1 Introduction

The input–output model proposed by Leontief (1951) is possibly the first approximation to network theory in firms’ economy. This model allows one to analyze the interdependence of industries, considering how the production of one industry is demanded by others as inputs. Based on this work, Hirschman (1958), Rasmussen (1958) and Chenery and Watanabe (1958) extend the IO analysis by incorporating the forward–backward linkages of a production network. Since then, a large number of studies have applied input–output models. A deep literature review about them is provided by Bon (2018).

From these contributions, the analysis of Input–output networks has been expanded gradually incorporating its topological characteristics with the support of the Social Network Analysis (SNA). This field integrates quantitative techniques from the graph theory, which was applied for the first time by Campbell (1975) and later used to explore social structures and the role of agents and their relationships (Fu et al. 2017; Scott 2017; Aroche Reyes 2019; Galety et al. 2022). Here, we can remark upon one of the biggest topics: Centrality.

Centrality is one of the main features analyzed in Input–output networks.Footnote 1 The relevance of the role played by sectors in the input–output linkages has been used to quantify their resilience in the study of diverse economic issues. Technological progress, financial development, productivity dynamics, and foreign trade are some examples of economic phenomena that have been empirically analyzed using network theory. For instance, Shih and Chang (2009) and Huang et al. (2011) investigate the structure of international technology diffusion and the innovative capacity by measuring its centralities. Andrieş et al. (2022) and Borochin and Rush (2022) estimate the degree of interconnectedness and quantify the linkages between global financial systems and other institutions. Blöchl et al. (2011), Xu and Liang (2019) and Costa et al. (2022) rank sectors’ centrality within trade network in order to understand the structure of world economies. de Santana Ribeiro et al. (2022) analyze the productive interdependence using I-O tables at the regional level and obtained that the interconnectedness across regions allows their recovery in the case of a shock.

A sector’s centrality has gained importance in the study of intersectoral relationships, but also in the field of shock’s diffusion. Acemoglu et al. (2012) and Carvalho (2014) argue that productivity shocks can spread in the business system and generate macroeconomic fluctuations. On the one hand, commercial relationships propagate shocks from one sector to its neighbors (i.e. first-order connections) and extend these effects to other interrelated sectors (i.e. higher-order connections) in the production network throughout high central industries. On the other hand, if the role of sectors as input suppliers is highly heterogeneous such that the power law holds, shocks have a large effect on macroeconomic fluctuations. According to the authors, both characteristics enable shocks to diffuse from buyer to buyer in a network, generating the so called “downstream” cascading effects (i.e. shocks propagate from buyer to buyer). Several investigations about diffusion in input–output networks share this theoretical approach, remarking the importance of sectors’ centrality and its power law distribution (e.g. Stella 2015; Bigio and La’O 2016; Carvalho et al. 2016; Atalay 2017; Grassi 2017; Baqaee 2018).

The main objective of this paper is to identify the most influential industries in Ecuador's Input–Output network in 2019, using four weighted centrality indices from Social Network Analysis: Degree Centrality, Closeness Centrality, Betweenness Centrality, and Alpha Centrality. To do so, we analyze the Ecuadorian Input–output network at the sectoral level in 2019, through the use of these four centrality indices for weighted graphs. The identification of the most influential sectors through their centrality in an economy is very relevant for policy considerations since it indicates their importance in the production network.

Ecuador is a developing country located in South America whose economy has been characterized as being undiversified, with a high concentration in the production of primary goods and low incorporation of added value. Extraction of crude oil represents 31.48%, and traditional products such as bananas, cocoa, coffee, and shrimp, represent 27.91% of total exports, for the year 2019 (Central Bank of Ecuador 2019b). Thus, the Ecuadorian economy depends to a large extent on these sectors, which constitutes a problem due to the price volatility and therefore, the vulnerability of the economy. In this sense, it is important to know whether these sectors are relevant in centrality terms, which would indicate their interconnectivity with other sectors and in turn, their influence on macroeconomic aggregates. The high dependence on agro-exports has been a discussion topic among policy makers. Consequently, in 2012, a project of Ecuadorian Productive Matrix Change was proposed. In this study, apart from the main analysis of centrality of sectors, the prioritized sectors in the framework of this project are analyzed in terms of their centrality. The results shed light on the relevance of these sectors and their changes between 2007 and 2019.

In this context, the main hypothesis of the present study is that the Key sectors in the Ecuadorian input–output network, according to the methodology of Chenery and Watanabe's (CW), are not necessarily the sectors with high centrality. The results show that the industries of wholesale and retail trade, transport and professional activities are the most relevant and influential sectors in the Ecuadorian economy, because they stand out in the four centrality indices analyzed. Answering our hypothesis, these sectors are not the Key sectors determined by the CW methodology, but rather Base sectors. Therefore, weighted centrality measures provide insights into sectors that possess strong forward linkages, which can amplify the impact of external shocks and public policies, when characteristics such as transactionality, proximity, and betweenness of IO network are considered.

