Discount Window Policy, Banking Crises, and Indeterminacy of Equilibrium

We examine optimal discount window policy in an economy with a linear investment technology and aggregate liquidity shocks. Unrestricted lending at the discount window prevents large shocks from causing banking crises, but leads to indeterminacy of stationary equilibrium. We show how a policy of offering discount-window loans at an above-market interest rate generates a unique stationary monetary equilibrium. Under such a policy, banking crises occur with positive probability in equilibrium, but a proper choice of interest rate can make the welfare loss due to these crises arbitrarily small. We then modify the model by introducing diminishing returns to investment and show that, in this case, the optimal policy may eliminate banking crises entirely.