sectoral scope and colocalisation of spanish manufacturing industries

Received: 28 November 2015 / Accepted: 5 November 2016 / Published online: 30 November 2016 Springer-Verlag Berlin Heidelberg 2016 Abstract In this paper, we use distance-based methods,

Received: 28 November 2015 / Accepted: 5 November 2016 / Published online: 30 November 2016

 Springer-Verlag Berlin Heidelberg 2016

Abstract In this paper, we use distance-based methods, specifically a slight ation of Ripley’s K function and a bivariate generalisation of this function, toexplore the detailed location pattern of the Spanish manufacturing industry, thescope of localisation and the tendency towards colocalisation between horizontallyand vertically linked industries To do so, we use micro-geographic data, consid-ering a narrowly defined industry classification Our results show heterogeneouslocation patterns, but with a significant tendency towards localisation The sectoralscope 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

vari-we find in the spatial location patterns among its industries Finally, although thepatterns 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% arevertically linked industries

Keywords Spatial location Distance-based method  Ripley’s K function Sectoral scope Colocalisation  Vertical and horizontal linkages

Department of Economics and Institute of International Economics, University Jaume I,

Campus Riu Sec, 12071 Castello´n, Spain

3 Department of Economics and Institute for Local Development, University Jaume I, Campus Riu Sec, 12071 Castello´n, Spain

DOI 10.1007/s10109-016-0242-x

1 Introduction

The most striking feature of the spatial distribution of economic activity is itsheterogeneity As has recently been highlighted by Ellison et al (2010), economicactivity 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 naturaladvantages Some regions simply possess a better environment for certain industriesthat attracts them to that area Similarly, it is also difficult to ensure whether theestablishments of two industries are located close to each other because they areattracted by similar characteristics or natural advantages of the area or because theyhave strong linkages and have deliberately decided to locate close to each other toexploit 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 ofVon Thu¨nen, Marshall and Weber up to more recent contributions from the ‘neweconomic geography’ initiated by Krugman (1991a).1

Although it is easy to define localisation or colocalisation as the tendency ofdifferent establishments or industries to opt for the company of other firms orindustries and as a result to locate together, it is more difficult to measure it properlyand to detect whether the location of firms or industries is conditioned by thelocation of other firms or industries That is, we should differentiate betweenexogenous causes for locating together, like natural advantages, and endogenousreasons, like strong linkages or synergies between firms or industries

Thus, the interest in theories that can explain the agglomeration of firms andindustries has also been extended, in recent years, to the development of empiricalmethods to quantify and characterise this tendency of individual firms and industries

to cluster in space The first generation of these measures—to use the terminologyemployed by Duranton and Overman (2005)—was based on indicators such as theHerfindahl or Gini indices, which did not take space into consideration.2The secondgeneration, initiated by Ellison and Glaeser (1997), began to take space intoaccount, but not in a proper way The Ellison and Glaeser index still usedadministrative units to measure the spatial distribution of economic activity, treatingspace as being discrete.3 Therefore, they restricted the analysis of spatialdistribution to just one administrative scale, ‘they transform points on a map intounits in boxes’.4Alternatively, the third generation of empirical measures of spatiallocalisation, developed by authors from different scientific fields (economics,geography and statistics), introduced the treatment of space as being continuous, bysimultaneously analysing multiple spatial scales These new measures are unbiased

1 For further details, see Von Thu¨nen ( 1826 ), Marshall ( 1890 ), Weber ( 1909 ), Hoover ( 1948 ), Krugman ( 1991b ), Venables ( 1995 ), Ottaviano and Puga ( 1998 ), Fujita et al ( 1999 ) or Puga ( 1999 , 2002 ).

