Financial Network Formation and Central Bank Policy

Abstract

Policy makers have long been concerned about the risk of a singular financial event destabilizing the financial system and causing a negative impact on real economic growth. There is a substantial literature focused on understanding the market microstructure of financial markets to gain insights into the development of financial crisis and contagion. In our paper, we address the important issue of how policy makers can promote financial network stability and social efficiency. By incorporating the literature of social and economic networks, the contribution of this paper is threefold. First, we incorporate a benevolent central bank (CB) as a social-welfare-maximizing actor in the financial network formation. The CB is in the center of a star shaped network and plays an important role by setting policy variables to facilitate the formation of a stable and efficient financial network. Second, we characterize how financial institutions choose to become member-banks (MB), bank-holding company subsidiaries (BHC), and non-banks (NB) in an endogenous process of financial network formation. Third, by incorporating the cost of unilaterally breaking up a link, we show that the risk-sharing financial network based on the ex ante agreements of the MBs and BHCs is stable and can lower the investment risks of all the members of the network. In our model, network formation is a three-stage game. In the first stage, financial institutions form links with the central bank to become the MBs. In the second stage, other financial institutions can continue to become MBs, BHCs or NBs. In the third stage, the capital shocks are realized and MBs and BHCs have to share the risk according to the ex ante risk sharing contract. We focus on the analysis of the ex ante network, and develop the necessary and sufficient conditions for endogenous network formation. We provide a characterization of the structure of stable networks where before realizing any shocks, no financial institution has any incentive to change position. Because there is no guarantee that the sufficient conditions can be satisfied such that the equilibrium network coincides with the socially optimum network, the CB has a crucial role in developing a best-possible financial network.