Economic complexity: Conceptual grounding of a new metrics for global competitiveness

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Abstract

The availability of data corresponding to the products exported by all countries provides an excellent dataset to test economic ideas and extracts new information about the process of economic development. The matrix of countries and exported products shows a marked triangular structure instead of the block-diagonal structure expected from Ricardian arguments of specialization. This observation points to the fact that diversification is instead the dominant effect in the globalized market. We discuss how to define a suitable non-monetary metrics for the value of diversification and the effective complexity of products. We discuss in detail the previous proposed approaches to assess this challenge and their limitations. We introduce a new approach to the definition of these metrics which seems to overcome the previous problems and we test it in a series of model systems.

Introduction

A recent strand of empirical literature (Hausmann and Rodrik, 2005, Hidalgo and Hausmann, 2009, Tacchella et al., 2012) which has proposed a complexity approach to international trade has emphasized the fact that relatively rich countries, i.e. countries ranking high as far as income per-capita is concerned, are also characterized by high diversification of the portfolio of internationally traded goods and services.

As an example of this observation, we report the binary export matrix country–product for the year 2000 in Fig. 1. By binary we mean that we consider a matrix where it is reported whether or not a country is an exporter of a product without considering export volumes. There exist standard methods to consistently define this binary matrix starting from the raw data of export which are usually expressed in US Dollars, defining thresholds over relative measures (Balassa, 1965, Hidalgo and Hausmann, 2009). The source of the raw data on the export flows is BACI's database (Gaulier and Zignago).

According to the basic Ricardian paradigm of international specialization (Ricardo, 1817), countries should export only few products so that the matrix should be block diagonal. This is far from true in reality as shown in Fig. 1.

This scenario resembles biological systems: for organisms and species, there are evidences that diversification usually gives an evolutionary advantage with respect to specialization. Too specialized species tend to become extinct when global and abrupt changes occur while species relying on a broader set of resources tend to survive. Similarly for countries, diversification of the productive structure may be due to a new type of competitive advantage – we can label this economic fitness – in the present globalized economic playground. In evolutionary terms, the higher the fitness of a country, the higher the probability of a relatively high income (with respect to countries with lower fitness).

Furthermore the triangular shape gives an additional and specific piece of information about the correlation between the composition of the export basket and the kind of products exported by a country. In fact we find that some countries have a large diversification of their production and consequently make almost all products, while scrolling down the rows of the matrix, the number of exported products decreases and countries become more and more specialized on a small subset of products which are exported by almost all countries.

In such a context, the key issue is therefore the quantitative assessment of the competitive advantage deriving from the diversification of a country. In other words we need to develop a quantitative method to answer the question how many times is the most competitive country more complex with respect to the 10th, to the 40th, to the last, given the matrix countries–products?

A first attempt towards a quantitative definition of the level of complexity of the productive system of a country is presented in Hidalgo and Hausmann (2009) where the authors introduce an iterative method aiming at quantifying the competitiveness of countries and the complexity of products. However, we argue that this method suffers from several conceptual, mathematical and economic flaws. In this paper we focus our attention only on conceptual aspects and discuss the main weak points of the method by the authors of Ref. Hidalgo and Hausmann (2009), called Method of Reflections. The economic and mathematical problems deriving from this methods are extensively discussed in Tacchella et al. (2012), Caldarelli et al. (2012) and Cristelli et al. (submitted for publication) where it can be also found the analysis and the results of the new metrics with respect to these two features.

The main reason underlying the failure of the Method of Reflections in correctly measuring the competitiveness of countries from the export matrix M is due to the linear relationship between the country competitiveness and product complexity. Conversely, we argue that a non-linear dependence between these two variables is the fundamental element in order to correctly translate the conceptual framework introduced in Hidalgo and Hausmann (2009) into mathematics. Differently from the Method of Reflections, our metrics defining the country fitness (i.e. competitiveness) and product complexity is the fixed point of two coupled non-linear maps. The non-linear iteration is crucial to bound the complexity of products by the fitness of the less competitive countries exporting them. This non-linear approach is consistent with the triangular shape of the country–product matrix. In this framework the observation that a product is made by a developed country gives a limited information on the complexity of the product itself because these countries export almost all products. On the other hand, when a country with low fitness is able to export a given product, very likely this product requires a low level of complexity. In particular the complexity of a product cannot be defined as the average of the fitnesses of the countries producing it as it happens for the Method of Reflections but must be weighted by the competitiveness of the productive systems of its exporters in a highly non-linear way, so that the information that such a product is produced by some scarcely competitive countries is sufficient to conclude that the complexity of the product is low. Consequently, the only possibility for a product to have a high complexity level is to be produced only by highly competitive countries.

The method represents a new approach for the fundamental assessment of the competitiveness of countries' productive systems and it also introduces a non-monetary measure for product complexity which defines an effective metrics of the value of products filtering out monetary biases such as labor cost, price market speculation, economical inefficiencies of commodities pricing, etc.

The paper is organized in the following way. We briefly discuss the Method of Reflections (Hidalgo and Hausmann, 2009) in Section 2. In Section 3 we discuss the mathematical formulation of the iteration metrics which we propose to be the simplest metrics consistent with the triangular-like pattern of the export matrix and the observation that diversification represents a competitive advantage in a evolutionary system like globalized economies. In Section 4, by three toy models we discuss the conceptual flaws of the method of reflections and why the variables defined in this framework are not a good measure for the competitiveness of countries. In this section we also show that, at least from a conceptual point of view, the metrics correctly grasp the level of competitiveness of countries. In Section 5 conclusions and perspectives are drawn.

Section snippets

The Method of Reflections

The Method of Reflections developed in Hidalgo and Hausmann (2009) introduces two variables. The former, kc, should measure the competitiveness of a country in terms of the diversification of the production while the latter, kp, is a proxy inversely correlated with the complexity of a product. In such a framework, the more a product is ubiquitous, the higher is the kp variable and the lower is the corresponding product complexity. From a mathematical point of view the Method of Reflection is

A new metrics for countries' competitiveness and products' complexity

In this section we propose a novel iterative method which, on one hand, reflects the original spirit of the theory of capabilities (Hidalgo and Hausmann, 2009) and on the other hand does not suffer from the conceptual and mathematical flaws of the Method of Reflections (Hidalgo and Hausmann, 2009).

In order to formulate a novel metrics for country competitiveness and product complexity, we start from the observation on the relation between diversification of countries and ubiquity of products as

Case study

In this section we discuss three simple toy models in order to compare the metrics discussed in this paper for the country complexity with the one in Hidalgo and Hausmann (2009). In fact we aim at testing which metrics is consistent with the conceptual framework of the capabilities. We propose three simple tests in order to:

  • discuss how the variables characterizing the complexity of countries converge to the self-consistent solution for both methods;

  • test whether or not the kc variables and the

Conclusions

In this paper we have discussed a novel method to define a self-consistent and non-monetary metrics for the competitiveness of countries and the complexity of products. Differently from the Method of Reflections (Hidalgo and Hausmann, 2009), this new metrics is able to grasp the level of competitiveness of a country. In order to consistently translate the conceptual framework of economic complexity we use a non-linear algorithm whose fixed point is the metrics for countries' fitness and

Acknowledgments

Authors thank the referees for all the fruitful suggestions and comments. We thank EU FET Open Projects FOC nr. 255987 and the PNR National Project CRISIS-Lab. for support.

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