2 See Krugman ( 1991a ) or Amiti ( 1997 ).

with respect to arbitrary changes in the spatial units and can allow us to know and tocompare the concentration intensity for each spatial scale Authors like Marcon andPuech (2003), Quah and Simpson (2003), Duranton and Overman (2005) and Arbia

et al (2008), among others, were the pioneers in introducing these methods intoeconomic geography More recently, papers by Duranton and Overman (2008),Marcon and Puech (2010) or Albert et al (2012) have developed several extensionsand improvements to these methodologies Since then, an increasing number ofstudies have appeared thanks to these methodological developments and thewidespread use of micro-geographic data Some examples are Nakajima et al.(2012), who examined the location patterns of Japanese manufacturing industries, inthe same way as Koh and Riedel (2014) did with the four-digit Germanmanufacturing and service industries Meanwhile, Barlet et al (2013) improvedthe test proposed by Duranton and Overman (2005), avoiding the bias with respect

to the number of plants, and studying the location patterns of service andmanufacturing industries in France In accordance with other localisation measures,Guimara˜es et al (2011) modified measures of spatial concentration by taking intoaccount neighbouring effects and applying the new instruments to the USA.Similarly, Behrens and Bougna (2015) used micro-geographic data to analyse theevolution of geographic concentration in Canada, applying the Duranton andOverman index and also integrating neighbourhood effects into the Ellison andGlaeser 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 ofmanufacturing firms: the sectoral scope of the location patterns of differentindustries and the tendency to colocalise among various industries whose activity isrelated either vertically or horizontally To do so, we apply an extension of Ripley’s

K function,5which allows us to assess the different tendencies to cluster in eachindustry while also enabling us to know whether concentration exists, its intensity ateach distance, and on what spatial scale its highest level is obtained Moreover, toanalyse colocalisation, we use the K-cross function6 and we incorporate amethodological improvement that, unlike other proposals, enables us to obtainresults that are closer to reality from the economic point of view

Specifically, using a narrowly defined industry classification, we analyse thepatterns 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 eachmanufacturing industry at the four-digit level, the results revealing that 68% of themshow localisation patterns Moreover, these industries reach their maximumconcentration at very heterogeneous distances Second, we check the sectoralscope, that is, whether the four-digit industries that are part of the same two-digitsector 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 wholetwo-digit sector Our results confirm that the more homogeneous the activities in aspecific sector are, the more similarities we find in the spatial location patterns

5

For further details, see Ripley ( 1976 , 1977 , 1979 ).

6

See Ripley ( 1981 ).

among their industries Third, we analyse the colocalisation patterns of the pairs ofindustries with relevant linkages, finding that 48% of these examined pairs arecolocalised Furthermore, 74% of colocalised industries are vertically linked.Finally, we show that the patterns of colocalisation detected are sensitive to themethodology used to construct the counterfactual that allows us to establish thestatistical significance of the results So, the more restrictive the methodology used,the more likely it is to reject the existence of colocalisation between pairs ofindustries, especially at short distances, thereby increasing the risk of rejectingactually existing colocalisation patterns In this case, the colocalised pairs ofindustries are reduced from 48 to 20%.

The remainder of the paper is organised as follows In Sect.2, we present thedata used in our analysis and the methodology employed In Sect.3, we introduceand discuss the main results obtained, taking into consideration the sectoral scope oflocalisation for industries at the four-digit level and their corresponding colocal-isation between vertically and horizontally linked industries Finally, in Sect.4, weconclude and discuss the final considerations

2 Data and methodology

2.1 Data

We use establishment-level data, for the year 2007, from the Analysis System ofIberian Balances database7 to carry out our empirical analysis For eachestablishment in our database, we know their geographical coordinates (longitudeand latitude), their number of employees8 and the kind of industrial activity theyperform Specifically, we have information about the codes of the NationalClassification of Economic Activities (NACE)9they belong to When we refer to allestablishments grouped into four-digit or two-digit NACE codes, we are speakingabout 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 beanalysed simultaneously In fact, through said geographical coordinates, we locatethe establishments, represented by dots, accurately in space without having anymodifiable areal unit problems (MAUP), that is, our results do not depend on theadministrative scale chosen

Our database is restricted to Spanish manufacturing firms located only on thepeninsula and not in the Canary and Balearic Islands, Ceuta or Melilla, and whichemploy at least ten workers This second requirement is due to the fact that mostestablishments with fewer than ten workers do not have the essential information(geographical coordinates) needed to carry out our analysis Moreover, we should

highlight the fact that some industries are not included in the analysis because thenumber of their establishments is too small to be able to apply the statisticalmethods.10 After considering all these requirements, our database contains 42,820establishments, 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 onRipley’s K function, K(r) This function is a distance-based method that measuresconcentration by counting the average number of neighbours each firm has within acircle 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 manydifferent scales simultaneously, depending on the value of ‘r’ we take intoaccount12; that is,

