Technical efficiency of Service Industries in the OECD

Transcription

1 Technical efficiency of Service Industries in the OECD José Luis Navarro Espigares 1,2 and José Aureliano Martín Segura 1 1 University of Granada, 2 Virgen de las Nieves University Hospital In this paper we calculate the production efficiency of each of the branches of the service sector in OECD countries. Then, we study the relationship between the efficiency of service industries and the productive efficiency of national economies. Finally, we analyse the relationship between the levels of efficiency and some variables that are assumed a priori to have some influence, such as the relative size of each industry, human capital, productive capital, labour productivity, and intensity of information technology and communication in the capital stock. We will determine if these relationships are influenced by some contextual variables such as the geographical area, the type of service, or the activity branch. Keywords: Total factor productivity, services efficiency, DEA, multilevel models. 1. Introduction The production structure of modern economies within the OECD is characterised by a large service sector that generates, on average, over 75% of gross value added. Moreover, industrial activities involve a high level of interaction with the branches of the service sector. Therefore, it is assumed that the production efficiency of these economies will be greatly affected by the degree of technical efficiency of service activities. This is one of the reasons why we are interested in the study of productivity in services. In addition, higher productivity of service producers can play a role in increasing a country s world market share in industrial products (Ark, Monnikhof, and Mulderwe, 1999). In this sense, the experience of several OECD countries shows that the service sector has made a large contribution to both employment and productivity growth over the past decade (OECD, 2005). Furthermore, the service sector encompasses a large number of activities with a remarkable diversity of behaviours and a high dispersion in technical efficiency. Thus, not only must the relative size of the service sector be taken into account, but its internal structure as well. This internal structure depends on the relative weight of each of the industries included in this aggregate. Quality factors have been recognised as a key component in measuring productivity (Rutkauskas & Paulavicien, 2005; Navarro & Hernández, 2011). However, because we work with aggregate data, quality factors have been omitted in our study. In this paper we calculate the production efficiency of each of the branches of the service sector in OECD countries in The first hypothesis is that the productive efficiency of a country is closely connected with the efficiency of the service sector. 1

2 To verify this first hypothesis, we analyse the relationship between the efficiency of service industries and the productive efficiency of national economies. The second hypothesis is that national service productivity in turn depends on the pattern of production specialisation in each country and the level of efficiency achieved in those service activities with a greater relative weight. The descriptive analysis will help us to check the last assumption. The impact of structural changes and intersectoral displacements on aggregate productivity is also important due to the relevant role that the service sector plays in developed economies in terms of production and employment (Cuadrado-Roura and Maroto-Sanchez, 2006; Maroto & Rubalcaba, 2008). Finally, we analyse the relationship between the levels of efficiency and some variables that are assumed a priori to have some influence, such as the relative size of each industry, human capital, productive capital, labour productivity, and intensity of information technology and communication in the capital stock. At this point, we will be interested in knowing if geographical and specialisation factors explain variability of productivity of the various service branches. Isaksson and Ng (2006) compared the results of total factor productivity (TFP) determinants through two modes of analysis cross-country analysis of large sets of countries and country case studies. Diverging views are evident in the case of structural change, the country case studies suggesting that it is important for TFP growth, while the cross-country regression evidence for it being weak. In our work, multilevel models supplement the traditional regression models and attempt to discover if variability in efficiency can be explained by geographical factors. Ark, Monnikhof and Mulderwe (1999) studied productivity in services from the perspective of an international comparative and found substantial differences in productivity across industries within the main service sectors. The relevant role played by service operations has been also highlighted in several publications (Rubalcaba & Kox, 2007; Rubalcaba & Gago, 2002). The main contribution of this paper is the structural composition approach based on the relative size of activity branches within the service sector. The combination of data envelopment analysis and multilevel regression models is also another element of innovation from the methodological point of view. In the next section, the most important methodological issues relating to the data sources and the analytical tools utilised are explained. Then we present the results, differentiating those relative to efficiency scores (by countries and by activity branch), the relationship between relative size and efficiency (at an OECD level and at a country level), the least squares econometric model, and the multilevel model. We end the work with some conclusions. 2. Methodology The data source utilised in this work is OECD National Accounts Statistics. This database includes data on final consumption expenditure of households, value added, labour input, capital formation, fixed assets, and non-financial accounts. Data were arrived at by following the System of National Accounts 1993 (SNA 1993) methodology and are internationally comparable. 2

3 The variables used for calculating technical efficiency were gross value added, labour input, and the consumption of fixed capital, broken down by detailed industries. The activities classification includes 16 categories, of which 10 categories correspond to service activities: Agriculture, hunting and forestry; Fishing; Mining and quarrying; Manufacturing; Electricity, gas and water supply; Construction; Wholesale and retail trade, repair of motor vehicles and household goods; Hotels and restaurants; Transport, storage and communication; Financial intermediation; Real estate, renting and business activities; Public administration, defence, and compulsory social security; Education; Health and social work; Other community, social and personal service activities; Private households with employed persons. Twenty-eight countries were included in the study: Austria, Belgium, Canada, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Israel, Italy, Japan, Korea, Luxembourg, Mexico, The Netherlands, New Zealand, Norway, Poland, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, and The United States. All data refer to We considered this year to be the most appropriate because, even though it was not the last to be published, it was not affected by the alterations introduced by the 2008 economic crisis. It is also the year closest in time for which we have information on selected variables for most OECD countries. After descriptive analysis of the data, we calculated the production efficiency of all the industries in different OECD countries. We also calculated the efficiency of national economies globally considered, and the clustering of activities included within the service sector. In this way we obtained three different efficiency rankings: one referring to national economies, another to the levels of efficiency in the service sector, and a third one to efficiency levels of each of the 10 service activities included in the OECD statistics. There are different methods of measuring efficiency which can be classified in two major groups: productivity indexes and frontier models. The measure of efficiency of production units has been linked to the study of frontier production functions, due to the necessity of standards to compare efficiency. Thus, the study of frontier production functions and the efficiency measure have the same origin in the recent literature, dating back to a work by Farrell in Frontier methods measure the performance of a production unit with respect to an efficiency production frontier which, for a collection of units, represents the maximum possible output for a given input. At the same time, frontier models can be parametric (deterministic or statistical) and non-parametric, depending on whether or not a specific form of the production function frontier is used. The Data Envelopment Analysis (DEA) is an analytical method for efficiency analysis based on non-parametric frontier models. In this work we use DEA because it is a flexible method, not restrictive in reference to technology and easy to implement in multiproduct contexts. DEA has been widely used in many industries, private and public as well. From the numerous formulations of DEA models, we preferred the formulation denominated under initials BCC that assumes variable returns to scale (VRS) (Banker, Charnes and Cooper, 1984). One of the advantages of this technique is that it allows the use of different measuring units for the considered input and output variables, 3

4 without any restriction. This is the reason DEA is employed to evaluate the efficiency of productive units in which the monetary appraisal of their outputs presents either measurement or definition difficulties. In any case, the choice of output and input variables that we include in the model depends on the knowledge of the concrete activity that is to be evaluated and on the available information. In addition, the DEA technique demands a certain balance among the number of analysed units and the number of variables included in the model. If this balance does not exit, we might conclude that all decision-making units (DMU) are efficient, except those that are completely dominated by using a larger quantity of every input to obtain lower quantities of all outputs. Bigger sample size, ceteris paribus, entails smaller proportions of efficient DMUs; and when a greater number of variables are considered, ceteris paribus, larger proportions of efficient units are arrived at. Although the DEA technique is widely used in the microeconomic studies, where decision-making units are equivalent to companies or even manufacturing plants, in this case our approach is macroeconomic and production units included in the models refer to branches of activity, groups of them, or even whole economies. DEA model configuration in this case is quite simple. We will use only one variable for output, the value added, and two variables for inputs, the input labour (data represent persons, full-time equivalent) and the consumption of fixed capital. The new System of National Accounts, which will be implemented around 2012, could recommend including here capital services rather than only consumption of fixed capital. Capital services cover consumption of fixed capital plus an estimate of the capital returns (Lequiller, F. & Blades, D., 2006). Value added and consumption of fixed capital are expressed in millions of national currency, in current prices. Since the statistics published by the OECD are expressed in national currencies, before including these variables in the efficiency model we have homogenised the two monetary variables (value added and capital consumption) through the Purchasing Power Index calculated by the OECD for The variant of the DEA model utilised assumes variable returns to scale, in particular the specification of Non-Decreasing Returns to Scale (NDRS). This is consistent with the use of units of disparate size and the orientation to output. Orientation defines the target output of the model in the sense of maximising output and trying to minimise inputs. In particular, we calculated two models: NDRS: Efficiency scores calculated with a Non Decreasing Returns to Scale DEA model in which all record of the table were incorporated in the peer group. NDRS2: Efficiency scores calculated with a Non Decreasing Returns to Scale DEA model in which all record of the table were incorporated in the peer group except those corresponding to branches Total Activity and Total Service Activities. Finally, we need to investigate the determinants of productivity in the service sector. The econometric analysis will help us to give some suggestions for policy-makers. We started with a traditional model in which we included 270 observation referred to the services branches. In this model we try to explain the efficiency scores obtained in the NRDS2 DEA by means seven variables, labour, capital consumption, ICT capital services, software capital services, human capital, relative size, and the apparent 4

