Andrea Zaccaria

On the convergence of the Fitness-Complexity Algorithm

Abstract We investigate the convergence properties of an algorithm which has been recently proposed to measure the competitiveness of countries and the quality of their exported products. These quantities are called respectively Fitness F and Complexity Q. The algorithm was originally based on the adjacency matrix M of the bipartite network connecting countries with the products they export, but can be applied to any bipartite network. The structure of the adjacency matrix turns to be essential to determine which countries and products converge to non zero values of F and Q. Also the speed of convergence to zero depends on the matrix structure. A major role is played by the shape of the ordered matrix and, in particular, only those matrices whose diagonal does not cross the empty part are guaranteed to have non zero values as outputs when the algorithm reaches the fixed point. We prove this result analytically for simplified structures of the matrix, and numerically for real cases. Finally, we propose some practical indications to take into account our results when the algorithm is applied.

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.

The complex dynamics of products and its asymptotic properties

We analyse global export data within the Economic Complexity framework. We couple the new economic dimension Complexity, which captures how sophisticated products are, with an index called logPRODY, a measure of the income of the respective exporters. Products’ aggregate motion is treated as a 2-dimensional dynamical system in the Complexity-logPRODY plane. We find that this motion can be explained by a quantitative model involving the competition on the markets, that can be mapped as a scalar field on the Complexity-logPRODY plane and acts in a way akin to a potential. This explains the movement of products towards areas of the plane in which the competition is higher. We analyse market composition in more detail, finding that for most products it tends, over time, to a characteristic configuration, which depends on the Complexity of the products. This market configuration, which we called asymptotic, is characterized by higher levels of competition.

How log-normal is your country? An analysis of the statistical distribution of the exported volumes of products

Abstract We have considered the statistical distributions of the volumes of 1131 products exported by 148 countries. We have found that the form of these distributions is not unique but heavily depends on the level of development of the nation, as expressed by macroeconomic indicators like GDP, GDP per capita, total export and a recently introduced measure for countries’ economic complexity called fitness. We have identified three major classes: a) an incomplete log-normal shape, truncated on the left side, for the less developed countries, b) a complete log-normal, with a wider range of volumes, for nations characterized by intermediate economy, and c) a strongly asymmetric shape for countries with a high degree of development. Finally, the log-normality hypothesis has been checked for the distributions of all the 148 countries through different tests, Kolmogorov-Smirnov and Cramér-Von Mises, confirming that it cannot be rejected only for the countries of intermediate economy.

Liquidity crises on different time scales.

We present an empirical analysis of the microstructure of financial markets and, in particular, of the static and dynamic properties of liquidity. We find that on relatively large time scales (15 min) large price fluctuations are connected to the failure of the subtle mechanism of compensation between the flows of market and limit orders: in other words, the missed revelation of the latent order book breaks the dynamical equilibrium between the flows, triggering the large price jumps. On smaller time scales (30 s), instead, the static depletion of the limit order book is an indicator of an intrinsic fragility of the system, which is related to a strongly nonlinear enhancement of the response. In order to quantify this phenomenon we introduce a measure of the liquidity imbalance present in the book and we show that it is correlated to both the sign and the magnitude of the next price movement. These findings provide a quantitative definition of the effective liquidity, which proves to be strongly dependent on the considered time scales.

Integrating services in the economic fitness approach

Economic Complexity is a set of network-based and algorithmic methods for the study of economic development and competitiveness. In this framework, Economic Fitness is an innovative approach that improves the mathematical and conceptual scheme. For convenience, these methods were originally conceived on trade in goods. This paper extends the Economic Fitness methodology to include a trade in services element to yield a universal matrix of world trade and thus provide a more complete picture of a countrys development and global competitiveness. The paper applies two algorithms to the universal trade in goods and services matrix to contrast country competitiveness and change in complexity and diversification when services are added to the traditional goods-only matrix. The results show that (i) the competitiveness of many countries was previously over- or underestimated, that is, many countries gain or lose positions in the ranking of economic fitness when services trade is considered alongside goods; and (ii) complex services tend to cluster with complex manufacturing, suggesting a common capabilities structure. These findings show how developing complex services aids diversification strategies for developing countries.

Correction: The complex dynamics of products and its asymptotic properties

[This corrects the article DOI: 10.1371/journal.pone.0177360.].

Reaction to Extreme Events in a Minimal Agent Based Model

We consider the issue of the overreaction of financial markets to a sudden price change. In particular, we focus on the price and the population dynamics which follows a large fluctuation. In order to investigate these aspects from different perspectives we discuss the known results for empirical data, the Lux-Marchesi model and a minimal agent based model which we have recently proposed. We show that, in this framework, the presence of a overreaction is deeply linked to the population dynamics. In particular, the presence of a destabilizing strategy in the market is a necessary condition to have an overshoot with respect to the exogenously induced price fluctuation. Finally, we analyze how the memory of the agents can quantitatively affect this behavior.

TIME EVOLUTION OF FINANCIAL CROSS-CORRELATION COEFFICIENTS ACROSS MARKET CRISIS

We investigate the time evolution of financial cross-correlation coefficients during financial crises and compare them to what is observed in periods of stability. We choose three main events, the Dot.Com Bubble, the market crisis which followed the attacks at the Twin Towers in 2001 and the recent subprime crisis. Each of them has a different nature and a different impact on the market, which we analyze by studying separately different economic sectors. As a general trend, we observe an increase of correlation during these high volatility periods and a broadening of the distributions of correlation coefficients. We then compare the spectra of the cross-correlation matrices, calculated in different periods of three years, with the distribution of eigenvalues predicted by the Random Matrix Theory. We find that these spectra are markedly perturbated during crisis periods. Finally we show how a simple stochastic model can produce similar results.