K rð Þ ¼ 1kN

XN i¼1

XN j¼1;i6¼j

wijI d ij

I d ij

¼ 1; dij r0; dij[ r



where dijis the distance between the ith and jth establishments; I(dij) is the indicatorfunction and takes a value of 1 if the distance between the ith and jth establishments

is lower than or equal to r, and 0 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

wijis 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 ofstudy.14

The next step in the evaluation of the location patterns of economic activity is todefine the counterfactuals that allow us to provide our results with statisticalrobustness The null hypothesis is usually a kind of randomly distributed set oflocations in the area of study Thus, if establishments were located at random in thestudy 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).

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).

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 inspace in a random and independent way Economic activities are spatiallyconcentrated 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 idiosyncratictendency of each industry to locate itself from the general tendency of manufac-turing firms to agglomerate

To avoid these drawbacks and to control for the overall agglomeration ofmanufacturing, we proceed in two steps First, we define MTM(r) as the differencebetween 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 do this, we constructsuitable confidence intervals using Monte Carlo simulations.15Specifically, for eachindustry, we construct counterfactuals by randomly drawing the same number ofpoints (establishments) as in each of the industries under consideration, but thelocation of these hypothetical establishments is restricted, as in Duranton andOverman (2005), to the sites where we can currently find establishments from thewhole manufacturing sector In this way, the construction of the confidence intervalallows us to assess the significance of departures from spatial patterns followed bythe whole of manufacturing and to control for industrial concentration When theestimated MTM(r) for a specific industry lies within the confidence interval, wecannot 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 ofthe confidence interval, the industry analysed is more concentrated than themanufacturing industry, while if it is below the lower bound of the confidenceinterval, then the analysed industry exhibits a more dispersed pattern thanmanufactures as a whole.16

Similarly, in order to analyse whether two industries, horizontally or verticallylinked, are colocalised, we have to consider a multivariate spatial point pattern To

do so, we use a K-cross function, Kij(r), where i = j and r is the radius, that is:

Kijð Þ ¼ kr  ikjA1X

k

Xl

I di k ;j l

¼ 1; dik ;jl r0; dik;jl[ r

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 nullhypothesis in order to construct the counterfactuals is rather more complicated.Furthermore, this choice will condition the interpretation of our results Indeed, wemust point out that the fact that two industries are located together does not alwaysmean that they deliberately locate close to each other to exploit synergies betweenthem Instead, they can possess similar location patterns only because the twoindustries 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-crossfunction can be compared, in two different ways

In the first way, for any two four-digit industries (i and j) we simulate the spatiallocation of establishments by randomly sampling the same number of points(establishments) of four-digit industry i (Ni) in the set of sites actually occupied byestablishments of two-digit sector I, which this industry belongs to (i [ I).18Then,

we use these simulations to compute the K-cross function, Kij(r), and construct theconfidence intervals.19In this case, the upper deviations of the estimated Kij(r) valuefrom randomness indicate that the establishments in the four-digit industry i [ I areattracted 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 significantevidence of a tendency of establishments in industry i to locate closer toestablishments of industry j (i ? j), instead of locating closer to other establish-ments from their own sector Alternatively, if the Kij(r) value lies below the lowerbound of the confidence interval, colocalisation will not exist and establishmentsfrom industry i will prefer to locate closer to establishments from their own sectorrather than to establishments from industry j Finally, if the value of Kij(r) liesbetween 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.

pattern of the establishments of industry j does not have a significant influence onthe location pattern of the establishments of industry i and these establishments willlocate close both to establishments of industry j and to establishments from theirown sector Furthermore, we use the same criterion to assess whether establishmentsfrom 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 thatcolocalisation exists in both ways This means that establishments in industry

i locate closer to establishments in industry j than to other establishments in theirown sector I, and vice versa, (i$ j); that is, establishments from both industriesshow mutual attraction In this way, more robustness is given to colocalisation andthe probability of ‘joint-localisation’ can be minimised