The production network depends to a large extent on these three sectors over time, as it does not present significant structural changes with respect to base year 2007. At the same time, the distribution of the productive sectors according to the centrality measures follow a power law. Therefore, we can expect, as literature establishes, that productivity shocks on the aforementioned sectors could give rise to cascade effects and generate variations of macroeconomic aggregates.

This paper contributes to the growing empirical literature that applies SNA on input–output networks to analyze the sectors’ ability to propagate economic shocks and generate cascade effects (e.g. Xu and Liang 2019; Villamar and Guananga 2019; Giammetti et al. 2020; Lavassani and Movahedi 2021; Costa et al. 2022). In addition, this research adds to the few studies done in the region (Contreras 2019; de Santana et al. 2022) by going further with the application of the alpha centrality (Ghosh and Lerman 2011), weighted closeness and weighted betweenness centrality (Opsahl et al. 2010) on an input–output network. Frequently, only weighted degree and alpha centralities have been used to analyze the importance of productive sectors in commercial relationships, however no researches have applied weighted closeness and betweenness centralities to our knowledge. These types of measures take into account the number of commercial relationships in which an industry participates directly or indirectly in the input–output network (as conventional closeness and betweenness non weight centralities), but also the buying-selling amount of these relationships. So, the relevance of a sector can be further explored in the value chains considering both intersectoral linkages and their economic exchange.

This study is structured as follows: Section 2 synthesizes the main theoretical and empirical investigations; Section 3 discusses the different tools used; Section 4 exposits the preliminary analysis of the Ecuadorian input–output network; Section 5 presents the main results; finally, Section 6 presents the main conclusions of the study and the possible recommendations to be implemented in future research.

2 Methodology

The main feature to describe in this study, as mentioned in the theory of shock diffusion, is the sector’s centrality. To this purpose, the Ecuador Input–Output Table for the year 2019 is used. This matrix shows the intersectoral commercial relationships between 70 productive sectors, divided according to the National Accounts Industry Classification (NAIC). This information was obtained from the System of National Accounts elaborated by the Central Bank of Ecuador.Footnote 2 The identification number of the sectors in this matrix, as well as their classification according to the Chenery and Watanabe methodology (CW classification), is shown in Appendix A.

In order to explain the methodology, the Ecuadorian input–output network will be represented as a directed and weighted graph \(G=\left(N, A\right)\), where \(N=\left\{1,\dots ,n\right\}\) is the set of productive sectors (i.e. vertices) and \(A={\left\{{a}_{ij}\right\}}_{n\times n}\) is the adjacency matrix of the input–output network (i.e. edges). Here, \({a}_{ij} \epsilon \left\{\mathrm{0,1}\right\}\) represents the commercial relationship between the sector \(i\) and the sector \(j\). If \({a}_{ij}=1\), then the sector \(i\) sells to the sector \(j\); otherwise, if \({a}_{ij}=0\), the sector \(i\) does not sell to the sector \(j\). Let \(w:A\to {\mathbb{R}}_{+}\) be the weighting function that assigns to each intersectoral link \({a}_{ij}\) the amount \({w}_{ij}=w\left({a}_{ij}\right)\) that the sector \(i\) sells to the sector \(j\).

The weighted centrality indices that will be applied on the Ecuadorian input–output network are: degree centrality, closeness centrality, betweenness centrality (Opsahl et al. 2010) and alpha centrality (Ghosh and Lerman 2011). The weighted degree centrality displays the economic relevance of industries in their industry-specific input–output network (i.e., their immediate buyers and sellers) meanwhile the weighted closeness centrality, betweenness centrality and alpha centrality are systemic measures that are calculated on the entire input–output network. The weighted closeness centrality gives an idea of how close a supplier is to the buyers through productive linkages between industries. The weighted betweenness centrality indicates the industry’s importance on any value chain formed in the production network. The weighted alpha centrality shows how far an exogenous sectorial shock can be propagated forward.

2.1 Weighted Degree Centrality

The weighted degree centrality \({C}_{i}^{d}\left(G\right)\) measures the total amount of direct commercial relationships that a vertex \(i\) makes with others. This index is calculated as follows:

$${C}_{i}^{d}\left(G\right)= \sum\limits_{j}^{n}{w}_{ij}, \forall\; i=1, . . . ,n$$
(1)

where \(n\) is the total number of vertices in the network. If this centrality index has a high value, the amount of direct commercial relationships for an economic sector is high, and therefore it is more central in the input–output network.

