Growth and Fluctuations for Small-Business Firms

Yoshi Fujiwara (), Hideaki Aoyama () and Wataru Souma ()
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Yoshi Fujiwara: ATR Network Informatics Laboratories
Hideaki Aoyama: Kyoto University
Wataru Souma: ATR Network Informatics Laboratories

A chapter in Practical Fruits of Econophysics, 2006, pp 291-295 from Springer

Abstract: Summary Small-business firms have qualitatively different characteristics of firm-size growth from those for large firms. Credit Risk Database (CRD) is the largest database of japanese small and midsize companies, which covers nearly 1 million small-business firms, more than 60% of all companies in Japan. By employing stock (total assets and debts) and flow (sales) quantities in the CRD, we show that Gibrat’s law breaks down for the small and midsize companies corresponding to non-power-law region, while the law asymptotically holds in the larger-size region, for all the variables examined. In fact, standard deviation σ of logarithmic growth rate r = log R = log(x 2/x 1) (where x 1 and x 2 are the variable for two successive years) scales as firm size becomes larger (σ ∝ x 1 − β)), but asymptotically approaches non-scaling regime (σ ∼ const). We also show that there is scaling relation of growth rates for different time-scales with which one observes firm-size. Standard deviation σ of growth rate r = log R = log(x t+Δt/x t) from time t and t + Δt scales as σ ∝ (Δt)−γ .

Keywords: company growth; Pareto-Zipf distribution; Gibrat law; scaling relation (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-28915-9_53

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DOI: 10.1007/4-431-28915-1_53

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