Smart Regions in the Italian context. From a theoretical to an empirical framework

The present study aims to examine the role the social and digital infrastructures might 1 have during the building process of the Smart Regions in the Italian context. Within this framework, 2 it is possible to identify some essential research questions, such as why the same regions are 3 growing faster than the other and which type of effects could be generated from the different 4 connectivity between the regions. Since the Smart Region concept is still composed of technical 5 reports, pilot projects and experiences from a limited number of cities on the international stage, 6 this work it is tried to use a new approach, applying either a neuronal model, the Self-Organizing 7 Maps, and the La Fuente (1995) multivariate regression approach, to extrapolate the existence 8 of possible future conditions for the rising of Smart Regions in Italy, studying the evolution 9 of the used database during the period 2005 – 2016. From the analysis what emerged is that 10 the only bridging social capital dimension, empirically speaking, feed the regional innovation 11 growth because the structure of social relationship facilitates interactions across social, political 12 and economic agents; but there are institutional deficits, most pronounced in Italy and other 13 European countries. 14

progress on those issues is understanding the role played by knowledge and its creation 87 process. Helping to understand this process, there is the notion of absorptive capacity.

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In particular, authors have affirmed that the absorptive capacity could be seen as a capacity at the regional level is to estimate regional knowledge production function 100 trying to incorporate factors of absorptive capacity at the regional level.

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In this context, links between knowledge, innovation and economic geography are com- regions. In this context, the Regional Innovation System (RIS hereafter) approach figures 115 out into the discussion about the variables that shape the knowledge generation and 116 innovation capacities of regions. So, why it was necessary to apply a systems perspective 117 at the regional level? Since RIS emphasises the importance of geographical proximity 118 for knowledge transferring and learning, on the one hand, and at the same time, it 119 legitimises the study of the innovation systems from a regional perspective on the other.

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With these characteristics, an investigation at the regional level perspective of innovation 121 system is justified. As could be seen in the previous sub-section, knowledge plays a vital role in 124 explaining the geography of innovation. This sub-section aims to answer the following 125 question: why does this innovation take place in this region and not elsewhere.

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A possible answer derives from the evolutionary way of thinking where the spatial 127 dynamics of knowledge are understood as cumulative, path-dependent and interactive.

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As a result, a primary driving force is the relatedness concept: relatedness between actors 129 could affect the nature and scope of knowledge spillovers, so, the relatedness's degree 130 and nature might differ from region to region. 7 From this perspective, the evolution   It follows that the performance groups, as shown in Figure 3.2 below, tend to be geo-199 graphically concentrated. In particular, as it is possible to see from the above Figure 3.5:

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• The Netherland and the United Kingdom improved the most their performances, 217 more than ten percentage points;

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• Sweden and Luxembourg increased their performances but at a lower rate, 5 % 219 and 7% percentage points respectively;   In particular, as it is possible to stress out from the following   what is it possible to say about the regional innovation level?

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As region are becoming essential engines of economic development, innovation perfor-282 mance deserves particular attention at the regional level 10  areas also more likely to be more innovative for several reasons, like for example: 294 295 10 It is necessary to stress out the the monitoring of the regional innovation performances was severly hindered by a lack of regional innovation data. below 50% of the European Union average.

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As shown in the radar graph below (Figure 3.14), the most innovative regions, on 312 average, perform best on most indicators (where in the graph the line for the Regional

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Modest Innovators is primarily embedded within the line of the Regional Strong Innovators. 314 315 Figure 14. Indicators score by regional performance groups Source: Regional Innovation Scoreboard, 2018 In particular, the line of the Regional Innovation Leadershas shown that they have the where, instead, the Regional Moderate Innovators have the highest average performance 318 level).

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Despite the variation in regional performance, regional performance groups mostly 321 match the similar European Innovation Scoreboard country performance, groups. between 50% and 90% of the European Union average; 331 1.
Regional Modest Innovators are located in countries previously identified as Modest 332 Innovators.

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As a consequence, the regional "poker of excellence" could be identified in some Moderate Following, introducing and using three sub-groups 12 within each performance group, 338 at the regional level, as shown in Figure 3.16 below.

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Figure 16. Regional performance groups Source:Regional Innovation Scoreboard, 2018 From the previous figure, it is possible to identify two key evidence: It is necessary to stress out, even if here it is not reported, that there are the most divergence in regional innovation systems' performance of with countries and capital regions (including the largest metropolitan capital areas) tending to perform better than other regions in the same countries. As it is possible to see from the previous Table 3.3, regional performance differences 347 are high within the Italian context, with the best performing region, Friuli -Venezia 348 Giulia, performing 70% higher than the lowest performing region, Sicilia. Comparing 349 the North and the South of Italy, it is possible to affirm that the innovation performance 350 is higher in more northern regions compared to the southern ones: for 12 regions, 351 performance has improved, in particular for Calabria (+7.7%) and Toscana (+6,6%) and 8 352 of them, performance has declined.

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In conclusion of this section, it is possible to explain the performance's changing over 354 time and making a comparison with the Regional Competitiveness Index. Regarding 355 the first aspect, the performance of the regional innovation systems changes over time.