2.2 Weighted Closeness Centrality

The weighted closeness centrality \({C}_{i}^{c }\left(G\right)\) measures the inverse of farness, which in turn, is the sum of distances of vertex \(i\) to all other nodes. Here, the distance is determined by the inverse of commercial relationships. This index is calculated as follows:

$${C}_{i}^{c }\left(G\right)=\frac{1}{\sum_{j}^{n}{d}_{ij}^{\alpha } }, \forall\; i=1, . . . ,n$$
(2)

where \({d}_{ij}^{\alpha }\) is the length of the shortest path between vertex \(i\) and vertex \(j\), based on the inverse of the commercial relationships. This length is measured as:

$$d_{ij}^\alpha=\min_{\phi\in\Phi_{\mathit{ij}}}\sum\limits_{(r,s)\in\phi}\frac1{{{(w}_{rs})}^\alpha}$$

where \({\Phi }_{ij}\) are all possible paths between vertex \(i\) and vertex \(j\), \((r, s)\) is an edge that belongs to the path \(\phi\) and \(\alpha\) is a synchronization parameter. This parameter is equal to 1 to exclusively consider the amounts of the commercial relationships in network for the calculation of the index.

A high closeness centrality indicates than an economic sector maintains a close relationship with the rest of the sectors in the input–output network, due to the high commercial amounts. Its reciprocal value could give an idea of the average number of commercial relationships between one sector with their final buyers.

2.3 Weighted Betweenness Centrality

The weighted betweenness centrality \({C}_{i}^{b }\left(G\right)\) shows how well a vertex \(i\) is located, according to the geodesic paths between all vertices in the input–output network, using Dijkstra's algorithm (1959). This index is calculated as follows:

$${C}_{i}^{b }\left(G\right)=\sum_{i|i\notin \left\{j,k\right\}}\sum_{j|j\notin \left\{i,k\right\}}\frac{{p}_{ij}^{\alpha }\left(k\right)}{{p}_{ij}^{\alpha }}, \forall\; i=1, . . . ,n$$
(3)

where \({p}_{ij}^{\alpha }\) is the number of geodesic paths between vertices \(i\) and \(j\), and \({p}_{ij}^{\alpha }\left(k\right)\) is the number of geodesic paths between vertices \(i\) and \(j\) passing exclusively through vertex \(k\) \(\left({p}_{ij}^{\alpha }\left(k\right)<{p}_{ij}^{\alpha }\right)\). In order to identify these geodesic paths, the distance is measured as:

$${d}_{ij}^{\alpha }\left(k\right)=\underset{\phi \in {\Phi }_{\mathit{ij}}\left(k\right)}{\mathrm{min}}\sum_{(r, s)\in \phi }{{(w}_{rs})}^{\alpha }$$

where \({\Phi }_{ij}\left(k\right)\) are all possible paths between vertex \(i\) and vertex \(j\) with an intermediate vertex \(k\notin \left\{i,j\right\}\), \((r, s)\) is an edge that belongs to the path \(\phi\) and \(\alpha\) is the synchronization parameter. This parameter is equal to 1 when considering the amounts of the commercial relationships in network.

When the weighted centrality index of betweenness takes high values, an economic sector appears more frequently in the geodesic paths that connects all pairs of sectors in the input–output network.

2.4 Weighted Alpha Centrality

The weighted alpha centrality \({C}^{a}\left(G\right)\) determines the influence of vertex \(i\) towards its neighbors and the neighbors of its neighbors, through exogenous shocks in the network. This influence is measured by adding the amounts of purchases and sales that vertices \(i\) conduct with other sectors. Therefore, the alpha index is proportional to the sum of the amounts of the vertices to which it is connected. This index is calculated vectorially as follows:

$${C}^{a}\left(G\right)= {\left(I-\omega {W}^{T}\right)}^{-1}e$$
(4)

where \({W}^{T}\) is the transpose of the weighted adjacency matrix \(W={\left\{{w}_{ij}\right\}}_{n\times n}\), \(\omega\) is a parameter that reflects the relative importance of endogenous factors in determining the centrality, \(e\) is a vector of exogenous perturbationsFootnote 3 and \(I\) is the identity matrix.

If the value of the alpha index is high, then the sector is central because its neighboring sectors have high commercial exchange. This index is analogous to the dispersion sensitivity index proposed by Rasmussen (1958), which measures how important a sector is in the forward linkage of a input–output network through exogenous economic shocks.Footnote 4 Also, Acemoglu et al. (2012) finds that the power law distribution of this index helps to explain the aggregate volatility of the economic system.

