When did unsystematic monetary policy have an effect on inflation?

An important stylized fact to emerge from VAR estimates is that exogenous monetary policy shocks (also labelled unsystematic monetary policy) have a delayed, persistent, hump-shaped effect on inflation. I argue that this empirical pattern is fragile. In particular, it disappears when one examines periods without large shifts in the level of inflation (such as 1984-2005). An important consequence is that the hump-shaped VAR estimated response of inflation is not appropriate to fit stylized models of the response of inflation around a stable steady state inflation level.