5 productivity of the labour factor. The software package E-Views 7 has been utilised for these calculations. Capital services represent the capital input. OECD capital services estimates are presented from 1985 to the most recent available period, and broken down by six or seven assets (depending on data availability from countries): IT equipment, communication equipment, other machinery and equipment, non-residential construction, transport equipment, software, other intangibles, and three aggregates: total information and communication technology (ICT), total non-ict and total products of agriculture, metal products and machinery. The variable related to labour; L (thousands) represents the employment in terms of persons (full-time employees). For capital consumption we used Consumption of fixed capital expressed in Purchasing Power Parities (PPP) in national currencies per US dollar (OECD = 1.00). Obtaining capital services measurements has long been recognised as the appropriate manner for capturing capital input in production and productivity analysis (OECD, 2003). Capital services are represented by two variables: ICT capital services: Contribution of total information and communication technology (ICT) capital goods to growth of capital services, based on harmonised price indices for ICT capital goods, in percentages. Software capital services: Contribution of software to growth of capital services, in percentages. The human capital variable refers to tertiary education graduation rates, and reflects the percentage of graduates to the population at the typical age of graduation. Relative size for the various activity branches was calculated as the result of dividing the value added of a production branch by the total activity value added of its country. The last variable is the apparent productivity of the labour factor: value added (VA) divided by the number of employees (L). One limitation regarding the data is that the variables Capital Consumption, ICT capital services, Software capital services, and Human Capital are only available at a country level. OECD does not publish these data broken down by activity branches. Furthermore, figures regarding the three variables ICT capital services, Software capital services, and Human Capital have been not published for 13 of the 28 studied countries (Czech Republic, Estonia, France, Greece, Hungary, Israel, Korea, Luxemburg, Mexico, Norway, Poland, Slovak Republic, Slovenia). In a second stage, after solving the econometric model with individual data, we investigate whether our database responds to a multilevel structure. The relevant fact in this type of structure is that we can expect individuals from a group to be more similar among themselves than individuals pertaining to different groups. In our work there are several variables (country, type of service, and activity branches) that can be considered as contextual variables. So they can be used as a criterion on which to build hierarchical structures. Our main interest will be to determine if records corresponding to a specific group (e.g. country) show a reduced efficiency variance in comparison with the variance observed in the whole observation group. 5