Our second way to construct counterfactuals relies on the test proposed byDuranton and Overman (2005,2008) In this case, the alternative is to randomlysample the same number of points as the sum of establishments belonging to the twoindustries (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 theconfidence intervals.20 Hence, when the estimated Kij(r) value is higher than theupper bound of the confidence interval, it means that establishments in theseindustries are attracted to each other even after controlling for whatever tendencythey 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 toestablishments in this industry than establishments in one’s own industry’.21Obviously, the way the counterfactual is built defines the conditioning factors ofthe underlying spatial randomness of our null hypothesis, and changes the intuitionbehind the test we are performing The key question is: what is the alternative toevaluate the significance of the tendency of establishments in an industry i to becloser to establishments in a linked industry j? In sum, in this paper we propose twoalternatives First, this tendency will be stronger than the tendency to be locatedcloser to other establishments in their own two-digit sector (which henceforth wewill call the ‘broad test’ of colocalisation) or, second, closer to establishments intheir own four-digit industry (hereafter called the ‘narrow test’ of colocalisation)

3 Empirical results

3.1 Localisation in four-digit industries

The analysis of the spatial location pattern of the Spanish manufacturingindustries shows that 61 of the 90 four-digit industries considered (68%) are

concentrated,22 whereas 16 industries (18%) are dispersed, and 13 (14%) do notpresent any significant differences from the location pattern of the wholemanufacturing.

Focusing on those industries that have a higher tendency to spatial concentrationthan the whole manufacturing, Fig.1shows the cumulative percentage of industriesthat reach their maximum level of concentration (maximum MTM value) at eachdistance 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, thatthere is a considerable change in the rate of incorporation of new industries thatreach their highest level of concentration from 90 km onwards

In fact, a large number of industries (30%) reach their highest level ofconcentration at very short distances (between 0 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 atdistances 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 MTMvalue is themaximum difference between Kiand KTM, and given that KTMvalues do not remainconstant when the radius becomes larger, the interpretation of the MTMvalue is notindependent on the behaviour of KTM Hence, industries that reach their maximumlevel 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 ofconcentration at a distance of 60 km and from this distance onwards itsconcentration becomes lower, even showing dispersion patterns beyond 150 km.Hence, those industries that reach their MTMpeak at distances of \60 km are of

Fig 1 Cumulative percentage of industries that reach their maximum concentration level (maximum MTM) at different distances

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.

Table 1 Location patterns of Spanish manufacturing industries (MTM)

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

1824 Manufacture of other wearing apparel and accessories 0.05 200

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

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 – –

2932 Manufacture of agricultural and forestry machinery -0.02 88

2953 Manufacture of machinery for food, beverage and

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

3420 Manufacture of bodies (coachwork) for motor vehicles -0.01 130

greater importance in our analysis, since this evidence could be interpreted as stronglocalisation.

Table1gives detailed information about the location patterns of a representativesample of the 90 industries analysed.23This sample contains industries belonging toall the sectors analysed and not only those that are concentrated, as in Fig.1 Ittherefore also includes industries that present dispersion patterns and industries that

do not present significant differences from the manufacturing industry as a whole.The first column of Table1shows the four-digit code and name of the industries.Its last two columns show the significant extreme value of the MTMfunction and thedistance (r) at which this value is reached A positive extreme value of the MTMfunction means that at the critical value of radius r, there is a maximum; that is, forthis radius the highest level of concentration at all possible radii is reached.Similarly, a negative extreme value of the MTMfunction indicates that at radius r,there is a minimum; that is, for this radius the highest level of dispersion at allpossible radii is reached Therefore, in this table, the spatial location pattern of eachindustry is characterised by two specific features: (1) the intensity of the cluster(extreme value of the MTMfunction), and (2) the distance at which this highest/lowest intensity is reached (critical value of radius r)

As we can see in Table1, although there are similarities in the spatial distribution

of some of these industries, the dominant feature is the substantial variation amongthem The intensity and the distance at which the maximum concentration/dispersion is reached vary from industry to industry and this can encourage a largediversity of types of clusters

If we look at the intensity of concentration in Table1, it is easy to observe that,

on the one hand, textile-related industries, media-based industries, and related industries are among those with higher levels of spatial concentration,together with the ceramic manufacturing, an industry that is heavily localised inSpain.24 On the other hand, we find that mostly food and food-related industries,

chemical-Table 1 continued

value)a

r (critical value, km)

