Firm Growth Function and Extended-Gibrat’s Property
We analytically show that the logarithmic average sales of firms first follow power-law growth and subsequently follow exponential growth, if the growth-rate distributions of the sales obey the extended-Gibrat’s property and Gibrat’s law. Here, the extended-Gibrat’s property and Gibrat’s law are sta...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/9303480 |
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| author | Atushi Ishikawa Shouji Fujimoto Takayuki Mizuno Tsutomu Watanabe |
| author_facet | Atushi Ishikawa Shouji Fujimoto Takayuki Mizuno Tsutomu Watanabe |
| author_sort | Atushi Ishikawa |
| collection | DOAJ |
| description | We analytically show that the logarithmic average sales of firms first follow power-law growth and subsequently follow exponential growth, if the growth-rate distributions of the sales obey the extended-Gibrat’s property and Gibrat’s law. Here, the extended-Gibrat’s property and Gibrat’s law are statistically observed in short-term data, which denote the dependence of the growth-rate distributions on the initial values. In the derivation, we analytically show that the parameter of the extended-Gibrat’s property is identical to the power-law growth exponent and that it also decides the parameter of the exponential growth. By employing around one million bits of exhaustive sales data of Japanese firms in the ORBIS database, we confirmed our analytic results. |
| format | Article |
| id | doaj-art-0c489f5d0edb4212b88884f1e0d38d90 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-0c489f5d0edb4212b88884f1e0d38d902025-02-03T01:28:56ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/93034809303480Firm Growth Function and Extended-Gibrat’s PropertyAtushi Ishikawa0Shouji Fujimoto1Takayuki Mizuno2Tsutomu Watanabe3Kanazawa Gakuin University, 10 Sue, Kanazawa, Ishikawa 920-1392, JapanKanazawa Gakuin University, 10 Sue, Kanazawa, Ishikawa 920-1392, JapanNational Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, JapanGraduate School of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, JapanWe analytically show that the logarithmic average sales of firms first follow power-law growth and subsequently follow exponential growth, if the growth-rate distributions of the sales obey the extended-Gibrat’s property and Gibrat’s law. Here, the extended-Gibrat’s property and Gibrat’s law are statistically observed in short-term data, which denote the dependence of the growth-rate distributions on the initial values. In the derivation, we analytically show that the parameter of the extended-Gibrat’s property is identical to the power-law growth exponent and that it also decides the parameter of the exponential growth. By employing around one million bits of exhaustive sales data of Japanese firms in the ORBIS database, we confirmed our analytic results.http://dx.doi.org/10.1155/2016/9303480 |
| spellingShingle | Atushi Ishikawa Shouji Fujimoto Takayuki Mizuno Tsutomu Watanabe Firm Growth Function and Extended-Gibrat’s Property Advances in Mathematical Physics |
| title | Firm Growth Function and Extended-Gibrat’s Property |
| title_full | Firm Growth Function and Extended-Gibrat’s Property |
| title_fullStr | Firm Growth Function and Extended-Gibrat’s Property |
| title_full_unstemmed | Firm Growth Function and Extended-Gibrat’s Property |
| title_short | Firm Growth Function and Extended-Gibrat’s Property |
| title_sort | firm growth function and extended gibrat s property |
| url | http://dx.doi.org/10.1155/2016/9303480 |
| work_keys_str_mv | AT atushiishikawa firmgrowthfunctionandextendedgibratsproperty AT shoujifujimoto firmgrowthfunctionandextendedgibratsproperty AT takayukimizuno firmgrowthfunctionandextendedgibratsproperty AT tsutomuwatanabe firmgrowthfunctionandextendedgibratsproperty |