Theory of Zipf's law and beyond
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Bibliographic Information
Theory of Zipf's law and beyond
（Lecture notes in economics and mathematical systems, 632）
Springer, c2010
- : pbk
Available at / 37 libraries
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University of Toyama Library, Medical and Pharmaceutical Library図
: pbk331.19||S132t20102000698
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Note
Includes bibliographical references (p. 167-170) and index
Description and Table of Contents
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.
Table of Contents
- 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.
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