Developments in size and composition of Italian
regional clusters during the period 2000-2010: a
study using input-output tables
Author: Sietse Compagner, S2352966 Supervisor: prof. dr. Bart Los
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3 1 Introduction
In August 2013 a Bloomberg article reported the disappearance of an entire Italian electronic component factory overnight. The plant in question was completely dismantled, packaged and shipped to a new location in Poland during the employees‟ three-week summer holiday. The factory workers only received notice about the plant‟s new location after the entire plant had moved abroad.
This anecdote may be the most sensational symptom of the problems surrounding the deeply struggling Italian manufacturing sector, but it is hardly the only one. In the first decade of the 21st century 27,000 Italian companies shifted their production abroad, with Poland being a popular destination (Bloomberg, 2013). The main reasons given for this exodus of manufacturing activity are Italy‟s high taxes and labour costs, as well as its bloated bureaucracy. But in fact, the movement of Italian production to locations abroad is part of a greater process: the rise of global value chains. Global value chains (GVCs) are the outcome of a process of increasing fragmentation and international dispersion of production chains. This fragmentation of production processes is enabled by decreasing transport and communication costs, which allow firms to relocate production activities internationally. Evidently, Italy is not the only country that feels the effect of the emergence of GVCs. However, studying Italy is particularly interesting due to its peculiar economic geography. The country has a long history of economic divergence, with large differences between the wealthy northern regions and the underdeveloped southern regions. While the country‟s northern cities, such as Milan, have per capita GDP levels exceeding those of a country like Sweden, cities like Naples and Palermo in the south are economically more comparable to the Czech Republic (Citymetric, 2014). This north-south divide makes Italy one of the most economically divided countries in Europe today (Gonzáles, 2010).
This study focuses on Italy‟s economic divergence by assessing the effect of the forces driving the emergence of GVCs on the development of regional economies. The economic development of individual regions will be measured in terms of the development of clusters, which can provide an important source of economic growth according to authors such as Michael Porter. In addition to identifying and describing the composition of regional clusters in Italy, this study assesses whether the development of these clusters follows the patterns described by Paul Krugman‟s (1991) new economic geography (NEG) model. In doing so, this study aims to answer the following research question: Which industries
dominate Italian regional clusters between 2000 and 2010, and does the development of these clusters in terms of total size adhere to the theory of the NEG model?
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proposed by Oosterhaven et al. (2001), can be used to identify clusters through the identification of important transactions between industries within an economic system, called linkages. The dataset on which the methodology can be applied is introduced in section 4. Sections 4.1-4.4 explain which elements should be extracted from the dataset in order to conduct a cluster analysis on multiple levels of aggregation. Section 5.1 summarises and visualises the results of applying the cluster analysis to the dataset at different levels of aggregation. To test the findings from section 5.1 against Krugman‟s (1991) NEG model, section 5.2 includes an empirical analysis of the results. Finally, section 6 provides a conclusion, summarising the main findings and discussing potential further research.
2.1 The importance of clusters in regional development
Arguably one of the largest contributors to the field of cluster theory is Michael Porter, who defines clusters as “a geographically proximate group of interconnected companies and associated institutions in a particular field, linked by commonalities and complementarities.” (Porter, 1998, p. 199). Porter‟s work may have played a large role in the development of cluster literature, but it is based on theory that has been around since the beginning of the 20th century. Literature on agglomeration economies provides the basis of the argument that regional clustering translates into increased regional competitiveness. Authors like Marshall (1920) and Hoover (1948) describe the concept of agglomeration economies and external localisation economies respectively.
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between consumers and suppliers, or innovation and learning processes that often result from a concentration of economic activity in one or several regions.
The NEG model thus states that agglomeration makes regions more productive, resulting in a flow of economic activity from peripheral regions to the core regions. Krugman (1991) stresses two limitations of the NEG model: it is vastly oversimplified, and it does not predict the localisation of particular industries. However, the model is still highly relevant as it can be used to formalise observations of agglomeration patterns. This model can thus be of great help in analysing the clustering of Italy.
2.2 Global integration of production and agglomeration patterns
The NEG model introduced in section 2.1 predicts agglomeration patterns of economic (manufacturing) activity, based on centrifugal and centripetal forces. These centrifugal and centripetal forces are in turn influenced by numerous external factors. Developments in transport technology for instance, can decrease the cost of transportation, thereby lowering the centrifugal pressure within the model. Two factors with a particularly large impact on the mechanisms of the NEG model are assessed by Baldwin and Evenett (2012), who describe the developments of global transport and communication costs. These authors propose that a decrease in transport and communication costs has had a large effect on manufacturing production. Production became more and more mobile, leading to a fragmentation of production processes. More specifically, the authors identify two waves of unbundling that led to the rise of global value chains. Central to the first wave was the unbundling of production and consumption. Historically, production and consumption were bundled geographically, as few items could be profitably imported or exported. Countries thus produced mostly to satisfy domestic demand. The steam revolution that took place around the end of the 18th century changed this status quo. Innovations like railroads and steamships decreased the cost of transporting goods over large distances, leading to a concentration of manufacturing activities to benefit from scale economies. Decreasing transport costs allowed countries to specialise along comparative advantage lines, specialising in the production of one or several goods while using imports to satisfy demand for the remaining goods. The second wave of unbundling was driven by developments in communication technology and resulted in an unbundling of the production process itself. Developments in communication technology enabled the coordination of complex tasks over larger distances, allowing for a separation of activities in the production process. As „slicing up‟ the value chain became a possibility, wage differences between regions were the main force driving the concentration of specific tasks in one location. In essence, Baldwin and Evenett (2012) describe a process of increasing global integration of production, driven by scale economies and decreasing transport and communication costs. These findings are closely related to the mechanisms of the NEG model, as they describe a process of agglomeration of production activities, stimulated by weakening centrifugal forces such as decreasing transport costs.
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notion, stating that manufacturing activities “are particularly prone to fragmentation and have a high degree of international contestability”. According to the authors, the reason for this proneness to fragmentation is that manufacturing activities can be undertaken at any location, without loss of quality. This means that the manufacturing production process can be „sliced up‟ and dispersed globally without affecting the quality of the final good, allowing for the concentrate similar activities to enjoy the agglomeration and localisation economies described by Marshall (1920) and Hoover (1948).
The relation between increasing global integration of production on agglomeration patterns is confirmed by existing literature. Scott (2001) uses a broader definition of integration, describing it as “huge and ever-increasing amounts of economic activity (input-output chains, migration streams, foreign direct investment by multinational organisations, monetary flows, and so on) [that] now occur in the form of long-distance, cross-border relationships”, and finds that global integration has a diverging effect on regional economies. The author predicts that this divergence culminates into the rise of a new system of large city regions, a prediction that is largely in line with the core-periphery outcome described by the NEG model. Furthermore, Scott identifies two main drivers of this development: increasing geographic differentiation and locational specialisation. These driving forces behind regional divergence strongly coincide with the description of the second wave of unbundling by Baldwin and Evenett (2012).
