Measuring systemic importance of banks considering risk interactions: An ANOVA-like decomposition method

The systemic importance of a bank is usually measured by its effect on the banking system, conditional on the insolvency of the bank and solvency of other banks. However, banks encounter different kinds of shocks simultaneously in reality. So that, the conditional results give biased estimates of banks’ systemic importance when potential risks are ignored. Researchers like Tarashev et al. proposed the Shapley value method to deal with risk interactions, but it suffers heavy computational costs. This paper proposes an ANOVA-like decomposition method to measure the systemic importance of banks in more complicated and realistic environments, which considers both interactions and individual effects of multiple shocks and provides a more exact estimation of systemic importance. It is found that the method proposed in this paper fits well in the network models. And meanwhile, a discussion between the method proposed in this paper and the Shapley value method is made based on the numerical example, which aims to demonstrate it’s the advantages. The Shapley value method requires 2n subsystems, while the ANOVA-like decomposition method requires only n+1 model runs. In the application part, the proposed method is adopted to measure the systemic importance of 16 Chinese listed banks. With low computational costs, the model outputs the individual effect, interaction, and total effect of each bank. The results confirm that interactions of different shocks play a significant role in the systemic importance of a bank; thus, the total effect considering interactions should be adopted.