2.5 Clustering Analysis

Once the centrality measures are calculated, a clustering analysis using the k-means method is conducted. This method consists in constructing clusters focusing on the intra-class and inter-class similarity. The k-means algorithm starts with k non-empty subsets. After that, the centroids of the clusters are calculated and based on that, the algorithm assigns each sector to the cluster with the nearest centroid. Finally, it stops until the assignment is stable (Han et al. 2011).

3 Preliminary Statistics of Ecuadorian Input–Output Network

In the Ecuadorian input–output network, there are few big sectors that are suppliers and buyers of the majority of other sectors. This generates a star/like pattern of intersectoral relations, as shown in Fig. 1. The industries with the highest level of commercial exchange are construction (number 53 in figure), wholesale and retail (54), transport (58) and professional services (64).

Fig. 1
figure 1

Graph of the Ecuadorian input–output network. Source: Central Bank of Ecuador (2019b). Note: This graph shows the Ecuadorian cross-sectoral network according to the input-output matrix 2019. Vertices represent the 70 productive sectors of the economy, and their size shows their added value, classified according to the Appendix B. The NAIC identification number of these sectors is shown in the Appendix A. This figure is obtained by the Fruchterman-Reingold algorithm that accounts for the weight of the vertices; vertices inside (outside) the network have a higher (lower) commercial exchange. On the other hand, edges represent the amount of buying and selling transactions; and its size indicates the amount of the transaction made between two sectors. For graphic purposes, only the 15% largest commercial relationships are considered

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This is consistent with the center-periphery model of Everett and Borgatti (1999), where a group of sectors with strong links are found in the center of the network, while weakly connected sectors are relegated to peripheral positions. Given this structure, we can expect that microeconomic shocks on central sectors could diffuse through the network and generate macroeconomic fluctuations, as proposed by Acemoglu et al. (2012) for "star networks".

In Table 1, the main characteristics of the Ecuadorian input–output network are shown. The number of edges show that most of the 70 sectors (number of vertices) are related to each other through 4,510 buying and selling transactions. If all sectors were related to each other, 4,830 (70*69) edges would be possible. In the Ecuadorian case, 93% (network density) of the possible commercial relationships take place. This high density indicates that most sectors are directly related to each other (Coleman and Moré 1983). The diameter indicates that a maximum of 2 intersectoral relationships are required to be able to reach from one sector to another, considering the shortest.

Table 1 General statistics of the Ecuadorian input–output network
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As Table 1 shows, the length of the average path between sectors is 1.04 commercial relationships; that is, for one sector to be related to another it must perform at least 1 transaction approximately. The total non-weighted degree indicates that a sector records an average of 129 sale-purchase relationships. The average amount of these commercial relationships is USD$ 1,581.36 million (total weighted degree). In addition, one sector maintains business relationships with approximately 65 buyers (in-degree) and 65 suppliers (out-degree). The sectors of extraction of crude oil (12), manufacturing industries (50), transport and storage (58) and private teaching services (66) are buyers with the highest number of connections (66 in-degree), while postal and mail activities (59) have the lowest quantity of relationships, corresponding to 54. On the other hand, suppliers maintain a maximum of 70 (non-weighted out-degree) direct transactions on the network, however, manufacturing of tobacco products (32), public education services (non-market) (67) and health and social services (non-market) (69) have 0 out-degree connections.

Considering the total demand and supply, the Ecuadorian input–output network records an amount of USD$ 62,935 million. The total demand from the economic sectors is shown in Fig. 2. It is evident that the demand is concentrated in few sectors and that the gap between the first demanding sector and the next sectors is quite large. The construction sector records the highest demand for inputs, with USD$ 6,691 million, representing 10.63% of the total intermediate consumption at basic prices. The next sectors with the highest input demand are the wholesale and retail trade (54) and oil and natural gas extraction (12), with USD$ 4,081 million (6.80%) and USD$ 3,650 million (6.08%), respectively. The rest of the sectors (67 sectors) demand USD$ 23,239 million, despite that most of the sectors are interconnected (high density of 93%), few of them are highly interconnected because of their demand.

Fig. 2
figure 2

Demand by economic sectors, 2019. Source: Central Bank of Ecuador (2019b). Note: The bar chart represents the total intermediate consumption by sector of the Ecuadorian economy. The horizontal axis indicates the demand for each sector in millions of dollars, while the vertical axis indicates the 15 sectors with the highest demand in the country. In addition, the color of the bars shows the intensity of consumption in the sectors. The more tomato (blue) this color is, the higher (lower) its consumption

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The supply of economic sectors is shown in Fig. 3. The distribution of the supply is highly concentrated in few sectors but to a lesser extent than the demand. The first three supply sectors record shares around 10% each one. The sector with the highest supply corresponds to professional, technical, and administrative activities (64), which sells USD$ 9,823 million (15.61% of total production). It is very interesting that this sector is the main supplier to other sectors because it means that other sectors are performing based on training and technical assistance. In particular, this sector mainly provides services to itself (9.67%), to the wholesale and retail sector (54) with 8.64%, to the communications and information sector (60) with 8.17% and to transport and storage (58) with 8.04% of its total production. The second and third most important supply sectors are wholesale and retail, and transportation, which supply a total of USD$ 6,769 million and $USD 6,023 million (10.75% and 9.57%, respectively).

