Theory of Zipf's Law and Beyond (Lecture Notes in Economics

Theory of Zipf's Law and Beyond (Lecture Notes in Economics and Mathematical Systems, 632)

Zipfâ‚¬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 Gibratâ‚¬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 Zipfâ‚¬s law, providing a synthesis and extension of previous approaches. First, we show that combining Gibratâ‚¬s law at all rm levels with random processes of rmâ‚¬s births and deaths yield Zipfâ‚¬s law under a â‚¬Å“balanceâ‚¬Â condition between a rmâ‚¬s growth and death rate. We nd that Gibratâ‚¬s law of proportionate growth does not need to be strictly satis ed. As long as the volatility of rmsâ‚¬ 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 Zipfâ‚¬s law. This suggests that the occurrence of very large rms in the distri- tion of rm sizes described by Zipfâ‚¬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.
Country USA
Brand Springer
Manufacturer Springer
Binding Paperback
ItemPartNumber 44 black & white illustrations, 44 black
ReleaseDate 2009-11-17
UnitCount 1
EANs 9783642029455

Country	USA
Brand	Springer
Manufacturer	Springer
Binding	Paperback
ItemPartNumber	44 black & white illustrations, 44 black
ReleaseDate	2009-11-17
UnitCount	1
EANs	9783642029455

Theory of Zipf's Law and Beyond (Lecture Notes in Economics and Mathematical Systems, 632)

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