sectoral scope and colocalisation of spanish manufacturing industries

J Geogr Syst (2017) 19:65–92 DOI 10.1007/s10109-016-0242-x ORIGINAL ARTICLE Sectoral scope and colocalisation of Spanish manufacturing industries Marta R Casanova1 • Vicente Orts2 Jose´ M Albert3 • Received: 28 November 2015 / Accepted: November 2016 / Published online: 30 November 2016 Ó Springer-Verlag Berlin Heidelberg 2016 Abstract In this paper, we use distance-based methods, specifically a slight variation of Ripley’s K function and a bivariate generalisation of this function, to explore the detailed location pattern of the Spanish manufacturing industry, the scope of localisation and the tendency towards colocalisation between horizontally and vertically linked industries To so, we use micro-geographic data, considering a narrowly defined industry classification Our results show heterogeneous location patterns, but with a significant tendency towards localisation The sectoral scope is very sensitive to the degree of homogeneity of the activities in each sector The more homogeneous the activities in a specific sector are, the more similarities we find in the spatial location patterns among its industries Finally, although the patterns of colocalisation detected are sensitive to the counterfactuals used, between 20 and 48% of the pairs of industries with strong input–output linkages considered in this study show a significant tendency to colocalisation, and among them 74% are vertically linked industries Keywords Spatial location Á Distance-based method Á Ripley’s K function Á Sectoral scope Á Colocalisation Á Vertical and horizontal linkages JEL Classification C15 Á C60 Á R12 & Marta R Casanova marta.roig-casanova@uv.es Department of Applied Economics, University of Valencia, Av Tarongers, s/n, 46022 Valencia, Spain Department of Economics and Institute of International Economics, University Jaume I, Campus Riu Sec, 12071 Castello´n, Spain Department of Economics and Institute for Local Development, University Jaume I, Campus Riu Sec, 12071 Castello´n, Spain 123 66 M R Casanova et al Introduction The most striking feature of the spatial distribution of economic activity is its heterogeneity As has recently been highlighted by Ellison et al (2010), economic activity is geographically concentrated and this concentration is too pronounced to be explained by exogenous spatial differences in natural advantages alone Nonetheless, the observed concentration may also be due to these natural advantages Some regions simply possess a better environment for certain industries that attracts them to that area Similarly, it is also difficult to ensure whether the establishments of two industries are located close to each other because they are attracted by similar characteristics or natural advantages of the area or because they have strong linkages and have deliberately decided to locate close to each other to exploit synergies It is therefore not surprising that economists have paid attention to this tendency of firms and industries to become spatially localised since the pioneering works of Von Thuănen, Marshall and Weber up to more recent contributions from the ‘new economic geography’ initiated by Krugman (1991a).1 Although it is easy to define localisation or colocalisation as the tendency of different establishments or industries to opt for the company of other firms or industries and as a result to locate together, it is more difficult to measure it properly and to detect whether the location of firms or industries is conditioned by the location of other firms or industries That is, we should differentiate between exogenous causes for locating together, like natural advantages, and endogenous reasons, like strong linkages or synergies between firms or industries Thus, the interest in theories that can explain the agglomeration of firms and industries has also been extended, in recent years, to the development of empirical methods to quantify and characterise this tendency of individual firms and industries to cluster in space The first generation of these measures—to use the terminology employed by Duranton and Overman (2005)—was based on indicators such as the Herfindahl or Gini indices, which did not take space into consideration.2 The second generation, initiated by Ellison and Glaeser (1997), began to take space into account, but not in a proper way The Ellison and Glaeser index still used administrative units to measure the spatial distribution of economic activity, treating space as being discrete.3 Therefore, they restricted the analysis of spatial distribution to just one administrative scale, ‘they transform points on a map into units in boxes’.4 Alternatively, the third generation of empirical measures of spatial localisation, developed by authors from different scientific fields (economics, geography and statistics), introduced the treatment of space as being continuous, by simultaneously analysing multiple spatial scales These new measures are unbiased For further details, see Von Thuănen (1826), Marshall (1890), Weber (1909), Hoover (1948), Krugman (1991b), Venables (1995), Ottaviano and Puga (1998), Fujita et al (1999) or Puga (1999, 2002) See Krugman (1991a) or Amiti (1997) See Callejo´n (1997), Maurel and Se´dillot (1999), Bruălhart (2001), Rosenthal and Strange (2001), Alonso-Villar et al (2004), Devereux et al (2004) or De Dominicis et al (2007) Duranton and Overman (2005), p 1078 123 Sectoral scope and colocalisation of Spanish manufacturing… 67 with respect to arbitrary changes in the spatial units and can allow us to know and to compare the concentration intensity for each spatial scale Authors like Marcon and Puech (2003), Quah and Simpson (2003), Duranton and Overman (2005) and Arbia et al (2008), among others, were the pioneers in introducing these methods into economic geography More recently, papers by Duranton and Overman (2008), Marcon and Puech (2010) or Albert et al (2012) have developed several extensions and improvements to these methodologies Since then, an increasing number of studies have appeared thanks to these methodological developments and the widespread use of micro-geographic data Some examples are Nakajima et al (2012), who examined the location patterns of Japanese manufacturing industries, in the same way as Koh and Riedel (2014) did with the four-digit German manufacturing and service industries Meanwhile, Barlet et al (2013) improved the test proposed by Duranton and Overman (2005), avoiding the bias with respect to the number of plants, and studying the location patterns of service and manufacturing industries in France In accordance with other localisation measures, Guimara˜es et al (2011) modified measures of spatial concentration by taking into account neighbouring effects and applying the new instruments to the USA Similarly, Behrens and Bougna (2015) used micro-geographic data to analyse the evolution of geographic concentration in Canada, applying the Duranton and Overman index and also integrating neighbourhood effects into the Ellison and Glaeser index, in the same way as Guimara˜es et al (2011) In this paper, we use different measures belonging to this last generation in order to analyse two important issues characterising the spatial location patterns of manufacturing firms: the sectoral scope of the location patterns of different industries and the tendency to colocalise among various industries whose activity is related either vertically or horizontally To so, we apply an extension of Ripley’s K function,5 which allows us to assess the different tendencies to cluster in each industry while also enabling us to know whether concentration exists, its intensity at