Similar findings are presented by Charron (2016), who argues that the increasing concentration of activities in regions leads to the emergence of high productivity regions at the expense of less developed regions. The driving force behind this regional divergence is the increasing openness of countries, defined as their level of globalisation1 according to the KOF index of globalisation (Dreher, 2006). The KOF index provides an index value of globalisation, comprised of a weighted average of three elements of globalisation: economic, social and political. The index takes into account factors like trade and FDI, but also information like international tourism and migration. Charron (2016) finds that under increasing globalisation, more open regions – often urban and capital regions – become increasingly productive, while other regions – often the periphery – do not.
Extensive empirical evidence on the process of regional divergence under increasing openness is provided by Ezcurra and Rodríguez-Pose (2013), who analyse the relation between globalisation and regional inequality using panel data on 47 countries over the period 1990-2007. Again, the KOF index is used to provide an index of globalisation. The authors find a positive association between the degree of economic openness and the magnitude of within-country regional disparities, and conclude that globalisation leads to the emergence of losing and winning regions within countries.
2.3 The case of Italy
Sections 2.1 and 2.2 describe the theory supporting the economic significance of clusters, as well as the patterns in the agglomeration of production activity across regions. However, these sections do not assess the situation in individual countries. Since the focus of this study
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lies on Italy, it is important to have an understanding of the economic climate in terms of cluster structures in this country. This way, the results of the analysis presented in section 3.1 can be interpreted from an accurate perspective.
According to Chiarvesio et al. (2010) the work of Giacomo Becattini, an Italian economist, provides the basis for the early literature on Italian clusters. This literature describes a very particular type of clustering, strongly associated with Italy: the industrial district (ID). IDs are composed of a concentration of numerous small firms engaged in activities linked to a single specialised sector, located in a community clearly identifiable in terms of geography, history and culture. In this perspective, the supply chain of an ID is largely self-contained within the district, with external transactions occurring with suppliers of raw materials and final markets. Spatial proximity thus plays a critical role by reducing transaction costs in terms of control, information sharing and coordination. Their strong linkages, specialisation and homogenous cultural background have made the IDs a viable alternative development model to large-scale, vertically integrated firms in existing literature (Rabellotti et al., 2009).
Rabellotti et al. (2009) provide an extensive review of the literature on Italian IDs, which is highly fragmented and often only accessible to Italian readers. The overview presented by these authors describes IDs as the backbone of Italian manufacturing production up to the 1990s. Italian IDs were a large driver of Italian economic growth, performing well in terms of profits and employment, making them central players in the Italian manufacturing system. However, the literature also describes the decline of IDs after a slowdown in Italian economic growth starting in the second half of the 1990s. This slowdown in economic growth has raised questions regarding the effectiveness of these industrial clusters under forces of globalisation and innovation, as described by Baldwin and Evenett (2012). A main argument in this discussion is that the small scale of IDs is an obstacle to FDI, participation in GVCs or innovation. Like the work of Baldwin and Evenett (2012) and the description of agglomeration patterns according to the NEG model (Krugman, 1991), literature on Italian clusters is strongly oriented on manufacturing activity. The term industrial districts suggests that the districts are defined primarily by industrial production, a notion that is supported by the central role IDs play in Italian manufacturing.
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from the opportunities provided by the global economy, in order to retain their relevance. Although this analysis of Italy‟s clusters is strongly business-oriented, elements of Baldwin and Evenett‟s (2012) description of the unbundling process can be clearly recognised. The characteristics of the open network model show strong similarities with those of a global value chain, both processes entailing an internationalisation of a firm‟s production processes.
The literature presented in this section mainly relates to the composition and development of Italian clusters in general. The findings presented above can therefore only be related to the first part of the research question posed in the introduction: Which industries
dominate Italian regional clusters between 2000 and 2010? In terms of cluster composition,
this study is likely to find a dominance of the manufacturing industry in Italy‟s regional clusters. Both the literature on the agglomeration of production activity in general, and literature on the nature of Italian clusters allocate a large role to manufacturing activity. In case of Italy, this translates in clusters dominated by one manufacturing sector surrounded by smaller industries providing inputs. However, it is difficult to say how the role of manufacturing in Italian clusters will be affected by the transition towards more internationally oriented clusters, described (Chiarvesio et al., 2010). If this orientation involves the relocation of manufacturing activities to foreign locations, the consequences for the composition of Italian clusters are large.
The second part of the research question: Does the development of these clusters in
terms of total size adhere to the theory of the NEG model?, is more difficult to answer
directly based on the proposed literature. Because the NEG model introduced in section 2.1 and the literature on agglomeration presented in section 2.2 only provide a general indication of agglomeration patterns, the pattern of Italy‟s cluster development can only be predicted. Keeping in mind Italy‟s economical north-south divide illustrated by González (2010) and the core-periphery outcome proposed by the NEG model, the development of Italian regional clusters in terms of size should depict a growth of the northern clusters combined with a decline in southern clusters.
3.1An overview of cluster analysis methods based on input-output analysis
With cluster literature providing extensive material to support the economic relevance of cluster structures, the next step is to determine a method to identify and analyse these cluster. Following Porter‟s (1998) definition provided in section 2.1, the key aspect of a cluster are the linkages between its economic agents. Analysing the development of clusters empirically is difficult, as it is complicated if not impossible to quantify every interaction – both tangible and intangible – between economic agents. However, a reasonable approximation of these linkages is provided by input-output tables (IOTs). Input-output tables represent flows of intermediate goods between industries, as well as the flows of final goods to satisfy final demand. Such IOTs are organised as shown in figure 1 (Dietzenbacher, 2016).
Industries Final demand Total
Industries Z F x
Primary inputs W
Total x’
Figure 1: Stylised version of an input-output table (IOT) containing matrices Z, F, W and x. x’ is a transpose of
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Where Z is a square nxn matrix displaying the deliveries of intermediate goods between
industries. Sales of intermediate goods by industry i are noted along the rows of the matrix, while purchases of intermediate goods by industry j are noted along the columns. Consequently, element zij in matrix Z gives the monetary value of a goods flow from industry
i to industry j. The values along the diagonal of matrix Z denote the intra-industry sales, or
the goods used in the production of industry i, sourced from industry i. Final demand matrix F is an nxk matrix representing final demands for goods from industry n, by categories k.
Categories k include factors like private consumption and investments or exports. Element fij in matrix F gives the monetary value of the delivery of goods from industry i to final demand category j. Primary inputs matrix W is an mxn matrix with primary inputs used in production.
