Capability accumulation patterns across economic, innovation, and knowledge-production activities.

The evolution of economic and innovation systems at the national scale is shaped by a complex dynamics related to the multi-layer network connecting countries to the activities in which they are proficient. Each layer represents a different domain, related to the production of knowledge and goods: scientific research, technology innovation, industrial production and trade. Nestedness, a footprint of a complex dynamics, emerges as a persistent feature across these multiple kinds of activities (i.e. network layers). We observe that, in the layers of innovation and trade, the competitiveness of countries correlates unambiguously with their diversification, while the science layer shows some peculiar features. The evolution of the scientific domain leads to an increasingly modular structure, in which the most developed countries become relatively less active in the less advanced scientific fields, where emerging countries acquire prominence. This observation is in line with a capability-based view of the evolution of economic systems, but with a slight twist. Indeed, while the accumulation of specific know-how and skills is a fundamental step towards development, resource constraints force countries to acquire competitiveness in the more complex research fields at the expense of more basic, albeit less visible (or more crowded) ones. This tendency towards a relatively specialized basket of capabilities leads to a trade-off between the need to diversify in order to evolve and the need to allocate resources efficiently. Collaborative patterns among developed countries reduce the necessity to be competitive in the less sophisticated research fields, freeing resources for the more complex ones.

Unfolding the innovation system for the development of countries: coevolution of Science, Technology and Production.

We show that the space in which scientific, technological and economic activities interplay with each other can be mathematically shaped using techniques from statistical physics of networks. We build a holistic view of the innovation system as the tri-layered network of interactions among these many activities (scientific publication, patenting, and industrial production in different sectors), also taking into account the possible time delays. Within this construction we can identify which capabilities and prerequisites are needed to be competitive in a given activity, and even measure how much time is needed to transform, for instance, the technological know-how into economic wealth and scientific innovation, being able to make predictions with a very long time horizon. We find empirical evidence that, at the aggregate scale, technology is the best predictor for industrial and scientific production over the upcoming decades.

Coherent diversification in corporate technological portfolios.

We study the relationship between the performance of firms and their technological portfolios using tools borrowed from complexity science. In particular, we ask whether the accumulation of knowledge and capabilities associated with a coherent set of technologies leads firms to experience advantages in terms of productive efficiency. To this end, we analyze both the balance sheets and the patenting activity of about 70 thousand firms that have filed at least one patent over the period 2004-2013. We define a measure of corporate coherent diversification, based on the bipartite network linking companies with the technological fields in which they patent, and relate it to firm performance in terms of labor productivity. Our measure favors technological portfolios that can be decomposed into large blocks of closely related fields over portfolios with the same breadth of scope, but a more scattered diversification structure. We find that the coherent diversification of firms is quantitatively related with their economic performance and captures relevant information about their productive structure. In particular, we prove on a statistical basis that a naive definition of technological diversification can explain labor productivity only as a proxy of size and coherent diversification. This approach can be used to investigate possible synergies within firms and to recommend viable partners for mergers and acquisitions.

Correction: Dynamics in the Fitness-Income plane: Brazilian states vs World countries.

[This corrects the article DOI: 10.1371/journal.pone.0197616.].

Influence of Technological Innovations on Industrial Production: A Motif Analysis on the Multilayer Network.

In this work we aim at identifying combinations of technological advancements that reveal the presence of local capabilities for a given industrial production. To this end, we generated a multilayer network using country-level patent and trade data, and performed motif-based analysis on this network using a statistical-validation approach derived from maximum-entropy arguments. We show that in many cases the signal far exceeds the noise, providing robust evidence of synergies between different technologies that can lead to a competitive advantage in specific markets. Our results can be highly useful for policymakers to inform industrial and innovation policies.

Technology networks: the autocatalytic origins of innovation.

We analyse the autocatalytic structure of technological networks and evaluate its significance for the dynamics of innovation patenting. To this aim, we define a directed network of technological fields based on the International Patents Classification, in which a source node is connected to a receiver node via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random. We show that the evolution of the technology network is compatible with the presence of a growing autocatalytic structure, i.e. a portion of the network in which technological fields mutually benefit from being connected to one another. We further show that technological fields in the core of the autocatalytic set display greater fitness, i.e. they tend to appear in a greater number of patents, thus suggesting the presence of positive spillovers as well as positive reinforcement. Finally, we observe that core shifts take place whereby different groups of technology fields alternate within the autocatalytic structure; this points to the importance of recombinant innovation taking place between close as well as distant fields of the hierarchical classification of technological fields.

Dynamics in the Fitness-Income plane: Brazilian states vs World countries.