each distance, and on what spatial scale its highest level is obtained Moreover, to analyse colocalisation, we use the K-cross function6 and we incorporate a methodological improvement that, unlike other proposals, enables us to obtain results that are closer to reality from the economic point of view Specifically, using a narrowly defined industry classification, we analyse the patterns of intra- and inter-industry location of Spanish manufacturing sectors First, we focus on the patterns of location of the set of establishments making up each manufacturing industry at the four-digit level, the results revealing that 68% of them show localisation patterns Moreover, these industries reach their maximum concentration at very heterogeneous distances Second, we check the sectoral scope, that is, whether the four-digit industries that are part of the same two-digit sector have similar patterns of location among them (intra-sectoral homogeneity) and whether, at the same time, they are similar to the location pattern of the whole two-digit sector Our results confirm that the more homogeneous the activities in a specific sector are, the more similarities we find in the spatial location patterns For further details, see Ripley (1976, 1977, 1979) See Ripley (1981) 123 68 M R Casanova et al among their industries Third, we analyse the colocalisation patterns of the pairs of industries with relevant linkages, finding that 48% of these examined pairs are colocalised Furthermore, 74% of colocalised industries are vertically linked Finally, we show that the patterns of colocalisation detected are sensitive to the methodology used to construct the counterfactual that allows us to establish the statistical significance of the results So, the more restrictive the methodology used, the more likely it is to reject the existence of colocalisation between pairs of industries, especially at short distances, thereby increasing the risk of rejecting actually existing colocalisation patterns In this case, the colocalised pairs of industries are reduced from 48 to 20% The remainder of the paper is organised as follows In Sect 2, we present the data used in our analysis and the methodology employed In Sect 3, we introduce and discuss the main results obtained, taking into consideration the sectoral scope of localisation for industries at the four-digit level and their corresponding colocalisation between vertically and horizontally linked industries Finally, in Sect 4, we conclude and discuss the final considerations Data and methodology 2.1 Data We use establishment-level data, for the year 2007, from the Analysis System of Iberian Balances database7 to carry out our empirical analysis For each establishment in our database, we know their geographical coordinates (longitude and latitude), their number of employees8 and the kind of industrial activity they perform Specifically, we have information about the codes of the National Classification of Economic Activities (NACE)9 they belong to When we refer to all establishments grouped into four-digit or two-digit NACE codes, we are speaking about industries and sectors, respectively Note that each sector (two-digit code) includes several industries (four-digit code) The geographical coordinates allow us to treat space as being continuous instead of using a single administrative scale, thus allowing multiple spatial scales to be analysed simultaneously In fact, through said geographical coordinates, we locate the establishments, represented by dots, accurately in space without having any modifiable areal unit problems (MAUP), that is, our results not depend on the administrative scale chosen Our database is restricted to Spanish manufacturing firms located only on the peninsula and not in the Canary and Balearic Islands, Ceuta or Melilla, and which employ at least ten workers This second requirement is due to the fact that most establishments with fewer than ten workers not have the essential information (geographical coordinates) needed to carry out our analysis Moreover, we should SABI See ‘‘Appendix 1’’ (Table 2) NACE 93—Rev 123 Sectoral scope and colocalisation of Spanish manufacturing… 69 highlight the fact that some industries are not included in the analysis because the number of their establishments is too small to be able to apply the statistical methods.10 After considering all these requirements, our database contains 42,820 establishments, belonging to 90 industries and 19 sectors.11 2.2 Methodology: localisation and colocalisation The methods we are going to use follow Albert et al (2012) and are based on Ripley’s K function, K(r) This function is a distance-based method that measures concentration by counting the average number of neighbours each firm has within a circle of a given radius, ‘neighbours’ being understood to mean all the firms situated at a distance equal to or lower than the radius (r) From here on, firms will be treated as points The K(r) function describes the characteristics of the point patterns on many different scales simultaneously, depending on the value of ‘r’ we take into account12; that is, K r ị ẳ N N X X wij I dij kN i¼1 j¼1;i6¼j À Á I dij ¼ & 1; dij r 0; dij [ r where dij is the distance between the ith and jth establishments; I(dij) is the indicator function and takes a value of if the distance between the ith and jth establishments is lower than or equal to r, and otherwise; N is the total number of points observed in the studied area; k = N/A represents its density, A being the area of study13; and wij is the weighting factor to correct for border effects, and will be equal to the area of the circle divided by the intersection between the area of the circle and the area of study.14 The next step in the evaluation of the location patterns of economic activity is to define the counterfactuals that allow us to provide our results with statistical robustness The null hypothesis is usually a kind of randomly distributed set of locations in the area of study Thus, if establishments were located at random in the study area and independently from each other, we would have a location pattern 10 In some cases, this problem forced us to leave out some entire sectors, as is the case of Tobacco products (16), Coke, refined petroleum products (23), Office machinery and computers (30), and Recycling (37) 11 See ‘‘Appendix 2’’ 12 Although K(r) can be estimated for any r, due to bias originated by border effects, it is common practice to consider only r \ 25% of the length of the smallest side of the study area See Dixon (2002) 13 In the empirical analysis, we use a polygonal shape as the area of study, A, in order to adjust the delimitation of this area as closely as possible See ‘‘Appendix 3’’ 14 These border-effect corrections should be incorporated to avoid artificial decreases in K(r) when r increases, because the increase in the area of the circle under consideration is not followed by the increase in firms (outside the study area there are no firms) 123 70 M R Casanova et al known as complete spatial randomness (CSR) However, it is not altogether correct to use CSR as the null hypothesis because economic activity cannot be located in space in a random and independent way Economic activities are spatially concentrated for other reasons, very different to economic factors, for example, because of dissimilarities in such natural features as mountains, rivers or harbours Additionally, with CSR as our benchmark neither can we isolate the idiosyncratic tendency of each industry to locate itself from the general tendency of manufacturing firms to agglomerate To avoid these drawbacks and to control for the overall agglomeration of manufacturing, we