These inputs m include factors like wages and salaries, capital depreciation and imports. Element wij in matrix W gives the use of primary input of type i by industry j. Finally, x and x’ are vectors of gross outputs, where prime denotes a transposition of (column) vector x.
Matrix Z is the most important matrix in input-output analysis, providing an overview of the linkages between sectors in terms of intermediate goods flows. The ability of an IOT to summarise goods flows between industries makes it a suitable tool for the identification of clusters. At this point, it is important to note that IOTs provide an approximation, as they are constructed under a set of simplifying assumptions. First, the main issue is that the tables include industry data rather than firm data. This implies that these tables can only be used to identify linkages between sectors, not between individual firms or other economic agents. Another important note is that industries in the table are defined by a single product, i.e. each industry is assumed to produce only one product. This assumption can lead to a loss of accuracy, especially when industries are formulated too broadly.
However, IOTs cannot be readily used to identify clusters. Several preceding steps are required. Finding which sectors are strongly related by simply reading the input-output tables can be a time-consuming exercise, especially when no sectors are given in advance. This problem becomes only larger for tables with many sectors (Hoen, 2002).
A solution to this issue is to use cluster analysis. Literature on cluster analysis is widely available, and offers a range of different techniques. A rather straightforward method to identify clusters is the elementary cluster analysis. This method, proposed by Bijnen (1973), involves linking each individual industry in an input-output table to the industry it has the strongest ties with in terms of the transaction size. This method yields a cluster consisting of a network of industries, each linked to the industry it sells most to and buys most from. Although an argument in favour of this method would be its simplicity, linking industries based on only their largest transaction neglects the majority of flows between industries. Weaker, but potentially important linkages are neglected..
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similarity of transaction patterns, is to group industries that are most likely to interact with each other on a formal and informal level. Although the cluster analysis proposed by Feser and Bergman (2000) is useful in identifying clusters, it is limited to measuring the composition of clusters. Because clusters are identified based on their pattern of direct and indirect links, rather than the size of these links, there is no room for a measure of magnitude. The lack of a measure of magnitude means that this method of analysis is of no use in answering this study‟s research question.
A method of cluster analysis more suitable to the purposes of this study is proposed by Oosterhaven et al. (2001), who define clusters based on the absolute and relative size of transactions between industries in an IOT. The authors use Dutch input-output data to compare the size and composition of clusters in three Dutch regions.2 This method of cluster analysis requires the extraction of each region‟s intra- and inter-regional transactions zij from matrix Z. This yields a set of three sub-matrices per region r: intra-regional matrix Zrr, including transactions between industries i and j within region r; intermediate imports matrix Zor, including purchases of intermediate goods by industry i in home region r from industry j outside home region r; and intermediate exports matrix Zro, including sales of industry i in home region r to industry j outside home region r. With these matrices extracted, clusters can be determined by identifying direct and indirect linkages in each region. Direct linkages are transactions zij that exceed the average transaction size in the sub-matrices by a factor α. Indirect linkages relate to the relative size of transaction zij, measured in terms of an industry‟s total output. The method distinguishes between indirect forward linkages, measuring the relative size of intermediate sales, and indirect backward linkages, measuring the relative size of intermediate purchases. Transactions exceeding the average size in relative terms by a factor β are considered indirect linkages. Apart from assessing linkages between industries in both absolute and relative terms, this method allows for the measurement of transaction sizes. This means that identified clusters can be compared in terms of size as well as composition. Of the proposed methods, the analysis introduced above is most in line with the aim of this study. This method will therefore be used to identify regional clusters in Italy. A more detailed explanation of the identification of linkages in each region, and the calculation of coefficients α and β is provided in section 3.1.
A final method in the field of cluster analysis that deserves a mention is qualitative input-output analysis. This method is based on classifying transactions zij as either important or unimportant flows of goods using a filter rate. Any transaction smaller than the filter rate is deemed irrelevant and is assigned a zero, while any transaction above the filter rate is considered important and is assigned a one. This filtering process yields a binarised version of matrix Z showing only the most important transactions as ones. With the strength of the linkages between industries determined, the concentration of industries in regions is calculated using Gini-coefficients and the Herfindahl index. This methodology is applied by Titze et al. (2011), who use it to identify clusters and their regional integration in German NUTS-3 regions. Input-output data on a this level of aggregation is acquired by translating
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data on a national level based on an industry‟s share in the total industry employment for each region. A critical shortcoming of the method of analysis proposed here however, is the loss of data due to simplification. Using a filter rate eliminates the majority of the transactions, leading to a loss of potentially valuable data. Additionally, it is not possible distinguish between sizes of relevant flows, as all of these flows are defined by a single number.
3.2 Methodology – identification of linkages
The basis of identifying cluster structures in regions using IOTs is the identification of the most important transactions for each region within these tables. When these most important transactions, called linkages, are visualised they can be used to identify clusters. This study identifies these linkages following a methodology proposed by Oosterhaven et al. (2001), who define them using three sub-matrices for each region r, drawn from the Z matrix in an IOT: intra-regional matrix Zrr, including transactions between industries i and j within a region r; intermediate imports matrix Zor, including purchases of intermediate goods by industry i in home region r from industry j outside home region r; and intermediate exports matrix Zro, including sales of industry i in home region r to industry j outside home region r. The idea behind using these three sub-matrices as the basis of the cluster analysis is to stay as close to the structure of the dataset as possible. The three matrices allow for a distinction between important transactions flowing from industry i to industry j (one-side dependency), and important transactions flowing from industry i to industry j and from industry j to industry i (interdependency).
To determine which transactions zij in matrices Zrr, Zro and Zor are large enough to be considered a linkage in a cluster, each transaction is assessed along three criteria: the absolute size of transaction zij, the relative size of transaction zij as an intermediate sale, and the relative size of transaction zij as an intermediate purchase. The first criterion specifies that that the absolute size of a transaction should exceed a certain threshold to be considered a linkage. Transactions exceeding this threshold are called direct linkages. This condition is summarised in equation (1), where the height of the threshold is determined by α. In order to be considered a direct linkage, a transaction zij should be larger than the average intermediate transaction between any two sectors in matrices Zrr, Zro and Zor by a factor α.
𝑧𝑖𝑗 > 𝛼(𝐢′𝐙𝐫𝐫𝐢 + 𝐢′𝐙𝐫𝐨𝐢 + 𝐢′𝐙𝐨𝐫𝐢)/3n2 (1)
In equation (1),n represents the number of industries and i and i’ denote unit vectors of the appropriate size, included as a summation vector. The right-hand side of this equation calculates the average size of transaction zij, where the final term denotes the total number of transactions in the sub-matrices between the brackets. The total number of transactions zij in the three sub-matrices and is equal to their total number of cells. Please note that the term n2 assumes the included matrices to be of an nxn dimension.
