Accessibility gains and road transport infrastructure in Spain: A productivity approach based on the Malmquist index

Journal of Transport Geography 52 (2016) 143–152

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Journal of Transport Geography journal homepage: www.elsevier.com/locate/jtrangeo

Accessibility gains and road transport infrastructure in Spain: A productivity approach based on the Malmquist index Andrés Maroto, José Luis Zofío Departamento de Análisis Económico, Teoría Económica, Universidad Autónoma de Madrid, C/ Francisco Tomás y Valiente, 5, E-28049 Madrid, Spain

a r t i c l e

i n f o

Article history: Received 7 January 2015 Received in revised form 18 March 2016 Accepted 20 March 2016 Available online 19 April 2016 Keywords: Productivity change Malmquist indices Distance functions Accessibility Transport costs

a b s t r a c t Accessibility, the relative access to markets, is a strategic concept in all economic models with a spatial dimension and its prominence has been acknowledged in many economic research fields and policy debates. This paper is based on the assumption that infrastructure drives economic accessibility and, therefore, we can assimilate a production function approach where the road network constitutes a set of inputs yielding access to markets as output. Methodologically, we originally measure the infrastructure inputs accounting for the real used network and calculate a series of new final and intermediate demand gravity-based and locational indicators, which capture a wide range of economic transactions and represent different concepts of economic accessibility outputs. The value added of this paper is translating a non-parametric frontier approach (DEA) to a dynamic scope (Malmquist indices) by connecting the regional accessibility to the productivity of the road infrastructure inputs associated with each region. Results during 1995–2005 show a low relative accessibility of the Spanish NUTS-3 regions, although improvements have been greater over the last five years. Finally, we observe a U-inverted relationship between the accessibility gains during these years and the geographical localization. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction Accessibility is a term often used in transport and land-use studies. It is seen as being concerned with the opportunity available to people at a given location to take part in a particular set of activities. However, various other interpretations of the term have been made (see Jones (1981) and Geurs and van Wee (2004) for a revision of the definition and measurement). Accessibility, seen as the relative access to markets, is a key concept in all economic models with a spatial dimension. It drives trade flows at any scale, ranging from countries to urban areas, and its importance, therefore, has been acknowledged in trade theory, economic geography, and regional economics. In trade theory, relative market potential determines the spatial equilibrium of production across economies favoring those locations with better accessibility (i.e., through a trade freeness matrix, as in Behrens et al., 2007; Behrens and Ottaviano, 2008). In economic geography, this potential determines the mobility of firms and labor in terms of agglomeration and dispersion forces influenced by relative transport costs that are incorporated in real income relations (i.e., real wage equations, as in Fujita et al., 1999; Head and Mayer, 2004). Finally, in regional economics, improvements in accessibility should lead to economic development in the long run and, by implication, to greater economic cohesion understood as reductions in income inequality if accessibility increases in favor of less-developed regions (Vickerman et al., 1999).

E-mail addresses: [email protected] (A. Maroto), jose.zofi[email protected] (J.L. Zofío).

http://dx.doi.org/10.1016/j.jtrangeo.2016.03.008 0966-6923/© 2016 Elsevier Ltd. All rights reserved.

It is not surprising, therefore, that at national and regional levels governments design their infrastructure and transport policies with these concepts in mind. Any improvements in the transportation network change the relative access to markets of all regions, thereby triggering economic mechanisms that, in turn, result in changes in the distribution of economic activity. To ensure more effective integration of economic development and transport planning, policy guidelines require a greater consideration of accessibility issues (Halden, 2002). Despite the theoretical and political importance of accessibility, this concept is often misunderstood, poorly defined, and too simply measured, as it relies on partial indicators. Finding an operational and theoretically sound concept of accessibility is quite difficult and complex as there is no single best measure identified for it, and the choice depends on the type of the problem being studied and the statistical resources available (e.g., data availability). Indeed, it has been based traditionally on the analysis of some common isolated indicators frequently used in the literature (Gutiérrez, 2001). However, some authors, such as Martín et al. (2005) or Brida et al. (2014), have recently applied the non-parametric Data Envelopment Analysis (DEA) methodology (or some of its extensions, such as the Multi-Stage Network Data Envelopment Analysis (Qin et al., 2014)) to develop a synthetic accessibility index that combines the complementary information provided by the distinct accessibility indicators. The contribution of this study is to improve this non-parametric frontier approach for measuring static (year by year) productivity of the road network in terms of the accessibility it brings to each region, and to extend it to a dynamic setting by considering how such productivity—understood as the ratio of accessibility to road network—changes over time.

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Specifically, we use the DEA methodology to estimate Malmquist indices and their time variations, and rely on bootstrapping techniques to determine if they are statistically significant. The main advantage of this approach is that it allows us to analyze productivity change and break down variations in global accessibility into the changes in the accessibility of the leading regions—those where accessibility is higher and are categorized as efficient—and the convergence effects for those regions whose relative accessibility is lower—inefficient regions (i.e., whether new transport infrastructure investments plans are able to increase their accessibility not only in absolute terms, but also relatively to the efficient regions, so a catch-up process is observed). The rest of the paper is divided into five sections. Section 2 describes the calculation and selection of the road network that is categorized into three inputs producing six accessibility outputs—differentiating between those related to the final and intermediate demands. Section 3 presents the DEA methodology used to estimate Malmquist productivity indices in terms of accessibility, and its associated sources of change in terms of benchmark accessibility change and regional specific efficiency change. In Section 4, we apply this methodology to the productivity of road freight transport infrastructure in terms of accessibility of the Spanish NUTS-3 regions. Finally, Section 5 summarizes and concludes the research.

