dorsal/arxiv
View SchemaA Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment
| Authors | S. V. Buldyrev, F. Pammolli, M. Riccaboni, K. Yamasaki, D. Fu, K. Matia, H. E. Stanley |
|---|---|
| Categories | |
| ArXiv ID | physics/0609020 |
| URL | https://arxiv.org/abs/physics/0609020 |
| DOI | 10.1140/epjb/e2007-00165-8 |
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 $\phi=2+b/(1-b)$ 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 $\zeta=3$. 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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"abstract": "We present a preferential attachment growth model to obtain the distribution\n$P(K)$ of number of units $K$ in the classes which may represent business firms\nor other socio-economic entities. We found that $P(K)$ is described in its\ncentral part by a power law with an exponent $\\phi=2+b/(1-b)$ which depends on\nthe probability of entry of new classes, $b$. In a particular problem of city\npopulation this distribution is equivalent to the well known Zipf law. In the\nabsence of the new classes entry, the distribution $P(K)$ is exponential. Using\nanalytical form of $P(K)$ and assuming proportional growth for units, we derive\n$P(g)$, the distribution of business firm growth rates. The model predicts that\n$P(g)$ has a Laplacian cusp in the central part and asymptotic power-law tails\nwith an exponent $\\zeta=3$. We test the analytical expressions derived using\nheuristic arguments by simulations. The model might also explain the\nsize-variance relationship of the firm growth rates.",
"arxiv_id": "physics/0609020",
"authors": [
"S. V. Buldyrev",
"F. Pammolli",
"M. Riccaboni",
"K. Yamasaki",
"D. Fu",
"K. Matia",
"H. E. Stanley"
],
"categories": [
"physics.soc-ph",
"physics.data-an",
"q-fin.GN"
],
"doi": "10.1140/epjb/e2007-00165-8",
"title": "A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment",
"url": "https://arxiv.org/abs/physics/0609020"
},
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