Analysis of productive structure applying network theory: The Brazilian case

Structural Change and Economic Dynamics 53 (2020) 281–291

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Structural Change and Economic Dynamics journal homepage: www.elsevier.com/locate/strueco

Analysis of productive structure applying network theory: The Brazilian case Mariana Piaia Abreu a,∗, Renata R. Del-Vecchio b, Rosanna Grassi c a

Mackenzie Center for Economic Freedom, Brazil Federal Fluminense University, Brazil c Università Degli Studi di Milano-Bicocca, Italy b

a r t i c l e

i n f o

Article history: Received 31 October 2017 Revised 17 March 2020 Accepted 18 March 2020 Available online 20 March 2020

a b s t r a c t In this work, we intend to characterize the complexity of the Brazilian productive structure through network theory. We investigate how this structure is internally organized, from a network of knowledge, considering the occupations linking productive activities. Results reveal it is imperative for Brazil to rethink its productive structure to remove. the obstacles that prevent, or make it difficult, that the varied activities encompass more diversity of occupations.

JEL classification: D85 E24 J21 L14 L16 R11

© 2020 Elsevier B.V. All rights reserved.

Keywords: Productive structure Complex network Brazil Occupations

1. Introduction The aim of this work is to study how the Brazilian productive structure is internally organized, from a network of knowledge, considering the occupations (i.e., types of jobs) among productive activities. The idea is that it is easier to move from one productive activity to another if they have a common basis: in this case, the type of occupation. To this end, network theory can be a useful tool to describe the complexity of the productive structure. For Hausmann (2016), economic development depends on the accumulation of know-how, which can grow at a group level only through the increasing specialization of individuals, as they have a limited capacity to acquire knowledge. In this way, the accumulation of know-how by a particular group of individuals requires ever-increasing collaboration networks, to convert knowhow into a greater variety and complexity of production. For Hausmann et al. (2014), the complexity of an economy relates to

the multiplicity of knowledge embodied in it. Economic complexity then reflects the amount of knowledge embedded in the productive structure of the economy. Hidalgo et al. (2007) have found that countries face different development possibilities: poor countries tend to specialize in less complex productive activities, creating a set of development options underlying the current production. The literature shows that poorer countries, such as Brazil, tend to specialize in unqualified labor and products, hampering their walk in the product space1 to more complex activities, increasing the country’s income level (Cristelli et al., 2013; Hausmann et al., 2014; Pietronero et al., 2013). Therefore, based on the mentioned studies, some stylized facts are raised: (i) capacities determine the diversification of the productive structure, and thus of development opportunities; (ii) specialization at the personal level results in diversification at the regional level, that is, specialization at the micro-level results in macro-level diversification; (iii) developed countries employ more workers in manufacturing sectors and sophisticated services and

∗

Corresponding author. E-mail addresses: [email protected] (M.P. Abreu), [email protected] (R.R. Del-Vecchio), [email protected] (R. Grassi). https://doi.org/10.1016/j.strueco.2020.03.005 0954-349X/© 2020 Elsevier B.V. All rights reserved.

1

The network of relatedness between products.

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have a more complex production structure; (iv) underdeveloped countries have not been able to build a complex productive structure and find it difficult to train and employ workers in sophisticated employment and services’ sectors. Our contribution is to analyze the Brazilian productive structure through the interconnections between productive activities, highlighting complex patterns between them. To this end, it seems appropriate to use the methodology of complex networks to analyze the complexity of the productive structure. We start from the literature on the analysis of the productive structure, paying special attention to the Brazilian case. In the literature, the Index of Economic complexity (ECI index) is a well-known measure of the knowledge of an economy. The comparison between the index for Brazil and the TOP country in each year is a starting point for investigating the complexity. Indeed, the ECI index refers mainly to trade data between a country and other countries. However, research on the productive structure in the context of occupational sharing is imperative to understand the future opportunities for development and growth in Brazil, in addition to the obstacles that the Brazilian economy faces. With a networks tool, we can link the economic complexity of Brazil to the entire productive and occupational Brazilian structure, taking into account both the external and internal demand. Therefore, we present a network application to the Brazilian productive structure based on the idea of the relationship between productive activities and types of work.2 A brief review of the literature on the subject and some questions about the Brazilian structure are presented first, followed by a description of the applied methodology and analysis of results. We conclude with final considerations. 2. Analysis of the productive structure Hidalgo et al. (2007) propose analyzeing the product space through a network in which vertices are the products and links are the proximity between two products. The authors highlight that, in the literature, several factors can generate relatedness between products. Such factors include, the intensity of labor, land, and capital Leamer (1984); the level of technological sophistication Jaffé (2015), Lall (20 0 0); the inputs or outputs of the value chain of a product Dietzenbacher et al. (2013); and the necessary institutions Acemoglu et al. (2012), Rodrik et al. (2004). However, their work takes an agnostic approach based on the idea that two products relate if they require similar institutions, physical and technological factors, and others. This proximity measure3 brings the idea that a country’s ability to produce one product depends on its ability to produce other products. In studying the network of the product space of several countries, Hidalgo et al. (2007) realized that the most sophisticated products are located within a densely connected core (metal products, machinery, and chemicals). The less sophisticated products, in turn, occupy the periphery of the network (products with animals, in fishing and tropical origins, agriculture cereal, textiles, livestock and agriculture, mining, forestry, and paper products). Poor countries, such as Brazil, tend to be located on the periphery of product space, which hampers their movement in the sense of new products as they tend to specialize in activities and products of unskilled labor. The inability of a structural change to make these

