Lender of last resort policy in a global game and the role of depositors' aggregate behavior as signaling

Recent funding problems experienced by European sovereigns and the subsequent policy actions taken by European authorities have renewed interest in the international Lender of Last Resort (LLR). This paper constructs a global game LLR model applicable to both domestic and international contexts, and revisits Bagehot's classical statements about the LLR. Compared with the existing literature, our model can be characterized by the following assumptions: (1) the (domestic or international) LLR authority is an explicit player whose preference is based on the soundness of its own balance sheet as well as on whether commercial banks fail, (2) the authority cannot distinguish solvency and insolvency of the LLR user ex ante, (3) LLR lending rates are endogenously determined, and (4) the authority's decision making is set after observing depositors' aggregate behaviors. With this setup, we show that: (1) depositors' aggregate behavior of withdrawing their deposits operates as a perfect signal to the LLR authority about solvency, (2) the authority's optimal policy is to help only illiquid but solvent banks, (3) whenever the LLR facility is utilized, optimal lending rates are strictly positive, and (4) this optimal lending rates are punitive in the sense that they take the highest level possible under the restriction that the rates enable solvent but illiquid banks to survive. These results generally support Bagehot's statements as well as historical and current operations of LLR taken by international institutions and central banks.