þ Dt oðxt,yyÞ TC ¼Dt ocðxtþ1,ytþ1Þ Dtþ1 oc ðxtþ1,ytþ1ÞxDt ocðxt,ytÞ Dtþ1 oc ðxt,ytÞ1=2 SEC ¼Dtþ1 oc ðxtþ1,ytþ1ÞDtþ1 oðxtþ1,ytþ1Þ Dt ocðxt,ytÞDt oðxt,ytÞ 776 Evaluation Review 48(5) The term “D”refers to the distance functions, and the subscripts “oc”and “o” indicate whether these distances are defined based on the reference technologies or not, respectively. The expression, “PEC,”(pure efficiency change) is the change in technical efficiency with best practice technologies under variable returns to scale. The second expression, “TC,”(technological change) reflects the change occurring at the technological frontier; in other words, it reflects the shift of the efficient production frontier, which captures the actual progress or regression of the efficient provinces (Shen et al., 2013). The third expression, “SEC,”(scale efficiency change) measures the contribution of returns to scale to the change in productivity (Lovell, 2003). The combination of this component and PEC is called efficiency change and reflects the ability of an inefficient province to catch up with efficient provinces (Shen et al., 2013). In all three expressions, a value greater than 1 indicates higher efficiency, technological progress, and increasing returns to scale. In contrast, a value less than 1 in any of the three expressions reveals lower efficiency, a shrinking technological frontier, and diminishing returns to scale. The study was carried out for interurban roads, considered, in accordance with the Law on Traffic, Circulation of Motor Vehicles and Road Safety (RDL 6/2015), as “those roads of public domain and use designed, built and signposted primarily for the circulation of motor vehicles and whose purpose is to connect cities or towns.”Thus, the definitions of inputs and output, for establishing road safety efficiency, vary in scientific literature. Although scientific studies employ a multitude of variables as inputs and outputs, the concept of Safety Performance Indicators (SPI) has been very commonly employed in scientific research. SPIs are defined as “measures”that reflect the operational conditions of the road traffic system that influence its safety performance (Safetynet, 2005). Following the identification of SPIs established by Hermans et al. (2009) and Egilmez and McAvoy (2013), and based on the quality and availability of information at the provincial level for the delimited period (2014–2018), four groups of SPIs were defined in the present research: nThe investment effort in the system represented by the total investment per kilometer of interurban roads in each province. nThe use of the system measured by the number of vehicles that use the interurban roads of each of the provinces each year. Although this indicator can be considered negatively related to final output, some scientific research has found a negative relationship with the risk of death or injury in road accidents (S´ anchez et al., 2018,2020). nThe system conditions incorporated into the DEA through a variable proportion of high-capacity roads, including highways, freeways, and dual carriageways. These roads are characterized by their good design and capacity and therefore contribute to reducing road accidents. Tejada et al. 777 nThe personal safety in the system. This was considered in an efficiency analysis using two indicators. The first is the percentage of new vehicle registrations from the total vehicle fleet. Second, the number of people with a higher level of education is a proxy measure for the use of safety systems (we do not have disaggregated information on the use of safety systems at the provincial level), considering the positive relationship found between the rate of seatbelt use and the level of education of the population (Babio and Daponte, 2006;Demirer et al., 2012). The output-oriented DEA model requires the maximization of the output while maintaining the level of inputs. Obviously, the aim is not to maximize the cost of road accidents per million vehicle-kilometers traveled. Therefore, a transformation was applied to the output initially defined in Table 1. Using the transformation applied by Egilmez and McAvoy (2013), the final output is the average time it takes, in minutes, to lose one euro owing to the risk of death or injury in traffic accidents. To obtain this output, the time in a year (365 × 24 × 60 = 525,600 minutes) was divided by the cost per million vehicle-kilometers traveled (MVKT). With this modification