The relation between firm age distributions and the decay rate of firm activities in the united states and Japan

In this study, we investigated firm activity data in 2008 and 2014 in the United States and Japan. We reconfirmed that the decay rate of firm activity does not depend on firm age in Japan. This is consistent with the observation that firm age distribution follows an exponential function in Japan. At the same time, in the United States, we found that the decay rate of young firms is high and it becomes lower and settle a constant value as firms age. From these observations, we proposed the model that follows the property observed in the decay rate of firm activity. The constant decay rate in Japan is included as a particular case in this model. The model analytically leads to firm age distribution, the young firm in which deviates from an exponential function. This analytical feature is observed in empirical data in the United States. We confirmed the consistency of this analysis comparing parameters estimated from the decay rate with those from firm age distribution.