(vi) indirect costs, indti , associated with other administration overhead, operating expenses and commercial costs. Given the driving time for an arc: tta, the overall cost associated with traveling the whole length of an itinerary is: 0 1 0 1

 t d ¼ ∑ etl @ ∑ t ta A ¼ ∑ etl @ ∑ ta A l l a∈It a∈I t sa

TimeC ti j

ij ij 0 1 t   da A t t @ t t t t ∑ t ¼ labi þ amort þ f in þ ins þ taxi þ indi a∈It sa

With this information, the GTC between an transport zone of origin i and a destination j in period t is calculated using Geographical Information Science (GIS) techniques, including the existing (digitized) road networks from 1995 to 2005. Particularly, the GTC is the solution to the following minimization problem that identifies the least cost route t It⁎ ij in period t, among the set of itineraries Iij: !   X X t t t t ¼ DistC þ TimeC e GTC tij ¼ min ij ij k da t t I ij ∈Iij

þ

2. Infrastructure and accessibility

X

! etl

0 1 BX t C taA ¼ @ a∈I tij

l

This study is based on the assumption that infrastructure drives economic accessibility and, therefore, we can adopt a production function approach where the network of low, medium, and high capacity roads constitutes a set of inputs yielding access to markets as output. For a particular geographical area, the inputs that it uses when trading with itself and other regions (export and import flows) correspond to the road infrastructure that is used in these exchanges. A region uses its own infrastructure as well as that of neighboring areas (both adjacent and non-adjacent) so, therefore, it is mandatory to measure to what extent the existing road network is really used in commercial flows. Zofio et al. (2014) calculated generalized transportation costs, GTCs, for the Spanish regions (NUTS-2) and provinces (NUTS-3) assuming a cost minimizing behavior on the part of road freight firms. Spain classifies geographical areas according to the NUTS classification (Nomenclature of territorial units for statistics), which is a hierarchical system dividing up the EU's economic territory for the purpose of allowing socio-economic analyses of the regions. NUTS-2 (Comunidades Autónomas) are basic regions for the application of regional policies, while NUTS-3 (Provinces) are smaller geographical areas for specific diagnoses, such as the study undertaken here. Researchers have divided the Spanish territory into a total of 678 transport zones, as a result of aggregating almost 8000 municipalities, for which they calculate optimal itineraries between each zone i and the remaining destinations j using GIS and resorting to a least-cost algorithm. The digitized road network contains information about the transportation costs of using any arc. These economic costs are related to the distance and travel time: dta and tta = dta/sta, where sta corresponds to the legal speed limit of the arc. The economic distance unit costs in time t, denoted by etk, i.e., Euros per kilometer, include the following variables: (i) Fuel costs, fuelti; (ii) Toll costs, tollti; (iii) Accommodation and allowance costs, accom&allowt; (iv) Tire costs, tiret; and, (v) Vehicle maintenance and repairing operating costs, rep&mantt. Taking into account these operating costs, the total distance cost corresponding to an itinerary Itij is:

DistC ti j



k

t

a∈I tij

X l

k

! etl

0 1 t BX da C @ A; sta t

ð3Þ

a∈I ij

t

and whose associated optimal distance and time values are dij ¼ t ∑a∈It da ij

t and t t ij ¼ ∑a∈It t a . For each transport zone i, adding across ij

all other destinations j returns the optimal length of kilometers that each geographical zone uses in their commercial trade flows when t

exporting goods by road: Dt i ¼ ∑ j dij . As the digitized road network differentiates between high, medium, and low capacity roads, from the optimal solution we can recover the following vector with the ⁎ ⁎ ⁎ length of the roads by categories: (Dt,HC , Dt,MC , Dt,LC ). Aggregating i i i the results for individual transport zones by provinces, the distances in kilometres associated with these three types of roads correspond to the inputs yielding the following (output) accessibility to markets. 2.1. Accessibility output indicators The study of the impact of transport infrastructure has traditionally been based on the analysis of some common isolated indicators, each one yielding partial information (even if complementary) regarding relative market potentials. For this study we consider and introduce a series of final and intermediate demand indicators that capture a wide range of economic transactions, thereby representing different concepts of economic accessibility, particularly location and potential indices. 2.1.1. Final demand indicators With regard to final demand, we first consider the following location indicator: X LDF i

¼X

GDP j

j

GTC ij  GDP j

;

ð4Þ

j


 t ¼ ∑ ∑ etk da a∈I ti j

ð2Þ

ij

t



t

¼ ∑ f ueli;aðr;tÞ þ tolli;aðr¼1;tÞ þ accom&allowt þ tiret þ rep&mant t da a∈I ti j

ð1Þ Likewise, the economic unit costs associated with time, denoted by etl , i.e., Euros per hour, include the following variables: (i) Labor costs, labti ; (ii) Financial costs associated with the amortization, amortt; (iii) financing, finti ; (iv) Insurance costs, inst; (v) taxes, taxti ; and, finally

which represents the average of the destination economic activities weighted by the generalized transportation costs between the geographical area i and all destinations j. Economic activity is captured by the area's gross domestic product: GDPj, as a proxy of j's income, and therefore the potential final demand of j for goods produced in i (i.e., i exports to region j)—see Gutiérrez and Urbano (1996). The higher the value of LDF i , the better positioned (central) is i with respect to the geographical distribution of income across the whole geographical area (e.g., a country). Particularly, the better connected is

A. Maroto, J.L. Zofío / Journal of Transport Geography 52 (2016) 143–152

i with the remaining areas, the lower its generalized transportation costs, and the larger is the location indicator. As we want to measure the efficiency of the road infrastructure, LDF i should be a decreasing function in transport costs, so the higher the GTCij, the lower the accessibility, and vice versa. Note that since the efficiency analysis is based on the DF comparison of accessibility levels to the road network distance (Dt⁎ i ), Li reinforces the efficiency of regions whose optimal road length is both shorter and faster, resulting in lower GTCij. From a dynamic perspective, it is expected that, as the road network improves and operating costs reduce (e.g., more efficient engines consuming less fuel), generalized transportation costs decrease in time and, therefore, the accessibility indicator in terms of final demand increases. Nevertheless, changes in this indicator can also take place as a result of the changes in the distribution of GDPs across a country, with some areas growing at a higher pace than others. Therefore, relative accessibility in terms of final demand will depend on the areas' incomes and GTCs, which in turn depend on the road network and operating costs. A second indicator capturing accessibility levels in terms of final demand is the following economic accessibility potential index: P DF i ¼

X GDP j

:

GTC αij

j

ð5Þ

This index represents a gravity-based measure that captures the closeness of potential economic activity (income) to area i (see Harris (1954); Keeble et al. (1988); Linecker and Spence (1992); Smith and Gibb (1993); Ortega et al. (2014), among others). The standard definition of the index imposes a decay function on the generalized transport costs between the origin–destination (α parameter). In this study we adopt a neutral value α = 1 since the calculations of the GTCs already account for factors that result in economies or diseconomies of distance. 2.1.2. Export and import indicators for intermediate demand When accessing markets, firms and other economic agents in a given area are not only concerned with final demand, as they also produce intermediates for other industries. It is therefore necessary to incorporate trade in intermediates in our analysis. The compatibility between the exports' structure of a given area and that of an importing counterpart j is essential to understand the level of accessibility to intermediate goods markets. To capture the importance of this bilateral compatibility we introduce the following intermediate demand location indicator: X XLID i ¼

j

X j

" 10; 000− "