2 Specifically, occupation is a proxy for know-how. We understand know-how as (Hausmann, 2016, p. 13): “units of capability as elements of practical knowledge”. The author points out that capacities are not directly observable, nevertheless indirect methods exist for measuring complexity, using trade or production data. 3 Hidalgo et al. (2007) define the proximity ϕ between products i e j as the minimum of the minimum between the pairwise conditional probabilities of having Revealed Comparative Advantage (RCA): ϕ = min{P (RCAxi |RCAx j ), P (RCAx j |RCAxi )}.

connections, bringing the products closer, can be an explanation for the difficulties of some countries in converging to the income level of richer countries. Pietronero et al. (2013) argue that the analysis of complex systems offers new opportunities to map empirically the technology and capacity of countries and industrial sectors, to analyze their structures and to understand the dynamics of these economies. The economic growth, in this context, is understood as evolutionary processes of technologies and capacities. Pietronero et al. conclude that the diversification of the production and export agenda is important for the growth of a country. Specialization in certain products may have a significant leadership effect in a static situation; however, in a dynamic market qualities such as globalization, flexibility, and adaptability of production are essential for competitiveness and economic growth. For Pietronero et al., measuring complexity through the analysis of networks provides significant contributions, extending the study to the analysis of risk, investment opportunities, and industrial policy. The need for new methodologies that are better, able than are classic ones to capture the heterogeneity in development and economic growth has been stressed by Cristelli et al. (2013). Moving from the fact that developed countries have an extremely diversified production agenda, with products from the simplest to the most complex, whereas the least developed countries have only products exported by other countries, the authors propose a new quantitative approach. This new method is able to provide interesting results concerning the complexity and the different development of BRIC countries (Brazil, Russia, India, and China). Indeed, although they are emerging economic systems with a high rate of growth, the development of India and China has been different from that of Brazil and Russia and the method proposed captures this heterogeneity well. Hidalgo et al. (2009), Hausmann et al. (2014) present a vision of growth and economic development that assigns a central role to the complexity of a country’s economy through the interpretation of trade data as a bipartite network in which countries are linked to the products they export. Hidalgo et al. show that it is possible to quantify the complexity of a country’s economy. To this end they introduce the ECI which measures the knowledge of an economy. A positive (negative) value suggests that the economy is more (less) complex than is the average economy. The ECI ranks a country’s exports according to its diversity (how many products a given country produces) and its ubiquity (number of countries producing this product). Therefore, the economic complexity of a country depends on the complexity of the products it exports, on the number of complex products exported, and on how many countries also export the products. The most complex products are sophisticated chemicals and machinery, whereas raw materials or simple agricultural products are the least complex products. Fig. 1 represents the pattern of ECI in the last 50 years based on the data of Hausmann et al. (2014). As we are interested in investigating the complexity of the Brazilian economy, we focus in this study on the pattern of this specific country, compared to the first place of each year in the ECI (TOP #1). Analysis of this pattern is particularly important as a starting point to assess the complexity of Brazil. Indeed, Hidalgo et al. (2009) showed that this measure of complexity correlates with the level of income of a country, and deviations from this relationship are predictive of future growth. This indicates that development efforts should focus on generating the conditions that would allow complexity to emerge, generating sustainable growth and prosperity. Therefore, the complexity of an economy relates to the multiplicity of useful knowledge embodied in it. The economic complexity then reflects the amount of knowledge intrinsic in the productive structure of the economy. From this picture, it is remarkable that the economic complexity of Brazil is at the level of the 1970s. In 1999, the peak of the

M.P. Abreu, R.R. Del-Vecchio and R. Grassi / Structural Change and Economic Dynamics 53 (2020) 281–291

Fig. 1. Economics Complexity Index (ECI). Source: Elaborated by the authors from data of Hausmann et al. (2014).

