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

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

Statistical Properties of Demand Fluctuation in the Financial Market

We examine the out-of-equilibrium phase reported by Plerou {\it et. al.} in Nature, {\bf 421}, 130 (2003) using the data of the New York stock market (NYSE) between the years 2001 --2002. We find that the observed two phase phenomenon is an artifact of the definition of the control parameter coupled with the nature of the probability distribution function of the share volume. We reproduce the two phase behavior by a simple simulation demonstrating the absence of any collective phenomenon. We further report some interesting statistical regularities of the demand fluctuation of the financial market.