Zipf's Law for Firms: Relevance of Birth and Death Processes

27 Pages Posted: 15 Jan 2008 Last revised: 13 Apr 2010

Yannick Malevergne

Université Paris I Panthéon-Sorbonne - Laboratoire PRISM

Alexander I. Saichev

ETH Zurich - D-MTEC (Deceased)

Didier Sornette

Swiss Finance Institute; ETH Zürich - Department of Management, Technology, and Economics (D-MTEC)

Date Written: January 1, 2008

Abstract

Zipf's law states that, for most countries, the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but need to incorporate additional constraints and ingredients introducing deviations from it. We show that combining Gibrat's rule at all firm levels with random processes of firms' births and deaths yield Zipf's law under a "balance" condition between firm growth and their death rate. We predict deviations from Zipf's law under a variety of circumstances, which provides a framework for identifying the possible origin(s) of the many reports of deviations from the pure Zipf's law. Reciprocally, deviations from Zipf's law in a given economy provides a diagnostic, suggesting possible policy corrections.

JEL Classification: G11, G12

Suggested Citation

Malevergne, Yannick and Saichev, Alexander I. and Sornette, Didier, Zipf's Law for Firms: Relevance of Birth and Death Processes (January 1, 2008). Available at SSRN: https://ssrn.com/abstract=1083962 or http://dx.doi.org/10.2139/ssrn.1083962

Yannick Malevergne (Contact Author)

Université Paris I Panthéon-Sorbonne - Laboratoire PRISM ( email )

17 rue de la Sorbonne
Paris, 75005
France

Alexander I. Saichev

ETH Zurich - D-MTEC (Deceased)

Didier Sornette

Swiss Finance Institute ( email )

c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900
Switzerland

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

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