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sales per industry i as a share of the of total output of industry i are given by matrices Brr and Bro. Matrix Brr is constructed by dividing each element zij in matrix Zrr by a corresponding element xi from vector xr, as shown in equation (2).Vector xr is a column vector containing gross production values x for each industry i.
𝑏𝑖𝑗 = 𝑧𝑖𝑗
𝑥𝑖 (2)
Equation (2) is used to calculate elements bij in matrix Brr, which express the value of an intra-regional intermediate sale zij by industry i in terms of industry i‟s value of gross production. Coefficient matrix Bro can also be constructed by using equation (2), dividing each element zij in matrix Zro by a corresponding element xi, drawn from vector xr. In matrix Bro, each element bij denotes the value of an inter-regional intermediate sale, expressed as a share of gross production of selling industry i. In order to be considered a linkage, transactions bij in either of the coefficient matrices B should be larger than the average transaction in matrices Brr and Bro by a factor βr. This condition is summarised in equation (3), and transactions bij that adhere to this condition are referred to as indirect forward linkages.
𝑏𝑖𝑗 > βr(𝐢′𝐁𝐫𝐫𝐢 + 𝐢′𝐁𝐫𝐨𝐢)/2n2 (3)
Essentially, equation (3) shows the importance of a linkage from the selling industry‟s point of view. Furthermore, please note that this equation includes two elements between the brackets rather than three. Including a matrix containing the relative size of intermediate purchases in matrix Zor would not be appropriate, as this equation measures only the relative size of intermediate sales, or indirect forward linkages.
Instead, the relative size of intermediate purchases is assessed separately. To determine which intermediate purchases can be considered a linkage in relative terms, coefficient matrices are also constructed for the purchases of intermediate goods. These coefficient matrices denote the size of an intermediate purchase zij by industry j as a share of the gross production of industry j, and are included in matrices Arr and Aor. Matrix Arr is constructed by dividing each element zij in matrix Zrr by a corresponding element xj from vector xr’, as shown in equation (4). Vector xr’ is row vector containing gross production values x for each industry j.
𝑎𝑖𝑗 = 𝑧𝑖𝑗
𝑥𝑗 (4)
Equation (4) is used to calculate elements aij in matrix Arr, which express the value of an intra-regional intermediate purchase zij by industry j in terms of industry j‟s value of gross production. Coefficient matrix Aor can also be constructed using equation (4), dividing each element zij in matrix Zor by a corresponding element xj from vector xr’. In matrix Aor, each element aij denotes the value of an inter-regional intermediate purchase, expressed as a share of gross production of purchasing industry j. In order to be considered a linkage, transactions
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matrices Arr and Aor by a factor βc. This condition is summarised in equation (5), and transactions aij that adhere to this condition are referred to as indirect backward linkages. Essentially, equation (5) shows the importance of a linkage from the purchasing industry‟s point of view.
𝑎𝑖𝑗 > βc(𝐢′𝐀𝐫𝐫𝐢 + 𝐢′𝐀𝐨𝐫𝐢)/2n2 (5)
Now that the threshold equations (1), (3) and (5) are determined, they can be used to assess each transaction zij in matrices Zrr, Zro and Zor in terms of its absolute size, relative size as intermediate sale and relative size as an intermediate purchase. The identified direct and indirect linkages are used to determine the structure of a region‟s cluster. The general composition of a cluster will be formed by all direct linkages, the transactions adhering to equation (1). These linkages between industries form the „channels‟ through which intermediate goods flow. A cluster can be further specified by determining linkages that form the core or cores within the clusters. Linkages that form the core of a cluster are transactions that are considered large in absolute terms (i.e. transactions that comply with equation 1) as well as in terms of its relative size (i.e. transactions that that comply with either equation 3 or equation 5). Recall from equations (2) and (4) that the relative size of a transaction zij is given as coefficient bij or coefficient aij in matrices Brr, Bro, Arr and Aor. Cluster cores can therefore be identified by verifying whether a coefficient bij or aij corresponding to direct linkage zij is considered an indirect forward linkage or indirect backward linkage. More specifically, if a coefficient bij in matrix Brr or Bro is considered an indirect forward linkage, and its corresponding transaction zij matrix Zrr or Zro is considered a direct linkage, transaction zij is considered to be part of the core of a cluster. Similarly, if a coefficient aij in matrix Arr or Aor is considered an indirect backward linkage, and its corresponding transaction zij in matrix Zrr or Zor is considered a direct linkage, transaction zij is considered to be part of the core of a cluster.
Comparing these three sets of matrices is complex, as each 14x14 matrix Zrr, Zro, Zor, Brr, Bro, Arr and Aor contains 196 transactions. For this reasons, seven new matrices are constructed, each identical to one of the matrices Zrr, Zro, Zor, Brr, Bro, Arr and Aor, but containing only direct or indirect linkages. Such matrices can be created by setting each transaction zij, bij and aij that does not comply with condition (1), (3) or (5) to zero. This process effectively eliminates all transactions that cannot be considered a linkage by setting them to zero. For matrices Zrr, Zro and Zor, this yields three corresponding 14x14 matrices Rrr, Rro and Ror, each containing only the transactions classified as a direct linkage and zeroes otherwise. For matrices Brr and Bro, two corresponding 14x14 matrices Srr and Sro are created, containing all coefficients considered an indirect forward linkage and zeroes otherwise. Finally, for matrices Arr and Aro two corresponding 14x14 matrices Trr and Tro are created, containing all coefficients considered an indirect backward linkage and zeroes otherwise.
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in the appendix. Transactions rij in matrices Rrr, Rro, Ror are given in millions of euro‟s (current prices). The region and year are chosen randomly, and only serve as an illustration of what the matrices containing the identified linkages look like.
The sets of linkages tables will form the basis of the cluster analysis in section 5.1. By displaying the data in the tables in various ways, conclusions can be drawn regarding the development of clusters in terms of size and composition. For instance, by taking the sum of the value of all absolute transactions in matrices Rrr, Rro or Ror corresponding to a region r, the size of this region‟s cluster can be estimated. Alternatively, linkages between industries can be displayed graphically in order to visualise the composition of a cluster. An example of this graphic depiction is given in figure 10, and shows linkages as arrows between industries. In this figure, dashed arrows are used to denote transactions that are considered a direct linkage only. Thick arrows are used to denote transactions that are considered both a direct and indirect linkage, or the core of the cluster.
4.1 Constructing sub-matrices and gross output vectors
The methodology explained in section 3.1 requires a selection of matrices and vectors from IOTs. More specifically, the methodology requires specific sections of the Z matrix and x, and x’ vectors. This section will explain which elements are extracted from the complete matrix Z and vectors x and x’ to arrive at matrices Zrr, Zor and Zro and vectors xr and xr’ used in section 3.1.