of the output, the DEA model can be applied as defined because it aims to maximize the number of minutes it takes to have one euro of loss due to injuries or fatalities in traffic. Applying the concept of efficiency to the input and output indicators considered in this study allows us to define road safety efficiency as the weighted ratio between the time it takes for provinces to lose money due to traffic accident risk and the level of performance measures achieved by each Spanish province. Finally, it is important that the inputs and output show a level of correlation, which reinforces their consideration as variables to be included in the DEA model, and that the inputs have the same effect on the transformed output (costbymvkt 1 ). The correlation matrix shown in Table 2 indicates that all inputs are positively and significantly correlated with the transformation of the output. Appendix 2 presents the normality test for the variables. Although the variables do not follow a normal distribution, when the number of observations is greater than 30, nonnormality does not affect the sampling distribution of the statistic. Therefore, it is not a problem in other models, such as linear regression. Results The objectives of the present study are two-fold: I) to estimate the level of efficiency for Spanish provinces during 2014–2018; and ii) to Evaluate changes in road safety performance in these provinces. In relation to the efficiency of the Spanish provinces in road safety in each year of the study period (Table 3), it can be stated that their performance in improving the time it takes to lose one euro due to traffic accidents exceeded 778 Evaluation Review 48(5) Table 1. Inputs y Outputs. Inputs (I) and outputs (O) Definition Minimum Maximum Mean Standard deviation I1. Total investment per kilometer of interurban roads (1) (tipk) Investments (in thousands of €) in replacement and construction per kilometer of interurban roads 5.339 138.410 23.621 20.804 I2. Average vehicle intensity (1) (avi) Number of vehicles per year driving on interurban roads 328,114.630 7,358,053.793 1,575,890.879 1,281,210.709 I3. Proportion of high-capacity roads (1) (phcr) Percentage of high-capacity roads (highways, freeways and dual carriageways) with respect to the total. 3.543 29.688 10.801 5.168 I4. Proportion of new vehicles (2) (pnv) Percentage of new vehicles registered each year with respect to total number of vehicles 1.248 13.006 3.524 1.616 I5. Population with higher education (3) (hep) Number of people with higher education in the province 20,158.645 2,095,312.069 219,299.660 331,408.393 O1. Cost per MVKT (1) (2) (costbymvkt) Euros per million vehicle-kilometer traveled (MVKT) for road traffic accident victims 6511.760 29,415.821 15,260.658 4390.276 Fuente: (1) Ministry of Transport, Mobility and Urban Agenda; (2) General Directorate of Traffic; (3) National Statistical Institute. Tejada et al. 779 allows for evaluating efficiency with the most accurate and timely information. Moreover, their direct use in the empirical approach indirectly reflects the change that has taken place in Spain associated with the promotion of investment policies in road infrastructure, the renewal of the vehicle fleet, and the use of active safety systems. The findings constitute a source of information for public authorities responsible for road safety in Spain. Thus, the DEA estimates highlight the need to analyze the economic, geographical, and social characteristics, as well as the specific actions carried out by the provinces of Avila, Cuenca, Guadalajara, Madrid, Segovia, Soria, and Teruel, to define road safety policy more precisely in the future. The need to evaluate road safety performance was confirmed by analyzing the elements that changed from one year to the next. Therefore, MI provides a more specific characterization of the evolution of road safety efficiency in Spanish provinces. It identifies whether provinces increase or decrease their efficiency level, or whether they experience technological progress that leads to a shift in the production frontier. The results of the application of this index reveal that the heterogeneity in the changes in efficiency and technical changes registered by Spanish provinces does not allow us to identify a pattern of change. The geographical distribution of the changes in the main components of MI revealed two essential issues. First, the provincial distribution of efficiency