3430 Manufacture of accessories for motor vehicles and their

engines

3530 Manufacture of aircraft and spacecraft 0.07 82

3622 Manufacture of jewellery and related articles 0.09 63

a If values [ 0 there is a maximum (concentration), if values \ 0 there is a minimum (dispersion)

23 Information about the results for other industries is available upon request from the authors 24

Specifically, the industries that show the most concentrated location patterns are (1730) Finishing of textiles, (1930) Manufacture of footwear, (2954) Manufacture of machinery for textile, apparel and leather production, (2211) Publishing of books, (2213) Publishing of journals and periodicals, (2442) Manufacture of pharmaceutical preparations, and (2630) Manufacture of ceramic tiles and flags.

together with industries with a high dependence on natural resources, are theactivities that show the most dispersed location patterns.25 Like Duranton andOverman (2008), we do not find any particular characteristics among the mostconcentrated industries Thus, most of the textile-related industries are low-tech andpresumably their geographical concentration is due to historical trends; in the case

of media-based and chemical-related industries, their decision to concentrate may

be due to the search for skilled labour; and, finally, the ceramic manufacturing has amarkedly specialised industrial activity, as well as knowledge and technologicalspillovers that make its establishments form a well-known industrial district.Moreover, if we go further in the comparison of our results with those obtained byother authors, we realise that many similarities are to be found For instance,Duranton and Overman (2008) found that, in the UK, textile-related industries andmedia-based industries are amongst the most localised, while it is mostly food-related industries together with industries with high transport costs or a highdependence on natural resources that show dispersion Behrens and Bougna (2015),

in Canada, found that textile and publishing industries are among the most localisedindustries, while food and drink and wood industries are among the least localisedones They also added that most of the industries do not have extreme spatialpatterns, which is similar to the results for the UK and Spain Similarly, the analysisperformed by Koh and Riedel (2014), for the German manufacturing industry, alsosuggested that the especially traditional industries, like textile production, are theones which exhibit strong localisation patterns

Finally, the last column of Table1 allows us to know the spatial scale or therough size of the cluster of each industry, i.e the distance (radius) at which thehighest intensity of concentration is reached As can be seen, heterogeneity is thenorm, reaching peak concentration levels at distances ranging from 6 to 200 km.Thus, among the industries that reach their highest level of concentration at shortdistances (lower than 30 km) we can find Building and repairing of ships (3511),which reaches it at only 6 km; some textile and leather industries, like Manufacture

of other textiles (1754) or Manufacture of luggage, handbags, saddlery and harness(1920), which reach their highest concentration at distances of 19 and 29 km,respectively; and Manufacture of pulp, paper and paperboard (2112), at a distance

of 23 km However, we should note that, although these industries reach theirhighest level of concentration at very short distances, they do not have excessive

‘intensity’, that is, their maximum level of concentration is not very high We findonly one industry that meets both requirements Manufacture of ceramic tiles andflags (2630) presents a high level of concentration and this happens at shortdistances

Only when we combine the information on the value of the maximum intensity ofthe clusters with the distance at which it is achieved is it possible to give some idea

of the underlying reality in Table1for different industries Thus, in the first cases,

we are looking at industries with small clusters distributed throughout the study

25

Production and preserving of meat (1511), Production of meat and poultrymeat products (1513), Manufacture of machinery for food and beverage processing (2953); Saw milling and planing of wood, impregnation of wood (2010), Manufacture of builders’ carpentry and joinery (2030), Manufacture of agricultural and forestry machinery (2932).

area, but which also have a significant proportion of establishments distributedthroughout the space, although they are not located inside those clusters However,

in the second case, the level of concentration of the industry is much higher at shortdistances because most of its establishments are located in a single small cluster,and only a few establishments are situated outside this cluster

3.2 Sectoral scope: four-digit industries within two-digit sectors

Next, we examine whether related four-digit industries within the same two-digitsector tend to follow similar or different patterns of localisation

