A generalized preferential attachment model for
business firms growth rates |
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Authors: | S V Buldyrev F Pammolli M Riccaboni K Yamasaki D-F Fu K Matia H E Stanley |
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Institution: | (1) UNU-MERIT and Maastricht University, Maastricht, The Netherlands;(2) Vlerick Leuven Gent Management School, Catholic University of Leuven, Leuven, Belgium |
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Abstract: | We present a preferential attachment growth model to obtain the
distribution P(K) of number of units K in the classes which may
represent business firms or other socio-economic entities. We found
that P(K) is described in its central part by a power law with an
exponent ϕ = 2+b/(1-b) which depends on the probability of entry of new
classes, b. In a particular problem of city
population this distribution is equivalent to the well known Zipf
law. In the absence of the new classes entry, the
distribution P(K) is exponential.
Using analytical form of P(K) and assuming proportional growth
for units, we derive P(g), the distribution of business firm
growth rates. The model predicts that P(g) has a Laplacian cusp
in the central part and asymptotic power-law tails with an exponent
ζ = 3. We test the analytical expressions derived using
heuristic arguments by simulations. The model might also explain the
size-variance relationship of the firm growth rates. |
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Keywords: | |
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