and technological changes ratifies the behavior identified through the analysis of annual efficiency for Spanish provinces as a whole. Therefore, it can be stated that it is important to apply a specific analysis of the road accident rate between 2015 and 2016 due to the large number of provinces that recorded drops in efficiency and technical progress. Second, the variations in efficiency recorded in the final years of the study period (2016–2017 and 2017–2018) reveal a more concentrated geographical location of the best and worst road safety performances. Therefore, it is a priority for policymakers to assess the level of road accidents in relation to their resources in the northern provinces, parts of the provinces located on the shores of the Mediterranean, and some provinces in southern Spain. To this end, they should consider the performance achieved by the provinces in the center of the Peninsula and Balearic Islands. The results of the methodology applied in this study not only serve as a reference for policymakers in Spain but also for the scientific community at the international level. These findings are novel because of the absence of scientific research on road safety efficiency in Spain. The importance of the findings of this study for both the scientific community and policymakers is a basis for future research. Thus, the different ownerships of interurban roads implies a different level of investment and risk so that the evaluation of their efficiency in each of Spain’s provinces can provide a more precise definition of the level of road safety performance achieved. Moreover, the identification of the actions implemented by 786 Evaluation Review 48(5) efficient provinces in relation to each SPIs used in this research will allow, in the future, the determination of practices to be implemented in inefficient provinces. It should be noted that the findings obtained are limited by the lack of provincial information on variables that complement the domains with an impact on efficiency, such as alcohol and drug intake, cell phone use, or control on interurban roads. Therefore, the scientific community and political decision-makers must continue working to ensure that all Spanish provinces are on the production frontier in terms of road safety. Appendix The frontier diagram presents an example of a set of DMUs where the efficiency frontier consists of DMUs C, E, F, H, J, K, and L. The remaining DMUs below the efficiency frontier fail to maintain an efficiency of 1. For example, DMU D can be made more efficient by reducing its input consumption from X 0 to X 1 (input orientation) or by increasing output from Y 0 to Y 1 without consuming more inputs (output orientation). Importance of inputs in efficiency estimation Appendix 1. Diagram of frontier data envelopment analysis model. Tejada et al. 787 Appendix 2. Statistical Test for Normality. Skewness and kurtosis test Shapiro–Wilk test Adj chi2 Prob > chi2 W p-value Input 1 144.12 .000 .650 .000 Input 2 86.61 .000 .788 .000 Input 3 41.69 .000 .908 .000 Input 4 96.32 .000 .836 .000 Input 5 176.56 .000 .475 .000 Output 40.65 .000 .931 .000 Appendix 3. Sensitivity Analysis. Years Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 2014 .794 .703 .781 .762 .787 .793 2015 .815 .781 .802 .796 .809 .815 2016 .718 .646 .709 .713 .694 .717 2017 .763 .721 .748 .759 .756 .762 2018 .770 0.741 .765 .752 .755 .769 Average .772 .718 .761 .756 .760 .771 788 Evaluation Review 48(5) Appendix 4. Decomposition of Malmquist Index. Provinces 2014/2015 2015/2016 2016/2017 2017/2018 M PEC TEC SEC M PEC TEC SEC M PEC TEC SEC M PEC TEC SEC Almer´ ıa .793 .873 .910 .999 .680 .616 .877 1.260 1.399 1.587 1.105 .798 1.014 .925 1.024 1.070 C´ adiz 1.179 1.397 .867 .973 .851 .712 .993 1.204 .958 1.127 1.096 .775 1.142 1.029 .932 1.191 Córdoba 1.229 1.000 1.049 1.171 1.122 1.000 1.058 1.061 .892 1.000 .975 .915 .920 .924 .832 1.197 Granada 1.252 1.557 .862 .933 1.182 .964 1.037 1.182 .998 1.209 1.016 .812 1.131 1.188 .860 1.108 Huelva .710 .693 1.062 .966 .891 .923 .979 .987 .927 1.070 .915 .947 .972 1.051 .929 .996 Ja´ en 1.071 1.338 .835 .959 .741 .681 1.079 1.008 .838 1.025 .993 .823 1.046 1.068 .945 1.036 M´ alaga .948 1.000 1.008 .941 .866 .799 .905 1.197 .797 .980 1.039 .783 1.511 1.277 .996 1.188 Sevilla 1.323 1.346 .963 1.020 .666 .647 .924 1.113 1.034 1.216 1.043 .815 .952 .999 .910 1.047 Huesca 1.411 1.449 .972 1.002 .970 .791 1.332 .921 .747 .955 .722 1.084 .971 .988 1.017 .966 Teruel 1.067 1.000 1.015 1.051 .949 1.000 1.193 .795 .833 1.000 .783 1.063 1.308 1.000 1.036 1.263 Zaragoza .943 1.052 .915 .981 .887 .715 1.009 1.230 1.178 1.505 .939 .834 .856 .825 1.007 1.030 Asturias 1.240 1.337 .917 1.012 1.093 .896 .950 1.283 .713 .826 1.066 .809 .923 .862 .860 1.245 Islas Baleares .874 1.022 .781 1.094 1.148 .833 1.332 1.034 .915 1.162 .796 .990 1.102 1.194 1.122 .823 Las Palmas 1.062 1.000 1.085 .979 .589 .600 1.117 .878 1.297 1.316 .903 1.092 1.117 1.010 .852 1.298 Sta. Cruz de Tenerife .655 .769 .994 .858 .887 .762 1.382 .842 .938 1.102 .755 1.129 .934 .946 1.071 .922 Cantabria .792 1.000 .822 .964 1.285 1.009 1.207 1.055 .855 1.000 .851 1.005 .857 .951 .996 .905 ´ Avila .769 1.000 .991 .777 1.247 1.000 .957 1.302 1.147 1.000 1.064 1.078 .684 1.000 .925 .740 Burgos .846 .789 1.108 .969 .942 .975 .955 1.011 1.206 1.243 1.005 .965 .921 1.068 .816 1.056 León .785 1.000 1.093 .718 1.306 .937 .921 1.513 .867 .955 .845 1.074 .806 .821 1.018 .965 Palencia 1.470 1.237 1.046 1.136 .770 1.000 .830 .928 .919 1.000 .960 .957 1.092 1.000 .971 1.125 (continued) Tejada et al. 789 Appendix 4. (continued) Provinces 2014/2015 2015/2016 2016/2017 2017/2018 M PEC TEC SEC M PEC TEC SEC M PEC TEC SEC M PEC TEC SEC Salamanca .779 .732 1.069 .994 1.691 1.365 1.167 1.061 .729 1.000 .729 1.000 1.025 1.000 1.025 1.000 Segovia 1.023 1.000 1.023 1.000 .847 1.000 .847 1.000 1.120 1.000 1.120 1.000 .774 1.000 .774 1.000 Soria 1.253 1.000 1.253 1.000 .499 1.000 .782 .638 1.812 1.000 1.155 1.568 .654 1.000 .654 1.000 Valladolid .698 .809 .846 1.020 1.421 1.082 1.143 1.148 .720 .940 .871 .880 1.290 1.201 .990 1.085 Zamora .788 .823 .978 .979 1.011 1.300 .955 .815 .768 .694 .848 1.306 1.378 1.465 .978 .961 Albacete 1.128 1.131 1.012 .986 .773 .798 .927 1.045 1.092 1.399 .895 .872 1.238 1.095 1.009 1.120 Ciudad Real .802 .848 .983 .962 .875 .958 .883 1.035 .870 .946 .951 .967 1.192 1.193 .988 1.012 Cuenca .860 1.000 .860 1.000 .917 1.000 .917 1.000 1.025 1.000 1.025 1.000 .928 1.000 .928 1.000 Guadalajara .807 1.000 .807 1.000 1.512 1.000 1.512 1.000 .635 1.000 .635 1.000 1.208 1.000 1.208 1.000 Toledo 1.174 1.328 1.048 .843 .677 .589 .923 1.246 1.081 1.110 .959 1.016 1.820 1.406 1.056 1.226 Barcelona .992 1.090 .842 1.080 .908 .865 1.143 .919 .871 1.026 .876 .969 .919 .863 .944 1.129 Girona .855 .904 .953 .993 .837 .733 .995 1.148 1.260 1.397 .995 .907 .766 .794 .967 .997 Lleida .694 .848 .822 .995 1.162 .931 1.276 .978 1.013 1.145 .855 1.034 .875 .916 .980 .975 Tarragona .754 .763 .980 1.008 .904 .875 .862 1.198 1.400 1.538 1.119 .813 .882 .772 .911 1.253 Alicante 1.316 1.414 .904 1.029 .788 .694 .945 1.202 1.142 1.244 1.098 .836 .836 .806 .853 1.217 Castellón 1.116 1.219 .854 1.072 .685 .534 1.059 1.210 1.287 1.517 1.002 .846 .734 .773 .965 .985 Valencia 1.037 1.223 .867 .978 .786 .683 .997 1.155 .994 1.218 1.043 .783 .828 .828 .879 1.137 Badajoz 1.030 .789 1.180 1.108 1.324 1.268 .976 1.070 .742 .753 .997 .987 1.053 1.266 .795 1.047 C´ aceres 1.133 1.273 .872 1.021 .846 1.000 .846 1.000 .787 .860 1.049 .873 1.612 1.163 1.209 1.146 A Coruña 1.239 1.390 .826 1.078 .748 .633 1.173 1.007 1.025 1.259 .849 .958 .840 .885 .972 .978 (continued) 790 Evaluation Review 48(5) Appendix 4. (continued) Provinces 2014/2015 2015/2016 2016/2017 2017/2018 M PEC TEC SEC M PEC TEC SEC M PEC TEC SEC M PEC TEC SEC Lugo 1.185 .884 .891 1.504 .943 1.131 1.218 .684 1.397 1.000 .859 1.626 .935 1.000 .945 .989 Ourense 1.515 1.110 1.223 1.117 .742 .909 .848 .963 1.260 1.100 1.103 1.038 .615 .758 .814 .996 Pontevedra .890 1.027 .829 1.046 1.033 .880 1.164 1.008 1.132 1.367 .859 .964 .919 .968 .959 .990 Madrid .954 1.000 .881 1.083 .900 1.000 1.174 .767 .975 1.000 .945 1.031 1.203 1.000 .946 1.272 Murcia 1.357 1.557 .906 .963 .736 .687 .941 1.139 .790 .954 1.057 .783 1.026 1.049 .850 1.150 Navarra 1.597 1.348 1.115 1.062 1.003 1.000 1.003 1.000 .842 1.000 .997 .844 .733 .726 .872 1.158 ´ Alava .691 .839 1.143 .720 .824 .722 .870 1.311 .773 .944 1.090 .751 .848 .800 .890 1.191 Guip´ uzcoa .591 .703 .850 .989 1.402 1.175 1.077 1.107 .914 1.067 .974 .880 1.267 1.301 .885 1.101 Vizcaya .747 1.000 .857 .872 .841 .799 1.056 .997 1.190 1.252 .995 .956 .763 .899 .883 .961 La Rioja .757 .852 .864 1.029 .790 .562 1.099 1.278 .952 1.080 .987 .893 2.460 2.200 .878 1.273 M = Malmquist index; PEC = Pure efficiency change; TE = Technological change; SEC = Scale effect Change. 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