The IOTs from which the required elements are extracted, are provided by Thissen et al. (in preparation), who have constructed a set of IOTs containing input-output data for a set of 40 countries, denominated in millions of euro‟s (current prices). The IOTs include an aggregate „rest of the world‟ measure for all countries not specifically included, and span a time period between 2000 and 2010. The total dataset thus include 11 yearly IOTs with dimensions 3729x4789.These tables include matrices Z with dimensions 3724x3724 and vectors x and x’ of dimensions 3724x1 and 1x3724 respectively. Furthermore, the tables specify 14 different industries, and divide each country into regions on a NUTS-2 level of aggregation. This NUTS-2 specification allows for the allocation transactions between industries to individual regions, offering improved precision over studies based on national-level input-output data. The IOTs follow the structure shown in the stylised example in figure 1. However, because the tables include multiple countries rather than one, the contents of matrices Z, F, W differs slightly from the example in figure 1. The largest difference is the fact that intermediate exports and imports are included in matrix Z rather than final demand matrix F or primary inputs matrix W. Because matrix Z now includes multiple countries, exports of intermediate goods can be assigned a destination (industry j in region o, country c) instead of being aggregated with exports of final goods in matrix F. Similarly, imports of intermediate goods can be traced back to a foreign selling industry and are therefore excluded from primary input in matrix W. A simplified version of the IOTs provided by Thissen et al. (in preparation), containing 4 countries, 8 regions and two industries, is provided in figure 2.
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industry i and j in region r; Inter-regional imports matrix Cor a 3724x14 matrix including imports of intermediate goods by industry j in region r from each industry i outside region r; and inter-regional exports matrix Cro, a 14x3724 matrix including exports of intermediate goods by industry i in region r to each industry j outside region r.
From vectors x and x’, vectors xr and xr’ are drawn. Each vector xr includes gross output values of each industry i in region r. Similarly, each vector xr’ includes gross output values of each industry j in region r. The position of these extracted matrices and vectors for a particular region r in a simplified matrix Z, vector x and vector x’ are depicted in figure 2.
Figure 2: Simplified version of a matrix Z and vectors x and x’ in an IOT with multiple countries, divided into
regions. This example contains 4 countries and 8 regions, and specifies two industries: agriculture (Agri) and manufactures (Man). Shaded cells in matrix Z, from light to dark: intra-regional matrix Zrr, intermediate imports matrix Cor and intermediate exports matrix Cro. The shaded cells in vector x denote vector xr, shaded cells in vector x’ denote vector xr’.
Now that the appropriate matrices and vectors are extracted, several need to be resized. An examination of equation (1) in section 3.1 shows that the method used in this study assumes sub-matrices Z to be of a square (nxn) dimension. The assumption of square
dimensions of matrices Zrr, Zor and Zro is the result of the method‟s classification of transactions. In determining direct and indirect linkages, the method only identifies linkages between an industry i and j, regardless of their region of origin apart from in- or outside home region r. This classification of transactions can be illustrated using figure 2: a transaction from the agriculture industry in region o (country 1) to the manufacturing industry region r (country 2), cannot be distinguished from a transaction from the agriculture industry in region
o (country 3) to the manufacturing industry in region r (country 2). According to the method
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exports of industry i in region r to industry j outside region r. To illustrate, a simplified visualisation of the summation of an inter-regional exports matrix Cro into a square matrix Zrr is given in figure 3. The summation process of matrix Cor described above can be written algebraically by using a variant of a basic summation formula that is used to sum all elements in a column xj in a matrix X:
𝑥𝑗 = 𝑛𝑖=1𝑥𝑖𝑗 (10)
Equation (10) describes how each element in a particular column j in matrix X is summed into one element xj. This summation yields a row vector x in which each column xj describes the sum of elements in column j in the original matrix X.
The summation of elements in matrix Cor follows the same principle described in equation (10), with one adjustment. Instead of summing all elements cij in column j, elements are summed with an interval of 14. The interval of 14 is included such that each element in the transformed 14x14 includes only the transactions between industry i and j. Including the summation with an interval of 14 gives the following expression:
𝑧𝑖𝑗 = 𝑚𝑛=0𝑐 14𝑛+𝑖 𝑗 (11)
Where c(14n+i) j corresponds to each element cij in an original 3724x14 matrix Cor that is summed into element zij in a 14x14 matrix Zor. The upper limit of the summation m depends on the number of rows in matrix Cor, and accounts for the number of times a particular industry i is included in a matrix Cor. Variable m is calculated by dividing the number of rows in matrix Cor by 14, and subtracting 1. This yields an m value of 265 (3724 / 14 – 1). The subtraction of one is included to account for the fact that the summation starts at zero rather than one. With an upper limit of 265, the right-hand side of equation (11) thus sums all 266 inter-regional purchases by industry j in home region r from a particular industry i in each non-home region o. Due to the included interval, each summation in equation (11) includes only 1/14th of the total number of elements, yielding a matrix with 14 rows compared to the one-row vector x from equation (10).
The summation of matrix Cro depicted in equation (12) is similar to equation (11). However, this equation concerns a summation of elements cij in row i instead of column j.
𝑧𝑖𝑗 = 𝑚𝑛=0𝑐𝑖 (14𝑛+𝑗 ) (12)
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r to a particular industry j in each non-home region o. Due to the included interval, equation
(12) yields a matrix with 14 columns.
In sum, this section showed that matrix Zrr and vectors xr and xr’ can be extracted directly from matrix Z and vectors x and x’. Matrices Zor and Zro are created in two steps, extracting matrices Cor and Cro and resizing them to 14x14 matrices Zor and Zro. To construct the complete dataset required for the methodology in 3.1, the steps described above are repeated for each of Italy‟s 21 regions, and each of the eleven years in the 2000-2010 database. This yields a total of 231 (21 x 11) sets of matrices Zrr,Zor and Zro, as well as 231 pairs of vectors xr and xr’.
Figure 3: Visualisation of the transformation of a matrix Cro (top table) into a square matrix Zro (bottom table) through the summation of its columns. Industry j in each region o is denoted by the same shade of grey, which means that all columns with the same shade are considered as one transaction and can be summed. The matrix
Cro depicted above is equal to the matrix Cro depicted in the simplified matrix Z in figure 2.
4.2 Choosing threshold coefficients α and β
The choice of threshold coefficients α and β in equations (1), (3) and (5) is somewhat arbitrary, but can be based on some reasoning depending on the structure of the data. Coefficient values should be set as low as possible to allow for the inclusion of a sufficient amount of linkages, as long as the information can be summarised and plotted visually (Oosterhaven et al., 2001). To determine an appropriate value for α and β, equations (1-5) were applied to the set of matrices and vectors constructed in section 4.1, for different levels of α and β. For each coefficient level, the number of identified direct and indirect linkages in matrices Rrr, Rro, Ror, Srr, Sro, Trr and Tro is counted for each region r, and the results summarised in a table. The results of this counting exercise for the direct linkages (the total number of direct linkages found in matrix Rrr, Rro and Ror for each region r) in the year 2010 are shown in table 1. Table 1 thus shows the number of direct linkages for each of the 21 Italian regions, for the year 2010. The number of cells given the top left of the table shows the total number of possible transactions for region r, and is equal to the total number of cells in matrices Zrr, Zro and Zor (14 x 14 x 3). The number of direct linkages found in each region, for each level of α, are depicted in the columns of the table.
