Do Pareto-Zipf and Gibrat laws hold true? An analysis with European firms

Fujiwara, Y; Di Guilmi, C; Aoyama, H; Gallegati, M; Souma, W

Do Pareto-Zipf and Gibrat laws hold true? An analysis with European firms

Fujiwara, Y Di Guilmi, C

Aoyama, H Gallegati, M Souma, W

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Publication Type:: Journal Article
Citation:: Physica A: Statistical Mechanics and its Applications, 2004, 335 (1-2), pp. 197 - 216
Issue Date:: 2004-04-01

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Field	Value	Language
dc.contributor.author	Fujiwara, Y	en_US
dc.contributor.author	Di Guilmi, C https://orcid.org/0000-0001-7786-039X	en_US
dc.contributor.author	Aoyama, H	en_US
dc.contributor.author	Gallegati, M	en_US
dc.contributor.author	Souma, W	en_US
dc.date.issued	2004-04-01	en_US
dc.identifier.citation	Physica A: Statistical Mechanics and its Applications, 2004, 335 (1-2), pp. 197 - 216	en_US
dc.identifier.issn	0378-4371	en_US
dc.identifier.uri	http://hdl.handle.net/10453/8265
dc.description.abstract	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. © 2003 Elsevier B.V. All rights reserved.	en_US
dc.relation.ispartof	Physica A: Statistical Mechanics and its Applications	en_US
dc.relation.isbasedon	10.1016/j.physa.2003.12.015	en_US
dc.subject.classification	Fluids & Plasmas	en_US
dc.title	Do Pareto-Zipf and Gibrat laws hold true? An analysis with European firms	en_US
dc.type	Journal Article
utslib.citation.volume	1-2	en_US
utslib.citation.volume	335	en_US
utslib.for	0105 Mathematical Physics	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0206 Quantum Physics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Business/Economics Discipline
utslib.copyright.status	closed_access
pubs.issue	1-2	en_US
pubs.publication-status	Published	en_US
pubs.volume	335	en_US

Abstract:

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. © 2003 Elsevier B.V. All rights reserved.

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http://hdl.handle.net/10453/8265