Our results indicate that for many two-digit sectors, related industries within thesame sector tend to follow similar location patterns; that is, intra-sectoralhomogeneity appears Some examples are sectors (15) Food products andbeverages, (18) Wearing apparel and dressing, (27) Basic metals, (31) Electricalmachinery, (32) Radio, televisions and other appliances, (33) Instruments and (34)Motor vehicles and trailers For instance, sector 15 exhibits a more dispersedpattern than manufactures as a whole, reaching its maximum level of dispersion,with an intensity of -0.01, around the distance of 60 km, as do most of theindustries that are grouped in it.26 Duranton and Overman (2005) found similarresults, showing that for many of these previously mentioned two-digit sectors,related four-digit industries within these sectors tend to follow similar patterns ofdistribution

However, for other sectors, related industries tend to follow different locationpatterns This is the case of sector (36) Furniture and other products, where none ofits industries have a similar location pattern to that of the sector they belong, and thespatial distribution of each industry is very different from one to another This isprobably due to the fact that it is a sector with very varied activities grouped in it,like furniture, mattresses, jewellery, musical instruments, sports goods, toys, and soforth.27 Another example of intra-sectoral heterogeneity is sector (29) Othermachinery and equipment In this case, its industries present very heterogeneouspatterns of localisation, showing high levels of dispersion and concentration.Specifically, on the one hand, industries (2953) Manufacture of machinery for foodand beverage and (2932) Manufacture of agricultural and forestry machinery showdispersion patterns This happens because the main activity of these two industries

is related to other widely dispersed industries Thus, industry 2953 is verticallylinked to food-related industries and industry 2932 is vertically linked to industrieswith a high dependence on natural resources On the other hand, industry (2954)Manufacture of machinery for textile, apparel and leather production presentsconcentration patterns at short distances, due to the fact that it is vertically linked totextile industries, which are also concentrated at short distances These resultscoincide with those obtained in the UK by Duranton and Overman (2005), who say

26

See, for example, the two first industries in Table 1

27 Manufacture of office and shop furniture (3612), Manufacture of kitchen furniture (3613), Manufacture of mattresses (3615), Manufacture of jewellery and related articles (3622), Manufacture

of games and toys (3650).

that industries 2953 and 2932 present dispersion at all distances, while industry

2954 exhibits localisation for distances between 0 and 50 km

Lastly, there are other sectors where the heterogeneity among their industries isnot as high as in the previous examples, with industries with location patterns verysimilar to the sector as a whole and industries with completely different patterns oflocalisation coexisting within the same sector This is the case of sectors (17)Textiles and (22) Publishing, printing and recorded media, where two of theirindustries differ from the rest and from the spatial distribution of the aggregatedsector The same happens with sectors (25) Rubber and plastic products and (26)Other non-metallic mineral products, in which one industry presents locationpatterns 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 detailedanalysis when we combine information on the level of intensity with the distance atwhich it is achieved However, it is not feasible to offer a detailed description of thelocation pattern for all industries and sectors analysed Hence, we will use twoexamples to illustrate more accurately the magnitude of the differences highlighted

by the estimation of Ripley’s K functions

Figures2and3illustrate the case of industries (2213) Publishing of journals andperiodicals and (2630) Manufacture of ceramic tiles and flags, and theircorresponding two-digit sectors (22 and 26) Figures2a, c, 3a, c depict pointclouds for each industry and sector, where each dot corresponds to an establishment,and Figs.2b, d,3b, d show their MTMestimated functions.28

The point clouds clearly show that there are differences in the density anddistribution of establishments between each industry and its corresponding sector.However, just by looking at the clouds it is difficult to establish to what extent thespatial location patterns of the sectors and the industries concerned are different,how large these differences are, or how the degree of spatial concentration isaffected at each distance Thus, on examining the MTMestimated functions it is easy

to recognise that the most pronounced difference between the location pattern offour-digit industry and two-digit sector occurs in Fig.3 In fact, sector 26 showsdispersion patterns at all distances of the radius analysed, while industry 2630presents high levels of concentration In Fig.2, the difference between the spatiallocation 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 betweenFigs.2 and3is that, in both cases, the four-digit industries show higher levels ofconcentration than their respective two-digit sectors and this concentration isreached at much shorter distances

At this point, it should be added that although both industries presentconcentration patterns at short distances, the shape of their MTM curves is verydifferent In Figs.2d, 3d, we observe a common fast growth of the MTM value atshort distances of the radius, but when the maximum MTMis reached, the behaviour

of the MTMfunction 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.