index, the ECI was 0.63173, 29th in a ranking of 121 countries. In 2016, Brazil fell to 44th place, out of 124 countries, with -0.10302, suggesting that its complexity returned under an average economy. The loss of the complexity of the Brazilian economy is more remarkable when compared to the first place of each year in the ECI (TOP #1). The fall in ECI for Brazil suggests the need to analyze the internal productive structure. Thus, the construction of an internal network of special products brings the current domestic perspective to the beginning of the evaluation of what happened to the Brazilian economy. Gala, Camargo, Magacho, Rocha, 2017 consider the symbiotic relationship between the manufacturing sector and the sophisticated services’ sector in analyzing the technological development of countries. The authors combine the notions of complexity developed by Hausmann et al. (2014) with input-output matrices to assess the importance of job creation in advanced sectors. As expected, in the long run, the complexity of the economy is dependent on the generation of jobs associated with manufacturing and sophisticated services. These sectors present links that would have the potential to enhance the division of labor, something that does not occur in, for instance, agriculture and the processing of natural resources. Despite the importance of the industrial sector in Brazil, the productive structure is based largely on non-industrial sectors, such as services and raw materials. Borghi (2017) analyzes the input-output matrix to evaluate the role of the different sectors in the recovery of the Brazilian economy after 2008. The Brazilian economy benefited from the export cycle in the 20 0 0s. With the change in the world scenario and with the drop in commodity prices, the Brazilian economy stagnated. The author concludes that industrial sectors have a strong impact on the maintenance of output and employment, despite having lost space in the productive structure. The food and beverages, automobile, and oil refining sectors were identified as the main product generators in the economy, as opposed to the service sector. The sectors generating most employment are agriculture and livestock, clothing, leather and footwear, and other services. The interdependence between manufacturing and services has been the subject of research of several authors, such as Pisano and Shih (2009) and Rocha (2015), who highlight the synergistic and symbiotic relationship between these sectors. For Rocha (2015), even with services accounting for 70% of the total value-added, services are more production dependent than the opposite. Through the indexes of Hirschman Rasmussen threads, the author shows that the forward threads in the service sector are made up of approximately 40% manufacturing. A smaller portion of industrial production, 30%, is destined for services, in the form of either, in-

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puts or products. The primary sector is more dependent on manufacturing than services, with 70% of the forward chains being manufacturing. In terms of backward linkages, the manufacturing share declines for all analyzed periods, with approximately 30% of the demand for manufacturing services. In the case of back manufacturing links, the share of services increased in the period, though it was smaller than the share of manufacturing back links in services. In the primary sector, the composition of services increased, from manufacturing to manufacturing in the last period. Thus, the back links have been using more services in all sectors over time. Rocha (2015) compares the results of Brazil with South Korea and concludes that the main difference between the links of the Brazilian and South Korean economy is in the level of connections. Among the results, unlike what observed in Brazil, South Korea has an economy with higher manufacturing links both backward and forward; in particular, the backward linkage of manufacturing has a smaller share of services than does the backward linkage of manufacturing services. In this theme, Guerrieri and Meliciani (2005) indicate that the capacity for a country to develop services in the industrial sector depends on the composition of its economic and technological structure. Part of the sophisticated, knowledge-intensive and high productivity services (such as finance, engineering, design, consulting and telecommunications demand) depend on manufacturing. Therefore, the growth of the sophisticated services sector is closely related to the manufacturing industry. Gala, Camargo, Magacho, Rocha, 2017 empirically analyze the importance of these sophisticated services sectors and their connection to economic complexity and technological development. The authors emphasize the difficulty involved in empirically separating the manufacturing-related services from other types of service. To help, the classification follows the WIOD (World InputOutput Database Timmer et al., 2015b) and GGDC (Groningen Growth and Development Centre Timmer et al., 2015a). Data indicate that technologically dynamic emerging countries, such as South Korea, China, India, Indonesia, and Mexico, have shown remarkable improvement in their production structure measured by the ECI in the last 50 years. The main developed countries that show great participation of the employed population in sophisticated jobs and high economic complexity include, the United States, France, the United Kingdom, and Austria. All the above studies indicate the difficult situation in Brazil, with a drastic drop in the index of economic complexity, one of the worst results in emerging countries. 3. Methodology and data The way the division of labor takes place in Brazil is represented by means of a network of connections between productive activities through shared occupation. Thus, if a given occupation were present between two productive activities, there would be a weighted link between them, with weight given by the number of laborers. Fig. 2 shows a simple example of the network obtained. In this example, productive activities i and j share occupations, that is, activity i has three types of occupations – 1, 2, and 3 – that are also present in productive activity j. The same happens between activities j and z, which share 2 occupations, and activities i and z, with 1. The edges are weighted according to the total number of different occupations present in both productive activities; for instance, between activities i and j4 , we have three edges eij : ei j1 = wi j1 = 3, ei j2 = wi j2 = 2, and ei j3 = wi j3 = 2 (graph 4 wi j2 = 2, then there is 1 occupation in i and 1 in j. wi j1 = 3, then there are 2 occupations in i and 1 in j or vice versa.

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Fig. 2. Network G of productive activities from the perspective of occupations. Source: Elaborate by authors.

on the left side). In the right-hand side the same graph is depicted by substituting multiple weighted links with a single link, with  weight wi j = nk=1 wi j,k = 7, n = 1, 2, 3. We represent the Brazilian Productive System as a multigraph, where vertices correspond to the productive activities and edges identify the occupations (type of labor), shared by two productive activities. Data were collected from the Annual Social Information (RAIS) of the Ministry of Labor and Employment (Brasil, 2016). Production activities follow the National Classification of Economic Activities (CNAE), developed by the Brazilian Institute of Geography and Statistics, based on the third revision of the International Standard Industrial Classification, approved by the United Nations Statistical Commission The data obtained for occupancy are used according to the Brazilian Occupational Classification (CBO). We used 670 productive activities and 617 types of occupation, from the year 2016. Our aim is to capture, in this way, a more recent “picture” of the Brazilian situation. Given the relevant presence of sophisticated occupations in productive activities, it is possible to build a network of the productive system in which links between activities identify only sophisticated occupations. In this way, the network connects 670 productive activities (CNAE) and 259 types of occupations instead of 617 different occupations (CBO). To categorize occupations, we follow the classification of the WIOD (Timmer et al., 2015b) and the GGDC (Timmer et al., 2015a): processing, construction industry, mining and quarrying, non-sophisticated services, and sophisticated services (the same as used by Gala, Camargo, Magacho, Rocha, 2017, as mentioned). From the networks, it is possible to draw some information involving centrality measures.5 The centrality of a node indicates its importance in the network (Sabidussi, 1966). There are several definitions of vertex centrality in a network, depending on the application. Among them, some measures seem to better capture the characteristics of the studied network. The degree centrality quantifies the local activity of the vertex in the network (ki ). For weighted networks, a similar measure is the strength centrality (si ), which considers the weights of links. The eigenvector centrality (eigi ) quantifies the connection of a vertex with its neighbors that are themselves central (Bonacich, 1972). To measure the importance of a vertex, it can often be interesting to measure how this vertex interposes itself in communication. This can be assessed using the flow betweenness centrality (fbi ), which measures the position of a vertex considering the flow of information present in all paths (Freeman et al., 1991).