proceed in two steps First, we define MTM(r) as the difference between the K value of each set of industrial firms under consideration and the K value of the total manufacturing at radius r, that is: MTM(r) = K(r) - KTM(r) And second, we test the significance of departures from a random distribution, conditioned on the overall distribution of manufacturing To this, we construct suitable confidence intervals using Monte Carlo simulations.15 Specifically, for each industry, we construct counterfactuals by randomly drawing the same number of points (establishments) as in each of the industries under consideration, but the location of these hypothetical establishments is restricted, as in Duranton and Overman (2005), to the sites where we can currently find establishments from the whole manufacturing sector In this way, the construction of the confidence interval allows us to assess the significance of departures from spatial patterns followed by the whole of manufacturing and to control for industrial concentration When the estimated MTM(r) for a specific industry lies within the confidence interval, we cannot reject the null hypothesis that the location pattern of this industry is the same as that of manufactures as a whole If our estimation lies above the upper bound of the confidence interval, the industry analysed is more concentrated than the manufacturing industry, while if it is below the lower bound of the confidence interval, then the analysed industry exhibits a more dispersed pattern than manufactures as a whole.16 Similarly, in order to analyse whether two industries, horizontally or vertically linked, are colocalised, we have to consider a multivariate spatial point pattern To so, we use a K-cross function, Kij(r), where i = j and r is the radius, that is: À Á À ÁÀ1 X X Kij r ị ẳ ki kj A wik ; jl ÞI dik ;jl k l 15 In each case, we generate 1000 simulations, rejecting the non-significant values by using a 95% confidence interval 16 Given the properties of Ripley’s K function, our measure of localisation is comparable across industries and unbiased with respect to scale and aggregation Additionally, the construction of our confidence intervals gives an indication of the significance of the results, and control for industrial concentration and for the overall agglomeration of manufacturing Thus, our approach satisfies the five essential requirements that Duranton and Overman (2005) stated that any test which measures concentration should fulfil 123 Sectoral scope and colocalisation of Spanish manufacturing… À Á I dik ;jl ¼ & 71 1; dik ;jl r 0; dik ;jl [ r where dik ;jl is the distance between the kth location of type i and the lth location of À Á type j; I dik ;jl is the indicator function and takes a value of if the distance between the kth location of type i and the lth location of type j is lower than or equal to r, and otherwise; ki = Ni/A and kj = Nj/A represent the density of points of type i and j, respectively, A being the area of study, Ni and Nj being the total number of points of type i and type j observed in the studied area; and w(ik, jl) is the weighting factor to correct for border effects, the fraction of the circumference of a circle being centred at the kth location of process i with radius dik ;jl that lies inside the area of study As argued by Duranton and Overman (2005), in this case defining the null hypothesis in order to construct the counterfactuals is rather more complicated Furthermore, this choice will condition the interpretation of our results Indeed, we must point out that the fact that two industries are located together does not always mean that they deliberately locate close to each other to exploit synergies between them Instead, they can possess similar location patterns only because the two industries may be attracted by the same localised natural advantages.17 However, only in the first case can we speak of colocalisation in the proper sense of the term In this paper, we construct the counterfactuals, with which the estimated K-cross function can be compared, in two different ways In the first way, for any two four-digit industries (i and j) we simulate the spatial location of establishments by randomly sampling the same number of points (establishments) of four-digit industry i (Ni) in the set of sites actually occupied by establishments of two-digit sector I, which this industry belongs to (i [ I).18 Then, we use these simulations to compute the K-cross function, Kij(r), and construct the confidence intervals.19 In this case, the upper deviations of the estimated Kij(r) value from randomness indicate that the establishments in the four-digit industry i [ I are attracted by establishments of industry j [ J, even after controlling for any tendency of establishments of industry i to cluster with establishments in the remaining sector I they belong to In other words, we interpret this result as statistically significant evidence of a tendency of establishments in industry i to locate closer to establishments of industry j (i ? j), instead of locating closer to other establishments from their own sector Alternatively, if the Kij(r) value lies below the lower bound of the confidence interval, colocalisation will not exist and establishments from industry i will prefer to locate closer to establishments from their own sector rather than to establishments from industry j Finally, if the value of Kij(r) lies between the upper and the lower bounds of the confidence interval, the location 17 This possibility is what Duranton and Overman (2005) have called ‘joint-localization’ and specifically say that ‘measuring co-localization and distinguishing from joint-localization is much more complex than analysing localization’ 18 When industries i and j belong to the same sector, we sampled the representative points of industry i at sites occupied by the remaining establishments in sector I, excluding sites occupied by establishments of industry j 19 As in the previous case, we run 1000 simulations using Monte Carlo, rejecting the non-significant values by using a 95% confidence interval 123 72 M R Casanova et al pattern of the establishments of industry j does not have a significant influence on the location pattern of the establishments of industry i and these establishments will locate close both to establishments of industry j and to establishments from their own sector Furthermore, we use the same criterion to assess whether establishments from four-digit industry j, belonging to two-digit sector J (j [ J), are located closer to establishments from industry i than to other establishments in their own sector J (j ? i) Hence, using these criteria together allows us to consider that colocalisation exists in both ways This means that establishments in industry i locate closer to establishments in industry j than to other establishments in their own sector I, and vice versa, (i $ j); that is, establishments from both industries show mutual attraction In this way, more robustness is given to colocalisation and the probability of ‘joint-localisation’ can be minimised Our second way to construct counterfactuals relies on the test proposed by Duranton and Overman (2005, 2008) In this case, the alternative is to randomly sample the same number of points as the sum of establishments belonging to the two industries (Ni ? Nj) in all sites actually occupied by them As in the previous case, we use these simulations to compute the K-cross function, Kij(r), and construct the confidence intervals.20 Hence, when the estimated Kij(r) value is higher than the upper bound of the confidence interval, it means that establishments in these industries are attracted to each other