*2.2. Regionalization of the Italian Input-Output Table*

Regionalized Input–Output matrices make it possible to perform a linkage analysis that compares the importance of each sector in providing and buying goods and services for the remaining sectors. Unfortunately, the Italian Institute of Statistics (ISTAT) does not provide regionalized Input-Output Tables. As remarked by Hewings and Jensen (1988), nonsurvey methods regionalizing a national Input-Output Table (NIOT) have been developed, with the aim of avoiding the huge costs and considerable release delays associated with the construction of regional tables through direct surveys. Non-survey methodologies were based (i) on Location Quotients (LQs) or (ii) on constrained matrix-balancing approaches. The former methodologies included Simple and Cross-Industry LQs (SLQ and CILQ), along with refinements such as Round (RLQ) formula (Round 1983), Flegg FLQ formula (Flegg et al. 1995; Flegg and Webber 2000), as well as the augmented FLQ (AFLQ) approach (Flegg and Webber 2000). These methods hinged on the assumption that regions and nations employed the same production technology, with the implication that regional input coefficients only differed from their national counterparts for the fact that each region imports goods and services from other regions (Cuello et al. 1992). By contrast, constrained matrix-balancing procedures estimate unknown data from limited initial information and are subject to a set of linear constraints (e.g., Salvati and Zitti 2009). The most popular techniques include RAS and Cross-Entropy (CE) approaches (Schultz 1977) and those based on minimizing squared or absolute differences (Golan et al. 1994). However, such methods are more time-consuming than the LQ-based approach and normally require the solution of a constrained non-linear optimization problem, whereas the LQ-based methods are quick and simple to apply. The present study concentrates on the FLQ method briefly explained in Section 3, since it is one of the best-performing LQ-based approaches (Bonfiglio and Chelli 2008; Flegg and Tohmo 2016).

#### *2.3. Regionalization Methodologies Using Location Quotiens*

In this section, we review the most used location quotient (LQ) methods to estimate a Regional Input-Output Table (RIOT) representative of the 20 Italian regions. We used the most recent NIOT released by the Italian Institute of Statistics (ISTAT) for the year 2016. In Table 2, we show the national and regional IOT for an economic system of *k* sectors in block matrix notation, where:

National Input–Output Table Regional Input–Output Table


⎛ ⎜⎜⎝ **X**r **M**<sup>r</sup> **f** r 0 **x**r 0 (**v**<sup>r</sup> ) 0 0 ⎞ ⎟⎟⎠

(**x**<sup>r</sup> ) 0 0


Moreover, we define A<sup>n</sup> = an ij <sup>=</sup> xn ij xn j , R = rij <sup>=</sup> xr ij xr j , and Mr = mr ij <sup>=</sup> impr ij xr j as the matrices whose entries are the national technical coefficients, the regional input coefficients, and the regional import coefficients, respectively. Assuming that only NIOT (An) and the vector of the regional total sectorial output (x<sup>r</sup> <sup>j</sup> , j = 1, ... , k) are known, the LQ methods estimate the matrix of the regional input coefficients R by adjusting the national technical coefficient in the following way:

$$
\hat{\mathbf{r}}\_{\text{ij}} = \mathbf{a}\_{\text{ij}}^{\text{n}} \mathbf{q}\_{\text{ij}} \tag{5}
$$

where qij represents the degree of modification of the national coefficient. Interregional import coefficients (the entries of M<sup>r</sup> ) are estimated as the difference between the national and the estimated regional input coefficient:

$$\mathbf{m}^{\mathbf{r}}\_{\mathbf{i}\rangle} = \mathbf{a}^{\mathbf{n}}\_{\mathbf{i}\rangle} - \mathbf{\hat{r}}\_{\mathbf{i}\rangle} \tag{6}$$

