We model banks’ liquidity holding decision as a simultaneous game on an interbank borrowing network. We show that at the Nash equilibrium, the contributions of each bank to the network liquidity level and liquidity risk are distinct functions of its indegree and outdegree Katz-Bonacich centrality measures. A wedge between the planner and the market equilibria arises because individual banks do not internalize the effect of their liquidity choice on other banks’ liquidity benefit and risk exposure. The network can act as an absorbent or a multiplier of individual banks’ shocks. Using a sterling interbank network database from January 2006 to September 2010, we estimate the model in a spatial error framework, and find evidence for a substantial, and time varying, network risk: in the period before the Lehman crisis, the network is cohesive and liquidity holding decisions are complementary and there is a large network liquidity multiplier; during the 2007-08 crisis, the network becomes less clustered and liquidity holding less dependent on the network; after the crisis, during Quantitative Easing, the network liquidity multiplier becomes negative, implying a lower network potential for generating liquidity. The network impulse-response functions indicate that the risk key players during these periods vary, and are not necessarily the largest borrowers.
Also included in: AXA Working Paper 12