Fig. 3
figure 3

Supply by economic sectors, 2019. Source: Central Bank of Ecuador (2019b). Note: The bar chart represents the total production by sector of the Ecuadorian economy. The horizontal axis indicates the production of each sector in thousands of dollars, while the vertical axis indicates the 15 sectors with the highest production in the country. In addition, the color of the bars shows the intensity of the production of the sectors. The more tomato (blue) this color is, the higher (lower) its production

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4 Results

This section identifies the sectors with the greatest centrality in the Ecuadorian economy according to the four measures proposed: Weighted Degree Centrality, Closeness Centrality, Betweenness Centrality and Alpha Centrality. Furthermore, a clustering analysis is conducted to determine similarities in terms of centrality between sectors. Finally, the centrality of prioritized sectors within the Productive Matrix Change Project is analyzed.

4.1 Centrality Analysis

Table 2 shows the descriptive statistics regarding the weighted centrality indices of degree, closeness, betweennessFootnote 5 and alpha centrality for the 70 industries in the Ecuadorian network, using the Input–Output Matrix 2019. In order to visualize them, each of the centrality indices are plotted in the panels of Fig. 4, using a color scale for the nodes: if the node is red (yelow), its centrality index is high (low).

Table 2 Centrality measures statistics
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Fig. 4
figure 4

Graphs of Weighted Centrality Indices. Note: The Figure shows the indexes centrality of degree, closeness, betweenness and alpha in the Ecuadorian input–output network. The vertices represent the 70 productive sectors. The NAIC identification number of these sectors is shown in the Appendix A. The color of the vertices is related to the weighted centrality indices; that is, if the node is redder (more yellow), its centrality index is higher (lower). In addition, edges represent the amount of buying and selling transactions; and its size indicates the amount of the transaction made between two sectors. For graphic purposes, only the 15% largest commercial relationships are considered

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According to the degree-weighted centrality index (Fig. 4 - Panel A), commercial relationships of the productive sectors in Ecuador show high variability. The mean of the degree-weighted centrality is USD$ 1,798.14 million. There are 20 sectors that are above the mean and 50 sectors below the mean. There are 4 sectors that trade amounts greater than 7 billion dollars. The sectors that most boost the economy, by recording high level first-order relationships with suppliers and buyers, are professional activities (64), wholesale and retail (54), transportation (58) and construction (53). The sectors that record low levels of first-order relationships are: manufacture of tobacco products (32), manufacture of rubber products (41) and manufacture of farinaceous products (24).

The closeness index (Fig. 4 - Panel B) shows a great number of sectors that have a high proximity. These sectors are suppliers that rapidly interact with various industries in the network. This aspect facilitates quick access to inputs by suppliers and to carry out their production process. The mean of this index is 0.0329 and there are 31 sectors above the mean and 39 below it. The sectors that are closer to others are: professional activities (64), transportation (58), manufacture of refined petroleum products (38) and wholesale and retail (54). These sectors are close to others because they are direct providers in the input–output network. This relationship promotes commercial interaction, without the need for many intermediaries, which makes the exchange more dynamic in the input–output network. The sectors that are far away from suppliers and that need many intermediaries to carry out their production process are: manufacture of tobacco products (32), public (non-market) education services (67) and non-market health and social services (69).

The betweenness centrality index (Fig. 4 - Panel C) shows a polarized network, with only four sectors (circles 54, 58, 57 and 64) that actively participate intermediating between sectors and the rest of the sectors (66 sectors) participate to a lower extent intermediating transaction like manufacture of tobacco products (32), public (non-market) education services (67) and non-market health and social services (69). The mean of the betweenness-weighted centrality is 188 intersectoral relationships, and there are 10 sectors that are above the mean and 60 sectors below it. The high intermediary sectors are transportation (58), wholesale and retail (54), food service (57) and professional activities (64). These sectors are in strategic positions in the network since they channel transactions more efficiently in the economy. By contrast, the rest of sectors depend on those strategic sectors, so that a shock in the strategic sectors would affect them.