X

wXij

 2 X si −M sj

#

s

 2 X GTC ij  10; 000− wXi X si −Msj

#:

ð6Þ

145

Finally, to better account for intermediate demand compatibility, a second weight is applied when calculating Eq. (6) since i's export compatibility with j's imports is weighted by the percentage that i's exports to j represent on the aggregate value of i's exports to all regions: wXi ¼ X ij =∑ j X ij . In the same vein, and from the perspective of an area's production structure, firms in i will also be interested in having good access to regions from which they import intermediates. To capture imports' accessibility, we introduce the following accessibility indicator in terms of intermediates: X MLID i ¼

" 10;000−

j

X

"

X

 2 wM M si −X sj i

#

s

GTC ji  10;000−

X

 2 wM M si −X sj i

#

ð7Þ

s

j

whose structure and interpretation are the same as for the previous indicator related to exports' accessibility, but this time the compatibility is defined in terms of the percentage distribution of i's imports from j at the sector level. The dynamics of these export and import location indicators for intermediates are complex, since they depend on trade structures that are changing in time, but also on the evolution of GTCs. In general, as their final demand counterparts, both XLID i and MLID i are decreasing in GTCs, and increasing in export and import compatibility. Our second pair of indicators related to the trade of export and import intermediates also adopts the gravity-base structure of their final demand equivalent ((5)), defining as: X XP ID i ¼

X

"

2 X  s 10; 000− wi X i −M sj s

j

GTC αij

j

X MP ID i ¼

X j

j

"

# ;

 2 X 10; 000− wM M si −X sj i s

GTC αij

ð8Þ

# :

ð9Þ

These indicators capture the centrality of area i with respect to all regions taking into consideration the weighted compatibility of the export and import structures while the interpretation in terms of the decay function is the same as in Eq. (3). 3. Relative accessibility and transport infrastructure: the Malmquist productivity index

s

3.1. The DEA index of relative accessibility Both the intermediate demand export indicator in Eq. (6) as well as its following import counterpart Eq. (7) have been calculated at a five sector classification, s = 1,…,5, including: Agriculture, Energy, Intermediate manufactures, Capital goods, and Consumption goods. As its final demand counterpart, XLID i presents a similar structure with GTCs weighting the relative compatibility between the exports' structure of area i, corresponding to the vector of the percentage values of the s sectors in the total aggregate of exports Xsi , and the imports' structure of j, also represented by the percentage values of these sectors in the total value of imports, Msi . As for the numerical bounds, if the export and import structures are fully compatible by sectors, then (Xsi − M sj ) 2 = 0 ∀ s, and the exports' accessibility in terms of intermediate demand reaches a maximum value of 10,000. On the contrary if a match between exports and imports does not exist (e.g., if area i only exports agricultural products and j imports manufactures), then (Xsi − Msj )2 = 10,000 and region's i accessibility to region j is irrelevant in terms of exports of intermediate demand.

We consider the road network as the infrastructure input producing output accessibility of the studied geographical areas. The mathematical programming approach known as Data Envelopment Analysis (DEA) allows the measurement of relative efficiency across areas in terms of accessibility by constructing a reference frontier—benchmark—defined by those areas whose productivity in terms of output accessibility to the input road network is maximal (see Fried et al. (2008) for a general introduction to the measurement of efficiency and productivity using frontier techniques, both parametric (Stochastic Frontier Analysis, SFA) and non-parametric (Data Envelopment Analysis)). Particularly, let us denote by i = 1,…, I the set of geographical areas (provinces, regions, countries,…) observed in t = 1,…,T periods, whose accessibility in terms of final and intermediate demands, represented by the output vector: yti = t,ID 6 (Lt,FD , Pit,FD, XLit,ID, MLt,ID , MPt,ID i i , XPi i ) ∈ ℜ+, is produced by way of the input road network xti = (Dti , HC⁎, Dti , MC⁎, Dti , LC⁎) ∈ ℜ3+. To assess the

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efficiency level of each geographical area (xti , yti ) relative to the best observed accessibility across all areas, the following program is solved: 6 X

maxvtm ;μ tm

m¼1 3 X

μ tm ytim

  ¼ Dto xti ; yti

ð10Þ

ν tn xtin

n¼1

s.t. M X m¼1 N X n¼1 μ tm ≥

result of a better industrial matching. In contrast, M1,t 1 b 1 signals productivity decline, while M1,t 1 = 1 shows productivity stagnation. Following Färe et al. (1994), we can identify the sources of productivity change in accessibility by decomposing Eq. (11) into two mutually exclusive indices representing intertemporal efficiency change and the shift in the reference frontier of the geographical areas exhibiting the highest productivities—again superscripts refer to benchmark periods, while subscripts refer to the values of the different periods in which the observed area is evaluated: M1;t ¼ 1

μ tm ytjm ≤ 1;

j ¼ 1; …; I

νtn xtjn 0; ν tn ≥ 0;

where μ tn and νtn are the optimal output and input weights when evaluating the relative productivity of area i with respect to all j regions, including itself. Eq. (10) corresponds to the fractional formulation (ratio form), which after some transformations can be expressed as a linear program, and whose resulting objective function is linearly homogeneous of degree one, thereby defining a productivity frontier characterized by constant returns to scale (CRS) (Cooper et al., 2007:23). The maximum observed productivity levels are normalized to one, thanks to the first set of constraints and, therefore, the objective function represents a relative productivity level. As a result, the solution to Eq. (10) can be deemed as an efficiency level: i.e., a scalar representing the distance between observed accessibility and maximal accessibility, which we denote by DtO(xti , yti ) in the objective function, and where the subscript indicates that it can be interpreted as the maximum feasible expansion of the observed vector of outputs yti that would be necessary to reach the benchmark (maximal) productivity levels given the observed input levels xti . When DtO(xti , yti ) =1 the geographical area attains the maximum relative productivity in period t, presenting the higher accessibility values relative to the road network that it uses. On the contrary, DtO(xti , yti ) b 1 signals that the region is not as productive as its counterparts, and determines how far from the reference frontier is the area under evaluation. 3.2. The sources of accessibility gains in terms of productivity

      D1O xti ; yti D1O xti ; yti DtO xti ; yti 1;t t ¼        ¼ FC1;t  EC1;t : DtO xti ; yti D1O x1i ; y1i D1O x1i ; y1i