5

Definitions of centrality measures are reported in Appendix A.

Fig. 3. Network Brazilian production structure in 2016 from the occupations sharing. Source: Search results – Gephi 0.9.1 Bastian et al. (2009).

4. Analysis of results 4.1. Brazilian productive structure:shared occupations Based on the procedure discussed in the previous section, it is possible to construct the network representative of the Brazilian productive structure from the occupations shared between productive activities, following the classification of CNAE 2.0 and RAIS for Brazil in 2016, as shown in Fig. 3. In the network, vertices represent the productive activities, and their size is proportional to the strength centrality, which represents the number of occupations that an activity shares with others. The colors of vertices follow the 21 sections of the CNAE (from A to U).6 It is evident that the network has a strongly connected core and a less dense periphery. At the core of the network are the activities with the highest number of occupations, such as Public Administration (O), Accommodation and food (I), Construction (F), Commerce (G), and Administrative activities and complementary services (N). We observed the network to be complete, as all activities share at least one occupation. 6

The classification A–U of the productive activities is reported in Appendix B.

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Table 1 Strength and Eigenvector Centrality, and Participation Income. Source: Search results - Csardi and Nepusz (2006). Productive activities

Centralities measures

Id CNAE

Name

Strength centrality

Eigenvector centrality

o84116 i56112 f41204 g47113 q86101 h49302 n81214 g47814 g47440 n81125 k64701 h49400 k64328 k64336 o84256 k64387 k64107 a01709 b07251 h51307

Public Administration Restaurants and other food and beverage service establishments Building Construction Retail trade of general merchandise Hospital care activities Road transport of cargo Cleaning in buildings and in homes Retail sale of clothing Retail sale of hardware, wood and building materials Apartment Complex Investment Funds Ductwork transportation Investment Banks Development Banks Civil Defense Foreign exchange banks and other institutions Central Bank Hunting and related services Extraction of radioactive minerals Space transport

1,354,921,633 1,135,812,445 962,157,402 911,869,643 704,986,284 697,386,541 603,717,954 592,008,224 486,227,377 486,227,377 20,290,896 19,119,605 18,822,785 17,289,998 16,233,521 15,457,104 12,259,991 11,440,823 7,123,305 6,336,965

1 0.87633 0.7529 0.6908 0.5306 0.5223 0.4489 0.4564 0.3756 0.3659 0.0607 0.0444 0.0442 0.0385 0.0271 0.0337 0.0277 0.0264 0.0182 0.0136

The visual inspection of the network provides a first view from a macroscopic perspective. To thoroughly investigate the more central activities, some centrality measures, specifically, strength and eigenvector centrality, can be computed (Table 1). The strength centrality identifies which productive activities have a greater share of labor with other sectors. The eigenvector centrality indicates that a productive activity is more central if it is connected to other activities with high participation of occupations. It can be noted that the ranking obtained by the two measures is preserved, as expected by the computation of the Spearman Correlation (0.9993). This fact is in line with some studies on random networks and real-world scale-free networks (Li et al., 2015; Valente et al., 2008). The productive activities with greater centrality, namely with more shared occupations, are also the activities with greater participation in income,7 considering that participation in income is, on average, 0.15%. The activities with greater centrality are those involved in Commerce (G) and Administrative activities and complementary services (N). Public Administration, with an approximate 21% share in income, shares occupations with 307 other productive activities, approximately 46.6%. Among the less central activities, it is noticeable the presence of activities related to Financial Activities (K) and Transportation, warehousing and post offices (H). Of note are the Investment Banks, with a 0.1094% share in income, which shared occupation with all other activities of the network (669) and Civil Defense and the Central Bank, with a significant participation in income, and occupation sharing with 668 activities. These activities of low centrality and expressive participation in income have something in common, being activities linked to public administration. In addition, despite the low values of strength and eigenvector centrality, these activities are connected with almost all economic activities (e.g., they have a high degree centrality). This is because these sectors alone do not employ large numbers of workers, but are composed of occupations present in other activities. Fig. 4 shows the 20 occupations with the largest share of total employment (measured on the horizontal axis), which, together, accounted for approximately 50% of total employment in 2016.