6 Multilevel analysis is a suitable approach for taking into account the social context as well as the individual actors or subjects. This type of analysis strives to solve the most common problems encountered when the data is analysed at one level and the conclusions formulated at another level (Hox, 2002). In this sense, the best-known fallacies are the so-called ecological fallacy (inferences made at a lower level based on analyses performed at a higher level) and the atomistic fallacy (inferences drawn at a higher level based on analyses carried out at a lower level). The SPSS statistical package software has a procedure known as mixed that allows for adjustment of a particular type of model called hierarchical (Raudenbush and Bryk, 2002), multilevel (Goldstein, 2003), or random coefficients models (Longford, 1993). This procedure was utilised in this work. A multilevel model includes fixed effects and random effects as well. For this reason it is called mixed model. Traditional econometric models analyse data as a homogeneous group and they work with the characteristics of the individual records in level 1. The newer multilevel model creates various groups of data and this type of model allows each group to have its own intersection and slope. The variability in this second level is what characterises a multilevel model. The model reveals the relationship among the units in the first level and each one of subgroups in the second level. We will start with the simplest multilevel model, the Fully Unconditional (or Null) Model also called One-Way ANOVA with Random Effects. This is a model without explicative variables which provides a baseline comparison for conditional models. Then we will obtain some global fit statistics like the deviance. In statistics, deviance is a quality of fit statistic for a model that is often used for statistical hypothesis testing. This expression is simply 2 times the log-likelihood ratio (-2LL) of the reduced model compared to the full model. Here the full model is a model with a parameter for every observation so that the data is able to fit exactly. Deviance indicates the capacity of the proposed model to represent the observed data variability. The lower value of this statistic indicates a better fit of the model. The difference between two -2LL statistics corresponding to two different models can be used to evaluate the gain that we obtain when we add the effects by which both models differ. The assessment of a specific effect in SPSS mixed models is made by the Z Wald Statistic. This statistical test contrasts the null hypothesis which assumes that the effect of the added factor is equal to zero. Another interesting statistic is the intra-class correlation coefficient (ICC). It represents the percentage of total variability explained by the variability among the units of the second level. An ICC equal to one indicates that all variability is due to the factor, and a value equal to zero means that the factor does not contribute at all in reducing the variability of the dependent variable. In summary, the Null Model informs about the variability of intra and inter-unit in the second level. After detecting variability in level 2 we will utilise the regression analysis with an explicative variable in level 2 that explains the variability found in this level. In order to that, we will add to the model a centred co-variable that endeavours to forecast the average value of efficiency in each unit of the second level. The critical level of Z Wald Statistic indicates whether the efficiency level of units pertaining to level 2 differs after controlling by the co-variable included in the model. 6

7 A co-variable of level 2 is not useful for explaining the differences among the individual elements of the same unit, so in this third stage we need a co-variable of level 1 for explaining the intra-unit variability. Previous models are random intercept models because the only element that varies between two units of level 2 is the intercept. The next step enlarges our hypothesis by assuming that coefficients could also randomly vary from unit to unit. By means of a Random Coefficients Model we will check if the variance of slopes is bigger than zero and whether some relationship among slopes and intercepts exists. If we find that slopes and intercepts vary from unit to unit, the next step will be to determine which variables can explain these differences. This is the main characteristic of a multilevel model, i.e. to interpret the coefficients (intercepts and slopes) in level 1 as results of coefficients in level Results First we calculated three different efficiency rankings: one referring to national economies, another to the levels of efficiency in the service sector, and a third one to efficiency levels of each of the 10 service activities included in the OECD statistics. Table 1, arranged by a geographical criterion, contains the result of these three rankings. Each column was obtained from a combined analysis taking a group of 489 observations, one for each country and branch (all activities were included even those corresponding to non-service sector). In order to obtain more accurate data we made two different DEA models. The first one labelled as NDRS includes the two aggregate branches Total Activity and Total Service Activities, so in this model we handled 489 records. Data inserted in these columns have been obtained from this model. The second model, NDRS2 includes all records of the database except those corresponding to the aggregate branches. In total we managed 433 records. In this way efficiency scores calculated for the various activity branches are not affected by the large dimension of the two aggregate branches. This second model furnishes data for the rest of the columns in Table 1. All data utilised for this work and the scores obtained in models NDRS and NDRS2 are in Annex I. 7

