Some Distributions Associated with Bose-Einstein Statistics

Ijiri, Yuji; Simon, Herbert A.

doi:10.1073/pnas.72.5.1654

Cited by 70 publications

(22 citation statements)

References 5 publications

(5 reference statements)

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“…Then, new firms are added at rate α, and old products are removed every 1/δ new product assignments. In line with our empirical findings, this model leads to a Pareto distribution of the number of constituent business units [5]. Once captured, each elementary unit is assumed to grow in size following a geometric process which in logs reads ds t = adt + bdW t .…”

Section: Scaling Properties and Proportional Growthmentioning

confidence: 72%

“…Like in [5], each distinguishable arrangement of products at the firm level is assumed to have an equal probability of occurrence. Assignment or loss of business opportunities to firms is modelled by randomly selecting firm i proportionally to the number of its products N i .…”

Section: Scaling Properties and Proportional Growthmentioning

confidence: 99%

“…We introduce a general framework to account for the observed regularities, drawing some general implications on the mechanisms which sustain economic and industrial growth. We show that [1,5] can be extended to account for the shape of size and growth distributions, as well as for scaling relationships at different levels of aggregation. Products are considered as business opportunities which are captured and lost by firms, and then grow in size.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On size and growth of business firms

Fabritiis

Pammolli

Riccaboni

2003

Physica A: Statistical Mechanics and its Applications

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We study size and growth distributions of products and business firms in the context of a given industry. Firm size growth is analyzed in terms of two basic mechanisms, i.e. the increase of the number of new elementary business units and their size growth. We find a power-law relationship between size and the variance of growth rates for both firms and products, with an exponent between -0.17 and -0.15, with a remarkable stability upon aggregation. We then introduce a simple and general model of proportional growth for both the number of firm independent constituent units and their size, which conveys a good representation of the empirical evidences. This general and plausible generative process can account for the observed scaling in a wide variety of economic and industrial systems. Our findings contribute to shed light on the mechanisms that sustain economic growth in terms of the relationships between the size of economic entities and the number and size distribution of their elementary components.

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Section: Scaling Properties and Proportional Growthmentioning

confidence: 72%

Section: Scaling Properties and Proportional Growthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On size and growth of business firms

Fabritiis

Pammolli

Riccaboni

2003

Physica A: Statistical Mechanics and its Applications

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“…We explained in section 4 that non-self-averaging emerges when "size-effects" on probabilities are present. Ijiri andSimon (1975 and1977) present a model in which power-law emerges. The stochastic equilibrium in the macroeconomy must be analyzed by such models in which disturbing forces generate power-law and non-self-averaging.…”

Section: Discussionmentioning

confidence: 99%

The Nature of Equilibrium in Macroeconomics: A Critique of Equilibrium Search Theory

Guilmi

Yoshikawa

2008

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThe standard Walrasian equilibrium theory requires that the marginal value product of production factor such as labor is equal across firms and industries. However, productivity dispersion is widely observed in the real economy. Search theory allegedly fills this gap by encompassing apparent disequilibrium phenomena in the neoclassical equilibrium framework. Taking up Lucas and Prescott (1974) as a primary example, we show that the neoclassical search theory cannot explain the observed pattern of productivity dispersion. Non-self-averaging, a concept little known to economists, plays the major role. Empirical observation suggests strongly the presence of disturbing forces which dominate equilibrating forces due to optimizing behavior of economic agents. We must seek a new concept of equilibrium different from the standard Walrasian equilibrium in macroeconomics.Paper submitted to the special issue "Reconstructing Macroeconomics" (http://www.economics-ejournal.org/special-areas/special-issues) JEL: D50, E50, J64

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“…164-166) can also be used to show that the log-gamma probability density is based on Bose-Einstein statistics and, therefore, satisfies a crucial additivity requirement, something we now briefly develop (Ijiri & Simon, 1975). 15 We have previously noted that −log[x j (h)] is distributed as a gamma variate with parameters and h and so, if the x j (h) are independent, then Freund & Walpole (1987, pp.…”

mentioning

confidence: 97%