even after controlling for whatever tendency they have to cluster Note that this is an extremely restrictive and demanding test, because as Duranton and Overman said, ‘the desire to locate close to establishments in a vertically linked industry does not necessarily require locating closer to establishments in this industry than establishments in one’s own industry’.21 Obviously, the way the counterfactual is built defines the conditioning factors of the underlying spatial randomness of our null hypothesis, and changes the intuition behind the test we are performing The key question is: what is the alternative to evaluate the significance of the tendency of establishments in an industry i to be closer to establishments in a linked industry j? In sum, in this paper we propose two alternatives First, this tendency will be stronger than the tendency to be located closer to other establishments in their own two-digit sector (which henceforth we will call the ‘broad test’ of colocalisation) or, second, closer to establishments in their own four-digit industry (hereafter called the ‘narrow test’ of colocalisation) Empirical results 3.1 Localisation in four-digit industries The analysis of the spatial location pattern of the Spanish manufacturing industries shows that 61 of the 90 four-digit industries considered (68%) are 20 We also run 1000 simulations and use a 95% confidence interval to reject the non-significant values 21 Duranton and Overman (2008), p 239 123 Sectoral scope and colocalisation of Spanish manufacturing… 73 Fig Cumulative percentage of industries that reach their maximum concentration level (maximum MTM) at different distances concentrated,22 whereas 16 industries (18%) are dispersed, and 13 (14%) not present any significant differences from the location pattern of the whole manufacturing Focusing on those industries that have a higher tendency to spatial concentration than the whole manufacturing, Fig shows the cumulative percentage of industries that reach their maximum level of concentration (maximum MTM value) at each distance of the radius In this figure, we can observe that, first, this maximum intensity of concentration is reached at very different radii among the industries analysed and, second, that there is a considerable change in the rate of incorporation of new industries that reach their highest level of concentration from 90 km onwards In fact, a large number of industries (30%) reach their highest level of concentration at very short distances (between and 45 km), while another 20% reach their maximum concentration between 45 and 65 km This trend continues up to 90 km, and from this distance on the trend slows down considerably As a result, 75% of the concentrated industries reach their maximum level of concentration at distances lower than 90 km and only 25% reach their highest level of concentration at distances larger than 90 km Finally, we must take into account the fact that the maximum MTM value is the maximum difference between Ki and KTM, and given that KTM values not remain constant when the radius becomes larger, the interpretation of the MTM value is not independent on the behaviour of KTM Hence, industries that reach their maximum level of concentration at large distances will not be very important in our analysis, because the whole of the Spanish manufacturing (TM) reaches its maximum level of concentration at a distance of 60 km and from this distance onwards its concentration becomes lower, even showing dispersion patterns beyond 150 km Hence, those industries that reach their MTM peak at distances of \60 km are of 22 This result is similar to other European countries: France (63%), according to Barlet et al (2013), and Germany (71%), as Koh and Riedel (2014) found However, Behrens and Bougna (2015) observed that there is less industrial localisation in Canada, from 40 to 60%, depending on years 123 74 M R Casanova et al Table Location patterns of Spanish manufacturing industries (MTM) Industries (NACE 93—Rev 1) MTM (extreme value)a r (critical value, km) 1511 Production and preserving of meat -0.01 58 1513 Production of meat and poultry meat products -0.01 66 1725 Other textile weaving 0.10 65 1730 Finishing of textiles 0.34 85 1754 Manufacture of other textiles 0.01 19 1822 Manufacture of other outerwear 0.05 200 1824 Manufacture of other wearing apparel and accessories 0.05 200 1910 Tanning and dressing of leather 0.03 33 1930 Manufacture of footwear 0.16 38 2010 Saw milling and planing of wood, impregnation of wood -0.02 134 2030 Manufacture of builders’ carpentry and joinery -0.01 60 2112 Manufacture of pulp, paper and paperboard 0.01 23 2121 Manufacture of corrugated paper and paperboard 0.04 80 2211 Publishing of books 0.26 80 2212 Publishing of newspapers 0.09 190 2213 Publishing of journals and periodicals 0.33 50 2416 Manufacture of plastics in primary forms 0.05 75 2442 Manufacture of pharmaceutical preparations 0.17 50 2466 Manufacture of other chemical products 0.02 80 2513 Manufacture of other rubber products – – 2524 Manufacture of other plastic products 0.07 55 2612 Shaping and processing of flat glass 0.02 140 2630 Manufacture of ceramic tiles and flags 0.32 30 2640 Manufacture of other porcelain and ceramic products 0.01 122 2710 Manufacture of basic iron and steel and of ferro-alloys – – 2735 Other processing of iron – – 2861 Manufacture of cutlery 0.15 74 2863 Manufacture of locks and hinges 0.05 140 2932 Manufacture of agricultural and forestry machinery -0.02 88 2953 Manufacture of machinery for food, beverage and tobacco processing -0.04 200 2954 Manufacture of machinery for textile, apparel and leather production 0.10 44 3110 Manufacture of electric motors, generators, transformers 0.02 85 3150 Manufacture of domestic appliances 0.05 40 3210 Manufacture of electronic valves and tubes 0.10 126 3220 Manufacture of television and radio transmitters 0.13 112 3310 Manufacture of medical and surgical equipment 0.05 80 3320 Manufacture of instruments for measuring, testing, navigating 0.07 63 3420 Manufacture of bodies (coachwork) for motor vehicles -0.01 130 123 78 M R Casanova et al that industries 2953 and 2932 present dispersion at all distances, while industry 2954 exhibits localisation for distances between and 50 km Lastly, there are other sectors where the heterogeneity among their industries is not as high as in the previous examples, with industries with location patterns very similar to the sector as a whole and industries with completely different patterns of localisation coexisting within the same sector This is the case of sectors (17) Textiles and (22) Publishing, printing and recorded media, where two of their industries differ from the rest and from the spatial distribution of the aggregated sector The same happens with sectors (25) Rubber and plastic products and (26) Other non-metallic mineral products, in which one industry presents location patterns that are far more concentrated than the other industries and the sector itself Naturally, for each industry and sector it is possible to have a far more detailed analysis when we combine information on the level of intensity with the distance at which it is achieved However, it is not feasible to offer a detailed description of the location pattern for all industries and sectors analysed Hence, we will use two examples to illustrate more accurately the magnitude of the differences highlighted by the estimation of Ripley’s K functions Figures and illustrate the case of industries (2213) Publishing of journals and periodicals and (2630) Manufacture of ceramic tiles and flags, and their corresponding two-digit sectors (22 and 26) Figures 2a, c, 3a, c depict point