Shape of Growth Rate Distribution Determines the Type of Non-Gibrat's Property

Atushi Ishikawa, 温 石川, アツシ イシカワ, Shouji Fujimoto, 祥二 藤本, ショウジ フジモト, Takayuki Mizuno, 貴之 水野 and タカユキ ミズノ

No 1_v2, Working Paper Series from Center for Interfirm Network, Institute of Economic Research, Hitotsubashi University

Abstract: In this study, the authors examine exhaustive business data on Japanese firms, which cover nearly all companies in the mid- and large-scale ranges in terms of firm size, to reach several key findings on profits/sales distribution and business growth trends. First, detailed balance is observed not only in profits data but also in sales data. Furthermore, the growth-rate distribution of sales has wider tails than the linear growth-rate distribution of profits in log-log scale. On the one hand, in the mid-scale range of profits, the probability of positive growth decreases and the probability of negative growth increases symmetrically as the initial value increases. This is called Non-Gibrat's First Property. On the other hand, in the mid-scale range of sales, the probability of positive growth decreases as the initial value increases, while the probability of negative growth hardly changes. This is called Non-Gibrat's Second Property. Under detailed balance, Non-Gibrat's First and Second Properties are analytically derived from the linear and quadratic growth-rate distributions in log-log scale, respectively. In both cases, the log-normal distribution is inferred from Non-Gibrat's Properties and detailed balance. These analytic results are verified by empirical data. Consequently, this clarifies the notion that the difference in shapes between growth-rate distributions of sales and profits is closely related to the difference between the two Non-Gibrat's Properties in the mid-scale range.

Pages: 24 pages
Date: 2010-06-05
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