Macroscopic Structure and Evolution in the Japanese Production Network

We investigate the Japanese production network at firm-level, using the dataset of financial statements and supplier-customer relationship for one million firms in Japan collected by Tokyo Shoko Research Inc. from 2011 to 2016. Chakraborty et al. (2018) reported that the Japanese production network has a tightly-knit structure with a giant strongly connected component (GSCC) core surrounded by its upstream (IN) and downstream (OUT) components constituting two half shells. In this paper, we analyze its macroscopic structure and evolution. Generally, larger firms obey a power-law in size distribution (Pareto's law) and have a property that the variance in their growth rates does not depend on their size, (Gibrat's law). We focus on the relationship between the macroscopic network structure and firm size and growth rate measured by sales. Major results of this study are as follows. First, the firms obeying Pareto's law are mainly composed of GSCC, and the firms within the IN component tend to be smaller than the firms in the other components. Second, although about half of supplier-customer links are disrupted or reformed from 2011 to 2016, Japan's production network has stable firms that do not move between components of macroscopic structure. Third, we can observe Gibrat's law for such stable firms for each component, but the applicable region of firms located in the IN component is extremely small compared to the other components. The results obtained suggest that the macro hierarchy and stability of Japan's production network helps characterize the stability of firm growth.