7 The share of income means how much the productive activity contributed to the total income generated by all the activities.

Participation income

21.0851% 1.2686% 1.5962% 1.4266% 2.4277% 1.4419% 0.6451% 0.8434% 0.7999% 0.7940% 0.0004% 0.0335% 0.0106% 0.0588% 0.0003% 0.0692% 0.1094% 0.00002% 0.00002% 0.0010%

The gradation of colors shows the participation of these occupations in the totality of 670 different productive activities. In Fig. 4, it can be seen that the occupation with the greatest number of workers (8.88%), namely assistants and administrative assistants, is present in 69.40% of productive activities (465). Maintenance and construction workers, with 3.85% of total employees, is the third largest, being present in 442 productive activities (65.97%). The occupation with highest pervasiveness in productive activities is that of feeders of production lines, present in 97.16% of these (615 activities) and with 2.06% of total employment. On the other hand, traders in shops and markets, the second occupation with the largest number of workers (8.27%), is present in only 68 productive activities (10.15%), showing that a large number of workers does not mean that they are present in a large number of productive activities. Not only the number of occupations shared by activities, but also the position of productive activities is important. To assess the importance of activities in this perspective, the flow betweenness centrality is analyzed. Table 2 reports the activities with the highest and lowest values of this centrality. This measure indicates the maximum number of occupations among productive activities flowing through all possible connections. In this way, the activities with greater flow among the sectors are those that share strategic occupations. The productive activity that is between other activities and on whom they depend to pass to others will assume a strategical position. Indeed, they facilitate the division of labor, thus allowing the dissemination of knowledge in the system, by facilitating the transition through the occupations they share. The most central productive activity is the retail trade of other new products not previously specified. With a considerable participation in income, this activity is the second highest, with the greatest diversity of occupations (569: 90.60%), behind only Public Administration (591: 95.79%), but it has only 0.94% total employment. Cereal cultivation (403: 65.31%) and cattle raising (450: 72.93%) are traditional activities in Brazil. The high flow betweenness centrality expresses the relevance of the productive activities as intermediaries in the “intensity” of occupation they share. This suggests the simplicity of Brazil’s productive structure, and this result is in line with Felipe et al. (2012), who found that the less complex products are raw materials and commodities, wood, textiles and agricultural products. This mea-

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Fig. 4. Share of occupations in total employment and productive activities. Source: Search results.

Table 2 Flow Betweenness and Participation Income. Source: Search results - Csardi and Nepusz (2006). Productive activity

fbi

Id CNAE

Name

Flow betweenness

g47890 a01113 a01512 a01709 k64107 b07251

Retail sale of other new products unspecified before Cereal cultivation Cattle breeding Hunting and related services Central Bank Extraction of radioactive minerals

6.31975 2.7024 2.0962 0.1469 0.0808 0.04250

sure captures how these productive sectors are involved in all of the flow of shared occupation, showing that they are strategic activities for the country. The Central Bank, with a low centrality and a relatively low income shared, has only 10 different occupations (1.62%), of which the vast majority are technical occupations. This is different from the case of the Extraction of radioactive minerals (6: 0.97%) and Hunting and related services (12: 1.94%). 4.2. Brazilian productive structure: shared sophisticated occupations In this subsection we assess activities, and the occupations they share, by investigating the correlation between the measurements obtained through the network and other economic indicators. Fig. 5 represents the productive activities classified on the basis of the diversity of jobs and large sectors. In particular, the upper panel represents the productive activities of high strength centrality in the network, whereas the lower panel represents the activities of low strength centrality. The top

Participation income

0.57783% 0.0899% 0.3847% 0.00002% 0.0692% 0.,00002%

axis corresponds to the diversification of occupations: General Public Administration shares a large part of the 617 existing occupations with other sectors (95.79%), and Extraction of radioactive minerals, in turn, has the lowest diversification, with only six different occupations (0.97%). Among the activities of greater strength centrality, most of the job diversification is in unsophisticated services. However, in the activities with low strength centrality, despite the lack of diversification, the weight of sophisticated services is more relevant. The results obtained so far help in understanding the apparent limitation of the Brazilian productive structure, considering the occupations; that is, considering the distribution of know-how in the economy. The network representative of the Brazilian productive structure from the sophisticated occupations shared in 2016, is presented in Fig. 6. In this network, the bullets’ size, representing the productive activities, are dimensionally more similar than in the previous network (Fig. 3); that is, the number of connections, which corre-

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Fig. 5. Strength centrality of productive activities classified on the basis of the diversity of occupations and sophistication. Source: Search results.

