# Dependence of the decay rate of firm activities on firm age

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## Abstract

Using the ORBIS database that contains around 150 million firm-size data from all over the world, we investigated firm activity data in Germany, Spain, France, the United Kingdom, Italy, Japan, Korea, and the Netherlands and found that the decay rate of firm activities does not depend on firm age in Spain as in Japan. But in Germany, France, the United Kingdom, Italy, Korea, and the Netherlands, the decay rate of young firms is high and becomes lower and settles at a constant value as firms age. By approximating the decay rate of firm activities by an exponential function, we analytically derived the firm age distribution under the assumptions that the number of firms that is established annually is nearly constant and that the decay rate of firm activities does not change annually. Using empirical data from eight countries, we compared the parameters estimated by the decay rate of the firm activities with those by firm age distribution. Except in Spain and Germany, the two kinds of parameters estimated in two different ways were close to each other.

## Keywords

Econophysics Firm age distribution Decay rate of firm activity Dr. Jun-ichi Inoue## JEL Classification

D3## Notes

### Acknowledgements

This study was supported by JSPS KAKENHI Grants 24510212 and 24710156.

### Compliance with ethical standards

### Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this article.

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