ジップの法則とその応用 Theory of Zipf's Law and Beyond (Lecture Notes in Economics and Mathematical Systems)

ジップの法則とその応用<br>Theory of Zipf's Law and Beyond (Lecture Notes in Economics and Mathematical Systems)

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ジップの法則とその応用
Theory of Zipf's Law and Beyond (Lecture Notes in Economics and Mathematical Systems)

Saichev, Alexander/ Malevergne, Yannick/ Sornette, Didier

ウェブストア価格 ¥23,538（本体¥21,399）
Springer（2009/12発売）
外貨定価 US$ 109.99
ポイント 213pt

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製本 Paperback:紙装版/ペーパーバック版／ページ数 171 p.
言語 ENG
商品コード 9783642029455
DDC分類 657

基本説明

Contents - Continuous Gibrat’s Law and Gabaix’s Derivation of Zipf's Law; Flow of Firm Creation; Non-Stationary Mean Birth Rate; etc.

Full Description

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.

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.