The Lender Of Last Resort Model Of Imperfect Information

Most of the literature on bank runs takes the asset side of the bank activities as given and assumes that the bank's returns are determined by an exogenously given production function. The model of bank runs in this paper lets entrepreneurial sector endogened and gives a clear picture of where the bank's return comes from by using general equilibrium method, and shows how liquidity shock is transmitted from the entrepreneurial sector to the depositors via the banking system. This model shows that there exists a one to one mapping from the depositors'equilibrium strategy to an optimal contract prevailing in the economy. When there is no LOLR and the depositors have perfect information regarding the fundamentals of the bank, there exist multiple equilibria in depositors'strategies, where either everyone runs or no one runs. However, when the depositors have imperfect information regarding the fundamentals of the bank, the depositors who receive a signal below threshold will run, so there is a unique equilibrium in the depositors'strategy. Thus perfect information can actually be destablising relative to a small amount of noise. When there exist imperfectly informed LOLR, the economy can come back to the optimal level where no bank runs exist. In this case, LOLR is Pareto improvement in evidence. But when LOLR have imperfect information regarding the fundamentals of the bank, the conclusion that LOLR is Pareto improvement falls into ambiguity. On the one hand, LOLR is productive ex post as it can avoid inefficient liquidation. On the other hand, the presence of an imperfectly informed LOLR is conductive to the moral hazard problem, So it is ex ante inefficiency. This paper shows that the probability of insolvency of the banking system actually increases in the presence of the LOLR. This paper quantifies the expected costs of inefficientcy and benefits of efficiency. This paper shows that at enough low noise levels the benefits will outweigh the costs, so an imperfectly informed LOLR is Pareto improvement. The policy implication that stems from our model is that the banking system be as transparent as possible to the LOLR.