8 COUNTRY TOT: Total activity R: Total Service Activities G: Wholesale and retail trade; repair of motor vehicles and household goods H: Hotels and restaurants I: Transport, storage and communication J: Financial intermediation K: Real estate, renting and business activities L: Public administration and defence; compulsory social security M: Education N: Health and social work O: Other c ommunit y, social and personal service activities P: Private households with employed persons Austria Belgium Canada Czech Republic Denmark Estonia Finland France Germany Greece Hungary Ireland Israel Italy Japan Korea Luxembourg Mexico Netherlands New Zealand Norway Poland Slovak Republic Slovenia Spain Sweden Switzerland United States Geometric Mean Table 1: Countries efficiency In the first model (NDRS) we calculated the technical efficiency of the whole economy and the efficiency of the service sector for every country. Regarding the results obtained for the total activity, the efficiency ranking is led by the smaller economies: Estonia, Ireland and Luxembourg, followed by Mexico and the United States. The average efficiency level reached by the national economies is 74% on a scale from 0 to 100, while for the service sector the score is lower, about 57%. This result is clearly consistent with previous studies (Kox, 2006) and with the economic theory about services productivity (Baumol, 1967, 2002). Once having determined the level of efficiency for countries, we were interested in knowing if productivity of national economies is associated with productivity in the service sector. Figure 1 shows a strong association between the level of efficiency in the national economies and the efficiency of the service sector in every country. 8

9 Ireland Mexico United States Estonia Luxembourg Total Activity Efficiency Korea Norway Canada Sweden Belgium Italy y = x R² = Japan Czech Republic Service Activities Efficiency Fig. 1: Correlation between efficiency in the national economies and efficiency in their services activities This model is based on 489 decision-making units corresponding to the countries included in the study and all activity branches. Agriculture, manufacturing, etc are also evaluated in the DEA model. The linear function adjusted in the figure has an R 2 larger than 0.75, so more than 75% of the variability in the efficiency of national economies is explained by the efficiency in service activities. The positive sign of the coefficient signifies that an increment in the productivity of services implies a parallel increment in the productivity of national economies. The strength of this linear association is also reflected by the Pearson correlation coefficient equal to Four countries are at the top of the efficiency ranking for national economies: Estonia, Ireland, Luxemburg and Mexico. Only Estonia and Luxemburg are also in the top level of efficiency in the service sector. But some countries (e.g. Norway, Canada or Korea) maintain a notable gap between the productivity level of the economy and the productivity level of services. The reason is that they have other very efficient economic activities outside of the service sector. In the previous DEA model, efficiency of all the activities of all countries was evaluated. Real estate, renting and business activities, Wholesale and retail trade, repair of motor vehicles and household goods, and Financial Intermediation appeared as the most efficient service activities. At the bottom of the ranking, the branches of Hotels and restaurants and Private Households with employed persons appear as the least efficient services (Table 2). 9

10 ACTIVITY BRANCH Relative Size Efficiency NDRS2 K: Real estate, renting and business activities 18.56% D: Manufacturing 18.14% G: Wholesale and retail trade; repair of motor vehicles and household goods 12.19% J: Financial intermediation 6.40% I: Transport, storage and communication 7.51% C: Mining and quarrying 2.34% F: Construction 6.38% L: Public administration and defence; compulsory social security 6.21% N: Health and social work 6.09% E: Electricity, gas and water supply 2.49% M: Education 4.81% O: Other community, social and personal service activities 4.16% B: Fishing 0.12% A: Agriculture, hunting and forestry 2.19% 7.65 H: Hotels and restaurants 2.44% 7.61 P: Private households with employed persons 0.31% 6.06 Table 2: Relative size and efficiency of production activities In the OECD area, the correlation between the relative size of each of the 16 branches of activity and their relative size in terms of value added is very high (Pearson correlation coefficient: 0.962), indicating an appropriate specialisation of production in those industries that are more efficient. In addition, activities that have a greater separation of central tendency (Agriculture, hunting and forestry; Fishing; Electricity, gas and water supply; Mining and quarrying) do not belong to the service sector. By considering service activities, the relationship becomes stronger and the Pearson correlation coefficient goes up to Figure 2 depicts this association in two graphics, one for all production activities and another only for services NDRS Eff All banches y = x R² = NDRS Eff service banches y = x R² = % 5% 10% 15% 20% Relative size of all production branches 0 0% 5% 10% 15% 20% Relative size of service branches Fig. 2: Relationship between relative size and efficiency However, this situation is not replicated in every country, but we noted the existence of gaps between the level of efficiency and the relative size of production activities in national economies. We carried out a particular analysis for each OECD country in which we compared the efficiency (weighted with relative size) of their service activi- 10

