Do Pareto-Zipf and Gibrat laws hold true? An analysis with European firms
Do Pareto-Zipf and Gibrat laws hold true? An analysis with European firms
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DOI：
10.1016/j.physa.2003.12.015
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发表时间：
2004-04-01
影响因子：
3.3
通讯作者：
Souma, W
中科院分区：
文献类型：
--
作者：
Fujiwara, Y;Di Guilmi, C;Souma, W
通过采用详尽的名单，在欧洲国家的大公司，我们表明，上尾的公司规模的分布可以安装与幂律（帕累托-齐普夫定律），并在该地区的增长率，每个公司是独立的公司的规模（Gibrat的比例效应定律）。我们还发现，详细的平衡，我们调查的时期，在大规模的区域，经验概率为一个公司改变其规模从一个值到另一个是统计上相同的，其反向过程。本文证明了帕累托-齐普夫定律、吉卜拉特定律与详细平衡条件之间的若干关系。因此，我们表明，增长率的分布具有一个非平凡的关系之间的积极的一面和消极的一面，通过帕累托指数的值，实证证实。(C)2003 Elsevier B. V.保留所有权利。
By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find that detailed balance holds in the large-size region for periods we investigated; the empirical probability for a firm to change its size from a value to another is statistically the same as that for its reverse process. We prove several relationships among Pareto-Zipf's law, Gibrat's law and the condition of detailed balance. As a consequence, we show that the distribution of growth rate possesses a non-trivial relation between the positive side of the distribution and the negative side, through the value of Pareto index, as is confirmed empirically. (C) 2003 Elsevier B.V. All rights reserved.