Abstract
In this study, we observe the dependence of the inactive rate of firms on firm-size variables: total revenue, net income, total assets, and net assets. This is achieved using information on nearly all firms in Japan, Germany, Spain, France, the United Kingdom, Italy, Korea, and the Netherlands recorded in the Orbis database in 2015 and 2016. Here, the inactive rate means the transition rate of firms from an active state to an inactive state. First, we confirm that the financial variables in this database follow power laws in the range of large-scale data values but follow log-normal distributions in the range of mid-scale data values. Furthermore, we observe that the inactive rate of firms is constant regardless of the firm-size variables in the large-scale data range. Meanwhile, the inactive rate increases under a power-law function as financial variables decrease in the mid-scale data range. We also find that the boundary between the large- and mid-scale data ranges of the inactive rate of firms corresponds to the boundary between the power-law and log-normal distributions of the financial variables.
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Notes
Not only in Japan but also in other countries studied here, it was not clearly observed that the inactive rate of firms takes a constant value regardless of net income or net assets in the large-scale data range of the negative value. This is probably because data of the negative value is not necessarily exhaustive. In Italy, compared to other countries studied in this paper, it is thought that coverage of data of negative values was high.
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Acknowledgements
The authors thank the Yukawa Institute for Theoretical Physics (YITP) at Kyoto University. Discussions during the YITP workshop (YITP-W-17-14) on “Econo-physics 2017” provided a useful reference in completing this work.
Funding
This study was supported by JSPS KAKENHI Grant numbers 17K01277, 16H05904, and 18H03629, as well as funding for open collaborative research at the National Institute of Informatics (NII), Japan (FY2017).
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Ishikawa, A., Fujimoto, S. & Mizuno, T. Statistical law observed in inactive rate of firms. Evolut Inst Econ Rev 16, 201–212 (2019). https://doi.org/10.1007/s40844-018-0119-4
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DOI: https://doi.org/10.1007/s40844-018-0119-4