Staggered prices, the optimizing taylor rule and the irrelevance of the is curve

When the central bank minimizes a loss function depending upon the variability of inflation and the variability of output, the resultant interest rate policy rule is the so-called Taylor rule. In this context, the form and the parameters of the IS curve- whether this one is the old Keynesian function or a version of the Euler equation in output (the new IS)- are irrelevant in the determination of inflation and output. The solution of the model shows that the expected value of output is the natural one and the expected value of inflation is the target of the central bank. There is a tradeoff between the variances of these variables (inflation and output), nonetheless. Output and the real rate of interest will be more variable the more the central bank worries about the stability of inflation around its target.