The first LQ method introduced in the literature (Flegg and Tohmo 2016) was the Simple Location Quotient (SLQ), where the regional input coefficients are estimated as:

$$
\hat{\mathbf{r}}\_{\mathbf{i}\rangle} = \begin{cases}
\mathbf{a}\_{\mathbf{i}\rangle}^{\mathbf{n}} \cdot \text{SL}\mathbf{Q}\_{\mathbf{i}} & \text{if } \text{SL}\mathbf{Q}\_{\mathbf{i}} < 1 \\
\mathbf{a}\_{\mathbf{i}\rangle}^{\mathbf{n}} & \text{if } \text{SL}\mathbf{Q}\_{\mathbf{i}} \ge 1
\end{cases} \tag{7}
$$

and where SLQi is defined as:

$$\text{SLQ}\_{\text{i}} = \frac{\overset{\text{x}^{\text{r}}\_{\text{i}}}{\overset{\text{x}^{\text{r}}\_{\text{i}}}{\text{x}^{\text{n}}}}{\overset{\text{x}^{\text{n}}}{\overset{\text{x}^{\text{n}}}}} \tag{8}$$

and x<sup>r</sup> <sup>i</sup> and xn <sup>i</sup> are the total outputs of the i-th regional and national sector, respectively, where xn = ∑<sup>k</sup> <sup>i</sup>=<sup>1</sup> xn <sup>i</sup> and x<sup>r</sup> <sup>=</sup> <sup>∑</sup><sup>k</sup> <sup>i</sup>=<sup>1</sup> x<sup>r</sup> i .

Several other LQ methods have been proposed in the literature (Miller and Blair 2009). However, earlier studies (Bonfiglio and Chelli 2008; Hermannsson 2016; Morrissey 2016; Jahn 2017) have demonstrated how FLQ provides more accurate results than the other LQ methods and, based on such evidence, this method was chosen to estimate the 20 Italian RIOTs.

The basic idea underlying FLQs is that a region's propensity to import from other domestic regions is inversely and non-linearly related to its relative size (Ciommi et al. 2019). By incorporating explicit adjustments for interregional trade, the method provides more accurate estimates of regional input coefficients. As with other non-survey techniques, the main aim of the FLQ approach is to delineate an optimal frame to estimate input–output

tables that are representative of the regional economic structure (Lamonica et al. 2020). FLQ coefficients can be expressed as follows:

$$\text{FLQ}\_{\text{ij}} = \begin{cases} \text{CILQ}\_{\text{ij}} \lambda & \text{for i} \neq \text{j} \\ \text{SLQ}\_{\text{ij}} \lambda & \text{for i} = \text{j} \end{cases} \tag{9}$$

where λ stands for the relative size of the region and takes the following form:

$$\lambda = \left[ \log\_2 \left( 1 + \frac{\mathbf{x}^r}{\mathbf{x}^n} \right) \right]^\delta \tag{10}$$

and

$$\text{CILQ}\_{\text{ij}} = \frac{\mathbf{x}\_{\text{i}}^{\text{r}} / \mathbf{x}\_{\text{i}}^{\text{n}}}{\mathbf{x}\_{\text{j}}^{\text{r}} / \mathbf{x}\_{\text{j}}^{\text{n}}} = \frac{\text{SLQ}\_{\text{i}}}{\text{SLQ}\_{\text{j}}}$$

based on Flegg et al. (1995). Here, δ (0 ≤ δ < 1) is a sensitivity parameter that controls the degree of convexity in Equation (5). Referring to Flegg et al. (1995) for details, the larger the value of δ, the lower the value of λ, so that greater adjustments of regional imports are made. The implementation of the FLQ formula is carried out in line with other LQ methods:

$$\mathbf{f}\_{\mathrm{ij}} = \begin{cases} \mathbf{a}\_{\mathrm{ij}}^{\mathrm{n}} \mathrm{FLQ}\_{\mathrm{ij}} & \text{if } \mathrm{FLQ}\_{\mathrm{ij}} < 1\\ \mathbf{a}\_{\mathrm{ij}}^{\mathrm{n}} & \text{if } \mathrm{FLQ}\_{\mathrm{ij}} \ge 1 \end{cases} \tag{11}$$

To apply the FLQ, a value for the unknown parameter (δ) has to be chosen. A number of empirical studies (Flegg and Webber 2000; Flegg et al. 2016; Flegg and Tohmo 2016; Jahn et al. 2020) were devoted to find appropriate values of δ. In consideration of their results, a value of δ = 0.3 was considered appropriate in our case.