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In particular, it is possible to notice the presence of divergence process in the regional 357 performance with increasing performance differences between regions: the spread in the 358 regional innovation performance, measured by the sigma-convergence , has increased  In this framework, neurons become "selectively tuned" to various input patterns ( stimuli) or classes of input patterns during the course of the competitive learning stage. As a consequence, the location of the neurons become ordered and a meaningful "coordinate system" for the "input feature" is created on the lattice. The SOM algorithm distinguishes two stages, the competitive and the cooperative ones. In the first stage, the best-matching neurons are selected, for example, the "winner", as happens in the Kohonen Network appraoch; and in the second stage, the weights of the winner are adapted as well as those of its immediate lattice 14 neighbours. Competitive stage: for each input, it is selected the neuron with the smallest Euclidean distance, called the "winner", according the equation 3.1 : By the minimum Euclidean distance role, it is obtained a Voronoi tessellation of the input As it is possible to see from the previous figure, to each neuron correspond a region in the input space in which the boundaries are perpendicular bisector planes of lines of joining pairs of weight vectors 15 . Cooperative stage: In this stage is crucial the formation of the topographically-ordered maps in which the neuron weights are not modified independently of each other. During the learning process, not only the weight -vector of the winning neuron is updated but also those of the lattice neighbours. This is achieved with the neighbourhood function, centred at the winning neuron and decrease s with the lattice distance of the winning neuron; and the weight update rule in incremental mode 16 is: where Λ is the neighbourhood function. This function, being mostly Gaussian, the 396 previous equation 3.2 could be rewritten in the following way, if we suppose that the 397 neighborhood function follows a Gaussian distribution: An example of the effect of the neighbourhood function could be seen in Figure 3.19 400 below.  if found for all neurons, it is used for scaling these distances between 0 and 1; then the 423 lattice becomes a "grayscale" image. This lattice is called the U-Matrix.
where B is the total factor productivity, K is the firm's stock of capital, L is the second stage production function can be written as: Where c + y + τ > 1, c > 0, y > 0 and τ > 0. Putting 3.4 in 3.5, allows to obtain the 441 reduced form regional production function capturing specifically the impact of the on 442 the level digital and social capital infrastructures of aggregate regional output: Like in the traditional neoclassical model, it is assumed that under perfect competi-

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In equilibrium, the stock of capital in the region i is a function of the national capital 456 stock and the regional endowments of immobile factors: The reduced form per-worker regional production function (3.5) allows to identify 458 the relationship between the level of regional income per worker and the two types of 459 policy tools subject of analysis.

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Starting from the first step of the analysis, the following Tables; Table 3.5, Table 3.6 557 and  More profoundly, starting from the Table 3.6 above, it is possible to observe that the   In the last table, Table 3.7 below, it is possible to stress out the existence of cyclical 597 trends for two out of three variables used for the analysis: from -13,6% of Sicilia to 0,5% 598 of Trentino Alto Adige in GDP per capitaand from -0,5% of Sicilia to 5,3% of Trentino Alto

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Adige with regard to Employment rate. intensity, specialised in low-medium with technology products.

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In particular, this phenomenon could be explained analysing, more deeply, four main   646 23 In this context, statistical dissimilarity is translated into space distance and vice-versa. This feature is obtained due to the learning nature of the algorithm, as it was explained in the Section 2 of this chapter. Also, it is possible because the dataset has been mapped onto the surface of the SOM by adding each neurons up to color gradient. This map helps to define the agglomeration of the Italian regions. In this case, the color of the cells on the map represents the intra-cluster homogeneity degree: the cold colors represent a lack of homogeneity while the warm colors reveal the higher inter-cluster homogeneity degree.  The third correspondence is between GDP per capita and Employment rate proxies.For There are, also, severe disparities between Northern and Southern Italian regions regard-698 ing Regional Innovation Systems activities: the R & D Expenditure on regional GDP is 699 1,4% in the North and 0,9% in the South.

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It follows that regional imbalance in innovation has severely increased with two third 701 of innovation firs and three-quarters of instead, under the social capital effect point of view, it is possible to stress out that the bridging social capital dimension could be a crucial factor for the regional diversification because they act as s bridge between disconnected activities and as well as to enable the creation of new combinations of different standards of knowledge and capabilities: all of these dynamics boost the regional diversification, increasing the probability of developing new specialization in the Italian context, but also, in Europe, through the acquisition of new industrial specialization 24 . What about the other social capital dimension? Regarding the bounding social capital dimension, it could be potentially detrimental for the ability of regions to adapt and introduce new products: strongly embedded in the local economy, local activities might have a harder time to make crossover mobilisation and the combination of different skills and head necessary efforts to diversify. As it is possible to see, both positive and negative effects, the two sides of informal institutions, enable regions to allow to stay less closed to their existing activities when they diversify into new industries. Following the analysis with the third step through the multivariate regression model, the theoretical model between social capital and digital infrastructures and the level of income in the region, introduced in the Methodology section and derived from the regional income inequality model, could be tested empirically using the Italian regional panel data from 2006 to 2013 25 . To obtain the estimating equation, equation 3.8 is transformed by adding time subscripts and the error term. This allows empirical equation 3.9 to be obtained, i.e. a logarithmic relationship between income per worker and factor endowments in the 's region at time , including digital and social capital infrastructures. This relationship becomes: where ϕ t is a factor common to all regions that depends on the variables not included

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Data on employment in region lit concern all people who perform work that yields

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This new type of territorial capital could be fundamental for the individual de-765 velopment strategies which aim is to attract new activities and take the most from its 766 regional/territorial assets.