This paper addresses the question of what the central bank should do when the economy is hit by a large-scale negative demand shock and continues to be weak even after the short-term nominal interest rate reaches its lower bound. We solve the central bank's dynamic optimization problem with special attention to the non-negativity constraint on nominal interest rates, and find that the optimal policy is characterized by history-dependence : the central bank should make a commitment of keeping the short-term interest rate at zero until the accumulated sum of the output gap and the inflation rate in each period reaches a threshold level. We also find that the Bank of Japan's zero interest rate policy shares some characteristics of the optimal policy, including the Governor's announcement that the monetary policy board would keep the overnight interest rate at zero until "deflationary concerns are dispelled," but differs from it in the BOJ policy lacks history-dependence.