#### **3. Data and Indicators**

This study relied on the 2016 Italian Input-Output Table (IOT) using a disaggregation nomenclature of 63 sectors, and was retrieved from an official database (ISTAT 2020). The 63 sectors' classification was based on the NACE Rev.2 Statistical classification of economic activities in the European Community (EUROSTAT 2008). Unfortunately, the only available data at the regional level are related with the employment number and the added value of the 29 sectors' disaggregation (NACE Rev. 2). As a consequence, the National Input-Output Table was then reaggregated in 29 sectors that were used as the starting point for regionalization by means of the Flegg Location Quotient (FLQ), as pointed out in Section 2.2, which allowed for a comparative analysis at regional scale.

The regional sectorial employment number was used as a generalization of the national coefficient based on the fact that "in cases where regional output data are not consistently available, or where analysts feel it is appropriate, other measures of regional and national economic activity are often used—including employment (probably the most popular), personal income earned, value added, and so on, by sector" (Miller and Blair 2009, p. 349). Moreover, the practical calculation of Equations (1) and (2) requires the sectorial final demand as input data at the regional level. Unfortunately, these data are unavailable for Italy. To overcome this drawback, we assumed the regional share of the i-th sector as coinciding with the share allocated for the whole country economy. This assumption was derived from the fundamental input–output relationship **v'** i = if, and following the argumentations of Round (1983). Thus, the regional sectoral final demand was estimated as follows:

$$\mathbf{f\_i^t} = \mathbf{v^r} \frac{\mathbf{f\_i^n}}{\sum\_{i=1}^k \mathbf{f\_i^n}} \tag{12}$$

where v<sup>r</sup> = (vr ) *i* is the regional (total) added value.

#### **4. Results**

The pandemic-driven economic recession affected all areas of Italy. However, the drop in GDP has been partly attenuated at the regional level through the measures adopted by the national government and European authorities. The campaign of vaccination, the progressive easing of restrictions aimed at the containement of contagion, and the perseverance in the measures benefitting households and firms helped in sustaining the economic recovery. According to the quarterly indicator of the regional economy (ITER) elaborated by the Bank of Italy, recovery was particularly evident in Northern Italy. Exports have grown in all areas and investments appear higher than those planned. Positive signals were observed on incomes and consuption expenditures. Savings have continued to be addressed, due in large part to liquid financial instruments as deposits (Banca d'Italia 2020). National results in terms of linkage, that we obtained from the empirical analysis, are shown in Table 4. The forward and backward linkages were computed for the 29 industries of the Italian economy. In Table 5, following the taxonomy defined in the methodological Section 2.1, industries were classified in the relevant panel according to the following denominations: Key Sectors, Low Impact, Prime Vendors and Prime Users.

**Table 4.** Forward and backward linkage results for the 29 industries constituting the national economy.


**Table 4.** *Cont.*


**Table 5.** Classification of Italian industries according to their role in the economic interactions.


Each industry was assumed to be part of a network that developed through interindustry interactions. A set of interactions was given by the inflow of commodities, from raw materials to finished products, realized by the industry's intermediate purchases, and used for producing the industry's total output. These interactions, which define the role of each industry in the inter-sectoral interactions in the upstream supply chain, were then given by the backward linkage coefficient quantified in the last column of Table 4. The second set of interactions was the downstream network that involved processing the materials collected during the upstream stage into a finished product and the actual sale of the industry's total output to other industries. The last column of Table 4 displays the capability of each industry in activating the other industries downstream. In order to synthetize the features of each industry in the interaction, we rearranged the results in Table 4 according the linkage value, as shown in Section 2.1. Table 5 shows the resulting industry classifications at the national economy.

