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Growth and Fluctuations for Small-Business Firms

In: Practical Fruits of Econophysics

Author

Listed:
  • Yoshi Fujiwara

    (ATR Network Informatics Laboratories)

  • Hideaki Aoyama

    (Kyoto University)

  • Wataru Souma

    (ATR Network Informatics Laboratories)

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 .

Suggested Citation

  • Yoshi Fujiwara & Hideaki Aoyama & Wataru Souma, 2006. "Growth and Fluctuations for Small-Business Firms," Springer Books, in: Hideki Takayasu (ed.), Practical Fruits of Econophysics, pages 291-295, Springer.
    • Handle: RePEc:spr:sprchp:978-4-431-28915-9_53
    DOI: 10.1007/4-431-28915-1_53
    as

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