Fig. 6. Network of Brazilian production structure in 2016 from the sharing of sophisticated occupations. Source: Search results – Gephi 0.9.1 Bastian et al. (2009).

sponds to the nodes’ size, are similar. Thus, the sharing of sophisticated occupations occurs more homogeneously than does the sharing of all occupations. The top sectors of this network are the Industry of Transformation (C), the largest activity in size (connections) and the most central, Public Administration, defense and social security (O), Commerce (G) and Financial Administration, insurance and selected services (K). This last sector, although part of the inner center, is also present in the periphery of the network, as well as Education (P). Table 3 reports the strength and eigenvector centrality of the productive activities’ sharing of sophisticated occupations, as well as the participation in the income of each activity. As already observed for the general case, eigenvector and strength are highly correlated (0.9867). The first fact attracting attention is the share of income from activities with the highest share of sophisticated occupations (27.6231%), which is lower than the other network (32.385%). Disregarding the Public Administration, which alone has 21.0851%, the network with all occupations has 11.2434%, compared to only 6.5381% in the network with only sophisticated occupations. Among the 10 activities with the lowest strength centrality, the combined participation in income is 0.2832% for the first network, rising to only 0.8481% in the network with sophisticated occupations. The activities with the greatest strength centrality are those related to industry, such as manufacture of wearing apparel, except

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Table 3 Strength and Eigenvector centrality: sophisticated occupations. Source: search results - Csardi and Nepusz (2006). Productive activities

Centralities measures

Id CNAE

Name

Strength centrality

Eigenvector centrality

c14126 o84116 g45307 k64221 f41204 g45200 f42928 c31012 f42219 c29492 k64387 j61426 n80307 o84213 h51307 k64239 k64701 o84256 b07251 a01709

Manufacture of wearing apparel, except underwear Public Administration Trade of parts and accessories for motor vehicles Multiple banks with commercial portfolios Building Construction Maintenance and repair of motor vehicles Assembly of industrial plants and metal structures Manufacture of wooden furniture Works for the generation and distribution of electricity and for telecommunications Manufacture of parts and accessories for motor vehicles not classified elsewhere Foreign exchange banks and other institutions of monetary intermediation Pay-TV operators by microwave Private investigation activities Foreign relations Space transport Savings Banks Investment Funds Civil Defense Extraction of radioactive minerals Hunting and related services

205,250,457 122,050,967 110.390.977 109,907,692 83,323,948 79,011,229 75,959,907 73,044,534 70,352,178 65,179,117 1,276,101 1,170,765 1,125,697 819,552 661,280 538,696 331,199 209,691 67,644 8569

1.0000 0.5799 0.5284 0.4895 0.4220 0.3949 0.3876 0.3925 0.3653 0.3424 0.0110 0.0099 0.0093 0.0072 0.0056 0.0040 0.0026 0.0016 0.0004 0.0001

underwear, with 77.99% of sophisticated occupations; manufacture of wooden furniture (77.60%); and manufacturing of parts and motor vehicle accessories (77.22%), with a large part of the occupations related to the main activity. Public and general administration, the second activity that shares most sophisticated occupations, has 94.59% of all types of sophisticated occupations. The most representative occupation in this activity is the preparers and operators of conventional machine tools, with 25.31% of activity representative and 21.40% considering all the economic activities. Public administration is the activity with the highest number of biological scientists (57.61%) and statisticians (53.16%), and a large proportion of surveyors and cartographers (42.56%), biologists and related professionals (38.80%), metrology professionals (33.35%), and production technicians from the chemical, petrochemical, oil refining, gas and related industries (31.09%). Multiple banks with commercial portfolios also figure in activities with greater strength centrality, with only 51 different occupations (19.69%), due to the presence of occupations in general financial services. Fig. 7 shows the 20 occupations classified as sophisticated with the largest share of total employment, which, together, also made up approximately 50% of employment in 2016. The gradation of colors, as in Fig. 4, shows the participation of these occupations in the 670 different productive activities. The sophisticated occupation with the largest number of workers (4.86%) is that of administrative, financial, risk, and related management. These managers occupy 98.66% of productive activities. The same is true for product and sales promotion experts, constituting 4.73% of the workers in sophisticated jobs and occupying 93.29% of the activities. Information technology analysts stand out for occupying at 95.53%, of productive activities, employing 3.85% of workers. At the top of the figure, in occupations with less participation in productive activities, however, even these, are in at least half of the activities, showing different pattern respect to the first network. Table 4 shows the productive activities with the largest and smallest values of flow betweenness, when only sophisticated occupations are considered. The productive activities that stand out are activities linked to the information and communication sector, identifying these last as bridges when only sophisticated activities are considered. Activities with great flow betweenness centrality contain occupations that permeate the network.

Share of income

0.5520% 21.0851% 0,6084% 2.1156% 1.5962% 0.2456% 0.3433% 0.2758% 0.3543% 0.4469% 0.0003% 0.0004% 0.0004% 0.0653% 0.0010% 0.6710% 0.0004% 0.1094% 0.00002% 0.00002%

4.3. Correlation between centrality measures and selected economic indicators Centrality measures can be correlated also with other economic indicators, using Spearman correlation. The economic indicators used are total employment, total monthly income, average monthly income, occupational diversity and the effective diversity of occupation.8 Results are shown in Table 5. As expected, the flow betweenness shows a strong correlation with the strength and eigenvector (approximately 0.99). However, as seen in the previous analysis, two productive activities, cereal cultivation and cattle raising (second and third in the ranking, respectively), stand out in relation to these centralities; thus we focus the analysis on these cases. The flow betweenness centrality reveals the possible ways in which productive activity can flow from one node to another one through the occupations they share, maximizing flow (i.e., maximizing the amount of shared occupations). This is an interesting result, cereal cultivation and livestock farming, considered to be “unsophisticated” in Brazil, exhibit high mechanization and are undergoing a process of significant technological change. Thus, these activities that are part of the network sectors (Fig. 3), associated with low sophistication services, are probably connected to more sophisticated activities and, in turn, to more sophisticated occupations. The totality of jobs is positively correlated to all centrality measures of productive activities. The most intuitive relations are between the totality of jobs and the three measures of centrality of productive activities, which present a positive correlation. This means that the three variables move in the same direction: if the total number of jobs in the economy increases, the connection between productive activities also increases, as they will have more occupations linking them overall. Likewise, a proliferation of the ways in which the flow of occupations can move between activities corresponds to an increase in the total number of jobs.