clouds for each industry and sector, where each dot corresponds to an establishment, and Figs 2b, d, 3b, d show their MTM estimated functions.28 The point clouds clearly show that there are differences in the density and distribution of establishments between each industry and its corresponding sector However, just by looking at the clouds it is difficult to establish to what extent the spatial location patterns of the sectors and the industries concerned are different, how large these differences are, or how the degree of spatial concentration is affected at each distance Thus, on examining the MTM estimated functions it is easy to recognise that the most pronounced difference between the location pattern of four-digit industry and two-digit sector occurs in Fig In fact, sector 26 shows dispersion patterns at all distances of the radius analysed, while industry 2630 presents high levels of concentration In Fig 2, the difference between the spatial location pattern of four-digit industry and two-digit sector is smaller, because sector 22 is concentrated at every distance of the radius, but its intensity is not as elevated as that belonging to industry 2213 Nevertheless, the common feature between Figs and is that, in both cases, the four-digit industries show higher levels of concentration than their respective two-digit sectors and this concentration is reached at much shorter distances At this point, it should be added that although both industries present concentration patterns at short distances, the shape of their MTM curves is very different In Figs 2d, 3d, we observe a common fast growth of the MTM value at short distances of the radius, but when the maximum MTM is reached, the behaviour of the MTM function differs in the two industries On the one hand, industry 2213 (Fig 2d) reaches its maximum intensity (0.33) at a distance of 50 km and then the 28 The MTM estimated functions of all industries are available upon request from the authors 123 Sectoral scope and colocalisation of Spanish manufacturing… (a) (b) 22 Publishing, printing and recorded media M value 0.8 0.6 0.4 0.2 0 (c) 0.2 0.4 0.6 0.8 22 Publishing, printing and recorded media 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 Distance (km) (d) 2213 Publishing of Magazines 79 2213 Publishing of Magazines 0.35 0.30 M value 0.8 0.6 0.4 0.25 0.20 0.15 0.10 0.05 0.2 0.00 -0.05 0 0.2 0.4 0.6 0.8 Distance (km) Fig Relative location patterns of sector 22 and industry 2213 MTM value hardly decreases when the distance analysed becomes larger On the other hand, industry 2630 (Fig 3d) reaches its maximum intensity (0.32) at a distance of 30 km and when the distance becomes larger, the MTM value decreases very rapidly The rapid growth of the MTM value at small distances has an obvious explanation In both industries, most of the establishments are located within clusters rather than being spread (82% in industry 2213 and 78% in industry 2630) In fact, localisation leads to specialisation in particular jobs As a result, workers skilled in those jobs are attracted to that place and these localised industries are continuously fed by a regular supply of skilled labour that also attracts new firms into the industry Therefore, the majority of establishments in industries 2213 and 2630 are attracted over the years to specific locations and located in small clusters, thereby making the density of establishments at small distances very high and the intensity of concentration (the MTM value) very elevated at short distances Moreover, the reason why the MTM function does not behave in the same way when the radius becomes larger is because both industries possess a different number of clusters Industry 2213 has two huge clusters around Madrid and Barcelona, whereas industry 2630 has a single well-defined cluster around Castello´n Therefore, when our test counts the neighbours close to the establishments when the radius is increased, the value of MTM is maintained over large distances when more than one cluster exists In this way, the value of the MTM 123 80 M R Casanova et al (a) (b) 26 Other non-metallic mineral products M value 0.8 0.6 0.4 0.2 26 Other non-metallic mineral products 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 0 (c) 0.2 0.4 0.6 0.8 Distance (km) (d) 2630 Manufacture of ceramic tiles 2630 Manufacture of ceramic tiles 0.35 0.30 0.8 M value 0.25 0.6 0.4 0.20 0.15 0.10 0.05 0.00 0.2 -0.05 0 0.2 0.4 0.6 0.8 Distance (km) Fig Relative location patterns of sector 26 and industry 2630 function depends on (1) the relative number of establishments located within the clusters, (2) the number of clusters in the point pattern, and (3) the distance between these clusters.29 3.3 Colocalisation The next issue that we analyse concerns colocalisation patterns between pairs of industries with significant linkages We use the 2005 Spanish Input–Output Table30 to analyse the existence and magnitude of linkages between the different manufacturing industries This table gives information about the inter- and intraindustry flows between the industries and sectors of an economy, and it allows us to establish the degree of industrial interdependence (or linkages) between them Industries having the highest input–output linkages are good candidates to become colocalised for reasons other than the natural advantages of the places where they agglomerate 29 This function becomes an appropriate instrument to detect clusters and their interaction, as long as the distance between these clusters is less than 2r, that is, one-half the shortest dimension of the study area (in our case around 400 km) 30 The Spanish Input–Output Tables are published by the National Institute of Statistics (INE), (http:// www.ine.es/) 123 Percentage of colocalisation Sectoral scope and colocalisation of Spanish manufacturing… 81 100 80 60 40 20 0 50 100 150 200 Distance (km) Fig Percentage of pairs of industries colocalised at different distances (‘broad test’) An initial review provides us with a large number (thousands) of pairs of industries that may be eligible as candidates in our study, but it would be impractical to analyse all of them Hence, we focus on only the 168 pairs of industries with the strongest linkages, and we use the K-cross function to evaluate the tendency to colocalise among them.31 Figure shows the percentage of pairs of analysed industries that are colocalised at each distance of the radius (r), using the ‘broad test’ of colocalisation, as has been explained in the methodology section As can be seen in the figure, there is a higher percentage of pairs of industries that present colocalisation at short distances than at large distances Therefore, in the first 50 km, around 35% of the pairs of industries analysed present colocalisation patterns, while the remaining 65% show a higher attraction towards establishments from their own sector than towards establishments of the other industry considered The percentage of colocalised industries increases significantly at distances larger than 70 km, reaching their maximum at a distance of 90 km, where it is found that 48% of pairs of industries with stronger linkages are colocalised Finally, this percentage decreases rapidly from this distance onwards At a distance of above 120 km, the percentage of pairs of industries that are colocalised decreases to below 20% In sum, our results show that colocalisation is not a widespread phenomenon among the most linked industries Another relevant question is whether there are significant differences in the patterns of colocalisation between the pairs of industries that belong to the same sector, horizontally linked industries, and those pairs that belong to different