11 ties with the OECD average. In this way we can know the individual contribution of service branches to the national performance level in the service sector. Figure 3 gives us an example for the French service sector. COUNTRY ACTIVITY Size NDRS2 Sd Size Sd Eff Dif Nat vs Sd Share France G: Wholesale and retail trade; repair of motor vehicles and household goods % France H: Hotels and restaurants % France I: Transport, storage and communication % France J: Financial intermediation % France K: Real estate, renting and business activities % France L: Public administration and defence; compulsory social security % France M: Education % France N: Health and social work % France O: Other community, social and personal service activities % France P: Private households with employed persons % TOTAL SERVICE ACTIVITIES % 30% 25% 20% 15% 10% 5% 0% G H I J K L M N O P Relative Size Sd Size NDRS2 Sd Eff Fig. 3: Size and efficiency in the French services in comparison with the OECD average In this case France has a service sector larger than the average of the studied countries. 77% of French value added was generated by the service sector in 2006 while in the OECD this value scarcely achieves 70%.In addition the average level of efficiency is alto higher in France, thus we have a service sector larger and more efficient that has a positive contribution to the global performance of the French economy. The aggregate analysis should be explored with more details at the level of services branches. We can observe that most of the French relative advantage in terms of weighted efficiency is concentrated in Real estate, renting and business activities. In this branch the country develops a higher level of efficiency (green triangle) than the OECD average (red point), and furthermore the relative size of this branch is also larger in France. The same phenomenon, but in a less important dimension, can be observed in branch of Health and social work. That means that the French service sector presents a right strategy because it concentrates most of the value added generation in the branch in which its efficiency level has the greater comparative advantage. In the same way, extents of those branches where this economy has a lower level of efficiency are consequently smaller than the standard. 11

12 COUNTRY Relativ e Size NDRS2 Sd Size Sd Eff Dif Nat vs Sd G: Wholesale and retail trade; repair of motor vehicles and household goods H: Hotels and restaurants I: Transport, storage and communicati on J: Financial intermediati on K: Real estate, renting and business activities L: Public administratio n and defence; compulsory social security M: Education N: Health and social work O: Other community, social and personal service activities P: Private households with employed persons Austria Belgium Canada Czech Republic Denmark Estonia Finland France Germany Greece Hungary Ireland Israel Italy Japan Korea Luxembourg Mexico Netherlands New Zealand Norway Poland Slovak Republic Slovenia Spain Sweden Switzerland United States Table 3: Relative advantage and disadvantage in terms of efficiency in the service sector of OECD countries 12

13 Table 3 offers a resume of the national analyses. In the first three columns we find the name of the country, the relative size and the mean efficiency in its service sector. Column 4 and 5 reflect the average size and efficiency level in the OECD. The sixth column offers the difference between the efficiency of the country and the standard value in the OECD, in both cases weighted with the relative size. This column gives very useful information to know the gap between the service sector of a country and the group of comparison. We have coloured in green those cells corresponding to countries with positive scores, i.e. with a correct strategy in their structural composition and in their efficiency. In the right side of the table, the rest of the columns indicate the behaviour of the countries in the different services activities. In these columns red and green marks represent negative and positive values respectively. Cells coloured in yellow try to help in the identification of some relevant facts: The advantage of Greece is concentrated in three branches of traditional services: wholesale and retail trade; hotels and restaurants; and transports. Estonia and Mexico also concentrated their advantages in traditional service branches. Luxemburg, the country with de greatest advantage, has a significant concentration on Financial intermediation. Greece and Spain are the unique countries with a positive situation in the Hotel and restaurant branch. Estonia, France, Israel and the United States present the higher values in the activities related to Real estate, renting and business. This branch is the more efficient, so those countries with a good performance in this branch have a great contribution to the service sector productivity. Education activities show a very uniform behaviour for all countries. Denmark, Norway and Sweden concentrate the best level of efficiency in Health and social work activities. Finally, we need to investigate the determinants of productivity in the service sector. The econometric analysis will help us to give some suggestions for policy-makers. We started with a traditional model in which we included 270 observation referred to the services branches. In this model we try to explain the efficiency scores obtained in the NRDS2 DEA by means seven variables, labour (L), capital consumption (KC), ICT capital services (ICT), software capital services (SOFTCA), human capital (HCA), relative size (RSIZE), and the apparent productivity of the labour factor (VAL). Table 4 offers the summary of results obtained from the first model with eight variables. 13