8 The effective diversity of occupation corrects the diversity of occupation by the participation of each occupation. Thus, if an activity has two different occupations with equal participation (50%), the effective diversity would be 2; however, if the participation of one occupation in this activity is 99% and the other of 1%, the effective diversity becomes 1.058, a value close to one as the participation of an occupation is practically the whole of the representation in this activity.

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289

Fig. 7. Participation of sophisticated occupations in total employment and productive activities. Source: Search results. Table 4 Flow betweenness and participation income: sophisticated occupations. Source: Search results - Csardi and Nepusz (2006). Productive activity

fbi

Id CNAE

Name

Flow betweenness

j62015 n82997 g47814 j62091 j62031 o84256 a01709

Custom computer programs’ development Service activities mainly to companies not otherwise specified Retail sale of clothing and accessories Technical support, maintenance and other information technology services Non-custom computer programs’ development and licensing Civil Defense Hunting and related services

8.3400 8.3400 8.3370 8.3370 8.3370 0.6480 0.0120

The same reasoning can be applied to total income, which shows a positive correlation with centralities and the total employment. Thus, if there is a growth in total employment, the total income also increases, as do the connections and flow between activities. The diversity of occupations also shows a strongly positive correlation with centralities, total jobs, and total income. Interestingly, when the network is built, an increase in diversity is expected to increase the connections and flow between productive activities. The correlation between the total number of jobs and the diversity of occupations is also strongly positive, showing that the higher the amount of employment, the greater the diversity and the income. Interestingly, the average monthly income and the measures of centrality are negatively correlated. The most intuitive interpretation is that the increase in income occurs in occupations that are not present in many productive activities. These occupations do not connect several activities and do not increase the flow. What

Participation income

0.3183% 0.6413% 0.8334% 0.2434% 0.1845% 0.1094% 0.00002%

supports this reasoning is the fact that average monthly income also presents negative correlation with total monthly income and total employment, leading to the conclusion that the increase in employment occurs in low-income activities. The effective diversity of occupations presents a positive, but low correlation with centrality measures and monthly average, as well as a negative relation with the total monthly income. A possible interpretation of this result is that the increase in total employment will not increase the more diversified occupations. In addition, it shows that occupations with greater effective diversity have a higher monthly income. Examples of activities with a large effective diversity of occupations are: rental of machines and equipment not previously specified, with a low share of income (0.09%), and engineering services, with a significant share of income (0.62%). The engineering services are an atypical case, with only 45 workers in 14 different occupations and with high measures of centrality. This would be

290

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Table 5 Spearman rank correlation. Source: Search results. ∗ Correlation coefficients significant at the 1% level or lower.

Strength Centrality Eigenvector Centrality Flow Betweenness Centrality Total Employment Total Monthly Income Average Monthly Income Diversity of Occupations Effective Diversity of Occupations

Strength centrality

Eigenvector centrality

Flow betweenness centrality

Total employment

Total monthly income

Monthly income

Diversity of occupations

Effective diversity of occupations

1 0.9993∗ 0.9977∗ 0.8346∗ 0.7452∗ −0.3355∗ 0.9943∗ 0.2163∗

1 0.9970∗ 0.8309∗ 0.7403∗ −0.3390∗ 0.9934∗ 0.2203∗

1 0.8382∗ 0.7433∗ −0.3506∗ 0.9945∗ 0.2010∗

1 0.9368∗ −0.2902∗ 0.8498∗ −0.1736∗

1 −0.0202 0.7534∗ −0.1068∗

1 −0.3594∗ 0.2981∗

1 0.1887∗

1

the kind of productive activity with the potential to increase the complexity of the productive structure. 5. Conclusions In this paper, we used a network where links are the occupations among productive activities to study the internal organization of the Brazilian productive structure. The idea is that it is easier to move from one productive activity to another if they have a common basis in the type of occupation. Our research moves from the idea that the capacities determine the productive diversification. The findings suggest that, in line with the literature, specialization at the micro-level could contribute to diversification at the macro-level. Consequently, the capabilities of a country are crucial for understanding its development process. Another consequence is that poor countries are not able to build up and employ workers in sophisticated services and, thus, to present a complex productive structure. The analysis of the Brazilian productive structure starts from evaluating the evolution of the Economic Complexity Index. The productive activities at the core of the network are usually of a low level of sophistication, whereas the most sophisticated activities are on the periphery. Analyzing the correlation between the different indicators, we find that the increase in income occurs in occupations that are not in many productive activities, thus not increasing the network connections and the complexity of the productive structure. These results confirm the findings of Cristelli et al. (2013) and, indirectly, those of Hidalgo et al. (2009) and Hidalgo et al. (2007): the Brazilian economy is not very complex and, therefore, has less growth potential. The most central activities in the Brazilian economy are those that are not sophisticated, whereas the sophisticated ones are at the network periphery indicating great difficulty in improving knowledge and technology. The transition from less sophisticated activities to more sophisticated ones can be facilitated through the activities of high flow betweenness centrality between the areas. Increasing the effective diversity of occupations would increase the connection between productive activities and the average income. However, a simple increase in the number of workers would not make a difference, because the results suggest that this increase does not guarantee effective diversity. Therefore, it is imperative for Brazil to rethink its productive structure to remove the obstacles that prevent, or make it difficult, that the varied activities encompass more diversity of occupations. With this, the future production of goods would be facilitated, generating economic development. In more connected activities, most of the job diversification is in unsophisticated services. On the other hand, less connected activities show more sophisticated works. When analyzing only sophisticated occupations, both connections and occupational diversity become more homogeneous. The most connected activities are those with greater participation in income.