From this table, nine industries emerged as Key Sectors, and provided a relevant impulse to the production process in terms of both upstream and downstream interaction. Four industries emerged as Prime Users and Prime Vendors, respectively. Twelve industries actually proved to be Low Impact activities. More information could be attained by adopting the regional viewpoint. Considering a regional perspective, results similar to those obtained for the national economy, shown in Tables 4 and 5, were observed. In this way, a further development got results for each sector according to the role in the economic interaction and according to the regional allocation of the economic activity, since

the regional economic context easily influenced the efficiency of the economic interactions among industries. Here, we regrouped the five macro-regions into three groups: North, Center, and South. The islands were considered within the Southern region.

When compared with national outcomes, some specificities emerge. Table 6 shows the Low Impact sectors for all the Italian regions. As expected, regional outcomes reflected, in most cases, the national ones. Nevertheless, some regional aspects that did not reflect the national trend should be taken into consideration. The industry S1—crop and animal production, hunting and related service activities, and agricultural and hunting—result was classified as a 'Prime Vendor', (Table 7) since it provided its output to other industries, and its activities were allocated prevalently in the eight regions of the south. The textile industry (S5) emerged as a 'Prime User' (Table 8) in Veneto, Tuscany, Umbria, Abruzzo, Campania, and Apulia, and as a 'Prime Vendor' in Marche. The manufacture of rubber, plastic products, and other non-metallic mineral products (S8) was classified as a 'Low Impact' sector in Aosta Valley, Liguria, Sicily, Sardinia, Tuscany, Latium, Calabria, Campania, and Apulia, and as a 'Prime User' in Marche.

The accommodation and food service activities (S18) were classified as 'Prime Vendors' in Marche. In all the other regions of Italy, they were 'Prime Users', with the exception of Latium ('Low Impact'). In both Calabria and Latium, public administration (S24) was classified as a 'Prime User,' while in all other regions it was a low impact one. These findings are coherent with the geography of Latium, whose economic system gravitates to Rome, the Italian capital city, where most of central administrations are located. Public administration is regarded as the main customer for the providers of intermediate inputs; while in Calabria, a similar outcome may have depended on the limited development of the industrial system.

Additional specificities can be found with reference to S4—food, beverage and tobacco industry—emerging as a 'Key Sector' in all Italian regions, with the exception of Liguria, Lombardy, Tuscany, and Latium, where it was regarded as a 'Prime User' (Table 7) and in Marche, where it was classified as a 'Prime Vendor' (Table 8). With reference to the coke and petroleum industry (S7), exceptions emerged for Trentino Alto Adige, Umbria, Campania, Apulia, and Calabria, where this sector was classified as a 'Prime User', as well as for Aosta Valley, Friuli-Venezia-Giulia, and Basilicata, where it was classified as a 'Low Impact' sector.

The manufacture of metals (S9), in the well-known 'Industrial Triangle' encompassing Lombardy, Piedmont and Liguria, emerged as a 'Key Sector' (Table 9) because of the intense links between naval industries, machineries, aerospace, and automobiles concentrated in the area. Exceptions, in reference to the manufacture of computer and electronic devices (S10) with respect to the national classification (Key sector), emerged for Latium, Molise, Campania, Apulia, Basilicata, Calabria, Sicily, and Sardinia, where the sector emerged as a 'Prime User'. Electricity and gas (S11) in seven regions (Veneto, Friuli Venezia Giulia, Emilia Romagna, Tuscany, Marche, Abruzzo, and Campania), emerged as a 'Low Impact' sector. This was different from the national level in the remaining regions, where the sector was classified as a 'Key Sector.' Information and communication (S19) was revealed as a 'Prime Vendor' sector, while in Umbria, Marche, Abruzzo, Molise, Puglia, and Basilicata, it was classified as a 'Low Impact' Sector and as a 'Prime User' in Campania. The only region which included financial and insurance activities within 'Key Sectors' was Latium, while in Marche this sector was included within 'Prime Users'. Peculiarities for administrative and support service activities (S3) were observed in Liguria, Trentino Alto Adige, Veneto, Umbria, Molise, Calabria, and Sicily, where this activity was a 'Prime Vendor' and in Marche, where administrative and support services were a 'Prime User'.




**Table 7.** Prime Vendors in the Italian regions.


*Economies* **2022** , *10*, 300

**Table 8.** Prime Users in the Italian regions.


*Economies* **2022** , *10*, 300

**Table 9.** Key Sectors in the Italian regions.

Our results confirmed the performance of the industries linked to the so-called "Made in Italy" designation, which was intended as high-value, and mostly consisted of artisan and non-routinely products realized exclusively in Italy (Salvati and Zitti 2011). According to recent official statistics, the agri-food system as a whole (including agroindustry, wholesale and retail trade, and catering), produced 522 billion euros, and accounted for 15% of the country's gross domestic product, which thus ensured a prominent position in Europe. Significant growth was also observed in the last decade for the food industry (S4), +12% value added and +8% production index, which doubled the production of manufacturing.

The contribution of agriculture (S1) and the food industry (S4) was also particularly evident in Italy, which displayed an absolute growth in sales (1.3%) by 324 billion euros (CREA 2020). The manufacture of food products, beverages, and tobacco products (S4) emerged as a 'Key Sector' in most Italian regions, except for Liguria, Lombardy, Tuscany, and Latium, which were North-Central regions where it emerged as a Prime User. The role of the Prime User in the economic interactions also applied to this activity at the national level (see Table 4). Although the economic systems proved to be able to regain their average performance at pre-pandemic levels, the agri-food system in Italy seemed to call for supporting policy actions. At the same time, the manufacturing of textiles and wearing apparel (S5) is another industry with a longstanding tradition. Sales of this sector accounted for 9% of total manufacture, with wool and linen as the dominant yarn productions. Artisan products and the export of footwear were recognized to have a prominent role in the sector. While this activity was classified as 'Low Impact' in most regions, the linkage indices at the national level amounted to FL = 0.734 and BL = 0.913. At the regional level, however, six regions emerged as 'Prime Users': Veneto, Tuscany, Umbria, Abruzzo, Campania, and Apulia. In Marche, a well-known shoe production region, the industry arose as a 'Prime Vendor'.

Delocalization processes affected the most recent dynamics of this sector. Usually, delocalization operates by displacing Italian production towards low-cost countries, which possibly reduces (or subtracts) the technological assets developed by the creativity of Italian workers. The liberalization of international commerce, which involved more than half of the textile firms, was an additional factor influencing the recent development of the fiber and yarn industries. The prominent role of Italy in the global rank should be preserved with targeted duties and other supportive measures (Chiaradia 2019). The metal product industry (S9) produced the most investment goods, through which technical innovation can be transmitted to all branches of the economy. In this way, this activity supports the intrinsic competitiveness of the entire manufacturing sector, whose growth depends on the latent capacity of the industry to grow and renew.

#### **5. Discussion**

Since the 1950s, as a consequence of industrialization in emerging economies, the need for a universally recognized method to measure inter-industry linkages began to emerge (Rubino and Vitolla 2018). This method was aimed at assessing the relationship between and within industries by promoting the balanced development of the economic system and by optimizing the industrial structure of the national economy (Lamonica and Chelli 2018). After a short description of the literature related to linkage analysis, we focused on a specific methodology based on the Hypothetical Extraction Method approach, which measures the relative importance of a given sector by taking into account its net importance to the external connections with the other sectors (Lamonica et al. 2020). By means of a 'non-survey' regionalization method, i.e., the Flegg Location Quotient, we regionalized the Input–Output matrix of 2016 and applied linkage analysis at both the national and regional levels to highlight the relevance of the weights in the location of the sectors, based on *a-priori* classes, namely Low Impact sectors, Prime Vendors, Prime Buyers, and Key Sectors (OECD 2021).