FCt1,t (frontier change) captures the change in the reference frontier defined by those areas exhibiting the highest productivity levels in periods 1 and t. Again, FCt1,t N 1 implies that the road network productivity in terms of accessibility of the most productive areas in both periods (those with DtO(xti , yti ) = 1, t = 1, 2), increases over time. FCt1,t = 1 signals that the highest productivities remain constant, while FCt1,t b 1 implies that productivity reduces over time as a result of reductions in the accessibility output indicators. For example, this last result can be observed in the event of generalized transportation costs increasing as a result of more expensive operating costs or the lack of maintenance of the road network resulting in longer shipping times. Also, the distribution of economic activity or the general compatibility of exports and imports may decrease as a result of shifts in the production structures, decline of traditional industries, etc. The second term EC1,t 1,t (efficiency change) measures the intertemporal change in observed productivity with respect to the maximum reference values in each period. If EC1,t 1,t N 1, the area gets closer to the maximum productivity from the base to the current period, while if EC1,t 1,t = 1, its relative position does not change and, finally, EC1,t 1,t b 1 signals that the area is experiencing a worsening in its relative situation. It is possible to gain further insight on this latter efficiency change component by assessing the contribution that scale efficiency makes to overall efficiency change. Scale efficiency refers to the evaluation of the accessibility of a geographical area referred to a frontier benchmark that is characterized by similar values of outputs and inputs; that is, similar areas in terms of road infrastructure endowments and accessibility levels. To determine the role played by productive scale in overall efficiency change, a second level decomposition is necessary: EC1;t 1;t ¼

  ˆt xt ; yt  Dt xt ; yt =D ˆt xt ; yt  DtO xti ; yti D 1;t 1;t O O O  1 1  ¼ 1  i i    i i  1  i i  ¼ PEC1;t  SEC1;t ; ð13Þ 1 ˆ x1 ; y1 D1 x1 ; y1 =D ˆ x1 ; y1 DO xi ; yi D O

For any geographical area i observed in two time periods, the change in the relative productivity of the road network it uses in terms of the achieved accessibility can be defined resorting to the Malmquist productivity index introduced by Caves et al. (1982). Taking the first period as the base year for the index—subscript, productivity change for the observed values of area i from the first base year to t is defined as: M1;t 1 ¼

  D1O xti ; yti  : D1O x1i ; y1i

ð11Þ

Consequently, the Malmquist index yields the change in an area's productivity using the productivity levels of the base period as reference. There are productivity gains when the accessibility of a given region increases given the road network it uses in its commercial relations. By keeping the benchmark productivity values constant at the base year, if M1,t 1 N 1 the area's road network productivity in terms of accessibility increases; i.e. the output accessibility indicators increase as a result of reduction in the generalized transportation costs (e.g., driven by lower operating costs), the distribution of gross domestic products is more favorable (the economic performance of trading partners improves) or export and import compatibilities increase as a

ð12Þ

i

i

O

i

i

O

i

i

ˆ ðxt ; yt Þ corresponds to a modified formulation of program (10) where D O i i where the objective function is enhanced by adding scale parameter ωti . The resulting model is termed VRS, as the linearized objective function is not homogeneous, thereby characterizing a variable return to scale productivity frontier (Cooper et al., 2007: 91). The first term PEC1,t 1,t measures the change of what is known in the Malmquist literature as pure efficiency, as it corresponds to the change in the relative productivity of an observation considering similar benchmarks or peers. On the other hand, SEC1,t 1,t measures the change in the relative (scale) efficiency of a given area considering the productivity levels of all observations EC1,t 1,t, with respect to that achieved when compared to similar ones; 1,t 1,t i.e., SEC1,t 1,t = EC1,t/PEC1,t. Again, values of these indices greater than one would reflect that the evaluated area is getting closer to the production frontier, both in terms of areas that are alike, PEC1,t 1,t N 1, but also with respect to those that define the highest productivity in the whole geographical area: SEC1,t 1,t N 1. Values equal to one imply that the relative situation has not changed over time, and smaller than one that the area's efficiency with respect to other areas has worsened. Zofio (2007) discusses different interpretations for each of these terms from the perspective of production theory. t

A. Maroto, J.L. Zofío / Journal of Transport Geography 52 (2016) 143–152

4. The productivity of transport infrastructure in terms of accessibility: the Spanish case

Table 1 Descriptive statistics on inputs and outputs of the model. Source: Own elaboration.

4.1. Data We compiled a database for 45 NUTS-3 Spanish provinces (excluding those that are not accessible by road—Canary Islands, Balearic Islands, Ceuta, and Melilla) that includes inputs and outputs provided and generated by various agencies between 1995 and 2005. With regard to the outputs introduced in our model three different sources have been used. Interregional trade variables, both in terms of exports (Xsi ) and imports (Msj ), have been obtained from the C-Interreg database (www.c-interreg.es) (see Llano et al. (2010) for more information on this source elaborated for the project). Economic variables, mainly the regional GDPj, have been collected from the Regional Accounts (NUTS-2) provided by the National Institute of Statistics (INE, 2014). The first stage of the methodology relies on the calculation of the generalized transport costs (GTCij) to determine the length of roads representing the input vector xti = (Dt,HC⁎ , Dt,MC⁎ , Dt,LC⁎ ) ∈ ℜ3+ in i i i Eq. (10). In doing so, we use the stock of infrastructure in kilometers (distance, Di) disaggregated into the three types of roads by capacity (high, medium, and low). As presented in the second section, the value added by our approach consists in accounting for the network infrastructure that is really used in trade flows, instead of considering the simple aggregate of the overall physical length of all roads exiting within a given territory, thereby including only the road network that is effectively used, and corresponding to the solution to the generalized transportation cost minimization problem. Álvarez-Ayuso et al. (2014) further extend the concept of optimal physical network infrastructure (length in km) to that of an optimal capital stock measured in monetary units. They proposed a methodology that values the physical infrastructure in terms of capital stock at the arc level, which is later aggregated, differentiating between low, medium, and high capacity roads, into the concept of used capital stock. This new variable is then included in the production function approach to determine the effect of transport infrastructure on regional value added and economic growth. In a second stage, and using the previous statistical sources to compile our database, we estimate the two output indicators related to the final demand and the other four linked to intermediate demand indicators—reflecting complementarities in exporting– importing trade flows—as aforementioned in Sections 2.1.1 and 2.1.2; t,ID t,ID 6 i.e., yti = (Lt,FD , Pit,FD, XLit,ID, MLt,ID i i , XPi , MPi ) ∈ ℜ+ corresponding to the numerator of the accessibility index ((10)). A summary of the main descriptive statistics on inputs and outputs is displayed in Table 1. Pursuing the research objective assessed in the Introduction section, and based on the methodology and the results introduced, we have clustered the Spanish NUTS-3 provinces according to their generalized transport costs. Results are shown in Fig. 1, which shows the average of the GTCs corresponding to the transport zones located in each province to all other transport zones in Spain. Data on Spanish transport costs in the mid-90s confirm long-established ideas in the literature on transport accessibility, and reproduce the results obtained for other countries such as France (Combes and Lafourcade, 2005), as well as at the European level (Spiekermann and Nuebauer, 2002). Areas situated in central regions, especially Madrid, have the lowest GTCs due to their location and the network configuration of the Iberian Peninsula (lighter colors). Madrid and its surrounding provinces have a privileged geographical position in the center of the country. In the former case, as the administrative and economic capital of the country, Madrid has benefited from a highly inclusive and dense transport and communications network. For these reasons, a high proportion of the optimal road freight transport itineraries pass through the Madrid region. In contrast, the highest GTCs (darker colors) are located in peripheral regions, especially in Galicia, Asturias, and Catalonia. Based on the transport costs scale portrayed in Fig. 1, we have specified a core–periphery model with five regional clusters. By introducing