sectors, vertically linked industries.32 The question arises because when we observe the values of the diagonal of the input–output table, it is striking that these values are higher than those for other intersections, showing that there is a high percentage of intra-sectoral flows And the answer is no Of all the industries that present colocalisation patterns, only 26% correspond to horizontally linked pairs of 31 Given the large amount of information generated by this analysis, all the results are available upon request from the authors Here, we will only present some examples and offer a detailed description of the overall behaviour of our analysis 32 Of the 168 pairs of industries considered, approximately 50% are horizontally linked industries, and the other 50% are vertically linked industries 123 M R Casanova et al Percentage of colocalisation 82 100 80 60 40 20 0 50 100 150 200 Distance (km) Fig Percentage of pairs of industries colocalised at different distances (‘narrow test’) industries Therefore, the fact that industries belonging to the same sector have stronger linkages between them has no direct impact on higher levels of colocalisation Alternatively, in Fig 5, we observe the percentage of pairs of analysed industries that are colocalised at each distance of the radius (r) using the second way to construct the counterfactuals, that is, what we have called the ‘narrow test’ On the one hand, we see that a lower percentage of industries show colocalisation patterns if we compare these results with those obtained in Fig On the other hand, there is a higher percentage of pairs of industries that present colocalisation patterns at large distances of the radius, rather than at short distances In fact, the maximum percentage of colocalised industries (20%) is reached as of 130 km and persists at long distances This result is very similar to that obtained by Duranton and Overman, who found that in the UK colocalisation patterns increase at distances beyond 160 km The results obtained in Figs 4, are consistent with the construction of the counterfactuals Since most industries analysed show a tendency to spatial concentration at short distances, it is not surprising that this trend is imposed on the attraction of establishments in other industries over short distances, when our null hypothesis is very restrictive (‘narrow test’) Thus, in the first case, when we control for the tendency of firms to be located closer to other establishments in their own two-digit sector (‘broad test’ of colocalisation), we find more pairs of industries colocalised at shorter distances In the second case, when we control for the tendency of firms to be located closer to other establishments in their own four-digit industry (‘narrow test’ of colocalisation), the number of pairs of linked industries with colocalisation patterns decreases at short distances and increases significantly over long distances However, we must take into account that both tests may fail In the first case, although there is a tendency for establishments of industry i to locate near establishments of industry j, and we can reject conditional randomness, we may be facing some form of joint-localisation But in the second case, the test is extremely demanding and we may be unable to reject randomness despite strong forces pushing towards colocalisation if own-industry concentration forces 123 Sectoral scope and colocalisation of Spanish manufacturing… 83 Fig Colocalisation between industries 2213 and 2121 (‘broad test’ vs ‘narrow test’) dominate In other words, in this case we fail to detect industries that are effectively being colocalised Figure exemplifies the arguments discussed above Here, we observe the interaction that industry i (2213) Publishing of journals and periodicals maintains with industry j (2121) Manufacture of corrugated paper and paperboard The continuous lines represent the estimated value of Kij at every distance of r, and the dashed lines are the lower and upper bounds of the confidence intervals The difference between the left- and right-hand side of the Fig (6a, b) lies in the method of building the confidence interval On the left-hand side we control for the tendency of firms to be located closer to other establishments in their own two-digit sector (‘broad test’), while on the right-hand side we control for the tendency of firms to be located closer to other establishments in their own four-digit industry (‘narrow test’) In Fig 6a, the Kij(r) function lies above the upper bound of the confidence interval at every distance analysed This means that colocalisation between these two industries is significant at all radii and establishments of industry 2213 have a tendency to locate close to establishments of industry 2121, or at least closer than to establishments within their own sector, (22) Publishing, printing and recorded media However, the significance level of the function is almost negligible at short distances of the radius, meaning that at short distances the establishments of industry 2213 also have a strong tendency to be located close to establishments in their own sector In Fig 6b, we observe that the Kij(r) function lies below the lower bound of the confidence interval, or between the upper and the lower bounds, up to a distance of 70 km, lying above the upper bound from this distance onwards Thus, colocalisation will not be significant at short distances of the radius, this meaning that establishments of industry 2213 will prefer to locate closer to establishments in their own industry than to establishments of industry 2121 at these distances The key to explain the difference in the results lies in the location pattern of industry i Industry 2213 has very intense concentration patterns at short distances Hence, if own-industry concentration forces are strong and dominate, the narrow colocalisation test is likely to fail despite strong forces pushing towards colocalisation This does not mean that establishments of industry 2213 not 123 84 M R Casanova et al Fig Colocalisation between industries 3410 and 3430 (‘broad test’ vs ‘narrow test’) locate close to establishments of industry 2121 at small distances of the radius, but rather that the attraction towards the establishments in one’s own industry is stronger than the attraction towards the establishments in the vertically linked industry 2121 However, when we condition by the tendency of establishments to be located close to establishments in their own sector, a greater tendency appears between both industries considered to be colocalised We can therefore conclude that the location pattern of industry i affects the narrow test more than the alternative one The characteristics of the spatial location pattern of the sector or the industry that are behind the construction of the counterfactuals condition the capability of the test to accept or reject the proposed alternatives Rejecting conditional randomness, in the first case (‘broad test’), creates ‘false positives’, and being unable to reject conditional randomness, in the second case (‘narrow test’) it creates ‘false negatives’ Consequently, the analysis of the colocalisation patterns cannot be independent of the analysis of the location patterns of specific industries and sectors considered Finally, in Figs and 8, we have two industries that belong to the same two-digit sector of motor vehicles: industries 3410 Manufacture of motor vehicles and 3430 Manufacture of accessories for motor vehicles and their engines Traditionally, these assemblers and car suppliers have attempted to locate close to each other to minimise assembly time and reduce manufacturing costs Industry 3410 has barely any