The alpha centrality index (Fig. 4 - Panel D) shows few sectors of high importance in commercial exchange, considering the relationship with other industries that also trade high amounts. However, it presents a more balanced image than that shown in the betweenness index. The mean of the alpha-weighted centrality is 1.60, and there are 18 sectors that are above the mean and 52 sectors below it. Among the most central sectors, there are professional activities (64), wholesale and retail (54), transportation (58) and oilseed and industrial crops (5), where a negative shock will probably affect the client-industries of these sectors. In contrast, the sectors recording the lowest alpha centrality are manufacture of tobacco products (32), public (non-market) education services (67) and non-market health and social services (69). This means that they are slightly connected downward in the input–output network.

For more information, Appendix C shows the top 7 industries (that is, 10% of economic sectors) with the greatest centrality in each of the four indices.

Input–output networks are characterized by high heterogeneity of the sectors’ centrality in commercial relationships, regularly characterized in literature through a power law distribution (Carvalho 2014; Gabaix 2016). The power law distribution of the centrality indices was verified through the Kolmogorov–Smirnov goodness-of-fit test and Likelihood ratio test, which suggested that the distribution of the four centrality indices follow a power law, indicating the presence of few highly central sectors and a large concentration of sectors that have low centrality indices (Acemoglu et al. 2012). The tests performed for each centrality index can be seen in Appendix D (Tables 7, 8 and 9).

4.2 Clustering According to the Centrality Indices

Based on the four centrality indices, a clustering analysis is conducted to determine similarities in terms of centrality between sectors. In Fig. 5, Dimension 1 is explained by the degree, betweenness and alpha centrality indices in a 77.2%, while dimension 2 is explained by the closeness centrality index in a 12.5%.

Fig. 5
figure 5

Clustering K-means according to centrality indices. Source: Central Bank of Ecuador (2019b). Note: The variables that explain most of dimension 1 are the indexes of degree centrality, betweenness and alpha, meanwhile the index of closeness explains dimension 2. The NAIC identification number of the sectors is shown in Appendix A

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As seen in Table 3, Cluster A records the lowest mean value of all four indices, simultaneously cluster E records the highest mean value in the four indices. The average centrality of each of these indices is increasing across clusters, starting with cluster A, and then heading to cluster E. The list of sectors within these clusters can be seen in Appendix E.

Table 3 Mean and standard deviation of the five clusters
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Sectors with high centrality are grouped in Clusters D and E. They have a high capacity to diffuse productivity shocks, to generate cascade effects and to generate macroeconomic fluctuations. Among them, according to the CW classification, there are six base sectors, one motor sector, one island sector and one key sector. In other words, it can be argued that the CW classification loses sight of sectors that are relevant in terms of their transactionality, proximity, betweenness and linkages. With the CW classification, only one sector (Extraction of crude oil and natural gas) is identified as key sector that promotes production, by demanding and offering large amounts of inputs to the rest of the sectors (Table 4).

Table 4 Main sectors according to the centrality indexes
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The three sectors of cluster E represent 22.71% of the GDP and these are: wholesale and retail (54), professional activities (64) and transportation (58). These three sectors correspond, according to the CW classification, to base sectors; that is, they mostly generate forward linkages. These results are consistent with other economies in the world. For instance, Wholesale Trade has been pointed out as one of the most central sectors in Mexico (Contreras 2019), Brazil (de Santana Ribeiro et al. 2022) and Greece (Tsekeris 2017) using SNA. Professional, scientific and technical activities have also been identified as central in Brazil and Greece, based on the application of a non-weighted betweenness centrality.

The professional, technical, and administrative activities (64), as shown in Table 4, commercialize the highest amount of purchase-sale relationship, corresponding to USD$ 11,973.8 million and participate in 1,351 transactions out of a total of 4,510 (29.96%). This sector can reach its final buyers with around 12 commercial relationships (1/closeness = 1/0.0785). In addition, the professional, technical, and administrative activities increase their production by USD$ 7.81 for each additional dollar in intermediate consumption in this sector.

Wholesale and retail trade (54) is part of 2,524 transactions (55.96%) and trades directly with other sectors around USD$ 11,213.3 million, providing a great amount of inputs to the rest of the sectors. In addition, for each additional dollar in intermediate consumption in the wholesale and retail sectors, the production of this sector increases by USD$ 5.76 towards other activities. It takes approximately 14 (1/closeness = 1/0.068) commercial relationships in the input–output network to attain its final buyers.

The transportation and storage sector (58) trades around USD$ 9,768.6 million dollars and it is part of 2,910 intersectoral relationships (64.52%) in the production network. This sector is in charge of accelerating the Ecuadorian economy, because it promotes economic growth and development (Fernández 2017). This sector can reach its final buyers with around 13 (1/closeness = 1 / 0.0733) transactions. For each additional dollar in intermediate consumption of transportation and storage, its production increases by USD$ 4.32 towards other activities.