147

LDF PDF

XLDI

XPDI

MLDI

MPDI Outputs (6)

DHC (km) DMC (km)

DLC (km) Inputs (3) a

Mean St. Dev. Max. Min. Mean St. Dev. Max. Min. Mean St. Dev. Max. Min. Mean St. Dev. Max. Min. Mean St. Dev. Max. Min. Mean St. Dev. Max. Min. Mean St. Dev. Max. Min. Mean St. Dev. Max. Min. Mean St. Dev. Max. Min.

1995

2005

Variationa

0.0021 0.0004 0.0029 0.0013 9,169 7,757 54,612 3,378 0.0022 0.0006 0.0039 0.0013 0.12 0.04 0.27 0.05 0.0021 0.0006 0.0036 0.0012 0.12 0.05 0.28 0.06 46,305 17,110 79,876 15,293 116,492 42,881 209,299 38,075 142,963 54,941 258,213 43,240

0.0022 0.0004 0.0029 0.0014 12,148 9,383 67,461 4,922 0.00 0.00 0.00 0.00 0.11 0.04 0.22 0.05 0.0022 0.0006 0.0037 0.0012 0.11 0.04 0.22 0.05 67,595 24,317 113,994 23,226 102,996 38,952 188,695 32,617 134,668 52,027 247,112 40,455

0.18 −0.43 0.00 0.77 3.25 2.10 2.35 4.57 0.22 −0.12 −0.26 0.00 −0.45 −1.30 −1.75 −0.51 0.11 −0.25 0.28 0.00 −0.47 −1.64 −2.24 −1.26 4.60 4.21 4.27 5.19 −1.16 −0.92 −0.98 −1.43 −0.58 −0.53 −0.43 −0.64

Annual average growth rate (%).

this regional classification, which directly associates the geographical localization of the provinces and their generalized transport costs, we can discuss the efficiency and productivity results related to accessibility considering these different clusters. Clearly, the more peripheral ones are those with higher costs, while the more central regions present lower transport costs. The question is whether the investments undertaken to improve the grid nature of the Spanish road network have resulted in a reduction of accessibility differentials across regions. 4.2. Relative accessibility results: are peripheral regions less efficient? Results on relative accessibility obtained by applying the Data Envelopment Analysis (DEA) framework for the 1995 to 2005 period are summarized for the NUTS-2 Spanish regions in Table 2 and Figs. 2–3. The higher the score, the more accessible will be the region. As discussed in the methodological section, the most accessible regions in relative terms have a score equal to one. Both the accessibility scores and the Malmquist productivity indices reported in the next section have been calculated using the DEA toolbox developed by Álvarez-Ayuso et al. (2016) for MATLAB (www.dealtoolbox.com). Comparing the relative accessibility estimations across regions, two facts can be underlined. First, the average score is below 50%—in particular, 42.4%—in the decade analyzed herein. Despite improvements to the road infrastructure network, especially since the year 2000 (extending low and medium capacity roads to highways and motorways), the relative accessibility of the Spanish regions (in relation to the frontier benchmarked by Madrid) would remain relatively low. High capacity roads (in km) have increased between 1995 and 2005 up to 7.6% of the network, while low and medium capacity roads (in km) have

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Fig. 1. Regional clusters according to generalized transport costs (€), 1995.

decreased during the same period (− 1.1% and − 2.4%, respectively). Other than Madrid, which systematically ranks as the most accessible region, only a couple of Comunidades Autónomas (colored in green in Table 2) displayed a score above the average in 1995 and 2005. These are the Basque Country, with a relative accessibility up to 89% and 95.3% respectively, La Rioja (69.1% and 65.3%), and Castilla y León (55.7% and 53%). Additionally, the Cantabrian region in Northern Spain scores close to the national average. On the contrary, the accessibility in the rest of regions stands clearly below that average. The case of the Basque Country and Cantabria is worthy because they belong to peripheral clusters with generalized transportation costs above the Table 2 Regional accessibility in Spain, 1995–2005. Source: Authors' DEA calculations. 1995

Andalusia Aragón Asturias Cantabria Castilla y León Castilla–La Mancha Catalonia Com. Valenciana Extremadura Galicia Madrid Murcia Navarra Basque Country La Rioja Mean

95 95 D 95 O (x i , y i )

2005 05 05 D 05 O (x i , y i )

0.257 (13) 0.321 (11) 0.168 (15) 0.418 (5) 0.557 (4) 0.406 (6) 0.326 (10) 0.336 (9) 0.235 (14) 0.372 (7) 1.000 (1) 0.346 (8) 0.298 (12) 0.888 (2) 0.691 (3) 0.424

0.265 (13) 0.318 (11) 0.172 (15) 0.426 (5) 0.530 (4) 0.392 (6) 0.328 (10) 0.359 (8) 0.233 (14) 0.380 (7) 1.000 (1) 0.359 (8) 0.280 (12) 0.953 (2) 0.653 (3) 0.432

Variation Δ 05/95 95,05

EC 95,05 + 0.008 – 0.003 + 0.004 + 0.008 – 0.026 – 0.013 + 0.001 + 0.023 – 0.003 + 0.009 + 0.000 + 0.013 – 0.018 + 0.064 – 0.038 + 0.008

Notes: Accessibility scores for NUTS-2 regions calculated as the average of their NUTS-3 provinces Regional ranking in brackets.