concentration patterns and industry 3430 does not present any significant difference from the location pattern of the whole manufacturing Figure illustrates the interaction in the location patterns of establishments in industry 3410 (assemblers) and establishments in industry 3430 (suppliers) In Fig 7a, b, the solid lines are the same and represent the observed or empirical Kcross functions between both industries, while the dashed lines delimit the confidence interval The difference between the confidence intervals again lies in the test used, that is, in the way the counterfactuals are built (Fig 7a, ‘broad test’, and Fig 7b, ‘narrow test’ of colocalisation) 123 Sectoral scope and colocalisation of Spanish manufacturing… 85 Fig Colocalisation between industries 3430 and 3410 (‘broad test’ vs ‘narrow test’) In Fig 7a, the observed Kij(r) lies above the upper bound of the confidence interval at relatively short distances Specifically, this tells us that establishments in industry 3410, assemblers, tend to localise close to establishments in industry 3430, suppliers, from up to 101 km, or, at least, they locate closer to these than to establishments in their own sector However, if we look at Fig 7b, we can see that the Kij(r) function lies between the upper and the lower bounds of the confidence interval This means that colocalisation will not be significant at any distance analysed, but neither we find any codispersion patterns In the case of the automotive sector, it seems obvious that the industries analysed present a clear tendency towards colocalisation This is the result that is detected when our ‘broad test’ is used, while according to the ‘narrow test’ colocalisation would be rejected Evidently, one could argue that the tendency to colocalisation is not symmetrical (who attracts who?), and probably this is true A more detailed historical analysis of inputs and outputs in both industries could shed more light on this issue However, as we not have that information, we introduce Fig in order to add more details to the analysis of the colocalisation patterns of both industries Thus, Fig shows the interaction in the location patterns of establishments in industry 3430 and establishments in industry 3410, that is, the reverse case of Fig In Fig 8a, we observe that the pattern of behaviour of the observed Kij(r) is almost repeated, as in Fig 7a, lying above the upper bound of the confidence interval from up to 104 km This means that suppliers are also colocalised with assemblers at these distances Thus, we find colocalisation in both ways (i $ j), giving more robustness to our results discussed above In Fig 8b, we find again, as in Fig 7b, that the Kij(r) function lies between the upper and the lower bounds of the confidence interval at all the distances of the radius that were analysed Hence, with the ‘narrow test’, we not obtain codispersion at short distances, probably because both industries present individual location patterns which are not very concentrated In this way, the tendency of the establishments of both industries to locate closer to establishments in their own industry will not be stronger than the 123 86 M R Casanova et al tendency to locate closer to establishments of the other industry Therefore, we can conclude that these two industries analysed present a close positioning over the years Finally, in general terms, we observe that the way the counterfactuals are constructed somehow affects the interpretation of our results Since the two tests can be misleading, the joint use of them can give us a more accurate assessment of colocalisation patterns between two industries Using the ‘narrow test’, we would be able to detect less than half of the industries that have a relevant influence on the location pattern of other industries and locate close to them However, the number of industries with colocalisation patterns becomes more or less equal when we apply our ‘broad test’ in both ways (i $ j), as in the last example Hence, taking into account this mutual attraction, the number of pairs of industries showing colocalisation patterns is very similar, in both cases, and we can add more robustness to the analysis and minimise the probability of ‘joint-localisation’ Conclusions In this paper we extend the point pattern methodology of Albert et al (2012) to analyse the location and colocalisation patterns of Spanish manufacturing industries We use extensive micro-geographic data, with a more detailed industrial classification, in order to assess the tendencies to cluster in each four-digit industry relative to the whole of manufacturing, to measure the sectoral scope of localisation and to analyse the colocalisation patterns of the pairs of industries with relevant input–output linkages To this, we apply an extension of Ripley’s K function and a bivariate generalisation of this function, the K-cross function Both of them are distancebased methods, which allow us to treat space as being continuous and simultaneously analyse multiple spatial scales while avoiding the shortcomings of the administrative scale The analysis carried out provides us with a meaningful variety of results First, we find that 68% of the Spanish manufacturing industries present concentration patterns, whereas 18% are dispersed and 14% not present any significant differences from the location pattern of the manufacturing as a whole Second, a vast majority of the fourdigit industries that show concentration patterns are grouped in relatively small clusters, since 75% of them reach their maximum level of concentration at distances lower than 90 km Third, we observe that textile-related industries, media-based industries and chemical-related industries are listed as the most concentrated industries, whereas mostly food and food-related industries, together with industries with a high dependence on natural resources, are the activities that show the most dispersed location patterns These results coincide to a large extent with those obtained by other authors for other European countries According to the sectoral scope, we not find a widespread feature if we compare the location patterns of four-digit industries that are part of the same twodigit sector However, it seems that the more homogeneous the activities in a specific sector are, the more similarities we find in the spatial location patterns among their industries (intra-sectoral homogeneity) 123 Sectoral scope and colocalisation of Spanish manufacturing… 87 With regard to colocalisation, we obtain a rich harvest of results First, the existence of significant input–output linkages between different industries does not guarantee the spatial colocalisation of these industries Second, we find that establishments tend to locate closer to those in vertically linked industries than to establishments in horizontally linked industries So, 74% of colocalised industries are vertically linked This result suggests that the input–output linkages, although probably not the only factor generating a tendency towards inter-industrial spatial concentration, are an important source of externalities that encourage interindustrial agglomeration, especially in vertically linked industries Third, the number of pairs of industries that show colocalisation patterns varies depending on the method used to construct the counterfactuals, which allow us to establish the statistical significance of the results Thus, the more demanding the methodology used is, the more likely it is that actually existing colocalisation between pairs of industries will be rejected Specifically, when we use the ‘narrow test’, we find that only 20% of the total number of pairs of industries with stronger linkages