Cluster D is made up of 7 sectors that represent 27.83% of GDP. These sectors are mainly services, real estate activities and oil-related activities. The construction sector (53) stands out in the degree centrality, while financial services activities (61) with manufacture of refined petroleum (38) stand out in closeness centrality. Food, and beverage services (57) predominate in the betweenness centrality, while financial services activities (61) stand out in the alpha centrality.

Clusters A, B and C are mostly made up of primary activities, intensive in labor, belonging to informal sectors like agriculture, farming of cattle, fishing, and forestry. Given that Ecuador is a primary-exporter economy, it is striking that these sectors are among these clusters and not in clusters D and E with greater centrality. These primary sectors consolidate the productive matrix by generating high foreign exchange earnings and, therefore, a high share of GDP. This phenomenon is due to the fact that exports continue to be commodities with low added value, which is why they generate low local transactionality. Therefore, the fact that these sectors are not highly central could be considered as a good thing, since a shock to these sectors would not affect the rest of the input–output network.

To capture possible changes over time in the production network, the centrality measures are analyzed for 2007 and 2019. Table 5 indicates the results of a transition matrix of sectors considering their deciles between 2007 and 2019 and the rank correlation of centrality measures between 2007 and 2019. The different rank correlation measures show that rank positions of sectors are positively and highly correlated between 2007 and 2019, which means that if a sector had a high (low) position in the ranking in 2007, it is very likely that it also has a high (low) position in 2019. The Ecuadorian production network does not present significant structural changes.

Table 5 Rank changes and rank correlation between centralities of 2007 and 2019
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For all centrality measures, except for the degree centrality (44%), more than 65% of sectors keep their position in a given decile. The remaining percentage of sectors increase or decrease their centrality measures. As for the degree centrality, 33% of sectors decreased their position in degree centrality from 2007 to 2019. Regarding the closeness centrality, 13% of sectors dropped position between 2007 and 2019. For the betweenness and alpha centrality, around 17.5% of sectors decreased their rank over time. For more information, Appendix F shows the position changes in the four weighted centrality indices for the year 2007 and 2019.

Among the sectors that do not change to another the decile, we have the Wholesale Trade (54), Transportation (58) and Professional Activities (64), which were the most influential sectors in both 2007 and 2019. These sectors remain among the first positions in all centrality measures over time. It is worth noting that Professional activities changed its betweenness from the 6th position in 2007 to the 4th position in 2019. For the other measures, this sector was ranked in first place in both years.

4.3 Centrality of Prioritized Sectors of the Project of the Change of Ecuadorian Productive Matrix

The project of Change of Ecuadorian Productive Matrix (CEPM) proposed in 2012, aimed to diversify the country's supply, stimulate exports of non-oil goods, encourage innovation and development, and strengthen labor productivity. The prioritized sectors within this project, with their corresponding aggregate activities according to NAIC, are shown in Table 6.

Table 6 Prioritized sectors in the Productive Matrix Change Project
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Among all prioritized sectors, the aggregate sectors of Transportation and storage (58), Construction (53) and Oilseed and industrial cultivation (5) ranked in the first quartile of centrality in the Ecuadorian economy. Communications and information (60), Production of wood and wood products (36), Manufacture of base metals (45) and Manufacture of other chemicals (40) ranked in the second quartile of centrality. The rest of prioritized sectors ranked in the third quartile of centrality and no prioritized sector rank in the fourth quartile. To analyze whether these sectors increase in their relevance after their prioritization in the framework of the Change of the productive matrix,Footnote 6 a temporal analysis of their centrality measures is conducted (Appendix G). Four of them have increased their centrality position in the production network between 2007 and 2019: Manufacture of basic chemicals, fertilizers and primary plastics (39), Manufacturing of base metals (45), Communications and information (60) and Manufacture of other chemical products (40).

The Manufacture of basic chemicals, fertilizers and primary plastics (39) changed in average its centrality from the 44th position in 2007 to the 37th position in 2019 and it’s the only sector that has improved its 4 centrality indices analyzed. Therefore, it has increased its commercialized purchase and sale amounts (ranking up 10 positions), it has become closer to its final buyers (ranking up 10 positions), more efficient in intermediating transactions between sectors (ranking up 5 positions) and has expanded its production for other economic activities (ranking up 2 positions).

In 2007, Manufacturing of base metals (45) changed in average its centrality from 23th position to the 20th position in 2019, due to an increase of 5 positions in degree and alpha centralities, meaning that its ability to trade high amounts has improved and its production has expanded for other economic activities. In the same sense, it has increased its betweenness centrality, thereby improving its strategic position by being more efficient in network transactions (ranking up 3 positions). Its ability to relate to its end buyers was slightly affected, decreasing 2 positions according to closeness centrality.