national average (cluster 4), and yet their accessibility is larger and well above the mean value of 0.404. On the contrary, accessibility in the rest of regions stands well below that average. In particular, the lowest relative accessible regions are Asturias (16.8% and 17.2%), Extremadura (23.5% and 23.3%) and Andalusia (25.7% and 26.5%). Moreover, relative accessibility in most of the Spanish regions has been low in relation to the benchmarked ones, but it would have remained stable during these ten years (as average efficiency has not changed). The second relevant fact is the lack of any kind of convergence process during the analyzed period. Not only has there been a slight variation in the average relative accessibility (+ 0.008 during the decade), but the regional rankings during these years also remained the same. Although some of the less accessible regions in the mid-90s, such as Asturias (15th) or Andalusia (13th), have positively increased their relative scores during the following decade, some other laggard regions, such as Extremadura (14th), Navarra (12th) or Aragón (11th), have diverged even more from the accessibility optimal frontier. The result of these paths is the stability of the regional ranking during this period. Relating these results to the clusters introduced in the previous section in terms of transport costs and geographical localization, there are two key patterns worth highlighting. On one side, there is a direct association between that clustering and the relative accessibility scores estimated in this section. When average relative accessibility scores are computed within each cluster, it is observed that those regions closer to Madrid—clusters 2 and 3—are more accessible than more peripheral regions—4 and 5. With Madrid the benchmarking cluster again (with a relative accessibility of 100%), the average accessibility score in the mid-90s within clusters 2 and 3 was around 57% and 40%, respectively. On the opposite side, clusters 4 (38%) and 5 (32%) displayed lower accessibility scores in 1995. These results emphasize the determinant role that transportation costs play in estimating multidimensional aggregate accessibility by way of Data Envelopment Analysis techniques. To the extent that one may wonder if these cross-section year-by-year efficiency scores also define a core–periphery pattern, do they really

A. Maroto, J.L. Zofío / Journal of Transport Geography 52 (2016) 143–152

149

Fig. 2. Regional accessibility in Spain, 1995.

add information to the conclusions obtained from the GTCs in terms of the overall regional standings, or do they simply yield marginal changes above and below the respective national averages? To check the existence of this relationship, we have performed non-parametric comparisons of these two variables, generalized transport costs and the relative accessibility scores, particularly the Wilcoxon test for equality of medians and the Sign tests. Z statistics for both tests are, respectively, 5.97 (with a p-value equal to 0.000) and 6.71 (0.000), showing that both distributions are alike and, therefore, that GTCs can be used as good proxies of relative accessibility levels. Nevertheless, an interesting result emerges when portraying the heterogeneity in relative accessibility trends; i.e., an inverted U

relationship arises when efficiency variation in time is analyzed within each cluster (Fig. 4). The further away the region with respect to Madrid (defining the higher cluster), the larger the accessibility gains during this decade. In particular, those regions closer to Madrid (cluster 2) have worsened their average relative accessibility score from 1995 to 2005. Regions belonging to clusters 3 and, especially, 4 have experienced the opposite trend. For these clusters, the average accessibility score has increased during these years. However, there is a hedge to this geographical approximation process. Although those more peripheral regions, which belong to the fifth cluster, have also improved their relative accessibility score, they have done it to a lesser extent than those regions within the fourth cluster. These results suggest that

Fig. 3. Regional accessibility in Spain, 2005.

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Fig. 4. Accessibility variations within clusters, 1995–2005: EC95,05 95,05 . Source: Authors' calculations.

transport infrastructure investment policies, which have been unequally undertaken across the Spanish regions during the analyzed decade, might be more effective in terms of accessibility convergence for medium range clusters. For instance, regions such as Aragón, Castilla y León, Extremadura, or La Rioja, where the investment growth rates have remained below the Spanish average, have taken advantage of their medium-range localization in terms of accessibility gains. Investment in the Spanish road network increased annually by 6% between 1995 and 2005. This investment effort has increased since the 2000s, when the annual average growth rate was around 10%. However, these expenditures have not been equally distributed across regions. Some regions, such as Asturias, Cantabria, Catalonia, Galicia, or the Basque Country, showed investment growths above the average during the whole period. Other regions, such as Andalusia, Murcia, or Valenciana, benefited also from higher investment growths, although only during the 1990s. These results are statistically confirmed by bootstrapping the DEA estimators conforming the efficiency change term, following Simar and Wilson’s (1999) methodology. Results show that for clusters 2 and 4 these changes are driven by a few provinces, whose accessibility gains or losses are statistically significant. Indeed, only three provinces exhibit values that are statistically greater than one, while another three reflect efficiency losses being smaller than one, belonging to clusters 4 and 2, respectively. For the rest of the observations we cannot reject the hypothesis that efficiency remains unchanged and, therefore, the efficiency change index is equal to one. Thus, for the remaining clusters 3 and 5, the efficiency change value is not statistically different from one (see Appendix A for individual results. The bootstrapping analyses of the Malmquist, technical change, and efficiency change indices are also performed using the DEA toolbox developed by ÁlvarezAyuso et al. (2016), allowing for 2.000 replications and setting the confidence level at 5%. Results for the bootstrapped indices and the lower and upper bounds defining the confidence intervals are available upon request). These results might reflect that a denser grid in terms of road infrastructure, which has driven the infrastructure policy in Spain during these years instead of alternative options such as a hub-and-spoke network, cannot achieve accessibility convergence for all regions. Where that convergence is observed it is not equal in magnitude, as peripheral regions cannot exploit the new infrastructure to the same extent than other regions more centrally located. That is, the return to infrastructure investments is capped for remote geographical locations.