are colocalised Moreover, this tendency to locate close to other industries is higher at large distances of the radius, rather than at short distances, the maximum percentage of colocalised industries being reached from 130 km onwards This result coincides with that obtained by Duranton and Overman for the UK, which is to our knowledge the only study that has also addressed this issue Otherwise, when we employ the ‘broad test’, we observe that a higher number of industries show colocalisation patterns In fact, 48% of the total number of pairs of industries analysed are colocalised, the percentage of industries with colocalisation patterns at short distances now being higher than at large distances However, we believe that this result is not only an artefact of the design of the null hypothesis, but rather reflects the real contribution of other forces, such as the existence of a skilled labour market or greater mobility of labour at short distances In this work, following the path of what has been called the third generation, we have abandoned the use of CSR as a benchmark, building our own counterfactuals These have been adjusted to the specific reality under study and to the economic restrictions affecting industrial localisation However, this work, like other similar studies, enables us to establish a series of ‘stylised facts’ in a rigorous manner, but the reported evidence is basically descriptive In this way, an interesting extension of this type of work could be the design of tests for specific theoretical hypotheses This would allow us to discriminate between different causes of concentration of economic activity, at different spatial scales, although doing so is beyond the scope of this paper Acknowledgements The authors gratefully acknowledge financial support from the Ministerio de Ciencia e Innovacio´n (ECO2014-58975-P) and Generalitat Valenciana (PROMETEOII/2014/054) Appendix See Table 123 88 M R Casanova et al Table Main characteristics of Spanish manufacturing industries Industries (NACE 93—Rev 1) Number of plants Total employees Average plant size (employees) 1511 Production and preserving of meat 403 21,256 52.74 1513 Production of meat and poultry meat products 788 45,988 58.36 1725 Other textile weaving 181 6812 37.64 1730 Finishing of textiles 354 11,920 33.67 1754 Manufacture of other textiles 230 9327 40.55 1822 Manufacture of other outerwear 855 34,080 39.86 1824 Manufacture of other wearing apparel and accessories 655 17,735 27.08 1910 Tanning and dressing of leather 1930 Manufacture of footwear 2010 166 7378 44.45 1346 32,807 24.37 Saw milling and planing of wood, impregnation of wood 331 25,249 76.28 2030 Manufacture of builders’ carpentry and joinery 830 47,592 57.34 2112 Manufacture of pulp, paper and paperboard 147 14,122 96.07 2121 Manufacture of corrugated paper and paperboard 432 22,862 52.92 2211 Publishing of books 310 27,011 87.13 2212 Publishing of newspapers 259 22,732 87.77 2213 Publishing of journals and periodicals 223 11,716 52.54 2416 Manufacture of plastics in primary forms 118 7366 62.42 2442 Manufacture of pharmaceutical preparations 221 42,057 190.30 2466 Manufacture of other chemical products 237 17,057 71.97 2513 Manufacture of other rubber products 268 12,473 46.54 2524 Manufacture of other plastic products 1356 85,176 62.81 2612 Shaping and processing of flat glass 236 8298 35.16 2630 Manufacture of ceramic tiles and flags 287 28,846 100.51 2640 Manufacture of other porcelain and ceramic products 303 11,029 36.40 2710 Manufacture of basic iron and steel and of ferro-alloys 250 42,777 171.11 2735 Other processing of iron 54 4736 87.70 2861 Manufacture of cutlery 37 1459 39.43 2863 Manufacture of locks and hinges 223 9185 41.19 2932 Manufacture of agricultural and forestry machinery 188 4701 25.01 2953 Manufacture of machinery for food, beverage and tobacco 232 7264 31.31 2954 Manufacture of machinery for textile, leather production 77 3207 41.65 3110 Manufacture of electric motors, generators, transformers 134 8597 64.16 123 Sectoral scope and colocalisation of Spanish manufacturing… 89 Table continued Industries (NACE 93—Rev 1) Number of plants Total employees Average plant size (employees) 3150 Manufacture of domestic appliances 209 6981 33.40 3210 Manufacture of electronic valves and tubes 208 14,023 67.42 3220 Manufacture of television and radio transmitters 89 15,014 168.70 3310 Manufacture of medical and surgical equipment 163 6687 41.02 3320 Manufacture of instruments for measuring, testing, navigating 120 5486 45.72 3420 Manufacture of bodies (coachwork) for motor vehicles 297 13,215 44.49 3430 Manufacture of accessories for motor vehicles, their engines 529 94,109 177.90 3511 Building and repairing of ships 271 23,145 85.41 3530 Manufacture of aircraft and spacecraft 61 19,871 325.75 3622 Manufacture of jewellery and related articles 147 4004 27.24 3650 Manufacture of games and toys 104 3912 37.62 Appendix Spanish manufacturing activities are classified into 23 sectors according to ‘NACE 93—Rev 1’:33 (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) Food products and beverages Tobacco products Textiles Wearing apparel and dressing Tanning and dressing of leather Wood and products of wood Pulp, paper and paper products Publishing, printing and recorded media Coke, refined petroleum products Chemical and chemical products Rubber and plastic products Other non-metallic mineral products Basic metals Fabricated metal products Other machinery and equipment Office machinery and computers Electrical machinery 33 The analysis is restricted to nineteen sectors due to the small number of establishments in the other four (16, 23, 30 and 37) 123 90 M R Casanova et al (32) (33) (34) (35) (36) (37) Radio, televisions and other appliances Instruments Motor vehicles and trailers Other transport equipment Furniture and other products Recycling Appendix Currently, with existing computer equipment it is feasible to consider any arbitrary window A, albeit as complicated as a map of Spain In our case, the statistical software application employed allows suitable border corrections to be applied to any irregular polygonal shape, thereby simplifying the treatment of border effects In Fig 9, we can observe the polygonal shape that accurately delimits our territory and envelops the area of study This allows us to avoid the nuisance of empty spaces where no establishments are found, which are represented by the space marked with oblique lines in the figure This polygonal boundary was built by joining thirty-five points on the perimeter of the Spanish territory In previous works, a rectangular area was usually used due to the increasing complexity encountered when simulating random points inside the area and when correcting the border effects on convex shapes These drawbacks thus limited the empirical analysis to rectangular areas.34 In our case, the statistical software employed, ‘R’,35 allows us to apply suitable border corrections to any irregular Fig Polygonal-shaped envelope 34 For example, Marcon and Puech (2003) did not analyse the whole of France, but instead an industrial area of 40 40 km around Paris and a larger rectangular area of France, measuring 550 630 km, and they explicitly said that it was impossible to use the whole of France because of border-effect corrections 35 This software is downloadable from the following website: http://www.r-project.org/ 123 Sectoral scope and colocalisation of Spanish manufacturing… 91 polygonal shape, thereby avoiding the shortcomings associated to the use of a rectangular area as the area of study References Albert JM, Casanova MR, Orts V (2012) Spatial 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