The average centrality for Communications and information (60) in 2007 to 2019, changed from 21st position into the 19th position, principally to the greatest growth in the betweenness index, climbing 22 positions, which is why it has gained importance in this period analyzed by improving its strategic position as intermediary in the production network. Additionally, the degree centrality has a positive but small impact, since it has only increased by one position. However, the closeness and alpha indices have decreased by 5 and 9 positions respectively, which means that it has distanced itself from its final consumers and has decreased its production for other economic activities.

The average centrality of Manufacture of other chemical products (40) has increased its position from 2007 to 2019, from 26th position into 25th position, due to greater amounts traded with other productive sectors, as well as its relationship with final consumers, therefore, increasing 5 and 3 positions in the degree and closeness centralities, respectively. On the other hand, its ability to influence the production of other sectors decreased, as well as its role as an intermediary to facilitate the transactions between the productive sectors.

5 Conclusions

The objective of this study was to analyze at the sectoral level the Ecuadorian input–output network using indicators based on Social Network Analysis. Its main contribution is to provide details on the role played by sectors, through centrality indices. Theoretically, these features are mainly important to identify the most influential sectors for the diffusion of productivity shocks, the propagation of cascade effects and the generation of macroeconomic fluctuations.

According to the results, the sectors of wholesale and retail trade (54), transport (58), and professional activities (64) are the most influential in the Ecuadorian economy, because they prevail in the four centrality indices. Therefore, these sectors are capable of commercializing high amounts of purchases and sales (degree), have a strategic place to carry out efficient transactions (betweenness), increase their production for other economic activities (alpha), and are closer to their final consumers (closeness). The importance of these sectors is structural as they were also ranked in the first positions of all centrality measures in 2007. However, they are not key sectors according to Chenery and Watanabe's methodology, all are base sectors. In this sense, the weight centrality measures used in this paper highlight the relevance of sectors as they participate significantly in commercial relationships in the production network.

Overall, the production network does not change significantly since most of sectors remain in their same rank between 2007 and 2019. Furthermore, due to power law holds for centrality measures, these sectors can significantly predetermine the activity of the entire input–output network, so a productive shock on them could spread cascading effects downstream and generate aggregate fluctuations, as argued by Acemoglu et al. (2012) and Carvalho (2014). Regarding the prioritized sectors within the project of the Change of the Productive Matrix, our results show that 7 out of 12 prioritized sectors, are highly central in the Ecuadorian economy. This result indicates that their economic linkage impact would be positive as benefits directed to these central sectors very likely diffuse to other sectors in their network. From a public policy point of view, to change the productive matrix based on products with low value added towards a productive matrix with higher value added, it is important to promote sectors with linkages generation potential such as those sectors in cluster D (Construction, Extraction of crude oil and natural gas, Financial services activities, Food and beverage service, Real estate activities and Manufacture of refined petroleum and other products), considering the key role of most central sectors in cluster E (Professional and administrative activities, Wholesale and retail and Transport and storage). Policy implications of centrality on important phenomena such as employment and distribution are out of our scope since it needs an econometric estimation, for instance.

This analysis shows the empirical importance of SNA’s tools, as they allow us to identify the most important industries in the commercial relationships of the Ecuadorian production network. It could be complemented with other indexes to measure interindustry linkages under Leontief-based methodologies, such as hypothetical extraction (Dietzenbacher et al. 2019), average propagation length (Dietzenbacher et al. 2005) and structural path analysis (Xie et al. 2020). It should be noted that centralities indexes provide descriptive statistics of the most resilient and influential sectors in the IO system so they could give some ideas about the possible effects of an economic shock or public policy. However, they do not provide a counterfactual analysis in a general equilibrium setting. In this sense, extensive economy-wide models could be required in order to formulate public policy adequately or prevent exogenous shocks. In addition, to improve public policy actions to change the productive matrix, an analytic comparison with other economies producing products and services with high value added is needed.

Some possible recommendations are presented for a possible extension of this analysis. Econometric models can be used to quantify upstream and downstream cascading effects caused by a shock or public policy to a core industry. Another alternative is the dynamic analysis which measures the significance and the effect of variables such as employment, taxes, technology, and intermediate consumption in the total added value of the sectors. Applied general equilibrium models can also be used to evaluate ex-ante supply-side policies related to the most influential industries on employment, income distribution, government revenue, the trade balance, among others. Likewise, other policies such as financing strategies (i.e., taxation, private financing, and international loans) could be evaluated. The detection of communities in the input–output network is an analysis that provides information on patterns that are not so visible, such as, detecting highly connected communities that do not allow the dissemination of a productive shock, but that affects only that community. Finally, spatial analysis is one of the alternatives that can allow us to know the integration between the central, regional, and local levels, with the aim of improving the productivity of the economic system.