Non-Gibrat’s Property in the Mid-Scale Range

The distribution of the growth rate does not depend on the initial value in a large-scale range of firm-size variables, such as operating revenues, assets, current profits, and the number of employees. This is called Gibrat’s law. On the other hand, in the mid-scale range of firm-size variables, the growth-rate distribution changes regularly based on the initial value. This idea is referred to as the non-Gibrat’s property in this book. In this chapter we show that when the system is in equilibrium, a log-normal distribution of firm-size variables is derived from the non-Gibrat’s property in the mid-scale range. When the growth-rate distribution is linear on the log–log axis, it is analytically proven that the form of the system’s non-Gibrat’s property at equilibrium is uniquely determined. We then confirm that these properties can be observed with high accuracy in empirical data using the positive current profit data for Japanese firms in 1998 and 1999.