DebtRank Analysis of Financial Distress Propagation on a Production Network in Japan

Supplier-customer relationship among firms in a production network is the arena where financial distress propagates from distressed debtors of customers to their creditors of suppliers. While the events of bankruptcies can be observed easily, the underlying contagion effect of financial distress can have considerable consequences such as a chain of bankruptcies. DebtRank is a model to quantify the propagation of financial distress, which has been applied recently for analyzing and evaluating systemic risk for interbank contagion. Because the production network in Japan, which comprises more than one million firms as nodes and millions of supplier-customer relationship as links, is much larger than the interbank credit network, it has been a formidable task to study the model of DebtRank on such a large-scale production network. This work studies the financial distress propagation on the real data of a production network by employing an implementation of DebtRank on a supercomputer. We found that the DebtRank of individual firms has a significant correlation with firm-size with non-linearity, indicating that the DebtRank for big firms becomes much larger than what is expected naively. The analysis for individual sectors shows that, depending on the sector's position in the upstream and downstream, its DebtRank deviates from a linear relationship between DebtRank and sector size. In addition, one can measure vulnerability by using the DebtRank analysis, which is potentially useful to identify the likelihood of failures of firms in more vulnerable sectors.