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Economic Complexity

The spirit of Economic Complexity is to look at the interconnected structure that characterizes economy as a whole. Economy is today the most important "Big Data Science" and has to cope with the complexity emerging from this data. Vast multipartite networks connect countries to products, technologies to patents and patents to firms, consumers to producers and is from all these connections that economy gains its complexity. This discipline aims to define new algorithms and metrics to untangle this complexity.

=Background=

One of the major challenges faced by western countries and world economy after the financial crisis of 2007 and the following economic stagnancy is to find new schemes of thinking about the economic growth and innovation.

In this perspective, economic systems can be seen as an ecosystem in a highly changing environment where evolutionary concepts apply. Starting from the competitiveness of economic systems, differently from the standard visions of economic theories, is often not simply a matter of maximizing efficiency but rather the outcome of an adaptive process where all the other players must be considered at the same time. In some extents the country competitiveness represents, borrowing the term from Ecology, the fitness of the country in the globalized and highly interconnected world market. When measuring competitiveness these concepts must be taken into consideration and cannot be neglected to give an effective description of the present world economic playground.

Competing in dynamic and rapidly changing environments calls for a paradigm shift from the mainstream aggregated description of technology development and economic growth towards a novel vision in terms of evolutive process in dynamic and out-of-equilibrium ecosystems of technologies and industrial capabilities as shown in recent studies. The main challenge of this paradigm shift for economic theory consists in developing new metrics, measures, algorithms, methods to turn from qualitative to quantitive the intangibles assets that drive the technological development and country economic growth.

A first attempt in this direction is the Economic Complexity Index (ECI) proposed by Hidalgo and Hausmann. Pietronero and collaborators have recently proposed a different approach    to define a metrics for country competitiveness (country fitness) and product complexity which has several advantages with respect to ECI.

=The metrics for country fitness and product complexity =

General Framework
A novel framework has been proposed by Pietronero and collaborators to measure the competitiveness of the economic system of countries and the complexity of products. These metrics correspond to the measure of intangible information content about country economies and product sophistications and the comparison with monetary figures such as the Gross Domestic Product permits to identify hidden and future potential of growth.

The assessment of these metrics is data-driven and from a conceptual point of view this approach is similar to Google's PageRank: given the properties of the economic network, it introduces metrics to extract new information. In detail the starting point is represented by the empirical observation of a proxy for productive systems: the export country-product matrix. From this picture, diversification, differently from what expected from standard approaches, appears the key point to characterize the competitiveness of countries. In strong analogy with biological systems, in a dynamic and changing environment as the present globalized economy, diversification rather than specialization appears to achieve flexibility and robustness with respect to innovations and rapid changes of competitors and consequently drives the long-term competitiveness and success of countries. The nested structure of the country-product matrix implies that poorly diversified countries tend to produce only those products which are made by almost all countries while only the most diversified ones are able to produce the most exclusive products (see ).

Mathematical definition
From a mathematical point of view the nested structure of the country-product matrix calls for a strongly non-linear and extremal coupling between the level of sophistication of products (hereafter Q, the complexity of products) and the competitiveness of countries (hereafter F, the fitness of countries). Coherently with this observation, the fitness of a country, at each iteration, is simply defined as the diversification weighted by the complexity of products. Concerning the definition of the equations for product complexity two features must be taken into account. On one hand the more ubiquitous is a product, the smaller is its complexity. On the other hand the need of extremal coupling derives from the fact that the complexity of a product must be driven (and bounded) by the fitness of the worst producer.

