Ranking the economic importance of countries and industries

In the current era of worldwide market interdependencies, the global financial village has become increasingly vulnerable to systemic collapse. The global financial crisis has highlighted the necessity of understanding and quantifying the interdependencies among the world’s economies; developing new, effective approaches for risk evaluation; and providing mitigating solutions. We present a methodological framework for quantifying interdependencies in the global market and for evaluating risk levels in the worldwide financial network. The resulting information will enable policy and decision makers to better measure, understand and maintain financial stability. We use this methodology to rank the economic importance of each industry and country according to the global damage that would result from its failure. Our quantitative results shed new light on China’s increasing economic dominance over other economies, including that of the United States, as well as the global economy

The Growth of Business Firms: Theoretical Framework and Empirical Evidence

We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that the distribution is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. In this article, we test the model at different levels of aggregation in the economy, from products to firms to countries, and we find that the model's predictions agree with empirical growth distributions and size-variance relationships.Comment: 22 pages, 5 Postscript figures, uses revtex4. to be published in Proc. Natl. Acad. Sci. (2005

A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence

We introduce a model of proportional growth to explain the distribution $P(g)$ of business firm growth rates. The model predicts that $P(g)$ is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent $\zeta=3$. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. We test the model at different levels of aggregation in the economy, from products, to firms, to countries, and we find that the its predictions are in good agreement with empirical evidence on both growth distributions and size-variance relationships.Comment: 8 pages, 4 figure

A Generalized Preferential Attachment Model for Complex Systems

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. We investigate how the distribution depends on the initial conditions and changes from a pure exponential form for zero influx of new classes to a power law with an exponential cutoff form when the influx of new classes is substantial. We apply the model to study the growth dynamics of pharmaceutical industry.Comment: submitted to PR

A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence

We introduce a model of proportional growth to explain the distribution P(g) of business firm growth rates. The model predicts that P(g) is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent ζ = 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. We test the model at different levels of aggregation in the economy, from products, to firms, to countries, and we find that the its predictions are in good agreement with empirical evidence on both growth distributions and size-variance relationships.Gibrat Law; Firm Growth; Size Distribution

Preferential attachment and growth dynamics in complex systems

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. According to the model, the distribution changes from a pure exponential form for zero influx of new classes to a power law with an exponential cut-off form when the influx of new classes is substantial. Predictions of the model are tested through the analysis of a unique industrial database, which covers both elementary units (products) and classes (markets, firms) in a given industry (pharmaceuticals), covering the entire size distribution. The model’s predictions are in good agreement with the data. The paper sheds light on the emergence of the exponent τ ≈ 2 observed as a universal feature of many biological, social and economic problems.Firm Growth; Pareto Distribution; Pharmaceutical Industry

A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment

We present a preferential attachment growth model to obtain the distribution P(K) of number of units K in the classes which may represent business firms or other socio-economic entities. We found that P(K) is described in its central part by a power law with an exponent φ = 2+b/(1−b) which depends on the probability of entry of new classes, b. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution P(K) is exponential. Using analytical form of P(K) and assuming proportional growth for units, we derive P(g), the distribution of business firm growth rates. The model predicts that P(g) has a Laplacian cusp in the central part and asymptotic power-law tails with an exponent ζ = 3. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the size-variance relationship of the firm growth rates.firm growth, size distribution, Gibrat law, Zipf law

Scaling and memory of intraday volatility return intervals in stock market

We study the return interval $\tau$ between price volatilities that are above a certain threshold $q$ for 31 intraday datasets, including the Standard & Poor's 500 index and the 30 stocks that form the Dow Jones Industrial index. For different threshold $q$, the probability density function $P_q(\tau)$ scales with the mean interval $\bar{\tau}$ as $P_q(\tau)={\bar{\tau}}^{-1}f(\tau/\bar{\tau})$, similar to that found in daily volatilities. Since the intraday records have significantly more data points compared to the daily records, we could probe for much higher thresholds $q$ and still obtain good statistics. We find that the scaling function $f(x)$ is consistent for all 31 intraday datasets in various time resolutions, and the function is well approximated by the stretched exponential, $f(x)\sim e^{-a x^\gamma}$, with $\gamma=0.38\pm 0.05$ and $a=3.9\pm 0.5$, which indicates the existence of correlations. We analyze the conditional probability distribution $P_q(\tau|\tau_0)$ for $\tau$ following a certain interval $\tau_0$, and find $P_q(\tau|\tau_0)$ depends on $\tau_0$, which demonstrates memory in intraday return intervals. Also, we find that the mean conditional interval $$ increases with $\tau_0$, consistent with the memory found for $P_q(\tau|\tau_0)$. Moreover, we find that return interval records have long term correlations with correlation exponents similar to that of volatility records.Comment: 19 pages, 8 figure