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Identifier to cite or link to this item: https://hdl.handle.net/10086/19295

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Title
Emergence of power laws with different power-law exponents from reversal quasi-symmetry and Gibrat’s law
Creator
Creator Name
Ishikawa, Atushi Ishikawa, Atushi
石川, 温 石川, 温
イシカワ, アツシ イシカワ, アツシ
Affiliation
Affiliation Name
Kanazawa Gakuin University
Creator Name
Fujimoto, Shoji Fujimoto, Shoji
藤本, 祥二 藤本, 祥二
フジモト, ショウジ フジモト, ショウジ
Affiliation
Affiliation Name
Kanazawa Gakuin University
Creator Name
Watanabe, Tsutomu Watanabe, Tsutomu
渡辺, 努 渡辺, 努
ワタナベ, ツトム ワタナベ, ツトム
Affiliation
Affiliation Name
University of Tokyo
Creator Name
Mizuno, Takayuki Mizuno, Takayuki
水野, 貴之 水野, 貴之
ミズノ, タカユキ ミズノ, タカユキ
Affiliation
Affiliation Name
University of Tsukuba
Editor
Contributor Name
持続的成長を可能にする産業・金融ネットワークの設計 = Design of industry and financial network where sustained growth is enabled
Contributor Name
Institute of Economic Research, Hitotsubashi University
Affiliation
Affiliation Name
Hitotsubashi University
Abstract
To explore the emergence of power laws in social and economic phenomena, the authors discuss the mechanism whereby reversal quasi-symmetry and Gibrat’s law lead to power laws with different powerlaw exponents. Reversal quasi-symmetry is invariance under the exchange of variables in the joint PDF (probability density function). Gibrat’s law means that the conditional PDF of the exchange rate of variables does not depend on the initial value. By employing empirical worldwide data for firm size, from categories such as plant assets K, the number of employees L, and sales Y in the same year, reversal quasi-symmetry, Gibrat’s laws, and power-law distributions were observed. We note that relations between power-law exponents and the parameter of reversal quasi-symmetry in the same year were first confirmed. Reversal quasi-symmetry not only of two variables but also of three variables was considered. The authors claim the following. There is a plane in 3-dimensional space (log K, log L, log Y ) with respect to which the joint PDF PJ (K,L, Y ) is invariant under the exchange of variables. The plane accurately fits empirical data (K,L, Y ) that follow power-law distributions. This plane is known as the Cobb-Douglas production function, Y = AKαLβ which is frequently hypothesized in economics.
Publisher
Institute of Economic Research, Hitotsubashi University
Issued Date
2011-08
Language
English(eng)
Resource Type
technical report
Version Type
VoR
Is Part OfRelation -
Related Title
IFN Working Paper ; No. 9
Relation
Related Identifier
URI
  http://www.ier.hit-u.ac.jp/ifn/
Number of Pages
8
Sponsorship
近未来の課題解決を目指した実証的社会科学推進事業
Appears in Collections
Working Paper Series / Design of industry and financial network where sustained growth is enabled
URL
https://hdl.handle.net/10086/19295