This methodology provided an economically robust tool for building the 20 Italian regional input–output tables, in a regional framework where innovation is basically created by larger firms, with limited innovation results of small- and medium-enterprises (SMEs) representing the dominant part of the industrial system (Cainelli et al. 2019). Given the burden of bureaucratic procedures and the relevant delays in the completion of the third industrial revolution (Salvati et al. 2017), the ICT revolution was consolidated in terms of infrastructure (both technical and administrative), even in a context where the Italian industrial sectors revealed a markedly fragmented structure (Ghisellini and Ulgiati 2020). Under such conditions, the most suitable candidate for Industry 4.0 provisions might be medium/large firms, including multi-nationals (ISTAT 2016). Through internally organized competences, this type of firm is prepared to deal with managerial and financial issues, and is equipped to deal with international trade procedures (D'Ingiullo and Evangelista 2020), while small firms need to hire external abilities and, possibly, find further credit sources to cover the commonly long delays in the operation of public administration (Da Roit and Iannuzzi 2022).

This could mean that, as policy beneficiaries, large businesses will eventually crowd out the small firms that constitute the backbone of the Italian economy (Ciffolilli et al. 2019), and have relevant limitations in terms of innovation diffusion (Ciaschini 2022). Such weak performance of SMEs has also been observed in applied works, such as Muscettola (2015) and Bartoloni et al. (2020), in which the patterns of growth of a representative panel of Italian manufacturing firms were investigated. We observed that, although the estimates suggest that small firms grow faster than larger ones, the applied results did not show a significant change in the average size of businesses at the end of the period under investigation (Bugamelli et al. 2018).

The slow pace in the realization of the ICT infrastructures was in turn influenced by austerity policies on public expenditures in the area of technology (Ciffolilli et al. 2019). Since the 1980s, the funds for private and public institutions and universities have not been considered as policy priorities by governments (e.g., Corona 2019). A recent diminution of 19% of public funding for research that took place in the period between 2008 and 2016 may confirm this assumption. However, the decline in public research and university activities has progressively stimulated an improvement in research for R&D (Bigerna 2013). However, due to the weakening of the system of public research, the scientific goals recently attained could be only temporary (Cutrini and Salvati 2021). The observed emigration of younger researchers, due to easier and more rewarding job opportunities (e.g., Recanatesi et al. 2015), as well as higher research funding, is a context where competences are recognized is a key issue at stake in this development dimension (Bertolini and Giovannetti 2006). The persistent weakness of Italian firms in the technological innovation of human capital and corporate governance—and especially the insufficient improvement of the context in which business activity develops—has certainly influenced the low increase in total factor productivity (Cainelli et al. 2019) that has characterized the unfavorable trend in hourly productivity, which definitely determines lazy growth—or even stagnation—in present times.

### **6. Conclusions**

Based on the empirical data shown in this paper and the related discussion, some perplexities emerge on the topics of innovation, which are connected with the features of the Italian economy and social framework. The innovation policy is expected to strengthen regional innovation capabilities to increase regional competitiveness and nurture innovative and dynamic enterprises. Since its inception, the policy design has supported collaborative research and development (R&D), including through innovation clusters, and the promotion of partnerships in important areas such as the smart factory, Industry 4.0, life sciences, and the bio-economy. Yet, strong concentration in manufacturing and sophisticated/specific innovation activities within local core industries is at risk of decline, due to ongoing industrial transitions. Some specific features of the present Italian economy, characterized by the slowness of bureaucratic procedures with respect to other competing economies, as well as the swiftness of the political economic cycle (that weakens the monitoring process of innovative changes and influences the fragmented structure of sectors that are predominantly small- and medium- enterprises (SMEs)) tend to burden the innovation process and leave the entire load of innovation to the private sector. Policy should consider the results of regionalized IO exercises when designing general or disaggregated strategic instruments and measures aimed at fueling economic development through the leverage of industrial interlinkage improvements.

**Author Contributions:** Conceptualization, M.C. and F.M.C.; methodology, G.R.L. and C.C.; validation, C.C., L.S. and G.R.L. formal analysis, C.C.; resources, G.R.L., C.C. and L.S.; data curation, G.R.L. and C.C.; writing—original draft preparation, C.C.; writing—review and editing, C.C. and L.S. supervision, M.C., L.S. and F.M.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are openly available in Istat: https: //www.istat.it/it/archivio/253253, accessed on 13 November 2022.

**Conflicts of Interest:** The authors declare no conflict of interest.

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