Minimizing social welfare loss is one of the most important topics in monetary policy. In a standard forward-looking New Keynesian model, a central bank minimizes the quadratic terms of inflation rate and output gap. 1 In terms of minimizing social welfare losses, it has been pointed out that optimal precommitment under a timeless perspective is effective.However, when central banks in the actual world are considered, several problems arise in monetary policy design. First, the precommitment is difficult to implement, because it requires a central bank to be extremely patient. This leads to a normative analysis of how the policy maker can improve welfare losses under discretion when the policy maker does not have a commitment technology. Since pure optimal discretionary policies are inferior to 1 Woodford (2003) derives this quadratic loss function by approximating households' utility in the second order.