The conventional view is that a monetary policy shock has both supply‐side and demand‐side effects, at least in the short run. Barth and Ramey show that the supply‐side effect of a monetary policy shock may be greater than the demand‐side effect. We argue that it is crucial for monetary authorities to understand whether an increase in expected future inflation is due to supply shocks or demand shocks before applying contractionary policy to forestall inflation. We estimate a standard New Keynesian dynamic stochastic general equilibrium model with the cost channel of monetary policy for the South African economy to show that whether the South African Reserve Bank should apply contractionary policy to fight inflation depends critically on the nature of the disturbance. If an increase in expected future inflation is mainly due to supply shocks, the South African Reserve Bank should not apply contractionary policy to fight inflation, as this would lead to a persistent increase in inflation and a greater loss in output. Our estimation results also show that with a moderate level of cost‐channel effect and nominal rigidities, a New Keynesian dynamic stochastic general equilibrium model with the cost channel of monetary policy is able to mimic the price puzzle produced by an estimated vector autoregressive model.