14 Dependent Variable: Efficiency (NDRS2) Method: Least Squares Sample: Included observations: 134 Variable Coefficient Std. Error t-statistic Prob. L 1.25E KC 2.66E E ICT SOFTCA HCA RSIZE VAL C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info c riterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Table 4: Initial econometric model In a preliminary evaluation, this model could be considered a good model. It has a high R-squared and an adjusted R-squared, and it provides an acceptable fit (probability of F Statistic equal to zero). Individually considered, ICT, RSIZE and VAL variables are statistically significant. The value of Durbin-Watson Statistic is however quite low. We applied the redundant variables test to the previous model and confirmed that variables L, SOFTCA and HCA were redundant. With the rest of the non-redundant variables we adjusted a new model. This model presented linearity problems and we solved these problems with a semi-logarithmic model (Table 5). 14

15 Dependent Variable: LOG (Efficiency-NDSR2) Method: Least Squares Sample: Included observations: 154 Variable Coefficient Std. Error t-statistic Prob. KC 6.68E E ICT RSIZE VAL C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Table 5: Final econometric model This model maintains an acceptable fit (probability of F Statistic equal to zero) and the value of Durbin-Watson Statistic increased notably. Individually considered, ICT, RSIZE and VAL variables are statistically significant and they have positive coefficients. The model has been adjusted based on individual data, but we can presume that contextual variables (country, type of service, activity branch) determine a specific behavior for each of the groups resulting from these three classifications. As we stated in the methodological section, multilevel models interpret the coefficients (intercepts and slopes) in level 1 as results of coefficients in level 2. Thus, our first task is to check if some of our contextual variables can be used as a factor for level 2. Table 6 shows the results obtained from the various multilevel models. The first frame includes the so-called Random Effect Model or null model. Results from this model show that the Activity Branch variable is the only one that has a statistically significant variance of parameters. A critical level of the Z Wald Statistic less than 0.05 indicates that the variance of this factor is not equal to zero. For this reason, that variable can be used for establishing different groups in a multilevel model. Estimates about the parameters of covariance give information regarding the factor variance (how much efficiency varies among the various branches = ) and of residuals (how much efficiency varies inside each branch = ). The intra-class correlation coefficient [(171.15) / ( )] indicates that 51.89% of the total efficiency variability corresponds to the difference among the averages of the branches. 15

16 RANDOM EFFECT MODEL Fixed Effects Parameters Parameter Estimate Std Error Freedom Deeg. t Significance Country Intersection Type of Serv. Intersection Act. Branch Intersection Covariance Parameters Estimación Error típico Wald Z Significance ICC Residuals Country % Residuals Type of Service % Residuals Activity Branch % AVERAGE AS RESULTS REGRESSION MODEL Fixed Effects Parameters Estimate Std Error Freedom Deeg. t Significance Intersection HC_Centr Intersection ICT_Centr Intersection Soft_Centr Intersection Size_Centr Intersection VA_L_Centr Covariance Parameters Estimación Error típico Wald Z Significance ICC Residuals HC_Centr % Residuals ICT_Centr Residuals Soft_Centr Residuals Size_Centr % Residuals VA_L_Centr RANDOM EFFECT COVARIANCE MODEL Fixed Effects Parameters Estimate Std Error Freedom Deeg. t Significance Intersection Size_Centr HC_Centr Intersection Size_Centr ICT_Centr Intersection Size_Centr Soft_Centr Intersection Size_Centr VA_L_Centr Covariance Parameters Estimación Error típico Wald Z Significance ICC Residuals HC_Centr Residuals ICT_Centr % Residuals Soft_Centr Residuals VA_L_Centr RANDOM COEFFICIENTS REGRESSION MODEL Fixed Effects Parameters Estimate Std Error Freedom Deeg. t Significance Intersection Size_Centr Covariance Parameters Estimación Error típico Wald Z Significance ICC Residuals Size_Centr NE (1,1) % Size_Centr NE (2,1) Size_Centr NE (2,2)