4.3. Accessibility gains and transport infrastructure: productivity results Bearing in mind the clusters previously defined, we rely on the Malmquist index methodology to study overall accessibility growth, rather than other complementary approaches or indices used in the literature on transportation efficiency, such as the Revex ratio (Ison et al., 2011). We examine the sources contributing to its increase, and highlight the most relevant trends followed by the different NUTS-3 provinces. It is imperative to underline that these indices are calculated using the relative accessibility scores already discussed. Thus, some of the conclusions and interpretations in terms of temporal analysis that we summarize in the following section are directly linked and complement the results that have been already obtained. The average growth rates for the whole analyzed period (1995–2005) of the cumulative Malmquist index are presented in Table 3, sorted by regional location clusters that were statistically related to the generalized transport costs. Malmquist accessibility change within the Spanish NUTS-3 provinces increased from 1995 to 2005 by 15.4% = (1.154 − 1) ∗ 100. Medium–long range regions (cluster 4) significantly exceed this national average, increasing their accessibility by 21.6%. Among this group, some individual provinces such as Tarragona (26.3%), Seville (28.3%) and, especially, Guipuzcoa (34.4%) and Vizcaya (62.4%) notably improved their accessibility scores during this period. Long-range regions (cluster 5) experienced accessibility improvements over the average (16.6%). Some of these more peripheral Spanish provinces, such as Coruña or Barcelona, improved their accessibility above 20% during this decade. Regions included both in clusters 3 and 2 showed lower accessibility change (increasing by 12.7% and 8.3% respectively). Contrary to results found when the cross-period efficiency scores were analyzed (Table 2), these accessibility improvements are not limited to a certain geographical range, so the growth observed in the medium–long range and long-range regions are the highest ones. Again, to check the statistical significance of the calculated Malmquist indices, we have bootstrapped them following Simar and Wilson (1999) and, more recently, Gitto and Mancuso (2015). In this case, the null hypothesis positing the inexistence of productivity growth is rejected for all provinces, as individually reported in Appendix A. Looking at the decomposition of the Malmquist index in Eq. (12), the most influential driver of accessibility improvements is the upward shift of the benchmarking frontier—frontier change, also known as “technological change” in the conventional Malmquist index literature—led by the most accessible regions since FC presents a 14.3% increase. On

A. Maroto, J.L. Zofío / Journal of Transport Geography 52 (2016) 143–152 Table 3 Average inter-periodical cumulative accessibility change by clusters, 1995–2005. Source: Own elaboration.

All regions Mean St. Dev. Max. Min. Cluster 1 Mean Cluster 2 Mean St. Dev. Max. Min. Cluster 3 Mean St. Dev. Max. Min. Cluster 4 Mean St. Dev. Max. Min. Cluster 5 Mean St. Dev. Max. Min.

,05 M95 95

FC05 95 ,05

EC95,05 95,05

PEC95,05 95,05

SEC95,05 95,05

1.154 0.122 1.624 0.944

1.143 0.095 1.409 1.003

1.011 0.076 1.325 0.843

1.022 0.033 1.119 0.953

0.989 0.064 1.184 0.843

1.409

1.409

1.000

1.000

1.000

1.083 0.119 1.268 0.944

1.146 0.079 1.294 1.055

0.944 0.076 1.079 0.843

1.012 0.021 1.060 0.996

0.933 0.072 1.058 0.843

1.127 0.091 1.374 1.037

1.118 0.092 1.374 1.003

1.009 0.051 1.084 0.928

1.017 0.027 1.083 0.953

0.993 0.050 1.070 0.920

1.216 0.150 1.624 1.105

1.157 0.085 1.375 1.078

1.050 0.093 1.325 0.977

1.023 0.034 1.119 0.991

1.026 0.058 1.184 0.971

1.166 0.062 1.232 1.087

1.142 0.092 1.289 1.059

1.024 0.064 1.137 0.954

1.051 0.047 1.116 1.003

0.976 0.071 1.105 0.880

Note: We report mean values for all regions classified within each cluster — see Appendix A for individual provincial values.

the contrary, relative accessibility growth is barely boosted by convergence processes (efficiency changes) as EC95,05 95,05—efficiency change—contributes with a meager 1.1% cumulated increase, as we introduced when discussing the results related to static accessibility. The divergence of these values from unity is checked once again by resorting to the previous bootstrapping techniques. As the main driver of productivity change is technical progress, with values well above unity, the exercise yields the same result regarding its existence. However, as discussed in the previous section, this is not the case for efficiency change, whose values close to one suggest that there has not been a convergence process over the years and are not different from one statistically for the provinces belonging to clusters 3 and 5. Furthermore, pure efficiency change (PEC95,05 95,05) amounts 2.2% while the scale component (SEC95,05 95,05) even decreases by 1.1% during the whole period. Notice that only those provinces grouped in the second and fourth clusters show significant changes in the output–input mix size, either negative or positive, resulting in accessibility losses or improvements (SEC95,05 95,05). The positive behavior of these provinces in terms of scale changes has also translated into a higher convergence processes (efficiency contribution) for cluster 4—and the opposite for cluster 2. In particular, EC95,05 95,05 within cluster 4 amounts 5% with Vizcaya and Tarragona exhibiting the largest significant values. From these results we conclude that, as reported in Table 3 and confirmed statistically relying on bootstrapping techniques, there has not been a general catch-up process within the Spanish regions according to which less accessible regions would converge toward the efficient ones. The result is that the efficiency convergence in terms of accessibility is non-existent except for three provinces, while another three saw their situation deteriorate while the rest remained the same. 5. Conclusions Although accessibility, seen as the relative access to markets, has become a key concept in all economic models with a spatial dimension, and its role has been increasingly acknowledged in many economic research fields and policy planning debates, it is often a misunderstood, poorly defined, and ill-measured construct. This paper looked at this

151

concept from a new perspective, by assuming that infrastructure drives economic accessibility, and adopted a production function approach where the road network constitutes a set of inputs yielding access to markets as output. Therefore, enhancing the literature surveyed in the Introduction section, we presented a methodology that defines and enables studying accessibility in relative terms and not only in absolute terms as the normal one-sided and individual analysis of the accessibility indicators presented in Section 2 allows. Thus, using Data Envelopment Analysis we introduced a multidimensional approach that combines a set of six outputs, related to accessibility indicators that capture location and potential markets, both in terms of final and intermediate demands, and three inputs that account for the network infrastructure that is really used in trade flows by each region when reaching commercial markets. Both DEA relative (efficiency) accessibility and productivity change by way of the Malmquist index were calculated for Spanish NUTS-3 provinces in the 1995–2005 period, classifying provinces in five regional clusters according to a core–periphery typology based on GTC results. By introducing this classification that directly associates the geographical localization to the transport costs, we can discuss the efficiency and productivity results by relevant groups. As one of the most striking results, the average efficiency score was below 50% for the whole period. Despite the strong investment efforts and improvements of the road infrastructure network, relative accessibility of the Spanish provinces remains relatively low. Indeed, not only has regional accessibility been low, but it has also remained stable with the regional rankings unchanged, revealing the lack of any kind of convergence process during these ten years. As for the Malmquist index results, there have been accessibility gains as it presents a cumulated 15.4% growth from 1995 to 2005, mainly driven by the upward shift of the benchmarking frontier represented by the most central regions, particularly Madrid. Nevertheless, this growth is heterogeneous across regions, as a U-inverted relationship was observed when accessibility variation in time is analyzed within each regional cluster. On the positive side, the further the region is from the Madrid central benchmark region, the larger the accessibility gains during this decade. However, there is a hedge to this convergence process, as remote regions increase their accessibility to a lower extent. These results suggest that transport infrastructure policies, which have been equally undertaken across all regions, are more effective in terms of economic accessibility convergence for medium range clusters that significantly exceed the national average growth. These results show that the proposed methodology can be consistently applied in the field of economic geography so as to deal with multiple location and market potential indicators and draw relevant conclusions in terms of transport infrastructure policies and their effect on regional accessibility cohesion. Moreover, these sets of results are confirmed statistically through bootstrapping techniques. As for the weaknesses, besides the definition of the inputs and the outputs themselves that requires careful judgement (i.e., as the new export and import indicators for intermediate demand), the methodology adds greater complexity to the analysis as it involves the use of mathematical programming techniques, and results are dependent on the choice of DEA model. Indeed alternative efficiency models, additive, non-radial, etc., with their corresponding productivity indices are available, and different results would be obtained. In this respect, future developments of the analysis involve the use and definition of alternative outputs and inputs, and complementary DEA models, so as to perform sensitivity analyses and check the robustness of our results; e.g., using a capital stock measure of infrastructure in monetary values as input as presented in Álvarez-Ayuso et al. (2014), rather than physical units. Additionally, the ten year period should be extended so as to capture recent efficiency and productivity changes, and determine to what extent the economic crises have affected accessibility trends and regional cohesion, both from the output side represented by the reduction in regional GDPs and export and import flows, as well as the input side in the form of drastic reductions in transport infrastructure investments.