In this paper we introduce a novel algorithm, called Exogenous Fitness, to calculate the Fitness of subnational entities and we apply it to the states of Brazil. In the last decade, several indices were introduced to measure the competitiveness of countries by looking at the complexity of their export basket. Tacchella et al (2012) developed a non-monetary metric called Fitness. In this paper, after an overview about Brazil as a whole and the comparison with the other BRIC countries, we introduce a new methodology based on the Fitness algorithm, called Exogenous Fitness. Combining the results with the Gross Domestic Product per capita (GDPp), we look at the dynamics of the Brazilian states in the Fitness-Income plane. Two regimes are distinguishable: one with high predictability and the other with low predictability, showing a deep analogy with the heterogeneous dynamics of the World countries. Furthermore, we compare the ranking of the Brazilian states according to the Exogenous Fitness with the ranking obtained through two other techniques, namely Endogenous Fitness and Economic Complexity Index.

The Role of Complex Analysis in Modelling Economic Growth.

Development and growth are complex and tumultuous processes. Modern economic growth theories identify some key determinants of economic growth. However, the relative importance of the determinants remains unknown, and additional variables may help clarify the directions and dimensions of the interactions. The novel stream of literature on economic complexity goes beyond aggregate measures of productive inputs and considers instead a more granular and structural view of the productive possibilities of countries, i.e., their capabilities. Different endowments of capabilities are crucial ingredients in explaining differences in economic performances. In this paper we employ economic fitness, a measure of productive capabilities obtained through complex network techniques. Focusing on the combined roles of fitness and some more traditional drivers of growth-GDP per capita, capital intensity, employment ratio, life expectancy, human capital and total factor productivity-we build a bridge between economic growth theories and the economic complexity literature. Our findings show that fitness plays a crucial role in fostering economic growth and, when it is included in the analysis, can be either complementary to traditional drivers of growth or can completely overshadow them. Notably, for the most complex countries, which have the most diversified export baskets and the largest endowments of capabilities, fitness is complementary to the chosen growth determinants in enhancing economic growth. The empirical findings are in agreement with neoclassical and endogenous growth theories. By contrast, for countries with intermediate and low capability levels, fitness emerges as the key growth driver. This suggests that economic models should account for capabilities; in fact, describing the technological possibilities of countries solely in terms of their production functions may lead to a misinterpretation of the roles of factors.

A Technology-Based Classification of Firms: Can We Learn Something Looking Beyond Industry Classifications?

In this work we use clustering techniques to identify groups of firms competing in similar technological markets. Our clustering properly highlights technological similarities grouping together firms normally classified in different industrial sectors. Technological development leads to a continuous changing structure of industries and firms. For this reason, we propose a data driven approach to classify firms together allowing for fast adaptation of the classification to the changing technological landscape. In this respect we differentiate from previous taxonomic exercises of industries and innovation which are based on more general common features. In our empirical application, we use patent data as a proxy for the firms' capabilities of developing new solutions in different technological fields. On this basis, we extract what we define a Technologically Driven Classification (TDC). In order to validate the result of our exercise we use information theory to look at the amount of information explained by our clustering and the amount of information shared with an industrial classification. All-in-all, our approach provides a good grouping of firms on the basis of their technological capabilities and represents an attractive option to compare firms in the technological space and better characterise competition in technological markets.

Economic development and wage inequality: A complex system analysis.

Adapting methods from complex system analysis, this paper analyzes the features of the complex relationship between wage inequality and the development and industrialization of a country. Development is understood as a combination of a monetary index, GDP per capita, and a recently introduced measure of a country's economic complexity: Fitness. Initially the paper looks at wage inequality on a global scale, over the time period 1990-2008. Our empirical results show that globally the movement of wage inequality along with the ongoing industrialization of countries has followed a longitudinally persistent pattern comparable to the one theorized by Kuznets in the fifties: countries with an average level of development suffer the highest levels of wage inequality. Next, the study narrows its focus on wage inequality within the United States. By using data on wages and employment in the approximately 3100 US counties over the time interval 1990-2014, it generalizes the Fitness-Complexity metric for geographic units and industrial sectors, and then investigates wage inequality between NAICS industries. The empirical time and scale dependencies are consistent with a relation between wage inequality and development driven by institutional factors comparing countries, and by change in the structural compositions of sectors in a homogeneous institutional environment, such as the counties of the United States.

Complex Economies Have a Lateral Escape from the Poverty Trap.

We analyze the decisive role played by the complexity of economic systems at the onset of the industrialization process of countries over the past 50 years. Our analysis of the input growth dynamics, considering a further dimension through a recently introduced measure of economic complexity, reveals that more differentiated and more complex economies face a lower barrier (in terms of GDP per capita) when starting the transition towards industrialization. As a consequence, we can extend the classical concept of a one-dimensional poverty trap, by introducing a two-dimensional poverty trap: a country will start the industrialization process if it is rich enough (as in neo-classical economic theories), complex enough (using this new dimension and laterally escaping from the poverty trap), or a linear combination of the two. This naturally leads to the proposal of a Complex Index of Relative Development (CIRD) which shows, when analyzed as a function of the growth due to input, a shape of an upside down parabola similar to that expected from the standard economic theories when considering only the GDP per capita dimension.