Future research developments could be a further investigation of the role of occupations in Brazil, as well as the investigation of the separation between sophisticated and unsophisticated jobs and services. In addition, other definitions of connections between productive activities from occupations could be proposed. A temporal analysis could also be considered, to identify the structural changes that occurred in the productive structure. Appendix A In this Appendix we report some definitions about networks, useful in understanding the methodology applied in the analyses performed in the paper. For a more detailed treatment on networks we refer to Newman (2010). Network description formally refers to graph theory (West, 2001). A graph G is a pair G = (V, E ), composed by a set of n vertices V and a set of m edges E, formed by pairs of vertices. If a vertex admits more than one edge between them, then G is a multigraph. The set of edges E represents the adjacency relation between vertices, thus, if two vertices i and j are adjacent, or neighbors, an edge eij exists in E. The adjacency matrix A = A(G ) of a graph is a square matrix with rows and columns corresponding to the vertices of the graph, where the entry aij represents the number of edges between vertices i and j. A weighted graph has the entry ai j = wi j . Of course, being a multigraph, more than one link eij may occur between two vertices i and j, each with its weight. The degree centrality quantifies the local activity of the vertex in the network. This measure of centrality indicates the number of  links that vertex i has with its adjacents (ki = nk=1 ai j ). From this measure, we can infer the average degree of the network, which is given by k. For weighted graphs the measure also evaluates the weights. This measure is given by:

si =

n 

wi j

(1)

j=1

si is called the strength of the node i. The eigenvector centrality quantifies the connection of a vertex to its neighbors which are themselves central (Bonacich, 1972). Formally, the eigenvector centrality of the node i is defined as the ith component of the principal eigenvector x, that is:

xi = k

n 

ai j x j

(2)

j=1

where x is the eigenvector associated with the largest eigenvalue λ of the adjacency matrix, and k = 1/λ. In view of measuring the importance of a vertex, often it can be interesting to measure how this vertex stands between others on the paths of communication. This can be evaluated using the flow betweenness centrality, which measures the role/position of

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a vertex taking into account the flow of information present in all paths (Freeman et al., 1991). The flow on a graph G is the movement of a quantifiable resource along the edges of G, where the valuation represents how much is being transferred from one vertex to another. The value of the connection between vertices j and z determines the capacity wjz , which is the maximum amount of information that can pass between them. The total flow between pairs of vertices along all possible paths connecting them is what matters in this measure. Freeman et al. (1991) formalized the flow betweenness concept using the idea of the maximum flow of Ford and Fulkerson (1956). The maximum flow between vertices j and z is given by mjz , while mjz (i) is the maximum flow betweenness j and z passing through i. Dividing the flow that passes through i, by the total flow between all pairs of vertices, where i is neither a source nor a sink, we find the proportion of the flow depending on i:

n

f bi =

j
n

m jz (i )

j
m jz

(3)

Definition 3 differs from classical betweenness centrality of a vertex because it considers both geodesic and non-geodesic weighted paths. Appendix B We report here the classification of the activities according to the National Classification of Economic Activities(CNAE). ID

Productive activities

(A) (B) (C) (D) (E) (F) (G) (H) (I) (J) (K) (L) (M) (N) (O) (P) (Q) (R) (S) (T) (U)

Agriculture, livestock, forestry, fishing and aquaculture; Extractive industries Manufacturing Industries Electricity and gas Water, sewage, waste management and decontamination activities Construction Trade, repair of motor vehicles and motorcycles Transport, storage and mail Accommodation and food Information and Communication Financial, insurance and related services activities Real estate activities Professional, scientific and technical activities Administrative activities and complementary services Public administration, defense and social security Education Human health and social services Arts, culture, sport and recreation Other service activities Domestic services International organizations and other extraterritorial institutions

Supplementary material Supplementary material associated with this article can be found, in the online version, at 10.1016/j.strueco.2020.03.005. CRediT authorship contribution statement Mariana Piaia Abreu: Conceptualization, Funding acquisition, Formal analysis, Writing - original draft, Writing - review & editing. Renata R. Del-Vecchio: Conceptualization, Formal analysis, Writing - original draft, Writing - review & editing. Rosanna Grassi: Formal analysis, Writing - original draft, Writing - review & editing.

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