17 Table 6: Multilevel models results The second frame contains the results obtained from the Average as Results Regression Model. This model tries to identify which variables can explain the differences among the different branches (level 2). In this case, two variables Human capital and Relative Size present a statistically significant association with efficiency. The estimated coefficient for HC_Centr has negative sign, so when human capital increases the efficiency level decreases. Size_Centr however has a positive coefficient which indicates that branches with a larger size have a greater efficiency level. Nevertheless, these variables individually considered are not able to explain all the variability observed in each branch. The values less than 0.05 mean that branches maintain some differences in the level of efficiency after controlling by human capital and relative size. The third frame presents the results obtained in a more complete model in which we have included a new co-variable corresponding to level 1. This model seeks to explain the existing differences among the records from a same branch. In this case, the variable ICT_Centr proves to be a great complement to the Size_Centr variable. Finally the fourth frame shows the results from the Random Coefficients Regression Model. This model allows that both coefficients (slopes and intercepts) can vary among branches. The table displays the residuals variance (residuals), the intercepts variance [NE (1,1)], the slopes variance [NE (2,2)], and the intercepts and slopes covariance [NE (2,1)]. The null hypothesis is that the variance is equal to zero. This hypothesis is rejected for the intercepts but accepted for slopes. Thus, we can conclude that the intercepts for the various branches are different and the slopes are equal for every branch. These results can be also observed in Figure G: Wholesale and retail trade; repair of motor vehicles and household goods H: Hotels and restaurants I: Transport, storage and 80 communication 80 J: Financial intermediation Efficiency Efficiency 60 K: Real estate, renting and business activities L: Public administration and defence; compulsory social security 40 M: Education 20 N: Health and social work O: Other community, social and personal service activities 20 Relative Size of Activity Branches Relative Size of Activity Branches P: Private households with employed persons Fig. 4: Traditional vs. multilevel linear models 17

18 4. Conclusions In this paper we studied productivity in the various activity branches integrated within the service sector. We checked the association between the efficiency in the service sector and the efficiency in national economies. The relationship between relative size and efficiency was another point of our interest, both at a national and at an OECD level as well. Specifically, the hypotheses that we verified were the following: - The productive efficiency of a country is closely connected with the efficiency of the service sector. - National service productivity depends on the level of efficiency achieved in those service activities with a greater relative weight. - National service productivity depends on the pattern of production specialisation in each country. Estonia, Ireland, Luxemburg and Mexico obtained the highest efficiency scores. The connection between aggregate productivity and the efficiency of the service sector has been confirmed at the OECD level and at a country level as well. More than 75% of the efficiency variability in the countries is explained by the efficiency of the service sector. Real estate, renting and business activities, Wholesale and retail trade, repair of motor vehicles and household goods, and Financial Intermediation appeared as the most efficient service activities at an OECD level and for most national economies. These three activity branches also exhibit the largest relative size in the majority of the OECD countries. The highest productivity score achieved by business services confirms the results published in previous works. Nevertheless, we detected singular specialisation patterns in some countries. For this reason we have combined the efficiency level of each of the activity branches at a country level with the relative size of these branches. In this way we calculated a weighted efficiency score in which we took into account not only the efficiency but also the relative size of each branch for every country. The national weighted efficiency score was compared with the OECD average weighted efficiency score. This comparison makes it possible to identify undesirable situations in some national economies. Most of the countries with a lesser weighted efficiency score than the average show clear deficiencies either in the efficiency of some activity branches or in the relative size of these branches. In the results section we posed the French case as a good example regarding specialisation in service branches, but we found many other examples of an incorrect specialisation pattern. Switzerland, for example, has a Wholesale and retail trade; repair of motor vehicles and household goods activity branch with a lower level of efficiency than the OECD average while its relative size is higher. By reducing the relative size of this branch, the Swiss service sector and the Swiss economy in general could increase their efficiency levels. Other cases suggest great opportunities for improvement of the service sector productivity by increasing the level of efficiency in some specific branches. A lot of countries could 18