$$\left\{ \begin{array}{ccc} \tilde{F}_c^{(n)}&=&\sum_pM_{cp}Q_p^{(n-1)}\\\\ \tilde{Q}_p^{(n)}&=&\dfrac{1}{\sum_cM_{cp}\dfrac{1}{F_c^{(n-1)}}} \end{array} \right. \rightarrow \left\{ \begin{array}{ccc} {F}_c^{(n)}=\frac{\tilde{F}_c^{(n)}}{ \langle\tilde{F}_c^{(n)} \rangle_{c} } \\\\ {Q}_p^{(n)}=\frac{\tilde{Q}_p^{(n)}}{ \langle\tilde{Q}_p^{(n)} \rangle_{p} } \end{array} \right.$$

where $$M_{cp}$$ are the elements of the binary country product matrix of export (i.e a country is a relevant exporter of a product -$$M_{cp}=1$$- if the share of the country export basket of that product is larger than the share of the total world export of that product, otherwise $$M_{cp}=0$$). The index (n) refers to the order of the iteration. Therefore, at each iteration, the fitness F is defined as the number of exported product weighted by the product complexity Q of the previous iteration. On the other hand, coherently with the nestedness of the matrix $$M$$, the complexity Q must be related to the fitness F in a non-linear and extremal way. In fact the complexity of a product must be dominated and bounded by the fitness of the worst exporters (i.e lowest fitness). The above formula for the complexity corresponds to the simplest way to implement such dependence. In summary the algorithm combines iteratively successive measures on matrix rows and columns, in a spirit assimilable to Google's PageRank, refining at each iteration the information for F and Q. However, differently from PageRank method the present case deals with a bipartite network (the world wide web instead is a mono-partite network) and the nested structure requires a strongly non-linearity (the PageRank is instead a linear algorithm). The metrics for country fitness and product complexity is defined as the fixed point of this coupled equations which is obtained self-consistently and asymptotically by the iteration of the maps. At each step F and Q are renormalized such that their means are always 1.

The metrics F and Q constitute a new non-monetary and non-income based metrics which measures the level of complexity of a productive system and the level of complexity of a product. Concerning countries, Pietronero and collaborators argue that the Fitness is a measure for those intangible assets which set the level of competitiveness and resilience deriving from the productive capacity of a nation.

Results
These metrics have several advantages:
 * Consistency with the empirical evidence from the export country-product matrix that diversification plays a crucial role in the assessment of the competitiveness of countries. The metrics for countries proposed by Pietronero is indeed extensive with respect to the number of products.
 * Non-linear coupling between fitness and complexity required by the nested structure of the country-product matrix. The nested structure implies that the information on the complexity of a product must be bounded by the producers with the slowest fitness.
 * Broad and Pareto-like distribution of the metrics.
 * Each iteration of the method refines information contents and does not shrink information.

Several economic analyses can be carried out in the framework of this approach.

BRIC analysis
The expression BRIC countries was first used in a report of Goldman Sachs in 2001 and this group is composed of four countries (Brazil, Russia, India and China) which were supposed to dominate the world economy within 2050. BRIC were originally grouped with respect to the similar perspectives of rapid and above world average growth of their Gross Domestic Product (GDP). However, their growth outlooks are nowadays very different. While from a purely GDP-based point of view, the four countries are characterized by an above average growth, a very different picture appears when the evolution of economic competitiveness of their productive system is investigated as measured by the country fitness. In fact, according to this new metrics, a careful analysis of the export of Brazil and Russia would have highlighted the structural differences of the development path of Brazil and Russia with respect to India and China few years after the Goldman Sachs' report.

The most valuable information deriving from the fitness analysis is the evolution of the Brazilian competitiveness because of a very different behavior with respect to the monetary information. Brazil’s competitiveness shows a behavior similar to Russia’s one. This metrics points out that Brazil is not increasing the complexity of its productive systems, it is mainly fueling its growth through raw material and in general export of primary product. More accurate analyses by means of country spectroscopy confirm that Brazil is getting more and more dependent on primary products and reducing the average complexity of its productive systems. The comparison of the country spectroscopies for the four BRIC countries visually reveals the strong structural differences of the economic systems of these countries.

Application
Both metrics have been proposed to measure the hidden potential of growth of countries, the technological value of products out of monetary effects and to uncover medium-long term investment opportunities, especially in frontier and emerging markets.

The metrics for country fitness and product complexity have been used in a report of the Boston Consulting Group on Sweden growth and development perspectives.

= See also =
 * Complexity economics
 * Complexity
 * Economic Complexity Index (ECI)
 * Agent-based computational economics

= References =