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threshold value increases to (α = 5). The number of linkages in regions 10-21 on the other hand remains largely stable. Combined, the results in table 1 depict a divide between Italy‟s most northern regions (1-9) and the rest of the country (10-21) in terms of linkages. Furthermore, the larger number of linkages at low threshold levels in regions 1-9 suggests a more even distribution of transaction sizes in these regions. This can best be illustrated by looking at the low number of linkages in regions 10-21. The low number of linkages at a threshold value of (α = 1) suggests that a small number of transactions is responsible for a large share of the total value of intermediate transactions. Because the linkages depicted in table 1 do not specify industries or transaction values, the difference between the northern and southern regions should be discussed further in the results section 5.1.
Considering the wide scope of this study – the identification of cluster structures across multiple regions, over a period of 11 years – choosing a relatively high coefficient value for α and β is desirable to retain oversight. Although interesting, the inclusion of all linkages at a threshold value of (α =1) would make a clear visualisation and interpretation of the results highly complicated (not to mention highly labour-intensive). For this reason, a threshold value of (α = 7.5) is used for the remainder of this study, yielding an average of close to 10 linkages per region. Through a similar process, the coefficient values for the indirect forward and backward linkages are set at 6 times the average value (βr= 6 or βc= 6).
Table 1: Number of direct linkages per region on a NUTS-2 level, under varying values of α. Based on the 2010
IOT. The number of cells in the top left of the table denotes the total amount of transactions per region.
4.3 Sub-matrices and gross output vectors for NUTS-1 regions
As mentioned in section 4.1, the IOTs provided by Thissen et al. (in preparation) are constructed based on a NUTS-2 level of aggregation. Since NUTS-2 regions are relatively small geographically, regional clusters found on this level of aggregation can be allocated to a geographical location with a fairly high degree of precision. Another benefit of this NUTS-2 level of aggregation is that is particularly suitable to the case of Italy. Recall from section 2.3 that the structure of Italy‟s clusters is generally defined by a small spatial scale and a strong network of intra-regional linkages. The level of aggregation offered in the IOTs from Thissen et al. (in preparation) thus allows for an analysis of Italy‟s regional clusters on an appropriate level.
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and expanding beyond their local borders. In order to assess whether this trend has resulted in the emergence of spatially larger clusters with a stronger international orientation, this study also includes an analysis of Italy‟s clusters on a NUTS-1 and country level. To assess the NUTS-1 regions under the same conditions as the NUTS-2 regions, the α and β threshold coefficients determined in section 4.2 are kept constant across analyses. In order to properly conduct these analyses, matrices Zrr, Zor and Zro and vectors xr and xr’ are on a NUTS-1 and country level. The remainder of this section will be devoted to explaining the extraction of the required matrices and vectors for a NUTS-1 level cluster analysis. The extraction of the appropriate matrices and vectors for a country level cluster analysis are explained in section 4.4.
Matrices Zrr, Zro and Zor and vectors xr and xr’ used for a NUTS-1 level cluster analysis are also based on the IOTs introduced in section 4.1. However, because these IOTs are specified on a NUTS-2 level, matrices Zrr, Zro and Zor and vectors xr and xr’ are created by merging multiple NUTS-2 regions. The first step in creating these matrices is determining which NUTS-2 regions form one NUTS-1 region. The appropriate aggregation of NUTS-2 regions into NUTS-1 regions is based on the NUTS-classifications of Italian regions depicted in table 4 in the appendix. After it is determined which regions r from the IOTs form one NUTS-1 region, the correct elements can be extracted from matrix Z and vectors x.
First, the extraction of elements from matrix Z yields the following sub-matrices: intra-regional sales matrix Crr, an nxn matrix including all intra-regional transactions between
industry i and j within NUTS-1 region r; inter-regional imports matrix Cor, an 3724xn matrix
including imports of intermediate goods by industry j in NUTS-1 region r from each industry
i outside NUTS-1 region r; and inter-regional exports matrix Cro, an nx3724 matrix including
exports of intermediate goods by industry i in NUTS-1 region r to each industry j outside NUTS-1 region r.
The dimensions of these extracted matrices differ from those in section 4.1, since each NUTS-1 region r is now composed of multiple regions r. Italy‟s Nord-Ovest region for instance, is composed of four NUTS-2 regions (see table 4 in the appendix), giving its matrix Crr dimensions 56x56 instead of 14x14. By extension, its matrices Cro and Cor now have dimensions 56x3724 and 3724x70 respectively. The Isole region on the other hand, contains only two NUTS-2 regions, yielding matrices Crr, Cro and Cor matrices with dimensions
28x28, 28x3710 and 3710x28.
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Figure 4: Schematic depiction of matrix Z and vectors x and x’. The large shaded square in the centre of each
figure represents Italy within matrix Z, the surrounding white squares represent the remaining countries in the matrix. Numbers 1-21 represent each Italian NUTS-2 region. The horizontal grey bars represent matrix Cro for region 1 (left) and for region 1-4, which together make up the Nord-Ovest NUTS-1 region (right). The vertical grey bar represents matrix Cor for region 1 (left) and regions 1-4 (right). The small darkly shaded square in the centre denotes matrix Crr for region 1 (left) and regions 1-4 (right). The grey areas in the bars to the right and bottom of each figure represent corresponding vectors dr and dr’ respectively. For simplicity, the figures do not specify industries.
Now that the required elements are extracted in the form of matrices Crr, Cro and Cor and vectors dr and dr’, the elements can be summed to arrive at a set of matrices with dimensions 14x14 and vectors with dimensions 14x1 and 1x14. As mentioned earlier, the extracted matrices and vectors corresponding to a NUTS-1 region r contain elements from multiple regions r. The aggregation of multiple regions into one NUTS-1 region means that the aggregated NUTS-1 region r contains multiple identical industries i or j, from each of the included regions r. To illustrate: in a matrix Crr corresponding to the Nord-Ovest region, a particular industry (say, agriculture) is included four times, as each agricultural industry in a NUTS-2 region r is included separately. At this point it is important to emphasize that an aggregated NUTS-1 region should be approached as if it was one single region. So, returning to the example: the four agricultural industries in matrix Crr corresponding to the Nord-Ovest region should be merged into one agricultural industry representing the entire Nord-Ovest region. In other words, the extraction of the appropriate elements from matrix Z and vector x and x’ does not only entail merging multiple regions, but also their industries.