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Acknowledgments We are grateful to the editor, two anonymous referees and Javier Barbero for useful comments and suggestions. This research was supported by the Spanish Ministry for Economy and Competitiveness under grant ECO2013-46980-P. Appendix A

Table A.1 Average inter-periodical cumulated accessibility change by DMUs (NUTS-3 Spanish regions), 1995–2005. Source: Own elaboration. NUTS2

Andalusia

Aragón Asturias Cantabria

Castilla y León

Castilla-La Mancha

Catalunya

Com. Valenciana Extremadura

Galicia Madrid Murcia Navarra Basque Country La Rioja

DMUs (NUTS3) Almería Cádiz Córdoba Granada Huelva Jaén Málaga Sevilla Huesca Teruel Zaragoza Asturias Cantabria Ávila Burgos León Palencia Salamanca Segovia Soria Valladolid Zamora Albacete Ciudad real Cuenca Guadalajara Toledo Barcelona Girona Lleida Tarragona Alicante Castellón Valencia Badajoz Cáceres Coruña (a) Lugo Ourense Pontevedra Madrid Murcia Navarra Álava Guipúzcoa Vizcaya Rioja (la) Mean Max. Min. Range St. Dev.

05 M95, 95

FC05 95 ,05

1.138⁎ 1.205⁎ 1.088⁎ 1.123⁎ 1.188⁎ 1.103⁎ 1.105⁎ 1.283⁎ 1.145⁎ 1.037⁎ 1.083⁎ 1.087⁎ 1.110⁎ 1.063⁎ 1.091⁎ 1.199⁎ 1.089⁎ 1.112⁎ 1.248⁎ 0.944⁎ 1.000⁎ 1.134⁎ 1.080⁎ 1.093⁎ 1.061⁎ 0.986⁎ 1.268⁎ 1.230⁎ 1.090⁎ 1.121⁎ 1.263⁎ 1.360⁎ 1.112⁎ 1.059⁎ 1.129⁎ 1.058⁎ 1.232⁎ 1.183⁎ 1.150⁎ 1.134⁎ 1.409⁎ 1.107⁎ 1.094⁎ 1.374⁎ 1.343⁎ 1.624⁎ 1.105⁎

1.135⁎ 1.060⁎ 1.017⁎ 1.139⁎ 1.117⁎ 1.170⁎ 1.078⁎ 1.238⁎ 1.149⁎ 1.012⁎ 1.160⁎ 1.059⁎ 1.090⁎ 1.202⁎ 1.109⁎ 1.162⁎ 1.053⁎ 1.105⁎ 1.294⁎ 1.078⁎ 1.055⁎ 1.125⁎ 1.057⁎ 1.089⁎ 1.110⁎ 1.169⁎ 1.175⁎ 1.289⁎ 1.114⁎ 1.079⁎ 1.148⁎ 1.255⁎ 1.052⁎ 1.003⁎ 1.045⁎ 1.141⁎ 1.189⁎ 1.222⁎ 1.113⁎ 1.063⁎ 1.409⁎ 1.067⁎ 1.163⁎ 1.374⁎ 1.375⁎ 1.226⁎ 1.171⁎

1.154 1.624 0.944 0.680 0.122

1.143 1.409 1.003 0.406 0.095

,05 EC95 95 ,05

05 PEC95, 95, 05

,05 SEC95 95 ,05

1.002 1.137⁎ 1.069 0.986 1.064 0.943 1.025 1.036 0.996 1.024 0.933 1.027 1.019 0.885⁎

1.013 1.029 1.014 1.015 1.025 1.006 1.013 1.025 1.005 1.010 1.007 1.015 1.002 1.000 1.004 1.020 1.049 1.071 0.996 1.000 1.060 1.083 1.009 1.008 1.011 1.000 1.021 1.012 1.003 0.998 1.018 1.020 1.015 1.016 1.010 1.008 1.116 1.100 1.047 1.080 1.000 1.019 1.011 1.000 0.991 1.119⁎ 0.953 1.022 1.119 0.953 0.166 0.033

0.989 1.105⁎ 1.054 0.971 1.038 0.937 1.012 1.010 0.991 1.014 0.926 1.011 1.017 0.885⁎

0.983 1.032 1.033 1.007 0.965 0.876⁎ 0.947 1.008 1.021 1.004 0.956 0.843⁎ 1.079 0.954 0.978 1.038 1.100⁎ 1.084 1.056 1.056 1.081 0.928 1.036 0.968 1.033 1.067 1.000 1.037 0.940 1.000 0.977 1.325⁎ 0.944 1.011 1.325 0.843 0.481 0.076

0.980 1.012 0.985 0.940 0.969 0.876⁎ 0.894 0.931 1.012 0.996 0.946 0.843⁎ 1.058 0.943 0.976 1.040 1.080⁎ 1.063 1.040 1.039 1.070 0.920 0.928 0.880 0.987 0.988 1.000 1.018 0.929 1.000 0.986 1.184⁎ 0.991 0.989 1.184 0.843 0.340 0.064

Notes: “*” denotes that the Malmquist, technical change and efficiency change indices are different from one at the 5% significance level.

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