Theory of Zipf's Law and Beyond

1. Auflage 2009
ISBN: 978-3-642-02945-5
Verlag: Springer

Buch, Englisch, Band 632, 171 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 590 g

Reihe: Lecture Notes in Economics and Mathematical Systems

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.

Zielgruppe

Research

Autoren/Hrsg.

Saichev, Alexander I.

Malevergne, Yannick

Sornette, Didier

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Geldwirtschaft, Währungspolitik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Geschichte der VWL
• Wirtschaftswissenschaften Wirtschaftswissenschaften Wirtschaftsgeschichte
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Wirtschaftsgeschichte
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftstheorie, Wirtschaftsphilosophie

Inhaltsverzeichnis

Continuous Gibrat#x2019;s Law and Gabaix#x2019;s Derivation of Zipf#x2019;s Law.- Flow of Firm Creation.- Useful Properties of Realizations of the Geometric Brownian Motion.- Exit or #x201C;Death#x201D; of Firms.- Deviations from Gibrat#x2019;s Law and Implications for Generalized Zipf#x2019;s Laws.- Firm#x2019;s Sudden Deaths.- Non-stationary Mean Birth Rate.- Properties of the Realization Dependent Distribution of Firm Sizes.- Future Directions and Conclusions.