Because each aggregated NUTS-1 region is interpreted as a single region with fourteen different industries, the extracted matrices Crr, Cro and Cor and vectors dr and dr’ should be transformed into matrices of dimensions 14x14 and vectors of dimensions 14x1 and
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summed along both the rows and the columns. Second, extracted vectors dr and dr’ do not have dimensions 14x1 and 1x14 in this case, which means that they also require a summation.
Matrices Crr, Cro and Cor are summed by applying both equation (13) and (14) to each matrix individually. First, equation (13) describes how elements cij in a column j in matrix Crr, Cro or Cor are summed into element xij in column j of a matrix X. In equation (14), elements xij in each row i in matrix X are summed into element zij to arrive at a 14x14 matrix Zrr, Zro or Zor.
𝑥𝑖𝑗 = 𝑚𝑛=0𝑐 14𝑛+𝑖 𝑗 (13) 𝑧𝑖𝑗 = 𝑚𝑛=0𝑥𝑖 14𝑛+𝑗 (14)
The upper limit of summation m in equations (13) and (14) is included with the same purpose as in equations (11) and (12), and depends on either the number of rows or columns in matrix Crr, Cro or Cor that is being transformed. Because the dimensions of matrices Crr, Cro and Cor differ across NUTS-1 regions r, the value of m also differs across regions. A table of appropriate m values for matrices Crr, Cro and Cor for each NUTS-1 region can be found in table 3 in the appendix. To illustrate the summation process, a visualisation of a summation process is given in figure 5. This figure shows how elements cij from a matrix Crr are summed into elements zij in a 14x14 matrix Zrr, using the Nord-Ovest region as an example.
Applying equation (13) and (14) to the extracted matrices Crr, Cro or Cor is the last step in the creation of matrices Zrr, Zro and Zor. Applying these equations to the set of extracted matrices for each of Italy‟s five NUTS-1 regions, for each of the eleven years in the IOTs yields 55 (5 x 11) sets of 14x14 matrices Zrr, Zro and Zor. Element zij in matrix Zrr now includes all transactions between a particular industry i and j within NUTS-1 region r. Element zij in matrix Zor now describes the sum of intermediate goods imports from industry j outside NUTS-1 region r, to industry i in NUTS-1 region r. Similarly, element zij in matrix Zro now describes the sum of intermediate goods exports to industry joutsideNUTS-1region r, from industry i in NUTS-1 region r.
The final step in constructing the matrices and vectors that can be used to conduct a NUTS-1 level analysis, is resizing the extracted vectors dr and dr’ to dimensions 14x1 and
1x14 respectively. The summation of the vectors is given in equation (14) and (15).
𝑥𝑖 = 𝑚𝑛=0𝑑 14𝑛+𝑖 (15) 𝑥𝑗 = 𝑚𝑛=0𝑑 14𝑛+𝑗 (16)
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each of the eleven years in the IOTs yields 55 (5 x 11) sets of 14x1and 1x14 vectors xr or xr’. Element xi in vector xr now includes the gross output value of an industry i in NUTS-1 region
r. Similarly, each element xj in vector xr’ now includes the gross output value of an industry j in NUTS-1 region r.
Figure 5: Visualisation of the two-step summation of an extracted matrix Crr described in equations (13) and (14). The left table shows the extracted aggregated Crr matrix for the Nord-Ovest (NO) region containing NUTS-2 regions 1-4, denoted by numbers 1-4 on the top and left of the table. The numbers 1-14 in both tables are included to denote the 14 different industries specified by Thissen et al. (in preparation). All elements cij
from the aggregate matrix on the left that are summed into one element zij in the transformed 14x14 matrix Zrr
on the right are indicated by the same shade of grey.
4.4 Sub-matrices and gross output vectors on a country level
By now it should be clear that that the method used to identify linkages only distinguishes between two types of transactions: intra- and inter-regional transactions. By extension, this entails that the method also does not distinguish between inter-regional and international transactions. Analyses on a NUTS-2 and NUTS-1 level therefore do not allow for an assessment of Italy‟s regional clusters in an international context, because the international linkages cannot be isolated from the inter-regional transactions. This issue can be solved partially by including a country level analysis of direct and indirect linkages. Although a country level of aggregation does not allow for a comparison of clusters across regions, it can provide some insights in the embeddedness of the Italian input-output system in an international input-output system. On a national level of aggregation, all transactions between regions within the country are considered intra-regional, since the country is now considered region r. Transactions between regions are thus all included in sub-matrix Zrr, which automatically means that intermediate exports and imports matrices Zro and Zor include only international transactions. In sum, the inclusion of a country level analysis of Italian clusters does not assist in answering the research question directly, but it can be used to provide the identified regional clusters with some context regarding the international orientation of the Italian clusters in general.
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This aggregation yields the following sets of matrices: Crr matrix of dimensions
294x294; Cor matrix of dimensions 3710x294; and Cro of dimensions 294x3710 The corresponding dr and dr’ vectors have dimensions 294x1 and 1x294 respectively. A schematic extraction of these matrices and vectors is included in figure 6. The sub-matrices and vectors extracted on a country level are resized following the process explained in section 4.3, applying equations (13) and (14) to each matrix Crr, Cor and Cro, and equations (15) and (16) to the dr and dr’ vectors respectively. The appropriate m-values for equations (13-16) can be found in table 3 in the appendix. The extraction and resizing of the appropriate elements from matrix Z and vectors x and x’ yields a set of matrices Zrr, Zor and Zro and vectors xr and xr’ corresponding to Italy, for each of the eleven years included in the dataset, summing up to a total of eleven sets of matrices and eleven sets of vectors.
Sections 4.1, 4.3 and 4.4 described how the appropriate matrices and vectors should be drawn from the dataset to conduct an analysis of linkages on three levels of aggregation (NUTS-2, NUTS-1, and country level). In the following section, section 5.1, the results of applying the method explained in section 3.1 on each of these three levels of aggregation are visualised and analysed.
Figure 6: Schematic depiction of matrix Z and vectors x and x’. The large darkly shaded square in the centre
represents the country level matrix Crr for Italy. The surrounding squares represent the remaining countries in the matrix. Numbers 1-21 represent each of Italian region. The horizontal grey bar represents country level matrix Cro, the vertical grey bar represents country level matrix Cor. The grey areas in the bars to the right and bottom represent corresponding vectors dr and dr’ respectively. For simplicity, the figure does not specify industries.
5.1 Visualising and interpreting linkages
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development regarding size. Also, specific elements from the complete set of results can be highlighted to support findings regarding cluster compositions.3
5.1.1 Results – NUTS-2 level
The first step in the analysis is providing a clear overview of the size of clusters and development in cluster size for each region. The results of this overview are given in table 2. The first three columns in this table relate to the relative size of clusters, measured as the total value of all direct linkages per region in a particular year, divided by the region‟s gross production in that year. Column one gives the development of the relative cluster size over the complete period of observation, measured as in index value with base year 2000. Column two gives the average size of each cluster in relative terms, also measured over the entire observation period (2000-2010). Column three gives the standard deviation of the average relative cluster size given in column two. The last two columns in table 2 provide general statistics for each region, to give an idea of the size and economic significance of regions. Where column four includes a region‟s total population, measured at the 1st of January, 2001. Column five illustrates the productivity differences across Italian regions using GDP per capita values calculated over 2000.4 Finally, to give an indication of each region‟s geographical location, all regions located in the northern half of Italy are shaded light-grey. All regions located in Italy‟s southern half are shaded dark-grey.
The columns in table 2 contain several interesting results. The index values in column one show that clusters sizes have increased across all southern regions. In the northern regions on the other hand, indices indicate a trend of decreasing cluster sizes in most regions, with the Veneto and Toscana regions even losing roughly a quarter of their relative cluster size over the period 2000-2010. Furthermore, the average relative cluster sizes in column two show that the direct linkages within the clusters make up between 10 and 30 percent of the value of all transactions in the region on average. Column three includes the standard deviations of the average cluster sizes over the period 2000-2010. These standard deviations show the size distribution of clusters to be fairly stable across regions. Finally, the results in columns four and five provide some details regarding the characteristics of each region. First, column four shows that region sizes vary strongly in terms of population, even though all regions are classified as NUTS-2. Some regions have populations ranging in the millions, while other regions are scarcely larger than a medium-sized city. Second, the productivity data in column five show a clear distinction between the northern and southern regions. Without exception, the northern regions show productivity levels exceeding 40,000. In the south of Italy on the other hand, all productivity levels lie below this level, some even nearing values close to 20,000. This productivity division accurately represents the divide between Italy‟s affluent north and its underdeveloped south mentioned by Gonzáles (2010).
3 The complete set of tables containing the original output for each of the 21 NUTS-2 regions over the entire sample period is available upon request.
4
GDP data were calculated using 2000 gross output values from the IOTs in the dataset. Data were constructed by summing the values in each region‟s gross output vector xr corresponding to 2000. Regional population data
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Region
Δ 2000-2010 (index)
Avg. rel. cluster size Std. Dev. Pop. (1-1-2001) GDP/cap (2000) in euro’s Piemonte 93 0.22 0.017 4,219,421 54,462 Valle d‟Aosta 89 0.12 0.009 119,273 47,539 Liguria 109 0.20 0.022 1,578,998 45,223 Lombardia 177 0.10 0.024 9,004,084 50,611 Bolzano 88 0.24 0.024 461,101 60,118 Trento 94 0.27 0.019 474,310 51,238 Veneto 76 0.12 0.019 4,508,580 48,303 Friuli-Venezia-Giulia 97 0.27 0.025 1,181,238 49,785 Emilia-Romagna 90 0.14 0.011 3,983,566 51,099 Toscana 73 0.14 0.021 3,494,857 44,709 Umbria 105 0.26 0.017 824,187 41,108 Marche 89 0.24 0.021 1,446,785 44,091 Lazio 114 0.11 0.012 5,116,344 43,633 Abruzzo 112 0.21 0.014 1,261,300 34,688 Molise 115 0.24 0.016 321,468 31,820 Campania 146 0.15 0.030 5,708,137 23,569 Puglia 127 0.19 0.030 4,026,054 26,127 Basilicata 112 0.25 0.015 599,404 27,438 Calabria 106 0.19 0.022 2,018,722 25,121 Sicilia 109 0.20 0.011 4,978,068 26,439 Sardegna 133 0.21 0.024 1,634,795 30,642
Table 2: Summary statistics of Italian NUTS-2 regions. The first three columns relate to the relative size of the
clusters, measured as the sum of the value of all direct linkages in a region, divided by the region‟s gross output. Column 1 gives an index value of the change in relative cluster size over the period 2000-2010, with 2000 as base year. Column 2 gives the average relative cluster size over the period 2000-2010, and column 3 gives the standard deviation of the average relative cluster size. Columns 4 and 5 provide general information on each region by displaying their total population and productivity. To give an idea of the geographic location of the regions, regions located in the northern half of Italy are shaded light-grey. Regions in the southern half of Italy are shaded dark-grey.
To look at the distribution of regional cluster sizes more closely, all 21 Italian regions are ranked from large to small according to their relative cluster sizes. The results are shown in figure 7. The distribution of cluster sizes in figure 7 is based on data from a single year: the output of the NUTS-2 level analysis of linkages for the year 2007 and the corresponding regional gross output levels. The year 2007 is selected to exclude any effects of the economic crisis of 2008. According to figure 7, four of the five largest regions in terms of relative cluster size: Trento, Friuli-Venezia-Giulia, Umbria and Marche, are northern. The highest notation of a southern region is Basilicata, at position four. This dominance of northern clusters at the top of the size distribution is in line with the core-periphery structure described by the NEG model, as explained in section 2.1. However, the distribution of the remaining regions in terms of cluster size do not follow the NEG model.
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around one million. In contrast, the largest northern regions, where one would expect a large agglomeration of economic activity, are located mostly at the bottom of the distribution. In fact, the four regions in figure 7 with the smallest relative cluster size are all northern, and have populations ranging from just under 3.5 million to slightly over 9 million. Lombardia, Italy‟s largest region in terms of population, with one of the highest productivity levels, has a relative cluster size comparable to that of Valle d‟Aosta, a region with less than 120,000 inhabitants. In sum, the presence of northern clusters in both the top and bottom of the size distribution, as well as the low notations of some of the north‟s largest clusters display an agglomeration pattern that does not comply with the predictions of the NEG model.
Figure 7: Overview of relative cluster sizes of each Italian region on a NUTS-2 level, based on 2007 IOT data.
Relative regional cluster size is measured as the sum of all direct linkages within a region, divided by the region‟s gross output.
The peculiar size distribution displayed in figure 7 is assessed further through an analysis of the results matrices Rrr, Rro and Ror containing each region‟s direct linkages are consulted. A review of these tables across all regions and periods yielded three general observations. First, the composition of absolute linkages is fairly similar across regions. Although the sizes of the linkages differ across regions, linkages in each region are mostly related to the same set of industries. This set of industries consists of: the other
manufacturing (OM) industry; the real estate, renting and business activities (RRB) industry;
the distribution (DIS) industry; the coke, refined petroleum, nuclear fuel and chemicals etc.
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 Lazio Toscana Veneto Lombardia Aosta Emilia-Romagna Campania Calabria Sardegna Abruzzo Liguria Sicilia Bolzano Puglia Molise Piemonte Marche Basilicata Umbria Friuli-Venezia-Giulia Trento
