A stylised fact of monetary policymaking is that central banks do not immediately respond to new information but seem instead to prefer to wait until sufficient ‘evidence’ to warrant a change has accumulated. However, theoretical models of inflation targeting imply that an optimising central bank should continuously respond to shocks. This article attempts to explain this stylised fact by introducing a small menu cost which is incurred every time the central bank changes the interest rate. It is shown that this produces a relatively large range of inaction because this cost will induce the central bank to take the option value of the status quo into account. In other words, because action is costly, the central bank will have an incentive to wait and see whether or not the economy will move closer to the inflation target of its own accord. Next, the article analyses the implications for the time series properties of interest rates. In particular, we examine the effect of the interest rate sensitivity of aggregate demand, the slope of the Lucas supply function and the variance of demand shocks on the size of the interest rate step and the expected length of the time period till the next interest rate step. Finally, we analyse the effect of menu costs on inflationary expectations. In this respect we find that the economy will suffer from an inflationary bias if the cost of raising the interest rate exceeds the cost of lowering it.