Skip to main content
SpringerLink
Log in
Book cover

Theory of Zipf's Law and Beyond

  • Book
  • © 2010

Overview

Authors:
  1. Alex Saichev

    1. Mathematical Dept., State University of Nizhni Novgorod, Nizhny Novgorod, Russian Federation

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Yannick Malevergne

    1. Inst. Supérieur d'Economie de, Administration et de Gestion (ISEAG), Université St.-Etienne, St.-Etienne CX 2, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Didier Sornette

    1. Dept. Management,, Technologie und Ökonomie, ETH Zürich, Zürich, Switzerland

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 632)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Pages 1-9
    Download chapter PDF

  2. Introduction

    • Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 1-7

  3. Continuous Gibrat’s Law and Gabaix’s Derivation of Zipf’s Law

    • Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 9-18

  4. Flow of Firm Creation

    • Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 19-40

  5. Useful Properties of Realizations of the Geometric Brownian Motion

    • Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 41-57

  6. Exit or “Death” of Firms

    • Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 59-72

  7. Deviations from Gibrat’s Law and Implications for Generalized Zipf’s Laws

    • Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 73-95

  8. Firm’s Sudden Deaths

    • Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 97-122

  9. Non-stationary Mean Birth Rate

    • Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 123-145

  10. Properties of the Realization Dependent Distribution of Firm Sizes

    • Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 147-157

  11. Future Directions and Conclusions

    • Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 159-166

  12. Back Matter

    Pages 1-5
    Download chapter PDF
Back to top

Keywords

About this book

Zipf’s law is one of the few quantitative reproducible regularities found in e- nomics. It states that, for most countries, the size distributions of cities and of rms (with additional examples found in many other scienti c elds) are power laws with a speci c exponent: the number of cities and rms with a size greater thanS is inversely proportional toS. Most explanations start with Gibrat’s law of proportional growth but need to incorporate additional constraints and ingredients introducing deviations from it. Here, we present a general theoretical derivation of Zipf’s law, providing a synthesis and extension of previous approaches. First, we show that combining Gibrat’s law at all rm levels with random processes of rm’s births and deaths yield Zipf’s law under a “balance” condition between a rm’s growth and death rate. We nd that Gibrat’s law of proportionate growth does not need to be strictly satis ed. As long as the volatility of rms’ sizes increase asy- totically proportionally to the size of the rm and that the instantaneous growth rate increases not faster than the volatility, the distribution of rm sizes follows Zipf’s law. This suggests that the occurrence of very large rms in the distri- tion of rm sizes described by Zipf’s law is more a consequence of random growth than systematic returns: in particular, for large rms, volatility must dominate over the instantaneous growth rate.

Authors and Affiliations

  • Mathematical Dept., State University of Nizhni Novgorod, Nizhny Novgorod, Russian Federation

    Alex Saichev

  • Inst. Supérieur d'Economie de, Administration et de Gestion (ISEAG), Université St.-Etienne, St.-Etienne CX 2, France

    Yannick Malevergne

  • Dept. Management,, Technologie und Ökonomie, ETH Zürich, Zürich, Switzerland

    Didier Sornette

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation